Finite Group Databasebeta

← #35197207

Subgroups — #35197207

Order 20224.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777991C214yesmaximal, complemented
2#23777978C214yesmaximal, complemented
3#23777860C214yesmaximal, complemented
4#23777761C214yesmaximal, complemented
5#23777701C218yesmaximal, complemented
6#23777398C214yesmaximal, complemented
7#23777355C214yesmaximal, complemented
8#23777333C218yesmaximal, complemented
9#23777306C214yesmaximal, complemented
10#23777296C211yesmaximal, characteristic, complemented
11#23777294C211yesmaximal, characteristic, complemented
12#23777285C211yesmaximal, characteristic, complemented
13#23777275C211yesmaximal, characteristic, complemented
14#23777268C214yesmaximal, complemented
15#23777187C211yesmaximal, characteristic, complemented
16#23777181C211yesmaximal, characteristic, complemented
17#23777174C211yesmaximal, characteristic, complemented
18#23777056C211yesmaximal, characteristic, complemented
19#23777055C211yesmaximal, characteristic, complemented
20#23777043C211yesmaximal, characteristic, complemented
21#23777040C211yesmaximal, characteristic, complemented
22#23776695C211yesmaximal, characteristic, complemented
23#23776693C211yesmaximal, characteristic, complemented
24C2×#19099112C211yesmaximal, characteristic, complemented
25C79×#3500C211yesmaximal, characteristic, complemented
26C2×#14579208C2211yescharacteristic, complemented
27C2×#14579207C2211yescharacteristic
28C22×#11929625C2211yescharacteristic, complemented
29C22×#11929623C2211yescharacteristic, complemented
30#19099310C2218yescomplemented
31#19099309C2218yescomplemented
32#19099302C2218yescomplemented
33#19099301C2218yescomplemented
34#19099297C2218yescomplemented
35#19099296C2214yescomplemented
36#19099295C2214yescomplemented
37#19099295C2214yescomplemented
38#19099288C2214yescomplemented
39#19099285C2214yescomplemented
40#19099282C2214yescomplemented
41#19099282C2214yescomplemented
42#19099275C2218yescomplemented
43#19099267C2218yescomplemented
44#19099262C2218yescomplemented
45#19099262C2218yescomplemented
46#19099260C2218yescomplemented
47#19099256C2218yescomplemented
48#19099250C2218yescomplemented
49#19099243C2218yescomplemented
50#19099242C2218yescomplemented
51#19099239C2218yescomplemented
52#19099239C2218yescomplemented
53#19099233C2214yescomplemented
54#19099233C2214yescomplemented
55#19099232C2214yescomplemented
56#19099232C2214yescomplemented
57#19099232C2214yescomplemented
58#19099231C2214yescomplemented
59#19099231C2218yescomplemented
60Q8×C22⋊D79C2214yescomplemented
61#19099224C2214yescomplemented
62#19099224C2214yescomplemented
63#19099222C2214yescomplemented
64#19099221C2214yescomplemented
65#19099219C2214yescomplemented
66#19099216C2214yescomplemented
67#19099215C2214yescomplemented
68#19099212C2214yescomplemented
69#19099212C2214yescomplemented
70#19099212C2218yescomplemented
71#19099212C2214yescomplemented
72#19099209C2214yescomplemented
73#19099207C2214yescomplemented
74#19099207C2214yescomplemented
75#19099206C2214yescomplemented
76#19099204C2214yescomplemented
77#19099203C2218yescomplemented
78#19099202C2218yescomplemented
79#19099200C2218yescomplemented
80#19099200C2218yescomplemented
81D4×C22⋊D79C2218yes—
82D4×C22⋊D79C2214yescomplemented
83#19099184C2214yescomplemented
84#19099183C2218yescomplemented
85#19099182C2214yescomplemented
86#19099177C2218yescomplemented
87#19099173C2214yescomplemented
88#19099166C2214yescomplemented
89#19099165C2218yescomplemented
90#19099164C2218yescomplemented
91#19099163C2218yescomplemented
92#19099163C2218yescomplemented
93#19099162C2218yescomplemented
94#19099156C2218yescomplemented
95#19099151C2218yescomplemented
96#19099148C2218yescomplemented
97#19099147C2218yescomplemented
98#19099145C2218yescomplemented
99#19099140C2218yescomplemented
100#19099138C2212yescomplemented
101#19099137C2211yescharacteristic, complemented
102#19099137C2212yescomplemented
103#19099134C2211yescharacteristic
104#19099134C2211yescharacteristic, complemented
105#19099134C2212yescomplemented
106#19099130C2211yescharacteristic
107#19099130C2212yescomplemented
108#19099128C2214yescomplemented
109#19099128C2218yescomplemented
110#19099127C2211yescharacteristic
111#19099127C2211yescharacteristic, complemented
112#19099127C2214yescomplemented
113#19099127C2212yescomplemented
114#19099126C2212yescomplemented
115#19099124C2214yescomplemented
116#19099122C2214yescomplemented
117#19099120C2211yescharacteristic, complemented
118#19099118C2212yescomplemented
119#19099117C2212yescomplemented
120#19099116C2211yescharacteristic, complemented
121#19099115C2214yescomplemented
122#19099112C2214yescomplemented
123#19099112C2214yescomplemented
124#19099112C2214yescomplemented
125#19099112C2212yescomplemented
126#19099112C2214yescomplemented
127#19099111C2212yescomplemented
128#19099110C2212yescomplemented
129#19099109C2211yescharacteristic
130#19099109C2212yescomplemented
131#19099109C2212yescomplemented
132#19099108C2214yescomplemented
133C2×#14579159C2211yescharacteristic, complemented
134C2×#14579159C2212yescomplemented
135C2×#14579157C2211yescharacteristic
136C2×#14579157C2212yescomplemented
137#19099100C2212yescomplemented
138#19099097C2214yescomplemented
139#19099095C2212yescomplemented
140#19099095C2214yescomplemented
141#19099094C2214yescomplemented
142#19099093C2214yescomplemented
143#19099092C2214yescomplemented
144#19099092C2212yescomplemented
145#19099092C2212yescomplemented
146#19099091C2214yescomplemented
147C2×#14579149C2211yescharacteristic, complemented
148#124×D79C2212yescomplemented
149#19099075C2211yescharacteristic, complemented
150#19099073C2214yescomplemented
151#19099072C2214yescomplemented
152#19099070C2211yescharacteristic
153#19099070C2211yescharacteristic, complemented
154#19099070C2211yescharacteristic, complemented
155#19099070C2214yescomplemented
156#19099069C2214yescomplemented
157C2×#14579142C2214yescomplemented
158#123×D79C2214yescomplemented
159C2×#14579134C2214yescomplemented
160#19099042C2218yescomplemented
161#19099041C2211yescharacteristic, complemented
162#19099040C2211yescharacteristic, complemented
163#19099038C2211yescharacteristic, complemented
164#19099037C2211yescharacteristic, complemented
165#19099036C2218yescomplemented
166#41×Dic79C2211yescharacteristic
167#41×Dic79C2211yescharacteristic, complemented
168C4×#11929624C2211yescharacteristic, complemented
169C4×#11929624C2214yescomplemented
170C4×#11929623C2214yescomplemented
171C2×(C22⋊D79)⋊C4C2214yescomplemented
172C2×C42×D79C2211yescharacteristic, complemented
173C2×2−1+4×C79C2211yescharacteristic, complemented
174C2×H(5,𝔽2)×C79C2211yescharacteristic
175#548×C79C2214yescomplemented
176#546×C79C2218yescomplemented
177#546×C79C2214yescomplemented
178#536×C79C2211yescharacteristic
179#536×C79C2212yescomplemented
180#535×C79C2211yescharacteristic, complemented
181#535×C79C2212yescomplemented
182#532×C79C2211yescharacteristic
183#532×C79C2212yescomplemented
184C2×#124×C79C2211yescharacteristic, complemented
185C2×#124×C79C2212yescomplemented
186C4×#41×C79C2211yescharacteristic, complemented
187#14579208—44no—
188#14579207—44no—
189C2×#11929625—44no—
190C2×#11929625C2312yes—
191C2×#11929625C2314yes—
192C2×#11929625C2314yes—
193C2×#11929624C2311yescharacteristic
194C2×#11929624C2312yes—
195C2×#11929624C2312yes—
196C2×#11929624C2314yes—
197C2×#11929623—44no—
198C2×#11929623C2314yes—
199C2×#11929623C2318yes—
200C2×#11929623C2314yes—
201C2×#11929623C2312yes—
202C2×#11929623C2314yes—
203C2×#11929623C2314yes—
204C22×Dic158C2311yescharacteristic
205C22×Dic158C2312yes—
206C2×Q8×D79C2312yes—
207C22×D316C2311yescharacteristic
208C22×D316C2312yes—
209C22×D316C2312yes—
210C22×C22⋊D79C2314yes—
211C22×C22⋊D79C2318yes—
212C22×C22⋊D79C2312yes—
213C2×D4×D79C2314yes—
214C2×D4×D79C2312yes—
215C23×Dic79C2312yes—
216C22×C4×D79C2311yescharacteristic
217C22×C4×D79C2312yes—
218C22×C4×D79C2312yes—
219#14579161C2312yes—
220#14579160C2312yes—
221#14579159C2312yes—
222#14579159C2312yes—
223#14579159C2312yes—
224#14579159C2312yes—
225#14579159C2318yes—
226#14579159C2314yes—
227#14579159C2311yescharacteristic
228#14579159C2312yes—
229#14579157C2318yes—
230#14579157C2318yes—
231#14579157C2318yes—
232#14579157C2312yes—
233#14579157C2314yes—
234#14579157C2312yes—
235#14579157C2312yes—
236#14579157C2312yes—
237#14579157C2312yes—
238#14579157C2311yescharacteristic
239#14579156C2314yes—
240#14579156C2318yes—
241#14579155C2318yes—
242#14579154C2318yes—
243#14579154C2314yes—
244#14579154C2318yes—
245#14579154C2318yes—
246#14579154C2318yes—
247#14579154C2314yes—
248#14579154C2314yes—
249#14579153C2312yes—
250#14579152C2314yes—
251#14579152C2318yes—
252#14579152C2312yes—
253#14579151C2318yes—
254#14579151C2318yes—
255#14579151C2314yes—
256#14579150C2312yes—
257#14579150C2311yescharacteristic
258#14579150C2312yes—
259#14579150C2318yes—
260#14579150C2312yes—
261#14579149C2312yes—
262#14579149C2314yes—
263#14579149C2312yes—
264#14579148C2314yes—
265#14579148C2312yes—
266#14579148C2312yes—
267#14579148C2312yes—
268#14579148C2311yescharacteristic
269#14579147C2318yes—
270#14579147C2318yes—
271#14579147C2318yes—
272#14579147C2318yes—
273#14579147C2318yes—
274#14579147C2314yes—
275#14579146C2318yes—
276#14579146C2318yes—
277#14579146C2318yes—
278#14579146C2314yes—
279#14579145C2318yes—
280#14579145C2318yes—
281#14579145C2312yes—
282#14579144C2318yes—
283#14579144C2314yes—
284#14579144C2318yes—
285#14579144C2318yes—
286#14579143C2314yes—
287#14579143C2318yes—
288#14579143C2318yes—
289#14579143C2318yes—
290#14579143C2314yes—
291#14579143C2318yes—
292#14579143C2314yes—
293#14579142C2318yes—
294#14579142C2318yes—
295#14579142C2318yes—
296#14579142C2314yes—
297#14579142C2314yes—
298#14579142C2312yes—
299#14579142C2312yes—
300#14579142C2312yes—
301#14579141C2312yes—
302#14579141C2314yes—
303#14579140C2318yes—
304#14579140C2314yes—
305#14579140C2314yes—
306#14579140C2314yes—
307#14579139C2318yes—
308#14579139C2314yes—
309#14579139C2318yes—
310#14579138C2318yes—
311#14579138C2318yes—
312#14579138C2318yes—
313#14579138C2314yes—
314#14579137C2318yes—
315#14579137C2314yes—
316#14579137C2318yes—
317#14579137C2312yes—
318#14579137C2312yes—
319#14579137C2312yes—
320#14579136C2318yes—
321#14579136C2312yes—
322#14579135C2318yes—
323#14579135C2318yes—
324#14579135C2318yes—
325#14579135C2314yes—
326#14579135C2314yes—
327#14579134C2318yes—
328#14579134C2318yes—
329#14579134C2318yes—
330#14579134C2318yes—
331#14579134C2318yes—
332#14579134C2314yes—
333#14579134C2318yes—
334#14579134C2318yes—
335#14579133C2318yes—
336#14579133C2318yes—
337#14579133C2318yes—
338#14579133C2318yes—
339#14579133C2318yes—
340#14579133C2318yes—
341#14579133C2318yes—
342#14579133C2318yes—
343#14579133C2318yes—
344#14579133C2314yes—
345#14579132C2318yes—
346#14579132C2318yes—
347#14579132C2318yes—
348#14579132C2314yes—
349#14579132C2312yes—
350#14579132C2312yes—
351#14579132C2312yes—
352#14579132C2314yes—
353#14579131C2318yes—
354#14579131C2312yes—
355#14579130C2318yes—
356#14579130C2318yes—
357#14579130C2314yes—
358#14579129C2318yes—
359#14579129C2318yes—
360#14579129C2314yes—
361#14579129C2314yes—
362#14579129C2312yes—
363#14579129C2312yes—
364#14579129C2312yes—
365Q8×Dic79C2314yes—
366Q8×Dic79C2314yes—
367Q8×Dic79C2312yes—
368Q8×Dic79C2312yes—
369C4×Dic158C2314yes—
370C4×Dic158C2314yes—
371C4×Dic158C2312yes—
372C4×Dic158C2314yes—
373C4×Dic158C2314yes—
374#14579126C2314yes—
375#14579126C2318yes—
376#14579126C2314yes—
377C4×D316C2314yes—
378C4×D316C2314yes—
379C4×D316C2314yes—
380C4×D316C2312yes—
381D4×Dic79C2318yes—
382D4×Dic79C2314yes—
383D4×Dic79C2314yes—
384D4×Dic79C2314yes—
385D4×Dic79C2312yes—
386D4×Dic79C2314yes—
387D4×Dic79C2314yes—
388D4×Dic79C2312yes—
389#14579123C2314yes—
390C4×C22⋊D79C2318yes—
391C4×C22⋊D79C2314yes—
392C4×C22⋊D79C2318yes—
393C4×C22⋊D79C2318yes—
394C4×C22⋊D79C2314yes—
395C4×C22⋊D79C2318yes—
396C4×C22⋊D79C2318yes—
397C4×C22⋊D79C2314yes—
398C4×C22⋊D79C2314yes—
399C4×C22⋊D79C2314yes—
400C4×C22⋊D79C2314yes—
401C4×C22⋊D79C2314yes—
402(C22⋊D79)⋊C4C2318yes—
403(C22⋊D79)⋊C4C2318yes—
404(C22⋊D79)⋊C4C2318yes—
405(C22⋊D79)⋊C4C2318yes—
406(C22⋊D79)⋊C4C2318yes—
407(C22⋊D79)⋊C4C2318yes—
408(C22⋊D79)⋊C4C2318yes—
409(C22⋊D79)⋊C4C2314yes—
410(C22⋊D79)⋊C4C2314yes—
411(C22⋊D79)⋊C4C2318yes—
412#14579120C2312yes—
413#14579120C2311yescharacteristic
414#14579120C2312yes—
415#14579120C2314yes—
416#14579120C2314yes—
417#14579120C2311yescharacteristic
418#14579120C2311yescharacteristic
419#14579119C2314yes—
420#14579118C2312yes—
421#14579118C2318yes—
422#14579118C2314yes—
423#14579118C2314yes—
424#14579117C2314yes—
425#14579117C2318yes—
426#14579117C2314yes—
427#14579117C2314yes—
428#14579117C2318yes—
429C2×Dic79⋊C4C2318yes—
430C2×Dic79⋊C4C2318yes—
431C2×Dic79⋊C4C2314yes—
432C4⋊C4×D79C2318yes—
433C2×C22⋊Dic79C2318yes—
434C2×C22⋊Dic79C2314yes—
435C2×(C2×D79)⋊C4C2314yes—
436C22⋊C4×D79C2318yes—
437C22⋊C4×D79C2318yes—
438C22⋊C4×D79C2314yes—
439C2×C4×Dic79C2312yes—
440C2×C4×Dic79C2311yescharacteristic
441C2×C4×Dic79C2312yes—
442C2×C4×Dic79C2312yes—
443C42×D79C2312yes—
444C42×D79C2312yes—
445C42×D79C2312yes—
446C42×D79C2312yes—
447C42×D79C2312yes—
4482−1+4×C79—44no—
449H(5,𝔽2)×C79—44no—
450C2×#41×C79C2311yescharacteristic
451C2×#41×C79C2311yescharacteristic
452C2×#41×C79C2311yescharacteristic
453C2×#41×C79C2312yes—
454C2×#41×C79C2312yes—
455C2×#41×C79C2314yes—
456C2×#41×C79C2312yes—
457C2×#41×C79C2312yes—
458C22×Q8×C79C2311yescharacteristic
459C22×Q8×C79C2312yes—
460C22×Q8×C79C2312yes—
461C22×D4×C79C2311yescharacteristic
462C22×D4×C79C2314yes—
463C22×D4×C79C2312yes—
464C22×D4×C79C2312yes—
465C4⋊Q8×C79C2311yescharacteristic
466C4⋊Q8×C79C2312yes—
467#127×C79C2312yes—
468#127×C79C2311yescharacteristic
469#124×C79C2318yes—
470#124×C79C2312yes—
471#124×C79C2312yes—
472#124×C79C2312yes—
473#124×C79C2311yescharacteristic
474#124×C79C2312yes—
475#124×C79C2314yes—
476#124×C79C2311yescharacteristic
477#123×C79C2318yes—
478#123×C79C2314yes—
479C22⋊Q8×C79C2318yes—
480C22⋊Q8×C79C2314yes—
481#121×C79C2318yes—
482#121×C79C2318yes—
483#121×C79C2314yes—
484#121×C79C2314yes—
485#120×C79C2318yes—
486#120×C79C2314yes—
487C4×Q8×C79C2312yes—
488C4×D4×C79C2318yes—
489C4×D4×C79C2314yes—
490C4×D4×C79C2314yes—
491C4×D4×C79C2312yes—
492#117×C79C2312yes—
493#117×C79C2311yescharacteristic
494C2×C22⋊C4×C79C2318yes—
495C2×C22⋊C4×C79C2314yes—
496C2×C42×C79C2311yescharacteristic
497C2×C42×C79C2312yes—
498C23×D79C2412yes—
499C23×D79C2411yescharacteristic
500C23×D79C2414yes—
501#11929625—48no—
502#11929625—48no—
503#11929625—44no—
504#11929624—24no—
505#11929624—48no—
506#11929624—44no—
507#11929624—44no—
508#11929623—48no—
509#11929623—416no—
510#11929623—48no—
511#11929623—48no—
512#11929623—44no—
513#11929623—48no—
514C2×Dic158—24no—
515C2×Dic158—44no—
516C2×Dic158C2412yes—
517C2×Dic158C2412yes—
518C2×Dic158C2411yescharacteristic
519C2×Dic158C2414yes—
520C2×Dic158C2414yes—
521C2×Dic158C2414yes—
522Q8×D79—44no—
523C2×D316—24no—
524C2×D316—44no—
525C2×D316—44no—
526C2×D316C2411yescharacteristic
527C2×D316C2412yes—
528C2×D316C2412yes—
529C2×D316C2414yes—
530C2×D316C2418yes—
531C2×D316C2414yes—
532C2×C22⋊D79—48no—
533C2×C22⋊D79—416no—
534C2×C22⋊D79—44no—
535C2×C22⋊D79C2412yes—
536C2×C22⋊D79C2418yes—
537C2×C22⋊D79C2414yes—
538C2×C22⋊D79C2414yes—
539C2×C22⋊D79C2418yes—
540C2×C22⋊D79C2418yes—
541C2×C22⋊D79C2414yes—
542C2×C22⋊D79C2414yes—
543C2×C22⋊D79C2414yes—
544C2×C22⋊D79C2414yes—
545C2×C22⋊D79C2418yes—
546C2×C22⋊D79C2418yes—
547C2×C22⋊D79C2418yes—
548D4×D79—48no—
549D4×D79—44no—
550C22×Dic79—44no—
551C22×Dic79C2412yes—
552C22×Dic79C2414yes—
553C22×Dic79C2414yes—
554C22×Dic79C2412yes—
555C22×Dic79C2411yescharacteristic
556C22×Dic79C2414yes—
557C22×Dic79C2418yes—
558C22×Dic79C2418yes—
559C2×C4×D79—24no—
560C2×C4×D79—44no—
561C2×C4×D79—44no—
562C2×C4×D79C2412yes—
563C2×C4×D79C2412yes—
564C2×C4×D79C2412yes—
565C2×C4×D79C2412yes—
566C2×C4×D79C2412yes—
567C2×C4×D79C2414yes—
568C2×C4×D79C2418yes—
569C2×C4×D79C2414yes—
570C2×C4×D79C2414yes—
571C2×C4×D79C2418yes—
572C2×C4×D79C2412yes—
573C2×C4×D79C2412yes—
574C4⋊Dic79C2414yes—
575C4⋊Dic79C2414yes—
576C4⋊Dic79C2412yes—
577C4⋊Dic79C2412yes—
578C4⋊Dic79C2412yes—
579C4⋊Dic79C2414yes—
580C4⋊Dic79C2414yes—
581C4⋊Dic79C2414yes—
582C4⋊Dic79C2418yes—
583Dic79⋊C4C2414yes—
584Dic79⋊C4C2418yes—
585Dic79⋊C4C2418yes—
586Dic79⋊C4C2414yes—
587Dic79⋊C4C2414yes—
588Dic79⋊C4C2418yes—
589Dic79⋊C4C2418yes—
590Dic79⋊C4C2418yes—
591Dic79⋊C4C2414yes—
592Dic79⋊C4C2414yes—
593Dic79⋊C4C2414yes—
594Dic79⋊C4C2414yes—
595Dic79⋊C4C2418yes—
596Dic79⋊C4C2414yes—
597Dic79⋊C4C2414yes—
598C22⋊Dic79C2414yes—
599C22⋊Dic79C2412yes—
600C22⋊Dic79C2418yes—
601C22⋊Dic79C2412yes—
602C22⋊Dic79C2414yes—
603C22⋊Dic79C2418yes—
604C22⋊Dic79C2418yes—
605C22⋊Dic79C2412yes—
606C22⋊Dic79C2414yes—
607C22⋊Dic79C2418yes—
608C22⋊Dic79C2414yes—
609C22⋊Dic79C2414yes—
610C22⋊Dic79C2414yes—
611(C2×D79)⋊C4C2414yes—
612(C2×D79)⋊C4C2418yes—
613(C2×D79)⋊C4C2418yes—
614(C2×D79)⋊C4C2418yes—
615(C2×D79)⋊C4C2418yes—
616(C2×D79)⋊C4C2418yes—
617(C2×D79)⋊C4C2418yes—
618(C2×D79)⋊C4C2414yes—
619(C2×D79)⋊C4C2414yes—
620(C2×D79)⋊C4C2414yes—
621(C2×D79)⋊C4C2414yes—
622(C2×D79)⋊C4C2414yes—
623(C2×D79)⋊C4C2414yes—
624C4×Dic79C2411yescharacteristic
625C4×Dic79C2412yes—
626C4×Dic79C2412yes—
627C4×Dic79C2411yescharacteristic
628C4×Dic79C2412yes—
629C4×Dic79C2412yes—
630C4×Dic79C2412yes—
631C4×Dic79C2414yes—
632C4×Dic79C2412yes—
633C4×Dic79C2414yes—
634C4×Dic79C2414yes—
635C4×Dic79C2412yes—
636C4×Dic79C2412yes—
637C4×Dic79C2418yes—
638C4×Dic79C2418yes—
639C24×C79C2412yes—
640C24×C79C2414yes—
641#41×C79—24no—
642#41×C79—24no—
643#41×C79—24no—
644#41×C79—48no—
645#41×C79—44no—
646#41×C79—44no—
647#41×C79—44no—
648#41×C79—44no—
649C2×Q8×C79—24no—
650C2×Q8×C79—44no—
651C2×Q8×C79—44no—
652C2×Q8×C79C2411yescharacteristic
653C2×Q8×C79C2412yes—
654C2×Q8×C79C2412yes—
655C2×Q8×C79C2411yescharacteristic
656C2×Q8×C79C2411yescharacteristic
657C2×Q8×C79C2414yes—
658C2×D4×C79—24no—
659C2×D4×C79—44no—
660C2×D4×C79—44no—
661C2×D4×C79—48no—
662C2×D4×C79C2412yes—
663C2×D4×C79C2412yes—
664C2×D4×C79C2412yes—
665C2×D4×C79C2411yescharacteristic
666C2×D4×C79C2412yes—
667C2×D4×C79C2411yescharacteristic
668C2×D4×C79C2412yes—
669C2×D4×C79C2411yescharacteristic
670C2×D4×C79C2414yes—
671C2×D4×C79C2418yes—
672C2×D4×C79C2414yes—
673C2×D4×C79C2414yes—
674C2×D4×C79C2414yes—
675C22×C4×C79C2412yes—
676C22×C4×C79C2412yes—
677C22×C4×C79C2412yes—
678C22×C4×C79C2412yes—
679C22×C4×C79C2414yes—
680C22×C4×C79C2412yes—
681C22×C4×C79C2414yes—
682C22×C4×C79C2414yes—
683C22×C4×C79C2414yes—
684C22×C4×C79C2411yescharacteristic
685C4⋊C4×C79C2412yes—
686C4⋊C4×C79C2414yes—
687C4⋊C4×C79C2418yes—
688C4⋊C4×C79C2414yes—
689C22⋊C4×C79C2414yes—
690C22⋊C4×C79C2418yes—
691C22⋊C4×C79C2418yes—
692C22⋊C4×C79C2418yes—
693C22⋊C4×C79C2418yes—
694C22⋊C4×C79C2412yes—
695C22⋊C4×C79C2414yes—
696C22⋊C4×C79C2414yes—
697C42×C79C2411yescharacteristic
698C42×C79C2411yescharacteristic
699C42×C79C2412yes—
700C42×C79C2412yes—
701C42×C79C2414yes—
702C23×C79—24no—
703C23×C79—44no—
704C23×C79—48no—
705C23×C79—44no—
706C23×C79C2512yes—
707C23×C79C2512yes—
708C23×C79C2514yes—
709C23×C79C2512yes—
710C23×C79C2511yescharacteristic
711C22×D79—22no—
712C22×D79—24no—
713C22×D79—42no—
714C22×D79—44no—
715C22×D79—44no—
716C22×D79—48no—
717C22×D79C2512yes—
718C22×D79C2514yes—
719C22×D79C2512yes—
720Q8×C79—22no—
721Q8×C79—24no—
722Q8×C79—24no—
723Q8×C79—22no—
724Q8×C79—22no—
725Q8×C79—44no—
726D4×C79—24no—
727D4×C79—24no—
728D4×C79—24no—
729D4×C79—22no—
730D4×C79—24no—
731D4×C79—24no—
732D4×C79—22no—
733D4×C79—22no—
734D4×C79—48no—
735D4×C79—44no—
736D4×C79—44no—
737D4×C79—44no—
738D4×C79—44no—
739C2×C4×C79—24no—
740C2×C4×C79—24no—
741C2×C4×C79—24no—
742C2×C4×C79—24no—
743C2×C4×C79—42no—
744C2×C4×C79—44no—
745C2×C4×C79—44no—
746C2×C4×C79—44no—
747C2×C4×C79—44no—
748C2×C4×C79H(5,𝔽2)14yes—
749C2×C4×C79C2512yes—
750C2×C4×C79C2512yes—
751C2×C4×C79C2512yes—
752C2×C4×C79C2514yes—
753C2×C4×C79C2514yes—
754C2×C4×C79C2512yes—
755C2×C4×C79C2512yes—
756C2×C4×C79C2511yescharacteristic
757C2×C4×C79C2511yescharacteristic
758C22⋊D79—24no—
759C22⋊D79—216no—
760C22⋊D79—28no—
761C22⋊D79—44no—
762C22⋊D79—48no—
763C22⋊D79—48no—
764C22⋊D79—48no—
765C22⋊D79—48no—
766C22⋊D79—44no—
767C22⋊D79—48no—
768C22⋊D79—44no—
769C22⋊D79—44no—
770C22⋊D79—44no—
771C2×Dic79—22no—
772C2×Dic79—24no—
773C2×Dic79—24no—
774C2×Dic79—28no—
775C2×Dic79—28no—
776C2×Dic79—48no—
777C2×Dic79—44no—
778C2×Dic79—48no—
779C2×Dic79C2514yes—
780C2×Dic79C2514yes—
781C2×Dic79C2512yes—
782C2×Dic79C2512yes—
783C2×Dic79C2514yes—
784C2×Dic79C2514yes—
785C2×Dic79C2512yes—
786C2×Dic79C2512yes—
787D316—24no—
788D316—24no—
789D316—22no—
790D316—44no—
791D316—48no—
792D316—44no—
793C4×D79—24no—
794C4×D79—24no—
795C4×D79—24no—
796C4×D79—24no—
797C4×D79—24no—
798C4×D79—42no—
799C4×D79—42no—
800C4×D79—48no—
801C4×D79—44no—
802C4×D79—44no—
803C4×D79—48no—
804C4×D79—44no—
805Dic158—24no—
806Dic158—24no—
807Dic158—22no—
808Dic158—28no—
809Dic158—44no—
810Dic158—44no—
811C22×C79—22no—
812C22×C79—22no—
813C22×C79—22no—
814C22×C79—24no—
815C22×C79—22no—
816C22×C79—24no—
817C22×C79—28no—
818C22×C79—24no—
819C22×C79—24no—
820C22×C79—84no—
821C22×C79—164no—
822C22×C79C2×H(5,𝔽2)12yes—
823C22×C79C2611yescharacteristic
824C2×D79—22no—
825C2×D79—22no—
826C2×D79—24no—
827C2×D79—28no—
828C2×D79—24no—
829C2×D79—22no—
830C2×D79—22no—
831C2×D79—44no—
832C2×D79—84no—
833C2×D79—164no—
834C4×C79—22no—
835C4×C79—22no—
836C4×C79—22no—
837C4×C79—24no—
838C4×C79—22no—
839C4×C79—24no—
840C4×C79—22no—
841C4×C79C2×H(5,𝔽2)12yes—
842C4×C79C2×H(5,𝔽2)12yes—
843Dic79—22no—
844Dic79—24no—
845Dic79—22no—
846Dic79—24no—
847Dic79—22no—
848Dic79—24no—
849Dic79—24no—
850Dic79#58514yes—
851#62836—791nomaximal, Sylow
852C2×C79—22no—
853C2×C79—42no—
854C2×C79—42no—
855C2×C79—44no—
856C2×C79—42no—
857C2×C79C22×H(5,𝔽2)11yescharacteristic
858C2×C79C2×#58512yes—
859D79—42no—
860D79—44no—
861D79—42no—
862#3562—794no—
863#3562—794no—
864#3554—794no—
865#3546—794no—
866#3542—798no—
867#3517—794no—
868#3514—794no—
869#3513—798no—
870#3511—794no—
871#3510—791no—
872#3510—791no—
873#3509—791no—
874#3508—794no—
875#3508—791no—
876#3500—791no—
877#3500D7911yescharacteristic, complemented
878#3499—791no—
879#3498—791no—
880#3487—791no—
881#3487—791no—
882#3485—791no—
883#3485—791no—
884#3444—791no—
885#3444—791no—
886C2×#532—791no—
887C79#6283611yescharacteristic, complemented, Sylow
888C2×2−1+4—791no—
889C2×2−1+4C2×D7911yescharacteristic, complemented
890C2×H(5,𝔽2)—791no—
891C2×H(5,𝔽2)C2×D7911yescharacteristic
892C22×#41—791no—
893C22×#41—791no—
894#562—798no—
895#562—798no—
896#560—798no—
897#560—798no—
898#559—794no—
899#559—794no—
900#559—798no—
901#559—794no—
902#557—794no—
903#556—794no—
904#556—794no—
905#556—794no—
906#555—798no—
907#554—798no—
908#553—798no—
909#553—798no—
910#553—798no—
911#553—798no—
912#552—798no—
913#551—798no—
914#551—798no—
915#551—798no—
916#551—798no—
917#550—794no—
918#550—794no—
919#550—794no—
920#550—794no—
921#550—794no—
922#550—794no—
923#550—798no—
924D4×Q8—794no—
925#548—794no—
926#548—794no—
927#548—794no—
928#548—794no—
929#548—794no—
930#548C2×D7914yescomplemented
931#547—794no—
932#547—794no—
933#547—798no—
934#547—794no—
935#547—794no—
936#547—794no—
937#546—794no—
938#546—794no—
939#546—794no—
940#546—794no—
941#546—798no—
942#546—798no—
943#546—798no—
944#546—794no—
945#546—798no—
946#546C2×D7914yescomplemented
947#546C2×D7918yescomplemented
948D42—798no—
949D42—794no—
950#542—798no—
951#542—794no—
952#542—798no—
953#542—794no—
954#541—794no—
955#540—798no—
956#540—798no—
957#540—798no—
958#540—794no—
959#540—798no—
960#539—798no—
961#539—798no—
962#538—798no—
963#538—798no—
964#538—798no—
965#538—798no—
966#537—798no—
967#536—791no—
968#536—791no—
969#536—792no—
970#536—791no—
971#536—792no—
972#536—792no—
973#536C2×D7911yescharacteristic
974#536C2×D7912yescomplemented
975#535—791no—
976#535—791no—
977#535—794no—
978#535—792no—
979#535—791no—
980#535—792no—
981#535—792no—
982#535—794no—
983#535—798no—
984#535C2×D7911yescharacteristic, complemented
985#535C2×D7912yescomplemented
986#534—794no—
987#534—794no—
988#533—792no—
989#533—794no—
990#533—792no—
991#533—791no—
992#533—791no—
993#532—791no—
994#532—792no—
995#532—792no—
996#532—792no—
997#532—794no—
998#532—794no—
999#532—794no—
1000#532—794no—
1001#532—792no—
1002#532—794no—
1003#532—792no—
1004#532C2×D7911yescharacteristic
1005#532C2×D7912yescomplemented
1006C2×C4⋊Q8—791no—
1007C2×C4⋊Q8—792no—
1008C2×#127—791no—
1009C2×#127—792no—
1010#529—792no—
1011#529—792no—
1012#529—794no—
1013#529—794no—
1014#529—792no—
1015#529—794no—
1016#529—794no—
1017#529—792no—
1018#529—794no—
1019#529—794no—
1020C2×#124—792no—
1021C2×#124—791no—
1022C2×#124C2×D7911yescharacteristic, complemented
1023C2×#124C2×D7912yescomplemented
1024#525—791no—
1025#525—791no—
1026#525—791no—
1027#525—794no—
1028#525—794no—
1029#525—794no—
1030#525—794no—
1031#525—791no—
1032C2×#123—794no—
1033C2×#123—794no—
1034C2×#121—794no—
1035#520—798no—
1036#519—791no—
1037#519—791no—
1038#518—791no—
1039#518—791no—
1040#518—798no—
1041C4×#41—791no—
1042C4×#41—791no—
1043C4×#41—794no—
1044C4×#41—791no—
1045C4×#41—794no—
1046C4×#41C2×D7911yescharacteristic, complemented
1047C2×C4×D4—794no—
1048C22×C42—791no—
10492−1+4—44no—
10502−1+4—3164no—
1051H(5,𝔽2)—44no—
1052H(5,𝔽2)—3164no—
1053C2×#41—3164no—
1054C2×#41—3164no—
1055C2×#41—794no—
1056C2×#41—794no—
1057C2×#41—792no—
1058C2×#41—794no—
1059C2×#41—798no—
1060C2×#41—794no—
1061C2×#41—794no—
1062C2×#41—794no—
1063C2×#41—792no—
1064C2×#41—794no—
1065C2×#41—792no—
1066C2×#41—792no—
1067C2×#41—791no—
1068C2×#41C22×D7911yescharacteristic
1069C2×#41C22×D7911yescharacteristic
1070C2×#41C22×D7911yescharacteristic
1071C2×#41C22×D7914yes—
1072C2×#41C22×D7912yes—
1073C2×#41C22×D7912yes—
1074C2×#41C22×D7912yes—
1075C2×#41C22×D7912yes—
1076C22×Q8—792no—
1077C22×Q8—792no—
1078C22×Q8—791no—
1079C22×Q8C22×D7911yescharacteristic
1080C22×Q8C22×D7912yes—
1081C22×Q8C22×D7912yes—
1082C22×D4—794no—
1083C22×D4—798no—
1084C22×D4—792no—
1085C22×D4—794no—
1086C22×D4—792no—
1087C22×D4—792no—
1088C22×D4—792no—
1089C22×D4—791no—
1090C22×D4C22×D7911yescharacteristic
1091C22×D4C22×D7914yes—
1092C22×D4C22×D7912yes—
1093C22×D4C22×D7912yes—
1094C23×C4—792no—
1095C23×C4—792no—
1096C23×C4—792no—
1097C23×C4—791no—
1098C4⋊Q8—792no—
1099C4⋊Q8—791no—
1100C4⋊Q8—792no—
1101C4⋊Q8—794no—
1102C4⋊Q8—792no—
1103C4⋊Q8—792no—
1104C4⋊Q8—798no—
1105C4⋊Q8—792no—
1106C4⋊Q8—792no—
1107C4⋊Q8—792no—
1108C4⋊Q8C22×D7911yescharacteristic
1109C4⋊Q8C22×D7912yes—
1110#127—792no—
1111#127—791no—
1112#127—792no—
1113#127—794no—
1114#127—792no—
1115#127—792no—
1116#127—798no—
1117#127—792no—
1118#127—798no—
1119#127—798no—
1120#127C22×D7911yescharacteristic
1121#127C22×D7912yes—
1122#126—794no—
1123#126—798no—
1124#126—794no—
1125#126—794no—
1126#126—794no—
1127#126—798no—
1128#126—798no—
1129#126—798no—
1130#126—798no—
1131#126—798no—
1132#125—794no—
1133#125—792no—
1134#125—794no—
1135#125—798no—
1136#125—798no—
1137#125—798no—
1138#125—792no—
1139#124—792no—
1140#124—791no—
1141#124—792no—
1142#124—792no—
1143#124—798no—
1144#124—792no—
1145#124—791no—
1146#124—794no—
1147#124—792no—
1148#124—792no—
1149#124—798no—
1150#124—794no—
1151#124—798no—
1152#124—798no—
1153#124—798no—
1154#124—798no—
1155#124—792no—
1156#124—792no—
1157#124—794no—
1158#124C22×D7911yescharacteristic
1159#124C22×D7912yes—
1160#124C22×D7912yes—
1161#124C22×D7914yes—
1162#124C22×D7912yes—
1163#124C22×D7912yes—
1164#124C22×D7918yes—
1165#124C22×D7911yescharacteristic
1166#123—792no—
1167#123—792no—
1168#123—794no—
1169#123—794no—
1170#123—798no—
1171#123—798no—
1172#123—792no—
1173#123—798no—
1174#123—794no—
1175#123—798no—
1176#123—798no—
1177#123—798no—
1178#123—798no—
1179#123—794no—
1180#123—798no—
1181#123—798no—
1182#123—792no—
1183#123—798no—
1184#123—794no—
1185#123—794no—
1186#123—794no—
1187#123—798no—
1188#123—798no—
1189#123—798no—
1190#123—798no—
1191#123—798no—
1192#123C22×D7914yes—
1193#123C22×D7918yes—
1194C22⋊Q8—792no—
1195C22⋊Q8—792no—
1196C22⋊Q8—792no—
1197C22⋊Q8—798no—
1198C22⋊Q8—794no—
1199C22⋊Q8—798no—
1200C22⋊Q8—794no—
1201C22⋊Q8—794no—
1202C22⋊Q8—794no—
1203C22⋊Q8—798no—
1204C22⋊Q8—794no—
1205C22⋊Q8—792no—
1206C22⋊Q8—794no—
1207C22⋊Q8—798no—
1208C22⋊Q8—798no—
1209C22⋊Q8—794no—
1210C22⋊Q8—798no—
1211C22⋊Q8—798no—
1212C22⋊Q8—798no—
1213C22⋊Q8C22×D7914yes—
1214C22⋊Q8C22×D7918yes—
1215#121—794no—
1216#121—792no—
1217#121—792no—
1218#121—792no—
1219#121—794no—
1220#121—798no—
1221#121—798no—
1222#121—794no—
1223#121—798no—
1224#121—798no—
1225#121—798no—
1226#121—798no—
1227#121—798no—
1228#121—798no—
1229#121—798no—
1230#121—798no—
1231#121—798no—
1232#121—798no—
1233#121—794no—
1234#121—794no—
1235#121—798no—
1236#121—798no—
1237#121—798no—
1238#121—792no—
1239#121—798no—
1240#121—798no—
1241#121—798no—
1242#121—798no—
1243#121—798no—
1244#121—794no—
1245#121—798no—
1246#121—798no—
1247#121—798no—
1248#121C22×D7914yes—
1249#121C22×D7914yes—
1250#121C22×D7918yes—
1251#121C22×D7918yes—
1252#120—794no—
1253#120—798no—
1254#120—798no—
1255#120—792no—
1256#120—792no—
1257#120—792no—
1258#120—794no—
1259#120—794no—
1260#120—798no—
1261#120—798no—
1262#120—792no—
1263#120—798no—
1264#120C22×D7914yes—
1265#120C22×D7918yes—
1266C4×Q8—792no—
1267C4×Q8—792no—
1268C4×Q8—794no—
1269C4×Q8—794no—
1270C4×Q8—794no—
1271C4×Q8—794no—
1272C4×Q8—798no—
1273C4×Q8—794no—
1274C4×Q8—792no—
1275C4×Q8—794no—
1276C4×Q8—794no—
1277C4×Q8—794no—
1278C4×Q8C22×D7912yes—
1279C4×D4—794no—
1280C4×D4—794no—
1281C4×D4—792no—
1282C4×D4—794no—
1283C4×D4—792no—
1284C4×D4—794no—
1285C4×D4—794no—
1286C4×D4—798no—
1287C4×D4—794no—
1288C4×D4—794no—
1289C4×D4—794no—
1290C4×D4—794no—
1291C4×D4—794no—
1292C4×D4—794no—
1293C4×D4—794no—
1294C4×D4—798no—
1295C4×D4—798no—
1296C4×D4—798no—
1297C4×D4—798no—
1298C4×D4—798no—
1299C4×D4—794no—
1300C4×D4—798no—
1301C4×D4—798no—
1302C4×D4—798no—
1303C4×D4—798no—
1304C4×D4—794no—
1305C4×D4—794no—
1306C4×D4—798no—
1307C4×D4—798no—
1308C4×D4—798no—
1309C4×D4—798no—
1310C4×D4—794no—
1311C4×D4—794no—
1312C4×D4—792no—
1313C4×D4—794no—
1314C4×D4C22×D7914yes—
1315C4×D4C22×D7914yes—
1316C4×D4C22×D7912yes—
1317C4×D4C22×D7918yes—
1318#117—791no—
1319#117—791no—
1320#117—791no—
1321#117—792no—
1322#117—792no—
1323#117—794no—
1324#117—794no—
1325#117—794no—
1326#117—794no—
1327#117—794no—
1328#117—798no—
1329#117—794no—
1330#117—798no—
1331#117—794no—
1332#117—792no—
1333#117—794no—
1334#117—798no—
1335#117C22×D7911yescharacteristic
1336#117C22×D7912yes—
1337C2×C4⋊C4—794no—
1338C2×C4⋊C4—798no—
1339C2×C4⋊C4—798no—
1340C2×C4⋊C4—798no—
1341C2×C22⋊C4—794no—
1342C2×C22⋊C4—798no—
1343C2×C22⋊C4—794no—
1344C2×C22⋊C4—794no—
1345C2×C22⋊C4—798no—
1346C2×C22⋊C4—798no—
1347C2×C22⋊C4C22×D7914yes—
1348C2×C22⋊C4C22×D7918yes—
1349C2×C42—792no—
1350C2×C42—792no—
1351C2×C42—792no—
1352C2×C42—791no—
1353C2×C42—792no—
1354C2×C42—792no—
1355C2×C42—792no—
1356C2×C42—792no—
1357C2×C42—792no—
1358C2×C42C22×D7912yes—
1359C2×C42C22×D7911yescharacteristic
1360C24—794no—
1361C24—792no—
1362C24—791no—
1363C24C23×D7912yes—
1364C24C23×D7914yes—
1365#41—24no—
1366#41—24no—
1367#41—24no—
1368#41—48no—
1369#41—44no—
1370#41—44no—
1371#41—44no—
1372#41—44no—
1373#41—3164no—
1374#41—3164no—
1375#41—3168no—
1376#41—3168no—
1377#41—3168no—
1378#41—3164no—
1379#41—3168no—
1380#41—31616no—
1381#41—3168no—
1382#41—3168no—
1383#41—3164no—
1384#41—3168no—
1385#41—1584no—
1386C2×Q8—24no—
1387C2×Q8—44no—
1388C2×Q8—44no—
1389C2×Q8—3164no—
1390C2×Q8—3164no—
1391C2×Q8—794no—
1392C2×Q8—794no—
1393C2×Q8—794no—
1394C2×Q8—791no—
1395C2×Q8—792no—
1396C2×Q8—792no—
1397C2×Q8—1584no—
1398C2×Q8C23×D7911yescharacteristic
1399C2×Q8C23×D7912yes—
1400C2×Q8C23×D7911yescharacteristic
1401C2×Q8C23×D7912yes—
1402C2×Q8C23×D7911yescharacteristic
1403C2×Q8C23×D7914yes—
1404C2×D4—24no—
1405C2×D4—44no—
1406C2×D4—44no—
1407C2×D4—48no—
1408C2×D4—3164no—
1409C2×D4—3164no—
1410C2×D4—3168no—
1411C2×D4—3164no—
1412C2×D4—3164no—
1413C2×D4—3168no—
1414C2×D4—31616no—
1415C2×D4—794no—
1416C2×D4—794no—
1417C2×D4—798no—
1418C2×D4—798no—
1419C2×D4—798no—
1420C2×D4—798no—
1421C2×D4—794no—
1422C2×D4—794no—
1423C2×D4—794no—
1424C2×D4—798no—
1425C2×D4—794no—
1426C2×D4—798no—
1427C2×D4—792no—
1428C2×D4—794no—
1429C2×D4—798no—
1430C2×D4—794no—
1431C2×D4—791no—
1432C2×D4—792no—
1433C2×D4—792no—
1434C2×D4—1584no—
1435C2×D4C23×D7912yes—
1436C2×D4C23×D7912yes—
1437C2×D4C23×D7911yescharacteristic
1438C2×D4C23×D7912yes—
1439C2×D4C23×D7911yescharacteristic
1440C2×D4C23×D7912yes—
1441C2×D4C23×D7912yes—
1442C2×D4C23×D7911yescharacteristic
1443C2×D4C23×D7914yes—
1444C2×D4C23×D7918yes—
1445C2×D4C23×D7914yes—
1446C2×D4C23×D7914yes—
1447C2×D4C23×D7914yes—
1448C22×C4—3164no—
1449C22×C4—3164no—
1450C22×C4—3164no—
1451C22×C4—798no—
1452C22×C4—798no—
1453C22×C4—794no—
1454C22×C4—792no—
1455C22×C4—792no—
1456C22×C4—794no—
1457C22×C4—798no—
1458C22×C4—794no—
1459C22×C4—798no—
1460C22×C4—794no—
1461C22×C4—792no—
1462C22×C4—791no—
1463C22×C4—794no—
1464C22×C4—794no—
1465C22×C4—792no—
1466C22×C4—792no—
1467C22×C4—792no—
1468C22×C4—792no—
1469C22×C4—792no—
1470C22×C4—792no—
1471C22×C4—1584no—
1472C22×C4C23×D7912yes—
1473C22×C4C23×D7912yes—
1474C22×C4C23×D7912yes—
1475C22×C4C23×D7912yes—
1476C22×C4C23×D7912yes—
1477C22×C4C23×D7914yes—
1478C22×C4C23×D7914yes—
1479C22×C4C23×D7914yes—
1480C22×C4C23×D7914yes—
1481C22×C4C23×D7911yescharacteristic
1482C4⋊C4—794no—
1483C4⋊C4—798no—
1484C4⋊C4—794no—
1485C4⋊C4—794no—
1486C4⋊C4—798no—
1487C4⋊C4—798no—
1488C4⋊C4—798no—
1489C4⋊C4—798no—
1490C4⋊C4—794no—
1491C4⋊C4—794no—
1492C4⋊C4—794no—
1493C4⋊C4—794no—
1494C4⋊C4—794no—
1495C4⋊C4—794no—
1496C4⋊C4—798no—
1497C4⋊C4—794no—
1498C4⋊C4—792no—
1499C4⋊C4—792no—
1500C4⋊C4—792no—
1501C4⋊C4—794no—
1502C4⋊C4—794no—
1503C4⋊C4—794no—
1504C4⋊C4—794no—
1505C4⋊C4—798no—
1506C4⋊C4C23×D7918yes—
1507C4⋊C4C23×D7914yes—
1508C4⋊C4C23×D7912yes—
1509C4⋊C4C23×D7914yes—
1510C22⋊C4—792no—
1511C22⋊C4—794no—
1512C22⋊C4—792no—
1513C22⋊C4—794no—
1514C22⋊C4—798no—
1515C22⋊C4—798no—
1516C22⋊C4—798no—
1517C22⋊C4—792no—
1518C22⋊C4—794no—
1519C22⋊C4—794no—
1520C22⋊C4—798no—
1521C22⋊C4—794no—
1522C22⋊C4—794no—
1523C22⋊C4—794no—
1524C22⋊C4—798no—
1525C22⋊C4—798no—
1526C22⋊C4—798no—
1527C22⋊C4—798no—
1528C22⋊C4—798no—
1529C22⋊C4—798no—
1530C22⋊C4—794no—
1531C22⋊C4—794no—
1532C22⋊C4—794no—
1533C22⋊C4—794no—
1534C22⋊C4—794no—
1535C22⋊C4—794no—
1536C22⋊C4C23×D7914yes—
1537C22⋊C4C23×D7912yes—
1538C22⋊C4C23×D7918yes—
1539C22⋊C4C23×D7918yes—
1540C22⋊C4C23×D7918yes—
1541C22⋊C4C23×D7918yes—
1542C22⋊C4C23×D7914yes—
1543C22⋊C4C23×D7914yes—
1544C42—791no—
1545C42—792no—
1546C42—792no—
1547C42—791no—
1548C42—792no—
1549C42—792no—
1550C42—792no—
1551C42—794no—
1552C42—794no—
1553C42—792no—
1554C42—792no—
1555C42—794no—
1556C42—792no—
1557C42—798no—
1558C42—798no—
1559C42C23×D7911yescharacteristic
1560C42C23×D7911yescharacteristic
1561C42C23×D7912yes—
1562C42C23×D7914yes—
1563C42C23×D7912yes—
1564C23—24no—
1565C23—44no—
1566C23—44no—
1567C23—48no—
1568C23—3162no—
1569C23—3164no—
1570C23—3164no—
1571C23—3168no—
1572C23—794no—
1573C23—792no—
1574C23—792no—
1575C23—1582no—
1576C23—1584no—
1577C23C24×D7912yes—
1578C23C24×D7912yes—
1579C23C24×D7914yes—
1580C23C24×D7912yes—
1581C23C24×D7911yescharacteristic
1582Q8—24no—
1583Q8—24no—
1584Q8—22no—
1585Q8—22no—
1586Q8—22no—
1587Q8—44no—
1588Q8—3164no—
1589Q8—3164no—
1590Q8—1588no—
1591Q8—1582no—
1592Q8—1584no—
1593Q8—1584no—
1594D4—24no—
1595D4—24no—
1596D4—24no—
1597D4—24no—
1598D4—24no—
1599D4—22no—
1600D4—22no—
1601D4—22no—
1602D4—44no—
1603D4—44no—
1604D4—44no—
1605D4—48no—
1606D4—44no—
1607D4—3164no—
1608D4—3168no—
1609D4—3164no—
1610D4—3164no—
1611D4—3168no—
1612D4—3168no—
1613D4—3168no—
1614D4—3168no—
1615D4—3164no—
1616D4—3164no—
1617D4—3168no—
1618D4—3164no—
1619D4—3164no—
1620D4—1588no—
1621D4—15816no—
1622D4—1584no—
1623D4—1582no—
1624D4—1584no—
1625D4—1584no—
1626C2×C4—24no—
1627C2×C4—24no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—42no—
1631C2×C4—44no—
1632C2×C4—44no—
1633C2×C4—44no—
1634C2×C4—44no—
1635C2×C4—3168no—
1636C2×C4—3162no—
1637C2×C4—3162no—
1638C2×C4—3164no—
1639C2×C4—3164no—
1640C2×C4—3164no—
1641C2×C4—3168no—
1642C2×C4—3168no—
1643C2×C4—3164no—
1644C2×C4—3168no—
1645C2×C4—792no—
1646C2×C4—794no—
1647C2×C4—794no—
1648C2×C4—792no—
1649C2×C4—792no—
1650C2×C4—794no—
1651C2×C4—794no—
1652C2×C4—792no—
1653C2×C4—1584no—
1654C2×C4—1584no—
1655C2×C4—1584no—
1656C2×C4—1588no—
1657C2×C4—1588no—
1658C2×C4—1582no—
1659C2×C4—1584no—
1660C2×C4—1584no—
1661C2×C4—1584no—
1662C2×C4—1584no—
1663C2×C4#1457920614yes—
1664C2×C4C24×D7912yes—
1665C2×C4C24×D7912yes—
1666C2×C4C24×D7914yes—
1667C2×C4C24×D7912yes—
1668C2×C4C24×D7914yes—
1669C2×C4C24×D7912yes—
1670C2×C4C24×D7912yes—
1671C2×C4C24×D7911yescharacteristic
1672C2×C4C24×D7911yescharacteristic
1673C22—22no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—24no—
1678C22—24no—
1679C22—28no—
1680C22—24no—
1681C22—24no—
1682C22—84no—
1683C22—164no—
1684C22—3164no—
1685C22—6324no—
1686C22—1584no—
1687C22—1582no—
1688C22—1582no—
1689C22—1582no—
1690C22—1582no—
1691C22—1588no—
1692C22—1584no—
1693C22—12644no—
1694C22C2×#1457920612yes—
1695C22C25×D7911yescharacteristic
1696C4—22no—
1697C4—22no—
1698C4—22no—
1699C4—24no—
1700C4—22no—
1701C4—24no—
1702C4—22no—
1703C4—794no—
1704C4—1582no—
1705C4—1584no—
1706C4—1582no—
1707C4—1584no—
1708C4—1584no—
1709C4—1582no—
1710C4—1584no—
1711C4C2×#1457920612yes—
1712C4C2×#1457920612yes—
1713C2—22no—
1714C2—44no—
1715C2—42no—
1716C2—42no—
1717C2—42no—
1718C2—3162no—
1719C2—3164no—
1720C2—3162no—
1721C2C22×#1457920611yescharacteristic
1722C2#585×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3500C2
hypercenter#3500D79
hypocenterC79#62836
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3500

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777991C2semidirect
2. #23777978C2semidirect
3. #23777860C2semidirect
4. #23777761C2semidirect
5. #23777701C2semidirect
6. #23777398C2semidirect
7. #23777355C2semidirect
8. #23777333C2semidirect
9. #23777306C2semidirect
10. #23777296C2semidirect
11. #23777294C2semidirect
12. #23777285C2semidirect
13. #23777275C2semidirect
14. #23777268C2semidirect
15. #23777187C2semidirect
16. #23777181C2semidirect
17. #23777174C2semidirect
18. #23777056C2semidirect
19. #23777055C2semidirect
20. #23777043C2semidirect
21. #23777040C2semidirect
22. #23776695C2semidirect
23. #23776693C2semidirect
24. C2×#19099112C2semidirect
25. C79×#3500C2semidirect
26. C2×#14579208C22semidirect
28. C22×#11929625C22semidirect
29. C22×#11929623C22semidirect
30. #19099310C22semidirect
31. #19099309C22semidirect
32. #19099302C22semidirect
33. #19099301C22semidirect
34. #19099297C22semidirect
35. #19099296C22semidirect
36. #19099295C22semidirect
37. #19099295C22semidirect
38. #19099288C22semidirect
39. #19099285C22semidirect
40. #19099282C22semidirect
41. #19099282C22semidirect
42. #19099275C22semidirect
43. #19099267C22semidirect
44. #19099262C22semidirect
45. #19099262C22semidirect
46. #19099260C22semidirect
47. #19099256C22semidirect
48. #19099250C22semidirect
49. #19099243C22semidirect
50. #19099242C22semidirect
51. #19099239C22semidirect
52. #19099239C22semidirect
53. #19099233C22semidirect
54. #19099233C22semidirect
55. #19099232C22semidirect
56. #19099232C22semidirect
57. #19099232C22semidirect
58. #19099231C22semidirect
59. #19099231C22semidirect
60. Q8×C22⋊D79C22semidirect
61. #19099224C22semidirect
62. #19099224C22semidirect
63. #19099222C22semidirect
64. #19099221C22semidirect
65. #19099219C22semidirect
66. #19099216C22semidirect
67. #19099215C22semidirect
68. #19099212C22semidirect
69. #19099212C22semidirect
70. #19099212C22semidirect
71. #19099212C22semidirect
72. #19099209C22semidirect
73. #19099207C22semidirect
74. #19099207C22semidirect
75. #19099206C22semidirect
76. #19099204C22semidirect
77. #19099203C22semidirect
78. #19099202C22semidirect
79. #19099200C22semidirect
80. #19099200C22semidirect
82. D4×C22⋊D79C22semidirect
83. #19099184C22semidirect
84. #19099183C22semidirect
85. #19099182C22semidirect
86. #19099177C22semidirect
87. #19099173C22semidirect
88. #19099166C22semidirect
89. #19099165C22semidirect
90. #19099164C22semidirect
91. #19099163C22semidirect
92. #19099163C22semidirect
93. #19099162C22semidirect
94. #19099156C22semidirect
95. #19099151C22semidirect
96. #19099148C22semidirect
97. #19099147C22semidirect
98. #19099145C22semidirect
99. #19099140C22semidirect
100. #19099138C22semidirect
101. #19099137C22semidirect
102. #19099137C22semidirect
104. #19099134C22semidirect
105. #19099134C22semidirect
107. #19099130C22semidirect
108. #19099128C22semidirect
109. #19099128C22semidirect
111. #19099127C22semidirect
112. #19099127C22semidirect
113. #19099127C22semidirect
114. #19099126C22semidirect
115. #19099124C22semidirect
116. #19099122C22semidirect
117. #19099120C22semidirect
118. #19099118C22semidirect
119. #19099117C22semidirect
120. #19099116C22semidirect
121. #19099115C22semidirect
122. #19099112C22semidirect
123. #19099112C22semidirect
124. #19099112C22semidirect
125. #19099112C22semidirect
126. #19099112C22semidirect
127. #19099111C22semidirect
128. #19099110C22semidirect
130. #19099109C22semidirect
131. #19099109C22semidirect
132. #19099108C22semidirect
133. C2×#14579159C22semidirect
134. C2×#14579159C22semidirect
136. C2×#14579157C22semidirect
137. #19099100C22semidirect
138. #19099097C22semidirect
139. #19099095C22semidirect
140. #19099095C22semidirect
141. #19099094C22semidirect
142. #19099093C22semidirect
143. #19099092C22semidirect
144. #19099092C22semidirect
145. #19099092C22semidirect
146. #19099091C22semidirect
147. C2×#14579149C22semidirect
148. #124×D79C22semidirect
149. #19099075C22semidirect
150. #19099073C22semidirect
151. #19099072C22semidirect
153. #19099070C22semidirect
154. #19099070C22semidirect
155. #19099070C22semidirect
156. #19099069C22semidirect
157. C2×#14579142C22semidirect
158. #123×D79C22semidirect
159. C2×#14579134C22semidirect
160. #19099042C22semidirect
161. #19099041C22semidirect
162. #19099040C22semidirect
163. #19099038C22semidirect
164. #19099037C22semidirect
165. #19099036C22semidirect
167. #41×Dic79C22semidirect
168. C4×#11929624C22semidirect
169. C4×#11929624C22semidirect
170. C4×#11929623C22semidirect
171. C2×(C22⋊D79)⋊C4C22semidirect
172. C2×C42×D79C22semidirect
173. C2×2−1+4×C79C22semidirect
175. #548×C79C22semidirect
176. #546×C79C22semidirect
177. #546×C79C22semidirect
179. #536×C79C22semidirect
180. #535×C79C22semidirect
181. #535×C79C22semidirect
183. #532×C79C22semidirect
184. C2×#124×C79C22semidirect
185. C2×#124×C79C22semidirect
186. C4×#41×C79C22semidirect
877. #3500D79semidirect
887. C79#62836semidirect
889. C2×2−1+4C2×D79semidirect
930. #548C2×D79semidirect
946. #546C2×D79semidirect
947. #546C2×D79semidirect
974. #536C2×D79semidirect
984. #535C2×D79semidirect
985. #535C2×D79semidirect
1005. #532C2×D79semidirect
1022. C2×#124C2×D79semidirect
1023. C2×#124C2×D79semidirect
1046. C4×#41C2×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237779912
#237779782
#237778602
#237777612
#237777012
#237773982
#237773552
#237773332
#237773062
#237772962
#237772942
#237772852
#237772752
#237772682
#237771872
#237771812
#237771742
#237770562
#237770552
#237770432
#237770402
#237766952
#237766932
C2×#190991122
C79×#35002
#6283679