Finite Group Databasebeta

← #35197212

Subgroups — #35197212

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#23777989C214yesmaximal, complemented
2#23777974C214yesmaximal, complemented
3#23777858C214yesmaximal, complemented
4#23777759C214yesmaximal, complemented
5#23777703C218yesmaximal, complemented
6#23777403C214yesmaximal, complemented
7#23777354C214yesmaximal, complemented
8#23777326C218yesmaximal, complemented
9#23777306C214yesmaximal, complemented
10#23777297C211yesmaximal, characteristic, complemented
11#23777295C211yesmaximal, characteristic, complemented
12#23777281C211yesmaximal, characteristic, complemented
13#23777275C211yesmaximal, characteristic, complemented
14#23777270C214yesmaximal, complemented
15#23777194C211yesmaximal, characteristic, complemented
16#23777192C211yesmaximal, characteristic, complemented
17#23777181C211yesmaximal, characteristic, complemented
18#23777175C211yesmaximal, characteristic, complemented
19#23777054C211yesmaximal, characteristic, complemented
20#23777044C211yesmaximal, characteristic, complemented
21#23777042C211yesmaximal, characteristic, complemented
22#23776692C211yesmaximal, characteristic, complemented
23#23776692C211yesmaximal, characteristic, complemented
24C2×#19099109C211yesmaximal, characteristic, complemented
25C79×#3487C211yesmaximal, characteristic, complemented
26C2×#14579208C2211yescharacteristic, complemented
27C2×#14579207C2211yescharacteristic
28C2×#14579206C2211yescharacteristic
29C22×#11929624C2211yescharacteristic, complemented
30#19099308C2218yescomplemented
31#19099307C2218yescomplemented
32#19099301C2218yescomplemented
33#19099300C2218yescomplemented
34#19099299C2214yescomplemented
35#19099298C2214yescomplemented
36#19099296C2218yescomplemented
37#19099295C2214yescomplemented
38#19099291C2214yescomplemented
39#19099285C2214yescomplemented
40#19099285C2214yescomplemented
41#19099282C2214yescomplemented
42#19099275C2218yescomplemented
43#19099267C2218yescomplemented
44#19099263C2218yescomplemented
45#19099262C2218yescomplemented
46#19099256C2218yescomplemented
47#19099256C2218yescomplemented
48#19099246C2218yescomplemented
49#19099244C2218yescomplemented
50#19099242C2218yescomplemented
51#19099240C2218yescomplemented
52#19099237C2218yescomplemented
53#19099234C2214yescomplemented
54#19099233C2218yescomplemented
55#19099233C2214yescomplemented
56#19099231C2214yescomplemented
57#19099231C2214yescomplemented
58Q8×C22⋊D79C2214yescomplemented
59#19099224C2214yescomplemented
60#19099223C2214yescomplemented
61#19099222C2214yescomplemented
62#19099219C2214yescomplemented
63#19099218C2214yescomplemented
64#19099215C2214yescomplemented
65#19099212C2214yescomplemented
66#19099212C2214yescomplemented
67#19099212C2218yescomplemented
68#19099212C2214yescomplemented
69#19099210C2214yescomplemented
70#19099210C2214yescomplemented
71#19099209C2214yescomplemented
72#19099202C2218yescomplemented
73#19099202C2218yescomplemented
74#19099201C2214yescomplemented
75#19099201C2214yescomplemented
76#19099201C2218yescomplemented
77#19099201C2214yescomplemented
78#19099200C2218yescomplemented
79#19099200C2218yescomplemented
80#19099197C2214yescomplemented
81#19099195C2218yes—
82#19099185C2214yescomplemented
83#19099183C2218yescomplemented
84#19099180C2214yescomplemented
85#19099177C2218yescomplemented
86#19099171C2214yescomplemented
87#19099167C2218yescomplemented
88#19099166C2214yescomplemented
89#19099163C2218yescomplemented
90#19099163C2218yescomplemented
91#19099163C2218yescomplemented
92#19099159C2218yescomplemented
93#19099155C2218yescomplemented
94#19099150C2218yescomplemented
95#19099147C2218yescomplemented
96#19099146C2218yescomplemented
97#19099145C2218yescomplemented
98#19099140C2218yescomplemented
99#19099139C2211yescharacteristic
100#19099137C2211yescharacteristic
101#19099137C2211yescharacteristic, complemented
102#19099137C2212yescomplemented
103#19099137C2212yescomplemented
104#19099134C2211yescharacteristic, complemented
105#19099134C2212yescomplemented
106#19099133C2212yescomplemented
107#19099132C2211yescharacteristic
108#19099131C2212yescomplemented
109#19099128C2214yescomplemented
110#19099127C2211yescharacteristic, complemented
111#19099127C2212yescomplemented
112#19099126C2212yescomplemented
113#19099126C2218yescomplemented
114#19099126C2212yescomplemented
115#19099123C2214yescomplemented
116#19099122C2214yescomplemented
117#19099117C2214yescomplemented
118#19099116C2211yescharacteristic, complemented
119#19099116C2211yescharacteristic, complemented
120#19099115C2212yescomplemented
121#19099115C2212yescomplemented
122#19099112C2212yescomplemented
123#19099111C2212yescomplemented
124#19099109C2211yescharacteristic
125#19099109C2211yescharacteristic
126#19099109C2214yescomplemented
127#19099109C2214yescomplemented
128#19099109C2214yescomplemented
129#19099109C2212yescomplemented
130#19099109C2212yescomplemented
131#19099109C2214yescomplemented
132#19099108C2214yescomplemented
133#19099108C2212yescomplemented
134#19099108C2212yescomplemented
135C2×#14579159C2211yescharacteristic, complemented
136C2×#14579159C2212yescomplemented
137C2×#14579157C2211yescharacteristic
138#127×D79C2212yescomplemented
139#19099100C2214yescomplemented
140#19099099C2212yescomplemented
141#19099099C2212yescomplemented
142#19099094C2214yescomplemented
143#19099094C2212yescomplemented
144#19099094C2212yescomplemented
145#19099093C2214yescomplemented
146#19099093C2214yescomplemented
147#19099090C2214yescomplemented
148#19099090C2214yescomplemented
149C2×#14579150C2211yescharacteristic, complemented
150C2×#14579150C2212yescomplemented
151C2×#14579148C2211yescharacteristic, complemented
152#124×D79C2212yescomplemented
153#19099074C2211yescharacteristic
154#19099074C2211yescharacteristic, complemented
155#19099071C2214yescomplemented
156#19099069C2214yescomplemented
157#19099069C2214yescomplemented
158C2×#14579144C2214yescomplemented
159#123×D79C2214yescomplemented
160C2×#14579133C2214yescomplemented
161#19099042C2218yescomplemented
162#19099040C2211yescharacteristic, complemented
163#19099038C2211yescharacteristic, complemented
164#19099037C2211yescharacteristic, complemented
165#19099035C2218yescomplemented
166#41×Dic79C2211yescharacteristic, complemented
167#41×Dic79C2211yescharacteristic, complemented
168#19099031C2211yescharacteristic
169#19099031C2211yescharacteristic, complemented
170C4×#11929623C2214yescomplemented
171C4×#11929623C2214yescomplemented
172C2×C4×C22⋊D79C2214yescomplemented
173C22×C4×Dic79C2211yescharacteristic, complemented
174C2×2−1+4×C79C2211yescharacteristic, complemented
175C22×#41×C79C2211yescharacteristic, complemented
176#550×C79C2214yescomplemented
177#550×C79C2214yescomplemented
178#548×C79C2214yescomplemented
179#548×C79C2214yescomplemented
180#535×C79C2211yescharacteristic
181#535×C79C2214yescomplemented
182#535×C79C2211yescharacteristic, complemented
183#525×C79C2211yescharacteristic, complemented
184#525×C79C2211yescharacteristic, complemented
185#525×C79C2214yescomplemented
186#519×C79C2211yescharacteristic, complemented
187#14579208—44no—
188#14579207—44no—
189#14579206—44no—
190C2×#11929625C2312yes—
191C2×#11929624—44no—
192C2×#11929624C2311yescharacteristic
193C2×#11929624C2311yescharacteristic
194C2×#11929624C2312yes—
195C2×#11929624C2312yes—
196C2×#11929624C2314yes—
197C2×#11929624C2314yes—
198C2×#11929623C2312yes—
199C2×#11929623C2312yes—
200C2×#11929623C2314yes—
201C2×#11929623C2318yes—
202C2×#11929623C2314yes—
203C2×#11929623C2312yes—
204C2×#11929623C2314yes—
205C22×Dic158C2311yescharacteristic
206C22×Dic158C2312yes—
207C2×Q8×D79C2312yes—
208C22×D316C2311yescharacteristic
209C22×D316C2312yes—
210C22×C22⋊D79C2314yes—
211C22×C22⋊D79C2314yes—
212C22×C22⋊D79C2312yes—
213C2×D4×D79C2312yes—
214C2×D4×D79C2312yes—
215C2×D4×D79C2314yes—
216C2×D4×D79C2312yes—
217C2×D4×D79C2318yes—
218C23×Dic79C2312yes—
219C22×C4×D79C2312yes—
220#14579161C2312yes—
221#14579160C2312yes—
222#14579160C2312yes—
223#14579159C2312yes—
224#14579159C2311yescharacteristic
225#14579159C2312yes—
226#14579159C2312yes—
227#14579159C2312yes—
228#14579159C2318yes—
229#14579159C2314yes—
230#14579159C2311yescharacteristic
231#14579159C2312yes—
232#14579158C2312yes—
233#14579157C2318yes—
234#14579157C2318yes—
235#14579157C2312yes—
236#14579157C2314yes—
237#14579157C2312yes—
238#14579157C2311yescharacteristic
239#14579157C2312yes—
240#14579157C2311yescharacteristic
241#14579156C2318yes—
242#14579156C2314yes—
243#14579156C2318yes—
244#14579156C2314yes—
245#14579155C2318yes—
246#14579155C2318yes—
247#14579154C2314yes—
248#14579154C2318yes—
249#14579154C2318yes—
250#14579154C2314yes—
251#14579153C2318yes—
252#14579152C2312yes—
253#14579152C2312yes—
254#14579151C2314yes—
255#14579151C2318yes—
256#14579151C2318yes—
257#14579151C2314yes—
258#14579150C2312yes—
259#14579150C2312yes—
260#14579150C2311yescharacteristic
261#14579150C2312yes—
262#14579150C2312yes—
263#14579150C2318yes—
264#14579150C2314yes—
265#14579150C2311yescharacteristic
266#14579150C2312yes—
267#14579149C2312yes—
268#14579149C2318yes—
269#14579149C2312yes—
270#14579148C2318yes—
271#14579148C2312yes—
272#14579148C2312yes—
273#14579148C2314yes—
274#14579148C2312yes—
275#14579148C2311yescharacteristic
276#14579148C2311yescharacteristic
277#14579147C2314yes—
278#14579147C2318yes—
279#14579147C2318yes—
280#14579147C2318yes—
281#14579147C2314yes—
282#14579146C2318yes—
283#14579146C2318yes—
284#14579146C2318yes—
285#14579145C2314yes—
286#14579145C2314yes—
287#14579145C2318yes—
288#14579145C2314yes—
289#14579144C2314yes—
290#14579144C2318yes—
291#14579144C2318yes—
292#14579144C2314yes—
293#14579144C2318yes—
294#14579144C2318yes—
295#14579144C2312yes—
296#14579144C2312yes—
297#14579143C2318yes—
298#14579143C2318yes—
299#14579143C2318yes—
300#14579143C2318yes—
301#14579142C2318yes—
302#14579142C2318yes—
303#14579142C2314yes—
304#14579142C2318yes—
305#14579142C2318yes—
306#14579142C2314yes—
307#14579142C2314yes—
308#14579141C2314yes—
309#14579140C2318yes—
310#14579140C2314yes—
311#14579140C2312yes—
312#14579140C2312yes—
313#14579139C2318yes—
314#14579139C2318yes—
315#14579139C2318yes—
316#14579138C2314yes—
317#14579138C2318yes—
318#14579138C2318yes—
319#14579138C2314yes—
320#14579138C2314yes—
321#14579138C2314yes—
322#14579137C2314yes—
323#14579137C2318yes—
324#14579137C2318yes—
325#14579137C2314yes—
326#14579136C2314yes—
327#14579135C2318yes—
328#14579135C2314yes—
329#14579135C2312yes—
330#14579135C2312yes—
331#14579134C2318yes—
332#14579134C2318yes—
333#14579134C2318yes—
334#14579134C2318yes—
335#14579134C2318yes—
336#14579133C2318yes—
337#14579133C2318yes—
338#14579133C2318yes—
339#14579133C2318yes—
340#14579133C2318yes—
341#14579133C2318yes—
342#14579133C2318yes—
343#14579133C2318yes—
344#14579133C2314yes—
345#14579133C2318yes—
346#14579133C2318yes—
347#14579133C2318yes—
348#14579133C2314yes—
349#14579133C2314yes—
350#14579133C2318yes—
351#14579133C2314yes—
352#14579133C2318yes—
353#14579132C2318yes—
354#14579132C2318yes—
355#14579132C2318yes—
356#14579131C2318yes—
357#14579131C2314yes—
358#14579130C2312yes—
359#14579130C2312yes—
360#14579129C2318yes—
361#14579129C2318yes—
362#14579129C2318yes—
363#14579129C2318yes—
364#14579129C2318yes—
365#14579129C2314yes—
366Q8×Dic79C2312yes—
367Q8×Dic79C2312yes—
368C4×Dic158C2314yes—
369C4×Dic158C2318yes—
370C4×Dic158C2314yes—
371C4×Dic158C2314yes—
372#14579126C2314yes—
373#14579126C2314yes—
374#14579126C2312yes—
375#14579126C2312yes—
376#14579126C2314yes—
377C4×D316C2318yes—
378C4×D316C2314yes—
379D4×Dic79C2314yes—
380D4×Dic79C2318yes—
381D4×Dic79C2314yes—
382D4×Dic79C2318yes—
383D4×Dic79C2314yes—
384D4×Dic79C2314yes—
385D4×Dic79C2314yes—
386D4×Dic79C2312yes—
387D4×Dic79C2312yes—
388D4×Dic79C2314yes—
389#14579123C2318yes—
390#14579123C2314yes—
391#14579123C2312yes—
392#14579123C2312yes—
393C4×C22⋊D79C2318yes—
394C4×C22⋊D79C2318yes—
395C4×C22⋊D79C2318yes—
396C4×C22⋊D79C2318yes—
397C4×C22⋊D79C2314yes—
398C4×C22⋊D79C2314yes—
399C4×C22⋊D79C2314yes—
400C4×C22⋊D79C2314yes—
401C4×C22⋊D79C2318yes—
402C4×C22⋊D79C2318yes—
403(C22⋊D79)⋊C4C2318yes—
404(C22⋊D79)⋊C4C2314yes—
405(C22⋊D79)⋊C4C2314yes—
406(C22⋊D79)⋊C4C2318yes—
407(C22⋊D79)⋊C4C2318yes—
408(C22⋊D79)⋊C4C2314yes—
409(C22⋊D79)⋊C4C2314yes—
410(C22⋊D79)⋊C4C2314yes—
411(C22⋊D79)⋊C4C2314yes—
412#14579120C2311yescharacteristic
413#14579120C2312yes—
414#14579120C2312yes—
415#14579120C2311yescharacteristic
416#14579119C2314yes—
417#14579119C2314yes—
418#14579118C2318yes—
419#14579118C2312yes—
420#14579118C2312yes—
421#14579118C2318yes—
422#14579117C2314yes—
423#14579117C2314yes—
424#14579117C2318yes—
425#14579117C2314yes—
426#14579117C2314yes—
427#14579117C2314yes—
428C2×Dic79⋊C4C2318yes—
429C2×Dic79⋊C4C2318yes—
430C2×Dic79⋊C4C2314yes—
431C4⋊C4×D79C2318yes—
432C2×C22⋊Dic79C2314yes—
433C2×C22⋊Dic79C2314yes—
434C2×(C2×D79)⋊C4C2318yes—
435C2×(C2×D79)⋊C4C2318yes—
436C2×(C2×D79)⋊C4C2314yes—
437C22⋊C4×D79C2318yes—
438C22⋊C4×D79C2318yes—
439C22⋊C4×D79C2314yes—
440C2×C4×Dic79C2312yes—
441C2×C4×Dic79C2312yes—
442C2×C4×Dic79C2312yes—
443C2×C4×Dic79C2311yescharacteristic
444C2×C4×Dic79C2311yescharacteristic
445C2×C4×Dic79C2312yes—
446C2×C4×Dic79C2312yes—
447C2×C4×Dic79C2312yes—
448C2×C4×Dic79C2312yes—
449C42×D79C2312yes—
450C42×D79C2312yes—
4512−1+4×C79—44no—
452C2×#41×C79—44no—
453C2×#41×C79C2311yescharacteristic
454C2×#41×C79C2311yescharacteristic
455C2×#41×C79C2314yes—
456C2×#41×C79C2312yes—
457C2×#41×C79C2314yes—
458C2×#41×C79C2314yes—
459C2×#41×C79C2312yes—
460C22×Q8×C79C2311yescharacteristic
461C22×Q8×C79C2312yes—
462C22×Q8×C79C2312yes—
463C22×D4×C79C2311yescharacteristic
464C22×D4×C79C2312yes—
465C23×C4×C79C2311yescharacteristic
466C23×C4×C79C2312yes—
467#127×C79C2318yes—
468#127×C79C2312yes—
469#127×C79C2312yes—
470#124×C79C2318yes—
471#124×C79C2312yes—
472#124×C79C2312yes—
473#123×C79C2312yes—
474#123×C79C2312yes—
475C22⋊Q8×C79C2318yes—
476C22⋊Q8×C79C2312yes—
477C22⋊Q8×C79C2312yes—
478#121×C79C2318yes—
479#121×C79C2318yes—
480#121×C79C2318yes—
481#121×C79C2314yes—
482#121×C79C2314yes—
483#121×C79C2312yes—
484#121×C79C2312yes—
485#120×C79C2314yes—
486#120×C79C2314yes—
487#120×C79C2312yes—
488#120×C79C2312yes—
489C4×Q8×C79C2314yes—
490C4×Q8×C79C2314yes—
491C4×D4×C79C2318yes—
492C4×D4×C79C2318yes—
493C4×D4×C79C2314yes—
494C4×D4×C79C2314yes—
495#117×C79C2311yescharacteristic
496#117×C79C2314yes—
497#117×C79C2311yescharacteristic
498C23×D79C2412yes—
499C23×D79C2414yes—
500C23×D79C2414yes—
501#11929625—44no—
502#11929624—24no—
503#11929624—24no—
504#11929624—48no—
505#11929624—48no—
506#11929624—44no—
507#11929624—44no—
508#11929623—48no—
509#11929623—48no—
510#11929623—416no—
511#11929623—44no—
512#11929623—44no—
513#11929623—44no—
514#11929623—48no—
515C2×Dic158—24no—
516C2×Dic158—44no—
517C2×Dic158C2412yes—
518C2×Dic158C2411yescharacteristic
519C2×Dic158C2412yes—
520C2×Dic158C2414yes—
521C2×Dic158C2411yescharacteristic
522C2×Dic158C2414yes—
523C2×Dic158C2414yes—
524Q8×D79—44no—
525C2×D316—24no—
526C2×D316—44no—
527C2×D316C2411yescharacteristic
528C2×D316C2412yes—
529C2×D316C2412yes—
530C2×D316C2411yescharacteristic
531C2×D316C2414yes—
532C2×D316C2418yes—
533C2×C22⋊D79—48no—
534C2×C22⋊D79—48no—
535C2×C22⋊D79—44no—
536C2×C22⋊D79C2412yes—
537C2×C22⋊D79C2418yes—
538C2×C22⋊D79C2414yes—
539C2×C22⋊D79C2412yes—
540C2×C22⋊D79C2414yes—
541C2×C22⋊D79C2414yes—
542C2×C22⋊D79C2414yes—
543C2×C22⋊D79C2414yes—
544C2×C22⋊D79C2418yes—
545C2×C22⋊D79C2414yes—
546C2×C22⋊D79C2414yes—
547C2×C22⋊D79C2418yes—
548C2×C22⋊D79C2414yes—
549C2×C22⋊D79C2418yes—
550D4×D79—416no—
551D4×D79—48no—
552D4×D79—44no—
553D4×D79—44no—
554D4×D79—44no—
555C22×Dic79—44no—
556C22×Dic79C2412yes—
557C22×Dic79C2414yes—
558C22×Dic79C2412yes—
559C22×Dic79C2412yes—
560C22×Dic79C2412yes—
561C22×Dic79C2414yes—
562C22×Dic79C2414yes—
563C22×Dic79C2414yes—
564C22×Dic79C2418yes—
565C22×Dic79C2412yes—
566C22×Dic79C2412yes—
567C22×Dic79C2412yes—
568C2×C4×D79—44no—
569C2×C4×D79C2412yes—
570C2×C4×D79C2412yes—
571C2×C4×D79C2414yes—
572C2×C4×D79C2414yes—
573C2×C4×D79C2414yes—
574C2×C4×D79C2418yes—
575C2×C4×D79C2418yes—
576C2×C4×D79C2414yes—
577C4⋊Dic79C2418yes—
578C4⋊Dic79C2414yes—
579C4⋊Dic79C2414yes—
580C4⋊Dic79C2412yes—
581C4⋊Dic79C2412yes—
582C4⋊Dic79C2414yes—
583C4⋊Dic79C2414yes—
584Dic79⋊C4C2414yes—
585Dic79⋊C4C2418yes—
586Dic79⋊C4C2414yes—
587Dic79⋊C4C2414yes—
588Dic79⋊C4C2418yes—
589Dic79⋊C4C2418yes—
590Dic79⋊C4C2418yes—
591Dic79⋊C4C2418yes—
592Dic79⋊C4C2414yes—
593Dic79⋊C4C2414yes—
594Dic79⋊C4C2414yes—
595Dic79⋊C4C2414yes—
596Dic79⋊C4C2414yes—
597Dic79⋊C4C2418yes—
598Dic79⋊C4C2414yes—
599Dic79⋊C4C2414yes—
600C22⋊Dic79C2412yes—
601C22⋊Dic79C2418yes—
602C22⋊Dic79C2418yes—
603C22⋊Dic79C2412yes—
604C22⋊Dic79C2418yes—
605C22⋊Dic79C2418yes—
606C22⋊Dic79C2414yes—
607C22⋊Dic79C2414yes—
608C22⋊Dic79C2414yes—
609C22⋊Dic79C2414yes—
610C22⋊Dic79C2414yes—
611C22⋊Dic79C2414yes—
612(C2×D79)⋊C4C2414yes—
613(C2×D79)⋊C4C2414yes—
614(C2×D79)⋊C4C2418yes—
615(C2×D79)⋊C4C2418yes—
616(C2×D79)⋊C4C2418yes—
617(C2×D79)⋊C4C2418yes—
618(C2×D79)⋊C4C2414yes—
619(C2×D79)⋊C4C2418yes—
620(C2×D79)⋊C4C2418yes—
621(C2×D79)⋊C4C2418yes—
622(C2×D79)⋊C4C2418yes—
623(C2×D79)⋊C4C2414yes—
624(C2×D79)⋊C4C2414yes—
625(C2×D79)⋊C4C2414yes—
626C4×Dic79C2411yescharacteristic
627C4×Dic79C2411yescharacteristic
628C4×Dic79C2414yes—
629C4×Dic79C2414yes—
630C4×Dic79C2412yes—
631C4×Dic79C2412yes—
632C4×Dic79C2411yescharacteristic
633C4×Dic79C2411yescharacteristic
634C4×Dic79C2412yes—
635C4×Dic79C2412yes—
636C4×Dic79C2412yes—
637C4×Dic79C2412yes—
638C4×Dic79C2414yes—
639C4×Dic79C2414yes—
640C4×Dic79C2412yes—
641C4×Dic79C2412yes—
642C4×Dic79C2418yes—
643C24×C79C2412yes—
644C24×C79C2411yescharacteristic
645#41×C79—24no—
646#41×C79—24no—
647#41×C79—48no—
648#41×C79—48no—
649#41×C79—48no—
650#41×C79—44no—
651#41×C79—44no—
652C2×Q8×C79—24no—
653C2×Q8×C79—44no—
654C2×Q8×C79—44no—
655C2×Q8×C79C2411yescharacteristic
656C2×Q8×C79C2411yescharacteristic
657C2×Q8×C79C2412yes—
658C2×Q8×C79C2412yes—
659C2×Q8×C79C2414yes—
660C2×D4×C79—24no—
661C2×D4×C79—44no—
662C2×D4×C79C2412yes—
663C2×D4×C79C2411yescharacteristic
664C2×D4×C79C2412yes—
665C2×D4×C79C2412yes—
666C2×D4×C79C2412yes—
667C2×D4×C79C2411yescharacteristic
668C2×D4×C79C2414yes—
669C2×D4×C79C2418yes—
670C2×D4×C79C2414yes—
671C2×D4×C79C2418yes—
672C2×D4×C79C2418yes—
673C2×D4×C79C2414yes—
674C22×C4×C79—24no—
675C22×C4×C79—44no—
676C22×C4×C79C2412yes—
677C22×C4×C79C2412yes—
678C22×C4×C79C2412yes—
679C22×C4×C79C2412yes—
680C22×C4×C79C2412yes—
681C22×C4×C79C2411yescharacteristic
682C22×C4×C79C2414yes—
683C22×C4×C79C2414yes—
684C22×C4×C79C2418yes—
685C22×C4×C79C2411yescharacteristic
686C4⋊C4×C79C2412yes—
687C4⋊C4×C79C2412yes—
688C4⋊C4×C79C2418yes—
689C4⋊C4×C79C2414yes—
690C4⋊C4×C79C2414yes—
691C22⋊C4×C79C2412yes—
692C22⋊C4×C79C2412yes—
693C22⋊C4×C79C2414yes—
694C22⋊C4×C79C2414yes—
695C22⋊C4×C79C2418yes—
696C22⋊C4×C79C2418yes—
697C22⋊C4×C79C2414yes—
698C22⋊C4×C79C2414yes—
699C42×C79C2412yes—
700C42×C79C2412yes—
701C42×C79C2418yes—
702C23×C79—22no—
703C23×C79—24no—
704C23×C79—42no—
705C23×C79—44no—
706C23×C79C2512yes—
707C23×C79C2514yes—
708C23×C79C2512yes—
709C23×C79C2512yes—
710C23×C79C2511yescharacteristic
711C22×D79—24no—
712C22×D79—44no—
713C22×D79—44no—
714C22×D79—44no—
715C22×D79—48no—
716C22×D79—48no—
717C22×D79C2512yes—
718C22×D79C2512yes—
719C22×D79C2514yes—
720Q8×C79—22no—
721Q8×C79—22no—
722Q8×C79—24no—
723Q8×C79—24no—
724Q8×C79—44no—
725D4×C79—24no—
726D4×C79—24no—
727D4×C79—22no—
728D4×C79—24no—
729D4×C79—24no—
730D4×C79—22no—
731D4×C79—48no—
732D4×C79—48no—
733D4×C79—44no—
734D4×C79—44no—
735D4×C79—48no—
736D4×C79—44no—
737C2×C4×C79—22no—
738C2×C4×C79—24no—
739C2×C4×C79—24no—
740C2×C4×C79—24no—
741C2×C4×C79—24no—
742C2×C4×C79—24no—
743C2×C4×C79—48no—
744C2×C4×C79—44no—
745C2×C4×C79—44no—
746C2×C4×C79H(5,𝔽2)14yes—
747C2×C4×C79C2512yes—
748C2×C4×C79C2514yes—
749C2×C4×C79C2512yes—
750C2×C4×C79C2512yes—
751C2×C4×C79C2514yes—
752C2×C4×C79C2514yes—
753C2×C4×C79C2511yescharacteristic
754C2×C4×C79C2511yescharacteristic
755C22⋊D79—24no—
756C22⋊D79—24no—
757C22⋊D79—28no—
758C22⋊D79—216no—
759C22⋊D79—44no—
760C22⋊D79—44no—
761C22⋊D79—44no—
762C22⋊D79—48no—
763C22⋊D79—48no—
764C22⋊D79—48no—
765C22⋊D79—44no—
766C22⋊D79—44no—
767C22⋊D79—44no—
768C22⋊D79—44no—
769C2×Dic79—24no—
770C2×Dic79—24no—
771C2×Dic79—24no—
772C2×Dic79—24no—
773C2×Dic79—28no—
774C2×Dic79—42no—
775C2×Dic79—42no—
776C2×Dic79—42no—
777C2×Dic79—44no—
778C2×Dic79—44no—
779C2×Dic79—48no—
780C2×Dic79—44no—
781C2×Dic79C2512yes—
782C2×Dic79C2512yes—
783C2×Dic79C2514yes—
784C2×Dic79C2512yes—
785C2×Dic79C2514yes—
786C2×Dic79C2512yes—
787C2×Dic79C2514yes—
788C2×Dic79C2512yes—
789C2×Dic79C2512yes—
790D316—22no—
791D316—22no—
792D316—24no—
793D316—24no—
794D316—44no—
795D316—48no—
796C4×D79—24no—
797C4×D79—24no—
798C4×D79—28no—
799C4×D79—48no—
800C4×D79—44no—
801C4×D79—44no—
802C4×D79—48no—
803C4×D79—44no—
804Dic158—24no—
805Dic158—24no—
806Dic158—22no—
807Dic158—22no—
808Dic158—28no—
809Dic158—44no—
810Dic158—44no—
811C22×C79—22no—
812C22×C79—22no—
813C22×C79—22no—
814C22×C79—22no—
815C22×C79—24no—
816C22×C79—28no—
817C22×C79—24no—
818C22×C79—24no—
819C22×C79—22no—
820C22×C79—22no—
821C22×C79—44no—
822C22×C79—84no—
823C22×C79C2×H(5,𝔽2)12yes—
824C22×C79C2611yescharacteristic
825C2×D79—22no—
826C2×D79—22no—
827C2×D79—24no—
828C2×D79—28no—
829C2×D79—24no—
830C2×D79—24no—
831C2×D79—84no—
832C2×D79—164no—
833C2×D79—164no—
834C4×C79—22no—
835C4×C79—24no—
836C4×C79—22no—
837C4×C79—22no—
838C4×C79—24no—
839C4×C79—24no—
840C4×C79C2×H(5,𝔽2)12yes—
841C4×C79C2×H(5,𝔽2)12yes—
842Dic79—22no—
843Dic79—22no—
844Dic79—24no—
845Dic79—22no—
846Dic79—24no—
847Dic79—22no—
848Dic79—24no—
849Dic79—22no—
850Dic79#58514yes—
851#62836—791nomaximal, Sylow
852C2×C79—22no—
853C2×C79—42no—
854C2×C79—44no—
855C2×C79—42no—
856C2×C79—42no—
857C2×C79C22×H(5,𝔽2)11yescharacteristic
858C2×C79C2×#58512yes—
859D79—44no—
860D79—42no—
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#3500—791no—
878#3499—791no—
879#3498—791no—
880#3487—791no—
881#3487D7911yescharacteristic, complemented
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)—791no—
892C22×#41—791no—
893C22×#41C2×D7911yescharacteristic, complemented
894#562—798no—
895#562—798no—
896#560—798no—
897#560—798no—
898#559—794no—
899#559—794no—
900#559—794no—
901#559—798no—
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—798no—
918#550—794no—
919#550—794no—
920#550—794no—
921#550—794no—
922#550C2×D7914yescomplemented
923#550C2×D7914yescomplemented
924D4×Q8—794no—
925#548—794no—
926#548—794no—
927#548—794no—
928#548—794no—
929#548C2×D7914yescomplemented
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—798no—
941#546—798no—
942#546—798no—
943#546—794no—
944#546—794no—
945#546—798no—
946#546—798no—
947#546—794no—
948D42—794no—
949D42—798no—
950#542—798no—
951#542—798no—
952#542—794no—
953#542—794no—
954#541—794no—
955#540—798no—
956#540—798no—
957#540—798no—
958#540—798no—
959#540—794no—
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—792no—
969#536—791no—
970#536—791no—
971#536—792no—
972#536—792no—
973#536—792no—
974#536—791no—
975#535—791no—
976#535—792no—
977#535—792no—
978#535—792no—
979#535—798no—
980#535—792no—
981#535—794no—
982#535—791no—
983#535C2×D7911yescharacteristic
984#535C2×D7911yescharacteristic, complemented
985#535C2×D7914yescomplemented
986#534—794no—
987#534—794no—
988#533—792no—
989#533—792no—
990#533—794no—
991#533—791no—
992#533—791no—
993#532—794no—
994#532—794no—
995#532—794no—
996#532—794no—
997#532—791no—
998#532—791no—
999#532—792no—
1000#532—792no—
1001#532—792no—
1002#532—792no—
1003#532—792no—
1004#532—792no—
1005#532—794no—
1006C2×C4⋊Q8—791no—
1007C2×C4⋊Q8—792no—
1008C2×#127—791no—
1009C2×#127—792no—
1010#529—794no—
1011#529—794no—
1012#529—792no—
1013#529—792no—
1014#529—792no—
1015#529—792no—
1016#529—794no—
1017#529—794no—
1018#529—794no—
1019#529—794no—
1020C2×#124—791no—
1021C2×#124—792no—
1022C2×#124—791no—
1023C2×#124—792no—
1024#525—791no—
1025#525—791no—
1026#525—794no—
1027#525—794no—
1028#525—794no—
1029#525C2×D7911yescharacteristic, complemented
1030#525C2×D7911yescharacteristic, complemented
1031#525C2×D7914yescomplemented
1032C2×#123—794no—
1033C2×#123—794no—
1034C2×#121—794no—
1035#520—798no—
1036#519—791no—
1037#519C2×D7911yescharacteristic, complemented
1038#518—791no—
1039#518—798no—
1040#518—791no—
1041C4×#41—791no—
1042C4×#41—791no—
1043C4×#41—794no—
1044C4×#41—794no—
1045C4×#41—791no—
1046C4×#41—791no—
1047C2×C4×D4—794no—
1048C22×C42—791no—
10492−1+4—44no—
10502−1+4—3164no—
1051H(5,𝔽2)—3164no—
1052H(5,𝔽2)—3164no—
1053C2×#41—44no—
1054C2×#41—3164no—
1055C2×#41—792no—
1056C2×#41—794no—
1057C2×#41—794no—
1058C2×#41—798no—
1059C2×#41—794no—
1060C2×#41—792no—
1061C2×#41—792no—
1062C2×#41—792no—
1063C2×#41—794no—
1064C2×#41—794no—
1065C2×#41—792no—
1066C2×#41—792no—
1067C2×#41—791no—
1068C2×#41—791no—
1069C2×#41C22×D7911yescharacteristic
1070C2×#41C22×D7911yescharacteristic
1071C2×#41C22×D7914yes—
1072C2×#41C22×D7914yes—
1073C2×#41C22×D7914yes—
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—792no—
1084C22×D4—794no—
1085C22×D4—798no—
1086C22×D4—794no—
1087C22×D4—792no—
1088C22×D4—792no—
1089C22×D4—792no—
1090C22×D4—792no—
1091C22×D4—791no—
1092C22×D4C22×D7911yescharacteristic
1093C22×D4C22×D7912yes—
1094C23×C4—792no—
1095C23×C4—792no—
1096C23×C4C22×D7911yescharacteristic
1097C23×C4C22×D7912yes—
1098C4⋊Q8—791no—
1099C4⋊Q8—792no—
1100C4⋊Q8—792no—
1101C4⋊Q8—794no—
1102C4⋊Q8—792no—
1103C4⋊Q8—792no—
1104C4⋊Q8—798no—
1105C4⋊Q8—791no—
1106C4⋊Q8—792no—
1107C4⋊Q8—792no—
1108C4⋊Q8—792no—
1109C4⋊Q8—792no—
1110#127—791no—
1111#127—792no—
1112#127—792no—
1113#127—794no—
1114#127—798no—
1115#127—791no—
1116#127—792no—
1117#127—798no—
1118#127—792no—
1119#127C22×D7912yes—
1120#127C22×D7912yes—
1121#127C22×D7918yes—
1122#126—794no—
1123#126—794no—
1124#126—798no—
1125#126—798no—
1126#126—794no—
1127#126—794no—
1128#126—798no—
1129#126—798no—
1130#126—798no—
1131#126—798no—
1132#125—792no—
1133#125—794no—
1134#125—792no—
1135#125—794no—
1136#125—798no—
1137#125—798no—
1138#125—798no—
1139#124—791no—
1140#124—792no—
1141#124—792no—
1142#124—794no—
1143#124—792no—
1144#124—792no—
1145#124—798no—
1146#124—791no—
1147#124—792no—
1148#124—792no—
1149#124—792no—
1150#124—794no—
1151#124—791no—
1152#124—791no—
1153#124—792no—
1154#124—798no—
1155#124—798no—
1156#124—794no—
1157#124—794no—
1158#124—798no—
1159#124—798no—
1160#124—792no—
1161#124—792no—
1162#124—798no—
1163#124C22×D7912yes—
1164#124C22×D7912yes—
1165#124C22×D7918yes—
1166#123—794no—
1167#123—794no—
1168#123—794no—
1169#123—798no—
1170#123—798no—
1171#123—798no—
1172#123—798no—
1173#123—792no—
1174#123—792no—
1175#123—794no—
1176#123—794no—
1177#123—798no—
1178#123—798no—
1179#123—798no—
1180#123—798no—
1181#123—798no—
1182#123—798no—
1183#123—798no—
1184#123—794no—
1185#123—798no—
1186#123—794no—
1187#123—794no—
1188#123—798no—
1189#123—798no—
1190#123—798no—
1191#123—798no—
1192#123C22×D7912yes—
1193#123C22×D7912yes—
1194C22⋊Q8—794no—
1195C22⋊Q8—794no—
1196C22⋊Q8—798no—
1197C22⋊Q8—798no—
1198C22⋊Q8—792no—
1199C22⋊Q8—792no—
1200C22⋊Q8—794no—
1201C22⋊Q8—798no—
1202C22⋊Q8—798no—
1203C22⋊Q8—794no—
1204C22⋊Q8—798no—
1205C22⋊Q8—798no—
1206C22⋊Q8—794no—
1207C22⋊Q8—794no—
1208C22⋊Q8—794no—
1209C22⋊Q8—794no—
1210C22⋊Q8—798no—
1211C22⋊Q8—798no—
1212C22⋊Q8C22×D7912yes—
1213C22⋊Q8C22×D7912yes—
1214C22⋊Q8C22×D7918yes—
1215#121—798no—
1216#121—798no—
1217#121—798no—
1218#121—798no—
1219#121—794no—
1220#121—794no—
1221#121—794no—
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—798no—
1234#121—798no—
1235#121—792no—
1236#121—792no—
1237#121—794no—
1238#121—798no—
1239#121—794no—
1240#121—798no—
1241#121—798no—
1242#121—798no—
1243#121—798no—
1244#121—798no—
1245#121C22×D7912yes—
1246#121C22×D7912yes—
1247#121C22×D7918yes—
1248#121C22×D7914yes—
1249#121C22×D7914yes—
1250#121C22×D7918yes—
1251#121C22×D7918yes—
1252#120—792no—
1253#120—792no—
1254#120—794no—
1255#120—798no—
1256#120—798no—
1257#120—798no—
1258#120—798no—
1259#120—798no—
1260#120—794no—
1261#120—798no—
1262#120C22×D7912yes—
1263#120C22×D7912yes—
1264#120C22×D7914yes—
1265#120C22×D7914yes—
1266C4×Q8—792no—
1267C4×Q8—792no—
1268C4×Q8—794no—
1269C4×Q8—792no—
1270C4×Q8—792no—
1271C4×Q8—794no—
1272C4×Q8—794no—
1273C4×Q8—794no—
1274C4×Q8—794no—
1275C4×Q8—794no—
1276C4×Q8—798no—
1277C4×Q8C22×D7914yes—
1278C4×Q8C22×D7914yes—
1279C4×D4—794no—
1280C4×D4—794no—
1281C4×D4—794no—
1282C4×D4—794no—
1283C4×D4—792no—
1284C4×D4—792no—
1285C4×D4—798no—
1286C4×D4—794no—
1287C4×D4—794no—
1288C4×D4—798no—
1289C4×D4—798no—
1290C4×D4—798no—
1291C4×D4—798no—
1292C4×D4—798no—
1293C4×D4—794no—
1294C4×D4—794no—
1295C4×D4—794no—
1296C4×D4—794no—
1297C4×D4—798no—
1298C4×D4—798no—
1299C4×D4—792no—
1300C4×D4—792no—
1301C4×D4—798no—
1302C4×D4—794no—
1303C4×D4—794no—
1304C4×D4—794no—
1305C4×D4—794no—
1306C4×D4—794no—
1307C4×D4—794no—
1308C4×D4—794no—
1309C4×D4—798no—
1310C4×D4—798no—
1311C4×D4—798no—
1312C4×D4—798no—
1313C4×D4—794no—
1314C4×D4C22×D7914yes—
1315C4×D4C22×D7914yes—
1316C4×D4C22×D7918yes—
1317C4×D4C22×D7918yes—
1318#117—791no—
1319#117—791no—
1320#117—792no—
1321#117—792no—
1322#117—794no—
1323#117—794no—
1324#117—794no—
1325#117—794no—
1326#117—794no—
1327#117—794no—
1328#117—794no—
1329#117—798no—
1330#117—792no—
1331#117—792no—
1332#117—798no—
1333#117—798no—
1334#117C22×D7911yescharacteristic
1335#117C22×D7911yescharacteristic
1336#117C22×D7914yes—
1337C2×C4⋊C4—794no—
1338C2×C4⋊C4—798no—
1339C2×C4⋊C4—798no—
1340C2×C4⋊C4—798no—
1341C2×C22⋊C4—794no—
1342C2×C22⋊C4—794no—
1343C2×C22⋊C4—794no—
1344C2×C22⋊C4—798no—
1345C2×C22⋊C4—798no—
1346C2×C22⋊C4—794no—
1347C2×C22⋊C4—798no—
1348C2×C22⋊C4—798no—
1349C2×C42—792no—
1350C2×C42—792no—
1351C2×C42—792no—
1352C2×C42—791no—
1353C2×C42—792no—
1354C2×C42—791no—
1355C2×C42—792no—
1356C2×C42—792no—
1357C2×C42—792no—
1358C2×C42—792no—
1359C2×C42—792no—
1360C24—794no—
1361C24—794no—
1362C24—792no—
1363C24C23×D7912yes—
1364C24C23×D7911yescharacteristic
1365#41—24no—
1366#41—24no—
1367#41—48no—
1368#41—48no—
1369#41—48no—
1370#41—44no—
1371#41—44no—
1372#41—3168no—
1373#41—3168no—
1374#41—3164no—
1375#41—3164no—
1376#41—3164no—
1377#41—3164no—
1378#41—3164no—
1379#41—3168no—
1380#41—3168no—
1381#41—31616no—
1382#41—3164no—
1383#41—3168no—
1384#41—1584no—
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—791no—
1398C2×Q8—1584no—
1399C2×Q8C23×D7911yescharacteristic
1400C2×Q8C23×D7911yescharacteristic
1401C2×Q8C23×D7912yes—
1402C2×Q8C23×D7912yes—
1403C2×Q8C23×D7914yes—
1404C2×D4—24no—
1405C2×D4—44no—
1406C2×D4—3164no—
1407C2×D4—3168no—
1408C2×D4—3168no—
1409C2×D4—3164no—
1410C2×D4—3164no—
1411C2×D4—3164no—
1412C2×D4—31616no—
1413C2×D4—3164no—
1414C2×D4—3168no—
1415C2×D4—794no—
1416C2×D4—794no—
1417C2×D4—794no—
1418C2×D4—798no—
1419C2×D4—798no—
1420C2×D4—794no—
1421C2×D4—794no—
1422C2×D4—798no—
1423C2×D4—794no—
1424C2×D4—794no—
1425C2×D4—794no—
1426C2×D4—798no—
1427C2×D4—792no—
1428C2×D4—792no—
1429C2×D4—798no—
1430C2×D4—794no—
1431C2×D4—791no—
1432C2×D4—791no—
1433C2×D4—792no—
1434C2×D4—792no—
1435C2×D4—1584no—
1436C2×D4C23×D7912yes—
1437C2×D4C23×D7912yes—
1438C2×D4C23×D7911yescharacteristic
1439C2×D4C23×D7912yes—
1440C2×D4C23×D7912yes—
1441C2×D4C23×D7911yescharacteristic
1442C2×D4C23×D7914yes—
1443C2×D4C23×D7918yes—
1444C2×D4C23×D7918yes—
1445C2×D4C23×D7914yes—
1446C2×D4C23×D7914yes—
1447C2×D4C23×D7918yes—
1448C22×C4—24no—
1449C22×C4—44no—
1450C22×C4—3164no—
1451C22×C4—3164no—
1452C22×C4—792no—
1453C22×C4—792no—
1454C22×C4—792no—
1455C22×C4—794no—
1456C22×C4—798no—
1457C22×C4—794no—
1458C22×C4—794no—
1459C22×C4—794no—
1460C22×C4—798no—
1461C22×C4—794no—
1462C22×C4—798no—
1463C22×C4—794no—
1464C22×C4—792no—
1465C22×C4—792no—
1466C22×C4—792no—
1467C22×C4—794no—
1468C22×C4—792no—
1469C22×C4—794no—
1470C22×C4—792no—
1471C22×C4—792no—
1472C22×C4C23×D7912yes—
1473C22×C4C23×D7912yes—
1474C22×C4C23×D7911yescharacteristic
1475C22×C4C23×D7912yes—
1476C22×C4C23×D7912yes—
1477C22×C4C23×D7912yes—
1478C22×C4C23×D7914yes—
1479C22×C4C23×D7918yes—
1480C22×C4C23×D7914yes—
1481C22×C4C23×D7911yescharacteristic
1482C4⋊C4—794no—
1483C4⋊C4—794no—
1484C4⋊C4—798no—
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—794no—
1497C4⋊C4—798no—
1498C4⋊C4—798no—
1499C4⋊C4—792no—
1500C4⋊C4—794no—
1501C4⋊C4—792no—
1502C4⋊C4—794no—
1503C4⋊C4—794no—
1504C4⋊C4—794no—
1505C4⋊C4C23×D7914yes—
1506C4⋊C4C23×D7914yes—
1507C4⋊C4C23×D7912yes—
1508C4⋊C4C23×D7912yes—
1509C4⋊C4C23×D7918yes—
1510C22⋊C4—792no—
1511C22⋊C4—792no—
1512C22⋊C4—798no—
1513C22⋊C4—798no—
1514C22⋊C4—798no—
1515C22⋊C4—798no—
1516C22⋊C4—794no—
1517C22⋊C4—794no—
1518C22⋊C4—794no—
1519C22⋊C4—794no—
1520C22⋊C4—794no—
1521C22⋊C4—794no—
1522C22⋊C4—794no—
1523C22⋊C4—794no—
1524C22⋊C4—794no—
1525C22⋊C4—798no—
1526C22⋊C4—798no—
1527C22⋊C4—798no—
1528C22⋊C4—798no—
1529C22⋊C4—798no—
1530C22⋊C4—798no—
1531C22⋊C4—798no—
1532C22⋊C4—794no—
1533C22⋊C4—798no—
1534C22⋊C4—794no—
1535C22⋊C4—794no—
1536C22⋊C4C23×D7914yes—
1537C22⋊C4C23×D7912yes—
1538C22⋊C4C23×D7918yes—
1539C22⋊C4C23×D7912yes—
1540C22⋊C4C23×D7914yes—
1541C22⋊C4C23×D7918yes—
1542C22⋊C4C23×D7914yes—
1543C22⋊C4C23×D7914yes—
1544C42—791no—
1545C42—791no—
1546C42—792no—
1547C42—792no—
1548C42—791no—
1549C42—791no—
1550C42—792no—
1551C42—792no—
1552C42—792no—
1553C42—792no—
1554C42—794no—
1555C42—794no—
1556C42—794no—
1557C42—792no—
1558C42—792no—
1559C42—794no—
1560C42—798no—
1561C42C23×D7912yes—
1562C42C23×D7912yes—
1563C42C23×D7918yes—
1564C23—22no—
1565C23—24no—
1566C23—42no—
1567C23—44no—
1568C23—3164no—
1569C23—3164no—
1570C23—3164no—
1571C23—3168no—
1572C23—3168no—
1573C23—792no—
1574C23—794no—
1575C23—792no—
1576C23—1584no—
1577C23C24×D7912yes—
1578C23C24×D7914yes—
1579C23C24×D7912yes—
1580C23C24×D7912yes—
1581C23C24×D7911yescharacteristic
1582Q8—24no—
1583Q8—24no—
1584Q8—22no—
1585Q8—22no—
1586Q8—44no—
1587Q8—3164no—
1588Q8—3164no—
1589Q8—1588no—
1590Q8—1582no—
1591Q8—1584no—
1592Q8—1584no—
1593Q8—1582no—
1594D4—24no—
1595D4—24no—
1596D4—24no—
1597D4—24no—
1598D4—22no—
1599D4—22no—
1600D4—48no—
1601D4—48no—
1602D4—44no—
1603D4—44no—
1604D4—48no—
1605D4—44no—
1606D4—3164no—
1607D4—3168no—
1608D4—3164no—
1609D4—3164no—
1610D4—3164no—
1611D4—3168no—
1612D4—3168no—
1613D4—3164no—
1614D4—3164no—
1615D4—3168no—
1616D4—3164no—
1617D4—3164no—
1618D4—1588no—
1619D4—15816no—
1620D4—1584no—
1621D4—1584no—
1622D4—1582no—
1623D4—1582no—
1624D4—1584no—
1625D4—1584no—
1626C2×C4—22no—
1627C2×C4—24no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—24no—
1632C2×C4—48no—
1633C2×C4—44no—
1634C2×C4—44no—
1635C2×C4—3168no—
1636C2×C4—3164no—
1637C2×C4—3164no—
1638C2×C4—3164no—
1639C2×C4—3168no—
1640C2×C4—3162no—
1641C2×C4—3162no—
1642C2×C4—3162no—
1643C2×C4—3164no—
1644C2×C4—3164no—
1645C2×C4—3164no—
1646C2×C4—3168no—
1647C2×C4—792no—
1648C2×C4—792no—
1649C2×C4—792no—
1650C2×C4—794no—
1651C2×C4—792no—
1652C2×C4—794no—
1653C2×C4—794no—
1654C2×C4—792no—
1655C2×C4—792no—
1656C2×C4—1588no—
1657C2×C4—1584no—
1658C2×C4—1584no—
1659C2×C4—1584no—
1660C2×C4—1588no—
1661C2×C4—1584no—
1662C2×C4—1584no—
1663C2×C4—1584no—
1664C2×C4#1457920614yes—
1665C2×C4C24×D7912yes—
1666C2×C4C24×D7914yes—
1667C2×C4C24×D7912yes—
1668C2×C4C24×D7912yes—
1669C2×C4C24×D7914yes—
1670C2×C4C24×D7914yes—
1671C2×C4C24×D7911yescharacteristic
1672C2×C4C24×D7911yescharacteristic
1673C22—22no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—24no—
1678C22—22no—
1679C22—22no—
1680C22—24no—
1681C22—28no—
1682C22—24no—
1683C22—44no—
1684C22—84no—
1685C22—6324no—
1686C22—1584no—
1687C22—1582no—
1688C22—1582no—
1689C22—1588no—
1690C22—1584no—
1691C22—1584no—
1692C22—12644no—
1693C22—12644no—
1694C22C2×#1457920612yes—
1695C22C25×D7911yescharacteristic
1696C4—22no—
1697C4—24no—
1698C4—22no—
1699C4—22no—
1700C4—24no—
1701C4—24no—
1702C4—794no—
1703C4—1582no—
1704C4—1584no—
1705C4—1582no—
1706C4—1582no—
1707C4—1584no—
1708C4—1584no—
1709C4—1582no—
1710C4—1582no—
1711C4C2×#1457920612yes—
1712C4C2×#1457920612yes—
1713C2—22no—
1714C2—42no—
1715C2—44no—
1716C2—42no—
1717C2—42no—
1718C2—3164no—
1719C2—3162no—
1720C2—3162no—
1721C2C22×#1457920611yescharacteristic
1722C2#585×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3487C2
hypercenter#3487D79
hypocenterC79#62836
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. #23777989C2semidirect
2. #23777974C2semidirect
3. #23777858C2semidirect
4. #23777759C2semidirect
5. #23777703C2semidirect
6. #23777403C2semidirect
7. #23777354C2semidirect
8. #23777326C2semidirect
9. #23777306C2semidirect
10. #23777297C2semidirect
11. #23777295C2semidirect
12. #23777281C2semidirect
13. #23777275C2semidirect
14. #23777270C2semidirect
15. #23777194C2semidirect
16. #23777192C2semidirect
17. #23777181C2semidirect
18. #23777175C2semidirect
19. #23777054C2semidirect
20. #23777044C2semidirect
21. #23777042C2semidirect
22. #23776692C2semidirect
23. #23776692C2semidirect
24. C2×#19099109C2semidirect
25. C79×#3487C2semidirect
26. C2×#14579208C22semidirect
29. C22×#11929624C22semidirect
30. #19099308C22semidirect
31. #19099307C22semidirect
32. #19099301C22semidirect
33. #19099300C22semidirect
34. #19099299C22semidirect
35. #19099298C22semidirect
36. #19099296C22semidirect
37. #19099295C22semidirect
38. #19099291C22semidirect
39. #19099285C22semidirect
40. #19099285C22semidirect
41. #19099282C22semidirect
42. #19099275C22semidirect
43. #19099267C22semidirect
44. #19099263C22semidirect
45. #19099262C22semidirect
46. #19099256C22semidirect
47. #19099256C22semidirect
48. #19099246C22semidirect
49. #19099244C22semidirect
50. #19099242C22semidirect
51. #19099240C22semidirect
52. #19099237C22semidirect
53. #19099234C22semidirect
54. #19099233C22semidirect
55. #19099233C22semidirect
56. #19099231C22semidirect
57. #19099231C22semidirect
58. Q8×C22⋊D79C22semidirect
59. #19099224C22semidirect
60. #19099223C22semidirect
61. #19099222C22semidirect
62. #19099219C22semidirect
63. #19099218C22semidirect
64. #19099215C22semidirect
65. #19099212C22semidirect
66. #19099212C22semidirect
67. #19099212C22semidirect
68. #19099212C22semidirect
69. #19099210C22semidirect
70. #19099210C22semidirect
71. #19099209C22semidirect
72. #19099202C22semidirect
73. #19099202C22semidirect
74. #19099201C22semidirect
75. #19099201C22semidirect
76. #19099201C22semidirect
77. #19099201C22semidirect
78. #19099200C22semidirect
79. #19099200C22semidirect
80. #19099197C22semidirect
82. #19099185C22semidirect
83. #19099183C22semidirect
84. #19099180C22semidirect
85. #19099177C22semidirect
86. #19099171C22semidirect
87. #19099167C22semidirect
88. #19099166C22semidirect
89. #19099163C22semidirect
90. #19099163C22semidirect
91. #19099163C22semidirect
92. #19099159C22semidirect
93. #19099155C22semidirect
94. #19099150C22semidirect
95. #19099147C22semidirect
96. #19099146C22semidirect
97. #19099145C22semidirect
98. #19099140C22semidirect
101. #19099137C22semidirect
102. #19099137C22semidirect
103. #19099137C22semidirect
104. #19099134C22semidirect
105. #19099134C22semidirect
106. #19099133C22semidirect
108. #19099131C22semidirect
109. #19099128C22semidirect
110. #19099127C22semidirect
111. #19099127C22semidirect
112. #19099126C22semidirect
113. #19099126C22semidirect
114. #19099126C22semidirect
115. #19099123C22semidirect
116. #19099122C22semidirect
117. #19099117C22semidirect
118. #19099116C22semidirect
119. #19099116C22semidirect
120. #19099115C22semidirect
121. #19099115C22semidirect
122. #19099112C22semidirect
123. #19099111C22semidirect
126. #19099109C22semidirect
127. #19099109C22semidirect
128. #19099109C22semidirect
129. #19099109C22semidirect
130. #19099109C22semidirect
131. #19099109C22semidirect
132. #19099108C22semidirect
133. #19099108C22semidirect
134. #19099108C22semidirect
135. C2×#14579159C22semidirect
136. C2×#14579159C22semidirect
138. #127×D79C22semidirect
139. #19099100C22semidirect
140. #19099099C22semidirect
141. #19099099C22semidirect
142. #19099094C22semidirect
143. #19099094C22semidirect
144. #19099094C22semidirect
145. #19099093C22semidirect
146. #19099093C22semidirect
147. #19099090C22semidirect
148. #19099090C22semidirect
149. C2×#14579150C22semidirect
150. C2×#14579150C22semidirect
151. C2×#14579148C22semidirect
152. #124×D79C22semidirect
154. #19099074C22semidirect
155. #19099071C22semidirect
156. #19099069C22semidirect
157. #19099069C22semidirect
158. C2×#14579144C22semidirect
159. #123×D79C22semidirect
160. C2×#14579133C22semidirect
161. #19099042C22semidirect
162. #19099040C22semidirect
163. #19099038C22semidirect
164. #19099037C22semidirect
165. #19099035C22semidirect
166. #41×Dic79C22semidirect
167. #41×Dic79C22semidirect
169. #19099031C22semidirect
170. C4×#11929623C22semidirect
171. C4×#11929623C22semidirect
172. C2×C4×C22⋊D79C22semidirect
173. C22×C4×Dic79C22semidirect
174. C2×2−1+4×C79C22semidirect
175. C22×#41×C79C22semidirect
176. #550×C79C22semidirect
177. #550×C79C22semidirect
178. #548×C79C22semidirect
179. #548×C79C22semidirect
181. #535×C79C22semidirect
182. #535×C79C22semidirect
183. #525×C79C22semidirect
184. #525×C79C22semidirect
185. #525×C79C22semidirect
186. #519×C79C22semidirect
881. #3487D79semidirect
887. C79#62836semidirect
889. C2×2−1+4C2×D79semidirect
893. C22×#41C2×D79semidirect
922. #550C2×D79semidirect
923. #550C2×D79semidirect
929. #548C2×D79semidirect
930. #548C2×D79semidirect
984. #535C2×D79semidirect
985. #535C2×D79semidirect
1029. #525C2×D79semidirect
1030. #525C2×D79semidirect
1031. #525C2×D79semidirect
1037. #519C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779892
#237779742
#237778582
#237777592
#237777032
#237774032
#237773542
#237773262
#237773062
#237772972
#237772952
#237772812
#237772752
#237772702
#237771942
#237771922
#237771812
#237771752
#237770542
#237770442
#237770422
#237766922
C2×#190991092
C79×#34872
#6283679