Finite Group Databasebeta

← #35197362

Subgroups — #35197362

Order 20224.

7066 conjugacy classes of subgroups.

The subgroup lattice has 1558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777504C214yesmaximal, complemented
2#23777500C214yesmaximal, complemented
3#23777482C214yesmaximal, complemented
4#23777478C214yesmaximal, complemented
5#23777403C214yesmaximal, complemented
6#23777399C214yesmaximal, complemented
7#23777388C214yesmaximal, complemented
8#23777384C214yesmaximal, complemented
9#23777252C211yesmaximal, characteristic, complemented
10#23777247C214yesmaximal, complemented
11#23777205C211yesmaximal, characteristic, complemented
12#23777166C211yesmaximal, characteristic, complemented
13#23777103C212yesmaximal, complemented
14#23777101C214yesmaximal, complemented
15#23777056C212yesmaximal, complemented
16#23776818C214yesmaximal, complemented
17#23776813C212yesmaximal, complemented
18#23776792C211yesmaximal, characteristic, complemented
19#23776789C211yesmaximal, characteristic, complemented
20#23776782C214yesmaximal, complemented
21#23776611C212yesmaximal, complemented
22C2×#19099042C211yesmaximal, characteristic, complemented
23C79×#3506C211yesmaximal, characteristic, complemented
24C2×#14579208C2212yes—
25C22×#11929623C2211yescharacteristic
26#19099297C2218yescomplemented
27#19099296C2214yescomplemented
28#19099295C2218yescomplemented
29Q8×Dic158C2212yescomplemented
30#19099293C2212yescomplemented
31#19099291C2214yescomplemented
32#19099291C2212yescomplemented
33#19099290C2214yescomplemented
34#19099288C2212yescomplemented
35#19099283C2212yescomplemented
36#19099280C2218yescomplemented
37#19099278C2212yescomplemented
38#19099275C2218yescomplemented
39#19099273C2214yescomplemented
40#19099272C2218yescomplemented
41#19099268C2214yescomplemented
42#19099267C2218yescomplemented
43#19099264C2218yescomplemented
44#19099263C2214yescomplemented
45#19099263C2214yescomplemented
46#19099262C2218yescomplemented
47#19099257C2214yescomplemented
48#19099256C2218yescomplemented
49#19099256C2218yescomplemented
50#19099254C2214yescomplemented
51#19099252C2214yescomplemented
52#19099250C2218yescomplemented
53#19099246C2218yescomplemented
54#19099234C2212yescomplemented
55#19099234C2212yescomplemented
56#19099233C2214yes—
57#19099233C2214yes—
58#19099233C2212yescomplemented
59#19099231C2214yes—
60#19099231C2214yes—
61#19099231C2218yescomplemented
62D4×Dic158C2212yescomplemented
63#19099228C2212yescomplemented
64#19099222C2214yescomplemented
65#19099221C2214yes—
66#19099221C2214yes—
67#19099221C2214yescomplemented
68#19099219C2214yes—
69#19099219C2214yes—
70#19099218C2214yescomplemented
71#19099218C2212yescomplemented
72#19099214C2214yescomplemented
73#19099212C2218yescomplemented
74#19099211C2218yescomplemented
75#19099211C2218yescomplemented
76#19099192C2214yes—
77#19099191C2212yes—
78#19099187C2212yescomplemented
79#19099187C2212yescomplemented
80#19099183C2218yescomplemented
81#19099182C2212yescomplemented
82#19099182C2212yescomplemented
83#19099182C2214yescomplemented
84#19099181C2218yescomplemented
85#19099181C2218yescomplemented
86#19099180C2214yescomplemented
87#19099177C2218yescomplemented
88#19099176C2212yescomplemented
89#19099174C2212yescomplemented
90#19099170C2218yescomplemented
91#19099169C2212yescomplemented
92#19099167C2212yescomplemented
93#19099167C2214yescomplemented
94#19099166C2214yescomplemented
95#19099165C2218yescomplemented
96#19099163C2218yescomplemented
97#19099163C2218yescomplemented
98#19099162C2212yes—
99#19099162C2212yes—
100#19099158C2212yes—
101#19099158C2212yes—
102#19099155C2218yes—
103#19099153C2212yes—
104#19099153C2212yes—
105#19099151C2214yes—
106#19099150C2212yes—
107#19099150C2212yes—
108#19099148C2218yes—
109#19099141C2212yes—
110#19099140C2214yes—
111#19099130C2212yes—
112#19099128C2218yes—
113#19099120C2211yescharacteristic
114#19099115C2214yes—
115#19099113C2211yescharacteristic
116#19099111C2214yescomplemented
117#19099110C2218yescomplemented
118#19099109C2218yescomplemented
119#19099108C2214yes—
120#19099108C2214yescomplemented
121#19099100C2214yescomplemented
122#19099100C2214yescomplemented
123#19099096C2218yescomplemented
124#19099094C2218yescomplemented
125#19099094C2214yescomplemented
126#19099093C2214yescomplemented
127#19099093C2214yescomplemented
128#19099093C2218yescomplemented
129#19099092C2218yescomplemented
130#19099092C2214yescomplemented
131#19099091C2218yescomplemented
132#19099090C2218yescomplemented
133#19099075C2212yes—
134#19099074C2214yes—
135#19099072C2218yes—
136#19099070C2212yes—
137#19099069C2218yes—
138#19099069C2218yes—
139#19099044C2212yes—
140#19099044C2214yescomplemented
141#19099042C2218yes—
142#19099042C2214yes—
143#19099042C2214yes—
144#19099042C2214yes—
145#19099042C2214yes—
146#19099042C2214yescomplemented
147#19099040C2212yes—
148#19099040C2214yescomplemented
149#19099039C2214yescomplemented
150#41×Dic79C2212yes—
151#19099031C2212yes—
152#19099031C2214yescomplemented
153C4×#11929623C2218yes—
154C4×#11929623C2214yescomplemented
155C2×C4×Dic158C2211yescharacteristic
156C2×#14579126C2211yescharacteristic
157C2×#14579126C2214yescomplemented
158C4×Q8×D79C2214yescomplemented
159C2×D4×Dic79C2211yescharacteristic
160C2×C4×C22⋊D79C2212yes—
161C2×(C22⋊D79)⋊C4C2212yes—
162C2×#14579118C2211yescharacteristic
163C2×#14579117C2212yes—
164C22×Dic79⋊C4C2212yes—
165C2×C4⋊C4×D79C2211yescharacteristic
166#559×C79C2214yescomplemented
167#556×C79C2212yescomplemented
168#555×C79C2212yescomplemented
169#553×C79C2214yescomplemented
170#550×C79C2212yescomplemented
171#547×C79C2212yescomplemented
172#538×C79C2214yes—
173#535×C79C2212yes—
174#533×C79C2211yescharacteristic
175#532×C79C2211yescharacteristic
176#525×C79C2214yes—
177#520×C79C2212yes—
178C2×C4×D4×C79C2211yescharacteristic
179#14579208—216no—
180C2×#11929624C2312yes—
181C2×#11929624C2314yes—
182C2×#11929624C2314yes—
183C2×#11929624C2318yes—
184C2×#11929623—28no—
185C2×#11929623C2318yes—
186C2×#11929623C2314yes—
187C2×#11929623C2314yes—
188C2×#11929623C2314yes—
189C2×#11929623C2318yes—
190C22×Dic158C2314yes—
191C22×Dic158C2311yescharacteristic
192C2×Q8×D79C2314yes—
193C22×C22⋊D79C2312yes—
194C23×Dic79C2312yes—
195C23×Dic79C2312yes—
196C22×C4×D79C2311yescharacteristic
197C22×C4×D79C2312yes—
198#14579161C2311yescharacteristic
199#14579161C2311yescharacteristic
200#14579161C2311yescharacteristic
201#14579161C2314yes—
202#14579160C2314yes—
203#14579160C2314yes—
204#14579160C2314yes—
205#14579160C2318yes—
206#14579159C2314yes—
207#14579159C2318yes—
208#14579158C2311yescharacteristic
209#14579157C2314yes—
210#14579157C2318yes—
211#14579157C2318yes—
212#14579157C2314yes—
213#14579156C2314yes—
214#14579156C2314yes—
215#14579156C2314yes—
216#14579156C2314yes—
217#14579156C2314yes—
218#14579156C2314yes—
219#14579155C2318yes—
220#14579154C2318yes—
221#14579154C2318yes—
222#14579154C2318yes—
223#14579154C2318yes—
224#14579154C2314yes—
225#14579154C2314yes—
226#14579153C2318yes—
227#14579153C2312yes—
228#14579153C2314yes—
229#14579152C2314yes—
230#14579152C2314yes—
231#14579152C2314yes—
232#14579151C2318yes—
233#14579151C2314yes—
234#14579151C2314yes—
235#14579151C2318yes—
236#14579151C2318yes—
237#14579151C2318yes—
238#14579150C2314yes—
239#14579150C2314yes—
240#14579149C2312yes—
241#14579148C2318yes—
242#14579148C2314yes—
243#14579147C2318yes—
244#14579147C2314yes—
245#14579147C2314yes—
246#14579147C2318yes—
247#14579147C2318yes—
248#14579147C2318yes—
249#14579147C2318yes—
250#14579146C2314yes—
251#14579146C2314yes—
252#14579146C2314yes—
253#14579146C2314yes—
254#14579146C2318yes—
255#14579145C2314yes—
256#14579145C2314yes—
257#14579145C2314yes—
258#14579145C2318yes—
259#14579144C2318yes—
260#14579144C2318yes—
261#14579143C2318yes—
262#14579143C2318yes—
263#14579143C2318yes—
264#14579143C2318yes—
265#14579142C2318yes—
266#14579142C2314yes—
267#14579142C2314yes—
268#14579142C2314yes—
269#14579142C2318yes—
270#14579141C2312yes—
271#14579141C2312yes—
272#14579140C2314yes—
273#14579140C2312yes—
274#14579140C2312yes—
275#14579140C2318yes—
276#14579140C2314yes—
277#14579139C2318yes—
278#14579139C2318yes—
279#14579139C2318yes—
280#14579138C2318yes—
281#14579138C2318yes—
282#14579138C2314yes—
283#14579138C2314yes—
284#14579138C2318yes—
285#14579138C2318yes—
286#14579138C2318yes—
287#14579137C2314yes—
288#14579137C2314yes—
289#14579137C2314yes—
290#14579137C2312yes—
291#14579137C2312yes—
292#14579136C2314yes—
293#14579136C2314yes—
294#14579136C2312yes—
295#14579136C2312yes—
296#14579135C2312yes—
297#14579135C2314yes—
298#14579135C2312yes—
299#14579135C2314yes—
300#14579134C2318yes—
301#14579134C2318yes—
302#14579134C2318yes—
303#14579134C2318yes—
304#14579134C2318yes—
305#14579133C2318yes—
306#14579133C2318yes—
307#14579133C2318yes—
308#14579133C2314yes—
309#14579133C2314yes—
310#14579133C2318yes—
311#14579133C2318yes—
312#14579133C2318yes—
313#14579133C2318yes—
314#14579133C2318yes—
315#14579132C2314yes—
316#14579132C2318yes—
317#14579132C2312yes—
318#14579132C2312yes—
319#14579132C2314yes—
320#14579132C2314yes—
321#14579131C2314yes—
322#14579130C2318yes—
323#14579129C2314yes—
324Q8×Dic79C2312yes—
325Q8×Dic79C2312yes—
326Q8×Dic79C2314yes—
327C4×Dic158C2318yes—
328C4×Dic158C2314yes—
329C4×Dic158C2314yes—
330C4×Dic158C2312yes—
331C4×Dic158C2312yes—
332C4×Dic158C2312yes—
333C4×Dic158C2312yes—
334C4×Dic158C2312yes—
335C4×Dic158C2318yes—
336C4×Dic158C2312yes—
337#14579126C2318yes—
338#14579126C2312yes—
339#14579126C2312yes—
340#14579126C2314yes—
341#14579126C2314yes—
342#14579126C2318yes—
343#14579126C2318yes—
344#14579126C2314yes—
345#14579126C2314yes—
346#14579126C2314yes—
347#14579126C2314yes—
348C4×D316C2314yes—
349C4×D316C2312yes—
350C4×D316C2314yes—
351C4×D316C2312yes—
352C4×D316C2318yes—
353D4×Dic79C2314yes—
354D4×Dic79C2314yes—
355D4×Dic79C2314yes—
356D4×Dic79C2312yes—
357D4×Dic79C2314yes—
358D4×Dic79C2312yes—
359D4×Dic79C2318yes—
360D4×Dic79C2318yes—
361D4×Dic79C2314yes—
362D4×Dic79C2318yes—
363#14579123C2312yes—
364#14579123C2312yes—
365#14579123C2314yes—
366#14579123C2314yes—
367C4×C22⋊D79C2318yes—
368C4×C22⋊D79C2318yes—
369C4×C22⋊D79C2318yes—
370C4×C22⋊D79C2318yes—
371C4×C22⋊D79C2318yes—
372C4×C22⋊D79C2314yes—
373C4×C22⋊D79C2314yes—
374C4×C22⋊D79C2318yes—
375C4×C22⋊D79C2318yes—
376(C22⋊D79)⋊C4C2314yes—
377(C22⋊D79)⋊C4C2314yes—
378(C22⋊D79)⋊C4C2318yes—
379(C22⋊D79)⋊C4C2318yes—
380(C22⋊D79)⋊C4C2318yes—
381(C22⋊D79)⋊C4C2318yes—
382(C22⋊D79)⋊C4C2318yes—
383(C22⋊D79)⋊C4C2318yes—
384(C22⋊D79)⋊C4C2318yes—
385(C22⋊D79)⋊C4C2318yes—
386#14579120C2314yes—
387#14579120C2312yes—
388#14579120C2314yes—
389#14579119C2318yes—
390#14579119C2314yes—
391#14579118C2312yes—
392#14579118C2314yes—
393#14579118C2312yes—
394#14579118C2312yes—
395#14579118C2312yes—
396#14579118C2318yes—
397#14579118C2318yes—
398#14579117C2318yes—
399#14579117C2318yes—
400#14579117C2318yes—
401#14579117C2318yes—
402#14579117C2318yes—
403#14579117C2318yes—
404C2×C4⋊Dic79C2311yescharacteristic
405C2×Dic79⋊C4C2312yes—
406C2×Dic79⋊C4C2312yes—
407C2×Dic79⋊C4C2311yescharacteristic
408C2×Dic79⋊C4C2311yescharacteristic
409C2×Dic79⋊C4C2318yes—
410C2×Dic79⋊C4C2318yes—
411C2×Dic79⋊C4C2318yes—
412C2×Dic79⋊C4C2312yes—
413C4⋊C4×D79C2318yes—
414C4⋊C4×D79C2314yes—
415C4⋊C4×D79C2314yes—
416C4⋊C4×D79C2314yes—
417C2×C22⋊Dic79C2312yes—
418C2×(C2×D79)⋊C4C2311yescharacteristic
419C2×(C2×D79)⋊C4C2311yescharacteristic
420C2×C4×Dic79C2312yes—
421C2×C4×Dic79C2312yes—
422C2×C4×Dic79C2311yescharacteristic
423C2×C4×Dic79C2318yes—
424C2×C4×Dic79C2314yes—
425C42×D79C2318yes—
426C42×D79C2314yes—
427C2×#41×C79C2312yes—
428C2×#41×C79C2314yes—
429C22×D4×C79C2311yescharacteristic
430C23×C4×C79C2312yes—
431C4⋊Q8×C79C2311yescharacteristic
432C4⋊Q8×C79C2311yescharacteristic
433C4⋊Q8×C79C2311yescharacteristic
434#127×C79C2311yescharacteristic
435#127×C79C2314yes—
436#126×C79C2318yes—
437#125×C79C2312yes—
438#124×C79C2318yes—
439#124×C79C2312yes—
440#124×C79C2314yes—
441#123×C79C2318yes—
442#123×C79C2318yes—
443C22⋊Q8×C79C2312yes—
444C22⋊Q8×C79C2312yes—
445C22⋊Q8×C79C2314yes—
446#121×C79C2312yes—
447#121×C79C2312yes—
448#121×C79C2314yes—
449#121×C79C2318yes—
450#121×C79C2314yes—
451#121×C79C2314yes—
452#120×C79C2318yes—
453C4×Q8×C79C2314yes—
454C4×Q8×C79C2312yes—
455C4×Q8×C79C2312yes—
456C4×D4×C79C2318yes—
457C4×D4×C79C2312yes—
458C4×D4×C79C2314yes—
459C4×D4×C79C2312yes—
460C4×D4×C79C2312yes—
461C4×D4×C79C2312yes—
462C4×D4×C79C2312yes—
463C4×D4×C79C2312yes—
464C4×D4×C79C2318yes—
465#117×C79C2312yes—
466#117×C79C2314yes—
467#117×C79C2314yes—
468C2×C4⋊C4×C79C2314yes—
469C2×C4⋊C4×C79C2311yescharacteristic
470C2×C22⋊C4×C79C2312yes—
471C2×C42×C79C2311yescharacteristic
472C23×D79C2411yescharacteristic
473#11929624—216no—
474#11929624—28no—
475#11929624—84no—
476#11929624—88no—
477#11929623—232no—
478#11929623—216no—
479#11929623—216no—
480#11929623—216no—
481#11929623—88no—
482C2×Dic158—216no—
483C2×Dic158#4118yescomplemented
484C2×Dic158C2418yes—
485C2×Dic158C2412yes—
486C2×Dic158C2418yes—
487C2×Dic158C2412yes—
488C2×Dic158C2412yes—
489C2×Dic158C2412yes—
490C2×Dic158C2412yes—
491Q8×D79—216no—
492C2×D316C2412yes—
493C2×D316C2414yes—
494C2×D316C2412yes—
495C2×D316C2412yes—
496C2×D316C2414yes—
497C2×C22⋊D79—28no—
498C2×C22⋊D79C2414yes—
499C2×C22⋊D79C2418yes—
500C2×C22⋊D79C2418yes—
501C2×C22⋊D79C2418yes—
502C2×C22⋊D79C2418yes—
503C2×C22⋊D79C2414yes—
504C2×C22⋊D79C2418yes—
505C2×C22⋊D79C2414yes—
506C22×Dic79—28no—
507C22×Dic79—82no—
508C22×Dic79C2418yes—
509C22×Dic79C2418yes—
510C22×Dic79C2411yescharacteristic
511C22×Dic79C2414yes—
512C22×Dic79C2418yes—
513C22×Dic79C2411yescharacteristic
514C22×Dic79C2414yes—
515C22×Dic79C2411yescharacteristic
516C22×Dic79C2412yes—
517C22×Dic79C2412yes—
518C2×C4×D79—24no—
519C2×C4×D79—82no—
520C2×C4×D79C2418yes—
521C2×C4×D79C2414yes—
522C2×C4×D79C2412yes—
523C2×C4×D79C2412yes—
524C2×C4×D79C2414yes—
525C2×C4×D79C2418yes—
526C2×C4×D79C2418yes—
527C2×C4×D79C2414yes—
528C4⋊Dic79C2412yes—
529C4⋊Dic79C2412yes—
530C4⋊Dic79C2412yes—
531C4⋊Dic79C2414yes—
532C4⋊Dic79C2412yes—
533C4⋊Dic79C2414yes—
534C4⋊Dic79C2412yes—
535C4⋊Dic79C2412yes—
536C4⋊Dic79C2412yes—
537C4⋊Dic79C2414yes—
538C4⋊Dic79C2414yes—
539C4⋊Dic79C2418yes—
540C4⋊Dic79C2412yes—
541Dic79⋊C4C2418yes—
542Dic79⋊C4C2418yes—
543Dic79⋊C4C2418yes—
544Dic79⋊C4C2418yes—
545Dic79⋊C4C2412yes—
546Dic79⋊C4C2412yes—
547Dic79⋊C4C2414yes—
548Dic79⋊C4C2414yes—
549Dic79⋊C4C2414yes—
550Dic79⋊C4C2412yes—
551Dic79⋊C4C2412yes—
552Dic79⋊C4C2418yes—
553Dic79⋊C4C2414yes—
554Dic79⋊C4C2418yes—
555Dic79⋊C4C2418yes—
556Dic79⋊C4C2414yes—
557Dic79⋊C4C2414yes—
558Dic79⋊C4C2418yes—
559Dic79⋊C4C2414yes—
560Dic79⋊C4C2414yes—
561C22⋊Dic79C2418yes—
562C22⋊Dic79C2414yes—
563C22⋊Dic79C2414yes—
564C22⋊Dic79C2414yes—
565C22⋊Dic79C2418yes—
566C22⋊Dic79C2418yes—
567C22⋊Dic79C2414yes—
568C22⋊Dic79C2418yes—
569C22⋊Dic79C2414yes—
570(C2×D79)⋊C4C2412yes—
571(C2×D79)⋊C4C2412yes—
572(C2×D79)⋊C4C2412yes—
573(C2×D79)⋊C4C2412yes—
574(C2×D79)⋊C4C2414yes—
575(C2×D79)⋊C4C2414yes—
576(C2×D79)⋊C4C2414yes—
577(C2×D79)⋊C4C2414yes—
578(C2×D79)⋊C4C2418yes—
579(C2×D79)⋊C4C2414yes—
580(C2×D79)⋊C4C2414yes—
581(C2×D79)⋊C4C2414yes—
582(C2×D79)⋊C4C2418yes—
583(C2×D79)⋊C4C2414yes—
584(C2×D79)⋊C4C2414yes—
585(C2×D79)⋊C4C2414yes—
586C4×Dic79C2412yes—
587C4×Dic79C2414yes—
588C4×Dic79C2418yes—
589C4×Dic79C2414yes—
590C4×Dic79C2414yes—
591C4×Dic79C2418yes—
592C4×Dic79C2412yes—
593C4×Dic79C2414yes—
594C4×Dic79C2414yes—
595C4×Dic79C2414yes—
596C4×Dic79C2418yes—
597C4×Dic79C2418yes—
598C4×Dic79C2414yes—
599C24×C79C2412yes—
600#41×C79—28no—
601#41×C79—84no—
602C2×Q8×C79C2412yes—
603C2×Q8×C79C2412yes—
604C2×Q8×C79C2412yes—
605C2×D4×C79—24no—
606C2×D4×C79C2414yes—
607C2×D4×C79C2412yes—
608C2×D4×C79C2412yes—
609C2×D4×C79C2412yes—
610C2×D4×C79C2418yes—
611C2×D4×C79C2418yes—
612C2×D4×C79C2412yes—
613C2×D4×C79C2412yes—
614C22×C4×C79—82no—
615C22×C4×C79C2414yes—
616C22×C4×C79C2418yes—
617C22×C4×C79C2414yes—
618C22×C4×C79C2411yescharacteristic
619C22×C4×C79C2411yescharacteristic
620C22×C4×C79C2412yes—
621C22×C4×C79C2414yes—
622C22×C4×C79C2411yescharacteristic
623C4⋊C4×C79C2412yes—
624C4⋊C4×C79C2412yes—
625C4⋊C4×C79C2412yes—
626C4⋊C4×C79C2418yes—
627C4⋊C4×C79C2412yes—
628C4⋊C4×C79C2412yes—
629C4⋊C4×C79C2412yes—
630C4⋊C4×C79C2414yes—
631C4⋊C4×C79C2412yes—
632C4⋊C4×C79C2414yes—
633C4⋊C4×C79C2412yes—
634C22⋊C4×C79C2414yes—
635C22⋊C4×C79C2414yes—
636C22⋊C4×C79C2414yes—
637C22⋊C4×C79C2418yes—
638C22⋊C4×C79C2418yes—
639C22⋊C4×C79C2414yes—
640C22⋊C4×C79C2418yes—
641C22⋊C4×C79C2414yes—
642C42×C79C2411yescharacteristic
643C42×C79C2411yescharacteristic
644C42×C79C2411yescharacteristic
645C42×C79C2411yescharacteristic
646C42×C79C2418yes—
647C42×C79C2414yes—
648C23×C79—24no—
649C23×C79—42no—
650C23×C79—42no—
651C23×C79C2514yes—
652C23×C79C2514yes—
653C23×C79C2511yescharacteristic
654C22×D79—22no—
655C22×D79—41no—
656C22×D79—41no—
657C22×D79C2512yes—
658C22×D79C2514yes—
659Q8×C79—24no—
660Q8×C79—42no—
661Q8×C79—42no—
662D4×C79—28no—
663D4×C79—24no—
664D4×C79—24no—
665D4×C79—24no—
666D4×C79—48no—
667D4×C79—42no—
668D4×C79—48no—
669D4×C79—42no—
670C2×C4×C79—28no—
671C2×C4×C79—42no—
672C2×C4×C79—44no—
673C2×C4×C79—48no—
674C2×C4×C79—41no—
675C2×C4×C79—44no—
676C2×C4×C79—41no—
677C2×C4×C79C2×#4114yes—
678C2×C4×C79C2511yescharacteristic
679C2×C4×C79C2511yescharacteristic
680C2×C4×C79C2514yes—
681C2×C4×C79C2514yes—
682C2×C4×C79C2514yes—
683C2×C4×C79C2514yes—
684C2×C4×C79C2511yescharacteristic
685C2×C4×C79C2511yescharacteristic
686C2×C4×C79C2511yescharacteristic
687C2×C4×C79C2511yescharacteristic
688C22⋊D79—28no—
689C22⋊D79—216no—
690C22⋊D79—216no—
691C22⋊D79—44no—
692C22⋊D79—48no—
693C22⋊D79—48no—
694C22⋊D79—48no—
695C22⋊D79—44no—
696C2×Dic79—22no—
697C2×Dic79—216no—
698C2×Dic79—216no—
699C2×Dic79—42no—
700C2×Dic79—41no—
701C2×Dic79—48no—
702C2×Dic79—44no—
703C2×Dic79—41no—
704C2×Dic79—44no—
705C2×Dic79C2×#4118yes—
706C2×Dic79C2512yes—
707C2×Dic79C2512yes—
708C2×Dic79C2514yes—
709C2×Dic79C2514yes—
710C2×Dic79C2514yes—
711C2×Dic79C2514yes—
712C2×Dic79C2512yes—
713C2×Dic79C2514yes—
714D316—24no—
715D316—42no—
716D316—44no—
717D316—42no—
718D316—44no—
719C4×D79—24no—
720C4×D79—24no—
721C4×D79—28no—
722C4×D79—216no—
723C4×D79—48no—
724C4×D79—44no—
725C4×D79—44no—
726C4×D79—48no—
727Dic158—24no—
728Dic158—216no—
729Dic158—42no—
730Dic158—48no—
731Dic158—42no—
732Dic158C2×#4118yes—
733Dic158C2×#4118yes—
734C22×C79—21no—
735C22×C79—21no—
736C22×C79—24no—
737C22×C79—24no—
738C22×C79—24no—
739C22×C79—24no—
740C22×C79—24no—
741C22×C79—24no—
742C22×C79—48no—
743C22×C79C22×#4112yes—
744C22×C79C2611yescharacteristic
745C2×D79—22no—
746C2×D79—24no—
747C2×D79—24no—
748C2×D79—22no—
749C2×D79—22no—
750C2×D79—24no—
751C2×D79—44no—
752C4×C79—24no—
753C4×C79—21no—
754C4×C79—21no—
755C4×C79—24no—
756C4×C79—24no—
757C4×C79—21no—
758C4×C79—21no—
759C4×C79—24no—
760C4×C79C22×#4112yes—
761C4×C79C22×#4112yes—
762Dic79—24no—
763Dic79—22no—
764Dic79—24no—
765Dic79—24no—
766Dic79—22no—
767Dic79—24no—
768Dic79—22no—
769Dic79C22×#4118yes—
770#62851—791nomaximal, Sylow
771C2×C79—22no—
772C2×C79—44no—
773C2×C79—44no—
774C2×C79C23×#4111yescharacteristic
775C2×C79H(7,𝔽2)11yescharacteristic
776C2×C792−1+611yescharacteristic
777D79—44no—
778D79—42no—
779#3524—794no—
780#3524—794no—
781#3522—794no—
782#3522—794no—
783#3517—794no—
784#3517—794no—
785#3516—794no—
786#3516—794no—
787#3506—794no—
788#3506—791no—
789#3506D7911yescharacteristic, complemented
790#3502—791no—
791#3497—791no—
792#3492—794no—
793#3492—792no—
794#3487—792no—
795#3460—792no—
796#3460—794no—
797#3455—794no—
798#3455—791no—
799#3455—791no—
800C4×2−1+4—792no—
801C2×#520—791no—
802C79#6285111yescharacteristic, complemented, Sylow
803C2×2−1+4—792no—
804C22×#41—791no—
805#559—798no—
806#559—798no—
807#559—794no—
808#559C2×D7914yescomplemented
809Q82—792no—
810Q82—792no—
811#557—792no—
812#557—794no—
813#557—794no—
814#557—792no—
815#556—798no—
816#556—792no—
817#556C2×D7912yescomplemented
818#555—798no—
819#555—792no—
820#555C2×D7912yescomplemented
821#554—798no—
822#554—794no—
823#554—798no—
824#554—794no—
825#553—798no—
826#553—798no—
827#553—798no—
828#553—798no—
829#553—794no—
830#553—794no—
831#553—794no—
832#553C2×D7914yescomplemented
833#552—798no—
834#552—794no—
835#552—798no—
836#552—794no—
837#550—794no—
838#550—794no—
839#550—792no—
840#550—794no—
841#550—794no—
842#550—798no—
843#550—792no—
844#550—792no—
845#550C2×D7912yescomplemented
846D4×Q8—792no—
847D4×Q8—792no—
848#548—794no—
849#548—794no—
850#548—794no—
851#548—794no—
852#548—794no—
853#548—794no—
854#547—798no—
855#547—798no—
856#547—798no—
857#547—794no—
858#547—792no—
859#547—794no—
860#547C2×D7912yescomplemented
861#544—794no—
862#544—792no—
863#542—792no—
864#542—792no—
865#542—798no—
866#542—792no—
867#542—792no—
868#542—794no—
869#542—798no—
870#542—798no—
871#542—798no—
872#542—794no—
873#541—792no—
874#541—798no—
875#541—792no—
876#540—792no—
877#540—794no—
878#540—792no—
879#540—798no—
880#540—798no—
881#540—798no—
882#540—794no—
883#539—792no—
884#539—792no—
885#539—792no—
886#539—792no—
887#539—798no—
888#538—792no—
889#538—792no—
890#538—792no—
891#538—792no—
892#538—798no—
893#538—794no—
894#538C2×D7914yes—
895#537—792no—
896#537—794no—
897#535—792no—
898#535—798no—
899#535C2×D7912yes—
900#533—794no—
901#533—791no—
902#533C2×D7911yescharacteristic
903#532—798no—
904#532—794no—
905#532—794no—
906#532—794no—
907#532—798no—
908#532—791no—
909#532C2×D7911yescharacteristic
910#529—798no—
911#529—798no—
912#529—794no—
913#529—798no—
914#529—798no—
915#529—794no—
916#529—794no—
917#529—794no—
918#529—794no—
919#529—794no—
920#529—798no—
921#529—798no—
922#525—792no—
923#525—794no—
924#525—798no—
925#525—798no—
926#525—798no—
927#525—792no—
928#525C2×D7914yes—
929#520—794no—
930#520—794no—
931#520—794no—
932#520—794no—
933#520—798no—
934#520—794no—
935#520—792no—
936#520—794no—
937#520C2×D7912yes—
938#519—794no—
939#519—792no—
940#519—794no—
941C4×#41—792no—
942C4×#41—798no—
943C4×#41—794no—
944C4×#41—792no—
945C4×#41—794no—
946C2×C4×Q8—794no—
947C2×C4×Q8—791no—
948C2×C4×Q8—794no—
949C2×C4×Q8—791no—
950C2×C4×D4—791no—
951C2×C4×D4—792no—
952C2×C4×D4—792no—
953C2×C4×D4C2×D7911yescharacteristic
954C2×#117—792no—
955C2×#117—791no—
956C22×C4⋊C4—792no—
957C22×C4⋊C4—791no—
9582−1+4—15816no—
959C2×#41—798no—
960C2×#41—798no—
961C2×#41—794no—
962C2×#41—794no—
963C2×#41—794no—
964C2×#41—794no—
965C2×#41—798no—
966C2×#41—792no—
967C2×#41—794no—
968C2×#41—1588no—
969C2×#41C22×D7912yes—
970C2×#41C22×D7914yes—
971C22×Q8—794no—
972C22×Q8—791no—
973C22×Q8—794no—
974C22×D4—792no—
975C22×D4C22×D7911yescharacteristic
976C23×C4—792no—
977C23×C4—792no—
978C23×C4—792no—
979C23×C4—791no—
980C23×C4C22×D7912yes—
981C4⋊Q8—798no—
982C4⋊Q8—794no—
983C4⋊Q8—794no—
984C4⋊Q8—798no—
985C4⋊Q8—794no—
986C4⋊Q8—794no—
987C4⋊Q8—791no—
988C4⋊Q8—794no—
989C4⋊Q8—791no—
990C4⋊Q8—791no—
991C4⋊Q8C22×D7911yescharacteristic
992C4⋊Q8C22×D7911yescharacteristic
993C4⋊Q8C22×D7911yescharacteristic
994#127—794no—
995#127—798no—
996#127—798no—
997#127—794no—
998#127—791no—
999#127C22×D7914yes—
1000#127C22×D7911yescharacteristic
1001#126—794no—
1002#126—794no—
1003#126—794no—
1004#126—794no—
1005#126—794no—
1006#126—794no—
1007#126—798no—
1008#126—798no—
1009#126—794no—
1010#126—798no—
1011#126—794no—
1012#126—798no—
1013#126—798no—
1014#126C22×D7918yes—
1015#125—794no—
1016#125—794no—
1017#125—798no—
1018#125—794no—
1019#125—794no—
1020#125—798no—
1021#125—798no—
1022#125—794no—
1023#125—798no—
1024#125—798no—
1025#125—794no—
1026#125—792no—
1027#125C22×D7912yes—
1028#124—794no—
1029#124—794no—
1030#124—798no—
1031#124—794no—
1032#124—798no—
1033#124—794no—
1034#124—798no—
1035#124—798no—
1036#124—794no—
1037#124—798no—
1038#124—798no—
1039#124—792no—
1040#124C22×D7914yes—
1041#124C22×D7918yes—
1042#124C22×D7912yes—
1043#123—794no—
1044#123—798no—
1045#123—798no—
1046#123—794no—
1047#123—794no—
1048#123—798no—
1049#123—798no—
1050#123—798no—
1051#123—794no—
1052#123—794no—
1053#123—794no—
1054#123—794no—
1055#123—794no—
1056#123—798no—
1057#123—798no—
1058#123—798no—
1059#123—794no—
1060#123—798no—
1061#123—794no—
1062#123—798no—
1063#123C22×D7918yes—
1064#123C22×D7918yes—
1065C22⋊Q8—792no—
1066C22⋊Q8—792no—
1067C22⋊Q8—794no—
1068C22⋊Q8—794no—
1069C22⋊Q8—794no—
1070C22⋊Q8—792no—
1071C22⋊Q8—794no—
1072C22⋊Q8—794no—
1073C22⋊Q8—798no—
1074C22⋊Q8—792no—
1075C22⋊Q8—792no—
1076C22⋊Q8—792no—
1077C22⋊Q8—798no—
1078C22⋊Q8—798no—
1079C22⋊Q8—798no—
1080C22⋊Q8—798no—
1081C22⋊Q8—798no—
1082C22⋊Q8—798no—
1083C22⋊Q8—798no—
1084C22⋊Q8—794no—
1085C22⋊Q8—798no—
1086C22⋊Q8—794no—
1087C22⋊Q8C22×D7912yes—
1088C22⋊Q8C22×D7914yes—
1089C22⋊Q8C22×D7912yes—
1090#121—798no—
1091#121—798no—
1092#121—792no—
1093#121—798no—
1094#121—792no—
1095#121—798no—
1096#121—798no—
1097#121—798no—
1098#121—794no—
1099#121—794no—
1100#121—798no—
1101#121—794no—
1102#121—794no—
1103#121—798no—
1104#121—794no—
1105#121—798no—
1106#121—792no—
1107#121—794no—
1108#121—792no—
1109#121—794no—
1110#121—792no—
1111#121—792no—
1112#121—794no—
1113#121—794no—
1114#121—798no—
1115#121—798no—
1116#121—798no—
1117#121—798no—
1118#121—798no—
1119#121C22×D7912yes—
1120#121C22×D7914yes—
1121#121C22×D7914yes—
1122#121C22×D7918yes—
1123#121C22×D7912yes—
1124#121C22×D7914yes—
1125#120—798no—
1126#120—794no—
1127#120—794no—
1128#120C22×D7918yes—
1129C4×Q8—792no—
1130C4×Q8—792no—
1131C4×Q8—794no—
1132C4×Q8—794no—
1133C4×Q8—794no—
1134C4×Q8—798no—
1135C4×Q8—792no—
1136C4×Q8—794no—
1137C4×Q8—798no—
1138C4×Q8—794no—
1139C4×Q8—792no—
1140C4×Q8—794no—
1141C4×Q8—798no—
1142C4×Q8—794no—
1143C4×Q8—794no—
1144C4×Q8—798no—
1145C4×Q8—792no—
1146C4×Q8—792no—
1147C4×Q8—792no—
1148C4×Q8—792no—
1149C4×Q8—798no—
1150C4×Q8—794no—
1151C4×Q8—792no—
1152C4×Q8—792no—
1153C4×Q8C22×D7914yes—
1154C4×Q8C22×D7912yes—
1155C4×Q8C22×D7912yes—
1156C4×D4—794no—
1157C4×D4—794no—
1158C4×D4—794no—
1159C4×D4—792no—
1160C4×D4—794no—
1161C4×D4—792no—
1162C4×D4—798no—
1163C4×D4—798no—
1164C4×D4—798no—
1165C4×D4—794no—
1166C4×D4—798no—
1167C4×D4—798no—
1168C4×D4—798no—
1169C4×D4—798no—
1170C4×D4—798no—
1171C4×D4—794no—
1172C4×D4—794no—
1173C4×D4—798no—
1174C4×D4—798no—
1175C4×D4—792no—
1176C4×D4—792no—
1177C4×D4—794no—
1178C4×D4—794no—
1179C4×D4—798no—
1180C4×D4—798no—
1181C4×D4—794no—
1182C4×D4—798no—
1183C4×D4—794no—
1184C4×D4—798no—
1185C4×D4—798no—
1186C4×D4—798no—
1187C4×D4—798no—
1188C4×D4—798no—
1189C4×D4—794no—
1190C4×D4—794no—
1191C4×D4—798no—
1192C4×D4—792no—
1193C4×D4—792no—
1194C4×D4C22×D7912yes—
1195C4×D4C22×D7912yes—
1196C4×D4C22×D7912yes—
1197C4×D4C22×D7912yes—
1198C4×D4C22×D7918yes—
1199C4×D4C22×D7914yes—
1200C4×D4C22×D7918yes—
1201C4×D4C22×D7912yes—
1202C4×D4C22×D7912yes—
1203#117—792no—
1204#117—794no—
1205#117—794no—
1206#117—798no—
1207#117—794no—
1208#117—798no—
1209#117—798no—
1210#117—798no—
1211#117—798no—
1212#117—798no—
1213#117—798no—
1214#117—792no—
1215#117—792no—
1216#117—792no—
1217#117—792no—
1218#117—794no—
1219#117—798no—
1220#117—798no—
1221#117C22×D7912yes—
1222#117C22×D7914yes—
1223#117C22×D7914yes—
1224C2×C4⋊C4—791no—
1225C2×C4⋊C4—792no—
1226C2×C4⋊C4—792no—
1227C2×C4⋊C4—792no—
1228C2×C4⋊C4—791no—
1229C2×C4⋊C4—798no—
1230C2×C4⋊C4—798no—
1231C2×C4⋊C4—791no—
1232C2×C4⋊C4—798no—
1233C2×C4⋊C4—794no—
1234C2×C4⋊C4—794no—
1235C2×C4⋊C4—798no—
1236C2×C4⋊C4—794no—
1237C2×C4⋊C4C22×D7911yescharacteristic
1238C2×C4⋊C4C22×D7914yes—
1239C2×C22⋊C4—792no—
1240C2×C22⋊C4—791no—
1241C2×C22⋊C4—791no—
1242C2×C22⋊C4C22×D7912yes—
1243C2×C42—791no—
1244C2×C42—792no—
1245C2×C42—792no—
1246C2×C42—794no—
1247C2×C42—798no—
1248C2×C42—794no—
1249C2×C42—798no—
1250C2×C42C22×D7911yescharacteristic
1251C24—791no—
1252C24C23×D7912yes—
1253#41—28no—
1254#41—84no—
1255#41—6324no—
1256#41—6328no—
1257#41—6328no—
1258#41—15816no—
1259#41—15832no—
1260#41—15816no—
1261#41—15816no—
1262#41—15816no—
1263#41—1588no—
1264C2×Q8—798no—
1265C2×Q8—792no—
1266C2×Q8—792no—
1267C2×Q8—798no—
1268C2×Q8—792no—
1269C2×Q8—792no—
1270C2×Q8—798no—
1271C2×Q8—792no—
1272C2×Q8—15816no—
1273C2×Q8—15816no—
1274C2×Q8C23×D7912yes—
1275C2×Q8C23×D7912yes—
1276C2×Q8C23×D7912yes—
1277C2×D4—24no—
1278C2×D4—794no—
1279C2×D4—798no—
1280C2×D4—794no—
1281C2×D4—798no—
1282C2×D4—798no—
1283C2×D4—794no—
1284C2×D4—798no—
1285C2×D4—798no—
1286C2×D4—794no—
1287C2×D4—792no—
1288C2×D4—794no—
1289C2×D4—792no—
1290C2×D4—792no—
1291C2×D4—1588no—
1292C2×D4C23×D7914yes—
1293C2×D4C23×D7912yes—
1294C2×D4C23×D7912yes—
1295C2×D4C23×D7912yes—
1296C2×D4C23×D7918yes—
1297C2×D4C23×D7912yes—
1298C2×D4C23×D7918yes—
1299C2×D4C23×D7912yes—
1300C22×C4—82no—
1301C22×C4—791no—
1302C22×C4—794no—
1303C22×C4—791no—
1304C22×C4—792no—
1305C22×C4—794no—
1306C22×C4—798no—
1307C22×C4—794no—
1308C22×C4—794no—
1309C22×C4—798no—
1310C22×C4—798no—
1311C22×C4—792no—
1312C22×C4—798no—
1313C22×C4—791no—
1314C22×C4—798no—
1315C22×C4—798no—
1316C22×C4—794no—
1317C22×C4—792no—
1318C22×C4—792no—
1319C22×C4—6322no—
1320C22×C4—6322no—
1321C22×C4—1588no—
1322C22×C4—1584no—
1323C22×C4C23×D7914yes—
1324C22×C4C23×D7911yescharacteristic
1325C22×C4C23×D7912yes—
1326C22×C4C23×D7918yes—
1327C22×C4C23×D7911yescharacteristic
1328C22×C4C23×D7914yes—
1329C22×C4C23×D7914yes—
1330C22×C4C23×D7911yescharacteristic
1331C4⋊C4—798no—
1332C4⋊C4—792no—
1333C4⋊C4—792no—
1334C4⋊C4—798no—
1335C4⋊C4—794no—
1336C4⋊C4—794no—
1337C4⋊C4—798no—
1338C4⋊C4—794no—
1339C4⋊C4—798no—
1340C4⋊C4—792no—
1341C4⋊C4—792no—
1342C4⋊C4—798no—
1343C4⋊C4—794no—
1344C4⋊C4—798no—
1345C4⋊C4—798no—
1346C4⋊C4—794no—
1347C4⋊C4—794no—
1348C4⋊C4—794no—
1349C4⋊C4—798no—
1350C4⋊C4—794no—
1351C4⋊C4—792no—
1352C4⋊C4—792no—
1353C4⋊C4—792no—
1354C4⋊C4—794no—
1355C4⋊C4—792no—
1356C4⋊C4—794no—
1357C4⋊C4—792no—
1358C4⋊C4—792no—
1359C4⋊C4—792no—
1360C4⋊C4—794no—
1361C4⋊C4—794no—
1362C4⋊C4—798no—
1363C4⋊C4—792no—
1364C4⋊C4C23×D7912yes—
1365C4⋊C4C23×D7912yes—
1366C4⋊C4C23×D7918yes—
1367C4⋊C4C23×D7912yes—
1368C4⋊C4C23×D7912yes—
1369C4⋊C4C23×D7912yes—
1370C4⋊C4C23×D7912yes—
1371C4⋊C4C23×D7912yes—
1372C4⋊C4C23×D7914yes—
1373C4⋊C4C23×D7914yes—
1374C4⋊C4C23×D7912yes—
1375C22⋊C4—798no—
1376C22⋊C4—794no—
1377C22⋊C4—794no—
1378C22⋊C4—794no—
1379C22⋊C4—798no—
1380C22⋊C4—798no—
1381C22⋊C4—794no—
1382C22⋊C4—798no—
1383C22⋊C4—794no—
1384C22⋊C4—792no—
1385C22⋊C4—792no—
1386C22⋊C4—792no—
1387C22⋊C4—792no—
1388C22⋊C4—798no—
1389C22⋊C4—794no—
1390C22⋊C4—794no—
1391C22⋊C4—794no—
1392C22⋊C4—794no—
1393C22⋊C4—794no—
1394C22⋊C4—794no—
1395C22⋊C4—794no—
1396C22⋊C4—794no—
1397C22⋊C4—798no—
1398C22⋊C4—794no—
1399C22⋊C4—794no—
1400C22⋊C4C23×D7914yes—
1401C22⋊C4C23×D7914yes—
1402C22⋊C4C23×D7914yes—
1403C22⋊C4C23×D7918yes—
1404C22⋊C4C23×D7918yes—
1405C22⋊C4C23×D7918yes—
1406C22⋊C4C23×D7914yes—
1407C22⋊C4C23×D7914yes—
1408C42—798no—
1409C42—792no—
1410C42—792no—
1411C42—794no—
1412C42—794no—
1413C42—794no—
1414C42—798no—
1415C42—794no—
1416C42—794no—
1417C42—794no—
1418C42—798no—
1419C42—798no—
1420C42—794no—
1421C42C23×D7918yes—
1422C42C23×D7914yes—
1423C42C23×D7911yescharacteristic
1424C42C23×D7911yescharacteristic
1425C42C23×D7911yescharacteristic
1426C42C23×D7911yescharacteristic
1427C23—24no—
1428C23—42no—
1429C23—42no—
1430C23—3161no—
1431C23—3161no—
1432C23—792no—
1433C23—794no—
1434C23—1582no—
1435C23C24×D7914yes—
1436C23C24×D7914yes—
1437C23C24×D7911yescharacteristic
1438Q8—24no—
1439Q8—42no—
1440Q8—42no—
1441Q8—3162no—
1442Q8—3168no—
1443Q8—3162no—
1444Q8—798no—
1445Q8—798no—
1446Q8—15816no—
1447Q8—1584no—
1448D4—28no—
1449D4—24no—
1450D4—24no—
1451D4—24no—
1452D4—42no—
1453D4—48no—
1454D4—42no—
1455D4—48no—
1456D4—3162no—
1457D4—3164no—
1458D4—3162no—
1459D4—3164no—
1460D4—3164no—
1461D4—3168no—
1462D4—3168no—
1463D4—3168no—
1464D4—3164no—
1465D4—15816no—
1466D4—15816no—
1467D4—1588no—
1468D4—1584no—
1469C2×C4—28no—
1470C2×C4—41no—
1471C2×C4—42no—
1472C2×C4—44no—
1473C2×C4—44no—
1474C2×C4—41no—
1475C2×C4—48no—
1476C2×C4—3168no—
1477C2×C4—3168no—
1478C2×C4—3164no—
1479C2×C4—3164no—
1480C2×C4—3161no—
1481C2×C4—3162no—
1482C2×C4—3168no—
1483C2×C4—3164no—
1484C2×C4—3161no—
1485C2×C4—3164no—
1486C2×C4—794no—
1487C2×C4—798no—
1488C2×C4—792no—
1489C2×C4—794no—
1490C2×C4—792no—
1491C2×C4—794no—
1492C2×C4—794no—
1493C2×C4—794no—
1494C2×C4—792no—
1495C2×C4—15816no—
1496C2×C4—15816no—
1497C2×C4—15816no—
1498C2×C4—1582no—
1499C2×C4—1584no—
1500C2×C4—1584no—
1501C2×C4—1588no—
1502C2×C4#41×D7914yes—
1503C2×C4C24×D7911yescharacteristic
1504C2×C4C24×D7911yescharacteristic
1505C2×C4C24×D7914yes—
1506C2×C4C24×D7914yes—
1507C2×C4C24×D7914yes—
1508C2×C4C24×D7914yes—
1509C2×C4C24×D7911yescharacteristic
1510C2×C4C24×D7911yescharacteristic
1511C2×C4C24×D7911yescharacteristic
1512C2×C4C24×D7911yescharacteristic
1513C22—21no—
1514C22—21no—
1515C22—24no—
1516C22—24no—
1517C22—24no—
1518C22—24no—
1519C22—24no—
1520C22—24no—
1521C22—48no—
1522C22—3164no—
1523C22—1584no—
1524C22—1582no—
1525C22—1582no—
1526C22—1584no—
1527C22—1584no—
1528C22—1582no—
1529C22C2×#41×D7912yes—
1530C22C25×D7911yescharacteristic
1531C4—24no—
1532C4—24no—
1533C4—21no—
1534C4—21no—
1535C4—24no—
1536C4—21no—
1537C4—21no—
1538C4—24no—
1539C4—798no—
1540C4—1582no—
1541C4—1584no—
1542C4—1582no—
1543C4—1584no—
1544C4—1584no—
1545C4—1582no—
1546C4—1584no—
1547C4C2×#41×D7912yes—
1548C4C2×#41×D7912yes—
1549C2—22no—
1550C2—44no—
1551C2—44no—
1552C2—3162no—
1553C2—3164no—
1554C2C22×#41×D7911yescharacteristic
1555C2#2377821011yescharacteristic
1556C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3506C2
hypercenter#3506D79
hypocenterC79#62851
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #23777504C2semidirect
2. #23777500C2semidirect
3. #23777482C2semidirect
4. #23777478C2semidirect
5. #23777403C2semidirect
6. #23777399C2semidirect
7. #23777388C2semidirect
8. #23777384C2semidirect
9. #23777252C2semidirect
10. #23777247C2semidirect
11. #23777205C2semidirect
12. #23777166C2semidirect
13. #23777103C2semidirect
14. #23777101C2semidirect
15. #23777056C2semidirect
16. #23776818C2semidirect
17. #23776813C2semidirect
18. #23776792C2semidirect
19. #23776789C2semidirect
20. #23776782C2semidirect
21. #23776611C2semidirect
22. C2×#19099042C2semidirect
23. C79×#3506C2semidirect
26. #19099297C22semidirect
27. #19099296C22semidirect
28. #19099295C22semidirect
29. Q8×Dic158C22semidirect
30. #19099293C22semidirect
31. #19099291C22semidirect
32. #19099291C22semidirect
33. #19099290C22semidirect
34. #19099288C22semidirect
35. #19099283C22semidirect
36. #19099280C22semidirect
37. #19099278C22semidirect
38. #19099275C22semidirect
39. #19099273C22semidirect
40. #19099272C22semidirect
41. #19099268C22semidirect
42. #19099267C22semidirect
43. #19099264C22semidirect
44. #19099263C22semidirect
45. #19099263C22semidirect
46. #19099262C22semidirect
47. #19099257C22semidirect
48. #19099256C22semidirect
49. #19099256C22semidirect
50. #19099254C22semidirect
51. #19099252C22semidirect
52. #19099250C22semidirect
53. #19099246C22semidirect
54. #19099234C22semidirect
55. #19099234C22semidirect
58. #19099233C22semidirect
61. #19099231C22semidirect
62. D4×Dic158C22semidirect
63. #19099228C22semidirect
64. #19099222C22semidirect
67. #19099221C22semidirect
70. #19099218C22semidirect
71. #19099218C22semidirect
72. #19099214C22semidirect
73. #19099212C22semidirect
74. #19099211C22semidirect
75. #19099211C22semidirect
78. #19099187C22semidirect
79. #19099187C22semidirect
80. #19099183C22semidirect
81. #19099182C22semidirect
82. #19099182C22semidirect
83. #19099182C22semidirect
84. #19099181C22semidirect
85. #19099181C22semidirect
86. #19099180C22semidirect
87. #19099177C22semidirect
88. #19099176C22semidirect
89. #19099174C22semidirect
90. #19099170C22semidirect
91. #19099169C22semidirect
92. #19099167C22semidirect
93. #19099167C22semidirect
94. #19099166C22semidirect
95. #19099165C22semidirect
96. #19099163C22semidirect
97. #19099163C22semidirect
116. #19099111C22semidirect
117. #19099110C22semidirect
118. #19099109C22semidirect
120. #19099108C22semidirect
121. #19099100C22semidirect
122. #19099100C22semidirect
123. #19099096C22semidirect
124. #19099094C22semidirect
125. #19099094C22semidirect
126. #19099093C22semidirect
127. #19099093C22semidirect
128. #19099093C22semidirect
129. #19099092C22semidirect
130. #19099092C22semidirect
131. #19099091C22semidirect
132. #19099090C22semidirect
140. #19099044C22semidirect
146. #19099042C22semidirect
148. #19099040C22semidirect
149. #19099039C22semidirect
152. #19099031C22semidirect
154. C4×#11929623C22semidirect
157. C2×#14579126C22semidirect
158. C4×Q8×D79C22semidirect
166. #559×C79C22semidirect
167. #556×C79C22semidirect
168. #555×C79C22semidirect
169. #553×C79C22semidirect
170. #550×C79C22semidirect
171. #547×C79C22semidirect
483. C2×Dic158#41semidirect
789. #3506D79semidirect
802. C79#62851semidirect
808. #559C2×D79semidirect
817. #556C2×D79semidirect
820. #555C2×D79semidirect
832. #553C2×D79semidirect
845. #550C2×D79semidirect
860. #547C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237775042
#237775002
#237774822
#237774782
#237774032
#237773992
#237773882
#237773842
#237772522
#237772472
#237772052
#237771662
#237771032
#237771012
#237770562
#237768182
#237768132
#237767922
#237767892
#237767822
#237766112
C2×#190990422
C79×#35062
#6285179