Finite Group Databasebeta

← #35197361

Subgroups — #35197361

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#23777507C214yesmaximal, complemented
2#23777505C214yesmaximal, complemented
3#23777483C214yesmaximal, complemented
4#23777481C214yesmaximal, complemented
5#23777404C214yesmaximal, complemented
6#23777402C214yesmaximal, complemented
7#23777391C214yesmaximal, complemented
8#23777389C214yesmaximal, complemented
9#23777254C211yesmaximal, characteristic, complemented
10#23777249C211yesmaximal, characteristic, complemented
11#23777247C214yesmaximal, complemented
12#23777205C211yesmaximal, characteristic, complemented
13#23777166C211yesmaximal, characteristic, complemented
14#23777106C212yesmaximal, complemented
15#23777105C214yesmaximal, complemented
16#23777054C212yesmaximal, complemented
17#23776819C214yesmaximal, complemented
18#23776816C212yesmaximal, complemented
19#23776790C211yesmaximal, characteristic, complemented
20#23776786C214yesmaximal, complemented
21C4×#14579208C212yesmaximal, complemented
22C2×#19099043C211yesmaximal, characteristic, complemented
23C79×#3455C211yesmaximal, characteristic, complemented
24C2×#14579208C2212yes—
25C22×#11929624C2211yescharacteristic
26#19099298C2214yescomplemented
27#19099297C2218yescomplemented
28#19099295C2214yescomplemented
29#19099295C2218yescomplemented
30Q8×Dic158C2212yescomplemented
31#19099293C2212yescomplemented
32#19099291C2214yescomplemented
33#19099291C2212yescomplemented
34#19099290C2214yescomplemented
35#19099288C2212yescomplemented
36#19099287C2212yescomplemented
37#19099286C2212yescomplemented
38#19099280C2218yescomplemented
39#19099279C2212yescomplemented
40#19099278C2212yescomplemented
41#19099275C2218yescomplemented
42#19099271C2214yescomplemented
43#19099270C2214yescomplemented
44#19099269C2218yescomplemented
45#19099267C2218yescomplemented
46#19099266C2214yescomplemented
47#19099265C2214yescomplemented
48#19099264C2218yescomplemented
49#19099264C2218yescomplemented
50#19099259C2214yescomplemented
51#19099259C2214yescomplemented
52#19099258C2218yescomplemented
53#19099256C2218yescomplemented
54#19099255C2214yescomplemented
55#19099253C2214yescomplemented
56#19099249C2218yescomplemented
57#19099245C2218yescomplemented
58#19099235C2212yescomplemented
59#19099234C2214yes—
60#19099234C2214yes—
61#19099234C2212yescomplemented
62#19099233C2212yescomplemented
63#19099233C2212yescomplemented
64#19099231C2214yes—
65#19099231C2214yes—
66#19099231C2218yescomplemented
67D4×Dic158C2212yescomplemented
68#19099228C2212yescomplemented
69#19099223C2214yes—
70#19099223C2214yes—
71#19099222C2214yes—
72#19099222C2214yes—
73#19099222C2214yescomplemented
74#19099221C2214yescomplemented
75#19099217C2214yescomplemented
76#19099217C2212yescomplemented
77#19099216C2212yescomplemented
78#19099215C2218yescomplemented
79#19099213C2214yescomplemented
80#19099211C2218yescomplemented
81#19099211C2218yescomplemented
82#19099192C2214yes—
83#19099191C2212yes—
84#19099185C2214yescomplemented
85#19099184C2212yescomplemented
86#19099184C2212yescomplemented
87#19099184C2214yescomplemented
88#19099183C2218yescomplemented
89#19099179C2218yescomplemented
90#19099179C2218yescomplemented
91#19099177C2218yescomplemented
92#19099175C2212yescomplemented
93#19099172C2218yescomplemented
94#19099168C2212yescomplemented
95#19099168C2214yescomplemented
96#19099165C2218yescomplemented
97#19099165C2218yescomplemented
98#19099164C2214yescomplemented
99#19099163C2218yescomplemented
100#19099160C2212yes—
101#19099160C2212yes—
102#19099157C2218yes—
103#19099153C2214yes—
104#19099151C2212yes—
105#19099151C2212yes—
106#19099150C2214yes—
107#19099146C2218yes—
108#19099141C2212yes—
109#19099140C2214yes—
110#19099132C2212yes—
111#19099128C2218yes—
112#19099127C2212yes—
113#19099120C2211yescharacteristic
114#19099115C2214yes—
115#19099113C2211yescharacteristic
116#19099113C2214yescomplemented
117#19099112C2218yescomplemented
118#19099110C2214yescomplemented
119#19099108C2214yes—
120#19099108C2218yescomplemented
121#19099100C2214yescomplemented
122#19099099C2218yescomplemented
123#19099098C2218yescomplemented
124#19099097C2214yescomplemented
125#19099096C2218yescomplemented
126#19099096C2218yescomplemented
127#19099091C2214yescomplemented
128#19099091C2214yescomplemented
129#19099090C2218yescomplemented
130#19099090C2218yescomplemented
131#19099076C2214yes—
132#19099074C2212yes—
133#19099073C2214yes—
134#19099072C2218yes—
135#19099071C2218yes—
136#19099069C2218yes—
137#19099046C2212yes—
138#19099043C2214yes—
139#19099043C2214yes—
140#19099043C2214yes—
141#19099043C2214yes—
142#19099043C2212yes—
143#19099043C2214yescomplemented
144#19099042C2218yes—
145#19099042C2214yescomplemented
146#19099040C2212yes—
147#19099040C2214yescomplemented
148#19099039C2214yescomplemented
149C4×#11929624C2212yes—
150C4×#11929624C2214yescomplemented
151C4×#11929623C2218yes—
152C4×#11929623C2214yescomplemented
153C2×C4×Dic158C2211yescharacteristic
154C2×C4×Dic158C2211yescharacteristic
155C2×C4×Dic158C2214yescomplemented
156C4×Q8×D79C2214yescomplemented
157C2×C4×D316C2211yescharacteristic
158C2×C4×D316C2211yescharacteristic
159C2×(C22⋊D79)⋊C4C2212yes—
160C2×(C22⋊D79)⋊C4C2212yes—
161C2×#14579119C2212yes—
162C22×C4⋊Dic79C2211yescharacteristic
163C2×C4⋊C4×D79C2212yes—
164#542×C79C2212yescomplemented
165#542×C79C2212yescomplemented
166#541×C79C2212yescomplemented
167#540×C79C2212yescomplemented
168#539×C79C2212yes—
169#539×C79C2212yes—
170#538×C79C2212yes—
171#538×C79C2212yes—
172#533×C79C2211yescharacteristic
173#532×C79C2211yescharacteristic
174#529×C79C2214yescomplemented
175#529×C79C2214yescomplemented
176#525×C79C2212yes—
177C4×#41×C79C2212yes—
178C2×#117×C79C2211yescharacteristic
179#14579208—216no—
180C2×#11929625C2314yes—
181C2×#11929624—28no—
182C2×#11929624C2312yes—
183C2×#11929624C2314yes—
184C2×#11929624C2314yes—
185C2×#11929624C2314yes—
186C2×#11929624C2318yes—
187C2×#11929623C2318yes—
188C2×#11929623C2314yes—
189C2×#11929623C2314yes—
190C2×#11929623C2318yes—
191C22×Dic158C2314yes—
192C22×Dic158C2311yescharacteristic
193C2×Q8×D79C2314yes—
194C22×D316C2311yescharacteristic
195C22×C22⋊D79C2312yes—
196C23×Dic79C2312yes—
197C22×C4×D79C2312yes—
198C22×C4×D79C2312yes—
199C22×C4×D79C2312yes—
200#14579161C2311yescharacteristic
201#14579161C2311yescharacteristic
202#14579161C2311yescharacteristic
203#14579161C2314yes—
204#14579160C2314yes—
205#14579160C2314yes—
206#14579160C2318yes—
207#14579160C2314yes—
208#14579159C2318yes—
209#14579159C2314yes—
210#14579158C2311yescharacteristic
211#14579158C2314yes—
212#14579157C2318yes—
213#14579157C2314yes—
214#14579157C2314yes—
215#14579157C2318yes—
216#14579156C2318yes—
217#14579156C2318yes—
218#14579156C2318yes—
219#14579156C2318yes—
220#14579156C2314yes—
221#14579156C2314yes—
222#14579155C2318yes—
223#14579154C2314yes—
224#14579154C2314yes—
225#14579154C2318yes—
226#14579153C2312yes—
227#14579153C2314yes—
228#14579152C2318yes—
229#14579152C2314yes—
230#14579151C2318yes—
231#14579151C2314yes—
232#14579151C2314yes—
233#14579151C2318yes—
234#14579151C2318yes—
235#14579151C2318yes—
236#14579150C2318yes—
237#14579150C2314yes—
238#14579149C2318yes—
239#14579149C2312yes—
240#14579149C2314yes—
241#14579147C2318yes—
242#14579147C2318yes—
243#14579147C2314yes—
244#14579147C2314yes—
245#14579147C2318yes—
246#14579147C2318yes—
247#14579147C2318yes—
248#14579146C2318yes—
249#14579146C2318yes—
250#14579146C2314yes—
251#14579146C2314yes—
252#14579146C2318yes—
253#14579146C2318yes—
254#14579145C2318yes—
255#14579145C2318yes—
256#14579145C2318yes—
257#14579144C2318yes—
258#14579144C2314yes—
259#14579143C2314yes—
260#14579143C2314yes—
261#14579143C2318yes—
262#14579143C2318yes—
263#14579143C2318yes—
264#14579142C2318yes—
265#14579141C2318yes—
266#14579141C2314yes—
267#14579140C2314yes—
268#14579140C2312yes—
269#14579140C2312yes—
270#14579140C2312yes—
271#14579140C2312yes—
272#14579139C2318yes—
273#14579139C2314yes—
274#14579139C2314yes—
275#14579139C2318yes—
276#14579139C2318yes—
277#14579139C2318yes—
278#14579138C2318yes—
279#14579138C2318yes—
280#14579138C2318yes—
281#14579138C2318yes—
282#14579137C2314yes—
283#14579137C2314yes—
284#14579136C2318yes—
285#14579136C2314yes—
286#14579136C2314yes—
287#14579136C2314yes—
288#14579135C2312yes—
289#14579135C2314yes—
290#14579135C2318yes—
291#14579135C2312yes—
292#14579135C2312yes—
293#14579135C2312yes—
294#14579135C2314yes—
295#14579135C2314yes—
296#14579134C2318yes—
297#14579134C2318yes—
298#14579134C2314yes—
299#14579134C2314yes—
300#14579134C2318yes—
301#14579134C2318yes—
302#14579134C2318yes—
303#14579134C2318yes—
304#14579134C2318yes—
305#14579133C2318yes—
306#14579133C2318yes—
307#14579133C2318yes—
308#14579133C2318yes—
309#14579133C2318yes—
310#14579133C2318yes—
311#14579132C2314yes—
312#14579132C2314yes—
313#14579131C2318yes—
314#14579130C2314yes—
315#14579129C2318yes—
316Q8×Dic79C2314yes—
317Q8×Dic79C2314yes—
318C4×Dic158C2318yes—
319C4×Dic158C2312yes—
320C4×Dic158C2312yes—
321C4×Dic158C2312yes—
322C4×Dic158C2314yes—
323C4×Dic158C2314yes—
324C4×Dic158C2312yes—
325C4×Dic158C2312yes—
326C4×Dic158C2312yes—
327C4×Dic158C2312yes—
328C4×Dic158C2318yes—
329C4×Dic158C2314yes—
330C4×Dic158C2314yes—
331C4×Dic158C2314yes—
332C4×Dic158C2312yes—
333#14579126C2318yes—
334#14579126C2314yes—
335#14579126C2314yes—
336#14579126C2318yes—
337#14579126C2318yes—
338#14579126C2314yes—
339C4×D316C2314yes—
340C4×D316C2312yes—
341C4×D316C2314yes—
342C4×D316C2312yes—
343C4×D316C2312yes—
344C4×D316C2312yes—
345C4×D316C2314yes—
346C4×D316C2312yes—
347C4×D316C2312yes—
348C4×D316C2312yes—
349C4×D316C2312yes—
350C4×D316C2318yes—
351D4×Dic79C2318yes—
352D4×Dic79C2314yes—
353D4×Dic79C2314yes—
354D4×Dic79C2318yes—
355#14579123C2318yes—
356#14579123C2318yes—
357#14579123C2314yes—
358#14579123C2318yes—
359C4×C22⋊D79C2314yes—
360C4×C22⋊D79C2314yes—
361C4×C22⋊D79C2318yes—
362C4×C22⋊D79C2314yes—
363C4×C22⋊D79C2318yes—
364C4×C22⋊D79C2314yes—
365C4×C22⋊D79C2318yes—
366(C22⋊D79)⋊C4C2318yes—
367(C22⋊D79)⋊C4C2318yes—
368(C22⋊D79)⋊C4C2318yes—
369(C22⋊D79)⋊C4C2318yes—
370(C22⋊D79)⋊C4C2318yes—
371(C22⋊D79)⋊C4C2318yes—
372(C22⋊D79)⋊C4C2318yes—
373(C22⋊D79)⋊C4C2318yes—
374(C22⋊D79)⋊C4C2318yes—
375(C22⋊D79)⋊C4C2318yes—
376(C22⋊D79)⋊C4C2318yes—
377(C22⋊D79)⋊C4C2318yes—
378#14579120C2312yes—
379#14579120C2314yes—
380#14579119C2318yes—
381#14579119C2318yes—
382#14579119C2318yes—
383#14579119C2314yes—
384#14579119C2314yes—
385#14579119C2314yes—
386#14579118C2314yes—
387#14579118C2318yes—
388#14579118C2318yes—
389#14579117C2318yes—
390#14579117C2318yes—
391#14579117C2318yes—
392#14579117C2318yes—
393C2×C4⋊Dic79C2311yescharacteristic
394C2×C4⋊Dic79C2312yes—
395C2×C4⋊Dic79C2314yes—
396C2×C4⋊Dic79C2314yes—
397C2×C4⋊Dic79C2314yes—
398C2×C4⋊Dic79C2311yescharacteristic
399C2×Dic79⋊C4C2312yes—
400C2×Dic79⋊C4C2318yes—
401C2×Dic79⋊C4C2312yes—
402C4⋊C4×D79C2318yes—
403C4⋊C4×D79C2318yes—
404C4⋊C4×D79C2314yes—
405C4⋊C4×D79C2318yes—
406C2×(C2×D79)⋊C4C2312yes—
407C2×(C2×D79)⋊C4C2312yes—
408C2×C4×Dic79C2312yes—
409C2×C4×Dic79C2312yes—
410C2×C4×Dic79C2318yes—
411C42×D79C2318yes—
412C42×D79C2314yes—
413C2×#41×C79C2312yes—
414C23×C4×C79C2311yescharacteristic
415C4⋊Q8×C79C2311yescharacteristic
416C4⋊Q8×C79C2311yescharacteristic
417C4⋊Q8×C79C2311yescharacteristic
418#127×C79C2311yescharacteristic
419#126×C79C2314yes—
420#126×C79C2314yes—
421#126×C79C2314yes—
422#126×C79C2314yes—
423#125×C79C2314yes—
424#125×C79C2314yes—
425#125×C79C2312yes—
426#124×C79C2314yes—
427#124×C79C2312yes—
428#124×C79C2314yes—
429#123×C79C2314yes—
430#123×C79C2314yes—
431#123×C79C2314yes—
432#123×C79C2314yes—
433#123×C79C2314yes—
434C22⋊Q8×C79C2312yes—
435C22⋊Q8×C79C2314yes—
436C22⋊Q8×C79C2312yes—
437C22⋊Q8×C79C2314yes—
438C22⋊Q8×C79C2312yes—
439C22⋊Q8×C79C2312yes—
440#121×C79C2312yes—
441#121×C79C2312yes—
442#121×C79C2314yes—
443#121×C79C2312yes—
444#121×C79C2312yes—
445#121×C79C2314yes—
446#120×C79C2314yes—
447C4×Q8×C79C2312yes—
448C4×Q8×C79C2312yes—
449C4×Q8×C79C2312yes—
450C4×Q8×C79C2312yes—
451C4×D4×C79C2314yes—
452C4×D4×C79C2312yes—
453C4×D4×C79C2314yes—
454C4×D4×C79C2312yes—
455C4×D4×C79C2314yes—
456C4×D4×C79C2312yes—
457C4×D4×C79C2314yes—
458C4×D4×C79C2312yes—
459#117×C79C2312yes—
460#117×C79C2314yes—
461#117×C79C2312yes—
462#117×C79C2312yes—
463#117×C79C2312yes—
464#117×C79C2312yes—
465C2×C4⋊C4×C79C2311yescharacteristic
466C2×C4⋊C4×C79C2311yescharacteristic
467C2×C22⋊C4×C79C2311yescharacteristic
468C2×C22⋊C4×C79C2311yescharacteristic
469C2×C42×C79C2311yescharacteristic
470C2×C42×C79C2311yescharacteristic
471C2×C42×C79C2314yes—
472C23×D79C2412yes—
473#11929625—84no—
474#11929624—216no—
475#11929624—216no—
476#11929624—216no—
477#11929624—28no—
478#11929624—88no—
479#11929623—232no—
480#11929623—216no—
481#11929623—88no—
482#11929623—84no—
483C2×Dic158—216no—
484C2×Dic158#4118yescomplemented
485C2×Dic158C2418yes—
486C2×Dic158C2412yes—
487C2×Dic158C2412yes—
488C2×Dic158C2418yes—
489C2×Dic158C2412yes—
490C2×Dic158C2412yes—
491C2×Dic158C2412yes—
492Q8×D79—216no—
493C2×D316—24no—
494C2×D316C2412yes—
495C2×D316C2412yes—
496C2×D316C2412yes—
497C2×D316C2418yes—
498C2×D316C2412yes—
499C2×D316C2418yes—
500C2×D316C2412yes—
501C2×C22⋊D79—28no—
502C2×C22⋊D79C2414yes—
503C2×C22⋊D79C2418yes—
504C2×C22⋊D79C2418yes—
505C2×C22⋊D79C2414yes—
506C2×C22⋊D79C2418yes—
507C2×C22⋊D79C2418yes—
508C2×C22⋊D79C2418yes—
509C2×C22⋊D79C2414yes—
510C22×Dic79—82no—
511C22×Dic79C2418yes—
512C22×Dic79C2418yes—
513C22×Dic79C2418yes—
514C22×Dic79C2412yes—
515C22×Dic79C2412yes—
516C22×Dic79C2412yes—
517C2×C4×D79—28no—
518C2×C4×D79—82no—
519C2×C4×D79—82no—
520C2×C4×D79C2418yes—
521C2×C4×D79C2414yes—
522C2×C4×D79C2418yes—
523C2×C4×D79C2418yes—
524C2×C4×D79C2414yes—
525C2×C4×D79C2414yes—
526C2×C4×D79C2418yes—
527C2×C4×D79C2414yes—
528C2×C4×D79C2414yes—
529C4⋊Dic79C2412yes—
530C4⋊Dic79C2418yes—
531C4⋊Dic79C2418yes—
532C4⋊Dic79C2412yes—
533C4⋊Dic79C2412yes—
534C4⋊Dic79C2412yes—
535C4⋊Dic79C2412yes—
536C4⋊Dic79C2412yes—
537C4⋊Dic79C2412yes—
538C4⋊Dic79C2412yes—
539C4⋊Dic79C2412yes—
540C4⋊Dic79C2418yes—
541C4⋊Dic79C2412yes—
542Dic79⋊C4C2418yes—
543Dic79⋊C4C2414yes—
544Dic79⋊C4C2414yes—
545Dic79⋊C4C2418yes—
546Dic79⋊C4C2418yes—
547Dic79⋊C4C2414yes—
548Dic79⋊C4C2418yes—
549Dic79⋊C4C2414yes—
550Dic79⋊C4C2418yes—
551Dic79⋊C4C2418yes—
552Dic79⋊C4C2414yes—
553Dic79⋊C4C2414yes—
554Dic79⋊C4C2414yes—
555Dic79⋊C4C2418yes—
556Dic79⋊C4C2414yes—
557C22⋊Dic79C2414yes—
558C22⋊Dic79C2418yes—
559C22⋊Dic79C2414yes—
560C22⋊Dic79C2414yes—
561C22⋊Dic79C2418yes—
562(C2×D79)⋊C4C2414yes—
563(C2×D79)⋊C4C2418yes—
564(C2×D79)⋊C4C2414yes—
565(C2×D79)⋊C4C2414yes—
566(C2×D79)⋊C4C2418yes—
567(C2×D79)⋊C4C2414yes—
568(C2×D79)⋊C4C2418yes—
569(C2×D79)⋊C4C2418yes—
570(C2×D79)⋊C4C2414yes—
571(C2×D79)⋊C4C2418yes—
572(C2×D79)⋊C4C2418yes—
573(C2×D79)⋊C4C2418yes—
574(C2×D79)⋊C4C2414yes—
575(C2×D79)⋊C4C2414yes—
576(C2×D79)⋊C4C2414yes—
577C4×Dic79C2418yes—
578C4×Dic79C2414yes—
579C4×Dic79C2414yes—
580C4×Dic79C2418yes—
581C4×Dic79C2418yes—
582C4×Dic79C2414yes—
583C4×Dic79C2418yes—
584C4×Dic79C2418yes—
585C4×Dic79C2414yes—
586C4×Dic79C2414yes—
587C24×C79C2411yescharacteristic
588#41×C79—28no—
589C2×Q8×C79C2412yes—
590C2×Q8×C79C2412yes—
591C2×Q8×C79C2412yes—
592C2×D4×C79C2414yes—
593C2×D4×C79C2412yes—
594C2×D4×C79C2414yes—
595C2×D4×C79C2412yes—
596C2×D4×C79C2414yes—
597C2×D4×C79C2412yes—
598C22×C4×C79—24no—
599C22×C4×C79C2414yes—
600C22×C4×C79C2412yes—
601C22×C4×C79C2412yes—
602C22×C4×C79C2411yescharacteristic
603C22×C4×C79C2414yes—
604C22×C4×C79C2411yescharacteristic
605C22×C4×C79C2411yescharacteristic
606C22×C4×C79C2411yescharacteristic
607C22×C4×C79C2411yescharacteristic
608C22×C4×C79C2414yes—
609C22×C4×C79C2411yescharacteristic
610C4⋊C4×C79C2412yes—
611C4⋊C4×C79C2412yes—
612C4⋊C4×C79C2412yes—
613C4⋊C4×C79C2412yes—
614C4⋊C4×C79C2412yes—
615C4⋊C4×C79C2412yes—
616C4⋊C4×C79C2414yes—
617C4⋊C4×C79C2414yes—
618C4⋊C4×C79C2412yes—
619C4⋊C4×C79C2412yes—
620C4⋊C4×C79C2414yes—
621C4⋊C4×C79C2414yes—
622C4⋊C4×C79C2414yes—
623C4⋊C4×C79C2414yes—
624C4⋊C4×C79C2412yes—
625C4⋊C4×C79C2412yes—
626C22⋊C4×C79C2412yes—
627C22⋊C4×C79C2412yes—
628C22⋊C4×C79C2412yes—
629C22⋊C4×C79C2412yes—
630C22⋊C4×C79C2414yes—
631C22⋊C4×C79C2414yes—
632C22⋊C4×C79C2414yes—
633C22⋊C4×C79C2414yes—
634C22⋊C4×C79C2414yes—
635C22⋊C4×C79C2414yes—
636C22⋊C4×C79C2414yes—
637C22⋊C4×C79C2414yes—
638C22⋊C4×C79C2414yes—
639C42×C79C2412yes—
640C42×C79C2412yes—
641C42×C79C2411yescharacteristic
642C42×C79C2411yescharacteristic
643C42×C79C2414yes—
644C42×C79C2411yescharacteristic
645C42×C79C2411yescharacteristic
646C42×C79C2414yes—
647C42×C79C2414yes—
648C23×C79—22no—
649C23×C79—41no—
650C23×C79—41no—
651C23×C79C2512yes—
652C23×C79C2514yes—
653C23×C79C2511yescharacteristic
654C22×D79—24no—
655C22×D79—42no—
656C22×D79—42no—
657C22×D79C2514yes—
658C22×D79C2514yes—
659Q8×C79—24no—
660Q8×C79—42no—
661Q8×C79—42no—
662D4×C79—28no—
663D4×C79—24no—
664D4×C79—42no—
665D4×C79—44no—
666D4×C79—42no—
667D4×C79—44no—
668C2×C4×C79—22no—
669C2×C4×C79—28no—
670C2×C4×C79—24no—
671C2×C4×C79—24no—
672C2×C4×C79—41no—
673C2×C4×C79—41no—
674C2×C4×C79—44no—
675C2×C4×C79—41no—
676C2×C4×C79—44no—
677C2×C4×C79—41no—
678C2×C4×C79C2×#4114yes—
679C2×C4×C79C2512yes—
680C2×C4×C79C2511yescharacteristic
681C2×C4×C79C2514yes—
682C2×C4×C79C2511yescharacteristic
683C2×C4×C79C2514yes—
684C2×C4×C79C2512yes—
685C2×C4×C79C2514yes—
686C2×C4×C79C2512yes—
687C2×C4×C79C2511yescharacteristic
688C2×C4×C79C2511yescharacteristic
689C2×C4×C79C2511yescharacteristic
690C2×C4×C79C2511yescharacteristic
691C22⋊D79—28no—
692C22⋊D79—216no—
693C22⋊D79—216no—
694C22⋊D79—48no—
695C22⋊D79—44no—
696C22⋊D79—44no—
697C22⋊D79—48no—
698C22⋊D79—48no—
699C2×Dic79—216no—
700C2×Dic79—42no—
701C2×Dic79—42no—
702C2×Dic79—48no—
703C2×Dic79—48no—
704C2×Dic79C2×#4118yes—
705C2×Dic79C2514yes—
706C2×Dic79C2514yes—
707C2×Dic79C2514yes—
708C2×Dic79C2514yes—
709C2×Dic79C2514yes—
710C2×Dic79C2514yes—
711D316—24no—
712D316—24no—
713D316—24no—
714D316—42no—
715D316—48no—
716D316—48no—
717D316—42no—
718C4×D79—28no—
719C4×D79—216no—
720C4×D79—216no—
721C4×D79—44no—
722C4×D79—48no—
723C4×D79—44no—
724C4×D79—44no—
725C4×D79—48no—
726C4×D79—44no—
727Dic158—24no—
728Dic158—216no—
729Dic158—42no—
730Dic158—42no—
731Dic158—48no—
732Dic158C2×#4118yes—
733Dic158C2×#4118yes—
734C22×C79—21no—
735C22×C79—21no—
736C22×C79—22no—
737C22×C79—24no—
738C22×C79—24no—
739C22×C79—22no—
740C22×C79—24no—
741C22×C79—22no—
742C22×C79—44no—
743C22×C79C22×#4112yes—
744C22×C79C2611yescharacteristic
745C2×D79—24no—
746C2×D79—24no—
747C2×D79—24no—
748C2×D79—24no—
749C2×D79—24no—
750C2×D79—24no—
751C2×D79—48no—
752C4×C79—22no—
753C4×C79—24no—
754C4×C79—22no—
755C4×C79—21no—
756C4×C79—24no—
757C4×C79—21no—
758C4×C79—22no—
759C4×C79—21no—
760C4×C79—24no—
761C4×C79—21no—
762C4×C79C22×#4112yes—
763C4×C79C22×#4112yes—
764Dic79—24no—
765Dic79—24no—
766Dic79—24no—
767Dic79—24no—
768Dic79—24no—
769Dic79C22×#4118yes—
770#62851—791nomaximal, Sylow
771C2×C79—22no—
772C2×C79—44no—
773C2×C79—42no—
774C2×C79C23×#4111yescharacteristic
775C2×C79H(7,𝔽2)11yescharacteristic
776C2×C792−1+611yescharacteristic
777D79—44no—
778D79—44no—
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#3506—791no—
790#3502—791no—
791#3497—791no—
792#3492—794no—
793#3492—792no—
794#3487—792no—
795#3460—794no—
796#3460—792no—
797#3455—794no—
798#3455—791no—
799#3455D7911yescharacteristic, complemented
800C4×2−1+4—792no—
801C2×#520—791no—
802C79#6285111yescharacteristic, complemented, Sylow
803C2×2−1+4—792no—
804C22×#41—791no—
805#559—794no—
806#559—798no—
807#559—798no—
808#559—794no—
809Q82—792no—
810Q82—792no—
811#557—792no—
812#557—794no—
813#557—794no—
814#557—792no—
815#556—792no—
816#556—798no—
817#556—792no—
818#555—792no—
819#555—798no—
820#555—792no—
821#554—798no—
822#554—798no—
823#554—794no—
824#554—794no—
825#553—798no—
826#553—798no—
827#553—794no—
828#553—798no—
829#553—798no—
830#553—794no—
831#553—794no—
832#553—794no—
833#552—798no—
834#552—798no—
835#552—794no—
836#552—794no—
837#550—792no—
838#550—792no—
839#550—794no—
840#550—794no—
841#550—798no—
842#550—792no—
843#550—794no—
844#550—794no—
845#550—792no—
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—792no—
855#547—798no—
856#547—798no—
857#547—798no—
858#547—794no—
859#547—794no—
860#547—792no—
861#544—794no—
862#544—792no—
863#542—798no—
864#542—798no—
865#542—798no—
866#542—798no—
867#542—794no—
868#542—792no—
869#542—792no—
870#542—794no—
871#542C2×D7912yescomplemented
872#542C2×D7912yescomplemented
873#541—798no—
874#541—792no—
875#541C2×D7912yescomplemented
876#540—798no—
877#540—798no—
878#540—798no—
879#540—794no—
880#540—792no—
881#540—794no—
882#540C2×D7912yescomplemented
883#539—798no—
884#539—792no—
885#539—792no—
886#539C2×D7912yes—
887#539C2×D7912yes—
888#538—794no—
889#538—794no—
890#538—798no—
891#538—792no—
892#538—792no—
893#538C2×D7912yes—
894#538C2×D7912yes—
895#537—792no—
896#537—794no—
897#535—792no—
898#535—798no—
899#535—792no—
900#533—794no—
901#533—791no—
902#533C2×D7911yescharacteristic
903#532—798no—
904#532—794no—
905#532—798no—
906#532—794no—
907#532—791no—
908#532—794no—
909#532C2×D7911yescharacteristic
910#529—798no—
911#529—798no—
912#529—798no—
913#529—798no—
914#529—798no—
915#529—798no—
916#529—794no—
917#529—794no—
918#529—794no—
919#529—794no—
920#529C2×D7914yescomplemented
921#529C2×D7914yescomplemented
922#525—792no—
923#525—798no—
924#525—794no—
925#525—794no—
926#525—798no—
927#525—798no—
928#525C2×D7912yes—
929#520—792no—
930#520—798no—
931#520—794no—
932#520—794no—
933#520—794no—
934#520—794no—
935#520—794no—
936#520—792no—
937#520—794no—
938#519—794no—
939#519—792no—
940#519—794no—
941C4×#41—798no—
942C4×#41—794no—
943C4×#41—792no—
944C4×#41—794no—
945C4×#41C2×D7912yes—
946C2×C4×Q8—794no—
947C2×C4×Q8—791no—
948C2×C4×Q8—791no—
949C2×C4×Q8—794no—
950C2×C4×D4—792no—
951C2×C4×D4—792no—
952C2×C4×D4—791no—
953C2×C4×D4—791no—
954C2×#117—792no—
955C2×#117C2×D7911yescharacteristic
956C22×C4⋊C4—791no—
957C22×C4⋊C4—792no—
9582−1+4—15816no—
959C2×#41—794no—
960C2×#41—794no—
961C2×#41—798no—
962C2×#41—798no—
963C2×#41—794no—
964C2×#41—798no—
965C2×#41—792no—
966C2×#41—794no—
967C2×#41—794no—
968C2×#41—794no—
969C2×#41—1588no—
970C2×#41C22×D7912yes—
971C22×Q8—794no—
972C22×Q8—791no—
973C22×Q8—794no—
974C22×D4—792no—
975C22×D4—791no—
976C23×C4—792no—
977C23×C4—792no—
978C23×C4—792no—
979C23×C4—792no—
980C23×C4C22×D7911yescharacteristic
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—794no—
999#127—791no—
1000#127C22×D7911yescharacteristic
1001#126—798no—
1002#126—794no—
1003#126—798no—
1004#126—798no—
1005#126—798no—
1006#126—794no—
1007#126—794no—
1008#126—794no—
1009#126—798no—
1010#126—798no—
1011#126C22×D7914yes—
1012#126C22×D7914yes—
1013#126C22×D7914yes—
1014#126C22×D7914yes—
1015#125—794no—
1016#125—798no—
1017#125—794no—
1018#125—798no—
1019#125—798no—
1020#125—798no—
1021#125—794no—
1022#125—798no—
1023#125—794no—
1024#125—792no—
1025#125C22×D7914yes—
1026#125C22×D7914yes—
1027#125C22×D7912yes—
1028#124—794no—
1029#124—798no—
1030#124—794no—
1031#124—798no—
1032#124—798no—
1033#124—798no—
1034#124—798no—
1035#124—794no—
1036#124—798no—
1037#124—798no—
1038#124—794no—
1039#124—792no—
1040#124C22×D7914yes—
1041#124C22×D7914yes—
1042#124C22×D7912yes—
1043#123—798no—
1044#123—794no—
1045#123—798no—
1046#123—798no—
1047#123—798no—
1048#123—798no—
1049#123—794no—
1050#123—798no—
1051#123—794no—
1052#123—798no—
1053#123—798no—
1054#123—798no—
1055#123—794no—
1056#123—794no—
1057#123—798no—
1058#123—798no—
1059#123—798no—
1060#123C22×D7914yes—
1061#123C22×D7914yes—
1062#123C22×D7914yes—
1063#123C22×D7914yes—
1064#123C22×D7914yes—
1065C22⋊Q8—794no—
1066C22⋊Q8—794no—
1067C22⋊Q8—792no—
1068C22⋊Q8—792no—
1069C22⋊Q8—792no—
1070C22⋊Q8—794no—
1071C22⋊Q8—792no—
1072C22⋊Q8—798no—
1073C22⋊Q8—798no—
1074C22⋊Q8—798no—
1075C22⋊Q8—794no—
1076C22⋊Q8—794no—
1077C22⋊Q8—798no—
1078C22⋊Q8—794no—
1079C22⋊Q8—798no—
1080C22⋊Q8—798no—
1081C22⋊Q8—798no—
1082C22⋊Q8—798no—
1083C22⋊Q8—798no—
1084C22⋊Q8C22×D7912yes—
1085C22⋊Q8C22×D7912yes—
1086C22⋊Q8C22×D7912yes—
1087C22⋊Q8C22×D7914yes—
1088C22⋊Q8C22×D7914yes—
1089C22⋊Q8C22×D7912yes—
1090#121—798no—
1091#121—794no—
1092#121—798no—
1093#121—798no—
1094#121—798no—
1095#121—798no—
1096#121—794no—
1097#121—798no—
1098#121—792no—
1099#121—792no—
1100#121—792no—
1101#121—798no—
1102#121—794no—
1103#121—792no—
1104#121—794no—
1105#121—794no—
1106#121—794no—
1107#121—794no—
1108#121—798no—
1109#121—794no—
1110#121—798no—
1111#121—798no—
1112#121—798no—
1113#121—798no—
1114#121—794no—
1115#121—798no—
1116#121—794no—
1117#121—798no—
1118#121—798no—
1119#121C22×D7912yes—
1120#121C22×D7912yes—
1121#121C22×D7912yes—
1122#121C22×D7914yes—
1123#121C22×D7914yes—
1124#121C22×D7912yes—
1125#120—794no—
1126#120—798no—
1127#120—798no—
1128#120C22×D7914yes—
1129C4×Q8—794no—
1130C4×Q8—794no—
1131C4×Q8—794no—
1132C4×Q8—798no—
1133C4×Q8—798no—
1134C4×Q8—794no—
1135C4×Q8—798no—
1136C4×Q8—794no—
1137C4×Q8—794no—
1138C4×Q8—794no—
1139C4×Q8—798no—
1140C4×Q8—792no—
1141C4×Q8—794no—
1142C4×Q8—794no—
1143C4×Q8—798no—
1144C4×Q8—792no—
1145C4×Q8—792no—
1146C4×Q8—792no—
1147C4×Q8—792no—
1148C4×Q8—792no—
1149C4×Q8—794no—
1150C4×Q8—792no—
1151C4×Q8—792no—
1152C4×Q8C22×D7912yes—
1153C4×Q8C22×D7912yes—
1154C4×Q8C22×D7912yes—
1155C4×Q8C22×D7912yes—
1156C4×D4—798no—
1157C4×D4—794no—
1158C4×D4—798no—
1159C4×D4—794no—
1160C4×D4—794no—
1161C4×D4—798no—
1162C4×D4—794no—
1163C4×D4—798no—
1164C4×D4—794no—
1165C4×D4—794no—
1166C4×D4—798no—
1167C4×D4—798no—
1168C4×D4—798no—
1169C4×D4—798no—
1170C4×D4—794no—
1171C4×D4—798no—
1172C4×D4—798no—
1173C4×D4—798no—
1174C4×D4—798no—
1175C4×D4—798no—
1176C4×D4—798no—
1177C4×D4—798no—
1178C4×D4—798no—
1179C4×D4—798no—
1180C4×D4—798no—
1181C4×D4—798no—
1182C4×D4—798no—
1183C4×D4—794no—
1184C4×D4—794no—
1185C4×D4—792no—
1186C4×D4—792no—
1187C4×D4—792no—
1188C4×D4—792no—
1189C4×D4—792no—
1190C4×D4—792no—
1191C4×D4—794no—
1192C4×D4—798no—
1193C4×D4—792no—
1194C4×D4—792no—
1195C4×D4C22×D7914yes—
1196C4×D4C22×D7912yes—
1197C4×D4C22×D7914yes—
1198C4×D4C22×D7912yes—
1199C4×D4C22×D7914yes—
1200C4×D4C22×D7914yes—
1201C4×D4C22×D7912yes—
1202C4×D4C22×D7912yes—
1203#117—792no—
1204#117—794no—
1205#117—798no—
1206#117—798no—
1207#117—798no—
1208#117—794no—
1209#117—794no—
1210#117—794no—
1211#117—798no—
1212#117—798no—
1213#117—798no—
1214#117—798no—
1215#117—794no—
1216#117—798no—
1217#117—798no—
1218#117C22×D7912yes—
1219#117C22×D7912yes—
1220#117C22×D7912yes—
1221#117C22×D7912yes—
1222#117C22×D7912yes—
1223#117C22×D7914yes—
1224C2×C4⋊C4—792no—
1225C2×C4⋊C4—792no—
1226C2×C4⋊C4—791no—
1227C2×C4⋊C4—792no—
1228C2×C4⋊C4—791no—
1229C2×C4⋊C4—794no—
1230C2×C4⋊C4—794no—
1231C2×C4⋊C4—798no—
1232C2×C4⋊C4—794no—
1233C2×C4⋊C4—798no—
1234C2×C4⋊C4—798no—
1235C2×C4⋊C4—798no—
1236C2×C4⋊C4—794no—
1237C2×C4⋊C4C22×D7911yescharacteristic
1238C2×C4⋊C4C22×D7911yescharacteristic
1239C2×C22⋊C4—792no—
1240C2×C22⋊C4—792no—
1241C2×C22⋊C4C22×D7911yescharacteristic
1242C2×C22⋊C4C22×D7911yescharacteristic
1243C2×C42—792no—
1244C2×C42—792no—
1245C2×C42—798no—
1246C2×C42—798no—
1247C2×C42—794no—
1248C2×C42C22×D7911yescharacteristic
1249C2×C42C22×D7911yescharacteristic
1250C2×C42C22×D7914yes—
1251C24—792no—
1252C24C23×D7911yescharacteristic
1253#41—28no—
1254#41—6328no—
1255#41—6324no—
1256#41—6328no—
1257#41—6324no—
1258#41—15816no—
1259#41—15816no—
1260#41—15816no—
1261#41—15832no—
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—798no—
1278C2×D4—794no—
1279C2×D4—798no—
1280C2×D4—794no—
1281C2×D4—798no—
1282C2×D4—794no—
1283C2×D4—798no—
1284C2×D4—798no—
1285C2×D4—798no—
1286C2×D4—792no—
1287C2×D4—798no—
1288C2×D4—792no—
1289C2×D4—792no—
1290C2×D4—792no—
1291C2×D4—792no—
1292C2×D4—1588no—
1293C2×D4—1584no—
1294C2×D4C23×D7914yes—
1295C2×D4C23×D7912yes—
1296C2×D4C23×D7914yes—
1297C2×D4C23×D7912yes—
1298C2×D4C23×D7914yes—
1299C2×D4C23×D7912yes—
1300C22×C4—24no—
1301C22×C4—792no—
1302C22×C4—792no—
1303C22×C4—798no—
1304C22×C4—798no—
1305C22×C4—794no—
1306C22×C4—798no—
1307C22×C4—794no—
1308C22×C4—794no—
1309C22×C4—794no—
1310C22×C4—798no—
1311C22×C4—792no—
1312C22×C4—798no—
1313C22×C4—798no—
1314C22×C4—794no—
1315C22×C4—798no—
1316C22×C4—6322no—
1317C22×C4—6322no—
1318C22×C4—6322no—
1319C22×C4—1588no—
1320C22×C4C23×D7914yes—
1321C22×C4C23×D7911yescharacteristic
1322C22×C4C23×D7912yes—
1323C22×C4C23×D7912yes—
1324C22×C4C23×D7911yescharacteristic
1325C22×C4C23×D7911yescharacteristic
1326C22×C4C23×D7914yes—
1327C22×C4C23×D7911yescharacteristic
1328C22×C4C23×D7911yescharacteristic
1329C22×C4C23×D7914yes—
1330C22×C4C23×D7911yescharacteristic
1331C4⋊C4—798no—
1332C4⋊C4—794no—
1333C4⋊C4—794no—
1334C4⋊C4—798no—
1335C4⋊C4—798no—
1336C4⋊C4—794no—
1337C4⋊C4—798no—
1338C4⋊C4—794no—
1339C4⋊C4—798no—
1340C4⋊C4—798no—
1341C4⋊C4—794no—
1342C4⋊C4—794no—
1343C4⋊C4—794no—
1344C4⋊C4—798no—
1345C4⋊C4—794no—
1346C4⋊C4—792no—
1347C4⋊C4—792no—
1348C4⋊C4—798no—
1349C4⋊C4—792no—
1350C4⋊C4—792no—
1351C4⋊C4—792no—
1352C4⋊C4—798no—
1353C4⋊C4—792no—
1354C4⋊C4—792no—
1355C4⋊C4—792no—
1356C4⋊C4—792no—
1357C4⋊C4—798no—
1358C4⋊C4—792no—
1359C4⋊C4C23×D7912yes—
1360C4⋊C4C23×D7912yes—
1361C4⋊C4C23×D7912yes—
1362C4⋊C4C23×D7914yes—
1363C4⋊C4C23×D7912yes—
1364C4⋊C4C23×D7912yes—
1365C4⋊C4C23×D7912yes—
1366C4⋊C4C23×D7914yes—
1367C4⋊C4C23×D7912yes—
1368C4⋊C4C23×D7912yes—
1369C4⋊C4C23×D7912yes—
1370C4⋊C4C23×D7914yes—
1371C4⋊C4C23×D7914yes—
1372C4⋊C4C23×D7914yes—
1373C4⋊C4C23×D7914yes—
1374C4⋊C4C23×D7912yes—
1375C22⋊C4—794no—
1376C22⋊C4—798no—
1377C22⋊C4—794no—
1378C22⋊C4—794no—
1379C22⋊C4—798no—
1380C22⋊C4—794no—
1381C22⋊C4—798no—
1382C22⋊C4—794no—
1383C22⋊C4—794no—
1384C22⋊C4—798no—
1385C22⋊C4—794no—
1386C22⋊C4—798no—
1387C22⋊C4—798no—
1388C22⋊C4—798no—
1389C22⋊C4—798no—
1390C22⋊C4—794no—
1391C22⋊C4—794no—
1392C22⋊C4—798no—
1393C22⋊C4—794no—
1394C22⋊C4—794no—
1395C22⋊C4C23×D7912yes—
1396C22⋊C4C23×D7912yes—
1397C22⋊C4C23×D7912yes—
1398C22⋊C4C23×D7912yes—
1399C22⋊C4C23×D7914yes—
1400C22⋊C4C23×D7914yes—
1401C22⋊C4C23×D7914yes—
1402C22⋊C4C23×D7914yes—
1403C22⋊C4C23×D7914yes—
1404C22⋊C4C23×D7914yes—
1405C22⋊C4C23×D7914yes—
1406C22⋊C4C23×D7914yes—
1407C22⋊C4C23×D7914yes—
1408C42—798no—
1409C42—794no—
1410C42—798no—
1411C42—794no—
1412C42—798no—
1413C42—794no—
1414C42—794no—
1415C42—798no—
1416C42—798no—
1417C42—794no—
1418C42C23×D7912yes—
1419C42C23×D7914yes—
1420C42C23×D7912yes—
1421C42C23×D7914yes—
1422C42C23×D7911yescharacteristic
1423C42C23×D7911yescharacteristic
1424C42C23×D7911yescharacteristic
1425C42C23×D7911yescharacteristic
1426C42C23×D7914yes—
1427C23—22no—
1428C23—41no—
1429C23—41no—
1430C23—3162no—
1431C23—3162no—
1432C23—794no—
1433C23—794no—
1434C23—1584no—
1435C23C24×D7912yes—
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—42no—
1451D4—44no—
1452D4—42no—
1453D4—44no—
1454D4—3162no—
1455D4—3168no—
1456D4—3162no—
1457D4—3168no—
1458D4—3168no—
1459D4—3164no—
1460D4—3168no—
1461D4—3168no—
1462D4—3164no—
1463D4—15816no—
1464D4—15816no—
1465D4—1588no—
1466D4—1584no—
1467D4—1584no—
1468D4—1584no—
1469C2×C4—22no—
1470C2×C4—24no—
1471C2×C4—24no—
1472C2×C4—28no—
1473C2×C4—41no—
1474C2×C4—41no—
1475C2×C4—41no—
1476C2×C4—44no—
1477C2×C4—41no—
1478C2×C4—44no—
1479C2×C4—3168no—
1480C2×C4—3164no—
1481C2×C4—3164no—
1482C2×C4—3164no—
1483C2×C4—3168no—
1484C2×C4—3164no—
1485C2×C4—3162no—
1486C2×C4—3162no—
1487C2×C4—3168no—
1488C2×C4—3168no—
1489C2×C4—794no—
1490C2×C4—798no—
1491C2×C4—794no—
1492C2×C4—794no—
1493C2×C4—794no—
1494C2×C4—794no—
1495C2×C4—794no—
1496C2×C4—15816no—
1497C2×C4—15816no—
1498C2×C4—15816no—
1499C2×C4—1588no—
1500C2×C4#41×D7914yes—
1501C2×C4C24×D7912yes—
1502C2×C4C24×D7911yescharacteristic
1503C2×C4C24×D7914yes—
1504C2×C4C24×D7911yescharacteristic
1505C2×C4C24×D7912yes—
1506C2×C4C24×D7914yes—
1507C2×C4C24×D7914yes—
1508C2×C4C24×D7911yescharacteristic
1509C2×C4C24×D7911yescharacteristic
1510C2×C4C24×D7912yes—
1511C2×C4C24×D7911yescharacteristic
1512C2×C4C24×D7911yescharacteristic
1513C22—21no—
1514C22—21no—
1515C22—22no—
1516C22—24no—
1517C22—24no—
1518C22—22no—
1519C22—24no—
1520C22—22no—
1521C22—44no—
1522C22—3168no—
1523C22—1584no—
1524C22—1584no—
1525C22—1584no—
1526C22—1584no—
1527C22—1584no—
1528C22—1584no—
1529C22C2×#41×D7912yes—
1530C22C25×D7911yescharacteristic
1531C4—22no—
1532C4—24no—
1533C4—22no—
1534C4—21no—
1535C4—21no—
1536C4—24no—
1537C4—22no—
1538C4—21no—
1539C4—24no—
1540C4—21no—
1541C4—798no—
1542C4—1584no—
1543C4—1584no—
1544C4—1584no—
1545C4—1584no—
1546C4—1584no—
1547C4C2×#41×D7912yes—
1548C4C2×#41×D7912yes—
1549C2—22no—
1550C2—42no—
1551C2—44no—
1552C2—3164no—
1553C2—3164no—
1554C2C22×#41×D7911yescharacteristic
1555C2#2377821111yescharacteristic
1556C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3455C2
hypercenter#3455D79
hypocenterC79#62851
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. #23777507C2semidirect
2. #23777505C2semidirect
3. #23777483C2semidirect
4. #23777481C2semidirect
5. #23777404C2semidirect
6. #23777402C2semidirect
7. #23777391C2semidirect
8. #23777389C2semidirect
9. #23777254C2semidirect
10. #23777249C2semidirect
11. #23777247C2semidirect
12. #23777205C2semidirect
13. #23777166C2semidirect
14. #23777106C2semidirect
15. #23777105C2semidirect
16. #23777054C2semidirect
17. #23776819C2semidirect
18. #23776816C2semidirect
19. #23776790C2semidirect
20. #23776786C2semidirect
21. C4×#14579208C2semidirect
22. C2×#19099043C2semidirect
23. C79×#3455C2semidirect
26. #19099298C22semidirect
27. #19099297C22semidirect
28. #19099295C22semidirect
29. #19099295C22semidirect
30. Q8×Dic158C22semidirect
31. #19099293C22semidirect
32. #19099291C22semidirect
33. #19099291C22semidirect
34. #19099290C22semidirect
35. #19099288C22semidirect
36. #19099287C22semidirect
37. #19099286C22semidirect
38. #19099280C22semidirect
39. #19099279C22semidirect
40. #19099278C22semidirect
41. #19099275C22semidirect
42. #19099271C22semidirect
43. #19099270C22semidirect
44. #19099269C22semidirect
45. #19099267C22semidirect
46. #19099266C22semidirect
47. #19099265C22semidirect
48. #19099264C22semidirect
49. #19099264C22semidirect
50. #19099259C22semidirect
51. #19099259C22semidirect
52. #19099258C22semidirect
53. #19099256C22semidirect
54. #19099255C22semidirect
55. #19099253C22semidirect
56. #19099249C22semidirect
57. #19099245C22semidirect
58. #19099235C22semidirect
61. #19099234C22semidirect
62. #19099233C22semidirect
63. #19099233C22semidirect
66. #19099231C22semidirect
67. D4×Dic158C22semidirect
68. #19099228C22semidirect
73. #19099222C22semidirect
74. #19099221C22semidirect
75. #19099217C22semidirect
76. #19099217C22semidirect
77. #19099216C22semidirect
78. #19099215C22semidirect
79. #19099213C22semidirect
80. #19099211C22semidirect
81. #19099211C22semidirect
84. #19099185C22semidirect
85. #19099184C22semidirect
86. #19099184C22semidirect
87. #19099184C22semidirect
88. #19099183C22semidirect
89. #19099179C22semidirect
90. #19099179C22semidirect
91. #19099177C22semidirect
92. #19099175C22semidirect
93. #19099172C22semidirect
94. #19099168C22semidirect
95. #19099168C22semidirect
96. #19099165C22semidirect
97. #19099165C22semidirect
98. #19099164C22semidirect
99. #19099163C22semidirect
116. #19099113C22semidirect
117. #19099112C22semidirect
118. #19099110C22semidirect
120. #19099108C22semidirect
121. #19099100C22semidirect
122. #19099099C22semidirect
123. #19099098C22semidirect
124. #19099097C22semidirect
125. #19099096C22semidirect
126. #19099096C22semidirect
127. #19099091C22semidirect
128. #19099091C22semidirect
129. #19099090C22semidirect
130. #19099090C22semidirect
143. #19099043C22semidirect
145. #19099042C22semidirect
147. #19099040C22semidirect
148. #19099039C22semidirect
150. C4×#11929624C22semidirect
152. C4×#11929623C22semidirect
155. C2×C4×Dic158C22semidirect
156. C4×Q8×D79C22semidirect
164. #542×C79C22semidirect
165. #542×C79C22semidirect
166. #541×C79C22semidirect
167. #540×C79C22semidirect
174. #529×C79C22semidirect
175. #529×C79C22semidirect
484. C2×Dic158#41semidirect
799. #3455D79semidirect
802. C79#62851semidirect
871. #542C2×D79semidirect
872. #542C2×D79semidirect
875. #541C2×D79semidirect
882. #540C2×D79semidirect
920. #529C2×D79semidirect
921. #529C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237775072
#237775052
#237774832
#237774812
#237774042
#237774022
#237773912
#237773892
#237772542
#237772492
#237772472
#237772052
#237771662
#237771062
#237771052
#237770542
#237768192
#237768162
#237767902
#237767862
C4×#145792082
C2×#190990432
C79×#34552
#6285179