Finite Group Databasebeta

← #35197156

Subgroups — #35197156

Order 20224.

7050 conjugacy classes of subgroups.

The subgroup lattice has 1426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777839C214yesmaximal, complemented
2#23777835C214yesmaximal, complemented
3#23777833C218yesmaximal, complemented
4#23777742C214yesmaximal, complemented
5#23777736C214yesmaximal, complemented
6#23777309C212yesmaximal, complemented
7#23777303C212yesmaximal, complemented
8#23777302C214yesmaximal, complemented
9#23777278C214yesmaximal, complemented
10#23777215C212yesmaximal, complemented
11#23777214C214yesmaximal, complemented
12#23777213C212yesmaximal, complemented
13#23777179C214yesmaximal, complemented
14#23777109C211yesmaximal, characteristic, complemented
15#23777106C212yesmaximal, complemented
16#23777101C214yesmaximal, complemented
17#23777047C214yesmaximal, complemented
18#23776692C212yesmaximal, complemented
19C22×#14579160C211yesmaximal, characteristic, complemented
20C79×#3492C211yesmaximal, characteristic, complemented
21C2×#14579208C2214yes—
22C23×Dic158C2212yes—
23#19099317C2218yescomplemented
24#19099316C2218yescomplemented
25#19099315C2218yescomplemented
26#19099314C2218yescomplemented
27Q8×Dic158C2214yescomplemented
28#19099293C2214yescomplemented
29#19099290C2218yescomplemented
30#19099290C2214yescomplemented
31#19099289C2214yescomplemented
32#19099284C2214yescomplemented
33#19099281C2214yescomplemented
34#19099280C2218yescomplemented
35#19099277C2214yescomplemented
36#19099276C2214yescomplemented
37#19099272C2218yes—
38#19099272C2214yescomplemented
39#19099271C2214yes—
40#19099271C2214yescomplemented
41#19099270C2214yes—
42#19099269C2214yescomplemented
43#19099268C2214yes—
44#19099268C2214yescomplemented
45#19099267C2218yes—
46#19099265C2214yes—
47#19099262C2218yes—
48#19099261C2214yes—
49#19099259C2214yes—
50#19099256C2218yes—
51#19099255C2214yes—
52#19099253C2214yes—
53#19099250C2218yes—
54#19099248C2214yes—
55#19099246C2218yes—
56D4×Dic158C2218yes—
57D4×Dic158C2218yes—
58D4×Dic158C2214yescomplemented
59#19099228C2214yescomplemented
60#19099226C2218yes—
61#19099226C2218yes—
62#19099226C2218yescomplemented
63#19099222C2218yes—
64#19099222C2218yes—
65#19099219C2218yes—
66#19099219C2218yes—
67#19099217C2214yes—
68#19099214C2214yes—
69#19099214C2214yescomplemented
70#19099213C2214yes—
71#19099213C2214yescomplemented
72#19099212C2218yes—
73#19099211C2218yes—
74#19099211C2218yescomplemented
75#19099194C2211yescharacteristic
76#19099194C2214yescomplemented
77#19099193C2218yescomplemented
78#19099193C2214yescomplemented
79#19099192C2214yes—
80#19099192C2218yescomplemented
81#19099191C2212yes—
82#19099191C2214yescomplemented
83#19099190C2214yescomplemented
84#19099186C2214yescomplemented
85#19099185C2214yescomplemented
86#19099181C2218yescomplemented
87#19099180C2214yescomplemented
88#19099179C2218yescomplemented
89#19099178C2214yescomplemented
90#19099172C2218yescomplemented
91#19099170C2218yescomplemented
92#19099162C2214yes—
93#19099160C2214yes—
94#19099158C2214yes—
95#19099157C2218yes—
96#19099155C2218yes—
97#19099144C2211yescharacteristic
98#19099141C2212yes—
99#19099140C2214yes—
100#19099139C2214yes—
101#19099136C2218yescomplemented
102#19099135C2218yes—
103#19099135C2218yes—
104#19099135C2218yescomplemented
105#19099134C2214yes—
106#19099119C2214yescomplemented
107#19099117C2214yescomplemented
108#19099116C2212yes—
109#19099116C2214yescomplemented
110#19099115C2212yes—
111#19099115C2212yes—
112#19099115C2214yescomplemented
113#19099110C2214yescomplemented
114#19099109C2212yes—
115#19099108C2212yes—
116#19099108C2212yes—
117#19099108C2214yescomplemented
118C2×#14579160C2214yes—
119C2×#14579160C2212yes—
120C2×#14579160C2212yes—
121C2×#14579160C2214yes—
122C2×#14579160C2214yes—
123C2×#14579160C2214yes—
124C2×#14579160C2214yes—
125C2×#14579160C2214yescomplemented
126C4⋊Q8×D79C2214yescomplemented
127#19099099C2212yes—
128#19099099C2212yes—
129#19099094C2212yes—
130#19099094C2212yes—
131#19099093C2214yes—
132#19099093C2214yes—
133#19099090C2214yes—
134#19099090C2214yes—
135#19099074C2214yes—
136#19099074C2212yes—
137#19099069C2214yes—
138#19099069C2218yes—
139#19099069C2214yes—
140#19099046C2212yes—
141#19099044C2212yes—
142#19099043C2212yes—
143#19099042C2218yes—
144#19099040C2214yes—
145#41×Dic79C2212yes—
146#19099031C2212yes—
147C4×#11929623C2214yes—
148C4×#11929623C2214yes—
149C22×C4⋊Dic79C2211yescharacteristic
150C22×Dic79⋊C4C2212yes—
151C22×C4×Dic79C2211yescharacteristic
152#554×C79C2214yes—
153#553×C79C2214yes—
154#552×C79C2214yes—
155#547×C79C2214yes—
156#544×C79C2211yescharacteristic
157#539×C79C2214yes—
158#537×C79C2211yescharacteristic
159#525×C79C2214yes—
160#525×C79C2212yes—
161#520×C79C2212yes—
162C22×C4⋊C4×C79C2211yescharacteristic
163#14579208—416no—
164C2×#11929624C2312yes—
165C2×#11929624C2318yes—
166C2×#11929624C2314yes—
167C2×#11929623C2314yes—
168C2×#11929623C2314yes—
169C2×#11929623C2318yes—
170C2×#11929623C2318yes—
171C22×Dic158—48no—
172C22×Dic158C2314yes—
173C22×Dic158C2314yes—
174C22×Dic158C2318yes—
175C22×Dic158C2314yes—
176C22×Dic158C2318yes—
177C22×Dic158C2314yes—
178C2×Q8×D79C2318yes—
179C23×Dic79C2311yescharacteristic
180C23×Dic79C2311yescharacteristic
181C23×Dic79C2312yes—
182#14579161C2318yes—
183#14579161C2314yes—
184#14579160C2318yes—
185#14579160C2318yes—
186#14579160C2314yes—
187#14579160C2318yes—
188#14579160C2314yes—
189#14579160C2314yes—
190#14579160C2314yes—
191#14579160C2318yes—
192#14579160C2318yes—
193#14579160C2318yes—
194#14579160C2318yes—
195#14579160C2314yes—
196#14579160C2314yes—
197#14579160C2318yes—
198#14579160C2314yes—
199#14579160C2314yes—
200#14579160C2318yes—
201#14579160C2312yes—
202#14579160C2314yes—
203#14579160C2314yes—
204#14579160C2312yes—
205#14579159C2318yes—
206#14579159C2318yes—
207#14579159C2312yes—
208#14579157C2312yes—
209#14579156C2318yes—
210#14579156C2318yes—
211#14579156C2318yes—
212#14579156C2314yes—
213#14579156C2314yes—
214#14579155C2318yes—
215#14579154C2318yes—
216#14579154C2318yes—
217#14579154C2318yes—
218#14579154C2314yes—
219#14579154C2314yes—
220#14579153C2318yes—
221#14579153C2314yes—
222#14579152C2318yes—
223#14579152C2318yes—
224#14579152C2312yes—
225#14579152C2314yes—
226#14579152C2312yes—
227#14579152C2314yes—
228#14579151C2318yes—
229#14579151C2318yes—
230#14579151C2318yes—
231#14579151C2318yes—
232#14579151C2314yes—
233#14579151C2318yes—
234#14579151C2318yes—
235#14579151C2314yes—
236#14579150C2312yes—
237#14579149C2318yes—
238#14579148C2312yes—
239#14579148C2318yes—
240#14579147C2314yes—
241#14579147C2318yes—
242#14579147C2318yes—
243#14579147C2314yes—
244#14579147C2318yes—
245#14579147C2318yes—
246#14579146C2318yes—
247#14579146C2318yes—
248#14579145C2314yes—
249#14579145C2318yes—
250#14579145C2314yes—
251#14579145C2318yes—
252#14579144C2318yes—
253#14579144C2314yes—
254#14579144C2318yes—
255#14579143C2318yes—
256#14579143C2318yes—
257#14579142C2314yes—
258#14579142C2318yes—
259#14579142C2318yes—
260#14579142C2314yes—
261#14579141C2318yes—
262#14579141C2318yes—
263#14579141C2318yes—
264#14579141C2314yes—
265#14579140C2318yes—
266#14579140C2314yes—
267#14579140C2314yes—
268#14579140C2314yes—
269#14579140C2318yes—
270#14579140C2318yes—
271#14579140C2312yes—
272#14579140C2312yes—
273#14579139C2318yes—
274#14579139C2318yes—
275#14579139C2318yes—
276#14579139C2318yes—
277#14579139C2318yes—
278#14579139C2318yes—
279#14579139C2318yes—
280#14579138C2318yes—
281#14579138C2318yes—
282#14579138C2318yes—
283#14579138C2318yes—
284#14579138C2318yes—
285#14579138C2318yes—
286#14579138C2318yes—
287#14579138C2318yes—
288#14579138C2318yes—
289#14579138C2314yes—
290#14579138C2314yes—
291#14579138C2314yes—
292#14579138C2314yes—
293#14579137C2318yes—
294#14579137C2314yes—
295#14579136C2314yes—
296#14579135C2314yes—
297#14579135C2314yes—
298#14579135C2314yes—
299#14579135C2312yes—
300#14579135C2312yes—
301#14579134C2318yes—
302#14579133C2318yes—
303#14579133C2318yes—
304#14579133C2318yes—
305#14579133C2314yes—
306#14579133C2314yes—
307#14579133C2314yes—
308#14579133C2314yes—
309#14579132C2314yes—
310#14579130C2314yes—
311Q8×Dic79C2314yes—
312Q8×Dic79C2312yes—
313Q8×Dic79C2312yes—
314C4×Dic158C2318yes—
315C4×Dic158C2318yes—
316C4×Dic158C2314yes—
317C4×Dic158C2318yes—
318C4×Dic158C2314yes—
319C4×Dic158C2314yes—
320#14579126C2318yes—
321#14579126C2318yes—
322#14579126C2314yes—
323#14579126C2318yes—
324#14579126C2314yes—
325#14579126C2312yes—
326#14579126C2314yes—
327#14579126C2312yes—
328C4×D316C2314yes—
329D4×Dic79C2318yes—
330D4×Dic79C2318yes—
331D4×Dic79C2314yes—
332D4×Dic79C2314yes—
333D4×Dic79C2312yes—
334D4×Dic79C2314yes—
335D4×Dic79C2314yes—
336D4×Dic79C2314yes—
337D4×Dic79C2312yes—
338#14579123C2314yes—
339#14579123C2312yes—
340#14579123C2312yes—
341C4×C22⋊D79C2318yes—
342C4×C22⋊D79C2318yes—
343C4×C22⋊D79C2318yes—
344C4×C22⋊D79C2314yes—
345C4×C22⋊D79C2314yes—
346C4×C22⋊D79C2314yes—
347C4×C22⋊D79C2314yes—
348(C22⋊D79)⋊C4C2318yes—
349(C22⋊D79)⋊C4C2318yes—
350(C22⋊D79)⋊C4C2318yes—
351(C22⋊D79)⋊C4C2314yes—
352(C22⋊D79)⋊C4C2314yes—
353(C22⋊D79)⋊C4C2314yes—
354(C22⋊D79)⋊C4C2314yes—
355(C22⋊D79)⋊C4C2314yes—
356(C22⋊D79)⋊C4C2314yes—
357#14579120C2314yes—
358#14579120C2312yes—
359#14579120C2314yes—
360#14579120C2314yes—
361#14579119C2314yes—
362#14579119C2314yes—
363#14579119C2314yes—
364#14579119C2314yes—
365#14579118C2314yes—
366#14579118C2318yes—
367#14579117C2314yes—
368#14579117C2314yes—
369#14579117C2314yes—
370#14579117C2318yes—
371#14579117C2318yes—
372#14579117C2314yes—
373C2×C4⋊Dic79C2312yes—
374C2×C4⋊Dic79C2312yes—
375C2×C4⋊Dic79C2314yes—
376C2×C4⋊Dic79C2314yes—
377C2×C4⋊Dic79C2314yes—
378C2×Dic79⋊C4C2314yes—
379C2×Dic79⋊C4C2314yes—
380C2×Dic79⋊C4C2318yes—
381C2×Dic79⋊C4C2318yes—
382C2×Dic79⋊C4C2314yes—
383C2×Dic79⋊C4C2314yes—
384C4⋊C4×D79C2314yes—
385C4⋊C4×D79C2318yes—
386C4⋊C4×D79C2314yes—
387C2×C4×Dic79C2312yes—
388C2×C4×Dic79C2312yes—
389C2×C4×Dic79C2312yes—
390C2×C4×Dic79C2312yes—
391C2×C4×Dic79C2312yes—
392C2×C4×Dic79C2312yes—
393C2×C4×Dic79C2314yes—
394C42×D79C2314yes—
395C2×#41×C79C2312yes—
396C2×#41×C79C2314yes—
397C23×C4×C79C2311yescharacteristic
398C23×C4×C79C2312yes—
399C4⋊Q8×C79C2314yes—
400#126×C79C2318yes—
401#125×C79C2318yes—
402#125×C79C2314yes—
403#123×C79C2314yes—
404#123×C79C2318yes—
405#123×C79C2318yes—
406C22⋊Q8×C79C2318yes—
407C22⋊Q8×C79C2314yes—
408C22⋊Q8×C79C2314yes—
409C22⋊Q8×C79C2314yes—
410C22⋊Q8×C79C2312yes—
411C22⋊Q8×C79C2312yes—
412#121×C79C2314yes—
413#121×C79C2314yes—
414#121×C79C2312yes—
415#121×C79C2314yes—
416#121×C79C2312yes—
417#120×C79C2314yes—
418C4×Q8×C79C2314yes—
419C4×D4×C79C2318yes—
420C4×D4×C79C2314yes—
421C4×D4×C79C2314yes—
422C4×D4×C79C2318yes—
423C4×D4×C79C2314yes—
424#117×C79C2314yes—
425#117×C79C2312yes—
426#117×C79C2314yes—
427C2×C4⋊C4×C79C2311yescharacteristic
428C2×C4⋊C4×C79C2312yes—
429C2×C4⋊C4×C79C2314yes—
430C2×C4⋊C4×C79C2314yes—
431C2×C4⋊C4×C79C2311yescharacteristic
432C2×C4⋊C4×C79C2314yes—
433#11929624—28no—
434#11929624—48no—
435#11929624—416no—
436#11929623—216no—
437#11929623—216no—
438#11929623—416no—
439#11929623—416no—
440C2×Dic158—216no—
441C2×Dic158—48no—
442C2×Dic158—48no—
443C2×Dic158—416no—
444C2×Dic158—48no—
445C2×Dic158—416no—
446C2×Dic158C2414yes—
447C2×Dic158C2418yes—
448C2×Dic158C2418yes—
449C2×Dic158C2414yes—
450C2×Dic158C2412yes—
451C2×Dic158C2418yes—
452C2×Dic158C2418yes—
453C2×Dic158C2418yes—
454C2×Dic158C2414yes—
455Q8×D79—416no—
456C2×D316C2412yes—
457C2×D316C2414yes—
458C2×C22⋊D79C2414yes—
459C2×C22⋊D79C2414yes—
460C2×C22⋊D79C2414yes—
461C2×C22⋊D79C2414yes—
462C2×C22⋊D79C2414yes—
463C2×C22⋊D79C2418yes—
464C22×Dic79—24no—
465C22×Dic79—24no—
466C22×Dic79—44no—
467C22×Dic79C2412yes—
468C22×Dic79C2412yes—
469C22×Dic79C2411yescharacteristic
470C22×Dic79C2414yes—
471C22×Dic79C2414yes—
472C22×Dic79C2414yes—
473C22×Dic79C2412yes—
474C22×Dic79C2412yes—
475C22×Dic79C2411yescharacteristic
476C22×Dic79C2414yes—
477C22×Dic79C2414yes—
478C22×Dic79C2418yes—
479C22×Dic79C2411yescharacteristic
480C22×Dic79C2411yescharacteristic
481C2×C4×D79C2414yes—
482C2×C4×D79C2414yes—
483C2×C4×D79C2414yes—
484C2×C4×D79C2418yes—
485C2×C4×D79C2418yes—
486C4⋊Dic79C2412yes—
487C4⋊Dic79C2414yes—
488C4⋊Dic79C2418yes—
489C4⋊Dic79C2414yes—
490C4⋊Dic79C2418yes—
491C4⋊Dic79C2418yes—
492C4⋊Dic79C2412yes—
493C4⋊Dic79C2414yes—
494C4⋊Dic79C2414yes—
495C4⋊Dic79C2414yes—
496C4⋊Dic79C2414yes—
497C4⋊Dic79C2414yes—
498C4⋊Dic79C2414yes—
499Dic79⋊C4C2414yes—
500Dic79⋊C4C2418yes—
501Dic79⋊C4C2418yes—
502Dic79⋊C4C2418yes—
503Dic79⋊C4C2418yes—
504Dic79⋊C4C2418yes—
505Dic79⋊C4C2418yes—
506Dic79⋊C4C2418yes—
507Dic79⋊C4C2418yes—
508Dic79⋊C4C2414yes—
509Dic79⋊C4C2414yes—
510Dic79⋊C4C2414yes—
511Dic79⋊C4C2414yes—
512Dic79⋊C4C2414yes—
513Dic79⋊C4C2414yes—
514Dic79⋊C4C2414yes—
515Dic79⋊C4C2418yes—
516Dic79⋊C4C2418yes—
517Dic79⋊C4C2414yes—
518Dic79⋊C4C2414yes—
519C22⋊Dic79C2414yes—
520C22⋊Dic79C2414yes—
521C22⋊Dic79C2418yes—
522C22⋊Dic79C2414yes—
523C22⋊Dic79C2414yes—
524C22⋊Dic79C2414yes—
525C22⋊Dic79C2418yes—
526C22⋊Dic79C2414yes—
527C22⋊Dic79C2414yes—
528(C2×D79)⋊C4C2418yes—
529(C2×D79)⋊C4C2414yes—
530(C2×D79)⋊C4C2414yes—
531(C2×D79)⋊C4C2418yes—
532(C2×D79)⋊C4C2414yes—
533(C2×D79)⋊C4C2414yes—
534(C2×D79)⋊C4C2414yes—
535(C2×D79)⋊C4C2414yes—
536(C2×D79)⋊C4C2418yes—
537(C2×D79)⋊C4C2418yes—
538C4×Dic79C2412yes—
539C4×Dic79C2414yes—
540C4×Dic79C2414yes—
541C4×Dic79C2412yes—
542C4×Dic79C2412yes—
543C4×Dic79C2412yes—
544C4×Dic79C2412yes—
545C4×Dic79C2412yes—
546C4×Dic79C2412yes—
547C4×Dic79C2412yes—
548C4×Dic79C2414yes—
549C4×Dic79C2414yes—
550C4×Dic79C2414yes—
551C4×Dic79C2418yes—
552C4×Dic79C2418yes—
553C4×Dic79C2418yes—
554C24×C79C2411yescharacteristic
555#41×C79—28no—
556#41×C79—48no—
557C2×Q8×C79C2412yes—
558C2×Q8×C79C2414yes—
559C2×D4×C79C2414yes—
560C2×D4×C79C2414yes—
561C2×D4×C79C2414yes—
562C2×D4×C79C2412yes—
563C2×D4×C79C2414yes—
564C22×C4×C79—24no—
565C22×C4×C79—44no—
566C22×C4×C79C2414yes—
567C22×C4×C79C2412yes—
568C22×C4×C79C2412yes—
569C22×C4×C79C2411yescharacteristic
570C22×C4×C79C2414yes—
571C22×C4×C79C2412yes—
572C22×C4×C79C2414yes—
573C22×C4×C79C2412yes—
574C22×C4×C79C2418yes—
575C22×C4×C79C2411yescharacteristic
576C4⋊C4×C79C2414yes—
577C4⋊C4×C79C2414yes—
578C4⋊C4×C79C2418yes—
579C4⋊C4×C79C2412yes—
580C4⋊C4×C79C2418yes—
581C4⋊C4×C79C2412yes—
582C4⋊C4×C79C2414yes—
583C4⋊C4×C79C2414yes—
584C4⋊C4×C79C2414yes—
585C4⋊C4×C79C2418yes—
586C4⋊C4×C79C2414yes—
587C22⋊C4×C79C2414yes—
588C22⋊C4×C79C2414yes—
589C22⋊C4×C79C2418yes—
590C22⋊C4×C79C2414yes—
591C22⋊C4×C79C2418yes—
592C22⋊C4×C79C2414yes—
593C22⋊C4×C79C2414yes—
594C42×C79C2418yes—
595C42×C79C2414yes—
596C23×C79—22no—
597C23×C79—22no—
598C23×C79—22no—
599C23×C79C2514yes—
600C23×C79C2511yescharacteristic
601C23×C79C2511yescharacteristic
602C23×C79C2511yescharacteristic
603C22×D79C2514yes—
604Q8×C79—24no—
605Q8×C79—44no—
606D4×C79—28no—
607D4×C79—28no—
608D4×C79—28no—
609D4×C79—24no—
610D4×C79—44no—
611C2×C4×C79—28no—
612C2×C4×C79—22no—
613C2×C4×C79—24no—
614C2×C4×C79—24no—
615C2×C4×C79—28no—
616C2×C4×C79—42no—
617C2×C4×C79—44no—
618C2×C4×C79—42no—
619C2×C4×C79—48no—
620C2×C4×C792−1+414yescomplemented
621C2×C4×C79C2514yes—
622C2×C4×C79C2512yes—
623C2×C4×C79C2514yes—
624C2×C4×C79C2514yes—
625C2×C4×C79C2514yes—
626C2×C4×C79C2514yes—
627C2×C4×C79C2512yes—
628C22⋊D79—28no—
629C22⋊D79—28no—
630C22⋊D79—28no—
631C22⋊D79—28no—
632C22⋊D79—28no—
633C22⋊D79—48no—
634C2×Dic79—22no—
635C2×Dic79—28no—
636C2×Dic79—22no—
637C2×Dic79—24no—
638C2×Dic79—24no—
639C2×Dic79—28no—
640C2×Dic79—24no—
641C2×Dic79—24no—
642C2×Dic79—28no—
643C2×Dic79—44no—
644C2×Dic79—44no—
645C2×Dic79—48no—
646C2×Dic79H(5,𝔽2)14yes—
647C2×Dic792−1+414yescomplemented
648C2×Dic79C2514yes—
649C2×Dic79C2514yes—
650C2×Dic79C2512yes—
651C2×Dic79C2512yes—
652C2×Dic79C2518yes—
653C2×Dic79C2514yes—
654C2×Dic79C2512yes—
655C2×Dic79C2512yes—
656D316—24no—
657D316—44no—
658C4×D79—28no—
659C4×D79—28no—
660C4×D79—28no—
661C4×D79—48no—
662C4×D79—48no—
663Dic158—24no—
664Dic158—28no—
665Dic158—216no—
666Dic158—216no—
667Dic158—28no—
668Dic158—48no—
669Dic158—48no—
670Dic158—48no—
671Dic158—44no—
672C22×C79—28no—
673C22×C79—21no—
674C22×C79—21no—
675C22×C79—21no—
676C22×C79—21no—
677C22×C79—21no—
678C22×C79—21no—
679C22×C79—24no—
680C22×C79—24no—
681C22×C79—24no—
682C22×C79C2×H(5,𝔽2)12yes—
683C22×C79C2×2−1+412yes—
684C22×C79C2×2−1+412yes—
685C22×C79C2611yescharacteristic
686C2×D79—24no—
687C2×D79—24no—
688C2×D79—24no—
689C4×C79—24no—
690C4×C79—24no—
691C4×C79—24no—
692C4×C79—22no—
693C4×C79—24no—
694C4×C79—24no—
695C4×C79C2×2−1+414yes—
696Dic79—24no—
697Dic79—28no—
698Dic79—22no—
699Dic79—24no—
700Dic79—24no—
701Dic79—22no—
702Dic79C2×H(5,𝔽2)14yes—
703Dic79C2×2−1+414yes—
704#62833—791nomaximal, Sylow
705C2×C79—22no—
706C2×C79—22no—
707C2×C79—22no—
708C2×C79—44no—
709C2×C79C22×H(5,𝔽2)11yescharacteristic
710C2×C79C22×2−1+411yescharacteristic
711C2×C79C22×2−1+411yescharacteristic
712D79—44no—
713#3552—794no—
714#3552—794no—
715#3552—798no—
716#3544—794no—
717#3544—794no—
718#3511—794no—
719#3511—792no—
720#3511—792no—
721#3509—794no—
722#3503—794no—
723#3503—792no—
724#3503—792no—
725#3499—794no—
726#3492—794no—
727#3492—792no—
728#3492—791no—
729#3492D7911yescharacteristic, complemented
730#3486—794no—
731#3444—792no—
732C22×C4⋊Q8—791no—
733C79#6283311yescharacteristic, complemented, Sylow
734C2×2−1+4—794no—
735C23×Q8—792no—
736#563—798no—
737#563—798no—
738#563—798no—
739#563—798no—
740Q82—794no—
741Q82—794no—
742#557—798no—
743#557—794no—
744#557—794no—
745#556—798no—
746#556—794no—
747#556—794no—
748#555—794no—
749#555—794no—
750#554—794no—
751#554—798no—
752#554—794no—
753#554—794no—
754#554—794no—
755#554—798no—
756#554—794no—
757#554—794no—
758#554—794no—
759#554C2×D7914yes—
760#553—798no—
761#553—794no—
762#553—794no—
763#553—798no—
764#553—794no—
765#553C2×D7914yes—
766#552—798no—
767#552—794no—
768#552—794no—
769#552—798no—
770#552—794no—
771#552C2×D7914yes—
772D4×Q8—794no—
773D4×Q8—798no—
774D4×Q8—798no—
775D4×Q8—798no—
776D4×Q8—798no—
777D4×Q8—798no—
778D4×Q8—794no—
779#548—798no—
780#548—798no—
781#548—798no—
782#548—798no—
783#547—798no—
784#547—798no—
785#547—798no—
786#547—794no—
787#547—794no—
788#547—794no—
789#547—794no—
790#547—794no—
791#547C2×D7914yes—
792#544—794no—
793#544—798no—
794#544—794no—
795#544—794no—
796#544—798no—
797#544—792no—
798#544—794no—
799#544—791no—
800#544—794no—
801#544C2×D7911yescharacteristic
802#542—798no—
803#542—798no—
804#542—794no—
805#542—794no—
806#542—794no—
807#542—794no—
808#541—798no—
809#541—798no—
810#539—798no—
811#539—794no—
812#539—794no—
813#539—798no—
814#539—794no—
815#539C2×D7914yes—
816#537—792no—
817#537—794no—
818#537—791no—
819#537C2×D7911yescharacteristic
820#536—794no—
821#536—798no—
822#536—798no—
823#536—798no—
824#536—798no—
825#536—794no—
826#533—794no—
827#533—792no—
828#533—792no—
829#533—794no—
830#533—794no—
831#533—792no—
832#533—794no—
833#532—792no—
834#532—792no—
835#532—792no—
836#532—794no—
837#532—794no—
838C2×C4⋊Q8—794no—
839C2×C4⋊Q8—794no—
840C2×C4⋊Q8—794no—
841C2×C4⋊Q8—792no—
842C2×C4⋊Q8—792no—
843C2×C4⋊Q8—794no—
844C2×C4⋊Q8—794no—
845C2×C4⋊Q8—794no—
846C2×C4⋊Q8—794no—
847#529—794no—
848#529—794no—
849#529—792no—
850#529—792no—
851#529—792no—
852#529—792no—
853#529—794no—
854#529—794no—
855#525—792no—
856#525—794no—
857#525—794no—
858#525—794no—
859#525—798no—
860#525C2×D7912yes—
861#525C2×D7914yes—
862#520—792no—
863#520—798no—
864#520—792no—
865#520—792no—
866#520C2×D7912yes—
867#519—794no—
868C4×#41—792no—
869C4×#41—794no—
870C4×#41—794no—
871C4×#41—792no—
872C22×C4⋊C4—792no—
873C22×C4⋊C4—791no—
874C22×C4⋊C4C2×D7911yescharacteristic
875C22×C42—791no—
8762−1+4—31616no—
877C2×#41—798no—
878C2×#41—798no—
879C2×#41—794no—
880C2×#41—794no—
881C2×#41—794no—
882C2×#41—798no—
883C2×#41—792no—
884C2×#41C22×D7912yes—
885C2×#41C22×D7914yes—
886C22×Q8—3168no—
887C22×Q8—798no—
888C22×Q8—794no—
889C22×Q8—794no—
890C22×Q8—798no—
891C22×Q8—794no—
892C22×Q8—798no—
893C22×Q8—794no—
894C23×C4—792no—
895C23×C4—791no—
896C23×C4—791no—
897C23×C4C22×D7911yescharacteristic
898C23×C4C22×D7912yes—
899C4⋊Q8—798no—
900C4⋊Q8—792no—
901C4⋊Q8—798no—
902C4⋊Q8—792no—
903C4⋊Q8—794no—
904C4⋊Q8—794no—
905C4⋊Q8—798no—
906C4⋊Q8—798no—
907C4⋊Q8—794no—
908C4⋊Q8—794no—
909C4⋊Q8—798no—
910C4⋊Q8—794no—
911C4⋊Q8—794no—
912C4⋊Q8—794no—
913C4⋊Q8—794no—
914C4⋊Q8—798no—
915C4⋊Q8—798no—
916C4⋊Q8—798no—
917C4⋊Q8—798no—
918C4⋊Q8—794no—
919C4⋊Q8—794no—
920C4⋊Q8—792no—
921C4⋊Q8—798no—
922C4⋊Q8—798no—
923C4⋊Q8—794no—
924C4⋊Q8—798no—
925C4⋊Q8C22×D7914yes—
926#127—792no—
927#126—794no—
928#126—794no—
929#126—798no—
930#126—798no—
931#126—798no—
932#126—794no—
933#126—794no—
934#126—798no—
935#126—798no—
936#126—798no—
937#126—798no—
938#126C22×D7918yes—
939#125—794no—
940#125—794no—
941#125—792no—
942#125—792no—
943#125—798no—
944#125—798no—
945#125—794no—
946#125—794no—
947#125—798no—
948#125—798no—
949#125—798no—
950#125—798no—
951#125—798no—
952#125—798no—
953#125—794no—
954#125—798no—
955#125C22×D7914yes—
956#125C22×D7918yes—
957#124—792no—
958#124—792no—
959#124—798no—
960#124—794no—
961#124—794no—
962#124—798no—
963#124—798no—
964#124—798no—
965#124—798no—
966#124—798no—
967#123—794no—
968#123—794no—
969#123—798no—
970#123—798no—
971#123—794no—
972#123—798no—
973#123—798no—
974#123—798no—
975#123—798no—
976#123—794no—
977#123—794no—
978#123—798no—
979#123—798no—
980#123—798no—
981#123—798no—
982#123C22×D7914yes—
983#123C22×D7918yes—
984#123C22×D7918yes—
985C22⋊Q8—794no—
986C22⋊Q8—798no—
987C22⋊Q8—792no—
988C22⋊Q8—792no—
989C22⋊Q8—794no—
990C22⋊Q8—794no—
991C22⋊Q8—794no—
992C22⋊Q8—798no—
993C22⋊Q8—798no—
994C22⋊Q8—798no—
995C22⋊Q8—798no—
996C22⋊Q8—798no—
997C22⋊Q8—798no—
998C22⋊Q8—794no—
999C22⋊Q8—798no—
1000C22⋊Q8—798no—
1001C22⋊Q8—798no—
1002C22⋊Q8—798no—
1003C22⋊Q8—798no—
1004C22⋊Q8—798no—
1005C22⋊Q8—798no—
1006C22⋊Q8—794no—
1007C22⋊Q8—794no—
1008C22⋊Q8—794no—
1009C22⋊Q8—794no—
1010C22⋊Q8—798no—
1011C22⋊Q8—798no—
1012C22⋊Q8—798no—
1013C22⋊Q8—798no—
1014C22⋊Q8—798no—
1015C22⋊Q8—798no—
1016C22⋊Q8—798no—
1017C22⋊Q8—798no—
1018C22⋊Q8—798no—
1019C22⋊Q8C22×D7912yes—
1020C22⋊Q8C22×D7912yes—
1021C22⋊Q8C22×D7914yes—
1022C22⋊Q8C22×D7914yes—
1023C22⋊Q8C22×D7914yes—
1024C22⋊Q8C22×D7918yes—
1025#121—794no—
1026#121—794no—
1027#121—794no—
1028#121—794no—
1029#121—798no—
1030#121—798no—
1031#121—794no—
1032#121—798no—
1033#121—792no—
1034#121—792no—
1035#121—794no—
1036#121—794no—
1037#121—794no—
1038#121—794no—
1039#121—798no—
1040#121C22×D7912yes—
1041#121C22×D7912yes—
1042#121C22×D7914yes—
1043#121C22×D7914yes—
1044#121C22×D7914yes—
1045#120—794no—
1046#120C22×D7914yes—
1047C4×Q8—792no—
1048C4×Q8—792no—
1049C4×Q8—794no—
1050C4×Q8—794no—
1051C4×Q8—792no—
1052C4×Q8—794no—
1053C4×Q8—792no—
1054C4×Q8—798no—
1055C4×Q8—798no—
1056C4×Q8—798no—
1057C4×Q8—794no—
1058C4×Q8—794no—
1059C4×Q8—794no—
1060C4×Q8—798no—
1061C4×Q8—798no—
1062C4×Q8—798no—
1063C4×Q8—794no—
1064C4×Q8C22×D7914yes—
1065C4×D4—794no—
1066C4×D4—794no—
1067C4×D4—794no—
1068C4×D4—794no—
1069C4×D4—792no—
1070C4×D4—792no—
1071C4×D4—798no—
1072C4×D4—798no—
1073C4×D4—794no—
1074C4×D4—794no—
1075C4×D4—794no—
1076C4×D4—794no—
1077C4×D4—794no—
1078C4×D4—798no—
1079C4×D4—798no—
1080C4×D4—798no—
1081C4×D4—792no—
1082C4×D4—792no—
1083C4×D4—794no—
1084C4×D4—794no—
1085C4×D4—794no—
1086C4×D4—794no—
1087C4×D4—794no—
1088C4×D4—794no—
1089C4×D4—794no—
1090C4×D4—798no—
1091C4×D4—798no—
1092C4×D4—798no—
1093C4×D4—794no—
1094C4×D4C22×D7914yes—
1095C4×D4C22×D7914yes—
1096C4×D4C22×D7918yes—
1097C4×D4C22×D7918yes—
1098C4×D4C22×D7914yes—
1099#117—792no—
1100#117—794no—
1101#117—794no—
1102#117—794no—
1103#117—794no—
1104#117—794no—
1105#117—794no—
1106#117—794no—
1107#117—794no—
1108#117—794no—
1109#117—794no—
1110#117—794no—
1111#117—798no—
1112#117—798no—
1113#117—794no—
1114#117—798no—
1115#117C22×D7912yes—
1116#117C22×D7914yes—
1117#117C22×D7914yes—
1118C2×C4⋊C4—794no—
1119C2×C4⋊C4—792no—
1120C2×C4⋊C4—794no—
1121C2×C4⋊C4—792no—
1122C2×C4⋊C4—798no—
1123C2×C4⋊C4—794no—
1124C2×C4⋊C4—794no—
1125C2×C4⋊C4—794no—
1126C2×C4⋊C4—794no—
1127C2×C4⋊C4—798no—
1128C2×C4⋊C4—794no—
1129C2×C4⋊C4—798no—
1130C2×C4⋊C4—794no—
1131C2×C4⋊C4—794no—
1132C2×C4⋊C4C22×D7911yescharacteristic
1133C2×C4⋊C4C22×D7911yescharacteristic
1134C2×C4⋊C4C22×D7912yes—
1135C2×C4⋊C4C22×D7914yes—
1136C2×C4⋊C4C22×D7914yes—
1137C2×C4⋊C4C22×D7914yes—
1138C2×C42—794no—
1139C2×C42—792no—
1140C2×C42—792no—
1141C2×C42—792no—
1142C2×C42—792no—
1143C2×C42—792no—
1144C2×C42—792no—
1145C2×C42—794no—
1146C24C23×D7911yescharacteristic
1147#41—28no—
1148#41—48no—
1149#41—3168no—
1150#41—31616no—
1151#41—31616no—
1152#41—31616no—
1153#41—15816no—
1154#41—15816no—
1155#41—1588no—
1156C2×Q8—3168no—
1157C2×Q8—3168no—
1158C2×Q8—31616no—
1159C2×Q8—3168no—
1160C2×Q8—31616no—
1161C2×Q8—31616no—
1162C2×Q8—798no—
1163C2×Q8—794no—
1164C2×Q8—798no—
1165C2×Q8—798no—
1166C2×Q8—794no—
1167C2×Q8—792no—
1168C2×Q8—798no—
1169C2×Q8—794no—
1170C2×Q8—798no—
1171C2×Q8—15816no—
1172C2×Q8C23×D7912yes—
1173C2×Q8C23×D7914yes—
1174C2×D4—798no—
1175C2×D4—794no—
1176C2×D4—794no—
1177C2×D4—794no—
1178C2×D4—794no—
1179C2×D4—794no—
1180C2×D4—794no—
1181C2×D4—792no—
1182C2×D4C23×D7914yes—
1183C2×D4C23×D7912yes—
1184C2×D4C23×D7914yes—
1185C2×D4C23×D7914yes—
1186C2×D4C23×D7914yes—
1187C22×C4—24no—
1188C22×C4—44no—
1189C22×C4—3164no—
1190C22×C4—794no—
1191C22×C4—794no—
1192C22×C4—798no—
1193C22×C4—798no—
1194C22×C4—798no—
1195C22×C4—791no—
1196C22×C4—791no—
1197C22×C4—792no—
1198C22×C4—792no—
1199C22×C4—791no—
1200C22×C4—792no—
1201C22×C4—792no—
1202C22×C4—791no—
1203C22×C4—794no—
1204C22×C4—794no—
1205C22×C4—794no—
1206C22×C4—794no—
1207C22×C4—794no—
1208C22×C4—794no—
1209C22×C4—1584no—
1210C22×C4—1584no—
1211C22×C4C23×D7912yes—
1212C22×C4C23×D7912yes—
1213C22×C4C23×D7911yescharacteristic
1214C22×C4C23×D7914yes—
1215C22×C4C23×D7914yes—
1216C22×C4C23×D7912yes—
1217C22×C4C23×D7914yes—
1218C22×C4C23×D7912yes—
1219C22×C4C23×D7918yes—
1220C22×C4C23×D7911yescharacteristic
1221C4⋊C4—798no—
1222C4⋊C4—794no—
1223C4⋊C4—798no—
1224C4⋊C4—798no—
1225C4⋊C4—798no—
1226C4⋊C4—798no—
1227C4⋊C4—798no—
1228C4⋊C4—798no—
1229C4⋊C4—798no—
1230C4⋊C4—794no—
1231C4⋊C4—794no—
1232C4⋊C4—794no—
1233C4⋊C4—794no—
1234C4⋊C4—794no—
1235C4⋊C4—794no—
1236C4⋊C4—794no—
1237C4⋊C4—794no—
1238C4⋊C4—794no—
1239C4⋊C4—798no—
1240C4⋊C4—798no—
1241C4⋊C4—792no—
1242C4⋊C4—794no—
1243C4⋊C4—794no—
1244C4⋊C4—798no—
1245C4⋊C4—798no—
1246C4⋊C4—798no—
1247C4⋊C4—792no—
1248C4⋊C4—794no—
1249C4⋊C4—794no—
1250C4⋊C4—794no—
1251C4⋊C4—794no—
1252C4⋊C4—794no—
1253C4⋊C4—794no—
1254C4⋊C4C23×D7912yes—
1255C4⋊C4C23×D7914yes—
1256C4⋊C4C23×D7918yes—
1257C4⋊C4C23×D7914yes—
1258C4⋊C4C23×D7918yes—
1259C4⋊C4C23×D7918yes—
1260C4⋊C4C23×D7912yes—
1261C4⋊C4C23×D7914yes—
1262C4⋊C4C23×D7914yes—
1263C4⋊C4C23×D7914yes—
1264C4⋊C4C23×D7914yes—
1265C22⋊C4—794no—
1266C22⋊C4—794no—
1267C22⋊C4—794no—
1268C22⋊C4—798no—
1269C22⋊C4—798no—
1270C22⋊C4—794no—
1271C22⋊C4—794no—
1272C22⋊C4—794no—
1273C22⋊C4—794no—
1274C22⋊C4—798no—
1275C22⋊C4—798no—
1276C22⋊C4—798no—
1277C22⋊C4—798no—
1278C22⋊C4—794no—
1279C22⋊C4—794no—
1280C22⋊C4—794no—
1281C22⋊C4—794no—
1282C22⋊C4—794no—
1283C22⋊C4—794no—
1284C22⋊C4C23×D7914yes—
1285C22⋊C4C23×D7914yes—
1286C22⋊C4C23×D7918yes—
1287C22⋊C4C23×D7914yes—
1288C22⋊C4C23×D7914yes—
1289C22⋊C4C23×D7914yes—
1290C22⋊C4C23×D7918yes—
1291C42—792no—
1292C42—792no—
1293C42—792no—
1294C42—792no—
1295C42—792no—
1296C42—792no—
1297C42—792no—
1298C42—792no—
1299C42—794no—
1300C42—794no—
1301C42—794no—
1302C42—794no—
1303C42—794no—
1304C42—798no—
1305C42—798no—
1306C42—798no—
1307C42C23×D7914yes—
1308C42C23×D7918yes—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—794no—
1313C23C24×D7914yes—
1314C23C24×D7911yescharacteristic
1315C23C24×D7911yescharacteristic
1316C23C24×D7911yescharacteristic
1317Q8—24no—
1318Q8—44no—
1319Q8—3168no—
1320Q8—3168no—
1321Q8—3164no—
1322Q8—3168no—
1323Q8—1588no—
1324Q8—15816no—
1325Q8—15816no—
1326Q8—1588no—
1327Q8—1584no—
1328D4—28no—
1329D4—28no—
1330D4—28no—
1331D4—24no—
1332D4—44no—
1333D4—3164no—
1334D4—3168no—
1335D4—1588no—
1336D4—1588no—
1337D4—1588no—
1338D4—1588no—
1339D4—1588no—
1340D4—1584no—
1341C2×C4—28no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—28no—
1346C2×C4—42no—
1347C2×C4—44no—
1348C2×C4—42no—
1349C2×C4—48no—
1350C2×C4—3168no—
1351C2×C4—3168no—
1352C2×C4—3164no—
1353C2×C4—3164no—
1354C2×C4—3168no—
1355C2×C4—794no—
1356C2×C4—794no—
1357C2×C4—792no—
1358C2×C4—792no—
1359C2×C4—794no—
1360C2×C4—794no—
1361C2×C4—792no—
1362C2×C4—792no—
1363C2×C4—798no—
1364C2×C4—794no—
1365C2×C4—1588no—
1366C2×C4—1588no—
1367C2×C4—1584no—
1368C2×C4—1584no—
1369C2×C4—1584no—
1370C2×C4—1584no—
1371C2×C4—1588no—
1372C2×C4—1588no—
1373C2×C4—1588no—
1374C2×C4—1582no—
1375C2×C4—1582no—
1376C2×C4—1588no—
1377C2×C4#1457920814yescomplemented
1378C2×C4C24×D7914yes—
1379C2×C4C24×D7912yes—
1380C2×C4C24×D7914yes—
1381C2×C4C24×D7914yes—
1382C2×C4C24×D7914yes—
1383C2×C4C24×D7914yes—
1384C2×C4C24×D7912yes—
1385C22—28no—
1386C22—21no—
1387C22—21no—
1388C22—21no—
1389C22—21no—
1390C22—21no—
1391C22—21no—
1392C22—24no—
1393C22—24no—
1394C22—24no—
1395C22—1584no—
1396C22—1584no—
1397C22—1584no—
1398C22H(5,𝔽2)×D7912yes—
1399C222−1+4×D7912yes—
1400C22C2×#1457920812yes—
1401C22C25×D7911yescharacteristic
1402C4—24no—
1403C4—24no—
1404C4—24no—
1405C4—24no—
1406C4—22no—
1407C4—24no—
1408C4—794no—
1409C4—794no—
1410C4—1588no—
1411C4—1584no—
1412C4—1582no—
1413C4—1582no—
1414C4—1584no—
1415C4—1584no—
1416C4C2×#1457920814yes—
1417C2—22no—
1418C2—22no—
1419C2—22no—
1420C2—44no—
1421C2—3164no—
1422C2C2×H(5,𝔽2)×D7911yescharacteristic
1423C2C2×2−1+4×D7911yescharacteristic
1424C2C22×#1457920811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3492C2
hypercenter#3492D79
hypocenterC79#62833
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #23777839C2semidirect
2. #23777835C2semidirect
3. #23777833C2semidirect
4. #23777742C2semidirect
5. #23777736C2semidirect
6. #23777309C2semidirect
7. #23777303C2semidirect
8. #23777302C2semidirect
9. #23777278C2semidirect
10. #23777215C2semidirect
11. #23777214C2semidirect
12. #23777213C2semidirect
13. #23777179C2semidirect
14. #23777109C2semidirect
15. #23777106C2semidirect
16. #23777101C2semidirect
17. #23777047C2semidirect
18. #23776692C2semidirect
19. C22×#14579160C2semidirect
20. C79×#3492C2semidirect
23. #19099317C22semidirect
24. #19099316C22semidirect
25. #19099315C22semidirect
26. #19099314C22semidirect
27. Q8×Dic158C22semidirect
28. #19099293C22semidirect
29. #19099290C22semidirect
30. #19099290C22semidirect
31. #19099289C22semidirect
32. #19099284C22semidirect
33. #19099281C22semidirect
34. #19099280C22semidirect
35. #19099277C22semidirect
36. #19099276C22semidirect
38. #19099272C22semidirect
40. #19099271C22semidirect
42. #19099269C22semidirect
44. #19099268C22semidirect
58. D4×Dic158C22semidirect
59. #19099228C22semidirect
62. #19099226C22semidirect
69. #19099214C22semidirect
71. #19099213C22semidirect
74. #19099211C22semidirect
76. #19099194C22semidirect
77. #19099193C22semidirect
78. #19099193C22semidirect
80. #19099192C22semidirect
82. #19099191C22semidirect
83. #19099190C22semidirect
84. #19099186C22semidirect
85. #19099185C22semidirect
86. #19099181C22semidirect
87. #19099180C22semidirect
88. #19099179C22semidirect
89. #19099178C22semidirect
90. #19099172C22semidirect
91. #19099170C22semidirect
101. #19099136C22semidirect
104. #19099135C22semidirect
106. #19099119C22semidirect
107. #19099117C22semidirect
109. #19099116C22semidirect
112. #19099115C22semidirect
113. #19099110C22semidirect
117. #19099108C22semidirect
125. C2×#14579160C22semidirect
126. C4⋊Q8×D79C22semidirect
620. C2×C4×C792−1+4semidirect
647. C2×Dic792−1+4semidirect
729. #3492D79semidirect
733. C79#62833semidirect
1377. C2×C4#14579208semidirect

Maximal subgroups

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

subgroupindex
#237778392
#237778352
#237778332
#237777422
#237777362
#237773092
#237773032
#237773022
#237772782
#237772152
#237772142
#237772132
#237771792
#237771092
#237771062
#237771012
#237770472
#237766922
C22×#145791602
C79×#34922
#6283379