Finite Group Databasebeta

← #35197218

Subgroups — #35197218

Order 20224.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777976C218yesmaximal, complemented
2#23777872C214yesmaximal, complemented
3#23777773C214yesmaximal, complemented
4#23777717C218yesmaximal, complemented
5#23777405C214yesmaximal, complemented
6#23777362C214yesmaximal, complemented
7#23777335C218yesmaximal, complemented
8#23777313C214yesmaximal, complemented
9#23777299C212yesmaximal, complemented
10#23777284C211yesmaximal, characteristic, complemented
11#23777276C211yesmaximal, characteristic, complemented
12#23777269C214yesmaximal, complemented
13#23777194C212yesmaximal, complemented
14#23777173C211yesmaximal, characteristic, complemented
15#23777055C212yesmaximal, complemented
16#23777043C212yesmaximal, complemented
17#23776695C211yesmaximal, characteristic, complemented
18#23776693C211yesmaximal, characteristic, complemented
19C2×#19099114C211yesmaximal, characteristic, complemented
20C79×#3499C211yesmaximal, characteristic, complemented
21C2×#14579207C2212yes—
22C22×#11929625C2212yescomplemented
23#19099309C22116yescomplemented
24#19099303C22116yescomplemented
25#19099298C2214yescomplemented
26#19099296C2218yescomplemented
27#19099295C2218yescomplemented
28#19099288C2214yescomplemented
29#19099287C2214yescomplemented
30#19099287C2218yescomplemented
31#19099279C2218yescomplemented
32#19099274C2218yescomplemented
33#19099261C2218yescomplemented
34#19099261C2218yescomplemented
35#19099258C22116yescomplemented
36#19099248C2218yescomplemented
37#19099240C22116yescomplemented
38#19099236C22116yescomplemented
39#19099234C2214yescomplemented
40#19099234C2214yescomplemented
41#19099232C2218yescomplemented
42#19099232C2218yescomplemented
43#19099231C2218yescomplemented
44#19099224C2218yescomplemented
45#19099224C2218yescomplemented
46#19099224C2218yescomplemented
47#19099216C2218yescomplemented
48#19099215C2218yescomplemented
49#19099210C2218yescomplemented
50#19099209C2218yescomplemented
51#19099208C2218yescomplemented
52#19099206C2218yescomplemented
53#19099204C2218yescomplemented
54#19099201C22116yescomplemented
55#19099201C2218yescomplemented
56D4×D316C2214yescomplemented
57#19099197C2218yes—
58#19099187C2218yescomplemented
59#19099187C2218yescomplemented
60#19099186C2218yescomplemented
61#19099174C2214yescomplemented
62#19099168C2214yescomplemented
63#19099166C2218yescomplemented
64#19099165C22116yescomplemented
65#19099164C2218yescomplemented
66#19099159C22116yescomplemented
67#19099153C22116yescomplemented
68#19099149C22116yescomplemented
69#19099144C2218yescomplemented
70#19099137C2212yes—
71#19099137C2214yescomplemented
72#19099131C2214yescomplemented
73#19099129C2218yescomplemented
74#19099127C2212yes—
75#19099127C2212yescomplemented
76#19099127C2218yescomplemented
77#19099127C2214yescomplemented
78#19099124C2218yescomplemented
79#19099120C2211yescharacteristic, complemented
80#19099118C2214yescomplemented
81#19099118C2212yescomplemented
82#19099117C2212yescomplemented
83#19099116C2211yescharacteristic, complemented
84#19099114C2212yescomplemented
85#19099114C2214yescomplemented
86#19099114C2214yescomplemented
87#19099114C2214yescomplemented
88#19099114C2214yescomplemented
89#19099113C2214yescomplemented
90#19099111C2212yescomplemented
91#19099110C2212yescomplemented
92#19099109C2211yescharacteristic
93#19099109C2214yescomplemented
94C2×#14579158C2211yescharacteristic
95#127×D79C2212yescomplemented
96#19099100C2212yescomplemented
97#19099099C2218yescomplemented
98#19099095C2214yescomplemented
99#19099095C2212yescomplemented
100#19099094C2214yescomplemented
101#19099093C2214yescomplemented
102#19099092C2214yescomplemented
103#19099091C2214yescomplemented
104C2×#14579150C2212yescomplemented
105C2×#14579150C2214yescomplemented
106#19099075C2211yescharacteristic
107#19099073C2214yescomplemented
108#19099072C2214yescomplemented
109#19099070C2212yescomplemented
110#19099070C2211yescharacteristic, complemented
111#19099070C2218yescomplemented
112#123×D79C2218yescomplemented
113C2×#14579136C2214yescomplemented
114#19099044C2218yescomplemented
115#19099041C2212yescomplemented
116#19099037C2212yescomplemented
117#19099035C2218yescomplemented
118#41×Dic79C2212yescomplemented
119C4×#11929624C2211yescharacteristic
120C4×#11929624C2214yescomplemented
121C4×#11929623C2214yescomplemented
122C2×#14579123C2214yescomplemented
123C2×C42×D79C2211yescharacteristic, complemented
124C2×2−1+4×C79C2212yescomplemented
125D4×Q8×C79C2214yescomplemented
126#547×C79C2218yescomplemented
127#547×C79C2214yescomplemented
128#536×C79C2212yescomplemented
129#536×C79C2214yescomplemented
130#532×C79C2211yescharacteristic
131#532×C79C2212yescomplemented
132C2×C4⋊Q8×C79C2211yescharacteristic, complemented
133C2×C4⋊Q8×C79C2212yescomplemented
134C4×#41×C79C2211yescharacteristic, complemented
135#14579207—48no—
136C2×#11929625—48no—
137C2×#11929625C2314yes—
138C2×#11929625C2318yes—
139C2×#11929625C2318yes—
140C2×#11929624C2311yescharacteristic
141C2×#11929624C2314yes—
142C2×#11929624C2314yes—
143C2×#11929624C2318yes—
144C2×#11929623C2314yes—
145C22×D316C2312yes—
146C22×D316C2314yes—
147C22×D316C2314yes—
148C22×D316C2314yes—
149C2×D4×D79C2318yes—
150C2×D4×D79C2314yes—
151C2×D4×D79C2318yes—
152C22×C4×D79C2311yescharacteristic
153C22×C4×D79C2312yes—
154C22×C4×D79C2314yes—
155#14579161C2312yes—
156#14579160C2312yes—
157#14579159C2314yes—
158#14579159C2311yescharacteristic
159#14579158C2312yes—
160#14579158C2314yes—
161#14579158C2312yes—
162#14579157C2318yes—
163#14579157C23116yes—
164#14579157C2314yes—
165#14579157C2314yes—
166#14579157C2311yescharacteristic
167#14579156C23116yes—
168#14579156C23116yes—
169#14579156C23116yes—
170#14579156C2314yes—
171#14579154C2318yes—
172#14579154C2314yes—
173#14579153C2312yes—
174#14579152C2318yes—
175#14579152C2314yes—
176#14579152C2312yes—
177#14579151C2314yes—
178#14579151C23116yes—
179#14579150C2314yes—
180#14579150C2314yes—
181#14579150C2314yes—
182#14579150C23116yes—
183#14579150C23116yes—
184#14579150C2318yes—
185#14579150C2314yes—
186#14579150C2311yescharacteristic
187#14579150C2314yes—
188#14579149C2318yes—
189#14579148C2314yes—
190#14579148C2311yescharacteristic
191#14579147C2314yes—
192#14579147C23116yes—
193#14579146C23116yes—
194#14579146C2314yes—
195#14579146C23116yes—
196#14579146C23116yes—
197#14579145C23116yes—
198#14579145C2312yes—
199#14579144C2318yes—
200#14579144C23116yes—
201#14579143C23116yes—
202#14579143C23116yes—
203#14579143C2314yes—
204#14579143C2318yes—
205#14579142C2314yes—
206#14579142C2312yes—
207#14579141C2314yes—
208#14579141C23116yes—
209#14579141C2318yes—
210#14579141C2312yes—
211#14579140C2314yes—
212#14579139C2314yes—
213#14579138C2314yes—
214#14579137C2318yes—
215#14579137C23116yes—
216#14579137C23116yes—
217#14579137C2314yes—
218#14579137C2312yes—
219#14579136C23116yes—
220#14579136C2318yes—
221#14579136C2318yes—
222#14579136C2318yes—
223#14579136C2312yes—
224#14579136C2318yes—
225#14579136C2318yes—
226#14579135C23116yes—
227#14579135C23116yes—
228#14579135C23116yes—
229#14579135C2318yes—
230#14579135C2318yes—
231#14579135C2318yes—
232#14579134C23116yes—
233#14579134C23116yes—
234#14579134C23116yes—
235#14579134C2314yes—
236#14579133C23116yes—
237#14579133C2314yes—
238#14579132C23116yes—
239#14579132C2314yes—
240#14579132C2314yes—
241#14579132C2312yes—
242#14579131C23116yes—
243#14579131C23116yes—
244#14579131C2312yes—
245#14579129C23116yes—
246#14579129C2318yes—
247#14579129C2318yes—
248#14579129C2312yes—
249#14579129C2314yes—
250Q8×Dic79C2318yes—
251Q8×Dic79C2318yes—
252Q8×Dic79C2314yes—
253C4×Dic158C2312yes—
254C4×Dic158C2314yes—
255C4×Dic158C2314yes—
256C4×Dic158C2314yes—
257#14579126C2314yes—
258#14579126C2318yes—
259C4×D316C2318yes—
260C4×D316C2318yes—
261C4×D316C2312yes—
262C4×D316C2314yes—
263C4×D316C2314yes—
264D4×Dic79C2314yes—
265D4×Dic79C2318yes—
266D4×Dic79C2314yes—
267#14579123C2318yes—
268#14579123C2318yes—
269#14579123C2318yes—
270#14579123C2318yes—
271#14579123C2318yes—
272#14579123C2318yes—
273C4×C22⋊D79C23116yes—
274C4×C22⋊D79C23116yes—
275C4×C22⋊D79C23116yes—
276C4×C22⋊D79C2314yes—
277C4×C22⋊D79C2314yes—
278C4×C22⋊D79C2318yes—
279C4×C22⋊D79C2314yes—
280C4×C22⋊D79C2314yes—
281C4×C22⋊D79C2314yes—
282(C22⋊D79)⋊C4C2318yes—
283(C22⋊D79)⋊C4C23116yes—
284#14579120C2312yes—
285#14579120C2314yes—
286#14579120C2314yes—
287#14579120C2318yes—
288#14579120C2311yescharacteristic
289#14579119C23116yes—
290#14579119C2318yes—
291#14579119C2314yes—
292#14579118C2314yes—
293#14579118C2312yes—
294#14579118C2314yes—
295#14579117C2318yes—
296C4⋊C4×D79C23116yes—
297C2×(C2×D79)⋊C4C23116yes—
298C2×(C2×D79)⋊C4C2318yes—
299C22⋊C4×D79C23116yes—
300C22⋊C4×D79C2318yes—
301C2×C4×Dic79C2312yes—
302C2×C4×Dic79C2311yescharacteristic
303C2×C4×Dic79C2314yes—
304C42×D79C2312yes—
305C42×D79C2312yes—
306C42×D79C2312yes—
307C42×D79C2312yes—
308C42×D79C2312yes—
3092−1+4×C79—48no—
310C2×#41×C79C2312yes—
311C2×#41×C79C2311yescharacteristic
312C2×#41×C79C2314yes—
313C2×#41×C79C2318yes—
314C2×#41×C79C2314yes—
315C22×Q8×C79C2312yes—
316C22×Q8×C79C2314yes—
317C22×Q8×C79C2314yes—
318C4⋊Q8×C79C2312yes—
319C4⋊Q8×C79C2318yes—
320C4⋊Q8×C79C2314yes—
321C4⋊Q8×C79C2311yescharacteristic
322C4⋊Q8×C79C2312yes—
323C4⋊Q8×C79C2314yes—
324#127×C79C2311yescharacteristic
325#124×C79C2314yes—
326#124×C79C2312yes—
327#123×C79C23116yes—
328#123×C79C2318yes—
329C22⋊Q8×C79C23116yes—
330C22⋊Q8×C79C2318yes—
331#121×C79C2318yes—
332#121×C79C2314yes—
333C4×Q8×C79C2312yes—
334C4×D4×C79C2318yes—
335C4×D4×C79C2314yes—
336C4×D4×C79C2314yes—
337C4×D4×C79C2312yes—
338#117×C79C2312yes—
339#117×C79C2311yescharacteristic
340C2×C4⋊C4×C79C2318yes—
341C2×C4⋊C4×C79C2314yes—
342C2×C42×C79C2311yescharacteristic
343C2×C42×C79C2312yes—
344C23×D79C2414yes—
345C23×D79C2411yescharacteristic
346C23×D79C2418yes—
347#11929625—416no—
348#11929625—416no—
349#11929625—48no—
350#11929624—24no—
351#11929624—416no—
352#11929624—48no—
353#11929624—48no—
354#11929623—48no—
355C2×Dic158C2414yes—
356C2×Dic158C2411yescharacteristic
357C2×Dic158C2414yes—
358C2×D316—28no—
359C2×D316—48no—
360C2×D316—48no—
361C2×D316—48no—
362C2×D316C2414yes—
363C2×D316C2418yes—
364C2×D316C2411yescharacteristic
365C2×D316C2414yes—
366C2×D316C2414yes—
367C2×D316C24116yes—
368C2×D316C2418yes—
369C2×D316C2418yes—
370C2×C22⋊D79C2412yes—
371C2×C22⋊D79C2418yes—
372C2×C22⋊D79C2414yes—
373C2×C22⋊D79C24116yes—
374C2×C22⋊D79C2414yes—
375C2×C22⋊D79C2418yes—
376C2×C22⋊D79C24116yes—
377D4×D79—416no—
378D4×D79—48no—
379D4×D79—416no—
380C22×Dic79C2411yescharacteristic
381C22×Dic79C2418yes—
382C22×Dic79C2412yes—
383C2×C4×D79—24no—
384C2×C4×D79—48no—
385C2×C4×D79—44no—
386C2×C4×D79C2412yes—
387C2×C4×D79C2412yes—
388C2×C4×D79C2412yes—
389C2×C4×D79C2414yes—
390C2×C4×D79C2412yes—
391C2×C4×D79C2412yes—
392C2×C4×D79C2418yes—
393C2×C4×D79C24116yes—
394C2×C4×D79C24116yes—
395C2×C4×D79C2412yes—
396C2×C4×D79C2412yes—
397C4⋊Dic79C2414yes—
398C4⋊Dic79C2414yes—
399C4⋊Dic79C2414yes—
400C4⋊Dic79C2414yes—
401C4⋊Dic79C2418yes—
402C4⋊Dic79C2412yes—
403C4⋊Dic79C24116yes—
404Dic79⋊C4C2418yes—
405Dic79⋊C4C24116yes—
406Dic79⋊C4C2418yes—
407Dic79⋊C4C2414yes—
408Dic79⋊C4C2414yes—
409Dic79⋊C4C2414yes—
410Dic79⋊C4C2414yes—
411Dic79⋊C4C2414yes—
412C22⋊Dic79C2418yes—
413C22⋊Dic79C2414yes—
414C22⋊Dic79C2412yes—
415C22⋊Dic79C2414yes—
416C22⋊Dic79C2414yes—
417C22⋊Dic79C2418yes—
418(C2×D79)⋊C4C2414yes—
419(C2×D79)⋊C4C24116yes—
420(C2×D79)⋊C4C24116yes—
421(C2×D79)⋊C4C2414yes—
422(C2×D79)⋊C4C24116yes—
423(C2×D79)⋊C4C24116yes—
424(C2×D79)⋊C4C24116yes—
425(C2×D79)⋊C4C2414yes—
426(C2×D79)⋊C4C2414yes—
427(C2×D79)⋊C4C2414yes—
428(C2×D79)⋊C4C2418yes—
429(C2×D79)⋊C4C24116yes—
430C4×Dic79C2411yescharacteristic
431C4×Dic79C2412yes—
432C4×Dic79C2412yes—
433C4×Dic79C2411yescharacteristic
434C4×Dic79C2412yes—
435C4×Dic79C2412yes—
436C4×Dic79C2412yes—
437C4×Dic79C2414yes—
438C4×Dic79C2412yes—
439C4×Dic79C2418yes—
440C4×Dic79C2414yes—
441C4×Dic79C24116yes—
442#41×C79—28no—
443#41×C79—24no—
444#41×C79—416no—
445#41×C79—48no—
446#41×C79—48no—
447C2×Q8×C79—28no—
448C2×Q8×C79—48no—
449C2×Q8×C79—48no—
450C2×Q8×C79C2414yes—
451C2×Q8×C79C2414yes—
452C2×Q8×C79C2412yes—
453C2×Q8×C79C2411yescharacteristic
454C2×Q8×C79C2418yes—
455C2×D4×C79C2414yes—
456C2×D4×C79C2412yes—
457C2×D4×C79C2411yescharacteristic
458C2×D4×C79C2414yes—
459C2×D4×C79C2412yes—
460C2×D4×C79C2418yes—
461C22×C4×C79C2414yes—
462C22×C4×C79C2414yes—
463C22×C4×C79C2412yes—
464C22×C4×C79C2412yes—
465C22×C4×C79C2414yes—
466C22×C4×C79C2418yes—
467C22×C4×C79C2418yes—
468C22×C4×C79C2411yescharacteristic
469C4⋊C4×C79C2414yes—
470C4⋊C4×C79C2418yes—
471C4⋊C4×C79C24116yes—
472C4⋊C4×C79C2418yes—
473C4⋊C4×C79C2412yes—
474C4⋊C4×C79C2414yes—
475C22⋊C4×C79C2412yes—
476C22⋊C4×C79C2414yes—
477C22⋊C4×C79C24116yes—
478C22⋊C4×C79C2418yes—
479C42×C79C2411yescharacteristic
480C42×C79C2411yescharacteristic
481C42×C79C2412yes—
482C42×C79C2412yes—
483C42×C79C2414yes—
484C23×C79C2514yes—
485C23×C79C2512yes—
486C23×C79C2511yescharacteristic
487C22×D79—22no—
488C22×D79—28no—
489C22×D79—42no—
490C22×D79—48no—
491C22×D79—48no—
492C22×D79—416no—
493C22×D79C2512yes—
494C22×D79C2518yes—
495C22×D79C2512yes—
496Q8×C79—28no—
497Q8×C79—28no—
498Q8×C79—24no—
499Q8×C79—22no—
500Q8×C79—48no—
501D4×C79—28no—
502D4×C79—24no—
503D4×C79—24no—
504D4×C79—22no—
505D4×C79—28no—
506D4×C79—48no—
507C2×C4×C79—28no—
508C2×C4×C79—28no—
509C2×C4×C79—24no—
510C2×C4×C79—24no—
511C2×C4×C79—28no—
512C2×C4×C79—48no—
513C2×C4×C79—48no—
514C2×C4×C79H(5,𝔽2)14yes—
515C2×C4×C79C2514yes—
516C2×C4×C79C2518yes—
517C2×C4×C79C2512yes—
518C2×C4×C79C2512yes—
519C2×C4×C79C2514yes—
520C2×C4×C79C2511yescharacteristic
521C2×C4×C79C2511yescharacteristic
522C2×C4×C79C2512yes—
523C22⋊D79—24no—
524C22⋊D79—48no—
525C22⋊D79—416no—
526C22⋊D79—48no—
527C22⋊D79—44no—
528C22⋊D79—416no—
529C22⋊D79—44no—
530C2×Dic79—22no—
531C2×Dic79—42no—
532C2×Dic79—48no—
533C2×Dic79C2512yes—
534C2×Dic79C2514yes—
535C2×Dic79C2512yes—
536C2×Dic79C2518yes—
537C2×Dic79C2512yes—
538C2×Dic79C2512yes—
539D316—28no—
540D316—28no—
541D316—22no—
542D316—216no—
543D316—48no—
544D316—48no—
545D316—416no—
546D316—44no—
547C4×D79—24no—
548C4×D79—24no—
549C4×D79—24no—
550C4×D79—24no—
551C4×D79—24no—
552C4×D79—28no—
553C4×D79—42no—
554C4×D79—42no—
555C4×D79—416no—
556C4×D79—48no—
557C4×D79—416no—
558Dic158—22no—
559Dic158—28no—
560Dic158—44no—
561C22×C79—22no—
562C22×C79—24no—
563C22×C79—22no—
564C22×C79—24no—
565C22×C79—28no—
566C22×C79C2×H(5,𝔽2)12yes—
567C22×C79C2611yescharacteristic
568C2×D79—22no—
569C2×D79—28no—
570C2×D79—22no—
571C2×D79—22no—
572C2×D79—216no—
573C2×D79—22no—
574C2×D79—24no—
575C2×D79—44no—
576C2×D79—88no—
577C2×D79—168no—
578C4×C79—22no—
579C4×C79—24no—
580C4×C79—28no—
581C4×C79—24no—
582C4×C79—22no—
583C4×C79C2×H(5,𝔽2)12yes—
584C4×C79C2×H(5,𝔽2)12yes—
585C4×C79#58514yes—
586Dic79—22no—
587Dic79—22no—
588Dic79—24no—
589Dic79—28no—
590Dic79—22no—
591Dic79—22no—
592#62836—791nomaximal, Sylow
593C2×C79—22no—
594C2×C79—44no—
595C2×C79—42no—
596C2×C79C22×H(5,𝔽2)11yescharacteristic
597C2×C79C2×#58512yes—
598D79—42no—
599D79—48no—
600D79—42no—
601#3562—798no—
602#3554—794no—
603#3546—794no—
604#3542—798no—
605#3517—794no—
606#3514—794no—
607#3513—798no—
608#3511—794no—
609#3510—792no—
610#3509—791no—
611#3508—794no—
612#3508—791no—
613#3500—792no—
614#3499D7911yescharacteristic, complemented
615#3498—791no—
616#3487—792no—
617#3485—792no—
618#3444—791no—
619#3444—791no—
620C2×#532—791no—
621C79#6283611yescharacteristic, complemented, Sylow
622C2×2−1+4C2×D7912yescomplemented
623C2×H(5,𝔽2)—792no—
624C22×#41—792no—
625#562—7916no—
626#560—7916no—
627#559—798no—
628#559—794no—
629#559—798no—
630#557—794no—
631#556—794no—
632#556—798no—
633#555—798no—
634#554—798no—
635#553—7916no—
636#553—798no—
637#553—798no—
638#552—798no—
639#551—7916no—
640#551—7916no—
641#550—798no—
642#550—798no—
643#550—798no—
644#550—794no—
645#550—794no—
646D4×Q8C2×D7914yescomplemented
647#548—798no—
648#548—798no—
649#548—798no—
650#547—798no—
651#547—798no—
652#547C2×D7918yescomplemented
653#547C2×D7914yescomplemented
654#546—798no—
655#546—7916no—
656#546—798no—
657#546—798no—
658#546—798no—
659#546—798no—
660#546—798no—
661D42—798no—
662D42—794no—
663#542—798no—
664#542—798no—
665#542—798no—
666#541—794no—
667#540—7916no—
668#540—798no—
669#540—798no—
670#540—794no—
671#539—7916no—
672#538—7916no—
673#538—7916no—
674#537—798no—
675#536—792no—
676#536—794no—
677#536C2×D7912yescomplemented
678#536C2×D7914yescomplemented
679#535—792no—
680#535—792no—
681#535—798no—
682#535—794no—
683#535—794no—
684#535—798no—
685#534—798no—
686#533—792no—
687#533—794no—
688#533—792no—
689#533—791no—
690#533—791no—
691#532—791no—
692#532—794no—
693#532—794no—
694#532—794no—
695#532—794no—
696#532—794no—
697#532—792no—
698#532—792no—
699#532—792no—
700#532—794no—
701#532C2×D7911yescharacteristic
702#532C2×D7912yescomplemented
703C2×C4⋊Q8C2×D7911yescharacteristic, complemented
704C2×C4⋊Q8C2×D7912yescomplemented
705C2×#127—792no—
706C2×#127—791no—
707#529—794no—
708#529—798no—
709#529—794no—
710#529—792no—
711#529—794no—
712#529—792no—
713#529—794no—
714#529—794no—
715C2×#124—792no—
716C2×#124—794no—
717#525—792no—
718#525—791no—
719#525—798no—
720#525—794no—
721#525—794no—
722#525—791no—
723C2×#123—798no—
724C2×#121—794no—
725#520—798no—
726#519—792no—
727#518—798no—
728#518—792no—
729C4×#41—792no—
730C4×#41—794no—
731C4×#41—791no—
732C4×#41—794no—
733C4×#41C2×D7911yescharacteristic, complemented
734C2×C4×D4—794no—
735C22×C42—791no—
7362−1+4—48no—
737H(5,𝔽2)—3168no—
738C2×#41—3168no—
739C2×#41—798no—
740C2×#41—798no—
741C2×#41—794no—
742C2×#41—794no—
743C2×#41—794no—
744C2×#41—798no—
745C2×#41—794no—
746C2×#41—791no—
747C2×#41C22×D7912yes—
748C2×#41C22×D7911yescharacteristic
749C2×#41C22×D7918yes—
750C2×#41C22×D7914yes—
751C2×#41C22×D7914yes—
752C22×Q8C22×D7912yes—
753C22×Q8C22×D7914yes—
754C22×Q8C22×D7914yes—
755C22×D4—798no—
756C22×D4—798no—
757C22×D4—794no—
758C22×D4—794no—
759C22×D4—794no—
760C22×D4—794no—
761C22×D4—792no—
762C23×C4—794no—
763C23×C4—792no—
764C23×C4—791no—
765C4⋊Q8—791no—
766C4⋊Q8—794no—
767C4⋊Q8—792no—
768C4⋊Q8—792no—
769C4⋊Q8C22×D7911yescharacteristic
770C4⋊Q8C22×D7912yes—
771C4⋊Q8C22×D7912yes—
772C4⋊Q8C22×D7914yes—
773C4⋊Q8C22×D7914yes—
774C4⋊Q8C22×D7918yes—
775#127—794no—
776#127—798no—
777#127—791no—
778#127—794no—
779#127—7916no—
780#127—792no—
781#127—792no—
782#127—794no—
783#127C22×D7911yescharacteristic
784#126—794no—
785#126—7916no—
786#126—7916no—
787#126—7916no—
788#126—798no—
789#126—794no—
790#125—792no—
791#125—794no—
792#125—794no—
793#125—798no—
794#125—7916no—
795#125—792no—
796#124—791no—
797#124—794no—
798#124—794no—
799#124—798no—
800#124—794no—
801#124—794no—
802#124—7916no—
803#124—794no—
804#124—7916no—
805#124—791no—
806#124—794no—
807#124—794no—
808#124—7916no—
809#124—798no—
810#124C22×D7912yes—
811#124C22×D7914yes—
812#123—794no—
813#123—792no—
814#123—798no—
815#123—7916no—
816#123—7916no—
817#123—794no—
818#123—7916no—
819#123—7916no—
820#123—792no—
821#123—7916no—
822#123—794no—
823#123—798no—
824#123—7916no—
825#123—7916no—
826#123C22×D7918yes—
827#123C22×D79116yes—
828C22⋊Q8—794no—
829C22⋊Q8—792no—
830C22⋊Q8—7916no—
831C22⋊Q8—798no—
832C22⋊Q8—7916no—
833C22⋊Q8—794no—
834C22⋊Q8—794no—
835C22⋊Q8—792no—
836C22⋊Q8—794no—
837C22⋊Q8—798no—
838C22⋊Q8—7916no—
839C22⋊Q8—794no—
840C22⋊Q8C22×D7918yes—
841C22⋊Q8C22×D79116yes—
842#121—794no—
843#121—794no—
844#121—794no—
845#121—792no—
846#121—7916no—
847#121—7916no—
848#121—798no—
849#121—798no—
850#121—798no—
851#121—7916no—
852#121—7916no—
853#121—7916no—
854#121—798no—
855#121—798no—
856#121—798no—
857#121—798no—
858#121—792no—
859#121—798no—
860#121—7916no—
861#121—794no—
862#121—7916no—
863#121—7916no—
864#121—7916no—
865#121C22×D7914yes—
866#121C22×D7918yes—
867#120—794no—
868#120—792no—
869#120—798no—
870#120—798no—
871#120—7916no—
872#120—792no—
873#120—7916no—
874#120—7916no—
875C4×Q8—794no—
876C4×Q8—798no—
877C4×Q8—798no—
878C4×Q8—794no—
879C4×Q8—798no—
880C4×Q8—792no—
881C4×Q8—794no—
882C4×Q8—794no—
883C4×Q8—794no—
884C4×Q8C22×D7912yes—
885C4×D4—794no—
886C4×D4—798no—
887C4×D4—794no—
888C4×D4—794no—
889C4×D4—798no—
890C4×D4—794no—
891C4×D4—794no—
892C4×D4—794no—
893C4×D4—794no—
894C4×D4—7916no—
895C4×D4—7916no—
896C4×D4—7916no—
897C4×D4—798no—
898C4×D4—798no—
899C4×D4—798no—
900C4×D4—798no—
901C4×D4—798no—
902C4×D4—798no—
903C4×D4—798no—
904C4×D4—7916no—
905C4×D4—794no—
906C4×D4—794no—
907C4×D4—792no—
908C4×D4—798no—
909C4×D4—798no—
910C4×D4C22×D7914yes—
911C4×D4C22×D7914yes—
912C4×D4C22×D7912yes—
913C4×D4C22×D7918yes—
914#117—792no—
915#117—791no—
916#117—794no—
917#117—794no—
918#117—798no—
919#117—794no—
920#117—798no—
921#117—7916no—
922#117—798no—
923#117—794no—
924#117—794no—
925#117—792no—
926#117C22×D7911yescharacteristic
927#117C22×D7912yes—
928C2×C4⋊C4—7916no—
929C2×C4⋊C4C22×D7914yes—
930C2×C4⋊C4C22×D7918yes—
931C2×C22⋊C4—798no—
932C2×C22⋊C4—7916no—
933C2×C22⋊C4—798no—
934C2×C22⋊C4—7916no—
935C2×C42—792no—
936C2×C42—794no—
937C2×C42—791no—
938C2×C42—792no—
939C2×C42—792no—
940C2×C42—792no—
941C2×C42—792no—
942C2×C42—792no—
943C2×C42C22×D7912yes—
944C2×C42C22×D7911yescharacteristic
945C24—798no—
946C24—794no—
947C24—791no—
948#41—28no—
949#41—24no—
950#41—416no—
951#41—48no—
952#41—48no—
953#41—31616no—
954#41—3168no—
955#41—3168no—
956#41—3168no—
957#41—31616no—
958#41—31616no—
959#41—3168no—
960#41—1584no—
961C2×Q8—28no—
962C2×Q8—48no—
963C2×Q8—48no—
964C2×Q8—794no—
965C2×Q8—794no—
966C2×Q8—791no—
967C2×Q8C23×D7914yes—
968C2×Q8C23×D7912yes—
969C2×Q8C23×D7914yes—
970C2×Q8C23×D7911yescharacteristic
971C2×Q8C23×D7918yes—
972C2×D4—3168no—
973C2×D4—3168no—
974C2×D4—3168no—
975C2×D4—31616no—
976C2×D4—31616no—
977C2×D4—3168no—
978C2×D4—794no—
979C2×D4—798no—
980C2×D4—7916no—
981C2×D4—7916no—
982C2×D4—794no—
983C2×D4—798no—
984C2×D4—792no—
985C2×D4—794no—
986C2×D4—798no—
987C2×D4—798no—
988C2×D4—7916no—
989C2×D4—798no—
990C2×D4—791no—
991C2×D4—794no—
992C2×D4—794no—
993C2×D4—1588no—
994C2×D4C23×D7914yes—
995C2×D4C23×D7912yes—
996C2×D4C23×D7914yes—
997C2×D4C23×D7912yes—
998C2×D4C23×D7911yescharacteristic
999C2×D4C23×D7918yes—
1000C22×C4—3168no—
1001C22×C4—3164no—
1002C22×C4—792no—
1003C22×C4—798no—
1004C22×C4—792no—
1005C22×C4—792no—
1006C22×C4—7916no—
1007C22×C4—7916no—
1008C22×C4—798no—
1009C22×C4—791no—
1010C22×C4—792no—
1011C22×C4—792no—
1012C22×C4—792no—
1013C22×C4—792no—
1014C22×C4—794no—
1015C22×C4—792no—
1016C22×C4—1584no—
1017C22×C4C23×D7912yes—
1018C22×C4C23×D7914yes—
1019C22×C4C23×D7914yes—
1020C22×C4C23×D7912yes—
1021C22×C4C23×D7914yes—
1022C22×C4C23×D7918yes—
1023C22×C4C23×D7918yes—
1024C22×C4C23×D7911yescharacteristic
1025C4⋊C4—798no—
1026C4⋊C4—7916no—
1027C4⋊C4—794no—
1028C4⋊C4—794no—
1029C4⋊C4—794no—
1030C4⋊C4—798no—
1031C4⋊C4—794no—
1032C4⋊C4—794no—
1033C4⋊C4—794no—
1034C4⋊C4—794no—
1035C4⋊C4—794no—
1036C4⋊C4—794no—
1037C4⋊C4—792no—
1038C4⋊C4—798no—
1039C4⋊C4—7916no—
1040C4⋊C4C23×D79116yes—
1041C4⋊C4C23×D7918yes—
1042C4⋊C4C23×D7914yes—
1043C4⋊C4C23×D7918yes—
1044C4⋊C4C23×D7912yes—
1045C4⋊C4C23×D7914yes—
1046C22⋊C4—794no—
1047C22⋊C4—798no—
1048C22⋊C4—792no—
1049C22⋊C4—794no—
1050C22⋊C4—794no—
1051C22⋊C4—798no—
1052C22⋊C4—794no—
1053C22⋊C4—794no—
1054C22⋊C4—7916no—
1055C22⋊C4—7916no—
1056C22⋊C4—7916no—
1057C22⋊C4—7916no—
1058C22⋊C4—7916no—
1059C22⋊C4—794no—
1060C22⋊C4—7916no—
1061C22⋊C4—794no—
1062C22⋊C4—798no—
1063C22⋊C4—794no—
1064C22⋊C4C23×D7912yes—
1065C22⋊C4C23×D79116yes—
1066C22⋊C4C23×D7918yes—
1067C22⋊C4C23×D7914yes—
1068C42—791no—
1069C42—792no—
1070C42—792no—
1071C42—791no—
1072C42—792no—
1073C42—792no—
1074C42—792no—
1075C42—798no—
1076C42—794no—
1077C42—794no—
1078C42—792no—
1079C42—7916no—
1080C42C23×D7911yescharacteristic
1081C42C23×D7911yescharacteristic
1082C42C23×D7912yes—
1083C42C23×D7914yes—
1084C42C23×D7912yes—
1085C23—3162no—
1086C23—3168no—
1087C23—3168no—
1088C23—31616no—
1089C23—792no—
1090C23—798no—
1091C23—792no—
1092C23—1582no—
1093C23—1588no—
1094C23C24×D7914yes—
1095C23C24×D7912yes—
1096C23C24×D7911yescharacteristic
1097Q8—28no—
1098Q8—28no—
1099Q8—22no—
1100Q8—24no—
1101Q8—48no—
1102Q8—3164no—
1103Q8—1582no—
1104Q8—1588no—
1105D4—28no—
1106D4—24no—
1107D4—24no—
1108D4—22no—
1109D4—28no—
1110D4—48no—
1111D4—3168no—
1112D4—31616no—
1113D4—3168no—
1114D4—3164no—
1115D4—3168no—
1116D4—31616no—
1117D4—31616no—
1118D4—3168no—
1119D4—3164no—
1120D4—3164no—
1121D4—1584no—
1122D4—1582no—
1123D4—1588no—
1124D4—1588no—
1125D4—15816no—
1126C2×C4—28no—
1127C2×C4—28no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—28no—
1131C2×C4—48no—
1132C2×C4—48no—
1133C2×C4—31616no—
1134C2×C4—3162no—
1135C2×C4—3162no—
1136C2×C4—3168no—
1137C2×C4—31616no—
1138C2×C4—3162no—
1139C2×C4—3168no—
1140C2×C4—792no—
1141C2×C4—794no—
1142C2×C4—792no—
1143C2×C4—798no—
1144C2×C4—792no—
1145C2×C4—792no—
1146C2×C4—1582no—
1147C2×C4—1584no—
1148C2×C4—1584no—
1149C2×C4—1584no—
1150C2×C4—1584no—
1151C2×C4—1584no—
1152C2×C4—1588no—
1153C2×C4#1457920614yes—
1154C2×C4C24×D7912yes—
1155C2×C4C24×D7914yes—
1156C2×C4C24×D7918yes—
1157C2×C4C24×D7912yes—
1158C2×C4C24×D7914yes—
1159C2×C4C24×D7911yescharacteristic
1160C2×C4C24×D7911yescharacteristic
1161C2×C4C24×D7912yes—
1162C22—22no—
1163C22—22no—
1164C22—24no—
1165C22—24no—
1166C22—28no—
1167C22—3164no—
1168C22—6328no—
1169C22—1588no—
1170C22—1582no—
1171C22—1582no—
1172C22—1582no—
1173C22—1582no—
1174C22—15816no—
1175C22—1584no—
1176C22—12648no—
1177C22C2×#1457920612yes—
1178C22C25×D7911yescharacteristic
1179C4—22no—
1180C4—24no—
1181C4—28no—
1182C4—24no—
1183C4—22no—
1184C4—1582no—
1185C4—1582no—
1186C4—1582no—
1187C4—1588no—
1188C4—1582no—
1189C4—1584no—
1190C4C2×#1457920612yes—
1191C4C2×#1457920612yes—
1192C4#1909940014yes—
1193C2—22no—
1194C2—44no—
1195C2—42no—
1196C2—3162no—
1197C2—3168no—
1198C2—3162no—
1199C2C22×#1457920611yescharacteristic
1200C2C2×#1909940012yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3499C2
hypercenter#3499D79
hypocenterC79#62836
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #23777976C2semidirect
2. #23777872C2semidirect
3. #23777773C2semidirect
4. #23777717C2semidirect
5. #23777405C2semidirect
6. #23777362C2semidirect
7. #23777335C2semidirect
8. #23777313C2semidirect
9. #23777299C2semidirect
10. #23777284C2semidirect
11. #23777276C2semidirect
12. #23777269C2semidirect
13. #23777194C2semidirect
14. #23777173C2semidirect
15. #23777055C2semidirect
16. #23777043C2semidirect
17. #23776695C2semidirect
18. #23776693C2semidirect
19. C2×#19099114C2semidirect
20. C79×#3499C2semidirect
22. C22×#11929625C22semidirect
23. #19099309C22semidirect
24. #19099303C22semidirect
25. #19099298C22semidirect
26. #19099296C22semidirect
27. #19099295C22semidirect
28. #19099288C22semidirect
29. #19099287C22semidirect
30. #19099287C22semidirect
31. #19099279C22semidirect
32. #19099274C22semidirect
33. #19099261C22semidirect
34. #19099261C22semidirect
35. #19099258C22semidirect
36. #19099248C22semidirect
37. #19099240C22semidirect
38. #19099236C22semidirect
39. #19099234C22semidirect
40. #19099234C22semidirect
41. #19099232C22semidirect
42. #19099232C22semidirect
43. #19099231C22semidirect
44. #19099224C22semidirect
45. #19099224C22semidirect
46. #19099224C22semidirect
47. #19099216C22semidirect
48. #19099215C22semidirect
49. #19099210C22semidirect
50. #19099209C22semidirect
51. #19099208C22semidirect
52. #19099206C22semidirect
53. #19099204C22semidirect
54. #19099201C22semidirect
55. #19099201C22semidirect
56. D4×D316C22semidirect
58. #19099187C22semidirect
59. #19099187C22semidirect
60. #19099186C22semidirect
61. #19099174C22semidirect
62. #19099168C22semidirect
63. #19099166C22semidirect
64. #19099165C22semidirect
65. #19099164C22semidirect
66. #19099159C22semidirect
67. #19099153C22semidirect
68. #19099149C22semidirect
69. #19099144C22semidirect
71. #19099137C22semidirect
72. #19099131C22semidirect
73. #19099129C22semidirect
75. #19099127C22semidirect
76. #19099127C22semidirect
77. #19099127C22semidirect
78. #19099124C22semidirect
79. #19099120C22semidirect
80. #19099118C22semidirect
81. #19099118C22semidirect
82. #19099117C22semidirect
83. #19099116C22semidirect
84. #19099114C22semidirect
85. #19099114C22semidirect
86. #19099114C22semidirect
87. #19099114C22semidirect
88. #19099114C22semidirect
89. #19099113C22semidirect
90. #19099111C22semidirect
91. #19099110C22semidirect
93. #19099109C22semidirect
95. #127×D79C22semidirect
96. #19099100C22semidirect
97. #19099099C22semidirect
98. #19099095C22semidirect
99. #19099095C22semidirect
100. #19099094C22semidirect
101. #19099093C22semidirect
102. #19099092C22semidirect
103. #19099091C22semidirect
104. C2×#14579150C22semidirect
105. C2×#14579150C22semidirect
107. #19099073C22semidirect
108. #19099072C22semidirect
109. #19099070C22semidirect
110. #19099070C22semidirect
111. #19099070C22semidirect
112. #123×D79C22semidirect
113. C2×#14579136C22semidirect
114. #19099044C22semidirect
115. #19099041C22semidirect
116. #19099037C22semidirect
117. #19099035C22semidirect
118. #41×Dic79C22semidirect
120. C4×#11929624C22semidirect
121. C4×#11929623C22semidirect
122. C2×#14579123C22semidirect
123. C2×C42×D79C22semidirect
124. C2×2−1+4×C79C22semidirect
125. D4×Q8×C79C22semidirect
126. #547×C79C22semidirect
127. #547×C79C22semidirect
128. #536×C79C22semidirect
129. #536×C79C22semidirect
131. #532×C79C22semidirect
132. C2×C4⋊Q8×C79C22semidirect
133. C2×C4⋊Q8×C79C22semidirect
134. C4×#41×C79C22semidirect
614. #3499D79semidirect
621. C79#62836semidirect
622. C2×2−1+4C2×D79semidirect
646. D4×Q8C2×D79semidirect
652. #547C2×D79semidirect
653. #547C2×D79semidirect
677. #536C2×D79semidirect
678. #536C2×D79semidirect
702. #532C2×D79semidirect
703. C2×C4⋊Q8C2×D79semidirect
704. C2×C4⋊Q8C2×D79semidirect
733. C4×#41C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779762
#237778722
#237777732
#237777172
#237774052
#237773622
#237773352
#237773132
#237772992
#237772842
#237772762
#237772692
#237771942
#237771732
#237770552
#237770432
#237766952
#237766932
C2×#190991142
C79×#34992
#6283679