Finite Group Databasebeta

← #35197208

Subgroups — #35197208

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#23777988C218yesmaximal, complemented
2#23777871C214yesmaximal, complemented
3#23777772C214yesmaximal, complemented
4#23777716C218yesmaximal, complemented
5#23777404C214yesmaximal, complemented
6#23777363C214yesmaximal, complemented
7#23777344C218yesmaximal, complemented
8#23777311C214yesmaximal, complemented
9#23777298C212yesmaximal, complemented
10#23777286C211yesmaximal, characteristic, complemented
11#23777276C211yesmaximal, characteristic, complemented
12#23777276C214yesmaximal, complemented
13#23777187C212yesmaximal, complemented
14#23777185C211yesmaximal, characteristic, complemented
15#23777178C211yesmaximal, characteristic, complemented
16#23777054C212yesmaximal, complemented
17#23777042C212yesmaximal, complemented
18#23776696C211yesmaximal, characteristic, complemented
19C2×#19099113C211yesmaximal, characteristic, complemented
20C79×#3444C211yesmaximal, characteristic, complemented
21C2×#14579208C2212yescomplemented
22C2×#14579207C2212yes—
23C22×#11929624C2212yescomplemented
24#19099309C22116yescomplemented
25#19099301C22116yescomplemented
26#19099298C2218yescomplemented
27#19099298C2218yescomplemented
28#19099298C2214yescomplemented
29#19099291C2214yescomplemented
30#19099286C2218yescomplemented
31#19099283C2214yescomplemented
32#19099278C2218yescomplemented
33#19099273C2218yescomplemented
34#19099264C22116yescomplemented
35#19099259C2218yescomplemented
36#19099259C2218yescomplemented
37#19099253C2218yescomplemented
38#19099240C22116yescomplemented
39#19099238C22116yescomplemented
40#19099235C2214yescomplemented
41#19099234C2218yescomplemented
42#19099234C2218yescomplemented
43#19099234C2214yescomplemented
44#19099231C2218yescomplemented
45Q8×D316C2214yescomplemented
46#19099223C2218yescomplemented
47#19099222C2218yescomplemented
48#19099222C2218yescomplemented
49#19099218C2218yescomplemented
50#19099217C2218yescomplemented
51#19099217C2214yescomplemented
52#19099215C2218yescomplemented
53#19099210C2218yescomplemented
54#19099209C2218yescomplemented
55#19099209C2218yescomplemented
56#19099209C2218yescomplemented
57#19099209C2218yescomplemented
58#19099209C2218yescomplemented
59#19099202C22116yescomplemented
60D4×D316C2218yes—
61D4×D316C2214yescomplemented
62#19099187C2218yescomplemented
63#19099184C2218yescomplemented
64#19099184C2218yescomplemented
65#19099175C2214yescomplemented
66#19099168C2218yescomplemented
67#19099168C2218yescomplemented
68#19099168C2214yescomplemented
69#19099165C22116yescomplemented
70#19099161C22116yescomplemented
71#19099149C22116yescomplemented
72#19099147C22116yescomplemented
73#19099141C2218yescomplemented
74#19099139C2212yescomplemented
75#19099139C2214yescomplemented
76#19099138C2214yescomplemented
77#19099134C2212yes—
78#19099132C2212yes—
79#19099132C2214yescomplemented
80#19099128C2218yescomplemented
81#19099127C2212yescomplemented
82#19099127C2218yescomplemented
83#19099126C2214yescomplemented
84#19099123C2218yescomplemented
85#19099120C2214yescomplemented
86#19099120C2211yescharacteristic, complemented
87#19099120C2212yescomplemented
88#19099113C2211yescharacteristic
89#19099113C2212yescomplemented
90#19099113C2214yescomplemented
91#19099113C2214yescomplemented
92#19099113C2214yescomplemented
93#19099113C2214yescomplemented
94#19099113C2212yescomplemented
95#19099113C2214yescomplemented
96#19099113C2212yescomplemented
97#19099112C2214yescomplemented
98C2×#14579161C2211yescharacteristic, complemented
99C2×#14579161C2212yescomplemented
100C2×#14579158C2211yescharacteristic
101C2×#14579158C2212yescomplemented
102#19099098C2218yescomplemented
103#19099097C2214yescomplemented
104#19099097C2214yescomplemented
105#19099097C2214yescomplemented
106C2×#14579149C2212yescomplemented
107#124×D79C2214yescomplemented
108#19099074C2212yescomplemented
109#19099074C2214yescomplemented
110#19099071C2218yescomplemented
111#123×D79C2218yescomplemented
112C2×#14579135C2214yescomplemented
113#19099043C2218yescomplemented
114#19099040C2212yescomplemented
115#19099037C2212yescomplemented
116#19099037C2218yescomplemented
117C4×#11929624C2212yescomplemented
118C4×#11929624C2214yescomplemented
119C2×C4×D316C2214yescomplemented
120#533×C79C2211yescharacteristic, complemented
121#533×C79C2212yescomplemented
122#532×C79C2211yescharacteristic
123#532×C79C2212yescomplemented
124#529×C79C2214yescomplemented
125#529×C79C2212yescomplemented
126#529×C79C2212yescomplemented
127#529×C79C2214yescomplemented
128#525×C79C2211yescharacteristic
129#525×C79C2211yescharacteristic, complemented
130#525×C79C2214yescomplemented
131C4×#41×C79C2211yescharacteristic
132C4×#41×C79C2214yescomplemented
133C4×#41×C79C2211yescharacteristic, complemented
134C22×C42×C79C2211yescharacteristic, complemented
135#14579208—48no—
136#14579207—48no—
137C2×#11929625C2314yes—
138C2×#11929624—48no—
139C2×#11929624C2312yes—
140C2×#11929624C2314yes—
141C2×#11929624C2314yes—
142C2×#11929624C2318yes—
143C2×#11929624C2314yes—
144C2×#11929624C2318yes—
145C2×#11929624C2318yes—
146C2×#11929623C2318yes—
147C2×#11929623C2314yes—
148C22×Dic158C2312yes—
149C22×Dic158C2314yes—
150C2×Q8×D79C2314yes—
151C22×D316C2312yes—
152C22×D316C2314yes—
153C22×D316C2314yes—
154C22×D316C2318yes—
155C22×C22⋊D79C2314yes—
156C2×D4×D79C2318yes—
157C2×D4×D79C2314yes—
158C22×C4×D79C2314yes—
159#14579161C2312yes—
160#14579161C2314yes—
161#14579161C2318yes—
162#14579161C2314yes—
163#14579161C2311yescharacteristic
164#14579161C2312yes—
165#14579161C2312yes—
166#14579159C2314yes—
167#14579158C2318yes—
168#14579158C2312yes—
169#14579158C2314yes—
170#14579158C2314yes—
171#14579158C2312yes—
172#14579158C2311yescharacteristic
173#14579157C23116yes—
174#14579157C2314yes—
175#14579156C23116yes—
176#14579156C23116yes—
177#14579155C2318yes—
178#14579154C23116yes—
179#14579153C2312yes—
180#14579153C2318yes—
181#14579153C2314yes—
182#14579151C23116yes—
183#14579150C2314yes—
184#14579150C23116yes—
185#14579149C2314yes—
186#14579149C2314yes—
187#14579149C2312yes—
188#14579149C2318yes—
189#14579149C2314yes—
190#14579149C2318yes—
191#14579149C2314yes—
192#14579149C2314yes—
193#14579148C2314yes—
194#14579147C23116yes—
195#14579147C23116yes—
196#14579146C23116yes—
197#14579146C23116yes—
198#14579146C23116yes—
199#14579146C23116yes—
200#14579146C23116yes—
201#14579145C23116yes—
202#14579145C2318yes—
203#14579144C2318yes—
204#14579144C2314yes—
205#14579143C23116yes—
206#14579143C23116yes—
207#14579142C2318yes—
208#14579141C23116yes—
209#14579141C2318yes—
210#14579140C2314yes—
211#14579140C2318yes—
212#14579140C2318yes—
213#14579140C2314yes—
214#14579140C2314yes—
215#14579139C23116yes—
216#14579139C23116yes—
217#14579137C23116yes—
218#14579136C23116yes—
219#14579136C2318yes—
220#14579135C2318yes—
221#14579135C2318yes—
222#14579135C2318yes—
223#14579135C2314yes—
224#14579135C2318yes—
225#14579135C2318yes—
226#14579135C2318yes—
227#14579135C2314yes—
228#14579135C2314yes—
229#14579135C2318yes—
230#14579135C2318yes—
231#14579134C23116yes—
232#14579134C23116yes—
233#14579134C23116yes—
234#14579134C23116yes—
235#14579134C23116yes—
236#14579133C23116yes—
237#14579133C23116yes—
238#14579132C23116yes—
239#14579131C23116yes—
240#14579131C2318yes—
241#14579130C2314yes—
242#14579129C23116yes—
243#14579129C23116yes—
244#14579129C2318yes—
245C4×Dic158C2318yes—
246C4×Dic158C2314yes—
247C4×Dic158C2318yes—
248C4×Dic158C2314yes—
249C4×Dic158C2314yes—
250#14579126C2318yes—
251C4×D316C2318yes—
252C4×D316C2314yes—
253C4×D316C2318yes—
254C4×D316C2318yes—
255C4×D316C2318yes—
256C4×D316C2318yes—
257C4×D316C2318yes—
258C4×D316C2314yes—
259C4×D316C2314yes—
260C4×D316C2318yes—
261C4×D316C2318yes—
262#14579123C23116yes—
263#14579123C23116yes—
264#14579123C2318yes—
265C4×C22⋊D79C2318yes—
266C4×C22⋊D79C2318yes—
267C4×C22⋊D79C2318yes—
268(C22⋊D79)⋊C4C23116yes—
269(C22⋊D79)⋊C4C23116yes—
270#14579120C2318yes—
271#14579120C2314yes—
272#14579120C2312yes—
273#14579119C23116yes—
274#14579118C2314yes—
275#14579118C2318yes—
276#14579117C2318yes—
277C2×C4⋊Dic79C2318yes—
278C2×C4⋊Dic79C2314yes—
279C4⋊C4×D79C23116yes—
280C2×(C2×D79)⋊C4C2318yes—
281C22⋊C4×D79C23116yes—
282C22⋊C4×D79C23116yes—
283C22⋊C4×D79C2318yes—
284C42×D79C2314yes—
285C2×#41×C79C2311yescharacteristic
286C2×#41×C79C2311yescharacteristic
287C2×#41×C79C2314yes—
288C23×C4×C79C2311yescharacteristic
289C23×C4×C79C2312yes—
290C4⋊Q8×C79C2311yescharacteristic
291C4⋊Q8×C79C2312yes—
292#127×C79C2311yescharacteristic
293#126×C79C2314yes—
294#126×C79C2314yes—
295#125×C79C2314yes—
296#125×C79C2312yes—
297#124×C79C2314yes—
298#124×C79C2311yescharacteristic
299#124×C79C2311yescharacteristic
300#123×C79C2314yes—
301#123×C79C2314yes—
302#123×C79C2312yes—
303#123×C79C2312yes—
304C22⋊Q8×C79C2312yes—
305C22⋊Q8×C79C2312yes—
306C22⋊Q8×C79C2314yes—
307C22⋊Q8×C79C2314yes—
308#121×C79C2314yes—
309#121×C79C2312yes—
310#121×C79C2312yes—
311#121×C79C2314yes—
312#120×C79C2312yes—
313#120×C79C2312yes—
314C4×Q8×C79C2312yes—
315C4×Q8×C79C2312yes—
316C4×Q8×C79C2314yes—
317C4×Q8×C79C2314yes—
318C4×D4×C79C2314yes—
319C4×D4×C79C2312yes—
320C4×D4×C79C2314yes—
321C4×D4×C79C2314yes—
322C4×D4×C79C2314yes—
323C4×D4×C79C2314yes—
324C4×D4×C79C2314yes—
325C4×D4×C79C2312yes—
326C4×D4×C79C2314yes—
327C4×D4×C79C2314yes—
328#117×C79C2312yes—
329#117×C79C2311yescharacteristic
330#117×C79C2314yes—
331#117×C79C2314yes—
332#117×C79C2312yes—
333#117×C79C2314yes—
334#117×C79C2311yescharacteristic
335C2×C42×C79C2311yescharacteristic
336C2×C42×C79C2312yes—
337C2×C42×C79C2312yes—
338C2×C42×C79C2312yes—
339C2×C42×C79C2312yes—
340C2×C42×C79C2311yescharacteristic
341C2×C42×C79C2312yes—
342C2×C42×C79C2312yes—
343C2×C42×C79C2312yes—
344C23×D79C2414yes—
345C23×D79C2418yes—
346#11929625—48no—
347#11929624—28no—
348#11929624—416no—
349#11929624—416no—
350#11929624—48no—
351#11929624—416no—
352#11929624—48no—
353#11929624—48no—
354#11929623—416no—
355#11929623—48no—
356C2×Dic158—28no—
357C2×Dic158—48no—
358C2×Dic158C2414yes—
359C2×Dic158C2414yes—
360C2×Dic158C2412yes—
361C2×Dic158C2414yes—
362C2×Dic158C2418yes—
363Q8×D79—48no—
364C2×D316—28no—
365C2×D316—48no—
366C2×D316—48no—
367C2×D316—416no—
368C2×D316C2414yes—
369C2×D316C2412yes—
370C2×D316C2414yes—
371C2×D316C2418yes—
372C2×D316C2414yes—
373C2×D316C2418yes—
374C2×D316C24116yes—
375C2×D316C2418yes—
376C2×C22⋊D79—48no—
377C2×C22⋊D79C2414yes—
378C2×C22⋊D79C2418yes—
379C2×C22⋊D79C24116yes—
380C2×C22⋊D79C24116yes—
381C2×C22⋊D79C2418yes—
382C2×C22⋊D79C2418yes—
383D4×D79—416no—
384D4×D79—48no—
385C22×Dic79C2414yes—
386C22×Dic79C2418yes—
387C2×C4×D79—48no—
388C2×C4×D79C2414yes—
389C2×C4×D79C2418yes—
390C2×C4×D79C24116yes—
391C2×C4×D79C2418yes—
392C2×C4×D79C2418yes—
393C2×C4×D79C24116yes—
394C4⋊Dic79C24116yes—
395C4⋊Dic79C2414yes—
396C4⋊Dic79C2418yes—
397C4⋊Dic79C2418yes—
398C4⋊Dic79C2414yes—
399C4⋊Dic79C2414yes—
400Dic79⋊C4C2418yes—
401Dic79⋊C4C24116yes—
402Dic79⋊C4C24116yes—
403Dic79⋊C4C2418yes—
404Dic79⋊C4C2418yes—
405C22⋊Dic79C2414yes—
406C22⋊Dic79C24116yes—
407C22⋊Dic79C2418yes—
408(C2×D79)⋊C4C2418yes—
409(C2×D79)⋊C4C24116yes—
410(C2×D79)⋊C4C24116yes—
411(C2×D79)⋊C4C24116yes—
412(C2×D79)⋊C4C24116yes—
413(C2×D79)⋊C4C24116yes—
414(C2×D79)⋊C4C2418yes—
415(C2×D79)⋊C4C2418yes—
416(C2×D79)⋊C4C24116yes—
417C4×Dic79C2418yes—
418C4×Dic79C2414yes—
419C4×Dic79C24116yes—
420C24×C79C2411yescharacteristic
421#41×C79—24no—
422#41×C79—24no—
423#41×C79—48no—
424C2×Q8×C79C2411yescharacteristic
425C2×Q8×C79C2411yescharacteristic
426C2×Q8×C79C2414yes—
427C2×D4×C79C2412yes—
428C2×D4×C79C2411yescharacteristic
429C2×D4×C79C2412yes—
430C2×D4×C79C2411yescharacteristic
431C2×D4×C79C2414yes—
432C2×D4×C79C2414yes—
433C2×D4×C79C2414yes—
434C22×C4×C79—24no—
435C22×C4×C79—44no—
436C22×C4×C79C2412yes—
437C22×C4×C79C2412yes—
438C22×C4×C79C2412yes—
439C22×C4×C79C2412yes—
440C22×C4×C79C2414yes—
441C22×C4×C79C2412yes—
442C22×C4×C79C2412yes—
443C22×C4×C79C2412yes—
444C22×C4×C79C2411yescharacteristic
445C22×C4×C79C2414yes—
446C22×C4×C79C2412yes—
447C22×C4×C79C2412yes—
448C22×C4×C79C2412yes—
449C22×C4×C79C2411yescharacteristic
450C4⋊C4×C79C2412yes—
451C4⋊C4×C79C2412yes—
452C4⋊C4×C79C2414yes—
453C4⋊C4×C79C2414yes—
454C4⋊C4×C79C2414yes—
455C4⋊C4×C79C2414yes—
456C4⋊C4×C79C2414yes—
457C4⋊C4×C79C2414yes—
458C4⋊C4×C79C2414yes—
459C4⋊C4×C79C2414yes—
460C22⋊C4×C79C2412yes—
461C22⋊C4×C79C2412yes—
462C22⋊C4×C79C2414yes—
463C22⋊C4×C79C2414yes—
464C22⋊C4×C79C2414yes—
465C22⋊C4×C79C2414yes—
466C22⋊C4×C79C2414yes—
467C22⋊C4×C79C2414yes—
468C22⋊C4×C79C2414yes—
469C22⋊C4×C79C2414yes—
470C42×C79C2411yescharacteristic
471C42×C79C2412yes—
472C42×C79C2411yescharacteristic
473C42×C79C2412yes—
474C42×C79C2412yes—
475C42×C79C2412yes—
476C42×C79C2411yescharacteristic
477C42×C79C2412yes—
478C42×C79C2412yes—
479C42×C79C2411yescharacteristic
480C42×C79C2412yes—
481C42×C79C2414yes—
482C42×C79C2414yes—
483C42×C79C2412yes—
484C23×C79—22no—
485C23×C79—42no—
486C23×C79C2512yes—
487C23×C79C2512yes—
488C23×C79C2512yes—
489C23×C79C2511yescharacteristic
490C22×D79—28no—
491C22×D79—48no—
492C22×D79—48no—
493C22×D79—416no—
494C22×D79C2514yes—
495C22×D79C2518yes—
496Q8×C79—22no—
497Q8×C79—22no—
498Q8×C79—44no—
499D4×C79—24no—
500D4×C79—24no—
501D4×C79—22no—
502D4×C79—22no—
503D4×C79—44no—
504D4×C79—44no—
505D4×C79—44no—
506C2×C4×C79—22no—
507C2×C4×C79—24no—
508C2×C4×C79—24no—
509C2×C4×C79—24no—
510C2×C4×C79—24no—
511C2×C4×C79—24no—
512C2×C4×C79—28no—
513C2×C4×C79—24no—
514C2×C4×C79—28no—
515C2×C4×C79—24no—
516C2×C4×C79—42no—
517C2×C4×C79—42no—
518C2×C4×C79—42no—
519C2×C4×C79H(5,𝔽2)14yes—
520C2×C4×C79C2512yes—
521C2×C4×C79C2514yes—
522C2×C4×C79C2512yes—
523C2×C4×C79C2514yes—
524C2×C4×C79C2512yes—
525C2×C4×C79C2512yes—
526C2×C4×C79C2512yes—
527C2×C4×C79C2512yes—
528C2×C4×C79C2511yescharacteristic
529C2×C4×C79C2511yescharacteristic
530C2×C4×C79C2512yes—
531C22⋊D79—28no—
532C22⋊D79—48no—
533C22⋊D79—416no—
534C22⋊D79—48no—
535C22⋊D79—48no—
536C22⋊D79—416no—
537C2×Dic79—28no—
538C2×Dic79—48no—
539C2×Dic79C2518yes—
540C2×Dic79C2514yes—
541C2×Dic79C2518yes—
542D316—28no—
543D316—28no—
544D316—24no—
545D316—216no—
546D316—28no—
547D316—48no—
548D316—48no—
549D316—416no—
550C4×D79—28no—
551C4×D79—416no—
552C4×D79—48no—
553C4×D79—48no—
554C4×D79—48no—
555C4×D79—416no—
556Dic158—28no—
557Dic158—28no—
558Dic158—24no—
559Dic158—28no—
560Dic158—48no—
561C22×C79—22no—
562C22×C79—22no—
563C22×C79—22no—
564C22×C79—22no—
565C22×C79—22no—
566C22×C79—24no—
567C22×C79—22no—
568C22×C79—24no—
569C22×C79—44no—
570C22×C79C2×H(5,𝔽2)12yes—
571C22×C79C2611yescharacteristic
572C2×D79—24no—
573C2×D79—28no—
574C2×D79—216no—
575C2×D79—28no—
576C2×D79—88no—
577C2×D79—168no—
578C4×C79—22no—
579C4×C79—22no—
580C4×C79—22no—
581C4×C79—22no—
582C4×C79—22no—
583C4×C79—22no—
584C4×C79—24no—
585C4×C79—24no—
586C4×C79C2×H(5,𝔽2)12yes—
587C4×C79C2×H(5,𝔽2)12yes—
588C4×C79#58514yes—
589Dic79—24no—
590Dic79—28no—
591Dic79—28no—
592#62836—791nomaximal, Sylow
593C2×C79—22no—
594C2×C79—42no—
595C2×C79—42no—
596C2×C79—42no—
597C2×C79C22×H(5,𝔽2)11yescharacteristic
598C2×C79C2×#58512yes—
599D79—48no—
600D79—44no—
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—791no—
612#3508—794no—
613#3500—792no—
614#3499—791no—
615#3498—791no—
616#3487—792no—
617#3485—792no—
618#3444—791no—
619#3444D7911yescharacteristic, complemented
620C2×#532—791no—
621C79#6283611yescharacteristic, complemented, Sylow
622C2×2−1+4—792no—
623C2×H(5,𝔽2)—792no—
624C22×#41—792no—
625#562—7916no—
626#560—7916no—
627#559—798no—
628#559—798no—
629#559—794no—
630#557—794no—
631#556—798no—
632#556—794no—
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—794no—
643#550—798no—
644#550—798no—
645#550—794no—
646D4×Q8—794no—
647#548—798no—
648#548—798no—
649#548—798no—
650#547—798no—
651#547—798no—
652#547—794no—
653#547—798no—
654#546—7916no—
655#546—798no—
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#536—792no—
678#536—794no—
679#535—792no—
680#535—798no—
681#535—794no—
682#535—798no—
683#535—792no—
684#535—794no—
685#534—798no—
686#533—791no—
687#533—792no—
688#533—794no—
689#533C2×D7911yescharacteristic, complemented
690#533C2×D7912yescomplemented
691#532—794no—
692#532—794no—
693#532—794no—
694#532—794no—
695#532—794no—
696#532—791no—
697#532—792no—
698#532—792no—
699#532—792no—
700#532—794no—
701#532C2×D7911yescharacteristic
702#532C2×D7912yescomplemented
703C2×C4⋊Q8—791no—
704C2×C4⋊Q8—792no—
705C2×#127—791no—
706C2×#127—792no—
707#529—798no—
708#529—794no—
709#529—794no—
710#529—794no—
711#529C2×D7914yescomplemented
712#529C2×D7912yescomplemented
713#529C2×D7912yescomplemented
714#529C2×D7914yescomplemented
715C2×#124—794no—
716C2×#124—792no—
717#525—792no—
718#525—794no—
719#525—798no—
720#525C2×D7911yescharacteristic
721#525C2×D7911yescharacteristic, complemented
722#525C2×D7914yescomplemented
723C2×#123—798no—
724C2×#121—794no—
725#520—798no—
726#519—792no—
727#518—792no—
728#518—798no—
729C4×#41—792no—
730C4×#41—794no—
731C4×#41C2×D7911yescharacteristic
732C4×#41C2×D7911yescharacteristic, complemented
733C4×#41C2×D7914yescomplemented
734C2×C4×D4—794no—
735C22×C42C2×D7911yescharacteristic, complemented
7362−1+4—3168no—
737H(5,𝔽2)—3168no—
738C2×#41—3168no—
739C2×#41—794no—
740C2×#41—798no—
741C2×#41—794no—
742C2×#41—794no—
743C2×#41—798no—
744C2×#41—798no—
745C2×#41—798no—
746C2×#41—794no—
747C2×#41—794no—
748C2×#41—792no—
749C2×#41C22×D7911yescharacteristic
750C2×#41C22×D7911yescharacteristic
751C2×#41C22×D7914yes—
752C22×Q8—794no—
753C22×Q8—794no—
754C22×Q8—792no—
755C22×D4—794no—
756C22×D4—798no—
757C22×D4—794no—
758C22×D4—794no—
759C22×D4—798no—
760C22×D4—794no—
761C22×D4—792no—
762C23×C4—794no—
763C23×C4C22×D7911yescharacteristic
764C23×C4C22×D7912yes—
765C4⋊Q8—794no—
766C4⋊Q8—792no—
767C4⋊Q8—791no—
768C4⋊Q8—792no—
769C4⋊Q8—794no—
770C4⋊Q8—794no—
771C4⋊Q8—798no—
772C4⋊Q8—792no—
773C4⋊Q8C22×D7911yescharacteristic
774C4⋊Q8C22×D7912yes—
775#127—794no—
776#127—7916no—
777#127—792no—
778#127—791no—
779#127—792no—
780#127—794no—
781#127—794no—
782#127—798no—
783#127C22×D7911yescharacteristic
784#126—7916no—
785#126—7916no—
786#126—7916no—
787#126—798no—
788#126C22×D7914yes—
789#126C22×D7914yes—
790#125—7916no—
791#125—792no—
792#125—794no—
793#125—798no—
794#125C22×D7912yes—
795#125C22×D7914yes—
796#124—794no—
797#124—7916no—
798#124—794no—
799#124—7916no—
800#124—7916no—
801#124—794no—
802#124—794no—
803#124—798no—
804#124—792no—
805#124—794no—
806#124—794no—
807#124—794no—
808#124—798no—
809#124C22×D7911yescharacteristic
810#124C22×D7911yescharacteristic
811#124C22×D7914yes—
812#123—798no—
813#123—794no—
814#123—798no—
815#123—7916no—
816#123—7916no—
817#123—7916no—
818#123—7916no—
819#123—7916no—
820#123—798no—
821#123—7916no—
822#123—7916no—
823#123—7916no—
824#123C22×D7912yes—
825#123C22×D7912yes—
826#123C22×D7914yes—
827#123C22×D7914yes—
828C22⋊Q8—7916no—
829C22⋊Q8—794no—
830C22⋊Q8—794no—
831C22⋊Q8—794no—
832C22⋊Q8—798no—
833C22⋊Q8—798no—
834C22⋊Q8—7916no—
835C22⋊Q8—798no—
836C22⋊Q8—7916no—
837C22⋊Q8—7916no—
838C22⋊Q8C22×D7912yes—
839C22⋊Q8C22×D7912yes—
840C22⋊Q8C22×D7914yes—
841C22⋊Q8C22×D7914yes—
842#121—7916no—
843#121—7916no—
844#121—7916no—
845#121—798no—
846#121—798no—
847#121—798no—
848#121—798no—
849#121—794no—
850#121—794no—
851#121—794no—
852#121—798no—
853#121—798no—
854#121—798no—
855#121—798no—
856#121—798no—
857#121—7916no—
858#121—7916no—
859#121—7916no—
860#121—7916no—
861#121—7916no—
862#121—7916no—
863#121C22×D7912yes—
864#121C22×D7914yes—
865#121C22×D7912yes—
866#121C22×D7914yes—
867#120—794no—
868#120—798no—
869#120—7916no—
870#120—7916no—
871#120—798no—
872#120—7916no—
873#120C22×D7912yes—
874#120C22×D7912yes—
875C4×Q8—798no—
876C4×Q8—794no—
877C4×Q8—794no—
878C4×Q8—794no—
879C4×Q8—798no—
880C4×Q8—798no—
881C4×Q8C22×D7912yes—
882C4×Q8C22×D7912yes—
883C4×Q8C22×D7914yes—
884C4×Q8C22×D7914yes—
885C4×D4—798no—
886C4×D4—798no—
887C4×D4—798no—
888C4×D4—7916no—
889C4×D4—7916no—
890C4×D4—798no—
891C4×D4—7916no—
892C4×D4—7916no—
893C4×D4—798no—
894C4×D4—798no—
895C4×D4—798no—
896C4×D4—798no—
897C4×D4—794no—
898C4×D4—794no—
899C4×D4—794no—
900C4×D4—798no—
901C4×D4—798no—
902C4×D4—798no—
903C4×D4—798no—
904C4×D4C22×D7914yes—
905C4×D4C22×D7912yes—
906C4×D4C22×D7914yes—
907C4×D4C22×D7914yes—
908C4×D4C22×D7914yes—
909C4×D4C22×D7914yes—
910C4×D4C22×D7914yes—
911C4×D4C22×D7914yes—
912C4×D4C22×D7914yes—
913C4×D4C22×D7912yes—
914#117—792no—
915#117—794no—
916#117—798no—
917#117—7916no—
918#117—798no—
919#117—794no—
920#117—798no—
921#117C22×D7911yescharacteristic
922#117C22×D7912yes—
923#117C22×D7911yescharacteristic
924#117C22×D7914yes—
925#117C22×D7914yes—
926#117C22×D7914yes—
927#117C22×D7912yes—
928C2×C4⋊C4—794no—
929C2×C4⋊C4—798no—
930C2×C4⋊C4—7916no—
931C2×C22⋊C4—798no—
932C2×C22⋊C4—798no—
933C2×C22⋊C4—7916no—
934C2×C22⋊C4—7916no—
935C2×C42—794no—
936C2×C42C22×D7912yes—
937C2×C42C22×D7911yescharacteristic
938C2×C42C22×D7912yes—
939C2×C42C22×D7912yes—
940C2×C42C22×D7911yescharacteristic
941C2×C42C22×D7912yes—
942C2×C42C22×D7912yes—
943C2×C42C22×D7912yes—
944C2×C42C22×D7912yes—
945C24—798no—
946C24—794no—
947C24C23×D7911yescharacteristic
948#41—24no—
949#41—24no—
950#41—48no—
951#41—31616no—
952#41—31616no—
953#41—3168no—
954#41—31616no—
955#41—3168no—
956#41—3168no—
957#41—3168no—
958#41—31616no—
959#41—3168no—
960#41—1588no—
961C2×Q8—3168no—
962C2×Q8—3168no—
963C2×Q8—798no—
964C2×Q8—794no—
965C2×Q8—794no—
966C2×Q8—792no—
967C2×Q8—794no—
968C2×Q8—1588no—
969C2×Q8C23×D7911yescharacteristic
970C2×Q8C23×D7911yescharacteristic
971C2×Q8C23×D7914yes—
972C2×D4—3168no—
973C2×D4—31616no—
974C2×D4—3168no—
975C2×D4—31616no—
976C2×D4—3168no—
977C2×D4—3168no—
978C2×D4—798no—
979C2×D4—7916no—
980C2×D4—798no—
981C2×D4—798no—
982C2×D4—7916no—
983C2×D4—794no—
984C2×D4—798no—
985C2×D4—7916no—
986C2×D4—798no—
987C2×D4—798no—
988C2×D4—794no—
989C2×D4—794no—
990C2×D4—792no—
991C2×D4—794no—
992C2×D4—1588no—
993C2×D4C23×D7912yes—
994C2×D4C23×D7912yes—
995C2×D4C23×D7911yescharacteristic
996C2×D4C23×D7911yescharacteristic
997C2×D4C23×D7914yes—
998C2×D4C23×D7914yes—
999C2×D4C23×D7914yes—
1000C22×C4—24no—
1001C22×C4—44no—
1002C22×C4—3168no—
1003C22×C4—798no—
1004C22×C4—798no—
1005C22×C4—7916no—
1006C22×C4—798no—
1007C22×C4—7916no—
1008C22×C4—798no—
1009C22×C4—794no—
1010C22×C4—794no—
1011C22×C4C23×D7912yes—
1012C22×C4C23×D7912yes—
1013C22×C4C23×D7912yes—
1014C22×C4C23×D7912yes—
1015C22×C4C23×D7912yes—
1016C22×C4C23×D7911yescharacteristic
1017C22×C4C23×D7914yes—
1018C22×C4C23×D7914yes—
1019C22×C4C23×D7912yes—
1020C22×C4C23×D7912yes—
1021C22×C4C23×D7912yes—
1022C22×C4C23×D7912yes—
1023C22×C4C23×D7912yes—
1024C22×C4C23×D7911yescharacteristic
1025C4⋊C4—798no—
1026C4⋊C4—7916no—
1027C4⋊C4—798no—
1028C4⋊C4—798no—
1029C4⋊C4—7916no—
1030C4⋊C4—798no—
1031C4⋊C4—794no—
1032C4⋊C4—7916no—
1033C4⋊C4—798no—
1034C4⋊C4—794no—
1035C4⋊C4—794no—
1036C4⋊C4C23×D7914yes—
1037C4⋊C4C23×D7914yes—
1038C4⋊C4C23×D7912yes—
1039C4⋊C4C23×D7914yes—
1040C4⋊C4C23×D7914yes—
1041C4⋊C4C23×D7912yes—
1042C4⋊C4C23×D7914yes—
1043C4⋊C4C23×D7914yes—
1044C4⋊C4C23×D7914yes—
1045C4⋊C4C23×D7914yes—
1046C22⋊C4—794no—
1047C22⋊C4—7916no—
1048C22⋊C4—798no—
1049C22⋊C4—798no—
1050C22⋊C4—7916no—
1051C22⋊C4—7916no—
1052C22⋊C4—7916no—
1053C22⋊C4—7916no—
1054C22⋊C4—7916no—
1055C22⋊C4—7916no—
1056C22⋊C4—798no—
1057C22⋊C4—798no—
1058C22⋊C4C23×D7912yes—
1059C22⋊C4C23×D7914yes—
1060C22⋊C4C23×D7914yes—
1061C22⋊C4C23×D7912yes—
1062C22⋊C4C23×D7914yes—
1063C22⋊C4C23×D7914yes—
1064C22⋊C4C23×D7914yes—
1065C22⋊C4C23×D7914yes—
1066C22⋊C4C23×D7914yes—
1067C22⋊C4C23×D7914yes—
1068C42—798no—
1069C42—794no—
1070C42—7916no—
1071C42C23×D7911yescharacteristic
1072C42C23×D7911yescharacteristic
1073C42C23×D7912yes—
1074C42C23×D7911yescharacteristic
1075C42C23×D7912yes—
1076C42C23×D7911yescharacteristic
1077C42C23×D7912yes—
1078C42C23×D7912yes—
1079C42C23×D7912yes—
1080C42C23×D7912yes—
1081C42C23×D7912yes—
1082C42C23×D7914yes—
1083C42C23×D7914yes—
1084C42C23×D7912yes—
1085C23—22no—
1086C23—42no—
1087C23—3168no—
1088C23—3168no—
1089C23—31616no—
1090C23—798no—
1091C23—794no—
1092C23—1588no—
1093C23C24×D7912yes—
1094C23C24×D7912yes—
1095C23C24×D7912yes—
1096C23C24×D7911yescharacteristic
1097Q8—22no—
1098Q8—22no—
1099Q8—44no—
1100Q8—3168no—
1101Q8—1584no—
1102Q8—1588no—
1103Q8—1588no—
1104Q8—1588no—
1105D4—24no—
1106D4—24no—
1107D4—22no—
1108D4—22no—
1109D4—44no—
1110D4—44no—
1111D4—44no—
1112D4—3168no—
1113D4—3168no—
1114D4—31616no—
1115D4—3168no—
1116D4—31616no—
1117D4—3168no—
1118D4—31616no—
1119D4—3168no—
1120D4—1588no—
1121D4—1584no—
1122D4—1588no—
1123D4—1588no—
1124D4—15816no—
1125D4—1588no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—28no—
1135C2×C4—28no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—31616no—
1140C2×C4—3168no—
1141C2×C4—3168no—
1142C2×C4—3168no—
1143C2×C4—31616no—
1144C2×C4—3168no—
1145C2×C4—798no—
1146C2×C4—798no—
1147C2×C4—794no—
1148C2×C4—1588no—
1149C2×C4—1588no—
1150C2×C4#1457920714yes—
1151C2×C4C24×D7912yes—
1152C2×C4C24×D7914yes—
1153C2×C4C24×D7912yes—
1154C2×C4C24×D7912yes—
1155C2×C4C24×D7912yes—
1156C2×C4C24×D7914yes—
1157C2×C4C24×D7912yes—
1158C2×C4C24×D7912yes—
1159C2×C4C24×D7911yescharacteristic
1160C2×C4C24×D7911yescharacteristic
1161C2×C4C24×D7912yes—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—24no—
1169C22—24no—
1170C22—44no—
1171C22—6328no—
1172C22—1588no—
1173C22—1584no—
1174C22—15816no—
1175C22—1588no—
1176C22—12648no—
1177C22C2×#1457920712yes—
1178C22C25×D7911yescharacteristic
1179C4—22no—
1180C4—22no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—22no—
1185C4—24no—
1186C4—24no—
1187C4—1588no—
1188C4—1584no—
1189C4—1588no—
1190C4C2×#1457920712yes—
1191C4C2×#1457920712yes—
1192C4#1909939914yes—
1193C2—22no—
1194C2—42no—
1195C2—42no—
1196C2—42no—
1197C2—3168no—
1198C2—3164no—
1199C2C22×#1457920711yescharacteristic
1200C2C2×#1909939912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3444C2
hypercenter#3444D79
hypocenterC79#62836
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #23777988C2semidirect
2. #23777871C2semidirect
3. #23777772C2semidirect
4. #23777716C2semidirect
5. #23777404C2semidirect
6. #23777363C2semidirect
7. #23777344C2semidirect
8. #23777311C2semidirect
9. #23777298C2semidirect
10. #23777286C2semidirect
11. #23777276C2semidirect
12. #23777276C2semidirect
13. #23777187C2semidirect
14. #23777185C2semidirect
15. #23777178C2semidirect
16. #23777054C2semidirect
17. #23777042C2semidirect
18. #23776696C2semidirect
19. C2×#19099113C2semidirect
20. C79×#3444C2semidirect
21. C2×#14579208C22semidirect
23. C22×#11929624C22semidirect
24. #19099309C22semidirect
25. #19099301C22semidirect
26. #19099298C22semidirect
27. #19099298C22semidirect
28. #19099298C22semidirect
29. #19099291C22semidirect
30. #19099286C22semidirect
31. #19099283C22semidirect
32. #19099278C22semidirect
33. #19099273C22semidirect
34. #19099264C22semidirect
35. #19099259C22semidirect
36. #19099259C22semidirect
37. #19099253C22semidirect
38. #19099240C22semidirect
39. #19099238C22semidirect
40. #19099235C22semidirect
41. #19099234C22semidirect
42. #19099234C22semidirect
43. #19099234C22semidirect
44. #19099231C22semidirect
45. Q8×D316C22semidirect
46. #19099223C22semidirect
47. #19099222C22semidirect
48. #19099222C22semidirect
49. #19099218C22semidirect
50. #19099217C22semidirect
51. #19099217C22semidirect
52. #19099215C22semidirect
53. #19099210C22semidirect
54. #19099209C22semidirect
55. #19099209C22semidirect
56. #19099209C22semidirect
57. #19099209C22semidirect
58. #19099209C22semidirect
59. #19099202C22semidirect
61. D4×D316C22semidirect
62. #19099187C22semidirect
63. #19099184C22semidirect
64. #19099184C22semidirect
65. #19099175C22semidirect
66. #19099168C22semidirect
67. #19099168C22semidirect
68. #19099168C22semidirect
69. #19099165C22semidirect
70. #19099161C22semidirect
71. #19099149C22semidirect
72. #19099147C22semidirect
73. #19099141C22semidirect
74. #19099139C22semidirect
75. #19099139C22semidirect
76. #19099138C22semidirect
79. #19099132C22semidirect
80. #19099128C22semidirect
81. #19099127C22semidirect
82. #19099127C22semidirect
83. #19099126C22semidirect
84. #19099123C22semidirect
85. #19099120C22semidirect
86. #19099120C22semidirect
87. #19099120C22semidirect
89. #19099113C22semidirect
90. #19099113C22semidirect
91. #19099113C22semidirect
92. #19099113C22semidirect
93. #19099113C22semidirect
94. #19099113C22semidirect
95. #19099113C22semidirect
96. #19099113C22semidirect
97. #19099112C22semidirect
98. C2×#14579161C22semidirect
99. C2×#14579161C22semidirect
101. C2×#14579158C22semidirect
102. #19099098C22semidirect
103. #19099097C22semidirect
104. #19099097C22semidirect
105. #19099097C22semidirect
106. C2×#14579149C22semidirect
107. #124×D79C22semidirect
108. #19099074C22semidirect
109. #19099074C22semidirect
110. #19099071C22semidirect
111. #123×D79C22semidirect
112. C2×#14579135C22semidirect
113. #19099043C22semidirect
114. #19099040C22semidirect
115. #19099037C22semidirect
116. #19099037C22semidirect
117. C4×#11929624C22semidirect
118. C4×#11929624C22semidirect
119. C2×C4×D316C22semidirect
120. #533×C79C22semidirect
121. #533×C79C22semidirect
123. #532×C79C22semidirect
124. #529×C79C22semidirect
125. #529×C79C22semidirect
126. #529×C79C22semidirect
127. #529×C79C22semidirect
129. #525×C79C22semidirect
130. #525×C79C22semidirect
132. C4×#41×C79C22semidirect
133. C4×#41×C79C22semidirect
134. C22×C42×C79C22semidirect
619. #3444D79semidirect
621. C79#62836semidirect
689. #533C2×D79semidirect
690. #533C2×D79semidirect
702. #532C2×D79semidirect
711. #529C2×D79semidirect
712. #529C2×D79semidirect
713. #529C2×D79semidirect
714. #529C2×D79semidirect
721. #525C2×D79semidirect
722. #525C2×D79semidirect
732. C4×#41C2×D79semidirect
733. C4×#41C2×D79semidirect
735. C22×C42C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779882
#237778712
#237777722
#237777162
#237774042
#237773632
#237773442
#237773112
#237772982
#237772862
#237772762
#237771872
#237771852
#237771782
#237770542
#237770422
#237766962
C2×#190991132
C79×#34442
#6283679