Finite Group Databasebeta

← #27124820

Subgroups — #27124820

Order 12032.

11346 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689958C212yesmaximal, complemented
2#20257174C218yesmaximal, complemented
3#20257167C214yesmaximal, complemented
4#20257160C214yesmaximal, complemented
5#20257157C212yesmaximal, complemented
6#20257154C212yesmaximal, complemented
7#20257152C211yesmaximal, characteristic, complemented
8#20257149C214yesmaximal, complemented
9#20257147C212yesmaximal, complemented
10#20257145C214yesmaximal, complemented
11#20256875C214yesmaximal, complemented
12#20256872C218yesmaximal, complemented
13D4×#10625352C214yesmaximal, complemented
14#20256716C212yesmaximal, complemented
15#20256714C214yesmaximal, complemented
16C2×#15689668C214yesmaximal, complemented
17#532×D47C212yesmaximal, complemented
18C2×C4×#10625352C211yesmaximal, characteristic, complemented
19C47×#3496C211yesmaximal, characteristic, complemented
20#15689958—232no—
21C2×#13094071C2214yescomplemented
22C2×#13094071C2218yescomplemented
23C2×#13094069C2218yescomplemented
24C2×#13094069C2212yescomplemented
25C2×#13094069C2218yescomplemented
26C22×#10625352C2211yescharacteristic
27C22×#10625352C2218yescomplemented
28C22×#10625352C2218yescomplemented
29C2×#41×D47C2218yescomplemented
30C2×#41×D47C2214yescomplemented
31#15689794C2214yescomplemented
32#15689793C2214yescomplemented
33#15689791C2218yescomplemented
34D4×Dic94C2214yescomplemented
35#15689788C2214yescomplemented
36#15689786C2218yescomplemented
37#15689783C2218yescomplemented
38#15689782C2218yescomplemented
39#15689781C2218yescomplemented
40#15689779C2218yescomplemented
41#15689777C2214yescomplemented
42#15689774C2218yescomplemented
43#15689773C2218yescomplemented
44#15689772C2218yescomplemented
45#15689771C22116yescomplemented
46#15689768C2218yescomplemented
47#15689767C2218yescomplemented
48#15689765C22116yescomplemented
49#15689763C22116yescomplemented
50#15689762C22116yescomplemented
51#15689761C2218yescomplemented
52#15689760C22116yescomplemented
53D4×D188C2214yescomplemented
54#15689757C2218yescomplemented
55D4×C22⋊D47C2218yescomplemented
56D4×C22⋊D47C2218yescomplemented
57#15689755C22116yescomplemented
58#15689704C2212yescomplemented
59#15689701C2214yescomplemented
60#15689700C2218yescomplemented
61#15689700C2218yescomplemented
62#15689696C2218yescomplemented
63#15689695C22116yescomplemented
64#15689689C2218yescomplemented
65#15689688C22116yescomplemented
66#15689685C2214yescomplemented
67#15689682C2218yescomplemented
68#15689681C2218yescomplemented
69#15689674C2212yescomplemented
70#15689673C2212yescomplemented
71#15689672C2214yescomplemented
72#15689671C2212yescomplemented
73#15689670C2214yescomplemented
74#15689670C2214yescomplemented
75#15689669C2214yescomplemented
76#15689668C2218yescomplemented
77#15689668C2218yescomplemented
78#15689668C2218yescomplemented
79#15689668C2218yescomplemented
80#15689668C2218yescomplemented
81#15689668C2218yescomplemented
82#15689668C2214yescomplemented
83#15689668C2214yescomplemented
84#15689668C2218yescomplemented
85C2×#13094023C2214yescomplemented
86C4⋊Q8×D47C2212yescomplemented
87C2×#13094020C2214yescomplemented
88#127×D47C2212yescomplemented
89C2×#13094010C2218yescomplemented
90#124×D47C2214yescomplemented
91#15689636C2218yescomplemented
92#15689633C2218yescomplemented
93#15689631C22116yescomplemented
94#15689629C22116yescomplemented
95C2×#13093998C2214yescomplemented
96C2×#13093996C2218yescomplemented
97#121×D47C2214yescomplemented
98#121×D47C2214yescomplemented
99C4×#10625352C2214yescomplemented
100C4×#10625352C2214yescomplemented
101C4×#10625352C2214yescomplemented
102C4×#10625352C2214yescomplemented
103C2×C4×Dic94C2211yescharacteristic, complemented
104C2×#13093989C2211yescharacteristic, complemented
105C2×D4×Dic47C2211yescharacteristic, complemented
106C2×D4×Dic47C2214yescomplemented
107C2×#13093986C2214yescomplemented
108C2×C4×C22⋊D47C2212yescomplemented
109C2×(C22⋊D47)⋊C4C2212yescomplemented
110C2×(C22⋊D47)⋊C4C2218yescomplemented
111C4×D4×D47C2214yescomplemented
112C4×D4×D47C2214yescomplemented
113C2×#13093982C2211yescharacteristic, complemented
114C2×#13093980C2212yescomplemented
115C22×C4×Dic47C2212yescomplemented
116C2×C42×D47C2211yescharacteristic, complemented
117C2×H(5,𝔽2)×C47C2212yescomplemented
118C47×#547C2214yescomplemented
119C47×#546C2218yescomplemented
120D42×C47C2214yescomplemented
121C47×#537C2212yescomplemented
122C47×#534C2214yescomplemented
123C47×#532C2212yescomplemented
124C2×#121×C47C2214yescomplemented
125C2×C4×D4×C47C2211yescharacteristic, complemented
126#13094071—264no—
127#13094071—232no—
128#13094069—216no—
129#13094069—264no—
130#13094069—264no—
131C2×#10625354C2314yes—
132C2×#10625350C23116yes—
133C2×#10625350C2318yes—
134C2×#10625350C2314yes—
135C2×#10625350C2318yes—
136C2×#10625352—264no—
137C2×#10625352—264no—
138C2×#10625352D4116yescomplemented
139C2×#10625352C23116yes—
140C2×#10625352C2318yes—
141C2×#10625352C2318yes—
142C2×#10625352C23116yes—
143C2×#10625352C2314yes—
144C2×#10625352C2318yes—
145C2×#10625352C23116yes—
146C2×#10625352C23116yes—
147C2×#10625352C2314yes—
148C2×#10625352C2314yes—
149#41×D47—264no—
150#41×D47—232no—
151C22×Dic94C2318yes—
152C22×Dic94C2318yes—
153C22×Dic94C2311yescharacteristic
154C2×Q8×D47C2318yes—
155C2×Q8×D47C2314yes—
156C22×D188C2314yes—
157C22×C22⋊D47C23116yes—
158C22×C22⋊D47C2318yes—
159C22×C22⋊D47C2318yes—
160C22×C22⋊D47C2318yes—
161C22×C22⋊D47C2312yes—
162C2×D4×D47C23116yes—
163C2×D4×D47C2318yes—
164C2×D4×D47C2318yes—
165C2×D4×D47C2314yes—
166C2×D4×D47C2314yes—
167C2×D4×D47C2314yes—
168C23×Dic47C2318yes—
169C23×Dic47C2312yes—
170C23×Dic47C2312yes—
171C22×C4×D47C2318yes—
172C22×C4×D47C2318yes—
173C22×C4×D47C2311yescharacteristic
174C22×C4×D47C2311yescharacteristic
175C22×C4×D47C2311yescharacteristic
176#13094024C2312yes—
177#13094023C2318yes—
178#13094023C2318yes—
179#13094023C2314yes—
180#13094023C2314yes—
181#13094023C2318yes—
182#13094022C2314yes—
183#13094021C2312yes—
184#13094020C2318yes—
185#13094020C2314yes—
186#13094020C2318yes—
187#13094020C2314yes—
188#13094020C2314yes—
189#13094020C2318yes—
190#13094013C2314yes—
191#13094012C2314yes—
192#13094011C2314yes—
193#13094010C23116yes—
194#13094010C23116yes—
195#13094010C2318yes—
196#13094010C2318yes—
197#13094010C23116yes—
198#13094009C23116yes—
199#13094008C23116yes—
200#13094007C23116yes—
201#13094006C23116yes—
202#13094005C23116yes—
203#13094004C2318yes—
204#13094003C2318yes—
205#13094002C23116yes—
206#13094002C23116yes—
207#13094001C23116yes—
208#13094001C23116yes—
209#13094000C2318yes—
210#13093999C2314yes—
211#13093999C2318yes—
212#13093999C2314yes—
213#13093998C2318yes—
214#13093998C2318yes—
215#13093998C2318yes—
216#13093998C2314yes—
217#13093998C2314yes—
218#13093998C2318yes—
219#13093997C2318yes—
220#13093997C23116yes—
221#13093997C23116yes—
222#13093997C2318yes—
223#13093996C23116yes—
224#13093996C23116yes—
225#13093996C23116yes—
226#13093996C23116yes—
227#13093996C2318yes—
228#13093996C2318yes—
229#13093996C23116yes—
230#13093995C2314yes—
231#13093995C2318yes—
232#13093995C2314yes—
233#13093994C23116yes—
234#13093994C23116yes—
235#13093993C23116yes—
236#13093992C23116yes—
237#13093992C23116yes—
238C4×Dic94C2314yes—
239C4×Dic94C2314yes—
240#13093989C2314yes—
241#13093989C2314yes—
242C4×D188C2314yes—
243C4×D188C2314yes—
244D4×Dic47C2314yes—
245D4×Dic47C2318yes—
246D4×Dic47C2318yes—
247D4×Dic47C2314yes—
248D4×Dic47C2314yes—
249D4×Dic47C2314yes—
250D4×Dic47C2318yes—
251#13093986C2318yes—
252#13093986C2318yes—
253#13093986C2314yes—
254#13093986C2314yes—
255#13093986C2318yes—
256C4×C22⋊D47C2318yes—
257C4×C22⋊D47C2318yes—
258C4×C22⋊D47C2318yes—
259C4×C22⋊D47C2318yes—
260(C22⋊D47)⋊C4C2318yes—
261(C22⋊D47)⋊C4C23116yes—
262(C22⋊D47)⋊C4C2318yes—
263(C22⋊D47)⋊C4C23116yes—
264(C22⋊D47)⋊C4C2318yes—
265(C22⋊D47)⋊C4C2318yes—
266(C22⋊D47)⋊C4C23116yes—
267#13093982C2314yes—
268#13093982C2314yes—
269#13093980C2318yes—
270#13093980C2318yes—
271C2×C4⋊Dic47C2314yes—
272C2×C4⋊Dic47C2311yescharacteristic
273C2×Dic47⋊C4C2318yes—
274C2×Dic47⋊C4C2312yes—
275C2×Dic47⋊C4C2312yes—
276C4⋊C4×D47C2314yes—
277C4⋊C4×D47C2314yes—
278C2×C22⋊Dic47C2318yes—
279C2×C22⋊Dic47C2312yes—
280C2×(C2×D47)⋊C4C2318yes—
281C2×(C2×D47)⋊C4C2318yes—
282C2×(C2×D47)⋊C4C2312yes—
283C22⋊C4×D47C2318yes—
284C22⋊C4×D47C2318yes—
285C2×C4×Dic47C2311yescharacteristic
286C2×C4×Dic47C2311yescharacteristic
287C2×C4×Dic47C2311yescharacteristic
288C2×C4×Dic47C2312yes—
289C2×C4×Dic47C2314yes—
290C2×C4×Dic47C2312yes—
291C2×C4×Dic47C2312yes—
292C2×C4×Dic47C2314yes—
293C2×C4×Dic47C2314yes—
294C2×C4×Dic47C2314yes—
295C42×D47C2312yes—
296C42×D47C2312yes—
297C42×D47C2312yes—
298C42×D47C2312yes—
299H(5,𝔽2)×C47—216no—
300C2×#41×C47C2318yes—
301C2×#41×C47C2314yes—
302C22×D4×C47C2318yes—
303C22×D4×C47C2318yes—
304C22×D4×C47C2314yes—
305C22×D4×C47C2311yescharacteristic
306C23×C4×C47C2312yes—
307C4⋊Q8×C47C2312yes—
308#127×C47C2312yes—
309#124×C47C2314yes—
310#123×C47C23116yes—
311C22⋊Q8×C47C2318yes—
312#121×C47C2318yes—
313#121×C47C2318yes—
314#121×C47C2318yes—
315#121×C47C2314yes—
316#121×C47C2318yes—
317#121×C47C2314yes—
318#120×C47C23116yes—
319C4×D4×C47C2314yes—
320C4×D4×C47C2314yes—
321C4×D4×C47C2314yes—
322C4×D4×C47C2314yes—
323C2×C4⋊C4×C47C2314yes—
324C2×C4⋊C4×C47C2311yescharacteristic
325C2×C22⋊C4×C47C2318yes—
326C2×C22⋊C4×C47C2312yes—
327C2×C42×C47C2311yescharacteristic
328C24×C47C2418yes—
329C24×C47C2412yes—
330C23×D47C2418yes—
331C23×D47C2418yes—
332C23×D47C2411yescharacteristic
333#41×C47—232no—
334#41×C47—216no—
335C2×Q8×C47C2414yes—
336C2×D4×C47—232no—
337C2×D4×C47—232no—
338C2×D4×C47—48no—
339C2×D4×C47C2×D418yescomplemented
340C2×D4×C47C2414yes—
341C2×D4×C47C24116yes—
342C2×D4×C47C2418yes—
343C2×D4×C47C2414yes—
344C2×D4×C47C2414yes—
345C2×D4×C47C2418yes—
346C2×D4×C47C2414yes—
347C22×C4×C47—44no—
348C22×C4×C47C2411yescharacteristic
349C22×C4×C47C2418yes—
350C22×C4×C47C2414yes—
351C22×C4×C47C2418yes—
352C22×C4×C47C2411yescharacteristic
353C22×C4×C47C2414yes—
354C22×C4×C47C2412yes—
355C22×C4×C47C2411yescharacteristic
356C2×C22⋊D47—232no—
357C2×C22⋊D47—264no—
358C2×C22⋊D47—232no—
359C2×C22⋊D47—416no—
360C2×C22⋊D47C2×D4116yescomplemented
361C2×C22⋊D47C2418yes—
362C2×C22⋊D47C2418yes—
363C2×C22⋊D47C24116yes—
364C2×C22⋊D47C2418yes—
365C2×C22⋊D47C24116yes—
366C2×C22⋊D47C2418yes—
367C2×C22⋊D47C24116yes—
368C2×C22⋊D47C2418yes—
369C2×C22⋊D47C2418yes—
370C22×Dic47—232no—
371C22×Dic47—44no—
372C22×Dic47C2×D4116yescomplemented
373C22×Dic47C2411yescharacteristic
374C22×Dic47C2414yes—
375C22×Dic47C2418yes—
376C22×Dic47C2418yes—
377C22×Dic47C24116yes—
378C22×Dic47C2414yes—
379C22×Dic47C2412yes—
380C22×Dic47C2411yescharacteristic
381C22×Dic47C2411yescharacteristic
382C22×Dic47C2412yes—
383C22×Dic47C2414yes—
384C22×Dic47C2414yes—
385#10625354—216no—
386Q8×D47—216no—
387Q8×D47—232no—
388#10625352—232no—
389#10625352—264no—
390#10625352—264no—
391#10625352—232no—
392#10625352—264no—
393#10625352—264no—
394#10625352—216no—
395#10625352—232no—
396#10625352C2×D4132yescomplemented
397#10625352C2×D4132yescomplemented
398D4×D47—232no—
399D4×D47—232no—
400D4×D47—264no—
401D4×D47—216no—
402D4×D47—48no—
403D4×D47—48no—
404#10625350—216no—
405#10625350—264no—
406#10625350—232no—
407#10625350—232no—
408C2×D188—48no—
409C2×D188C2414yes—
410C2×D188C2418yes—
411C2×D188C2414yes—
412C2×D188C2418yes—
413C2×D188C2414yes—
414C2×C4×D47—232no—
415C2×C4×D47—232no—
416C2×C4×D47—42no—
417C2×C4×D47—42no—
418C2×C4×D47C2×D418yescomplemented
419C2×C4×D47C2412yes—
420C2×C4×D47C2412yes—
421C2×C4×D47C2418yes—
422C2×C4×D47C2418yes—
423C2×C4×D47C24116yes—
424C2×C4×D47C2418yes—
425C2×C4×D47C2412yes—
426C2×C4×D47C2412yes—
427C2×C4×D47C2412yes—
428C2×C4×D47C2412yes—
429C2×Dic94—232no—
430C2×Dic94—232no—
431C2×Dic94C2×D418yescomplemented
432C2×Dic94C24116yes—
433C2×Dic94C2414yes—
434C2×Dic94C2418yes—
435C2×Dic94C2414yes—
436C4⋊C4×C47C2414yes—
437C4⋊C4×C47C2414yes—
438C4⋊C4×C47C2418yes—
439C4⋊C4×C47C2414yes—
440C22⋊C4×C47C2418yes—
441C22⋊C4×C47C2418yes—
442C22⋊C4×C47C24116yes—
443C22⋊C4×C47C2418yes—
444C42×C47C2412yes—
445C42×C47C2412yes—
446C22⋊Dic47C2418yes—
447C22⋊Dic47C2418yes—
448C22⋊Dic47C2418yes—
449C22⋊Dic47C24116yes—
450(C2×D47)⋊C4C2418yes—
451(C2×D47)⋊C4C2418yes—
452(C2×D47)⋊C4C2418yes—
453(C2×D47)⋊C4C2418yes—
454(C2×D47)⋊C4C2418yes—
455(C2×D47)⋊C4C24116yes—
456(C2×D47)⋊C4C24116yes—
457C4⋊Dic47C2414yes—
458C4⋊Dic47C2414yes—
459C4⋊Dic47C2414yes—
460C4⋊Dic47C2418yes—
461Dic47⋊C4C2418yes—
462Dic47⋊C4C2418yes—
463Dic47⋊C4C2418yes—
464Dic47⋊C4C2418yes—
465Dic47⋊C4C24116yes—
466C4×Dic47C2411yescharacteristic
467C4×Dic47C2411yescharacteristic
468C4×Dic47C2411yescharacteristic
469C4×Dic47C2411yescharacteristic
470C4×Dic47C2412yes—
471C4×Dic47C2412yes—
472C4×Dic47C2412yes—
473C4×Dic47C2412yes—
474C4×Dic47C2414yes—
475C4×Dic47C2414yes—
476C4×Dic47C2414yes—
477C4×Dic47C2414yes—
478C4×Dic47C2414yes—
479C4×Dic47C2414yes—
480C23×C47—216no—
481C23×C47—42no—
482C23×C47—42no—
483C23×C47—48no—
484C23×C47—48no—
485C23×C47C22×D418yes—
486C23×C47C2518yes—
487C23×C47C2514yes—
488C23×C47C2511yescharacteristic
489C22×D47—216no—
490C22×D47—216no—
491C22×D47—41no—
492C22×D47—41no—
493C22×D47—48no—
494C22×D47—48no—
495C22×D47—48no—
496C22×D47—48no—
497C22×D47C22×D414yes—
498C22×D47C2518yes—
499C22×D47C2512yes—
500Q8×C47—28no—
501D4×C47—232no—
502D4×C47—216no—
503D4×C47—28no—
504D4×C47—28no—
505D4×C47—44no—
506D4×C47—48no—
507D4×C47C22×D4116yes—
508C2×C4×C47—216no—
509C2×C4×C47—216no—
510C2×C4×C47—22no—
511C2×C4×C47—28no—
512C2×C4×C47—41no—
513C2×C4×C47—44no—
514C2×C4×C47—42no—
515C2×C4×C47C22×D414yes—
516C2×C4×C47C2511yescharacteristic
517C2×C4×C47C2514yes—
518C2×C4×C47C2512yes—
519C2×C4×C47C2518yes—
520C2×C4×C47C2512yes—
521C2×C4×C47C2511yescharacteristic
522C22⋊D47—232no—
523C22⋊D47—216no—
524C22⋊D47—216no—
525C22⋊D47—216no—
526C22⋊D47—232no—
527C22⋊D47—216no—
528C22⋊D47—48no—
529C22⋊D47—416no—
530C22⋊D47C22×D4132yes—
531C2×Dic47—216no—
532C2×Dic47—232no—
533C2×Dic47—216no—
534C2×Dic47—22no—
535C2×Dic47—28no—
536C2×Dic47—41no—
537C2×Dic47—44no—
538C2×Dic47—42no—
539C2×Dic47C22×D4116yes—
540C2×Dic47C22×D418yes—
541C2×Dic47C22×D4116yes—
542C2×Dic47C22×D414yes—
543C2×Dic47C2511yescharacteristic
544C2×Dic47C2512yes—
545C2×Dic47C2514yes—
546C2×Dic47C2518yes—
547C2×Dic47C2511yescharacteristic
548C2×Dic47C2511yescharacteristic
549C2×Dic47C2514yes—
550C2×Dic47C2511yescharacteristic
551D188—216no—
552D188—28no—
553D188—28no—
554D188—48no—
555D188—44no—
556C4×D47—216no—
557C4×D47—216no—
558C4×D47—24no—
559C4×D47—216no—
560C4×D47—232no—
561C4×D47—24no—
562C4×D47—42no—
563C4×D47—42no—
564C4×D47C22×D418yes—
565C4×D47C22×D418yes—
566Dic94—28no—
567Dic94—216no—
568Dic94—232no—
569Dic94C22×D4116yes—
570#62812—471nomaximal, Sylow
571C22×C47—21no—
572C22×C47—24no—
573C22×C47—21no—
574C22×C47—24no—
575C22×C47—28no—
576C22×C47—28no—
577C22×C47—28no—
578C22×C47—48no—
579C22×C47—816no—
580C22×C47C23×D418yes—
581C22×C47C23×D412yes—
582C22×C47C2611yescharacteristic
583C2×D47—22no—
584C2×D47—22no—
585C2×D47—28no—
586C2×D47—28no—
587C2×D47—28no—
588C2×D47—44no—
589C2×D47—816no—
590C2×D47—816no—
591C2×D47C23×D414yes—
592C4×C47—28no—
593C4×C47—22no—
594C4×C47—21no—
595C4×C47—24no—
596C4×C47C23×D414yes—
597C4×C47#58512yescomplemented
598Dic47—28no—
599Dic47—22no—
600Dic47—21no—
601Dic47—24no—
602Dic47C23×D412yes—
603Dic47C23×D418yes—
604Dic47C23×D412yes—
605Dic47#58512yescomplemented
606C2×#585—472no—
607#3500—478no—
608#3499—474no—
609#3498—474no—
610#3497—472no—
611#3497—472no—
612#3496—472no—
613#3496—474no—
614#3496—474no—
615#3496—471no—
616#3496D4711yescharacteristic, complemented
617D4×#41—474no—
618D4×#41—478no—
619D4×#41—474no—
620#3449—472no—
621#3449—474no—
622C2×#532—472no—
623C2×#532—474no—
624C2×C4×#41—471no—
625C2×C47—22no—
626C2×C47—28no—
627C2×C47—48no—
628C2×C47C24×D411yescharacteristic
629C2×C47C2×#58511yescharacteristic
630C2×C47C2×#58511yescharacteristic
631D47—24no—
632D47—48no—
633#585—9432no—
634C2×2−1+4—474no—
635C2×2−1+4—478no—
636C2×H(5,𝔽2)—478no—
637C2×H(5,𝔽2)—472no—
638C2×H(5,𝔽2)—478no—
639C2×H(5,𝔽2)C2×D4712yescomplemented
640C22×#41—474no—
641C22×#41—478no—
642C22×#41—471no—
643C22×#41—478no—
644C22×#41—478no—
645#550—474no—
646#550—478no—
647#550—474no—
648D4×Q8—474no—
649D4×Q8—478no—
650D4×Q8—474no—
651#548—478no—
652#548—478no—
653#548—478no—
654#548—478no—
655#547—478no—
656#547—4716no—
657#547—478no—
658#547—474no—
659#547—478no—
660#547C2×D4714yescomplemented
661#546—478no—
662#546—478no—
663#546—4716no—
664#546—4716no—
665#546—4716no—
666#546—478no—
667#546—4716no—
668#546C2×D4718yescomplemented
669D42—478no—
670D42—478no—
671D42—478no—
672D42—4716no—
673D42—474no—
674D42C2×D4714yescomplemented
675#537—474no—
676#537—478no—
677#537—478no—
678#537—472no—
679#537C2×D4712yescomplemented
680#536—4716no—
681#536—478no—
682#535—478no—
683#535—4716no—
684#534—478no—
685#534—478no—
686#534—474no—
687#534C2×D4714yescomplemented
688#532—474no—
689#532—472no—
690#532—472no—
691#532—474no—
692#532—474no—
693#532—474no—
694#532—478no—
695#532—478no—
696#532—478no—
697#532—478no—
698#532—478no—
699#532—478no—
700#532—478no—
701#532—474no—
702#532—474no—
703#532—472no—
704#532C2×D4712yescomplemented
705C2×C4⋊Q8—472no—
706C2×C4⋊Q8—474no—
707C2×#127—474no—
708C2×#127—472no—
709C2×#124—474no—
710C2×#124—478no—
711#525—4716no—
712#525—478no—
713#525—478no—
714#525—4716no—
715C2×#121—478no—
716C2×#121—474no—
717C2×#121—474no—
718C2×#121—474no—
719C2×#121C2×D4714yescomplemented
720C4×#41—474no—
721C4×#41—474no—
722C4×#41—474no—
723C4×#41—474no—
724C2×C4×Q8—471no—
725C2×C4×Q8—471no—
726C2×C4×D4—471no—
727C2×C4×D4—474no—
728C2×C4×D4—472no—
729C2×C4×D4—474no—
730C2×C4×D4—474no—
731C2×C4×D4—474no—
732C2×C4×D4—472no—
733C2×C4×D4—478no—
734C2×C4×D4C2×D4711yescharacteristic, complemented
735C2×#117—471no—
736C2×#117—472no—
737C22×C42—472no—
738C22×C42—471no—
739C47#6281211yescharacteristic, complemented, Sylow
7402−1+4—9432no—
7412−1+4—9464no—
742H(5,𝔽2)—216no—
743H(5,𝔽2)—9464no—
744H(5,𝔽2)—9464no—
745H(5,𝔽2)—9416no—
746C2×#41—474no—
747C2×#41—4716no—
748C2×#41—474no—
749C2×#41—474no—
750C2×#41—4716no—
751C2×#41—474no—
752C2×#41—478no—
753C2×#41—4716no—
754C2×#41—4716no—
755C2×#41—478no—
756C2×#41—4716no—
757C2×#41—478no—
758C2×#41—478no—
759C2×#41—474no—
760C2×#41—4716no—
761C2×#41—478no—
762C2×#41—9464no—
763C2×#41—9432no—
764C2×#41—9464no—
765C2×#41—9464no—
766C2×#41C22×D4714yes—
767C2×#41C22×D4718yes—
768C22×Q8—474no—
769C22×Q8—478no—
770C22×Q8—471no—
771C22×Q8—478no—
772C22×Q8—478no—
773C22×D4—472no—
774C22×D4—478no—
775C22×D4—478no—
776C22×D4—4716no—
777C22×D4—478no—
778C22×D4—478no—
779C22×D4—474no—
780C22×D4—4716no—
781C22×D4—478no—
782C22×D4—474no—
783C22×D4—474no—
784C22×D4—474no—
785C22×D4C22×D4718yes—
786C22×D4C22×D4718yes—
787C22×D4C22×D4714yes—
788C22×D4C22×D4711yescharacteristic
789C23×C4—472no—
790C23×C4—471no—
791C23×C4—478no—
792C23×C4—472no—
793C23×C4—478no—
794C23×C4—478no—
795C23×C4—471no—
796C23×C4—471no—
797C23×C4C22×D4712yes—
798C4⋊Q8—474no—
799C4⋊Q8—474no—
800C4⋊Q8—474no—
801C4⋊Q8—478no—
802C4⋊Q8—478no—
803C4⋊Q8—478no—
804C4⋊Q8—472no—
805C4⋊Q8C22×D4712yes—
806#127—474no—
807#127—478no—
808#127—474no—
809#127—478no—
810#127—474no—
811#127—478no—
812#127—472no—
813#127C22×D4712yes—
814#124—474no—
815#124—474no—
816#124—478no—
817#124—478no—
818#124—4716no—
819#124—4716no—
820#124—4716no—
821#124—474no—
822#124C22×D4714yes—
823#123—4716no—
824#123—4716no—
825#123—4716no—
826#123—4716no—
827#123—4716no—
828#123C22×D47116yes—
829C22⋊Q8—478no—
830C22⋊Q8—478no—
831C22⋊Q8—4716no—
832C22⋊Q8—4716no—
833C22⋊Q8—478no—
834C22⋊Q8—4716no—
835C22⋊Q8—4716no—
836C22⋊Q8C22×D4718yes—
837#121—478no—
838#121—4716no—
839#121—478no—
840#121—474no—
841#121—4716no—
842#121—474no—
843#121—4716no—
844#121—478no—
845#121—4716no—
846#121—4716no—
847#121—474no—
848#121—478no—
849#121—474no—
850#121—478no—
851#121—478no—
852#121—478no—
853#121—474no—
854#121—474no—
855#121—478no—
856#121—478no—
857#121—478no—
858#121—4716no—
859#121—4716no—
860#121C22×D4714yes—
861#121C22×D4714yes—
862#121C22×D4718yes—
863#121C22×D4718yes—
864#121C22×D4718yes—
865#121C22×D4718yes—
866#120—4716no—
867#120—4716no—
868#120—4716no—
869#120—4716no—
870#120—4716no—
871#120C22×D47116yes—
872C4×Q8—474no—
873C4×Q8—474no—
874C4×Q8—474no—
875C4×Q8—474no—
876C4×D4—474no—
877C4×D4—474no—
878C4×D4—474no—
879C4×D4—478no—
880C4×D4—474no—
881C4×D4—478no—
882C4×D4—478no—
883C4×D4—478no—
884C4×D4—478no—
885C4×D4—478no—
886C4×D4—478no—
887C4×D4—474no—
888C4×D4—474no—
889C4×D4—478no—
890C4×D4—478no—
891C4×D4—478no—
892C4×D4—478no—
893C4×D4—478no—
894C4×D4—478no—
895C4×D4—478no—
896C4×D4—4716no—
897C4×D4—4716no—
898C4×D4—4716no—
899C4×D4—474no—
900C4×D4—474no—
901C4×D4C22×D4714yes—
902C4×D4C22×D4714yes—
903C4×D4C22×D4714yes—
904C4×D4C22×D4714yes—
905#117—474no—
906#117—474no—
907#117—478no—
908#117—478no—
909C2×C4⋊C4—472no—
910C2×C4⋊C4—472no—
911C2×C4⋊C4—471no—
912C2×C4⋊C4—478no—
913C2×C4⋊C4—474no—
914C2×C4⋊C4—474no—
915C2×C4⋊C4—474no—
916C2×C4⋊C4C22×D4711yescharacteristic
917C2×C4⋊C4C22×D4714yes—
918C2×C22⋊C4—472no—
919C2×C22⋊C4—478no—
920C2×C22⋊C4—472no—
921C2×C22⋊C4—478no—
922C2×C22⋊C4—478no—
923C2×C22⋊C4—478no—
924C2×C22⋊C4—478no—
925C2×C22⋊C4C22×D4712yes—
926C2×C22⋊C4C22×D4718yes—
927C2×C42—472no—
928C2×C42—471no—
929C2×C42—474no—
930C2×C42—474no—
931C2×C42—472no—
932C2×C42—472no—
933C2×C42—471no—
934C2×C42—474no—
935C2×C42—474no—
936C2×C42—471no—
937C2×C42—472no—
938C2×C42—472no—
939C2×C42—472no—
940C2×C42—472no—
941C2×C42C22×D4711yescharacteristic
942C24—471no—
943C24—478no—
944C24—478no—
945C24C23×D4718yes—
946C24C23×D4712yes—
947#41—232no—
948#41—216no—
949#41—4732no—
950#41—4732no—
951#41—9432no—
952#41—9464no—
953#41—9432no—
954#41—9432no—
955#41—9464no—
956#41—9416no—
957#41—9464no—
958#41—9464no—
959#41—9416no—
960#41—9464no—
961#41—9432no—
962#41—9432no—
963#41—9416no—
964C2×Q8—478no—
965C2×Q8—474no—
966C2×Q8—4716no—
967C2×Q8—474no—
968C2×Q8—478no—
969C2×Q8—9432no—
970C2×Q8—9432no—
971C2×Q8—9416no—
972C2×Q8—9432no—
973C2×Q8C23×D4714yes—
974C2×D4—232no—
975C2×D4—232no—
976C2×D4—48no—
977C2×D4—4716no—
978C2×D4—478no—
979C2×D4—478no—
980C2×D4—478no—
981C2×D4—4716no—
982C2×D4—478no—
983C2×D4—4716no—
984C2×D4—478no—
985C2×D4—4716no—
986C2×D4—478no—
987C2×D4—474no—
988C2×D4—478no—
989C2×D4—474no—
990C2×D4—478no—
991C2×D4—474no—
992C2×D4—9416no—
993C2×D4—9432no—
994C2×D4—9464no—
995C2×D4—9432no—
996C2×D4—9464no—
997C2×D4—9432no—
998C2×D4—9432no—
999C2×D4—1888no—
1000C2×D4—1888no—
1001C2×D4—1888no—
1002C2×D4—18816no—
1003C2×D4D4×D4718yescomplemented
1004C2×D4C23×D4714yes—
1005C2×D4C23×D47116yes—
1006C2×D4C23×D4718yes—
1007C2×D4C23×D4714yes—
1008C2×D4C23×D4718yes—
1009C2×D4C23×D4714yes—
1010C2×D4C23×D4714yes—
1011C22×C4—44no—
1012C22×C4—4716no—
1013C22×C4—471no—
1014C22×C4—472no—
1015C22×C4—474no—
1016C22×C4—474no—
1017C22×C4—478no—
1018C22×C4—472no—
1019C22×C4—472no—
1020C22×C4—471no—
1021C22×C4—474no—
1022C22×C4—478no—
1023C22×C4—478no—
1024C22×C4—4716no—
1025C22×C4—474no—
1026C22×C4—472no—
1027C22×C4—471no—
1028C22×C4—472no—
1029C22×C4—472no—
1030C22×C4—478no—
1031C22×C4—478no—
1032C22×C4—4716no—
1033C22×C4—478no—
1034C22×C4—472no—
1035C22×C4—472no—
1036C22×C4—9432no—
1037C22×C4—9432no—
1038C22×C4—9432no—
1039C22×C4—1882no—
1040C22×C4—1882no—
1041C22×C4—1884no—
1042C22×C4C23×D4711yescharacteristic
1043C22×C4C23×D4714yes—
1044C22×C4C23×D4718yes—
1045C22×C4C23×D4718yes—
1046C22×C4C23×D4714yes—
1047C22×C4C23×D4712yes—
1048C22×C4C23×D4711yescharacteristic
1049C22×C4C23×D4711yescharacteristic
1050C4⋊C4—478no—
1051C4⋊C4—478no—
1052C4⋊C4—478no—
1053C4⋊C4—478no—
1054C4⋊C4—4716no—
1055C4⋊C4—474no—
1056C4⋊C4—474no—
1057C4⋊C4—478no—
1058C4⋊C4—474no—
1059C4⋊C4C23×D4714yes—
1060C4⋊C4C23×D4714yes—
1061C4⋊C4C23×D4714yes—
1062C4⋊C4C23×D4718yes—
1063C22⋊C4—478no—
1064C22⋊C4—478no—
1065C22⋊C4—478no—
1066C22⋊C4—4716no—
1067C22⋊C4—478no—
1068C22⋊C4—478no—
1069C22⋊C4—478no—
1070C22⋊C4—478no—
1071C22⋊C4—4716no—
1072C22⋊C4—4716no—
1073C22⋊C4—478no—
1074C22⋊C4C23×D4718yes—
1075C22⋊C4C23×D4718yes—
1076C22⋊C4C23×D4718yes—
1077C22⋊C4C23×D47116yes—
1078C42—471no—
1079C42—471no—
1080C42—471no—
1081C42—471no—
1082C42—474no—
1083C42—472no—
1084C42—474no—
1085C42—472no—
1086C42—474no—
1087C42—474no—
1088C42—472no—
1089C42—474no—
1090C42—472no—
1091C42—474no—
1092C42C23×D4712yes—
1093C42C23×D4712yes—
1094C23—216no—
1095C23—42no—
1096C23—42no—
1097C23—48no—
1098C23—48no—
1099C23—472no—
1100C23—474no—
1101C23—478no—
1102C23—9416no—
1103C23—9416no—
1104C23—1888no—
1105C23—1888no—
1106C23—1888no—
1107C23—1888no—
1108C23—1881no—
1109C23—1881no—
1110C23C2×D4×D4718yes—
1111C23C24×D4718yes—
1112C23C24×D4714yes—
1113C23C24×D4711yescharacteristic
1114Q8—28no—
1115Q8—4716no—
1116Q8—9416no—
1117Q8—9432no—
1118Q8—948no—
1119D4—232no—
1120D4—216no—
1121D4—28no—
1122D4—28no—
1123D4—48no—
1124D4—44no—
1125D4—4732no—
1126D4—9416no—
1127D4—9416no—
1128D4—9432no—
1129D4—9416no—
1130D4—9416no—
1131D4—9432no—
1132D4—9416no—
1133D4—948no—
1134D4—948no—
1135D4—1884no—
1136D4—1888no—
1137D4—18816no—
1138D4—1888no—
1139D4C2×D4×D47116yes—
1140C2×C4—216no—
1141C2×C4—216no—
1142C2×C4—22no—
1143C2×C4—28no—
1144C2×C4—44no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—474no—
1148C2×C4—4716no—
1149C2×C4—478no—
1150C2×C4—4716no—
1151C2×C4—471no—
1152C2×C4—471no—
1153C2×C4—471no—
1154C2×C4—474no—
1155C2×C4—478no—
1156C2×C4—478no—
1157C2×C4—471no—
1158C2×C4—474no—
1159C2×C4—472no—
1160C2×C4—478no—
1161C2×C4—9416no—
1162C2×C4—9432no—
1163C2×C4—944no—
1164C2×C4—9416no—
1165C2×C4—9416no—
1166C2×C4—9432no—
1167C2×C4—942no—
1168C2×C4—948no—
1169C2×C4—9416no—
1170C2×C4—9416no—
1171C2×C4—944no—
1172C2×C4—1882no—
1173C2×C4—1882no—
1174C2×C4—1884no—
1175C2×C4—1882no—
1176C2×C4—1881no—
1177C2×C4C2×D4×D4714yes—
1178C2×C4C24×D4711yescharacteristic
1179C2×C4C24×D4714yes—
1180C2×C4C24×D4712yes—
1181C2×C4C24×D4718yes—
1182C2×C4C24×D4712yes—
1183C2×C4C24×D4711yescharacteristic
1184C22—21no—
1185C22—24no—
1186C22—21no—
1187C22—24no—
1188C22—28no—
1189C22—28no—
1190C22—28no—
1191C22—48no—
1192C22—816no—
1193C22—474no—
1194C22—942no—
1195C22—942no—
1196C22—948no—
1197C22—948no—
1198C22—948no—
1199C22—37616no—
1200C22—37616no—
1201C22—1884no—
1202C22C22×D4×D4718yes—
1203C22C22×D4×D4712yes—
1204C22C25×D4711yescharacteristic
1205C4—28no—
1206C4—22no—
1207C4—21no—
1208C4—24no—
1209C4—472no—
1210C4—472no—
1211C4—478no—
1212C4—472no—
1213C4—948no—
1214C4—941no—
1215C4—944no—
1216C4—942no—
1217C4C22×D4×D4714yes—
1218C4#1568995812yescomplemented
1219C2—22no—
1220C2—28no—
1221C2—48no—
1222C2—944no—
1223C2—1888no—
1224C2C23×D4×D4711yescharacteristic
1225C2#585×D4711yescharacteristic
1226C2C2×#1568995811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3496C2
hypercenter#3496D47
hypocenterC47#62812
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. C2×#15689958C2semidirect
2. #20257174C2semidirect
3. #20257167C2semidirect
4. #20257160C2semidirect
5. #20257157C2semidirect
6. #20257154C2semidirect
7. #20257152C2semidirect
8. #20257149C2semidirect
9. #20257147C2semidirect
10. #20257145C2semidirect
11. #20256875C2semidirect
12. #20256872C2semidirect
13. D4×#10625352C2semidirect
14. #20256716C2semidirect
15. #20256714C2semidirect
16. C2×#15689668C2semidirect
17. #532×D47C2semidirect
18. C2×C4×#10625352C2semidirect
19. C47×#3496C2semidirect
21. C2×#13094071C22semidirect
22. C2×#13094071C22semidirect
23. C2×#13094069C22semidirect
24. C2×#13094069C22semidirect
25. C2×#13094069C22semidirect
27. C22×#10625352C22semidirect
28. C22×#10625352C22semidirect
29. C2×#41×D47C22semidirect
30. C2×#41×D47C22semidirect
31. #15689794C22semidirect
32. #15689793C22semidirect
33. #15689791C22semidirect
34. D4×Dic94C22semidirect
35. #15689788C22semidirect
36. #15689786C22semidirect
37. #15689783C22semidirect
38. #15689782C22semidirect
39. #15689781C22semidirect
40. #15689779C22semidirect
41. #15689777C22semidirect
42. #15689774C22semidirect
43. #15689773C22semidirect
44. #15689772C22semidirect
45. #15689771C22semidirect
46. #15689768C22semidirect
47. #15689767C22semidirect
48. #15689765C22semidirect
49. #15689763C22semidirect
50. #15689762C22semidirect
51. #15689761C22semidirect
52. #15689760C22semidirect
53. D4×D188C22semidirect
54. #15689757C22semidirect
55. D4×C22⋊D47C22semidirect
56. D4×C22⋊D47C22semidirect
57. #15689755C22semidirect
58. #15689704C22semidirect
59. #15689701C22semidirect
60. #15689700C22semidirect
61. #15689700C22semidirect
62. #15689696C22semidirect
63. #15689695C22semidirect
64. #15689689C22semidirect
65. #15689688C22semidirect
66. #15689685C22semidirect
67. #15689682C22semidirect
68. #15689681C22semidirect
69. #15689674C22semidirect
70. #15689673C22semidirect
71. #15689672C22semidirect
72. #15689671C22semidirect
73. #15689670C22semidirect
74. #15689670C22semidirect
75. #15689669C22semidirect
76. #15689668C22semidirect
77. #15689668C22semidirect
78. #15689668C22semidirect
79. #15689668C22semidirect
80. #15689668C22semidirect
81. #15689668C22semidirect
82. #15689668C22semidirect
83. #15689668C22semidirect
84. #15689668C22semidirect
85. C2×#13094023C22semidirect
86. C4⋊Q8×D47C22semidirect
87. C2×#13094020C22semidirect
88. #127×D47C22semidirect
89. C2×#13094010C22semidirect
90. #124×D47C22semidirect
91. #15689636C22semidirect
92. #15689633C22semidirect
93. #15689631C22semidirect
94. #15689629C22semidirect
95. C2×#13093998C22semidirect
96. C2×#13093996C22semidirect
97. #121×D47C22semidirect
98. #121×D47C22semidirect
99. C4×#10625352C22semidirect
100. C4×#10625352C22semidirect
101. C4×#10625352C22semidirect
102. C4×#10625352C22semidirect
103. C2×C4×Dic94C22semidirect
104. C2×#13093989C22semidirect
105. C2×D4×Dic47C22semidirect
106. C2×D4×Dic47C22semidirect
107. C2×#13093986C22semidirect
108. C2×C4×C22⋊D47C22semidirect
109. C2×(C22⋊D47)⋊C4C22semidirect
110. C2×(C22⋊D47)⋊C4C22semidirect
111. C4×D4×D47C22semidirect
112. C4×D4×D47C22semidirect
113. C2×#13093982C22semidirect
114. C2×#13093980C22semidirect
115. C22×C4×Dic47C22semidirect
116. C2×C42×D47C22semidirect
117. C2×H(5,𝔽2)×C47C22semidirect
118. C47×#547C22semidirect
119. C47×#546C22semidirect
120. D42×C47C22semidirect
121. C47×#537C22semidirect
122. C47×#534C22semidirect
123. C47×#532C22semidirect
124. C2×#121×C47C22semidirect
125. C2×C4×D4×C47C22semidirect
138. C2×#10625352D4semidirect
339. C2×D4×C47C2×D4semidirect
360. C2×C22⋊D47C2×D4semidirect
372. C22×Dic47C2×D4semidirect
396. #10625352C2×D4semidirect
397. #10625352C2×D4semidirect
418. C2×C4×D47C2×D4semidirect
431. C2×Dic94C2×D4semidirect
597. C4×C47#585semidirect
605. Dic47#585semidirect
616. #3496D47semidirect
639. C2×H(5,𝔽2)C2×D47semidirect
660. #547C2×D47semidirect
668. #546C2×D47semidirect
674. D42C2×D47semidirect
679. #537C2×D47semidirect
687. #534C2×D47semidirect
704. #532C2×D47semidirect
719. C2×#121C2×D47semidirect
734. C2×C4×D4C2×D47semidirect
739. C47#62812semidirect
1003. C2×D4D4×D47semidirect
1218. C4#15689958semidirect

Maximal subgroups

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

subgroupindex
C2×#156899582
#202571742
#202571672
#202571602
#202571572
#202571542
#202571522
#202571492
#202571472
#202571452
#202568752
#202568722
D4×#106253522
#202567162
#202567142
C2×#156896682
#532×D472
C2×C4×#106253522
C47×#34962
#6281247