Finite Group Databasebeta

← #26383126

Subgroups — #26383126

Order 12032.

2934 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689658C211yesmaximal, characteristic, complemented
2C2×C4×D4×D47C211yesmaximal, characteristic, complemented
3#20249291C214yesmaximal, complemented
4#20249257C211yesmaximal, characteristic, complemented
5#20249243C211yesmaximal, characteristic, complemented
6#20249240C211yesmaximal, characteristic, complemented
7#20249194C212yesmaximal, complemented
8#20249169C212yesmaximal, complemented
9#20249123C212yesmaximal, complemented
10#20249101C212yesmaximal, complemented
11#20246673C212yesmaximal, complemented
12#20246668C212yesmaximal, complemented
13#20246629C212yesmaximal, complemented
14#20246627C212yesmaximal, complemented
15#20245889C214yesmaximal, complemented
16#20245785C211yesmaximal, characteristic, complemented
17C47×#2633C211yesmaximal, characteristic, complemented
18C22×D4×D47C2211yescharacteristic
19C23×C4×D47C2212yes—
20#15689658—28no—
21C2×#13094019C2212yescomplemented
22C2×#13094012C2211yescharacteristic, complemented
23C2×#13094009C2212yes—
24C2×#13094004C2211yescharacteristic
25C2×#13093999C2211yescharacteristic
26C2×#13093994C2214yes—
27C2×#13093989C2211yescharacteristic, complemented
28C2×C4×D188C2211yescharacteristic
29C2×D4×Dic47C2211yescharacteristic
30C2×#13093986C2211yescharacteristic
31C2×#13093986C2212yes—
32C2×#13093986C2211yescharacteristic, complemented
33C2×#13093986C2214yescomplemented
34C2×C4×C22⋊D47C2212yes—
35C2×(C22⋊D47)⋊C4C2212yes—
36C2×(C22⋊D47)⋊C4C2214yescomplemented
37C4×D4×D47—28no—
38C2×#13093982C2212yescomplemented
39C2×C4⋊C4×D47C2211yescharacteristic
40C2×C22⋊C4×D47C2212yes—
41C2×C42×D47C2211yescharacteristic
42#15689064C2214yescomplemented
43#15689058C2214yescomplemented
44#15689058C2212yescomplemented
45#15689053C2212yescomplemented
46#15689050C2212yescomplemented
47#15689049C2212yescomplemented
48#15689049C2212yescomplemented
49#15689046C2214yescomplemented
50#15689045C2214yescomplemented
51#15689041C2214yescomplemented
52#15689040C2212yes—
53#15689038C2214yes—
54#15689038C2214yescomplemented
55#15689036C2212yescomplemented
56#15689035C2212yescomplemented
57#15689033C2212yes—
58#15689033C2212yescomplemented
59#15689032C2214yes—
60#15689032C2212yescomplemented
61#15689031C2212yes—
62#15689002C2214yescomplemented
63#15689001C2214yes—
64#15689001C2214yescomplemented
65#15688994C2214yes—
66#15688994C2214yescomplemented
67#15688991C2211yescharacteristic, complemented
68#15688987C2212yescomplemented
69#15688985C2212yes—
70#15688982C2212yes—
71#15688978C2214yes—
72#15688974C2212yescomplemented
73C22⋊C4×Dic47C2214yescomplemented
74#15688970C2212yes—
75#15688970C2214yescomplemented
76#15688968C2212yescomplemented
77C2×#125×C47C2211yescharacteristic, complemented
78C2×C4×D4×C47C2211yescharacteristic
79C47×#399C2212yescomplemented
80C47×#398C2212yescomplemented
81C47×#397C2212yescomplemented
82C47×#394C2212yes—
83C47×#385C2214yescomplemented
84C47×#383C2211yescharacteristic, complemented
85C24×D47C2312yes—
86C22×Dic94C2311yescharacteristic
87C22×D188C2312yes—
88C22×D188C2311yescharacteristic
89C22×D188C2314yes—
90C22×D188C2311yescharacteristic
91C22×C22⋊D47C2312yes—
92C22×C22⋊D47C2314yes—
93C2×D4×D47—28no—
94C2×D4×D47—24no—
95C23×Dic47C2312yes—
96C22×C4×D47—28no—
97C22×C4×D47—48no—
98C22×C4×D47C2312yes—
99C22×C4×D47C2312yes—
100C22×C4×D47C2311yescharacteristic
101C22×C4×D47C2311yescharacteristic
102C22×C4×D47C2312yes—
103C22×C4×D47C2312yes—
104C22×C4×D47C2311yescharacteristic
105#13094019—28no—
106#13094012—24no—
107#13094009—28no—
108#13094004—24no—
109#13093999—24no—
110#13093994—216no—
111#13093989—24no—
112C4×D188—24no—
113D4×Dic47—24no—
114#13093986—28no—
115#13093986—24no—
116#13093986—24no—
117#13093986—48no—
118C4×C22⋊D47—28no—
119(C22⋊D47)⋊C4—28no—
120(C22⋊D47)⋊C4—48no—
121#13093982—28no—
122C2×C4⋊Dic47C2312yes—
123C2×C4⋊Dic47C2311yescharacteristic
124C2×Dic47⋊C4C2312yes—
125C2×Dic47⋊C4C2312yes—
126C2×Dic47⋊C4C2314yes—
127C2×Dic47⋊C4C2314yes—
128C4⋊C4×D47—24no—
129C2×C22⋊Dic47C2312yes—
130C2×C22⋊Dic47C2314yes—
131C2×(C2×D47)⋊C4C2314yes—
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2312yes—
134C2×(C2×D47)⋊C4C2312yes—
135C2×(C2×D47)⋊C4C2312yes—
136C2×(C2×D47)⋊C4C2312yes—
137C2×(C2×D47)⋊C4C2312yes—
138C2×(C2×D47)⋊C4C2312yes—
139C2×(C2×D47)⋊C4C2312yes—
140C2×(C2×D47)⋊C4C2314yes—
141C2×(C2×D47)⋊C4C2314yes—
142C2×(C2×D47)⋊C4C2314yes—
143C2×(C2×D47)⋊C4C2314yes—
144C22⋊C4×D47—28no—
145C2×C4×Dic47C2314yes—
146C2×C4×Dic47C2312yes—
147C2×C4×Dic47C2311yescharacteristic
148C2×C4×Dic47C2311yescharacteristic
149C2×C4×Dic47C2311yescharacteristic
150C42×D47D418yescomplemented
151C47⋊#95C2312yes—
152C47⋊#95C2314yes—
153C47⋊#95C2312yes—
154C47⋊#95C2314yes—
155C47⋊#95C2314yes—
156C47⋊#95C2314yes—
157C47⋊#95C2312yes—
158C22×D4×C47C2311yescharacteristic
159C23×C4×C47C2312yes—
160#125×C47—24no—
161C4×D4×C47—24no—
162C2×C4⋊C4×C47C2312yes—
163C2×C4⋊C4×C47C2311yescharacteristic
164C2×C4⋊C4×C47C2312yes—
165C2×C4⋊C4×C47C2311yescharacteristic
166C2×C4⋊C4×C47C2311yescharacteristic
167C2×C4⋊C4×C47C2314yes—
168C2×C22⋊C4×C47C2314yes—
169C2×C22⋊C4×C47C2312yes—
170C2×C22⋊C4×C47C2314yes—
171C2×C42×C47C2311yescharacteristic
172#95×C47C2312yes—
173#95×C47C2312yes—
174#95×C47C2314yes—
175#95×C47C2312yes—
176C24×C47C2412yes—
177C23×D47—24no—
178C23×D47—24no—
179C23×D47—44no—
180C23×D47—44no—
181C23×D47#4118yes—
182C23×D47C2412yes—
183C23×D47C2412yes—
184C23×D47C2411yescharacteristic
185C2×D4×C47—24no—
186C2×D4×C47—22no—
187C22×C4×C47—24no—
188C22×C4×C47—44no—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
191C22×C4×C47C2414yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2411yescharacteristic
194C22×C4×C47C2411yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—24no—
197C2×C22⋊D47—24no—
198C2×C22⋊D47—28no—
199C2×C22⋊D47—24no—
200C2×C22⋊D47—44no—
201C2×C22⋊D47—44no—
202C22×Dic47—24no—
203C22×Dic47—28no—
204C22×Dic47C2414yes—
205C22×Dic47C2412yes—
206C22×Dic47C2412yes—
207C22×Dic47C2411yescharacteristic
208C22×Dic47C2411yescharacteristic
209C22×Dic47C2411yescharacteristic
210D4×D47—232no—
211C2×D188—24no—
212C2×D188—22no—
213C2×D188—24no—
214C2×D188—28no—
215C2×D188—28no—
216C2×D188—22no—
217C2×D188—44no—
218C2×D188—42no—
219C2×D188—44no—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—24no—
223C2×C4×D47—24no—
224C2×C4×D47—24no—
225C2×C4×D47—24no—
226C2×C4×D47—24no—
227C2×C4×D47—24no—
228C2×C4×D47—28no—
229C2×C4×D47—432no—
230C2×C4×D47—44no—
231C2×C4×D47—44no—
232C2×C4×D47—42no—
233C2×C4×D47C2×D414yes—
234C2×C4×D47C2×D414yes—
235C2×C4×D47C2×D414yes—
236C2×Dic94—22no—
237C2×Dic94—42no—
238C4⋊C4×C47—22no—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—22no—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—22no—
243C4⋊C4×C47—44no—
244C22⋊C4×C47—28no—
245C22⋊C4×C47—24no—
246C22⋊C4×C47—44no—
247C42×C47C2×D414yes—
248C22⋊Dic47—24no—
249C22⋊Dic47—44no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—28no—
252(C2×D47)⋊C4—28no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—44no—
260(C2×D47)⋊C4—44no—
261(C2×D47)⋊C4—44no—
262(C2×D47)⋊C4—44no—
263C4⋊Dic47—22no—
264C4⋊Dic47—24no—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4—44no—
268Dic47⋊C4—44no—
269C4×Dic47—24no—
270C4×Dic47—28no—
271C4×Dic47C2×D414yes—
272C4×Dic47C2×D414yes—
273C4×Dic47C2×D414yes—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—24no—
277C23×C47—24no—
278C23×C47C2×#4114yes—
279C23×C47C2511yescharacteristic
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—24no—
285C22×D47—24no—
286C22×D47—216no—
287C22×D47—22no—
288C22×D47—24no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—24no—
292C22×D47—416no—
293C22×D47—48no—
294C22×D47—48no—
295C22×D47—416no—
296C22×D47C22×D412yes—
297C22×D47C2×#4114yes—
298C22×D47C2×#4114yes—
299D4×C47—28no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—24no—
307C2×C4×C47—24no—
308C2×C4×C47—24no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—24no—
312C2×C4×C47—24no—
313C2×C4×C47—48no—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D412yes—
317C22⋊D47—216no—
318C22⋊D47—416no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—24no—
324C2×Dic47—24no—
325C2×Dic47—24no—
326C2×Dic47—24no—
327C2×Dic47—24no—
328C2×Dic47—48no—
329C2×Dic47C22×D412yes—
330C2×Dic47C22×D412yes—
331C2×Dic47C22×D412yes—
332C2×Dic47H(5,𝔽2)14yes—
333D188—28no—
334D188—44no—
335D188—416no—
336D188—48no—
337C4×D47—28no—
338C4×D47—28no—
339C4×D47—44no—
340C4×D47—48no—
341C4×D47—48no—
342C4×D47—48no—
343C4×D47—48no—
344Dic94—44no—
345#34593—471nomaximal, Sylow
346C22×C47—24no—
347C22×C47—28no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—44no—
351C22×C47C23×D411yescharacteristic
352C22×C47C22×#4112yes—
353C22×C47C2×H(5,𝔽2)12yes—
354C22×C47#58512yes—
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—28no—
358C2×D47—24no—
359C2×D47—28no—
360C2×D47—432no—
361C2×D47—42no—
362C2×D47—42no—
363C2×D47—44no—
364C2×D47—42no—
365C2×D47—42no—
366C2×D47—42no—
367C2×D47—44no—
368C2×D47—44no—
369C2×D47#52514yes—
370C4×C47—22no—
371C4×C47—22no—
372C4×C47—22no—
373C4×C47—42no—
374C4×C47—42no—
375C4×C47—42no—
376C4×C47—44no—
377Dic47—22no—
378Dic47—22no—
379Dic47—42no—
380Dic47—42no—
381Dic47—44no—
382Dic47#53514yes—
383C2×#529—471no—
384C22×C4×D4—471no—
385#2636—474no—
386#2633—471no—
387#2633D4711yescharacteristic, complemented
388#2631—471no—
389#2631—471no—
390#2626—472no—
391#2623—472no—
392#2617—472no—
393#2613—472no—
394#2398—472no—
395#2397—472no—
396#2392—472no—
397#2392—472no—
398C4×#120—474no—
399#2283—471no—
400C2×C47—44no—
401C2×C47C2×#52511yescharacteristic
402C2×C47C2×#53511yescharacteristic
403C2×C47#344911yescharacteristic
404C2×C47#345914yes—
405D47—24no—
406D47—44no—
407D47—82no—
408C23×D4—471no—
409C24×C4—472no—
410#529—948no—
411C2×#126—472no—
412C2×#125C2×D4711yescharacteristic, complemented
413C2×#124—471no—
414C2×#123—472no—
415C2×C22⋊Q8—471no—
416C2×#121—471no—
417C2×#120—474no—
418C2×C4×Q8—471no—
419C2×C4×D4—471no—
420C2×C4×D4—472no—
421C2×C4×D4—471no—
422C2×C4×D4—471no—
423C2×C4×D4—472no—
424C2×C4×D4—474no—
425C2×C4×D4—472no—
426C2×C4×D4—474no—
427C2×C4×D4—471no—
428C2×C4×D4—948no—
429C2×C4×D4C2×D4711yescharacteristic
430C2×#117—472no—
431C22×C4⋊C4—471no—
432C22×C22⋊C4—472no—
433C22×C42—471no—
434#400—474no—
435#399—474no—
436#399—472no—
437#399C2×D4712yescomplemented
438#398—472no—
439#398C2×D4712yescomplemented
440#397—472no—
441#397—472no—
442#397—472no—
443#397C2×D4712yescomplemented
444#396—474no—
445#396—474no—
446#394—472no—
447#394—474no—
448#394—474no—
449#394—474no—
450#394C2×D4712yes—
451#393—472no—
452#393—472no—
453#392—472no—
454#392—474no—
455#392—472no—
456#392—472no—
457#392—472no—
458#386—474no—
459#386—474no—
460#386—474no—
461#385—474no—
462#385—474no—
463#385C2×D4714yescomplemented
464#383—471no—
465#383C2×D4711yescharacteristic, complemented
466#382—472no—
467#381—472no—
468#380—472no—
469#379—474no—
470C4×C4⋊C4—472no—
471C4×C22⋊C4—474no—
472C4×C22⋊C4—472no—
473C4×C22⋊C4—474no—
474#376—472no—
475C47#3459311yescharacteristic, complemented, Sylow
476C25—472no—
477C22×Q8—471no—
478C22×D4—472no—
479C22×D4—474no—
480C22×D4—471no—
481C22×D4—472no—
482C22×D4—474no—
483C22×D4—471no—
484C22×D4—944no—
485C22×D4—948no—
486C22×D4C22×D4711yescharacteristic
487C23×C4—471no—
488C23×C4—471no—
489C23×C4—471no—
490C23×C4—472no—
491C23×C4—472no—
492C23×C4—472no—
493C23×C4—472no—
494C23×C4—472no—
495C23×C4—948no—
496C23×C4—1888no—
497C23×C4C22×D4712yes—
498#126—948no—
499#125—24no—
500#124—944no—
501#123—948no—
502C22⋊Q8—944no—
503#121—944no—
504#120—9416no—
505C4×Q8—944no—
506C4×D4—24no—
507C4×D4—948no—
508C4×D4—944no—
509C4×D4—944no—
510C4×D4—948no—
511C4×D4—944no—
512C4×D4—948no—
513C4×D4—944no—
514C4×D4—1888no—
515C4×D4—1888no—
516#117—948no—
517C2×C4⋊C4—472no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—472no—
520C2×C4⋊C4—472no—
521C2×C4⋊C4—474no—
522C2×C4⋊C4—474no—
523C2×C4⋊C4—944no—
524C2×C4⋊C4C22×D4711yescharacteristic
525C2×C4⋊C4C22×D4712yes—
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C4⋊C4C22×D4712yes—
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C4⋊C4C22×D4714yes—
530C2×C22⋊C4—472no—
531C2×C22⋊C4—472no—
532C2×C22⋊C4—472no—
533C2×C22⋊C4—472no—
534C2×C22⋊C4—472no—
535C2×C22⋊C4—472no—
536C2×C22⋊C4—472no—
537C2×C22⋊C4—472no—
538C2×C22⋊C4—474no—
539C2×C22⋊C4—474no—
540C2×C22⋊C4—474no—
541C2×C22⋊C4—474no—
542C2×C22⋊C4—474no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4—474no—
545C2×C22⋊C4—948no—
546C2×C22⋊C4C22×D4712yes—
547C2×C22⋊C4C22×D4714yes—
548C2×C22⋊C4C22×D4714yes—
549C2×C42—471no—
550C2×C42—471no—
551C2×C42—471no—
552C2×C42—478no—
553C2×C42—472no—
554C2×C42—474no—
555C2×C42C22×D4711yescharacteristic
556#95—472no—
557#95—474no—
558#95—472no—
559#95—474no—
560#95—474no—
561#95—474no—
562#95—472no—
563#95C22×D4712yes—
564#95C22×D4712yes—
565#95C22×D4714yes—
566#95C22×D4712yes—
567C24—471no—
568C24—472no—
569C24—478no—
570C24—472no—
571C24—944no—
572C24—944no—
573C24—1884no—
574C24—1884no—
575C24C23×D4712yes—
576C2×Q8—942no—
577C2×Q8—1882no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—944no—
581C2×D4—944no—
582C2×D4—948no—
583C2×D4—948no—
584C2×D4—944no—
585C2×D4—9432no—
586C2×D4—944no—
587C2×D4—944no—
588C2×D4—948no—
589C2×D4—942no—
590C2×D4—942no—
591C2×D4—1884no—
592C2×D4—1882no—
593C2×D4—1884no—
594C2×D4—1884no—
595C2×D4—1884no—
596C22×C4—24no—
597C22×C4—44no—
598C22×C4—471no—
599C22×C4—471no—
600C22×C4—471no—
601C22×C4—474no—
602C22×C4—474no—
603C22×C4—474no—
604C22×C4—474no—
605C22×C4—472no—
606C22×C4—472no—
607C22×C4—944no—
608C22×C4—944no—
609C22×C4—944no—
610C22×C4—944no—
611C22×C4—944no—
612C22×C4—948no—
613C22×C4—944no—
614C22×C4—944no—
615C22×C4—944no—
616C22×C4—948no—
617C22×C4—944no—
618C22×C4—1882no—
619C22×C4—1884no—
620C22×C4—1884no—
621C22×C4—18832no—
622C22×C4C23×D4714yes—
623C22×C4C23×D4712yes—
624C22×C4C23×D4712yes—
625C22×C4C23×D4712yes—
626C22×C4C23×D4711yescharacteristic
627C22×C4C23×D4711yescharacteristic
628C22×C4C23×D4711yescharacteristic
629C4⋊C4—22no—
630C4⋊C4—24no—
631C4⋊C4—22no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—44no—
635C4⋊C4—944no—
636C4⋊C4—944no—
637C4⋊C4—944no—
638C4⋊C4—942no—
639C4⋊C4—1884no—
640C4⋊C4—1884no—
641C22⋊C4—28no—
642C22⋊C4—24no—
643C22⋊C4—44no—
644C22⋊C4—944no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4—948no—
649C22⋊C4—948no—
650C22⋊C4—944no—
651C22⋊C4—944no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C22⋊C4—1884no—
655C22⋊C4—1884no—
656C22⋊C4—1884no—
657C22⋊C4—1884no—
658C22⋊C4—1884no—
659C42—474no—
660C42—474no—
661C42—474no—
662C42—944no—
663C42—948no—
664C42D4×D4714yes—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—472no—
670C23—474no—
671C23—474no—
672C23—9416no—
673C23—942no—
674C23—942no—
675C23—942no—
676C23—942no—
677C23—944no—
678C23—944no—
679C23—942no—
680C23—944no—
681C23—942no—
682C23—942no—
683C23—944no—
684C23—18816no—
685C23—1888no—
686C23—18816no—
687C23—1888no—
688C23#41×D4714yes—
689C23C24×D4711yescharacteristic
690Q8—1884no—
691D4—28no—
692D4—948no—
693D4—9416no—
694D4—1884no—
695D4—1888no—
696D4—18816no—
697D4—18816no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—48no—
712C2×C4—472no—
713C2×C4—474no—
714C2×C4—472no—
715C2×C4—472no—
716C2×C4—948no—
717C2×C4—948no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—944no—
723C2×C4—944no—
724C2×C4—944no—
725C2×C4—944no—
726C2×C4—944no—
727C2×C4—1884no—
728C2×C4—1888no—
729C2×C4—1888no—
730C2×C4—1888no—
731C2×C4—1888no—
732C2×C4—1888no—
733C2×C4C2×D4×D4712yes—
734C2×C4C2×D4×D4712yes—
735C2×C4C2×D4×D4712yes—
736C22—28no—
737C22—24no—
738C22—44no—
739C22—42no—
740C22—42no—
741C22—474no—
742C22—948no—
743C22—942no—
744C22—942no—
745C22—948no—
746C22—944no—
747C22—18832no—
748C22—1884no—
749C22—1884no—
750C22—1882no—
751C22—1882no—
752C22—1882no—
753C22—1884no—
754C22—1882no—
755C22—1882no—
756C22C22×D4×D4711yescharacteristic
757C22C2×#41×D4712yes—
758C22H(5,𝔽2)×D4712yes—
759C22#1568996012yes—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—44no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—474no—
768C4—942no—
769C4—942no—
770C4—1884no—
771C4—1882no—
772C4—1882no—
773C2—44no—
774C2—944no—
775C2—3762no—
776C2—1884no—
777C2#525×D4711yescharacteristic
778C2#535×D4711yescharacteristic
779C2#2025672011yescharacteristic
780C2#2025679614yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2633C2
hypercenter#2633D47
hypocenterC47#34593
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2633

Complements

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

NH ≅ G/Ntype
1. C2×#15689658C2semidirect
2. C2×C4×D4×D47C2semidirect
3. #20249291C2semidirect
4. #20249257C2semidirect
5. #20249243C2semidirect
6. #20249240C2semidirect
7. #20249194C2semidirect
8. #20249169C2semidirect
9. #20249123C2semidirect
10. #20249101C2semidirect
11. #20246673C2semidirect
12. #20246668C2semidirect
13. #20246629C2semidirect
14. #20246627C2semidirect
15. #20245889C2semidirect
16. #20245785C2semidirect
17. C47×#2633C2semidirect
21. C2×#13094019C22semidirect
22. C2×#13094012C22semidirect
27. C2×#13093989C22semidirect
32. C2×#13093986C22semidirect
33. C2×#13093986C22semidirect
36. C2×(C22⋊D47)⋊C4C22semidirect
38. C2×#13093982C22semidirect
42. #15689064C22semidirect
43. #15689058C22semidirect
44. #15689058C22semidirect
45. #15689053C22semidirect
46. #15689050C22semidirect
47. #15689049C22semidirect
48. #15689049C22semidirect
49. #15689046C22semidirect
50. #15689045C22semidirect
51. #15689041C22semidirect
54. #15689038C22semidirect
55. #15689036C22semidirect
56. #15689035C22semidirect
58. #15689033C22semidirect
60. #15689032C22semidirect
62. #15689002C22semidirect
64. #15689001C22semidirect
66. #15688994C22semidirect
67. #15688991C22semidirect
68. #15688987C22semidirect
72. #15688974C22semidirect
73. C22⋊C4×Dic47C22semidirect
75. #15688970C22semidirect
76. #15688968C22semidirect
77. C2×#125×C47C22semidirect
79. C47×#399C22semidirect
80. C47×#398C22semidirect
81. C47×#397C22semidirect
83. C47×#385C22semidirect
84. C47×#383C22semidirect
150. C42×D47D4semidirect
387. #2633D47semidirect
412. C2×#125C2×D47semidirect
437. #399C2×D47semidirect
439. #398C2×D47semidirect
443. #397C2×D47semidirect
463. #385C2×D47semidirect
465. #383C2×D47semidirect
475. C47#34593semidirect

Maximal subgroups

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

subgroupindex
C2×#156896582
C2×C4×D4×D472
#202492912
#202492572
#202492432
#202492402
#202491942
#202491692
#202491232
#202491012
#202466732
#202466682
#202466292
#202466272
#202458892
#202457852
C47×#26332
#3459347