Finite Group Databasebeta

← #26377096

Subgroups — #26377096

Order 12032.

2682 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094013C211yesmaximal, characteristic
2#20246499C214yesmaximal, complemented
3#20246464C212yesmaximal, complemented
4#20246455C212yesmaximal, complemented
5#20246240C212yesmaximal, complemented
6#20246234C212yesmaximal, complemented
7Q8×C22⋊Dic47C211yesmaximal, characteristic, complemented
8C22⋊C4×D188C211yesmaximal, characteristic
9#20246208C211yesmaximal, characteristic
10#20246200C214yesmaximal, complemented
11#20245985C212yesmaximal, complemented
12C4×#13094013C212yesmaximal, complemented
13#20245931C212yesmaximal, complemented
14#20245783C211yesmaximal, characteristic, complemented
15#20245740C212yesmaximal, complemented
16C4×#13093980C211yesmaximal, characteristic, complemented
17Q8×C22⋊C4×C47C211yesmaximal, characteristic, complemented
18C23×D188C2211yescharacteristic
19C2×#13094013C4116yescomplemented
20C2×#13094013C2211yescharacteristic
21C2×#13094013C2211yescharacteristic
22C2×#13094013C2211yescharacteristic
23C2×#13094013C2212yes—
24C2×#13094013C2211yescharacteristic
25C2×#13094013C2212yes—
26C2×Q8×Dic47C2212yescomplemented
27C2×C4×D188C2212yes—
28C2×#13093986C2212yes—
29C2×#13093980C2211yescharacteristic
30C2×#13093980C2211yescharacteristic
31C22×(C2×D47)⋊C4C2212yes—
32C22×(C2×D47)⋊C4C2212yes—
33C2×C22⋊C4×D47C2212yes—
34C2×C22⋊C4×D47C2212yes—
35C22×C4×Dic47C2211yescharacteristic
36#15689030C2212yescomplemented
37#15689030C2214yescomplemented
38#15689025C2212yes—
39#15689024C2212yes—
40#15689015C2214yescomplemented
41#15689015C2214yescomplemented
42#15689015C2214yescomplemented
43#15689014C2214yescomplemented
44#15689013C2214yescomplemented
45#15689013C2214yescomplemented
46#15689013C2214yescomplemented
47#15689012C2214yescomplemented
48#15689001C2214yes—
49#15689001C2214yes—
50#15688997C2214yescomplemented
51#15688994C2214yescomplemented
52#15688990C2212yescomplemented
53#15688988C2212yescomplemented
54#15688984C2212yes—
55#15688983C2211yescharacteristic
56#15688983C2212yes—
57#15688978C2212yes—
58#15688978C2212yes—
59C4⋊C4×Dic47C2212yescomplemented
60C4×Dic47⋊C4C2212yescomplemented
61#15688974C2212yescomplemented
62C22⋊C4×Dic47C2212yes—
63C22⋊C4×Dic47C2211yescharacteristic
64C22⋊C4×Dic47C2211yescharacteristic
65C4×(C2×D47)⋊C4C2214yescomplemented
66C4×(C2×D47)⋊C4C2214yescomplemented
67C4×(C2×D47)⋊C4C2214yescomplemented
68C4×C22⋊Dic47C2211yescharacteristic
69C4×C22⋊Dic47C2212yes—
70#15688970C2214yescomplemented
71#15688970C2214yescomplemented
72#15688970C2214yescomplemented
73#15688968C2212yescomplemented
74#15688968C2212yescomplemented
75C42×Dic47C2212yescomplemented
76C23×Q8×C47C2211yescharacteristic
77C2×C4×Q8×C47C2212yescomplemented
78C47×#391C2212yescomplemented
79C47×#391C2214yescomplemented
80C47×#380C2211yescharacteristic
81C47×#380C2212yes—
82C4×C22⋊C4×C47C2211yescharacteristic
83C4×C22⋊C4×C47C2212yes—
84C24×D47C2312yes—
85C22×D188—44no—
86C22×D188C2×C418yes—
87C22×D188C2311yescharacteristic
88C22×D188C2311yescharacteristic
89C22×D188C2312yes—
90C23×Dic47C2311yescharacteristic
91C23×Dic47C2311yescharacteristic
92C22×C4×D47C2314yes—
93C22×C4×D47C2314yes—
94#13094013C2×C418yescomplemented
95#13094013C2×C418yescomplemented
96#13094013C2×C418yescomplemented
97#13094013C2×C418yescomplemented
98#13094013C2×C4116yescomplemented
99#13094013C2×C4116yescomplemented
100Q8×Dic47—44no—
101C4×D188—44no—
102#13093986—44no—
103#13093980—24no—
104#13093980—24no—
105C2×C4⋊Dic47C2312yes—
106C2×C4⋊Dic47C2314yes—
107C2×Dic47⋊C4C2312yes—
108C2×Dic47⋊C4C2312yes—
109C2×C22⋊Dic47C2311yescharacteristic
110C2×C22⋊Dic47C2312yes—
111C2×C22⋊Dic47C2311yescharacteristic
112C2×(C2×D47)⋊C4C2×C4116yescomplemented
113C2×(C2×D47)⋊C4C2×C4116yescomplemented
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2312yes—
121C2×(C2×D47)⋊C4C2312yes—
122C2×(C2×D47)⋊C4C2312yes—
123C2×(C2×D47)⋊C4C2312yes—
124C2×(C2×D47)⋊C4C2312yes—
125C2×(C2×D47)⋊C4C2312yes—
126C2×(C2×D47)⋊C4C2312yes—
127C2×(C2×D47)⋊C4C2312yes—
128C22⋊C4×D47—28no—
129C22⋊C4×D47—28no—
130C2×C4×Dic47C2×C418yescomplemented
131C2×C4×Dic47C2312yes—
132C2×C4×Dic47C2312yes—
133C2×C4×Dic47C2312yes—
134C2×C4×Dic47C2312yes—
135C2×C4×Dic47C2312yes—
136C2×C4×Dic47C2314yes—
137C2×C4×Dic47C2314yes—
138C2×C4×Dic47C2311yescharacteristic
139C2×C4×Dic47C2311yescharacteristic
140C2×C4×Dic47C2311yescharacteristic
141C2×C4×Dic47C2311yescharacteristic
142C47⋊#95C2312yes—
143C47⋊#95C2314yes—
144C47⋊#95C2312yes—
145C47⋊#95C2312yes—
146C47⋊#95C2312yes—
147C47⋊#95C2314yes—
148C47⋊#95C2314yes—
149C47⋊#95C2314yes—
150C47⋊#95C2314yes—
151C22×Q8×C47—44no—
152C22×Q8×C47C2×C418yescomplemented
153C22×Q8×C47C2311yescharacteristic
154C22×Q8×C47C2311yescharacteristic
155C22×Q8×C47C2312yes—
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2312yes—
158C4×Q8×C47—44no—
159C2×C4⋊C4×C47C2312yes—
160C2×C4⋊C4×C47C2314yes—
161C2×C22⋊C4×C47C2311yescharacteristic
162C2×C22⋊C4×C47C2312yes—
163C2×C22⋊C4×C47C2311yescharacteristic
164C2×C42×C47C2312yes—
165C2×C42×C47C2314yes—
166#95×C47C2312yes—
167#95×C47C2312yes—
168#95×C47C2314yes—
169#95×C47C2314yes—
170C24×C47C2411yescharacteristic
171C23×D47—24no—
172C23×D47—24no—
173C23×D47—44no—
174C23×D47—44no—
175C23×D47C22×C418yes—
176C23×D47C2412yes—
177C23×D47C2412yes—
178C2×Q8×C47—24no—
179C2×Q8×C47—24no—
180C2×Q8×C47—44no—
181C2×Q8×C47—416no—
182C2×Q8×C47C22×C414yes—
183C2×Q8×C47C22×C414yes—
184C2×Q8×C47C22×C418yes—
185C22×C4×C47—24no—
186C22×C4×C47—44no—
187C22×C4×C47C22×C414yes—
188C22×C4×C47C22×C418yes—
189C22×C4×C47C2414yes—
190C22×C4×C47C2412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2411yescharacteristic
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2411yescharacteristic
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—42no—
199C22×Dic47C22×C414yes—
200C22×Dic47C22×C414yes—
201C22×Dic47C2414yes—
202C22×Dic47C2412yes—
203C22×Dic47C2411yescharacteristic
204C22×Dic47C2411yescharacteristic
205C22×Dic47C2411yescharacteristic
206C22×Dic47C2411yescharacteristic
207C22×Dic47C2412yes—
208C2×D188—24no—
209C2×D188—24no—
210C2×D188—416no—
211C2×D188—44no—
212C2×D188C22×C414yes—
213C2×D188C22×C414yes—
214C2×D188C22×C418yes—
215C2×C4×D47—28no—
216C2×C4×D47—28no—
217C2×C4×D47—44no—
218C2×C4×D47—44no—
219C2×C4×D47—44no—
220C2×C4×D47—44no—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—44no—
223C22⋊C4×C47—24no—
224C22⋊C4×C47—22no—
225C22⋊C4×C47#4114yes—
226C42×C47—24no—
227C42×C47—44no—
228C22⋊Dic47—24no—
229C22⋊Dic47—22no—
230C22⋊Dic47#4114yes—
231(C2×D47)⋊C4—28no—
232(C2×D47)⋊C4—28no—
233(C2×D47)⋊C4—44no—
234(C2×D47)⋊C4—44no—
235(C2×D47)⋊C4—44no—
236(C2×D47)⋊C4—44no—
237(C2×D47)⋊C4C22×C418yes—
238(C2×D47)⋊C4C22×C418yes—
239(C2×D47)⋊C4C22×C418yes—
240(C2×D47)⋊C4C22×C418yes—
241(C2×D47)⋊C4C22×C418yes—
242(C2×D47)⋊C4C22×C418yes—
243(C2×D47)⋊C4C22×C418yes—
244(C2×D47)⋊C4C22×C418yes—
245C4⋊Dic47—24no—
246C4⋊Dic47—44no—
247Dic47⋊C4—24no—
248Dic47⋊C4—24no—
249C4×Dic47—24no—
250C4×Dic47—24no—
251C4×Dic47—24no—
252C4×Dic47—42no—
253C4×Dic47—42no—
254C4×Dic47—44no—
255C4×Dic47—44no—
256C4×Dic47C22×C414yes—
257C4×Dic47C22×C414yes—
258C4×Dic47C22×C414yes—
259C4×Dic47C22×C414yes—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47C23×C412yes—
263C23×C47C2×#4112yes—
264C23×C47C2×#4112yes—
265C23×C47C2511yescharacteristic
266C22×D47—22no—
267C22×D47—22no—
268C22×D47—22no—
269C22×D47—22no—
270C22×D47—24no—
271C22×D47—24no—
272C22×D47—24no—
273C22×D47—24no—
274C22×D47—216no—
275C22×D47—48no—
276C22×D47—48no—
277C22×D47—88no—
278C22×D47—88no—
279C22×D47C23×C414yes—
280C22×D47C23×C414yes—
281Q8×C47—28no—
282Q8×C47—28no—
283Q8×C47—48no—
284C2×C4×C47—24no—
285C2×C4×C47—22no—
286C2×C4×C47—24no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—28no—
290C2×C4×C47—22no—
291C2×C4×C47—24no—
292C2×C4×C47—22no—
293C2×C4×C47—24no—
294C2×C4×C47—22no—
295C2×C4×C47—24no—
296C2×C4×C47—48no—
297C2×C4×C47C23×C412yes—
298C2×C4×C47C23×C414yes—
299C2×C4×C47C23×C414yes—
300C2×C4×C47C23×C412yes—
301C2×C4×C47C2×#4114yes—
302C2×C4×C47H(5,𝔽2)14yes—
303C2×Dic47—28no—
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47—21no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—24no—
314C2×Dic47—22no—
315C2×Dic47—24no—
316C2×Dic47—22no—
317C2×Dic47—24no—
318C2×Dic47—44no—
319C2×Dic47C23×C412yes—
320C2×Dic47C23×C412yes—
321C2×Dic47C23×C412yes—
322C2×Dic47C23×C412yes—
323C2×Dic47C2×#4114yes—
324D188—28no—
325D188—28no—
326D188—48no—
327C4×D47—88no—
328C4×D47—88no—
329#34240—471nomaximal, Sylow
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—24no—
333C22×C47—24no—
334C22×C47C4×#4114yes—
335C22×C47C24×C411yescharacteristic
336C22×C47C22×#4111yescharacteristic
337C22×C47C22×#4111yescharacteristic
338C22×C47C2×H(5,𝔽2)12yes—
339C22×C47#58512yes—
340C2×D47—24no—
341C2×D47—24no—
342C2×D47—24no—
343C2×D47—24no—
344C2×D47—24no—
345C2×D47—24no—
346C2×D47—44no—
347C2×D47—44no—
348C2×D47—44no—
349C2×D47—44no—
350C2×D47—816no—
351C4×C47—22no—
352C4×C47—24no—
353C4×C47—24no—
354C4×C47—24no—
355C4×C47—44no—
356C4×C47—42no—
357C4×C47#51814yes—
358Dic47—22no—
359Dic47—22no—
360Dic47—22no—
361Dic47—22no—
362Dic47—24no—
363Dic47—44no—
364Dic47—42no—
365C22×#124—471no—
366#2372—474no—
367#2367—472no—
368#2367—472no—
369#2342—472no—
370#2342—472no—
371Q8×C22⋊C4—471no—
372Q8×C22⋊C4D4711yescharacteristic, complemented
373D4×C22⋊C4—471no—
374D4×C22⋊C4—471no—
375#2337—474no—
376#2312—472no—
377C4×#124—472no—
378C4×#124—472no—
379#2283—471no—
380#2273—472no—
381C4×#117—471no—
382C2×C47—24no—
383C2×C47C2×C4×#4111yescharacteristic
384C2×C47C2×#51811yescharacteristic
385C2×C47#342811yescharacteristic
386C2×C47#351412yes—
387C2×C47#351412yes—
388D47—44no—
389D47—44no—
390C23×Q8C2×D4711yescharacteristic
391C23×D4—471no—
392C2×#124—4716no—
393C2×#124—472no—
394C2×#124—471no—
395C2×#124—471no—
396C2×#124—472no—
397C2×#124—471no—
398C2×#124—471no—
399C2×C4×Q8—472no—
400C2×C4×Q8C2×D4712yescomplemented
401C2×C4×D4—472no—
402C2×C4×D4—472no—
403C2×#117—471no—
404C2×#117—471no—
405C22×C22⋊C4—472no—
406C22×C22⋊C4—472no—
407C22×C22⋊C4—472no—
408C22×C22⋊C4—472no—
409C22×C42—471no—
410#391—474no—
411#391—472no—
412#391C2×D4714yescomplemented
413#391C2×D4712yescomplemented
414#390—472no—
415#390—472no—
416#388—474no—
417#388—474no—
418#388—474no—
419#388—474no—
420#388—474no—
421#388—474no—
422#388—474no—
423#388—474no—
424#386—474no—
425#386—474no—
426#385—474no—
427#385—474no—
428#383—472no—
429#382—472no—
430#381—472no—
431#380—472no—
432#380—471no—
433#380C2×D4712yes—
434#380C2×D4711yescharacteristic
435#379—472no—
436#379—472no—
437C4×C4⋊C4—472no—
438C4×C4⋊C4—472no—
439C4×C4⋊C4—472no—
440C4×C22⋊C4—471no—
441C4×C22⋊C4—472no—
442C4×C22⋊C4—471no—
443C4×C22⋊C4—472no—
444C4×C22⋊C4—471no—
445C4×C22⋊C4—474no—
446C4×C22⋊C4—474no—
447C4×C22⋊C4—474no—
448C4×C22⋊C4—474no—
449C4×C22⋊C4—474no—
450C4×C22⋊C4—474no—
451C4×C22⋊C4C2×D4711yescharacteristic
452C4×C22⋊C4C2×D4712yes—
453#376—472no—
454#376—472no—
455C43—472no—
456C47#3424011yescharacteristic, complemented, Sylow
457C25—472no—
458C22×Q8—44no—
459C22×Q8C4×D4718yescomplemented
460C22×Q8C22×D4711yescharacteristic
461C22×Q8C22×D4711yescharacteristic
462C22×Q8C22×D4712yes—
463C22×D4—478no—
464C22×D4—471no—
465C22×D4—471no—
466C22×D4—472no—
467C22×D4—1884no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4—474no—
471C23×C4—474no—
472C23×C4C22×D4711yescharacteristic
473C23×C4C22×D4712yes—
474#124—478no—
475#124—478no—
476#124—478no—
477#124—478no—
478#124—4716no—
479#124—4716no—
480C4×Q8—44no—
481C4×Q8—1884no—
482C4×D4—1884no—
483C4×D4—1884no—
484#117—944no—
485#117—944no—
486C2×C4⋊C4—472no—
487C2×C4⋊C4—472no—
488C2×C4⋊C4—472no—
489C2×C4⋊C4—474no—
490C2×C4⋊C4C22×D4712yes—
491C2×C4⋊C4C22×D4714yes—
492C2×C22⋊C4—471no—
493C2×C22⋊C4—4716no—
494C2×C22⋊C4—4716no—
495C2×C22⋊C4—472no—
496C2×C22⋊C4—472no—
497C2×C22⋊C4—472no—
498C2×C22⋊C4—472no—
499C2×C22⋊C4—472no—
500C2×C22⋊C4—472no—
501C2×C22⋊C4—472no—
502C2×C22⋊C4—472no—
503C2×C22⋊C4—472no—
504C2×C22⋊C4—471no—
505C2×C22⋊C4—474no—
506C2×C22⋊C4—474no—
507C2×C22⋊C4—474no—
508C2×C22⋊C4—474no—
509C2×C22⋊C4—474no—
510C2×C22⋊C4—474no—
511C2×C22⋊C4—948no—
512C2×C22⋊C4—948no—
513C2×C22⋊C4C22×D4712yes—
514C2×C22⋊C4C22×D4711yescharacteristic
515C2×C22⋊C4C22×D4711yescharacteristic
516C2×C42—478no—
517C2×C42—471no—
518C2×C42—471no—
519C2×C42—471no—
520C2×C42—471no—
521C2×C42—472no—
522C2×C42—472no—
523C2×C42—472no—
524C2×C42—474no—
525C2×C42—472no—
526C2×C42—472no—
527C2×C42—474no—
528C2×C42C22×D4712yes—
529C2×C42C22×D4714yes—
530#95—472no—
531#95—474no—
532#95—472no—
533#95—472no—
534#95—472no—
535#95—474no—
536#95—474no—
537#95—474no—
538#95—474no—
539#95C22×D4712yes—
540#95C22×D4712yes—
541#95C22×D4714yes—
542#95C22×D4714yes—
543C24—472no—
544C24—472no—
545C24—478no—
546C24—944no—
547C24—944no—
548C24—1884no—
549C24—1884no—
550C24C23×D4711yescharacteristic
551C2×Q8—24no—
552C2×Q8—24no—
553C2×Q8—44no—
554C2×Q8—416no—
555C2×Q8C2×C4×D4714yes—
556C2×Q8C2×C4×D4714yes—
557C2×Q8C2×C4×D4718yes—
558C2×D4—474no—
559C2×D4—474no—
560C2×D4—478no—
561C2×D4—944no—
562C2×D4—944no—
563C2×D4—18816no—
564C2×D4—1884no—
565C22×C4—24no—
566C22×C4—44no—
567C22×C4—474no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—471no—
571C22×C4—472no—
572C22×C4—471no—
573C22×C4—474no—
574C22×C4—474no—
575C22×C4—472no—
576C22×C4—948no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—948no—
580C22×C4—1884no—
581C22×C4—1884no—
582C22×C4—1884no—
583C22×C4—1884no—
584C22×C4—1882no—
585C22×C4C2×C4×D4714yes—
586C22×C4C2×C4×D4718yes—
587C22×C4C23×D4714yes—
588C22×C4C23×D4712yes—
589C22×C4C23×D4711yescharacteristic
590C22×C4C23×D4712yes—
591C22×C4C23×D4712yes—
592C22×C4C23×D4712yes—
593C22×C4C23×D4711yescharacteristic
594C4⋊C4—24no—
595C4⋊C4—44no—
596C4⋊C4—944no—
597C4⋊C4—944no—
598C4⋊C4—944no—
599C4⋊C4—1884no—
600C22⋊C4—24no—
601C22⋊C4—22no—
602C22⋊C4—474no—
603C22⋊C4—478no—
604C22⋊C4—478no—
605C22⋊C4—478no—
606C22⋊C4—478no—
607C22⋊C4—478no—
608C22⋊C4—478no—
609C22⋊C4—478no—
610C22⋊C4—478no—
611C22⋊C4—948no—
612C22⋊C4—944no—
613C22⋊C4—942no—
614C22⋊C4—948no—
615C22⋊C4—1884no—
616C22⋊C4—1884no—
617C22⋊C4—1884no—
618C22⋊C4—1884no—
619C22⋊C4#1062535414yes—
620C42—24no—
621C42—44no—
622C42—474no—
623C42—474no—
624C42—474no—
625C42—474no—
626C42—944no—
627C42—944no—
628C42—944no—
629C42—1882no—
630C42—1882no—
631C42—1884no—
632C42—1884no—
633C23—22no—
634C23—22no—
635C23—474no—
636C23—474no—
637C23—9416no—
638C23—942no—
639C23—942no—
640C23—942no—
641C23—942no—
642C23—944no—
643C23—944no—
644C23—944no—
645C23—944no—
646C23—3768no—
647C23—3768no—
648C23—1888no—
649C23—1888no—
650C23C22×C4×D4712yes—
651C23#41×D4712yes—
652C23C2×#1062535412yes—
653C23C24×D4711yescharacteristic
654Q8—28no—
655Q8—28no—
656Q8—48no—
657D4—948no—
658D4—948no—
659D4—1888no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—28no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—48no—
673C2×C4—472no—
674C2×C4—472no—
675C2×C4—472no—
676C2×C4—472no—
677C2×C4—474no—
678C2×C4—948no—
679C2×C4—941no—
680C2×C4—941no—
681C2×C4—941no—
682C2×C4—941no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—944no—
689C2×C4—942no—
690C2×C4—944no—
691C2×C4—942no—
692C2×C4—944no—
693C2×C4—3768no—
694C2×C4—3768no—
695C2×C4—1884no—
696C2×C4C22×C4×D4712yes—
697C2×C4C22×C4×D4714yes—
698C2×C4C22×C4×D4714yes—
699C2×C4C22×C4×D4712yes—
700C2×C4C2×#1062535414yes—
701C2×C4#1309406914yes—
702C22—22no—
703C22—24no—
704C22—24no—
705C22—22no—
706C22—944no—
707C22—944no—
708C22—944no—
709C22—944no—
710C22—944no—
711C22—944no—
712C22—37616no—
713C22—1884no—
714C22—1884no—
715C22—1884no—
716C22—1884no—
717C22C4×#1062535414yes—
718C22C23×C4×D4711yescharacteristic
719C22C2×#41×D4711yescharacteristic
720C22C22×#1062535411yescharacteristic
721C22C2×#1309406912yes—
722C22#1568996012yes—
723C4—22no—
724C4—24no—
725C4—24no—
726C4—24no—
727C4—44no—
728C4—42no—
729C4—942no—
730C4—942no—
731C4—944no—
732C4—942no—
733C4—942no—
734C4—1884no—
735C4—1882no—
736C4#1568959614yes—
737C2—24no—
738C2—1884no—
739C2—1884no—
740C2C2×C4×#1062535411yescharacteristic
741C2C2×#1568959611yescharacteristic
742C2#2025659011yescharacteristic
743C2#2025734212yes—
744C2#2025735012yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingQ8×C22⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC23×D188C22
hypercenterQ8×C22⋊C4D47
hypocenterC47#34240
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20246499C2semidirect
3. #20246464C2semidirect
4. #20246455C2semidirect
5. #20246240C2semidirect
6. #20246234C2semidirect
7. Q8×C22⋊Dic47C2semidirect
10. #20246200C2semidirect
11. #20245985C2semidirect
12. C4×#13094013C2semidirect
13. #20245931C2semidirect
14. #20245783C2semidirect
15. #20245740C2semidirect
16. C4×#13093980C2semidirect
17. Q8×C22⋊C4×C47C2semidirect
19. C2×#13094013C4semidirect
26. C2×Q8×Dic47C22semidirect
36. #15689030C22semidirect
37. #15689030C22semidirect
40. #15689015C22semidirect
41. #15689015C22semidirect
42. #15689015C22semidirect
43. #15689014C22semidirect
44. #15689013C22semidirect
45. #15689013C22semidirect
46. #15689013C22semidirect
47. #15689012C22semidirect
50. #15688997C22semidirect
51. #15688994C22semidirect
52. #15688990C22semidirect
53. #15688988C22semidirect
59. C4⋊C4×Dic47C22semidirect
60. C4×Dic47⋊C4C22semidirect
61. #15688974C22semidirect
65. C4×(C2×D47)⋊C4C22semidirect
66. C4×(C2×D47)⋊C4C22semidirect
67. C4×(C2×D47)⋊C4C22semidirect
70. #15688970C22semidirect
71. #15688970C22semidirect
72. #15688970C22semidirect
73. #15688968C22semidirect
74. #15688968C22semidirect
75. C42×Dic47C22semidirect
77. C2×C4×Q8×C47C22semidirect
78. C47×#391C22semidirect
79. C47×#391C22semidirect
94. #13094013C2×C4semidirect
95. #13094013C2×C4semidirect
96. #13094013C2×C4semidirect
97. #13094013C2×C4semidirect
98. #13094013C2×C4semidirect
99. #13094013C2×C4semidirect
112. C2×(C2×D47)⋊C4C2×C4semidirect
113. C2×(C2×D47)⋊C4C2×C4semidirect
130. C2×C4×Dic47C2×C4semidirect
152. C22×Q8×C47C2×C4semidirect
372. Q8×C22⋊C4D47semidirect
400. C2×C4×Q8C2×D47semidirect
412. #391C2×D47semidirect
413. #391C2×D47semidirect
456. C47#34240semidirect
459. C22×Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130940132
#202464992
#202464642
#202464552
#202462402
#202462342
Q8×C22⋊Dic472
C22⋊C4×D1882
#202462082
#202462002
#202459852
C4×#130940132
#202459312
#202457832
#202457402
C4×#130939802
Q8×C22⋊C4×C472
#3424047