Finite Group Databasebeta

← #26376711

Subgroups — #26376711

Order 12032.

2226 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689676C211yesmaximal, characteristic
2#20246486C212yesmaximal, complemented
3#20246480C212yesmaximal, complemented
4#20246475C212yesmaximal, complemented
5#20246447C212yesmaximal, complemented
6#20246346C212yesmaximal, complemented
7#20246346C212yesmaximal, complemented
8#20246343C212yesmaximal, complemented
9C4⋊C4×Dic94C212yesmaximal, complemented
10#20246116C214yesmaximal
11#20246011C211yesmaximal, characteristic
12#20246008C211yesmaximal, characteristic
13C4×#13094001C214yesmaximal
14#20245791C211yesmaximal, characteristic
15#20245745C211yesmaximal, characteristic
16C2×C4⋊C4×Dic47C211yesmaximal, characteristic
17C47×#2274C211yesmaximal, characteristic
18#15689676C4116yescomplemented
19C2×#13094023C2211yescharacteristic
20C2×#13094023C2211yescharacteristic
21C2×#13094015C2211yescharacteristic
22C2×#13094015C2211yescharacteristic
23C2×#13094001C2212yes—
24C2×#13094001C2212yes—
25C2×C4×Dic94C2214yes—
26C2×C4×Dic94C2212yes—
27C2×C4×Dic94C2212yes—
28C2×#13093983C2211yescharacteristic
29C2×#13093983C2211yescharacteristic
30C22×C4⋊Dic47C2211yescharacteristic
31C22×C4×Dic47C2212yes—
32C22×C4×Dic47C2211yescharacteristic
33#15689029C2214yes—
34#15689027C2214yes—
35#15689027C2214yes—
36#15689022C2212yes—
37#15689022C2212yes—
38#15689021C2214yes—
39#15689021C2212yes—
40#15689021C2212yes—
41#15689020C2214yes—
42#15689020C2214yes—
43#15689010C2214yes—
44#15689010C2214yes—
45#15689007C2214yes—
46#15689007C2214yes—
47#15689006C2214yes—
48#15689006C2214yes—
49#15688998C2214yes—
50#15688995C2214yes—
51#15688993C2212yes—
52#15688992C2211yescharacteristic
53#15688992C2211yescharacteristic
54#15688992C2212yes—
55#15688989C2212yes—
56#15688988C2211yescharacteristic
57#15688988C2211yescharacteristic
58#15688988C2212yes—
59#15688981C2212yes—
60#15688981C2212yes—
61C4⋊C4×Dic47C2212yes—
62C4⋊C4×Dic47C2212yes—
63C4⋊C4×Dic47C2212yes—
64C4⋊C4×Dic47C2212yes—
65C4⋊C4×Dic47C2212yes—
66C4⋊C4×Dic47C2212yes—
67C4⋊C4×Dic47C2212yes—
68C4⋊C4×Dic47C2212yes—
69C4×Dic47⋊C4C2212yes—
70C4×Dic47⋊C4C2212yes—
71C4×Dic47⋊C4C2214yes—
72C4×Dic47⋊C4C2214yes—
73C4×C4⋊Dic47C2214yes—
74C4×C22⋊Dic47C2214yes—
75C2×C47⋊#95C2212yes—
76C2×#117×C47C2211yescharacteristic
77C2×#117×C47C2211yescharacteristic
78C22×C4⋊C4×C47C2211yescharacteristic
79C4×C4⋊C4×C47C2212yes—
80C4×C4⋊C4×C47C2212yes—
81C4×C4⋊C4×C47C2212yes—
82C4×C4⋊C4×C47C2212yes—
83C4×C22⋊C4×C47C2214yes—
84C22×Dic94C2312yes—
85C22×Dic94C2312yes—
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2312yes—
88C23×Dic47C2311yescharacteristic
89#13094023C2×C418yescomplemented
90#13094023C2×C418yescomplemented
91#13094015C2×C418yescomplemented
92#13094015C2×C418yescomplemented
93#13094001C2×C4116yes—
94#13094001C2×C4116yes—
95C4×Dic94—48no—
96C4×Dic94C2×C4116yescomplemented
97C4×Dic94C2×C4116yescomplemented
98#13093983—24no—
99#13093983C2×C418yes—
100C2×C4⋊Dic47—24no—
101C2×C4⋊Dic47C2311yescharacteristic
102C2×C4⋊Dic47C2312yes—
103C2×C4⋊Dic47C2311yescharacteristic
104C2×C4⋊Dic47C2312yes—
105C2×C4⋊Dic47C2314yes—
106C2×C4⋊Dic47C2314yes—
107C2×C4⋊Dic47C2312yes—
108C2×C4⋊Dic47C2311yescharacteristic
109C2×C4⋊Dic47C2311yescharacteristic
110C2×C4⋊Dic47C2312yes—
111C2×Dic47⋊C4C2312yes—
112C2×Dic47⋊C4C2312yes—
113C2×Dic47⋊C4C2312yes—
114C2×Dic47⋊C4C2312yes—
115C2×Dic47⋊C4C2314yes—
116C2×Dic47⋊C4C2314yes—
117C2×Dic47⋊C4C2312yes—
118C2×Dic47⋊C4C2312yes—
119C2×Dic47⋊C4C2312yes—
120C2×Dic47⋊C4C2312yes—
121C2×C22⋊Dic47C2312yes—
122C2×C22⋊Dic47C2312yes—
123C2×C4×Dic47—44no—
124C2×C4×Dic47C2×C418yes—
125C2×C4×Dic47C2312yes—
126C2×C4×Dic47C2314yes—
127C2×C4×Dic47C2314yes—
128C2×C4×Dic47C2314yes—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2311yescharacteristic
131C2×C4×Dic47C2311yescharacteristic
132C2×C4×Dic47C2311yescharacteristic
133C2×C4×Dic47C2312yes—
134C2×C4×Dic47C2311yescharacteristic
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C47⋊#95C2312yes—
140C47⋊#95C2314yes—
141C47⋊#95C2312yes—
142C47⋊#95C2312yes—
143C47⋊#95C2312yes—
144C47⋊#95C2314yes—
145C47⋊#95C2314yes—
146C47⋊#95C2314yes—
147C23×C4×C47C2312yes—
148C23×C4×C47C2311yescharacteristic
149#117×C47—24no—
150#117×C47C2×C418yes—
151C2×C4⋊C4×C47Q818yescomplemented
152C2×C4⋊C4×C47C2311yescharacteristic
153C2×C4⋊C4×C47C2311yescharacteristic
154C2×C4⋊C4×C47C2311yescharacteristic
155C2×C4⋊C4×C47C2311yescharacteristic
156C2×C4⋊C4×C47C2312yes—
157C2×C4⋊C4×C47C2312yes—
158C2×C22⋊C4×C47C2312yes—
159C2×C22⋊C4×C47C2312yes—
160C2×C42×C47C2312yes—
161C2×C42×C47C2314yes—
162C2×C42×C47C2314yes—
163C2×C42×C47C2312yes—
164#95×C47C2314yes—
165#95×C47C2314yes—
166C24×C47C2411yescharacteristic
167C22×C4×C47—42no—
168C22×C4×C47—42no—
169C22×C4×C47C22×C414yes—
170C22×C4×C47C2×Q818yes—
171C22×C4×C47C2×Q814yes—
172C22×C4×C47#4114yes—
173C22×C4×C47C2412yes—
174C22×C4×C47C2412yes—
175C22×C4×C47C2412yes—
176C22×C4×C47C2412yes—
177C22×C4×C47C2414yes—
178C22×C4×C47C2411yescharacteristic
179C22×C4×C47C2411yescharacteristic
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—24no—
183C22×Dic47—42no—
184C22×Dic47—41no—
185C22×Dic47—41no—
186C22×Dic47—42no—
187C22×Dic47C22×C414yes—
188C22×Dic47C22×C414yes—
189C22×Dic47C2412yes—
190C22×Dic47C2414yes—
191C22×Dic47C2412yes—
192C22×Dic47C2411yescharacteristic
193C22×Dic47C2411yescharacteristic
194C22×Dic47C2412yes—
195C22×Dic47C2412yes—
196C22×Dic47C2411yescharacteristic
197C22×Dic47C2411yescharacteristic
198C2×Dic94—24no—
199C2×Dic94—24no—
200C2×Dic94—42no—
201C2×Dic94—42no—
202C2×Dic94C22×C418yes—
203C2×Dic94C22×C418yes—
204C4⋊C4×C47—22no—
205C4⋊C4×C47—22no—
206C4⋊C4×C47C22×C414yes—
207C4⋊C4×C47C22×C414yes—
208C4⋊C4×C47C2×Q818yes—
209C4⋊C4×C47C2×Q818yes—
210C22⋊C4×C47—24no—
211C22⋊C4×C47C22×C418yes—
212C42×C47—24no—
213C42×C47—44no—
214C42×C47—44no—
215C42×C47C22×C418yes—
216C22⋊Dic47—24no—
217C22⋊Dic47C22×C418yes—
218C4⋊Dic47—24no—
219C4⋊Dic47—24no—
220C4⋊Dic47—22no—
221C4⋊Dic47—22no—
222C4⋊Dic47—44no—
223C4⋊Dic47—44no—
224C4⋊Dic47C22×C414yes—
225C4⋊Dic47C22×C414yes—
226C4⋊Dic47C22×C418yes—
227C4⋊Dic47C22×C418yes—
228Dic47⋊C4—24no—
229Dic47⋊C4—24no—
230Dic47⋊C4—44no—
231Dic47⋊C4—42no—
232Dic47⋊C4—42no—
233Dic47⋊C4—44no—
234Dic47⋊C4C22×C418yes—
235Dic47⋊C4C22×C418yes—
236Dic47⋊C4C22×C418yes—
237Dic47⋊C4C22×C418yes—
238C4×Dic47—24no—
239C4×Dic47—28no—
240C4×Dic47—44no—
241C4×Dic47—44no—
242C4×Dic47—44no—
243C4×Dic47C22×C414yes—
244C4×Dic47C22×C414yes—
245C4×Dic47C22×C414yes—
246C4×Dic47C22×C414yes—
247C4×Dic47C22×C418yes—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47C23×C412yes—
253C23×C47C22×Q812yes—
254C23×C47C2×#4112yes—
255C23×C47C2511yescharacteristic
256C2×C4×C47—24no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—24no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—48no—
269C2×C4×C47C4×Q8116yescomplemented
270C2×C4×C47C23×C414yes—
271C2×C4×C47C23×C414yes—
272C2×C4×C47C23×C412yes—
273C2×C4×C47C23×C412yes—
274C2×C4×C47C22×Q818yes—
275C2×C4×C47C22×Q812yes—
276C2×C4×C47C22×Q812yes—
277C2×C4×C47C2×#4112yes—
278C2×C4×C47C2×#4112yes—
279C2×Dic47—21no—
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—21no—
283C2×Dic47—22no—
284C2×Dic47—22no—
285C2×Dic47—21no—
286C2×Dic47—21no—
287C2×Dic47—21no—
288C2×Dic47—21no—
289C2×Dic47—28no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—24no—
293C2×Dic47—24no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—24no—
299C2×Dic47—44no—
300C2×Dic47—48no—
301C2×Dic47C23×C412yes—
302C2×Dic47C23×C412yes—
303C2×Dic47C23×C412yes—
304C2×Dic47C23×C414yes—
305C2×Dic47C23×C414yes—
306C2×Dic47C23×C412yes—
307C2×Dic47H(5,𝔽2)12yes—
308C2×Dic472−1+412yes—
309Dic94—216no—
310Dic94—48no—
311#34213—471nomaximal, Sylow
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—22no—
316C22×C47—22no—
317C22×C47—22no—
318C22×C47C2×C4×Q814yes—
319C22×C47C24×C411yescharacteristic
320C22×C47C23×Q811yescharacteristic
321C22×C47C22×#4111yescharacteristic
322C22×C47C2×H(5,𝔽2)11yescharacteristic
323C22×C47C2×2−1+411yescharacteristic
324C22×C47#58511yescharacteristic
325C22×C47#58511yescharacteristic
326C4×C47—24no—
327C4×C47—24no—
328C4×C47—28no—
329C4×C47—42no—
330C4×C47—42no—
331C4×C47C2×C4×Q814yes—
332C4×C47C2×C4×Q814yes—
333Dic47—24no—
334Dic47—22no—
335Dic47—22no—
336Dic47—24no—
337Dic47—22no—
338Dic47—42no—
339Dic47—44no—
340Dic47—42no—
341Dic47#52014yes—
342C2×#533—471no—
343#2370—472no—
344#2370—472no—
345#2369—472no—
346#2365—472no—
347#2355—472no—
348#2355—472no—
349#2355—472no—
350Q8×C4⋊C4—472no—
351#2329—474no—
352#2317—471no—
353#2317—471no—
354C4×C22⋊Q8—474no—
355#2285—471no—
356#2274—471no—
357#2274D4711yescharacteristic
358C2×C4×C4⋊C4—471no—
359C2×C47—24no—
360C2×C47C22×C4×Q811yescharacteristic
361C2×C47C2×#52011yescharacteristic
362C2×C47#342811yescharacteristic
363C2×C47#350111yescharacteristic
364C2×C47#350211yescharacteristic
365C2×C47#350611yescharacteristic
366C2×C47#350711yescharacteristic
367#533—4716no—
368C2×C4⋊Q8—471no—
369C2×C4⋊Q8—471no—
370C2×#125—471no—
371C2×#125—471no—
372C2×C22⋊Q8—472no—
373C2×C22⋊Q8—472no—
374C2×C4×Q8—472no—
375C2×C4×Q8—472no—
376C2×C4×Q8—474no—
377C2×#117—471no—
378C2×#117—471no—
379C2×#117C2×D4711yescharacteristic
380C2×#117C2×D4711yescharacteristic
381C22×C4⋊C4—471no—
382C22×C4⋊C4C2×D4711yescharacteristic
383C22×C42—471no—
384C22×C42—472no—
385#391—474no—
386#391—474no—
387#391—474no—
388#389—472no—
389#389—472no—
390#389—472no—
391#389—472no—
392#389—474no—
393#389—474no—
394#389—474no—
395#387—474no—
396#387—474no—
397#387—474no—
398#387—474no—
399#387—474no—
400#387—474no—
401#385—474no—
402#385—474no—
403#384—472no—
404#384—471no—
405#384—471no—
406#384—472no—
407#382—472no—
408#382—471no—
409#382—471no—
410#382—472no—
411#380—472no—
412#380—472no—
413C4×C4⋊C4—472no—
414C4×C4⋊C4—472no—
415C4×C4⋊C4—472no—
416C4×C4⋊C4—472no—
417C4×C4⋊C4—472no—
418C4×C4⋊C4—472no—
419C4×C4⋊C4—472no—
420C4×C4⋊C4—472no—
421C4×C4⋊C4—474no—
422C4×C4⋊C4—474no—
423C4×C4⋊C4—474no—
424C4×C4⋊C4—472no—
425C4×C4⋊C4—472no—
426C4×C4⋊C4C2×D4712yes—
427C4×C4⋊C4C2×D4712yes—
428C4×C4⋊C4C2×D4712yes—
429C4×C4⋊C4C2×D4712yes—
430C4×C22⋊C4—474no—
431C4×C22⋊C4C2×D4714yes—
432C2×#95—472no—
433C47#3421311yescharacteristic, complemented, Sylow
434C22×Q8—472no—
435C22×Q8—472no—
436C23×C4—471no—
437C23×C4—471no—
438C23×C4—472no—
439C23×C4C22×D4712yes—
440C23×C4C22×D4711yescharacteristic
441C4⋊Q8—478no—
442C4⋊Q8—478no—
443#125—478no—
444#125—478no—
445C22⋊Q8—4716no—
446C22⋊Q8—4716no—
447C4×Q8—4716no—
448C4×Q8—4716no—
449C4×Q8—1888no—
450#117—24no—
451#117—478no—
452#117—944no—
453#117C4×D4718yes—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—471no—
456C2×C4⋊C4—472no—
457C2×C4⋊C4—472no—
458C2×C4⋊C4—472no—
459C2×C4⋊C4—472no—
460C2×C4⋊C4—472no—
461C2×C4⋊C4—472no—
462C2×C4⋊C4—472no—
463C2×C4⋊C4—472no—
464C2×C4⋊C4—471no—
465C2×C4⋊C4—471no—
466C2×C4⋊C4—472no—
467C2×C4⋊C4—472no—
468C2×C4⋊C4—474no—
469C2×C4⋊C4—474no—
470C2×C4⋊C4—472no—
471C2×C4⋊C4—472no—
472C2×C4⋊C4—474no—
473C2×C4⋊C4—474no—
474C2×C4⋊C4—944no—
475C2×C4⋊C4Dic9418yescomplemented
476C2×C4⋊C4C22×D4711yescharacteristic
477C2×C4⋊C4C22×D4711yescharacteristic
478C2×C4⋊C4C22×D4712yes—
479C2×C4⋊C4C22×D4712yes—
480C2×C4⋊C4C22×D4711yescharacteristic
481C2×C4⋊C4C22×D4711yescharacteristic
482C2×C22⋊C4—472no—
483C2×C22⋊C4—472no—
484C2×C22⋊C4C22×D4712yes—
485C2×C22⋊C4C22×D4712yes—
486C2×C42—478no—
487C2×C42—472no—
488C2×C42—471no—
489C2×C42—471no—
490C2×C42—471no—
491C2×C42—471no—
492C2×C42—472no—
493C2×C42—474no—
494C2×C42—474no—
495C2×C42—474no—
496C2×C42—474no—
497C2×C42—1884no—
498C2×C42C22×D4712yes—
499C2×C42C22×D4714yes—
500C2×C42C22×D4714yes—
501C2×C42C22×D4712yes—
502#95—474no—
503#95—474no—
504#95—474no—
505#95—474no—
506#95—472no—
507#95—472no—
508#95—472no—
509#95—472no—
510#95—474no—
511#95—474no—
512#95—474no—
513#95—474no—
514#95C22×D4714yes—
515#95C22×D4714yes—
516C24C23×D4711yescharacteristic
517C2×Q8—478no—
518C2×Q8—478no—
519C2×Q8—944no—
520C2×Q8—944no—
521C2×Q8—1882no—
522C2×Q8—1882no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—471no—
526C22×C4—474no—
527C22×C4—471no—
528C22×C4—471no—
529C22×C4—472no—
530C22×C4—472no—
531C22×C4—471no—
532C22×C4—474no—
533C22×C4—472no—
534C22×C4—474no—
535C22×C4—472no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—944no—
539C22×C4—1882no—
540C22×C4—1881no—
541C22×C4—1881no—
542C22×C4—1882no—
543C22×C4C2×Dic9418yes—
544C22×C4C2×Dic9414yes—
545C22×C4C2×C4×D4714yes—
546C22×C4#1062535014yes—
547C22×C4C23×D4712yes—
548C22×C4C23×D4712yes—
549C22×C4C23×D4712yes—
550C22×C4C23×D4712yes—
551C22×C4C23×D4714yes—
552C22×C4C23×D4711yescharacteristic
553C22×C4C23×D4711yescharacteristic
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—478no—
557C4⋊C4—478no—
558C4⋊C4—478no—
559C4⋊C4—478no—
560C4⋊C4—474no—
561C4⋊C4—474no—
562C4⋊C4—478no—
563C4⋊C4—478no—
564C4⋊C4—944no—
565C4⋊C4—944no—
566C4⋊C4—944no—
567C4⋊C4—944no—
568C4⋊C4—942no—
569C4⋊C4—942no—
570C4⋊C4—1882no—
571C4⋊C4—1882no—
572C4⋊C4—1884no—
573C4⋊C4—1884no—
574C4⋊C4—1884no—
575C4⋊C4—1884no—
576C4⋊C4C2×Dic9418yes—
577C4⋊C4C2×Dic9418yes—
578C4⋊C4C2×C4×D4714yes—
579C4⋊C4C2×C4×D4714yes—
580C22⋊C4—24no—
581C22⋊C4—478no—
582C22⋊C4—944no—
583C22⋊C4C2×C4×D4718yes—
584C42—24no—
585C42—44no—
586C42—44no—
587C42—474no—
588C42—474no—
589C42—474no—
590C42—474no—
591C42—478no—
592C42—948no—
593C42—944no—
594C42—1884no—
595C42—1884no—
596C42—1884no—
597C42C2×C4×D4718yes—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23C22×C4×D4712yes—
603C23C22×Dic9412yes—
604C23C2×#1062535012yes—
605C23C24×D4711yescharacteristic
606Q8—9416no—
607Q8—1888no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—48no—
621C2×C4—472no—
622C2×C4—472no—
623C2×C4—472no—
624C2×C4—472no—
625C2×C4—472no—
626C2×C4—472no—
627C2×C4—474no—
628C2×C4—474no—
629C2×C4—948no—
630C2×C4—941no—
631C2×C4—942no—
632C2×C4—941no—
633C2×C4—942no—
634C2×C4—942no—
635C2×C4—941no—
636C2×C4—941no—
637C2×C4—941no—
638C2×C4—942no—
639C2×C4—941no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—944no—
643C2×C4—944no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—944no—
649C2×C4—1884no—
650C2×C4—1888no—
651C2×C4C4×Dic94116yescomplemented
652C2×C4C22×C4×D4714yes—
653C2×C4C22×C4×D4714yes—
654C2×C4C22×C4×D4712yes—
655C2×C4C22×C4×D4712yes—
656C2×C4C22×Dic9418yes—
657C2×C4C22×Dic9412yes—
658C2×C4C22×Dic9412yes—
659C2×C4C2×#1062535012yes—
660C2×C4C2×#1062535012yes—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22C2×C4×Dic9414yes—
668C22C23×C4×D4711yescharacteristic
669C22C23×Dic9411yescharacteristic
670C22C22×#1062535011yescharacteristic
671C22H(5,𝔽2)×D4711yescharacteristic
672C222−1+4×D4711yescharacteristic
673C22#1568995811yescharacteristic
674C22#1568996011yescharacteristic
675C4—24no—
676C4—24no—
677C4—28no—
678C4—42no—
679C4—42no—
680C4—474no—
681C4—942no—
682C4—944no—
683C4—942no—
684C4—942no—
685C4—944no—
686C4—1884no—
687C4—1882no—
688C4—1882no—
689C4C2×C4×Dic9414yes—
690C4C2×C4×Dic9414yes—
691C2—24no—
692C2C22×C4×Dic9411yescharacteristic
693C2#520×D4711yescharacteristic
694C2#2025658811yescharacteristic
695C2#2025718611yescharacteristic
696C2#2025719411yescharacteristic
697C2#2025723311yescharacteristic
698C2#2025724611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2274C2
socle, cosocleC23×C47C25
prime radicalC24×C47C24
hypercenter#2274D47
hypocenterC47#34213
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. #20246486C2semidirect
3. #20246480C2semidirect
4. #20246475C2semidirect
5. #20246447C2semidirect
6. #20246346C2semidirect
7. #20246346C2semidirect
8. #20246343C2semidirect
9. C4⋊C4×Dic94C2semidirect
18. #15689676C4semidirect
89. #13094023C2×C4semidirect
90. #13094023C2×C4semidirect
91. #13094015C2×C4semidirect
92. #13094015C2×C4semidirect
96. C4×Dic94C2×C4semidirect
97. C4×Dic94C2×C4semidirect
151. C2×C4⋊C4×C47Q8semidirect
269. C2×C4×C47C4×Q8semidirect
433. C47#34213semidirect
475. C2×C4⋊C4Dic94semidirect
651. C2×C4C4×Dic94semidirect

Maximal subgroups

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

subgroupindex
C2×#156896762
#202464862
#202464802
#202464752
#202464472
#202463462
#202463432
C4⋊C4×Dic942
#202461162
#202460112
#202460082
C4×#130940012
#202457912
#202457452
C2×C4⋊C4×Dic472
C47×#22742
#3421347