Finite Group Databasebeta

← #26232373

Subgroups — #26232373

Order 12032.

1162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689651C211yesmaximal, characteristic
2C2×#15689202C211yesmaximal, characteristic, complemented
3C2×#15689196C211yesmaximal, characteristic, complemented
4#20244328C211yesmaximal, characteristic, complemented
5#20244324C211yesmaximal, characteristic, complemented
6#20243682C211yesmaximal, characteristic, complemented
7#20243682C211yesmaximal, characteristic, complemented
8#20243682C211yesmaximal, characteristic, complemented
9#20243677C211yesmaximal, characteristic, complemented
10#20243458C211yesmaximal, characteristic, complemented
11#20243455C211yesmaximal, characteristic, complemented
12#20243372C211yesmaximal, characteristic, complemented
13#20243083C211yesmaximal, characteristic, complemented
14#20243080C211yesmaximal, characteristic, complemented
15C47×#1750C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20#15689651—24no—
21#15689651—24no—
22C2×#13094019C411yescharacteristic
23C2×#13094017C411yescharacteristic
24C2×#13094014C411yescharacteristic
25C2×#13094010C411yescharacteristic
26C2×#13094009C411yescharacteristic
27C2×#13094006C411yescharacteristic
28C2×#13094002C411yescharacteristic
29C2×#13093997C411yescharacteristic
30C2×C4×Dic94C2211yescharacteristic
31C2×C4×D188C2211yescharacteristic
32C2×C4×C22⋊D47C2211yescharacteristic
33C2×C4×C22⋊D47C2211yescharacteristic
34C2×#13093981C2211yescharacteristic
35C2×C42×D47C2211yescharacteristic
36#15689202—24no—
37#15689196—24no—
38C2×C4⋊(C47⋊C8)C2211yescharacteristic
39C2×C4⋊(C47⋊C8)C2211yescharacteristic
40C2×C22⋊(C47⋊C8)C2211yescharacteristic
41C2×C22⋊(C47⋊C8)C2211yescharacteristic
42C2×(C2×D47)⋊C8C2211yescharacteristic
43C2×(C2×D47)⋊C8C2211yescharacteristic
44C2×(C2×D47)⋊C8C2211yescharacteristic
45C2×(C2×D47)⋊C8C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C2×#117×C47C2211yescharacteristic
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×#97×C47C2211yescharacteristic
60C2×C4×C8×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Dic94C2×C411yescharacteristic
64C22×D188C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C22×C22⋊D47C2×C411yescharacteristic
67C22×C4×D47C2×C411yescharacteristic
68C22×C4×D47C2×C411yescharacteristic
69C22×C4×D47C2311yescharacteristic
70C22×C4×D47C2311yescharacteristic
71C2×#10625324—22no—
72C2×#10625324—22no—
73C2×#10625324—22no—
74C2×#10625324—22no—
75C2×#10625324—22no—
76C2×#10625324—22no—
77C2×#10625324—41no—
78C2×#10625324—41no—
79C2×#10625324—41no—
80C22×C47⋊C8C2311yescharacteristic
81C22×C47⋊C8C2311yescharacteristic
82C22×C47⋊C8C2311yescharacteristic
83C22×C47⋊C8C2311yescharacteristic
84C2×C8×D47—22no—
85C2×C8×D47—22no—
86C2×C8×D47—41no—
87#13094019—24no—
88#13094017—24no—
89#13094014—24no—
90#13094010—24no—
91#13094009—24no—
92#13094006—24no—
93#13094002—24no—
94#13093997—24no—
95C4×Dic94—22no—
96C4×Dic94—22no—
97C4×D188D414yes—
98C4×D188D414yes—
99C4×C22⋊D47—22no—
100C4×C22⋊D47—22no—
101C4×C22⋊D47—22no—
102C4×C22⋊D47—22no—
103#13093981—22no—
104#13093981—22no—
105C2×C4⋊Dic47C2×C411yescharacteristic
106C2×C4⋊Dic47C2×C411yescharacteristic
107C2×Dic47⋊C4C2×C411yescharacteristic
108C2×Dic47⋊C4C2×C411yescharacteristic
109C2×Dic47⋊C4C2×C411yescharacteristic
110C2×Dic47⋊C4C2×C411yescharacteristic
111C2×Dic47⋊C4C2×C411yescharacteristic
112C2×Dic47⋊C4C2×C411yescharacteristic
113C2×C22⋊Dic47C2×C411yescharacteristic
114C2×C22⋊Dic47C2×C411yescharacteristic
115C2×(C2×D47)⋊C4C2×C411yescharacteristic
116C2×(C2×D47)⋊C4C2×C411yescharacteristic
117C2×(C2×D47)⋊C4C2×C411yescharacteristic
118C2×(C2×D47)⋊C4C2×C411yescharacteristic
119C2×(C2×D47)⋊C4C2×C411yescharacteristic
120C2×(C2×D47)⋊C4C2×C411yescharacteristic
121C2×C4×Dic47C2×C411yescharacteristic
122C2×C4×Dic47C2×C411yescharacteristic
123C2×C4×Dic47C2311yescharacteristic
124C2×C4×Dic47C2311yescharacteristic
125C42×D47—22no—
126C42×D47—22no—
127C4⋊(C47⋊C8)—22no—
128C4⋊(C47⋊C8)—22no—
129C22⋊(C47⋊C8)—41no—
130C22⋊(C47⋊C8)—41no—
131(C2×D47)⋊C8—22no—
132(C2×D47)⋊C8—22no—
133(C2×D47)⋊C8—22no—
134(C2×D47)⋊C8—22no—
135C23×C4×C47C2311yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139C22×C8×C47C2311yescharacteristic
140#117×C47—22no—
141#117×C47—22no—
142C2×C4⋊C4×C47C2×C411yescharacteristic
143C2×C4⋊C4×C47C2×C411yescharacteristic
144C2×C22⋊C4×C47C2×C411yescharacteristic
145C2×C22⋊C4×C47C2×C411yescharacteristic
146C2×C42×C47C2311yescharacteristic
147C2×C42×C47C2311yescharacteristic
148C22⋊C8×C47—22no—
149C22⋊C8×C47—22no—
150#97×C47—22no—
151C4×C8×C47—22no—
152C24×C47C22×C411yescharacteristic
153C23×D47C22×C411yescharacteristic
154C23×D47C22×C411yescharacteristic
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C22×C411yescharacteristic
165C22×C4×C47C22×C411yescharacteristic
166C22×C4×C47C2411yescharacteristic
167C2×C22⋊D47—22no—
168C2×C22⋊D47—22no—
169C2×C22⋊D47—22no—
170C2×C22⋊D47—41no—
171C2×C22⋊D47—41no—
172C2×C22⋊D47—41no—
173C22×Dic47C22×C411yescharacteristic
174C22×Dic47C22×C411yescharacteristic
175C22×Dic47C22×C411yescharacteristic
176C22×Dic47C22×C411yescharacteristic
177C22×Dic47C22×C411yescharacteristic
178C22×Dic47C22×C411yescharacteristic
179C2×D188—41no—
180C2×D188—41no—
181C2×D188C22⋊C414yes—
182C2×C4×D47—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—22no—
191C2×C4×D47—22no—
192C2×C4×D47—22no—
193C2×C4×D47—41no—
194C2×C4×D47—41no—
195C2×C4×D47—41no—
196C2×C4×D47C2×D412yes—
197C2×C4×D47C2×D412yes—
198C2×C4×D47C2×D412yes—
199C2×C4×D47C2×D412yes—
200C2×Dic94—22no—
201C2×Dic94—22no—
202C2×Dic94—41no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47#4112yes—
214C2×C8×C47#4112yes—
215C4⋊C4×C47—22no—
216C4⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C42×C47—21no—
220C42×C47—21no—
221C42×C47C2×D412yes—
222C42×C47C2×D412yes—
223C22⋊Dic47—22no—
224C22⋊Dic47—22no—
225(C2×D47)⋊C4—22no—
226(C2×D47)⋊C4—22no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4—22no—
229(C2×D47)⋊C4C22⋊C414yes—
230(C2×D47)⋊C4C22⋊C414yes—
231C4⋊Dic47—22no—
232C4⋊Dic47C22⋊C414yes—
233Dic47⋊C4—22no—
234Dic47⋊C4—22no—
235Dic47⋊C4—22no—
236Dic47⋊C4—22no—
237Dic47⋊C4—22no—
238Dic47⋊C4—22no—
239C4×Dic47—21no—
240C4×Dic47—21no—
241C4×Dic47—21no—
242C4×Dic47—21no—
243C4×Dic47—22no—
244C4×Dic47—22no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257#10625324—44no—
258#10625324—44no—
259#10625324—44no—
260C8×D47—44no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47C23×C411yescharacteristic
269C22×D47—21no—
270C22×D47—21no—
271C22×D47—21no—
272C22×D47—21no—
273C22×D47—21no—
274C22×D47—21no—
275C22×D47—21no—
276C22×D47—21no—
277C22×D47—21no—
278C22×D47—21no—
279C22×D47—21no—
280C22×D47—21no—
281C22×D47C2×C22⋊C412yes—
282C22×D47C2×C22⋊C412yes—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47C2×C22⋊C412yes—
301C2×C4×C47C2×C22⋊C412yes—
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47C2×#4111yescharacteristic
306C2×C4×C47H(5,𝔽2)11yescharacteristic
307C2×C4×C472−1+411yescharacteristic
308C22⋊D47—44no—
309C22⋊D47—44no—
310C2×Dic47—21no—
311C2×Dic47—21no—
312C2×Dic47—21no—
313C2×Dic47—21no—
314C2×Dic47—21no—
315C2×Dic47—21no—
316C2×Dic47—21no—
317C2×Dic47—21no—
318C2×Dic47—21no—
319C2×Dic47—21no—
320C2×Dic47—21no—
321C2×Dic47—21no—
322C2×Dic47—21no—
323C2×Dic47—21no—
324C2×Dic47—21no—
325C2×Dic47C2×C22⋊C412yes—
326C2×Dic47C2×C22⋊C412yes—
327C2×Dic47#13112yes—
328D188—44no—
329C4×D47—22no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—22no—
333C4×D47—22no—
334C4×D47—22no—
335C4×D47—22no—
336C4×D47—22no—
337C4×D47—44no—
338C4×D47—44no—
339Dic94—44no—
340C8×C47—22no—
341C8×C47—22no—
342C8×C47—41no—
343C8×C47—41no—
344C47⋊C8—41no—
345C47⋊C8—41no—
346C47⋊C8—41no—
347C47⋊C8—41no—
348#22472—471nomaximal, Sylow
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47C22×C22⋊C411yescharacteristic
357C22×C47C4×#4111yescharacteristic
358C22×C47#52011yescharacteristic
359C22×C47C2×#13111yescharacteristic
360C22×C47#56811yescharacteristic
361C22×C47#56811yescharacteristic
362C22×C47#56811yescharacteristic
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—22no—
368C2×D47—22no—
369C2×D47—41no—
370C2×D47—41no—
371C2×D47—41no—
372C2×D47—41no—
373C2×D47—41no—
374C2×D47—41no—
375C2×D47—41no—
376C2×D47—41no—
377C4×C47—22no—
378C4×C47—22no—
379C4×C47—41no—
380C4×C47—41no—
381C4×C47—41no—
382C4×C47#54611yescharacteristic
383C4×C47#54611yescharacteristic
384C4×C47#54711yescharacteristic
385C4×C47#54711yescharacteristic
386Dic47—22no—
387Dic47—22no—
388Dic47—22no—
389Dic47—41no—
390Dic47—41no—
391Dic47—41no—
392C2×#529—471no—
393C2×#436—471no—
394C2×#435—471no—
395#1985—471no—
396#1984—471no—
397#1870—471no—
398#1870—471no—
399#1870—471no—
400#1869—471no—
401#1818—471no—
402#1817—471no—
403#1798—471no—
404#1750D4711yescharacteristic, complemented
405#1729—471no—
406#1728—471no—
407C2×C47—81no—
408C2×C47#233911yescharacteristic
409C2×C47#287911yescharacteristic
410C2×C47#288011yescharacteristic
411C2×C47#296711yescharacteristic
412C2×C47#296911yescharacteristic
413C2×C47#299311yescharacteristic
414C2×C47#299511yescharacteristic
415D47—42no—
416D47—42no—
417C22×M16—471no—
418C22×M16—471no—
419C22×M16—471no—
420C23×C8—471no—
421#529—944no—
422#529—944no—
423C2×#126—471no—
424C2×#126—471no—
425C2×#125—471no—
426C2×#124—471no—
427C2×#123—471no—
428C2×#123—471no—
429C2×C22⋊Q8—471no—
430C2×#121—471no—
431C2×C4×Q8—471no—
432C2×C4×D4—471no—
433C2×C4×D4—471no—
434C2×C4×D4—471no—
435C2×#117—471no—
436C2×#117C2×D4711yescharacteristic
437C22×C42—471no—
438#436—944no—
439#435—944no—
440C2×C4⋊C8—471no—
441C2×C4⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×C22⋊C8—471no—
444C2×C22⋊C8—471no—
445C2×C22⋊C8—471no—
446C2×C22⋊C8—471no—
447C2×C22⋊C8—471no—
448C2×C22⋊C8C2×D4711yescharacteristic
449C2×C22⋊C8C2×D4711yescharacteristic
450C2×#97C2×D4711yescharacteristic
451C2×C4×C8C2×D4711yescharacteristic
452#336—471no—
453#336—471no—
454#336—471no—
455#336—471no—
456#336—471no—
457#336—471no—
458#336—471no—
459#336—471no—
460#336—471no—
461#336—471no—
462#336C2×D4711yescharacteristic
463#336C2×D4711yescharacteristic
464C47#2247211yescharacteristic, complemented, Sylow
465C22×Q8—471no—
466C22×D4—471no—
467C22×D4—471no—
468C22×D4—471no—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4C22×D4711yescharacteristic
474C2×M16—942no—
475C2×M16—942no—
476C2×M16—942no—
477C2×M16—942no—
478C2×M16—942no—
479C2×M16—942no—
480C2×M16—1881no—
481C2×M16—1881no—
482C2×M16—1881no—
483C22×C8—471no—
484C22×C8—471no—
485C22×C8—471no—
486C22×C8—471no—
487C22×C8—942no—
488C22×C8—942no—
489C22×C8—1881no—
490C22×C8C22×D4711yescharacteristic
491C22×C8C22×D4711yescharacteristic
492C22×C8C22×D4711yescharacteristic
493C22×C8C22×D4711yescharacteristic
494#126—944no—
495#126—944no—
496#125—944no—
497#124—944no—
498#123—944no—
499#123—944no—
500C22⋊Q8—944no—
501#121—944no—
502C4×Q8—942no—
503C4×Q8—942no—
504C4×D4—474no—
505C4×D4—474no—
506C4×D4—942no—
507C4×D4—942no—
508C4×D4—942no—
509C4×D4—942no—
510#117—22no—
511#117—22no—
512#117—942no—
513#117—942no—
514C2×C4⋊C4—471no—
515C2×C4⋊C4—471no—
516C2×C4⋊C4—471no—
517C2×C4⋊C4—471no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4C4×D4711yescharacteristic
523C2×C4⋊C4C4×D4711yescharacteristic
524C2×C22⋊C4—471no—
525C2×C22⋊C4—471no—
526C2×C22⋊C4—471no—
527C2×C22⋊C4—471no—
528C2×C22⋊C4—471no—
529C2×C22⋊C4—471no—
530C2×C22⋊C4—471no—
531C2×C22⋊C4—471no—
532C2×C22⋊C4C4×D4711yescharacteristic
533C2×C22⋊C4C4×D4711yescharacteristic
534C2×C42—471no—
535C2×C42—471no—
536C2×C42—471no—
537C2×C42—471no—
538C2×C42—942no—
539C2×C42—942no—
540C2×C42C22×D4711yescharacteristic
541C2×C42C22×D4711yescharacteristic
542C4⋊C8—942no—
543C4⋊C8—942no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—942no—
547C22⋊C8—942no—
548C22⋊C8—942no—
549C22⋊C8—942no—
550C22⋊C8—1881no—
551C22⋊C8—1881no—
552#97—22no—
553C4×C8—22no—
554C24—471no—
555C24—471no—
556C24C2×C4×D4711yescharacteristic
557C2×Q8—942no—
558C2×Q8—942no—
559C2×Q8—1881no—
560C2×D4—474no—
561C2×D4—942no—
562C2×D4—942no—
563C2×D4—942no—
564C2×D4—1881no—
565C2×D4—1881no—
566C2×D4—1881no—
567C2×D4—1881no—
568C2×D4—1881no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4—471no—
578C22×C4—472no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—472no—
582C22×C4—471no—
583C22×C4—471no—
584C22×C4—471no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—942no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—1881no—
597C22×C4—1881no—
598C22×C4—1881no—
599C22×C4C2×C4×D4711yescharacteristic
600C22×C4C2×C4×D4711yescharacteristic
601C22×C4C2×C4×D4711yescharacteristic
602C22×C4C2×C4×D4711yescharacteristic
603C22×C4C2×C4×D4711yescharacteristic
604C22×C4C23×D4711yescharacteristic
605M16—1884no—
606M16—1884no—
607M16—1884no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—941no—
619C2×C8—941no—
620C2×C8—941no—
621C2×C8—941no—
622C2×C8—941no—
623C2×C8—941no—
624C2×C8—941no—
625C2×C8—941no—
626C2×C8—941no—
627C2×C8—941no—
628C2×C8—941no—
629C2×C8—941no—
630C2×C8—1884no—
631C2×C8#1062535012yes—
632C2×C8#1062535012yes—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—474no—
636C4⋊C4—942no—
637C4⋊C4—942no—
638C4⋊C4—942no—
639C4⋊C4—942no—
640C4⋊C4—942no—
641C4⋊C4—942no—
642C4⋊C4—942no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—474no—
646C22⋊C4—474no—
647C22⋊C4—942no—
648C22⋊C4—942no—
649C22⋊C4—942no—
650C22⋊C4—942no—
651C22⋊C4—942no—
652C22⋊C4—942no—
653C42—21no—
654C42—21no—
655C42—942no—
656C42—942no—
657C42—941no—
658C42—941no—
659C42—941no—
660C42—941no—
661C42D4×D4712yes—
662C42D4×D4712yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—472no—
671C23—472no—
672C23—941no—
673C23—941no—
674C23—941no—
675C23—941no—
676C23—941no—
677C23—941no—
678C23—941no—
679C23—941no—
680C23—941no—
681C23—941no—
682C23—941no—
683C23—941no—
684C23C22×C4×D4711yescharacteristic
685Q8—1884no—
686D4—1884no—
687D4—1884no—
688D4—1884no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—472no—
707C2×C4—472no—
708C2×C4—472no—
709C2×C4—941no—
710C2×C4—941no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—941no—
714C2×C4—941no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—941no—
724C2×C4—941no—
725C2×C4—941no—
726C2×C4—941no—
727C2×C4—941no—
728C2×C4—941no—
729C2×C4—941no—
730C2×C4—941no—
731C2×C4—941no—
732C2×C4—1884no—
733C2×C4—1884no—
734C2×C4C22⋊C4×D4712yes—
735C2×C4C22⋊C4×D4712yes—
736C2×C4C2×D4×D4711yescharacteristic
737C2×C4C2×D4×D4711yescharacteristic
738C2×C4C2×#1062535011yescharacteristic
739C2×C4C2×#1062535011yescharacteristic
740C2×C4#1309407011yescharacteristic
741C2×C4#1309407111yescharacteristic
742C8—22no—
743C8—22no—
744C8—41no—
745C8—41no—
746C8—1881no—
747C8—1881no—
748C8—1881no—
749C8—1881no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—942no—
758C22—942no—
759C22—942no—
760C22—942no—
761C22—942no—
762C22—942no—
763C22—1881no—
764C22—1881no—
765C22—1881no—
766C22—1881no—
767C22—1881no—
768C22—1881no—
769C22—1881no—
770C22—1881no—
771C22C2×C22⋊C4×D4711yescharacteristic
772C22C4×#1062535011yescharacteristic
773C22#1568960311yescharacteristic
774C22#131×D4711yescharacteristic
775C22#1568988811yescharacteristic
776C22#1568988811yescharacteristic
777C22#1568988811yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—942no—
784C4—942no—
785C4—942no—
786C4—1881no—
787C4—1881no—
788C4—1881no—
789C4#1568976911yescharacteristic
790C4#1568976911yescharacteristic
791C4#1568977811yescharacteristic
792C4#1568977811yescharacteristic
793C2—81no—
794C2—1882no—
795C2—1882no—
796C2#2024621911yescharacteristic
797C2#2025183011yescharacteristic
798C2#2025183611yescharacteristic
799C2#2025236911yescharacteristic
800C2#2025238811yescharacteristic
801C2#2025253111yescharacteristic
802C2#2025255311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1750C2
prime radicalC2×#13093997C4
cosocleC22×C4×C47C24
hypercenter#1750D47
hypocenterC47#22472
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#15689202C2semidirect
3. C2×#15689196C2semidirect
4. #20244328C2semidirect
5. #20244324C2semidirect
6. #20243682C2semidirect
7. #20243682C2semidirect
8. #20243682C2semidirect
9. #20243677C2semidirect
10. #20243458C2semidirect
11. #20243455C2semidirect
12. #20243372C2semidirect
13. #20243083C2semidirect
14. #20243080C2semidirect
15. C47×#1750C2semidirect
404. #1750D47semidirect
464. C47#22472semidirect

Maximal subgroups

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

subgroupindex
C2×#156896512
C2×#156892022
C2×#156891962
#202443282
#202443242
#202436822
#202436772
#202434582
#202434552
#202433722
#202430832
#202430802
C47×#17502
#2247247