Finite Group Databasebeta

← #26232396

Subgroups — #26232396

Order 12032.

1168 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×#15689655C211yesmaximal, characteristic
2C2×#15689195C211yesmaximal, characteristic, complemented
3#20244328C211yesmaximal, characteristic, complemented
4#20244327C211yesmaximal, characteristic, complemented
5#20243685C211yesmaximal, characteristic, complemented
6#20243683C211yesmaximal, characteristic, complemented
7#20243680C211yesmaximal, characteristic, complemented
8#20243678C211yesmaximal, characteristic, complemented
9#20243457C211yesmaximal, characteristic, complemented
10#20243457C211yesmaximal, characteristic, complemented
11#20243365C211yesmaximal, characteristic, complemented
12#20243151C211yesmaximal, characteristic, complemented
13#20243086C211yesmaximal, characteristic, complemented
14#20243084C211yesmaximal, characteristic, complemented
15C2×C47×#435C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18#15689655—24no—
19#15689655—24no—
20C2×#13094017C411yescharacteristic
21C2×#13094017C411yescharacteristic
22C2×#13094015C411yescharacteristic
23C2×#13094011C411yescharacteristic
24C2×#13094006C411yescharacteristic
25C2×#13094006C411yescharacteristic
26C2×#13094004C411yescharacteristic
27C2×#13093995C411yescharacteristic
28C2×C4×Dic94C2211yescharacteristic
29C2×C4×C22⋊D47C2211yescharacteristic
30C2×C4×C22⋊D47C2211yescharacteristic
31C2×#13093983C2211yescharacteristic
32C2×#13093983C2211yescharacteristic
33C2×C42×D47C2211yescharacteristic
34#15689195—24no—
35C2×C4⋊(C47⋊C8)C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×(C2×D47)⋊C8C2211yescharacteristic
39C2×(C2×D47)⋊C8C2211yescharacteristic
40C2×(C2×D47)⋊C8C2211yescharacteristic
41C2×(C2×D47)⋊C8C2211yescharacteristic
42C2×#13093935C2211yescharacteristic
43#15688877C2211yescharacteristic
44#15688877C2211yescharacteristic
45#15688877C2211yescharacteristic
46#15688877C2211yescharacteristic
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55C22×M16×C47C2211yescharacteristic
56C23×C8×C47C2211yescharacteristic
57C2×C4×D4×C47C2211yescharacteristic
58C47×#435—24no—
59C2×C4⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C2×C22⋊C8×C47C2211yescharacteristic
62C2×#97×C47C2211yescharacteristic
63C22×Dic94C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C22×C4×D47C2×C411yescharacteristic
67C22×C4×D47C2×C411yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C2×#10625329—22no—
70C2×#10625329—22no—
71C2×#10625329—41no—
72C22×C47⋊C8—22no—
73C22×C47⋊C8—22no—
74C22×C47⋊C8—41no—
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79#13094017—24no—
80#13094017—24no—
81#13094015—24no—
82#13094011—24no—
83#13094006—24no—
84#13094006—24no—
85#13094004—24no—
86#13093995—24no—
87C4×Dic94—22no—
88C4×Dic94—22no—
89C4×C22⋊D47—22no—
90C4×C22⋊D47—22no—
91C4×C22⋊D47—22no—
92C4×C22⋊D47—22no—
93#13093983—22no—
94#13093983—22no—
95#13093983—22no—
96#13093983—22no—
97C2×C4⋊Dic47C2×C411yescharacteristic
98C2×C4⋊Dic47C2×C411yescharacteristic
99C2×C4⋊Dic47C2×C411yescharacteristic
100C2×C4⋊Dic47C2×C411yescharacteristic
101C2×C4⋊Dic47C2×C411yescharacteristic
102C2×Dic47⋊C4C2×C411yescharacteristic
103C2×Dic47⋊C4C2×C411yescharacteristic
104C2×Dic47⋊C4C2×C411yescharacteristic
105C2×Dic47⋊C4C2×C411yescharacteristic
106C2×C22⋊Dic47C2×C411yescharacteristic
107C2×C22⋊Dic47C2×C411yescharacteristic
108C2×C22⋊Dic47C2×C411yescharacteristic
109C2×C22⋊Dic47C2×C411yescharacteristic
110C2×C22⋊Dic47C2×C411yescharacteristic
111C2×C22⋊Dic47C2×C411yescharacteristic
112C2×(C2×D47)⋊C4C2×C411yescharacteristic
113C2×(C2×D47)⋊C4C2×C411yescharacteristic
114C2×C4×Dic47C2×C411yescharacteristic
115C2×C4×Dic47C2×C411yescharacteristic
116C2×C4×Dic47C2311yescharacteristic
117C2×C4×Dic47C2311yescharacteristic
118C2×C4×Dic47C2311yescharacteristic
119C42×D47—22no—
120C42×D47—22no—
121C4⋊(C47⋊C8)—22no—
122C22⋊(C47⋊C8)—22no—
123C22⋊(C47⋊C8)—22no—
124(C2×D47)⋊C8—22no—
125(C2×D47)⋊C8—22no—
126(C2×D47)⋊C8—41no—
127(C2×D47)⋊C8—41no—
128#13093935—22no—
129C22×D4×C47C2×C411yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C2×M16×C47—22no—
133C2×M16×C47—22no—
134C2×M16×C47—41no—
135C22×C8×C47—22no—
136C22×C8×C47—22no—
137C22×C8×C47—41no—
138C22×C8×C47C2311yescharacteristic
139C22×C8×C47C2311yescharacteristic
140C22×C8×C47C2311yescharacteristic
141C22×C8×C47C2311yescharacteristic
142C4×D4×C47D414yes—
143C4×D4×C47D414yes—
144C2×C4⋊C4×C47C2×C411yescharacteristic
145C2×C22⋊C4×C47C2×C411yescharacteristic
146C2×C22⋊C4×C47C2×C411yescharacteristic
147C2×C42×C47C2311yescharacteristic
148C4⋊C8×C47—22no—
149C22⋊C8×C47—22no—
150C22⋊C8×C47—22no—
151#97×C47—22no—
152C24×C47C22×C411yescharacteristic
153C24×C47C22×C411yescharacteristic
154C23×D47C22×C411yescharacteristic
155C2×D4×C47—41no—
156C2×D4×C47—41no—
157C2×D4×C47C22⋊C414yes—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47C22×C411yescharacteristic
167C22×C4×C47C22×C411yescharacteristic
168C22×C4×C47C22×C411yescharacteristic
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C2×D412yes—
171C22×C4×C47C2×D412yes—
172C22×C4×C47C2×D412yes—
173C22×C4×C47C2×D412yes—
174C22×C4×C47C2411yescharacteristic
175C2×C22⋊D47—22no—
176C2×C22⋊D47—22no—
177C2×C22⋊D47—22no—
178C2×C22⋊D47—22no—
179C2×C22⋊D47—41no—
180C2×C22⋊D47—41no—
181C22×Dic47C22×C411yescharacteristic
182C22×Dic47C22×C411yescharacteristic
183C22×Dic47C22×C411yescharacteristic
184C22×Dic47C22×C411yescharacteristic
185C22×Dic47C22×C411yescharacteristic
186C22×Dic47C22×C411yescharacteristic
187C22×Dic47C22×C411yescharacteristic
188C2×C4×D47—22no—
189C2×C4×D47—22no—
190C2×C4×D47—22no—
191C2×C4×D47—21no—
192C2×C4×D47—21no—
193C2×C4×D47—21no—
194C2×C4×D47—21no—
195C2×C4×D47—21no—
196C2×C4×D47—21no—
197C2×C4×D47—41no—
198C2×C4×D47—41no—
199C2×C4×D47—41no—
200C2×Dic94—22no—
201C2×Dic94—41no—
202C2×Dic94—41no—
203M16×C47—44no—
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—21no—
214C2×C8×C47—21no—
215C2×C8×C47—44no—
216C2×C8×C47#4112yes—
217C4⋊C4×C47C22⋊C414yes—
218C22⋊C4×C47C22⋊C414yes—
219C22⋊C4×C47C22⋊C414yes—
220C42×C47C2×D412yes—
221C42×C47C2×D412yes—
222C22⋊Dic47—22no—
223C22⋊Dic47—22no—
224C22⋊Dic47—22no—
225C22⋊Dic47—22no—
226C22⋊Dic47—22no—
227C22⋊Dic47—22no—
228(C2×D47)⋊C4—22no—
229(C2×D47)⋊C4—22no—
230C4⋊Dic47—22no—
231C4⋊Dic47—22no—
232C4⋊Dic47—22no—
233C4⋊Dic47—22no—
234C4⋊Dic47—22no—
235Dic47⋊C4—22no—
236Dic47⋊C4—22no—
237Dic47⋊C4—22no—
238Dic47⋊C4—22no—
239C4×Dic47—22no—
240C4×Dic47—22no—
241C4×Dic47—21no—
242C4×Dic47—21no—
243C4×Dic47—21no—
244C4×Dic47—21no—
245C4×Dic47—21no—
246C4×Dic47—21no—
247#10625329—44no—
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—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—44no—
260C2×C47⋊C8#4112yes—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—21no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47C2×C22⋊C412yes—
274C23×C47C2×C22⋊C412yes—
275C23×C47C23×C411yescharacteristic
276C22×D47—21no—
277C22×D47—21no—
278C22×D47—21no—
279C22×D47—21no—
280C22×D47—21no—
281C22×D47—21no—
282C22×D47#13112yes—
283D4×C47—44no—
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—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47C2×C22⋊C412yes—
301C2×C4×C47C2×C22⋊C412yes—
302C2×C4×C47C2×C22⋊C412yes—
303C2×C4×C47C2×C22⋊C412yes—
304C2×C4×C47C22×D411yescharacteristic
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C2×#4111yescharacteristic
307C2×C4×C47C2×#4111yescharacteristic
308C2×C4×C47H(5,𝔽2)11yescharacteristic
309C2×C4×C472−1+411yescharacteristic
310C22⋊D47—44no—
311C22⋊D47—44no—
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×Dic47—21no—
326C2×Dic47—21no—
327C2×Dic47—21no—
328C2×Dic47—21no—
329C2×Dic47—21no—
330C2×Dic47—21no—
331C2×Dic47—21no—
332C2×Dic47—21no—
333C4×D47—44no—
334C4×D47—44no—
335C4×D47—41no—
336C4×D47—41no—
337C4×D47—41no—
338C4×D47—41no—
339Dic94—44no—
340C8×C47—22no—
341C8×C47—41no—
342C8×C47—41no—
343C8×C47—41no—
344C47⋊C8—22no—
345C47⋊C8—41no—
346C47⋊C8—41no—
347C47⋊C8—41no—
348#22475—471nomaximal, Sylow
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—22no—
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47C22×C22⋊C411yescharacteristic
364C22×C47C4×#4111yescharacteristic
365C22×C47#52011yescharacteristic
366C22×C47C2×#13111yescharacteristic
367C22×C47#56811yescharacteristic
368C22×C47#56811yescharacteristic
369C22×C47#56811yescharacteristic
370C2×D47—22no—
371C2×D47—22no—
372C2×D47—22no—
373C2×D47—41no—
374C2×D47—41no—
375C2×D47—41no—
376C2×D47—41no—
377C4×C47—22no—
378C4×C47—22no—
379C4×C47—22no—
380C4×C47—22no—
381C4×C47#54611yescharacteristic
382C4×C47#54611yescharacteristic
383C4×C47#54711yescharacteristic
384C4×C47#54711yescharacteristic
385Dic47—41no—
386Dic47—41no—
387Dic47—41no—
388Dic47—41no—
389Dic47—41no—
390Dic47—41no—
391Dic47—41no—
392C2×#529—471no—
393C2×#435—471no—
394C2×#435D4711yescharacteristic, complemented
395#1985—471no—
396#1985—471no—
397#1870—471no—
398#1870—471no—
399#1869—471no—
400#1869—471no—
401#1818—471no—
402#1818—471no—
403#1797—471no—
404#1749—471no—
405#1729—471no—
406#1729—471no—
407C2×C47—42no—
408C2×C47—42no—
409C2×C47#233911yescharacteristic
410C2×C47#287911yescharacteristic
411C2×C47#288011yescharacteristic
412C2×C47#296711yescharacteristic
413C2×C47#296811yescharacteristic
414C2×C47#299211yescharacteristic
415C2×C47#299511yescharacteristic
416D47—42no—
417C22×M16—471no—
418C22×M16C2×D4711yescharacteristic
419C23×C8—471no—
420C23×C8C2×D4711yescharacteristic
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×D4C2×D4711yescharacteristic
435C2×#117—471no—
436C2×#117—471no—
437C22×C42—471no—
438#435—24no—
439#435—944no—
440C2×C4⋊C8—471no—
441C2×C4⋊C8C2×D4711yescharacteristic
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×#97—471no—
451C2×#97C2×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#336—471no—
463#336—471no—
464C47#2247511yescharacteristic, complemented, Sylow
465C22×Q8—471no—
466C22×D4—471no—
467C22×D4—471no—
468C22×D4C4×D4711yescharacteristic
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4C22×D4711yescharacteristic
473C23×C4C22×D4711yescharacteristic
474C2×M16—22no—
475C2×M16—22no—
476C2×M16—41no—
477C2×M16—942no—
478C2×M16—942no—
479C2×M16—1881no—
480C22×C8—22no—
481C22×C8—22no—
482C22×C8—41no—
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—942no—
505C4×D4—942no—
506C4×D4—942no—
507C4×D4—942no—
508C4×D4D18814yes—
509C4×D4C22⋊D4714yes—
510#117—942no—
511#117—942no—
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⋊C4—471no—
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—471no—
539C2×C42—942no—
540C2×C42—942no—
541C2×C42C22×D4711yescharacteristic
542C4⋊C8—22no—
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—
553#97—942no—
554C24—471no—
555C24C2×C4×D4711yescharacteristic
556C24C2×C4×D4711yescharacteristic
557C2×Q8—942no—
558C2×Q8—1881no—
559C2×Q8—1881no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—942no—
563C2×D4—942no—
564C2×D4—942no—
565C2×D4—942no—
566C2×D4—1881no—
567C2×D4—1881no—
568C2×D4(C2×D47)⋊C414yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—471no—
578C22×C4—471no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—471no—
582C22×C4—471no—
583C22×C4—471no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—942no—
587C22×C4—941no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—1881no—
594C22×C4—1881no—
595C22×C4—1881no—
596C22×C4C2×C4×D4711yescharacteristic
597C22×C4C2×C4×D4711yescharacteristic
598C22×C4C2×C4×D4711yescharacteristic
599C22×C4C2×C4×D4711yescharacteristic
600C22×C4C2×D18812yes—
601C22×C4C2×D18812yes—
602C22×C4C2×C22⋊D4712yes—
603C22×C4C2×C22⋊D4712yes—
604C22×C4C23×D4711yescharacteristic
605M16—44no—
606M16—1884no—
607C2×C8—21no—
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—44no—
619C2×C8—472no—
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—941no—
631C2×C8—1884no—
632C2×C8#1062535212yes—
633C4⋊C4—942no—
634C4⋊C4—942no—
635C4⋊C4—942no—
636C4⋊C4—942no—
637C4⋊C4—942no—
638C4⋊C4—942no—
639C4⋊C4—942no—
640C4⋊C4—942no—
641C4⋊C4—942no—
642C4⋊C4(C2×D47)⋊C414yes—
643C22⋊C4—942no—
644C22⋊C4—942no—
645C22⋊C4—942no—
646C22⋊C4—942no—
647C22⋊C4—942no—
648C22⋊C4—942no—
649C22⋊C4—942no—
650C22⋊C4—942no—
651C22⋊C4(C2×D47)⋊C414yes—
652C22⋊C4(C2×D47)⋊C414yes—
653C42—942no—
654C42—942no—
655C42—941no—
656C42—941no—
657C42—941no—
658C42—941no—
659C42—941no—
660C42—941no—
661C42C2×D18812yes—
662C42C2×C22⋊D4712yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—472no—
676C23—941no—
677C23—941no—
678C23—941no—
679C23—941no—
680C23—941no—
681C23—941no—
682C23C2×(C2×D47)⋊C412yes—
683C23C2×(C2×D47)⋊C412yes—
684C23C22×C4×D4711yescharacteristic
685Q8—1884no—
686D4—44no—
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—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—941no—
706C2×C4—941no—
707C2×C4—941no—
708C2×C4—941no—
709C2×C4—941no—
710C2×C4—941no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—941no—
714C2×C4—941no—
715C2×C4—941no—
716C2×C4—941no—
717C2×C4—941no—
718C2×C4—941no—
719C2×C4—941no—
720C2×C4—941no—
721C2×C4—941no—
722C2×C4—941no—
723C2×C4—941no—
724C2×C4—941no—
725C2×C4—941no—
726C2×C4—1884no—
727C2×C4—1884no—
728C2×C4—1881no—
729C2×C4—1881no—
730C2×C4—1881no—
731C2×C4—1881no—
732C2×C4C2×(C2×D47)⋊C412yes—
733C2×C4C2×(C2×D47)⋊C412yes—
734C2×C4C2×(C2×D47)⋊C412yes—
735C2×C4C2×(C2×D47)⋊C412yes—
736C2×C4C22×C22⋊D4711yescharacteristic
737C2×C4C22×D18811yescharacteristic
738C2×C4#41×D4711yescharacteristic
739C2×C4C2×#1062535211yescharacteristic
740C2×C4#1309406911yescharacteristic
741C2×C4#1309407111yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—942no—
747C8—1881no—
748C8—1881no—
749C8—1881no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—942no—
765C22—942no—
766C22—942no—
767C22—1881no—
768C22—1881no—
769C22—1881no—
770C22—1881no—
771C22C22×(C2×D47)⋊C411yescharacteristic
772C22C4×#1062535211yescharacteristic
773C22#1568960211yescharacteristic
774C22#131×D4711yescharacteristic
775C22#1568988811yescharacteristic
776C22#1568988911yescharacteristic
777C22#1568988911yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—1881no—
783C4—1881no—
784C4—1881no—
785C4—1881no—
786C4—1881no—
787C4—1881no—
788C4—1881no—
789C4#1568976711yescharacteristic
790C4#1568976811yescharacteristic
791C4#1568977211yescharacteristic
792C4#1568977711yescharacteristic
793C2—42no—
794C2—42no—
795C2—1882no—
796C2#2024621311yescharacteristic
797C2#2025183211yescharacteristic
798C2#2025183511yescharacteristic
799C2#2025237011yescharacteristic
800C2#2025237911yescharacteristic
801C2#2025252311yescharacteristic
802C2#2025255411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C47×#435C2
prime radicalC2×#13093995C4
cosocleC22×C4×C47C24
hypercenterC2×#435D47
hypocenterC47#22475
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#15689195C2semidirect
3. #20244328C2semidirect
4. #20244327C2semidirect
5. #20243685C2semidirect
6. #20243683C2semidirect
7. #20243680C2semidirect
8. #20243678C2semidirect
9. #20243457C2semidirect
10. #20243457C2semidirect
11. #20243365C2semidirect
12. #20243151C2semidirect
13. #20243086C2semidirect
14. #20243084C2semidirect
15. C2×C47×#435C2semidirect
394. C2×#435D47semidirect
464. C47#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#156896552
C2×#156891952
#202443282
#202443272
#202436852
#202436832
#202436802
#202436782
#202434572
#202433652
#202431512
#202430862
#202430842
C2×C47×#4352
#2247547