Finite Group Databasebeta

← #26225921

Subgroups — #26225921

Order 12032.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689651C211yesmaximal, characteristic
2C2×#15689184C211yesmaximal, characteristic, complemented
3#20244327C211yesmaximal, characteristic, complemented
4#20244323C211yesmaximal, characteristic, complemented
5#20244185C211yesmaximal, characteristic, complemented
6#20244181C211yesmaximal, characteristic, complemented
7#20243685C211yesmaximal, characteristic, complemented
8#20243685C211yesmaximal, characteristic, complemented
9#20243680C211yesmaximal, characteristic, complemented
10#20243680C211yesmaximal, characteristic, complemented
11#20243369C211yesmaximal, characteristic, complemented
12#20243369C211yesmaximal, characteristic, complemented
13#20243365C211yesmaximal, characteristic, complemented
14#20243365C211yesmaximal, characteristic, complemented
15C2×C47×#424C211yesmaximal, characteristic, complemented
16#15689651—24no—
17#15689651—24no—
18C2×#13094019C411yescharacteristic
19C2×#13094017C411yescharacteristic
20C2×#13094014C411yescharacteristic
21C2×#13094010C411yescharacteristic
22C2×#13094009C411yescharacteristic
23C2×#13094006C411yescharacteristic
24C2×#13094002C411yescharacteristic
25C2×#13093997C411yescharacteristic
26C2×C4×Dic94C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28C2×C4×C22⋊D47C2211yescharacteristic
29C2×C4×C22⋊D47C2211yescharacteristic
30C2×#13093981C2211yescharacteristic
31C2×C42×D47C2211yescharacteristic
32#15689184—24no—
33C2×C4⋊(C47⋊C8)C2211yescharacteristic
34C2×C4⋊(C47⋊C8)C2211yescharacteristic
35C2×C22⋊(C47⋊C8)C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×(C2×D47)⋊C8C2211yescharacteristic
38C2×(C2×D47)⋊C8C2211yescharacteristic
39C2×(C2×D47)⋊C8C2211yescharacteristic
40C2×(C2×D47)⋊C8C2211yescharacteristic
41C2×(C2×D47)⋊C8C2211yescharacteristic
42C2×(C2×D47)⋊C8C2211yescharacteristic
43C2×(C2×D47)⋊C8C2211yescharacteristic
44C2×(C2×D47)⋊C8C2211yescharacteristic
45C2×#13093935C2211yescharacteristic
46C2×C4×C47⋊C8C2211yescharacteristic
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55C22×M16×C47C2211yescharacteristic
56C23×C8×C47C2211yescharacteristic
57C2×#117×C47C2211yescharacteristic
58C47×#424—24no—
59C2×C4⋊C8×C47C2211yescharacteristic
60C2×C4⋊C8×C47C2211yescharacteristic
61C2×C4⋊C8×C47C2211yescharacteristic
62C2×C4⋊C8×C47C2211yescharacteristic
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
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13094019—24no—
76#13094017—24no—
77#13094014—24no—
78#13094010—24no—
79#13094009—24no—
80#13094006—24no—
81#13094002—24no—
82#13093997—24no—
83C4×Dic94—22no—
84C4×Dic94—22no—
85C4×D188—22no—
86C4×D188—22no—
87C4×C22⋊D47—22no—
88C4×C22⋊D47—22no—
89C4×C22⋊D47—22no—
90C4×C22⋊D47—22no—
91#13093981—22no—
92#13093981—22no—
93C2×C4⋊Dic47C2×C411yescharacteristic
94C2×C4⋊Dic47C2×C411yescharacteristic
95C2×Dic47⋊C4C2×C411yescharacteristic
96C2×Dic47⋊C4C2×C411yescharacteristic
97C2×Dic47⋊C4C2×C411yescharacteristic
98C2×Dic47⋊C4C2×C411yescharacteristic
99C2×Dic47⋊C4C2×C411yescharacteristic
100C2×Dic47⋊C4C2×C411yescharacteristic
101C2×C22⋊Dic47C2×C411yescharacteristic
102C2×C22⋊Dic47C2×C411yescharacteristic
103C2×(C2×D47)⋊C4C2×C411yescharacteristic
104C2×(C2×D47)⋊C4C2×C411yescharacteristic
105C2×(C2×D47)⋊C4C2×C411yescharacteristic
106C2×(C2×D47)⋊C4C2×C411yescharacteristic
107C2×(C2×D47)⋊C4C2×C411yescharacteristic
108C2×(C2×D47)⋊C4C2×C411yescharacteristic
109C2×C4×Dic47C2×C411yescharacteristic
110C2×C4×Dic47C2×C411yescharacteristic
111C2×C4×Dic47C2311yescharacteristic
112C2×C4×Dic47C2311yescharacteristic
113C42×D47—22no—
114C42×D47—22no—
115C4⋊(C47⋊C8)—22no—
116C4⋊(C47⋊C8)—22no—
117C22⋊(C47⋊C8)—22no—
118C22⋊(C47⋊C8)—22no—
119(C2×D47)⋊C8—41no—
120(C2×D47)⋊C8—41no—
121(C2×D47)⋊C8—41no—
122(C2×D47)⋊C8—41no—
123(C2×D47)⋊C8—41no—
124(C2×D47)⋊C8—41no—
125(C2×D47)⋊C8—41no—
126(C2×D47)⋊C8—41no—
127#13093935—22no—
128C4×C47⋊C8—22no—
129C23×C4×C47C2311yescharacteristic
130C2×M16×C47—22no—
131C2×M16×C47—41no—
132C2×M16×C47—41no—
133C22×C8×C47—22no—
134C22×C8×C47—41no—
135C22×C8×C47—41no—
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139C22×C8×C47C2311yescharacteristic
140#117×C47D414yes—
141#117×C47D414yes—
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
148C4⋊C8×C47—22no—
149C4⋊C8×C47—22no—
150C4⋊C8×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×C47C22×C411yescharacteristic
160C22×C4×C47C22×C411yescharacteristic
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C2×D412yes—
165C22×C4×C47C2×D412yes—
166C22×C4×C47C2411yescharacteristic
167C2×C22⋊D47—22no—
168C2×C22⋊D47—22no—
169C2×C22⋊D47—22no—
170C2×C22⋊D47—22no—
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—22no—
180C2×D188—22no—
181C2×D188—41no—
182C2×C4×D47—22no—
183C2×C4×D47—22no—
184C2×C4×D47—22no—
185C2×C4×D47—21no—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—21no—
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—22no—
198C2×C4×D47—41no—
199C2×C4×D47—41no—
200C2×Dic94—22no—
201C2×Dic94—22no—
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—21no—
216C2×C8×C47—44no—
217C4⋊C4×C47C22⋊C414yes—
218C4⋊C4×C47C22⋊C414yes—
219C22⋊C4×C47C22⋊C414yes—
220C22⋊C4×C47C22⋊C414yes—
221C42×C47C2×D412yes—
222C42×C47C2×D412yes—
223C42×C47C2×D412yes—
224C42×C47C2×D412yes—
225C22⋊Dic47—22no—
226C22⋊Dic47—22no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4—22no—
229(C2×D47)⋊C4—22no—
230(C2×D47)⋊C4—22no—
231(C2×D47)⋊C4—22no—
232(C2×D47)⋊C4—22no—
233C4⋊Dic47—22no—
234C4⋊Dic47—22no—
235Dic47⋊C4—22no—
236Dic47⋊C4—22no—
237Dic47⋊C4—22no—
238Dic47⋊C4—22no—
239Dic47⋊C4—22no—
240Dic47⋊C4—22no—
241C4×Dic47—22no—
242C4×Dic47—22no—
243C4×Dic47—21no—
244C4×Dic47—21no—
245C4×Dic47—21no—
246C4×Dic47—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—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—21no—
265C23×C47C2×C22⋊C412yes—
266C23×C47C23×C411yescharacteristic
267C22×D47—21no—
268C22×D47—21no—
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#13112yes—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
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—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47C2×C22⋊C412yes—
296C2×C4×C47C2×C22⋊C412yes—
297C2×C4×C47C2×C22⋊C412yes—
298C2×C4×C47C2×C22⋊C412yes—
299C2×C4×C47C2×C22⋊C412yes—
300C2×C4×C47C22×D411yescharacteristic
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C47H(5,𝔽2)11yescharacteristic
303C2×C4×C47H(5,𝔽2)11yescharacteristic
304C2×C4×C472−1+411yescharacteristic
305C2×C4×C472−1+411yescharacteristic
306C22⋊D47—44no—
307C22⋊D47—44no—
308C2×Dic47—21no—
309C2×Dic47—21no—
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×Dic47#13112yes—
326D188—44no—
327C4×D47—44no—
328C4×D47—44no—
329C4×D47—41no—
330C4×D47—41no—
331C4×D47—41no—
332C4×D47—41no—
333C4×D47—41no—
334C4×D47—41no—
335C4×D47—41no—
336C4×D47—41no—
337Dic94—44no—
338C8×C47—41no—
339C8×C47—41no—
340C8×C47—41no—
341C8×C47—41no—
342C47⋊C8—41no—
343C47⋊C8—41no—
344C47⋊C8—41no—
345C47⋊C8—41no—
346#21855—471nomaximal, Sylow
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47C22×C22⋊C411yescharacteristic
355C22×C47#52011yescharacteristic
356C22×C47#52011yescharacteristic
357C22×C47C2×#13111yescharacteristic
358C22×C47C2×#13111yescharacteristic
359C22×C47#56811yescharacteristic
360C22×C47#56811yescharacteristic
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—41no—
365C2×D47—41no—
366C2×D47—41no—
367C2×D47—41no—
368C2×D47—41no—
369C2×D47—41no—
370C2×D47—41no—
371C2×D47—41no—
372C2×D47—41no—
373C2×D47—41no—
374C2×D47—41no—
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—22no—
378C4×C47—22no—
379C4×C47—22no—
380C4×C47#53511yescharacteristic
381C4×C47#53611yescharacteristic
382C4×C47#53711yescharacteristic
383C4×C47#53711yescharacteristic
384Dic47—22no—
385Dic47—41no—
386Dic47—41no—
387Dic47—41no—
388Dic47—41no—
389Dic47—41no—
390C2×#529—471no—
391C2×#433—471no—
392C2×#424D4711yescharacteristic, complemented
393#1985—471no—
394#1984—471no—
395#1955—471no—
396#1954—471no—
397#1870—471no—
398#1870—471no—
399#1869—471no—
400#1869—471no—
401#1798—471no—
402#1798—471no—
403#1797—471no—
404#1797—471no—
405C2×C47—42no—
406C2×C47#231111yescharacteristic
407C2×C47#288011yescharacteristic
408C2×C47#288011yescharacteristic
409C2×C47#299211yescharacteristic
410C2×C47#299311yescharacteristic
411C2×C47#299411yescharacteristic
412C2×C47#299511yescharacteristic
413D47—42no—
414D47—81no—
415C22×M16C2×D4711yescharacteristic
416C23×C8C2×D4711yescharacteristic
417#529—944no—
418#529—944no—
419C2×#126—471no—
420C2×#126—471no—
421C2×#125—471no—
422C2×#124—471no—
423C2×#123—471no—
424C2×#123—471no—
425C2×C22⋊Q8—471no—
426C2×#121—471no—
427C2×C4×Q8—471no—
428C2×C4×D4—471no—
429C2×C4×D4—471no—
430C2×C4×D4—471no—
431C2×#117—471no—
432C2×#117C2×D4711yescharacteristic
433C22×C42—471no—
434#433—944no—
435#424—24no—
436C2×C4⋊C8—471no—
437C2×C4⋊C8—471no—
438C2×C4⋊C8C2×D4711yescharacteristic
439C2×C4⋊C8C2×D4711yescharacteristic
440C2×C4⋊C8C2×D4711yescharacteristic
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⋊C8—471no—
449C2×C22⋊C8—471no—
450C2×C22⋊C8—471no—
451C2×C22⋊C8—471no—
452C2×#97—471no—
453C2×C4×C8—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—
462C47#2185511yescharacteristic, complemented, Sylow
463C22×Q8—471no—
464C22×D4—471no—
465C22×D4—471no—
466C22×D4—471no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4C22×D4711yescharacteristic
472C2×M16—22no—
473C2×M16—41no—
474C2×M16—41no—
475C22×C8—22no—
476C22×C8—41no—
477C22×C8—41no—
478C22×C8—471no—
479C22×C8—471no—
480C22×C8—471no—
481C22×C8—471no—
482C22×C8C22×D4711yescharacteristic
483C22×C8C22×D4711yescharacteristic
484C22×C8C22×D4711yescharacteristic
485C22×C8C22×D4711yescharacteristic
486#126—944no—
487#126—944no—
488#125—944no—
489#124—944no—
490#123—944no—
491#123—944no—
492C22⋊Q8—944no—
493#121—944no—
494C4×Q8—942no—
495C4×Q8—942no—
496C4×D4—942no—
497C4×D4—942no—
498C4×D4—942no—
499C4×D4—942no—
500C4×D4—942no—
501C4×D4—942no—
502#117—942no—
503#117—942no—
504#117D18814yes—
505#117C22⋊D4714yes—
506C2×C4⋊C4—471no—
507C2×C4⋊C4—471no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—471no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—471no—
514C2×C4⋊C4C4×D4711yescharacteristic
515C2×C4⋊C4C4×D4711yescharacteristic
516C2×C22⋊C4—471no—
517C2×C22⋊C4—471no—
518C2×C22⋊C4—471no—
519C2×C22⋊C4—471no—
520C2×C22⋊C4—471no—
521C2×C22⋊C4—471no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—471no—
524C2×C22⋊C4C4×D4711yescharacteristic
525C2×C22⋊C4C4×D4711yescharacteristic
526C2×C42—471no—
527C2×C42—471no—
528C2×C42—471no—
529C2×C42—471no—
530C2×C42—942no—
531C2×C42—942no—
532C2×C42C22×D4711yescharacteristic
533C2×C42C22×D4711yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C4⋊C8—22no—
537C4⋊C8—22no—
538C4⋊C8—942no—
539C4⋊C8—942no—
540C22⋊C8—942no—
541C22⋊C8—942no—
542C22⋊C8—1881no—
543C22⋊C8—1881no—
544C22⋊C8—1881no—
545C22⋊C8—1881no—
546C22⋊C8—1881no—
547C22⋊C8—1881no—
548C22⋊C8—1881no—
549C22⋊C8—1881no—
550#97—942no—
551C4×C8—942no—
552C24—471no—
553C24—471no—
554C24C2×C4×D4711yescharacteristic
555C2×Q8—942no—
556C2×Q8—942no—
557C2×Q8—1881no—
558C2×D4—942no—
559C2×D4—942no—
560C2×D4—942no—
561C2×D4—942no—
562C2×D4—942no—
563C2×D4—942no—
564C2×D4—1881no—
565C2×D4—1881no—
566C2×D4—1881no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—471no—
572C22×C4—471no—
573C22×C4—471no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—941no—
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×C4C2×C4×D4711yescharacteristic
596C22×C4C2×C4×D4711yescharacteristic
597C22×C4C2×C4×D4711yescharacteristic
598C22×C4C2×C4×D4711yescharacteristic
599C22×C4C2×C4×D4711yescharacteristic
600C22×C4C2×D18812yes—
601C22×C4C2×C22⋊D4712yes—
602C22×C4C23×D4711yescharacteristic
603M16—44no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
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—44no—
617C2×C8—941no—
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—
629C4⋊C4—942no—
630C4⋊C4—942no—
631C4⋊C4—942no—
632C4⋊C4—942no—
633C4⋊C4—942no—
634C4⋊C4—942no—
635C4⋊C4—942no—
636C4⋊C4—942no—
637C4⋊C4(C2×D47)⋊C414yes—
638C4⋊C4(C2×D47)⋊C414yes—
639C22⋊C4—942no—
640C22⋊C4—942no—
641C22⋊C4—942no—
642C22⋊C4—942no—
643C22⋊C4—942no—
644C22⋊C4—942no—
645C22⋊C4—942no—
646C22⋊C4—942no—
647C22⋊C4(C2×D47)⋊C414yes—
648C22⋊C4(C2×D47)⋊C414yes—
649C42—942no—
650C42—942no—
651C42—941no—
652C42—941no—
653C42—941no—
654C42—941no—
655C42C2×D18812yes—
656C42C2×D18812yes—
657C42C2×C22⋊D4712yes—
658C42C2×C22⋊D4712yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—472no—
666C23—941no—
667C23—941no—
668C23—941no—
669C23—941no—
670C23—941no—
671C23—941no—
672C23—941no—
673C23—941no—
674C23—941no—
675C23—941no—
676C23—941no—
677C23—941no—
678C23—941no—
679C23C2×(C2×D47)⋊C412yes—
680C23C22×C4×D4711yescharacteristic
681Q8—1884no—
682D4—1884no—
683D4—1884no—
684D4—1884no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—472no—
700C2×C4—941no—
701C2×C4—941no—
702C2×C4—941no—
703C2×C4—941no—
704C2×C4—941no—
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—1884no—
718C2×C4—1884no—
719C2×C4—1881no—
720C2×C4—1881no—
721C2×C4—1881no—
722C2×C4—1881no—
723C2×C4—1881no—
724C2×C4—1881no—
725C2×C4—1881no—
726C2×C4—1881no—
727C2×C4C2×(C2×D47)⋊C412yes—
728C2×C4C2×(C2×D47)⋊C412yes—
729C2×C4C2×(C2×D47)⋊C412yes—
730C2×C4C2×(C2×D47)⋊C412yes—
731C2×C4C2×(C2×D47)⋊C412yes—
732C2×C4C22×C22⋊D4711yescharacteristic
733C2×C4C22×D18811yescharacteristic
734C2×C4#1309406911yescharacteristic
735C2×C4#1309406911yescharacteristic
736C2×C4#1309407211yescharacteristic
737C2×C4#1309407211yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—1881no—
743C8—1881no—
744C8—1881no—
745C8—1881no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—942no—
754C22—942no—
755C22—942no—
756C22—1881no—
757C22—1881no—
758C22—1881no—
759C22—1881no—
760C22—1881no—
761C22—1881no—
762C22—1881no—
763C22—1881no—
764C22—1881no—
765C22—1881no—
766C22—1881no—
767C22C22×(C2×D47)⋊C411yescharacteristic
768C22#1568960411yescharacteristic
769C22#1568960411yescharacteristic
770C22#131×D4711yescharacteristic
771C22#131×D4711yescharacteristic
772C22#1568988811yescharacteristic
773C22#1568988811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—942no—
780C4—1881no—
781C4—1881no—
782C4—1881no—
783C4—1881no—
784C4—1881no—
785C4#1568969011yescharacteristic
786C4#1568969711yescharacteristic
787C4#1568970411yescharacteristic
788C4#1568970411yescharacteristic
789C2—42no—
790C2—3761no—
791C2—1882no—
792C2#2024598111yescharacteristic
793C2#2025183511yescharacteristic
794C2#2025183511yescharacteristic
795C2#2025252511yescharacteristic
796C2#2025253511yescharacteristic
797C2#2025254611yescharacteristic
798C2#2025255611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C47×#424C2
prime radicalC2×#13093997C4
cosocleC22×C4×C47C24
hypercenterC2×#424D47
hypocenterC47#21855
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×#15689184C2semidirect
3. #20244327C2semidirect
4. #20244323C2semidirect
5. #20244185C2semidirect
6. #20244181C2semidirect
7. #20243685C2semidirect
8. #20243685C2semidirect
9. #20243680C2semidirect
10. #20243680C2semidirect
11. #20243369C2semidirect
12. #20243369C2semidirect
13. #20243365C2semidirect
14. #20243365C2semidirect
15. C2×C47×#424C2semidirect
392. C2×#424D47semidirect
462. C47#21855semidirect

Maximal subgroups

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

subgroupindex
C2×#156896512
C2×#156891842
#202443272
#202443232
#202441852
#202441812
#202436852
#202436802
#202433692
#202433652
C2×C47×#4242
#2185547