Finite Group Databasebeta

← #26233015

Subgroups — #26233015

Order 12032.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689660C211yesmaximal, characteristic
2C2×#15689254C211yesmaximal, characteristic, complemented
3#20244186C211yesmaximal, characteristic, complemented
4#20244186C211yesmaximal, characteristic, complemented
5#20244185C211yesmaximal, characteristic, complemented
6#20244185C211yesmaximal, characteristic, complemented
7#20244182C211yesmaximal, characteristic, complemented
8#20244181C211yesmaximal, characteristic, complemented
9#20243369C211yesmaximal, characteristic, complemented
10#20243369C211yesmaximal, characteristic, complemented
11#20243365C211yesmaximal, characteristic, complemented
12#20243157C211yesmaximal, characteristic, complemented
13#20243155C211yesmaximal, characteristic, complemented
14#20243151C211yesmaximal, characteristic, complemented
15C2×C47×#446C211yesmaximal, characteristic, complemented
16#15689660—24no—
17#15689660—24no—
18C2×#13094019C411yescharacteristic
19C2×#13094019C411yescharacteristic
20C2×#13094015C411yescharacteristic
21C2×#13094013C411yescharacteristic
22C2×#13094009C411yescharacteristic
23C2×#13094009C411yescharacteristic
24C2×#13094000C411yescharacteristic
25C2×#13093999C411yescharacteristic
26C2×C4×D188C2211yescharacteristic
27C2×C4×D188C2211yescharacteristic
28C2×C4×D188C2211yescharacteristic
29C2×#13093981C2211yescharacteristic
30C2×#13093981C2211yescharacteristic
31C2×C42×D47C2211yescharacteristic
32#15689254—24no—
33C2×C4⋊(C47⋊C8)C2211yescharacteristic
34C2×C4⋊(C47⋊C8)C2211yescharacteristic
35C2×C4⋊(C47⋊C8)C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
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×(C2×D47)⋊C8C2211yescharacteristic
46C2×(C2×D47)⋊C8C2211yescharacteristic
47C2×(C2×D47)⋊C8C2211yescharacteristic
48C2×#13093935C2211yescharacteristic
49C2×#13093935C2211yescharacteristic
50C2×C4×C47⋊C8C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55C2×C4×Q8×C47C2211yescharacteristic
56C47×#446—24no—
57C2×C4⋊C8×C47C2211yescharacteristic
58C2×C4⋊C8×C47C2211yescharacteristic
59C2×C4⋊C8×C47C2211yescharacteristic
60C2×#97×C47C2211yescharacteristic
61C2×#97×C47C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C22×D188C2×C411yescharacteristic
64C22×D188C2×C411yescharacteristic
65C22×D188C2×C411yescharacteristic
66C22×C4×D47C2×C411yescharacteristic
67C22×C4×D47C2×C411yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C22×C4×D47C2311yescharacteristic
70C22×C4×D47C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13094019—24no—
76#13094019—24no—
77#13094015—24no—
78#13094013—24no—
79#13094009—24no—
80#13094009—24no—
81#13094000—24no—
82#13093999—24no—
83C4×D188—22no—
84C4×D188—22no—
85C4×D188—22no—
86C4×D188—22no—
87C4×D188—22no—
88C4×D188—22no—
89#13093981—22no—
90#13093981—22no—
91#13093981—22no—
92#13093981—22no—
93C2×C4⋊Dic47C2×C411yescharacteristic
94C2×C4⋊Dic47C2×C411yescharacteristic
95C2×C4⋊Dic47C2×C411yescharacteristic
96C2×Dic47⋊C4C2×C411yescharacteristic
97C2×Dic47⋊C4C2×C411yescharacteristic
98C2×Dic47⋊C4C2×C411yescharacteristic
99C2×Dic47⋊C4C2×C411yescharacteristic
100C2×(C2×D47)⋊C4C2×C411yescharacteristic
101C2×(C2×D47)⋊C4C2×C411yescharacteristic
102C2×(C2×D47)⋊C4C2×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×(C2×D47)⋊C4C2×C411yescharacteristic
110C2×C4×Dic47C2×C411yescharacteristic
111C2×C4×Dic47C2×C411yescharacteristic
112C2×C4×Dic47C2311yescharacteristic
113C42×D47—22no—
114C42×D47—22no—
115C4⋊(C47⋊C8)—22no—
116C4⋊(C47⋊C8)—22no—
117C4⋊(C47⋊C8)—22no—
118(C2×D47)⋊C8—22no—
119(C2×D47)⋊C8—22no—
120(C2×D47)⋊C8—22no—
121(C2×D47)⋊C8—22no—
122(C2×D47)⋊C8—22no—
123(C2×D47)⋊C8—22no—
124(C2×D47)⋊C8—41no—
125(C2×D47)⋊C8—41no—
126(C2×D47)⋊C8—41no—
127(C2×D47)⋊C8—41no—
128(C2×D47)⋊C8—41no—
129(C2×D47)⋊C8—41no—
130#13093935—22no—
131#13093935—22no—
132C4×C47⋊C8—22no—
133C22×Q8×C47C2×C411yescharacteristic
134C22×C8×C47C2311yescharacteristic
135C22×C8×C47C2311yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C4×Q8×C47D414yes—
139C4×Q8×C47D414yes—
140C2×C4⋊C4×C47C2×C411yescharacteristic
141C2×C4⋊C4×C47C2×C411yescharacteristic
142C2×C4⋊C4×C47C2×C411yescharacteristic
143C2×C42×C47C2311yescharacteristic
144C2×C42×C47C2311yescharacteristic
145C2×C42×C47C2311yescharacteristic
146C4⋊C8×C47—22no—
147C4⋊C8×C47—22no—
148C4⋊C8×C47—22no—
149#97×C47—22no—
150#97×C47—22no—
151C4×C8×C47—22no—
152C23×D47C22×C411yescharacteristic
153C23×D47C22×C411yescharacteristic
154C23×D47C22×C411yescharacteristic
155C2×Q8×C47—41no—
156C2×Q8×C47—41no—
157C2×Q8×C47C22⋊C414yes—
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47C22×C411yescharacteristic
160C22×C4×C47C22×C411yescharacteristic
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C2411yescharacteristic
165C22×Dic47C22×C411yescharacteristic
166C22×Dic47C22×C411yescharacteristic
167C22×Dic47C22×C411yescharacteristic
168C22×Dic47C22×C411yescharacteristic
169C22×Dic47C22×C411yescharacteristic
170C2×D188—22no—
171C2×D188—22no—
172C2×D188—22no—
173C2×D188—22no—
174C2×D188—22no—
175C2×D188—41no—
176C2×D188—41no—
177C2×D188—41no—
178C2×D188—41no—
179C2×C4×D47—22no—
180C2×C4×D47—22no—
181C2×C4×D47—22no—
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—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—21no—
198C2×C4×D47—21no—
199C2×C4×D47—21no—
200C2×C4×D47—41no—
201C2×C4×D47—41no—
202C2×C4×D47—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—21no—
214C2×C8×C47#4112yes—
215C4⋊C4×C47C22⋊C414yes—
216C4⋊C4×C47C22⋊C414yes—
217C4⋊C4×C47C22⋊C414yes—
218C42×C47C2×D412yes—
219C42×C47C2×D412yes—
220C42×C47C2×D412yes—
221C42×C47C2×D412yes—
222C42×C47C2×D412yes—
223C42×C47C2×D412yes—
224(C2×D47)⋊C4—22no—
225(C2×D47)⋊C4—22no—
226(C2×D47)⋊C4—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—
233(C2×D47)⋊C4—22no—
234C4⋊Dic47—22no—
235C4⋊Dic47—22no—
236C4⋊Dic47—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—
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#4112yes—
257C23×C47C23×C411yescharacteristic
258C22×D47—21no—
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—21no—
266C22×D47—21no—
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#13112yes—
279Q8×C47—44no—
280C2×C4×C47—21no—
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—21no—
292C2×C4×C47C2×C22⋊C412yes—
293C2×C4×C47C2×C22⋊C412yes—
294C2×C4×C47C2×C22⋊C412yes—
295C2×C4×C47C2×C22⋊C412yes—
296C2×C4×C47C2×C22⋊C412yes—
297C2×C4×C47C2×C22⋊C412yes—
298C2×C4×C47C22×D411yescharacteristic
299C2×C4×C47C22×D411yescharacteristic
300C2×C4×C47C2×#4111yescharacteristic
301C2×C4×C47C2×#4111yescharacteristic
302C2×C4×C47H(5,𝔽2)11yescharacteristic
303C2×C4×C472−1+411yescharacteristic
304C2×Dic47—21no—
305C2×Dic47—21no—
306C2×Dic47—21no—
307C2×Dic47—21no—
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—
319D188—44no—
320D188—44no—
321D188—44no—
322C4×D47—44no—
323C4×D47—44no—
324C4×D47—41no—
325C4×D47—41no—
326C4×D47—41no—
327C4×D47—41no—
328C4×D47—41no—
329C4×D47—41no—
330C4×D47—41no—
331C4×D47—41no—
332C4×D47—41no—
333C4×D47—41no—
334C4×D47—41no—
335C4×D47—41no—
336C8×C47—22no—
337C8×C47—41no—
338C8×C47—41no—
339C8×C47—41no—
340C47⋊C8—22no—
341C47⋊C8—41no—
342C47⋊C8—41no—
343C47⋊C8—41no—
344#22533—471nomaximal, Sylow
345C22×C47C22×C22⋊C411yescharacteristic
346C22×C47C4×#4111yescharacteristic
347C22×C47#52011yescharacteristic
348C22×C47C2×#13111yescharacteristic
349C22×C47#56811yescharacteristic
350C22×C47#56811yescharacteristic
351C22×C47#56811yescharacteristic
352C2×D47—22no—
353C2×D47—22no—
354C2×D47—22no—
355C2×D47—41no—
356C2×D47—41no—
357C2×D47—41no—
358C2×D47—41no—
359C2×D47—41no—
360C2×D47—41no—
361C2×D47—41no—
362C2×D47—41no—
363C2×D47—41no—
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—
373C4×C47—22no—
374C4×C47—22no—
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—22no—
378C4×C47—22no—
379C4×C47#54811yescharacteristic
380C4×C47#54811yescharacteristic
381C4×C47#55011yescharacteristic
382C4×C47#55011yescharacteristic
383Dic47—41no—
384Dic47—41no—
385Dic47—41no—
386Dic47—41no—
387Dic47—41no—
388C2×#529—471no—
389C2×#446—471no—
390C2×#446D4711yescharacteristic, complemented
391#1955—471no—
392#1955—471no—
393#1955—471no—
394#1955—471no—
395#1954—471no—
396#1954—471no—
397#1798—471no—
398#1798—471no—
399#1797—471no—
400#1750—471no—
401#1750—471no—
402#1749—471no—
403C2×C47#234111yescharacteristic
404C2×C47#287911yescharacteristic
405C2×C47#288011yescharacteristic
406C2×C47#296711yescharacteristic
407C2×C47#296811yescharacteristic
408C2×C47#299211yescharacteristic
409C2×C47#299511yescharacteristic
410D47—42no—
411D47—81no—
412D47—81no—
413#529—944no—
414#529—944no—
415C2×#126—471no—
416C2×#126—471no—
417C2×#125—471no—
418C2×#124—471no—
419C2×#123—471no—
420C2×#123—471no—
421C2×C22⋊Q8—471no—
422C2×#121—471no—
423C2×C4×Q8C2×D4711yescharacteristic
424C2×C4×D4—471no—
425C2×C4×D4—471no—
426C2×C4×D4—471no—
427C2×#117—471no—
428C2×#117—471no—
429C22×C42—471no—
430#446—24no—
431#446—944no—
432C2×C4⋊C8—471no—
433C2×C4⋊C8—471no—
434C2×C4⋊C8—471no—
435C2×C4⋊C8C2×D4711yescharacteristic
436C2×C4⋊C8C2×D4711yescharacteristic
437C2×C4⋊C8C2×D4711yescharacteristic
438C2×C22⋊C8—471no—
439C2×C22⋊C8—471no—
440C2×C22⋊C8—471no—
441C2×C22⋊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⋊C8—471no—
449C2×C22⋊C8—471no—
450C2×#97—471no—
451C2×#97—471no—
452C2×#97C2×D4711yescharacteristic
453C2×#97C2×D4711yescharacteristic
454C2×C4×C8—471no—
455C2×C4×C8C2×D4711yescharacteristic
456#336—471no—
457#336—471no—
458#336—471no—
459#336—471no—
460C47#2253311yescharacteristic, complemented, Sylow
461C22×Q8C4×D4711yescharacteristic
462C22×D4—471no—
463C22×D4—471no—
464C22×D4—471no—
465C23×C4—471no—
466C23×C4—471no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—471no—
470C22×C8—471no—
471C22×C8—471no—
472C22×C8—471no—
473C22×C8—471no—
474C22×C8C22×D4711yescharacteristic
475C22×C8C22×D4711yescharacteristic
476C22×C8C22×D4711yescharacteristic
477C22×C8C22×D4711yescharacteristic
478#126—944no—
479#126—944no—
480#125—944no—
481#124—944no—
482#123—944no—
483#123—944no—
484C22⋊Q8—944no—
485#121—944no—
486C4×Q8D18814yes—
487C4×Q8C22⋊D4714yes—
488C4×D4—942no—
489C4×D4—942no—
490C4×D4—942no—
491C4×D4—942no—
492C4×D4—942no—
493C4×D4—942no—
494#117—942no—
495#117—942no—
496#117—942no—
497#117—942no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—471no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—471no—
505C2×C4⋊C4C4×D4711yescharacteristic
506C2×C4⋊C4C4×D4711yescharacteristic
507C2×C4⋊C4C4×D4711yescharacteristic
508C2×C22⋊C4—471no—
509C2×C22⋊C4—471no—
510C2×C22⋊C4—471no—
511C2×C22⋊C4—471no—
512C2×C22⋊C4—471no—
513C2×C22⋊C4—471no—
514C2×C22⋊C4—471no—
515C2×C22⋊C4—471no—
516C2×C22⋊C4—471no—
517C2×C22⋊C4—471no—
518C2×C42—471no—
519C2×C42—471no—
520C2×C42—471no—
521C2×C42—942no—
522C2×C42—942no—
523C2×C42C22×D4711yescharacteristic
524C2×C42C22×D4711yescharacteristic
525C2×C42C22×D4711yescharacteristic
526C4⋊C8—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—942no—
530C4⋊C8—942no—
531C4⋊C8—942no—
532C22⋊C8—942no—
533C22⋊C8—942no—
534C22⋊C8—942no—
535C22⋊C8—942no—
536C22⋊C8—942no—
537C22⋊C8—942no—
538C22⋊C8—1881no—
539C22⋊C8—1881no—
540C22⋊C8—1881no—
541C22⋊C8—1881no—
542C22⋊C8—1881no—
543C22⋊C8—1881no—
544#97—22no—
545#97—22no—
546#97—942no—
547#97—942no—
548C4×C8—22no—
549C4×C8—942no—
550C24—471no—
551C24—471no—
552C24—471no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8(C2×D47)⋊C414yes—
556C2×D4—942no—
557C2×D4—942no—
558C2×D4—942no—
559C2×D4—942no—
560C2×D4—942no—
561C2×D4—1881no—
562C2×D4—1881no—
563C2×D4—1881no—
564C2×D4—1881no—
565C22×C4—471no—
566C22×C4—471no—
567C22×C4—471no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—941no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
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—1881no—
592C22×C4—1881no—
593C22×C4—1881no—
594C22×C4C2×C4×D4711yescharacteristic
595C22×C4C2×C4×D4711yescharacteristic
596C22×C4C2×C4×D4711yescharacteristic
597C22×C4C2×C4×D4711yescharacteristic
598C22×C4C2×C4×D4711yescharacteristic
599C22×C4C2×C4×D4711yescharacteristic
600C22×C4C23×D4711yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
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—472no—
613C2×C8—941no—
614C2×C8—941no—
615C2×C8—941no—
616C2×C8—941no—
617C2×C8—941no—
618C2×C8—941no—
619C2×C8—941no—
620C2×C8—941no—
621C2×C8—941no—
622C2×C8—941no—
623C2×C8—941no—
624C2×C8#1062535412yes—
625C4⋊C4—942no—
626C4⋊C4—942no—
627C4⋊C4—942no—
628C4⋊C4—942no—
629C4⋊C4—942no—
630C4⋊C4—942no—
631C4⋊C4—942no—
632C4⋊C4(C2×D47)⋊C414yes—
633C4⋊C4(C2×D47)⋊C414yes—
634C4⋊C4(C2×D47)⋊C414yes—
635C22⋊C4—942no—
636C22⋊C4—942no—
637C22⋊C4—942no—
638C22⋊C4—942no—
639C22⋊C4—942no—
640C22⋊C4—942no—
641C22⋊C4—942no—
642C22⋊C4—942no—
643C22⋊C4—942no—
644C22⋊C4—942no—
645C42—942no—
646C42—942no—
647C42—941no—
648C42—941no—
649C42C2×D18812yes—
650C42C2×D18812yes—
651C42C2×D18812yes—
652C42C2×C22⋊D4712yes—
653C42C2×C22⋊D4712yes—
654C42C2×C22⋊D4712yes—
655C23—472no—
656C23—941no—
657C23—941no—
658C23—941no—
659C23—941no—
660C23—941no—
661C23—941no—
662C23—941no—
663C23—941no—
664C23—941no—
665C23—941no—
666C23—941no—
667C23—941no—
668C23—941no—
669C23—941no—
670C23—941no—
671C23—941no—
672C23—941no—
673C23—941no—
674C23—941no—
675C23—941no—
676C23C22×C4×D4711yescharacteristic
677Q8—44no—
678D4—1884no—
679D4—1884no—
680D4—1884no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
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—941no—
694C2×C4—941no—
695C2×C4—941no—
696C2×C4—941no—
697C2×C4—941no—
698C2×C4—941no—
699C2×C4—941no—
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—1884no—
709C2×C4—1884no—
710C2×C4—1881no—
711C2×C4—1881no—
712C2×C4—1881no—
713C2×C4—1881no—
714C2×C4—1881no—
715C2×C4—1881no—
716C2×C4—1881no—
717C2×C4—1881no—
718C2×C4—1881no—
719C2×C4—1881no—
720C2×C4—1881no—
721C2×C4—1881no—
722C2×C4C2×(C2×D47)⋊C412yes—
723C2×C4C2×(C2×D47)⋊C412yes—
724C2×C4C2×(C2×D47)⋊C412yes—
725C2×C4C2×(C2×D47)⋊C412yes—
726C2×C4C2×(C2×D47)⋊C412yes—
727C2×C4C2×(C2×D47)⋊C412yes—
728C2×C4C22×C22⋊D4711yescharacteristic
729C2×C4C22×D18811yescharacteristic
730C2×C4#41×D4711yescharacteristic
731C2×C4C2×#1062535411yescharacteristic
732C2×C4#1309407011yescharacteristic
733C2×C4#1309407211yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—942no—
739C8—1881no—
740C8—1881no—
741C8—1881no—
742C22—942no—
743C22—942no—
744C22—942no—
745C22—1881no—
746C22—1881no—
747C22—1881no—
748C22—1881no—
749C22—1881no—
750C22—1881no—
751C22—1881no—
752C22—1881no—
753C22—1881no—
754C22—1881no—
755C22—1881no—
756C22—1881no—
757C22—1881no—
758C22—1881no—
759C22—1881no—
760C22—1881no—
761C22—1881no—
762C22—1881no—
763C22C22×(C2×D47)⋊C411yescharacteristic
764C22C4×#1062535411yescharacteristic
765C22#1568960511yescharacteristic
766C22#131×D4711yescharacteristic
767C22#1568988811yescharacteristic
768C22#1568988911yescharacteristic
769C22#1568988911yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—1881no—
777C4—1881no—
778C4—1881no—
779C4—1881no—
780C4—1881no—
781C4#1568978411yescharacteristic
782C4#1568978511yescharacteristic
783C4#1568979211yescharacteristic
784C4#1568979511yescharacteristic
785C2—3761no—
786C2—3761no—
787C2—1882no—
788C2#2024622611yescharacteristic
789C2#2025183211yescharacteristic
790C2#2025183511yescharacteristic
791C2#2025237211yescharacteristic
792C2#2025238111yescharacteristic
793C2#2025252611yescharacteristic
794C2#2025255711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C47×#446C2
prime radicalC2×#13093999C4
cosocleC22×C4×C47C24
hypercenterC2×#446D47
hypocenterC47#22533
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#15689254C2semidirect
3. #20244186C2semidirect
4. #20244186C2semidirect
5. #20244185C2semidirect
6. #20244185C2semidirect
7. #20244182C2semidirect
8. #20244181C2semidirect
9. #20243369C2semidirect
10. #20243369C2semidirect
11. #20243365C2semidirect
12. #20243157C2semidirect
13. #20243155C2semidirect
14. #20243151C2semidirect
15. C2×C47×#446C2semidirect
390. C2×#446D47semidirect
460. C47#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#156896602
C2×#156892542
#202441862
#202441852
#202441822
#202441812
#202433692
#202433652
#202431572
#202431552
#202431512
C2×C47×#4462
#2253347