Finite Group Databasebeta

← #26232398

Subgroups — #26232398

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×#15689651C211yesmaximal, characteristic
2C2×#15689194C211yesmaximal, characteristic, complemented
3C2×#15689192C211yesmaximal, characteristic, complemented
4#20244326C211yesmaximal, characteristic, complemented
5#20244326C211yesmaximal, characteristic, complemented
6#20243685C211yesmaximal, characteristic, complemented
7#20243684C211yesmaximal, characteristic, complemented
8#20243680C211yesmaximal, characteristic, complemented
9#20243679C211yesmaximal, characteristic, complemented
10#20243459C211yesmaximal, characteristic, complemented
11#20243458C211yesmaximal, characteristic, complemented
12#20243367C211yesmaximal, characteristic, complemented
13#20243149C211yesmaximal, characteristic, complemented
14#20243083C211yesmaximal, characteristic, complemented
15C47×#1729C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18#15689651—24no—
19#15689651—24no—
20C2×#13094019C411yescharacteristic
21C2×#13094017C411yescharacteristic
22C2×#13094014C411yescharacteristic
23C2×#13094010C411yescharacteristic
24C2×#13094009C411yescharacteristic
25C2×#13094006C411yescharacteristic
26C2×#13094002C411yescharacteristic
27C2×#13093997C411yescharacteristic
28C2×C4×Dic94C2211yescharacteristic
29C2×C4×D188C2211yescharacteristic
30C2×C4×C22⋊D47C2211yescharacteristic
31C2×C4×C22⋊D47C2211yescharacteristic
32C2×#13093981C2211yescharacteristic
33C2×C42×D47C2211yescharacteristic
34#15689194—24no—
35#15689192—24no—
36C2×Dic47⋊C8C2211yescharacteristic
37C2×Dic47⋊C8C2211yescharacteristic
38C2×C22⋊(C47⋊C8)C2211yescharacteristic
39C2×C22⋊(C47⋊C8)C2211yescharacteristic
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×#13093934C2211yescharacteristic
47C2×#13093934C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51#15688878C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C22×M16×C47C2211yescharacteristic
57C23×C8×C47C2211yescharacteristic
58C2×#117×C47C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
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—41no—
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C2×C8×D47—22no—
79C2×C8×D47—22no—
80C2×C8×D47—41no—
81#13094019—24no—
82#13094017—24no—
83#13094014—24no—
84#13094010—24no—
85#13094009—24no—
86#13094006—24no—
87#13094002—24no—
88#13093997—24no—
89C4×Dic94—22no—
90C4×Dic94—22no—
91C4×D188—22no—
92C4×D188—22no—
93C4×C22⋊D47—22no—
94C4×C22⋊D47—22no—
95C4×C22⋊D47D414yes—
96C4×C22⋊D47D414yes—
97#13093981—22no—
98#13093981—22no—
99C2×C4⋊Dic47C2×C411yescharacteristic
100C2×C4⋊Dic47C2×C411yescharacteristic
101C2×Dic47⋊C4C2×C411yescharacteristic
102C2×Dic47⋊C4C2×C411yescharacteristic
103C2×Dic47⋊C4C2×C411yescharacteristic
104C2×Dic47⋊C4C2×C411yescharacteristic
105C2×Dic47⋊C4C2×C411yescharacteristic
106C2×Dic47⋊C4C2×C411yescharacteristic
107C2×C22⋊Dic47C2×C411yescharacteristic
108C2×C22⋊Dic47C2×C411yescharacteristic
109C2×(C2×D47)⋊C4C2×C411yescharacteristic
110C2×(C2×D47)⋊C4C2×C411yescharacteristic
111C2×(C2×D47)⋊C4C2×C411yescharacteristic
112C2×(C2×D47)⋊C4C2×C411yescharacteristic
113C2×(C2×D47)⋊C4C2×C411yescharacteristic
114C2×(C2×D47)⋊C4C2×C411yescharacteristic
115C2×C4×Dic47C2×C411yescharacteristic
116C2×C4×Dic47C2×C411yescharacteristic
117C2×C4×Dic47C2311yescharacteristic
118C2×C4×Dic47C2311yescharacteristic
119C42×D47—22no—
120C42×D47—22no—
121Dic47⋊C8—22no—
122Dic47⋊C8—22no—
123C22⋊(C47⋊C8)—22no—
124C22⋊(C47⋊C8)—22no—
125(C2×D47)⋊C8—22no—
126(C2×D47)⋊C8—22no—
127(C2×D47)⋊C8—22no—
128(C2×D47)⋊C8—22no—
129(C2×D47)⋊C8—41no—
130(C2×D47)⋊C8—41no—
131#13093934—22no—
132#13093934—22no—
133C23×C4×C47C2311yescharacteristic
134C2×M16×C47—22no—
135C2×M16×C47—22no—
136C2×M16×C47—41no—
137C22×C8×C47—22no—
138C22×C8×C47—22no—
139C22×C8×C47—41no—
140C22×C8×C47C2311yescharacteristic
141C22×C8×C47C2311yescharacteristic
142C22×C8×C47C2311yescharacteristic
143C22×C8×C47C2311yescharacteristic
144#117×C47—22no—
145#117×C47—22no—
146C2×C4⋊C4×C47C2×C411yescharacteristic
147C2×C4⋊C4×C47C2×C411yescharacteristic
148C2×C22⋊C4×C47C2×C411yescharacteristic
149C2×C22⋊C4×C47C2×C411yescharacteristic
150C2×C42×C47C2311yescharacteristic
151C2×C42×C47C2311yescharacteristic
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—41no—
170C2×C22⋊D47—41no—
171C2×C22⋊D47—41no—
172C2×C22⋊D47C22⋊C414yes—
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—21no—
183C2×C4×D47—21no—
184C2×C4×D47—21no—
185C2×C4×D47—21no—
186C2×C4×D47—22no—
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—22no—
194C2×C4×D47—22no—
195C2×C4×D47—41no—
196C2×C4×D47—41no—
197C2×C4×D47—41no—
198C2×C4×D47C2×D412yes—
199C2×C4×D47C2×D412yes—
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—44no—
215C2×C8×C47#4112yes—
216C2×C8×C47#4112yes—
217C4⋊C4×C47—22no—
218C4⋊C4×C47—22no—
219C22⋊C4×C47—22no—
220C22⋊C4×C47—22no—
221C42×C47—21no—
222C42×C47—21no—
223C42×C47—21no—
224C42×C47—21no—
225C22⋊Dic47—22no—
226C22⋊Dic47C22⋊C414yes—
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)⋊C4C22⋊C414yes—
233C4⋊Dic47—22no—
234C4⋊Dic47—22no—
235Dic47⋊C4—22no—
236Dic47⋊C4—22no—
237Dic47⋊C4—22no—
238Dic47⋊C4—22no—
239Dic47⋊C4—22no—
240Dic47⋊C4C22⋊C414yes—
241C4×Dic47—21no—
242C4×Dic47—21no—
243C4×Dic47—22no—
244C4×Dic47—22no—
245C4×Dic47C2×D412yes—
246C4×Dic47C2×D412yes—
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—
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×C47C2×C22⋊C412yes—
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×D47#13112yes—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
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—21no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
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×Dic47C2×C22⋊C412yes—
328D188—44no—
329C4×D47—22no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—22no—
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—22no—
342C8×C47—41no—
343C8×C47—41no—
344C47⋊C8—41no—
345C47⋊C8—41no—
346C47⋊C8—41no—
347C47⋊C8—41no—
348#22475—471nomaximal, Sylow
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—22no—
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—41no—
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×#435—471no—
394C2×#435—471no—
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#1729D4711yescharacteristic, complemented
407C2×C47—42no—
408C2×C47#233911yescharacteristic
409C2×C47#287911yescharacteristic
410C2×C47#288011yescharacteristic
411C2×C47#296711yescharacteristic
412C2×C47#296811yescharacteristic
413C2×C47#299211yescharacteristic
414C2×C47#299511yescharacteristic
415D47—42no—
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×D4—471no—
435C2×#117—471no—
436C2×#117C2×D4711yescharacteristic
437C22×C42—471no—
438#435—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⋊C8—471no—
449C2×C22⋊C8—471no—
450C2×#97—471no—
451C2×#97—471no—
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#336C2×D4711yescharacteristic
461#336C2×D4711yescharacteristic
462#336C2×D4711yescharacteristic
463#336C2×D4711yescharacteristic
464C47#2247511yescharacteristic, 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—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—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—942no—
545C22⋊C8—942no—
546C22⋊C8—942no—
547C22⋊C8—942no—
548C22⋊C8—942no—
549C22⋊C8—942no—
550C22⋊C8—1881no—
551C22⋊C8—1881no—
552#97—942no—
553#97—942no—
554C24—471no—
555C24—471no—
556C24C2×C4×D4711yescharacteristic
557C2×Q8—942no—
558C2×Q8—1881no—
559C2×Q8—1881no—
560C2×D4—474no—
561C2×D4—942no—
562C2×D4—942no—
563C2×D4—942no—
564C2×D4—942no—
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—471no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—472no—
577C22×C4—472no—
578C22×C4—471no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—942no—
582C22×C4—942no—
583C22×C4—942no—
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—941no—
594C22×C4—1881no—
595C22×C4—1881no—
596C22×C4—1881no—
597C22×C4C2×C4×D4711yescharacteristic
598C22×C4C2×C4×D4711yescharacteristic
599C22×C4C2×C4×D4711yescharacteristic
600C22×C4C2×C4×D4711yescharacteristic
601C22×C4C2×C4×D4711yescharacteristic
602C22×C4D4×D4712yes—
603C22×C4D4×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—44no—
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—21no—
656C42—21no—
657C42—472no—
658C42—472no—
659C42—942no—
660C42—942no—
661C42—941no—
662C42—941no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—472no—
670C23—472no—
671C23—941no—
672C23—941no—
673C23—941no—
674C23—941no—
675C23—941no—
676C23—941no—
677C23—941no—
678C23—941no—
679C23—941no—
680C23—941no—
681C23—941no—
682C23—941no—
683C23C22⋊C4×D4712yes—
684C23C22×C4×D4711yescharacteristic
685Q8—1884no—
686D4—1884no—
687D4—1884no—
688D4—1884no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—472no—
708C2×C4—472no—
709C2×C4—472no—
710C2×C4—941no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—941no—
714C2×C4—941no—
715C2×C4—941no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—941no—
721C2×C4—941no—
722C2×C4—941no—
723C2×C4—941no—
724C2×C4—941no—
725C2×C4—941no—
726C2×C4—941no—
727C2×C4—941no—
728C2×C4—941no—
729C2×C4—1884no—
730C2×C4—1884no—
731C2×C4—1881no—
732C2×C4—1881no—
733C2×C4—1881no—
734C2×C4—1881no—
735C2×C4C22⋊C4×D4712yes—
736C2×C4C2×D4×D4711yescharacteristic
737C2×C4C2×D4×D4711yescharacteristic
738C2×C4C2×#1062535011yescharacteristic
739C2×C4C2×#1062535011yescharacteristic
740C2×C4#1309406911yescharacteristic
741C2×C4#1309407211yescharacteristic
742C8—22no—
743C8—22no—
744C8—41no—
745C8—41no—
746C8—1881no—
747C8—1881no—
748C8—1881no—
749C8—1881no—
750C22—22no—
751C22—22no—
752C22—22no—
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#1568960411yescharacteristic
774C22#131×D4711yescharacteristic
775C22#1568988811yescharacteristic
776C22#1568988811yescharacteristic
777C22#1568988811yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—942no—
784C4—942no—
785C4—942no—
786C4—1881no—
787C4—1881no—
788C4—1881no—
789C4#1568976311yescharacteristic
790C4#1568976311yescharacteristic
791C4#1568977411yescharacteristic
792C4#1568977411yescharacteristic
793C2—42no—
794C2—1882no—
795C2—1882no—
796C2#2024621511yescharacteristic
797C2#2025183011yescharacteristic
798C2#2025183611yescharacteristic
799C2#2025236911yescharacteristic
800C2#2025237811yescharacteristic
801C2#2025252511yescharacteristic
802C2#2025255611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1729C2
prime radicalC2×#13093997C4
cosocleC22×C4×C47C24
hypercenter#1729D47
hypocenterC47#22475
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1729

Complements

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

NH ≅ G/Ntype
2. C2×#15689194C2semidirect
3. C2×#15689192C2semidirect
4. #20244326C2semidirect
5. #20244326C2semidirect
6. #20243685C2semidirect
7. #20243684C2semidirect
8. #20243680C2semidirect
9. #20243679C2semidirect
10. #20243459C2semidirect
11. #20243458C2semidirect
12. #20243367C2semidirect
13. #20243149C2semidirect
14. #20243083C2semidirect
15. C47×#1729C2semidirect
406. #1729D47semidirect
464. C47#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#156896512
C2×#156891942
C2×#156891922
#202443262
#202436852
#202436842
#202436802
#202436792
#202434592
#202434582
#202433672
#202431492
#202430832
C47×#17292
#2247547