Finite Group Databasebeta

← #26232402

Subgroups — #26232402

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×#15689653C211yesmaximal, characteristic
2C2×#15689197C211yesmaximal, characteristic, complemented
3C2×#15689194C211yesmaximal, characteristic, complemented
4#20244326C211yesmaximal, characteristic, complemented
5#20244326C211yesmaximal, characteristic, complemented
6#20243686C211yesmaximal, characteristic, complemented
7#20243682C211yesmaximal, characteristic, complemented
8#20243677C211yesmaximal, characteristic, complemented
9#20243458C211yesmaximal, characteristic, complemented
10#20243457C211yesmaximal, characteristic, complemented
11#20243366C211yesmaximal, characteristic, complemented
12#20243152C211yesmaximal, characteristic, complemented
13#20243084C211yesmaximal, characteristic, complemented
14#20243083C211yesmaximal, characteristic, complemented
15C47×#1869C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×C8×D47C2211yescharacteristic
19#15689653—24no—
20#15689653—24no—
21C2×#13094019C411yescharacteristic
22C2×#13094017C411yescharacteristic
23C2×#13094014C411yescharacteristic
24C2×#13094010C411yescharacteristic
25C2×#13094008C411yescharacteristic
26C2×#13094005C411yescharacteristic
27C2×#13094001C411yescharacteristic
28C2×#13093996C411yescharacteristic
29C2×C4×Dic94C2211yescharacteristic
30C2×C4×C22⋊D47C2211yescharacteristic
31C2×C4×C22⋊D47C2211yescharacteristic
32C2×#13093983C2211yescharacteristic
33C2×#13093981C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35#15689197—24no—
36#15689194—24no—
37C2×Dic47⋊C8C2211yescharacteristic
38C2×Dic47⋊C8C2211yescharacteristic
39C2×C22⋊(C47⋊C8)C2211yescharacteristic
40C2×C22⋊(C47⋊C8)C2211yescharacteristic
41C2×C22⋊(C47⋊C8)C2211yescharacteristic
42C2×(C2×D47)⋊C8C2211yescharacteristic
43C2×(C2×D47)⋊C8C2211yescharacteristic
44C2×#13093934C2211yescharacteristic
45C2×#13093934C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C23×C8×C47C2211yescharacteristic
57C2×C4×D4×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Dic94C2×C411yescharacteristic
64C22×C22⋊D47C2×C411yescharacteristic
65C22×C22⋊D47C2×C411yescharacteristic
66C23×Dic47C2×C411yescharacteristic
67C23×Dic47C2×C411yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C2×#10625329—22no—
70C2×#10625329—22no—
71C2×#10625329—41no—
72C2×#10625324—22no—
73C2×#10625324—22no—
74C2×#10625324—41no—
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79C2×C8×D47—22no—
80C2×C8×D47—22no—
81C2×C8×D47—41no—
82#13094019—24no—
83#13094017—24no—
84#13094014—24no—
85#13094010—24no—
86#13094008—24no—
87#13094005—24no—
88#13094001—24no—
89#13093996—24no—
90C4×Dic94—22no—
91C4×Dic94—22no—
92C4×C22⋊D47—22no—
93C4×C22⋊D47—22no—
94C4×C22⋊D47D414yes—
95C4×C22⋊D47D414yes—
96#13093983—22no—
97#13093983—22no—
98#13093981—22no—
99#13093981—22no—
100C2×C4⋊Dic47C2×C411yescharacteristic
101C2×C4⋊Dic47C2×C411yescharacteristic
102C2×C4⋊Dic47C2×C411yescharacteristic
103C2×Dic47⋊C4C2×C411yescharacteristic
104C2×Dic47⋊C4C2×C411yescharacteristic
105C2×Dic47⋊C4C2×C411yescharacteristic
106C2×Dic47⋊C4C2×C411yescharacteristic
107C2×Dic47⋊C4C2×C411yescharacteristic
108C2×Dic47⋊C4C2×C411yescharacteristic
109C2×C22⋊Dic47C2×C411yescharacteristic
110C2×C22⋊Dic47C2×C411yescharacteristic
111C2×C22⋊Dic47C2×C411yescharacteristic
112C2×C22⋊Dic47C2×C411yescharacteristic
113C2×(C2×D47)⋊C4C2×C411yescharacteristic
114C2×(C2×D47)⋊C4C2×C411yescharacteristic
115C2×(C2×D47)⋊C4C2×C411yescharacteristic
116C2×(C2×D47)⋊C4C2×C411yescharacteristic
117C2×C4×Dic47—22no—
118C2×C4×Dic47—22no—
119C2×C4×Dic47C2×C411yescharacteristic
120C2×C4×Dic47C2×C411yescharacteristic
121C2×C4×Dic47C2311yescharacteristic
122C2×C4×Dic47C2311yescharacteristic
123C2×C4×Dic47C2311yescharacteristic
124Dic47⋊C8—22no—
125Dic47⋊C8—22no—
126C22⋊(C47⋊C8)—22no—
127C22⋊(C47⋊C8)—22no—
128C22⋊(C47⋊C8)—41no—
129(C2×D47)⋊C8—22no—
130(C2×D47)⋊C8—22no—
131#13093934—22no—
132#13093934—22no—
133C22×D4×C47C2×C411yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C22×C8×C47—22no—
137C22×C8×C47—22no—
138C22×C8×C47—41no—
139C22×C8×C47C2311yescharacteristic
140C22×C8×C47C2311yescharacteristic
141C22×C8×C47C2311yescharacteristic
142C22×C8×C47C2311yescharacteristic
143C4×D4×C47—22no—
144C4×D4×C47—22no—
145C2×C4⋊C4×C47C2×C411yescharacteristic
146C2×C22⋊C4×C47C2×C411yescharacteristic
147C2×C22⋊C4×C47C2×C411yescharacteristic
148C2×C42×C47C2311yescharacteristic
149C22⋊C8×C47—22no—
150C22⋊C8×C47—22no—
151C22⋊C8×C47—41no—
152C24×C47C22×C411yescharacteristic
153C24×C47C22×C411yescharacteristic
154C23×D47C22×C411yescharacteristic
155C2×D4×C47—22no—
156C2×D4×C47—22no—
157C2×D4×C47—41no—
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×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47C22×C411yescharacteristic
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C22×C411yescharacteristic
171C22×C4×C47C22×C411yescharacteristic
172C22×C4×C47C2×D412yes—
173C22×C4×C47C2×D412yes—
174C22×C4×C47C2411yescharacteristic
175C2×C22⋊D47—22no—
176C2×C22⋊D47—22no—
177C2×C22⋊D47—41no—
178C2×C22⋊D47—41no—
179C2×C22⋊D47—41no—
180C2×C22⋊D47C22⋊C414yes—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—22no—
184C22×Dic47—41no—
185C22×Dic47—41no—
186C22×Dic47—41no—
187C22×Dic47C22×C411yescharacteristic
188C22×Dic47C22×C411yescharacteristic
189C22×Dic47C22×C411yescharacteristic
190C22×Dic47C22×C411yescharacteristic
191C22×Dic47C22×C411yescharacteristic
192C22×Dic47C22×C411yescharacteristic
193C22×Dic47C22×C411yescharacteristic
194C2×C4×D47—21no—
195C2×C4×D47—21no—
196C2×C4×D47—21no—
197C2×C4×D47—21no—
198C2×C4×D47C2×D412yes—
199C2×C4×D47C2×D412yes—
200C2×Dic94—22no—
201C2×Dic94—41no—
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—21no—
214C2×C8×C47—44no—
215C2×C8×C47#4112yes—
216C4⋊C4×C47—22no—
217C22⋊C4×C47—22no—
218C22⋊C4×C47—22no—
219C42×C47—21no—
220C42×C47—21no—
221C22⋊Dic47—22no—
222C22⋊Dic47—22no—
223C22⋊Dic47—22no—
224C22⋊Dic47C22⋊C414yes—
225(C2×D47)⋊C4—22no—
226(C2×D47)⋊C4—22no—
227(C2×D47)⋊C4—22no—
228(C2×D47)⋊C4C22⋊C414yes—
229C4⋊Dic47—22no—
230C4⋊Dic47—22no—
231C4⋊Dic47—22no—
232Dic47⋊C4—22no—
233Dic47⋊C4—22no—
234Dic47⋊C4—22no—
235Dic47⋊C4—22no—
236Dic47⋊C4—22no—
237Dic47⋊C4C22⋊C414yes—
238C4×Dic47—21no—
239C4×Dic47—21no—
240C4×Dic47—21no—
241C4×Dic47—21no—
242C4×Dic47—22no—
243C4×Dic47—22no—
244C4×Dic47C2×D412yes—
245C4×Dic47C2×D412yes—
246#10625329—44no—
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#4112yes—
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×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47C2×C22⋊C412yes—
274C23×C47#13112yes—
275C23×C47C23×C411yescharacteristic
276C22×D47—21no—
277C22×D47—21no—
278C22×D47—21no—
279C22×D47—21no—
280C22×D47—21no—
281C22×D47—21no—
282C22×D47C2×C22⋊C412yes—
283D4×C47—44no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
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—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
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—44no—
331C2×Dic47—44no—
332C2×Dic47C2×C22⋊C412yes—
333C2×Dic47C2×C22⋊C412yes—
334C2×Dic47C2×C22⋊C412yes—
335C4×D47—22no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—22no—
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—41no—
379C4×C47—41no—
380C4×C47—41no—
381C4×C47#54611yescharacteristic
382C4×C47#54611yescharacteristic
383C4×C47#54711yescharacteristic
384C4×C47#54711yescharacteristic
385Dic47—22no—
386Dic47—22no—
387Dic47—22no—
388Dic47—41no—
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#1869D4711yescharacteristic, complemented
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×M16—471no—
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—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⋊C8C2×D4711yescharacteristic
448C2×C22⋊C8C2×D4711yescharacteristic
449C2×C22⋊C8C2×D4711yescharacteristic
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#336—471no—
461#336—471no—
462#336C2×D4711yescharacteristic
463#336C2×D4711yescharacteristic
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—942no—
475C2×M16—942no—
476C2×M16—942no—
477C2×M16—942no—
478C2×M16—1881no—
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—22no—
505C4×D4—22no—
506C4×D4—474no—
507C4×D4—474no—
508C4×D4—942no—
509C4×D4—942no—
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—942no—
543C4⋊C8—942no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—41no—
547C22⋊C8—942no—
548C22⋊C8—942no—
549C22⋊C8—942no—
550C22⋊C8—942no—
551C22⋊C8—1881no—
552#97—942no—
553#97—942no—
554C24—471no—
555C24C2×C4×D4711yescharacteristic
556C24C2×C4×D4711yescharacteristic
557C2×Q8—942no—
558C2×Q8—1881no—
559C2×Q8—1881no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—41no—
563C2×D4—474no—
564C2×D4—942no—
565C2×D4—942no—
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—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—471no—
580C22×C4—471no—
581C22×C4—471no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—471no—
585C22×C4—471no—
586C22×C4—471no—
587C22×C4—471no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—942no—
595C22×C4—1881no—
596C22×C4—1881no—
597C22×C4—1881no—
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—1884no—
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—22no—
634C4⋊C4—474no—
635C4⋊C4—942no—
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—472no—
656C42—472no—
657C42—942no—
658C42—942no—
659C42—941no—
660C42—941no—
661C42—941no—
662C42—941no—
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—
682C23C22⋊C4×D4712yes—
683C23#1309403012yes—
684C23C22×C4×D4711yescharacteristic
685Q8—1884no—
686D4—44no—
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—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—472no—
709C2×C4—472no—
710C2×C4—472no—
711C2×C4—941no—
712C2×C4—941no—
713C2×C4—941no—
714C2×C4—941no—
715C2×C4—941no—
716C2×C4—941no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
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—941no—
730C2×C4—941no—
731C2×C4—941no—
732C2×C4—941no—
733C2×C4—1884no—
734C2×C4—1884no—
735C2×C4C22⋊C4×D4712yes—
736C2×C4C2×D4×D4711yescharacteristic
737C2×C4C2×D4×D4711yescharacteristic
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—
771C22C2×C22⋊C4×D4711yescharacteristic
772C22C4×#1062535211yescharacteristic
773C22#1568960211yescharacteristic
774C22C2×#1309403011yescharacteristic
775C22#1568988811yescharacteristic
776C22#1568988811yescharacteristic
777C22#1568988911yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—942no—
783C4—942no—
784C4—942no—
785C4—1881no—
786C4—1881no—
787C4—1881no—
788C4—1881no—
789C4#1568976011yescharacteristic
790C4#1568976211yescharacteristic
791C4#1568977111yescharacteristic
792C4#1568977311yescharacteristic
793C2—42no—
794C2—42no—
795C2—1882no—
796C2#2024621411yescharacteristic
797C2#2025183011yescharacteristic
798C2#2025183411yescharacteristic
799C2#2025236711yescharacteristic
800C2#2025237611yescharacteristic
801C2#2025252111yescharacteristic
802C2#2025255911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1869C2
prime radicalC2×#13093996C4
cosocleC22×C4×C47C24
hypercenter#1869D47
hypocenterC47#22475
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×#15689197C2semidirect
3. C2×#15689194C2semidirect
4. #20244326C2semidirect
5. #20244326C2semidirect
6. #20243686C2semidirect
7. #20243682C2semidirect
8. #20243677C2semidirect
9. #20243458C2semidirect
10. #20243457C2semidirect
11. #20243366C2semidirect
12. #20243152C2semidirect
13. #20243084C2semidirect
14. #20243083C2semidirect
15. C47×#1869C2semidirect
400. #1869D47semidirect
464. C47#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#156896532
C2×#156891972
C2×#156891942
#202443262
#202436862
#202436822
#202436772
#202434582
#202434572
#202433662
#202431522
#202430842
#202430832
C47×#18692
#2247547