Finite Group Databasebeta

← #26225714

Subgroups — #26225714

Order 12032.

1006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689677C211yesmaximal, characteristic
2C2×#15689183C211yesmaximal, characteristic
3C2×#15689182C211yesmaximal, characteristic
4#20244329C211yesmaximal, characteristic, complemented
5#20244327C211yesmaximal, characteristic, complemented
6#20244326C211yesmaximal, characteristic, complemented
7#20244326C211yesmaximal, characteristic, complemented
8#20244324C211yesmaximal, characteristic, complemented
9#20244322C211yesmaximal, characteristic, complemented
10#20244322C211yesmaximal, characteristic, complemented
11#20243458C211yesmaximal, characteristic
12#20243458C211yesmaximal, characteristic
13#20243455C211yesmaximal, characteristic
14#20243455C211yesmaximal, characteristic
15C47×#1984C211yesmaximal, characteristic, complemented
16#15689677—24no—
17#15689677—24no—
18C2×#13094023C411yescharacteristic
19C2×#13094022C411yescharacteristic
20C2×#13094014C411yescharacteristic
21C2×#13094014C411yescharacteristic
22C2×#13094004C411yescharacteristic
23C2×#13094002C411yescharacteristic
24C2×#13094002C411yescharacteristic
25C2×#13094000C411yescharacteristic
26C2×C4×Dic94C2211yescharacteristic
27C2×C4×Dic94C2211yescharacteristic
28C2×C4×Dic94C2211yescharacteristic
29C2×#13093981C2211yescharacteristic
30C2×#13093981C2211yescharacteristic
31C2×C42×D47C2211yescharacteristic
32#15689183—24no—
33#15689182—24no—
34C2×C4⋊(C47⋊C8)C2211yescharacteristic
35C2×Dic47⋊C8C2211yescharacteristic
36C2×Dic47⋊C8C2211yescharacteristic
37C2×(C2×D47)⋊C8C2211yescharacteristic
38C2×(C2×D47)⋊C8C2211yescharacteristic
39C2×(C2×D47)⋊C8C2211yescharacteristic
40C2×(C2×D47)⋊C8C2211yescharacteristic
41C2×#13093935C2211yescharacteristic
42C2×#13093934C2211yescharacteristic
43C2×C8×Dic47C2211yescharacteristic
44#15688878C2211yescharacteristic
45#15688878C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C2×C4×Q8×C47C2211yescharacteristic
57C2×C4⋊C8×C47C2211yescharacteristic
58C2×C4×C8×C47C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C47×#336C2211yescharacteristic
62C47×#336C2211yescharacteristic
63C22×Dic94C2×C411yescharacteristic
64C22×Dic94C2×C411yescharacteristic
65C22×Dic94C2×C411yescharacteristic
66C22×C4×D47C2×C411yescharacteristic
67C22×C4×D47C2×C411yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73#13094023—24no—
74#13094022—24no—
75#13094014—24no—
76#13094014—24no—
77#13094004—24no—
78#13094002—24no—
79#13094002—24no—
80#13094000—24no—
81C4×Dic94—22no—
82C4×Dic94—22no—
83C4×Dic94—22no—
84C4×Dic94—22no—
85C4×Dic94—22no—
86C4×Dic94—22no—
87#13093981—22no—
88#13093981—22no—
89#13093981D414yes—
90#13093981D414yes—
91C2×C4⋊Dic47C2×C411yescharacteristic
92C2×C4⋊Dic47C2×C411yescharacteristic
93C2×C4⋊Dic47C2×C411yescharacteristic
94C2×Dic47⋊C4C2×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×Dic47⋊C4C2×C411yescharacteristic
102C2×Dic47⋊C4C2×C411yescharacteristic
103C2×Dic47⋊C4C2×C411yescharacteristic
104C2×(C2×D47)⋊C4C2×C411yescharacteristic
105C2×(C2×D47)⋊C4C2×C411yescharacteristic
106C2×(C2×D47)⋊C4C2×C411yescharacteristic
107C2×(C2×D47)⋊C4C2×C411yescharacteristic
108C2×C4×Dic47C2×C411yescharacteristic
109C2×C4×Dic47C2×C411yescharacteristic
110C2×C4×Dic47C2311yescharacteristic
111C2×C4×Dic47C2311yescharacteristic
112C2×C4×Dic47C2311yescharacteristic
113C42×D47—22no—
114C42×D47—22no—
115C4⋊(C47⋊C8)—22no—
116Dic47⋊C8—22no—
117Dic47⋊C8—22no—
118(C2×D47)⋊C8—22no—
119(C2×D47)⋊C8—22no—
120(C2×D47)⋊C8—22no—
121(C2×D47)⋊C8—22no—
122#13093935—22no—
123#13093934—22no—
124C8×Dic47—22no—
125C22×Q8×C47C2×C411yescharacteristic
126C22×C8×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C4×Q8×C47—22no—
131C4×Q8×C47—22no—
132C2×C4⋊C4×C47C2×C411yescharacteristic
133C2×C4⋊C4×C47C2×C411yescharacteristic
134C2×C4⋊C4×C47C2×C411yescharacteristic
135C2×C42×C47C2311yescharacteristic
136C2×C42×C47C2311yescharacteristic
137C2×C42×C47C2311yescharacteristic
138C4⋊C8×C47—22no—
139C4×C8×C47—22no—
140C23×D47C22×C411yescharacteristic
141C2×Q8×C47—22no—
142C2×Q8×C47—22no—
143C2×Q8×C47—41no—
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C22×C411yescharacteristic
146C22×C4×C47C22×C411yescharacteristic
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C2411yescharacteristic
151C22×Dic47C22×C411yescharacteristic
152C22×Dic47C22×C411yescharacteristic
153C22×Dic47C22×C411yescharacteristic
154C22×Dic47C22×C411yescharacteristic
155C22×Dic47C22×C411yescharacteristic
156C22×Dic47C22×C411yescharacteristic
157C22×Dic47C22×C411yescharacteristic
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—41no—
167C2×C4×D47—41no—
168C2×C4×D47C2×D412yes—
169C2×C4×D47C2×D412yes—
170C2×Dic94—22no—
171C2×Dic94—22no—
172C2×Dic94—22no—
173C2×Dic94—22no—
174C2×Dic94—22no—
175C2×Dic94—22no—
176C2×Dic94—41no—
177C2×Dic94—41no—
178C2×Dic94—41no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—21no—
184C2×C8×C47—21no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C4⋊C4×C47—22no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—22no—
194C42×C47—21no—
195C42×C47—21no—
196C42×C47—21no—
197C42×C47—21no—
198C42×C47C2×D412yes—
199C42×C47C2×D412yes—
200(C2×D47)⋊C4—22no—
201(C2×D47)⋊C4—22no—
202(C2×D47)⋊C4C22⋊C414yes—
203(C2×D47)⋊C4C22⋊C414yes—
204C4⋊Dic47—22no—
205C4⋊Dic47—22no—
206C4⋊Dic47—22no—
207Dic47⋊C4—22no—
208Dic47⋊C4—22no—
209Dic47⋊C4—22no—
210Dic47⋊C4—22no—
211Dic47⋊C4—22no—
212Dic47⋊C4—22no—
213Dic47⋊C4—22no—
214Dic47⋊C4—22no—
215Dic47⋊C4C22⋊C414yes—
216Dic47⋊C4C22⋊C414yes—
217C4×Dic47—21no—
218C4×Dic47—21no—
219C4×Dic47—21no—
220C4×Dic47—21no—
221C4×Dic47—22no—
222C4×Dic47—22no—
223C4×Dic47C2×D412yes—
224C4×Dic47C2×D412yes—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C23×C47C23×C411yescharacteristic
238C22×D47—21no—
239C22×D47—21no—
240C22×D47—21no—
241C22×D47—21no—
242C22×D47—21no—
243C22×D47—21no—
244C22×D47C2×C22⋊C412yes—
245Q8×C47—44no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47C2×C22⋊C412yes—
262C2×C4×C47C2×C22⋊C412yes—
263C2×C4×C47#13112yes—
264C2×C4×C47C22×D411yescharacteristic
265C2×C4×C47C22×D411yescharacteristic
266C2×C4×C472−1+411yescharacteristic
267C2×C4×C472−1+411yescharacteristic
268C2×C4×C472−1+411yescharacteristic
269C2×C4×C472−1+411yescharacteristic
270C2×Dic47—21no—
271C2×Dic47—21no—
272C2×Dic47—21no—
273C2×Dic47—21no—
274C2×Dic47—21no—
275C2×Dic47—21no—
276C2×Dic47—21no—
277C2×Dic47—21no—
278C2×Dic47—21no—
279C2×Dic47—21no—
280C2×Dic47—21no—
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—21no—
286C2×Dic47—21no—
287C2×Dic47C2×C22⋊C412yes—
288C2×Dic47C2×C22⋊C412yes—
289C2×Dic47C2×C22⋊C412yes—
290C2×Dic47#13112yes—
291C4×D47—22no—
292C4×D47—22no—
293C4×D47—22no—
294C4×D47—22no—
295C4×D47—44no—
296C4×D47—44no—
297Dic94—44no—
298Dic94—44no—
299Dic94—44no—
300C8×C47—41no—
301C8×C47—41no—
302C8×C47—41no—
303C8×C47—41no—
304C47⋊C8—41no—
305C47⋊C8—41no—
306C47⋊C8—41no—
307C47⋊C8—41no—
308#21824—471nomaximal, Sylow
309C22×C47C22×C22⋊C411yescharacteristic
310C22×C47#51911yescharacteristic
311C22×C47#51911yescharacteristic
312C22×C47C2×#13111yescharacteristic
313C22×C47C2×#13111yescharacteristic
314C22×C47#56811yescharacteristic
315C22×C47#56811yescharacteristic
316C2×D47—22no—
317C2×D47—22no—
318C2×D47—22no—
319C2×D47—41no—
320C2×D47—41no—
321C2×D47—41no—
322C2×D47—41no—
323C4×C47—22no—
324C4×C47—22no—
325C4×C47—22no—
326C4×C47—41no—
327C4×C47—41no—
328C4×C47—41no—
329C4×C47#53611yescharacteristic
330C4×C47#53611yescharacteristic
331C4×C47#53611yescharacteristic
332C4×C47#53611yescharacteristic
333Dic47—22no—
334Dic47—22no—
335Dic47—22no—
336Dic47—22no—
337Dic47—41no—
338Dic47—41no—
339Dic47—41no—
340C2×#533—471no—
341C2×#433—471no—
342C2×#433—471no—
343#1985—471no—
344#1985—471no—
345#1985—471no—
346#1985—471no—
347#1984—471no—
348#1984—471no—
349#1984—471no—
350#1984D4711yescharacteristic, complemented
351#1818—471no—
352#1818—471no—
353#1817—471no—
354#1817—471no—
355C2×C47#231011yescharacteristic
356C2×C47#288011yescharacteristic
357C2×C47#288011yescharacteristic
358C2×C47#298511yescharacteristic
359C2×C47#298511yescharacteristic
360C2×C47#298611yescharacteristic
361C2×C47#298711yescharacteristic
362D47—42no—
363#533—944no—
364#533—944no—
365C2×C4⋊Q8—471no—
366C2×C4⋊Q8—471no—
367C2×#125—471no—
368C2×#125—471no—
369C2×C22⋊Q8—471no—
370C2×C22⋊Q8—471no—
371C2×C22⋊Q8—471no—
372C2×C22⋊Q8—471no—
373C2×C4×Q8—471no—
374C2×C4×Q8—471no—
375C2×C4×Q8—471no—
376C2×C4×Q8C2×D4711yescharacteristic
377C2×#117—471no—
378C2×#117—471no—
379C22×C42—471no—
380#433—944no—
381#433—944no—
382C2×C4⋊C8—471no—
383C2×C4⋊C8—471no—
384C2×C4⋊C8—471no—
385C2×C4⋊C8C2×D4711yescharacteristic
386C2×C22⋊C8—471no—
387C2×C22⋊C8—471no—
388C2×C22⋊C8—471no—
389C2×C22⋊C8—471no—
390C2×#97—471no—
391C2×#97—471no—
392C2×C4×C8—471no—
393C2×C4×C8C2×D4711yescharacteristic
394#336—471no—
395#336—471no—
396#336—471no—
397#336—471no—
398#336—471no—
399#336—471no—
400#336—471no—
401#336—471no—
402#336—471no—
403#336—471no—
404#336—471no—
405#336—471no—
406#336C2×D4711yescharacteristic
407#336C2×D4711yescharacteristic
408#336C2×D4711yescharacteristic
409#336C2×D4711yescharacteristic
410C47#2182411yescharacteristic, complemented, Sylow
411C22×Q8—471no—
412C22×Q8—471no—
413C22×Q8—471no—
414C22×Q8C4×D4711yescharacteristic
415C23×C4—471no—
416C23×C4—471no—
417C23×C4—471no—
418C22×C8—471no—
419C22×C8—471no—
420C22×C8—471no—
421C22×C8—471no—
422C22×C8C22×D4711yescharacteristic
423C22×C8C22×D4711yescharacteristic
424C22×C8C22×D4711yescharacteristic
425C22×C8C22×D4711yescharacteristic
426C4⋊Q8—944no—
427C4⋊Q8—944no—
428#125—944no—
429#125—944no—
430C22⋊Q8—944no—
431C22⋊Q8—944no—
432C22⋊Q8—944no—
433C22⋊Q8—944no—
434C4×Q8—22no—
435C4×Q8—22no—
436C4×Q8—942no—
437C4×Q8—942no—
438C4×Q8—942no—
439C4×Q8—942no—
440C4×Q8—942no—
441C4×Q8—942no—
442#117—474no—
443#117—474no—
444#117—942no—
445#117—942no—
446C2×C4⋊C4—471no—
447C2×C4⋊C4—471no—
448C2×C4⋊C4—471no—
449C2×C4⋊C4—471no—
450C2×C4⋊C4—471no—
451C2×C4⋊C4—471no—
452C2×C4⋊C4—471no—
453C2×C4⋊C4—471no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—471no—
456C2×C4⋊C4—471no—
457C2×C4⋊C4—471no—
458C2×C4⋊C4—471no—
459C2×C4⋊C4C4×D4711yescharacteristic
460C2×C4⋊C4C4×D4711yescharacteristic
461C2×C4⋊C4C4×D4711yescharacteristic
462C2×C22⋊C4—471no—
463C2×C22⋊C4—471no—
464C2×C22⋊C4—471no—
465C2×C22⋊C4—471no—
466C2×C42—471no—
467C2×C42—471no—
468C2×C42—471no—
469C2×C42—471no—
470C2×C42—471no—
471C2×C42—942no—
472C2×C42—942no—
473C2×C42C22×D4711yescharacteristic
474C2×C42C22×D4711yescharacteristic
475C2×C42C22×D4711yescharacteristic
476C4⋊C8—22no—
477C4⋊C8—942no—
478C4⋊C8—942no—
479C4⋊C8—942no—
480C22⋊C8—942no—
481C22⋊C8—942no—
482C22⋊C8—942no—
483C22⋊C8—942no—
484#97—942no—
485#97—942no—
486C4×C8—22no—
487C4×C8—942no—
488C24—471no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—41no—
492C2×Q8—942no—
493C2×Q8—942no—
494C2×Q8—942no—
495C2×Q8—942no—
496C2×Q8—942no—
497C2×Q8—942no—
498C2×Q8—1881no—
499C2×Q8—1881no—
500C2×Q8—1881no—
501C22×C4—471no—
502C22×C4—471no—
503C22×C4—471no—
504C22×C4—471no—
505C22×C4—472no—
506C22×C4—472no—
507C22×C4—471no—
508C22×C4—471no—
509C22×C4—471no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—942no—
513C22×C4—941no—
514C22×C4—941no—
515C22×C4—941no—
516C22×C4—941no—
517C22×C4—942no—
518C22×C4—1881no—
519C22×C4—1881no—
520C22×C4C2×C4×D4711yescharacteristic
521C22×C4C2×C4×D4711yescharacteristic
522C22×C4C2×C4×D4711yescharacteristic
523C22×C4C2×C4×D4711yescharacteristic
524C22×C4C2×C4×D4711yescharacteristic
525C22×C4C2×C4×D4711yescharacteristic
526C22×C4C23×D4711yescharacteristic
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—941no—
540C2×C8—941no—
541C2×C8—941no—
542C2×C8—941no—
543C2×C8—941no—
544C2×C8—941no—
545C2×C8—941no—
546C2×C8—941no—
547C2×C8—941no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—474no—
555C4⋊C4—474no—
556C4⋊C4—942no—
557C4⋊C4—942no—
558C4⋊C4—942no—
559C4⋊C4—942no—
560C4⋊C4—942no—
561C4⋊C4—942no—
562C4⋊C4—942no—
563C4⋊C4—942no—
564C4⋊C4—942no—
565C4⋊C4—942no—
566C4⋊C4—942no—
567C22⋊C4—474no—
568C22⋊C4—474no—
569C22⋊C4—942no—
570C22⋊C4—942no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—472no—
576C42—472no—
577C42—942no—
578C42—942no—
579C42—941no—
580C42—941no—
581C42—941no—
582C42—941no—
583C42D4×D4712yes—
584C42D4×D4712yes—
585C23—472no—
586C23—941no—
587C23—941no—
588C23—941no—
589C23—941no—
590C23—941no—
591C23—941no—
592C23C22×C4×D4711yescharacteristic
593Q8—44no—
594Q8—1884no—
595Q8—1884no—
596Q8—1884no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—472no—
613C2×C4—472no—
614C2×C4—472no—
615C2×C4—472no—
616C2×C4—941no—
617C2×C4—941no—
618C2×C4—941no—
619C2×C4—941no—
620C2×C4—941no—
621C2×C4—941no—
622C2×C4—941no—
623C2×C4—941no—
624C2×C4—942no—
625C2×C4—942no—
626C2×C4—942no—
627C2×C4—942no—
628C2×C4—941no—
629C2×C4—941no—
630C2×C4—941no—
631C2×C4—941no—
632C2×C4—941no—
633C2×C4—941no—
634C2×C4—941no—
635C2×C4—941no—
636C2×C4—941no—
637C2×C4—1884no—
638C2×C4—1884no—
639C2×C4C22⋊C4×D4712yes—
640C2×C4C22⋊C4×D4712yes—
641C2×C4#1309403012yes—
642C2×C4C2×D4×D4711yescharacteristic
643C2×C4C2×D4×D4711yescharacteristic
644C2×C4#1309407111yescharacteristic
645C2×C4#1309407111yescharacteristic
646C2×C4#1309407211yescharacteristic
647C2×C4#1309407211yescharacteristic
648C8—41no—
649C8—41no—
650C8—41no—
651C8—41no—
652C8—1881no—
653C8—1881no—
654C8—1881no—
655C8—1881no—
656C22—942no—
657C22—942no—
658C22—942no—
659C22—1881no—
660C22—1881no—
661C22—1881no—
662C22—1881no—
663C22C2×C22⋊C4×D4711yescharacteristic
664C22#1568959911yescharacteristic
665C22#1568959911yescharacteristic
666C22#131×D4711yescharacteristic
667C22C2×#1309403011yescharacteristic
668C22#1568988811yescharacteristic
669C22#1568988911yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—942no—
677C4—942no—
678C4—942no—
679C4—942no—
680C4—1881no—
681C4—1881no—
682C4—1881no—
683C4#1568969311yescharacteristic
684C4#1568969611yescharacteristic
685C4#1568969611yescharacteristic
686C4#1568969811yescharacteristic
687C2—1882no—
688C2#2024597111yescharacteristic
689C2#2025183411yescharacteristic
690C2#2025183611yescharacteristic
691C2#2025247911yescharacteristic
692C2#2025248111yescharacteristic
693C2#2025248811yescharacteristic
694C2#2025249111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1984C2
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1984D47
hypocenterC47#21824
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1984

Complements

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

NH ≅ G/Ntype
4. #20244329C2semidirect
5. #20244327C2semidirect
6. #20244326C2semidirect
7. #20244326C2semidirect
8. #20244324C2semidirect
9. #20244322C2semidirect
10. #20244322C2semidirect
15. C47×#1984C2semidirect
350. #1984D47semidirect
410. C47#21824semidirect

Maximal subgroups

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

subgroupindex
C2×#156896772
C2×#156891832
C2×#156891822
#202443292
#202443272
#202443262
#202443242
#202443222
#202434582
#202434552
C47×#19842
#2182447