Finite Group Databasebeta

← #26232658

Subgroups — #26232658

Order 12032.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689830C211yesmaximal, characteristic
2#20246317C211yesmaximal, characteristic
3#20244361C211yesmaximal, characteristic, complemented
4#20244339C211yesmaximal, characteristic, complemented
5#20243821C211yesmaximal, characteristic, complemented
6#20243811C211yesmaximal, characteristic, complemented
7#20243698C211yesmaximal, characteristic, complemented
8#20243693C211yesmaximal, characteristic, complemented
9#20243479C211yesmaximal, characteristic, complemented
10#20243475C211yesmaximal, characteristic, complemented
11#20243404C211yesmaximal, characteristic, complemented
12#20243219C211yesmaximal, characteristic, complemented
13#20243108C211yesmaximal, characteristic, complemented
14C2×#15688886C211yesmaximal, characteristic, complemented
15C2×C47×#435C211yesmaximal, characteristic
16#15689830—24no—
17#15689830C418yescomplemented
18C2×#13094024C2211yescharacteristic
19C2×#13094015—21no—
20C2×#13094003C2211yescharacteristic
21C2×#13094003C2211yescharacteristic
22C2×#13094001—21no—
23C2×#13094001—21no—
24C2×C4×Dic94C2211yescharacteristic
25C2×D4×Dic47—21no—
26C2×#13093983C2211yescharacteristic
27C22×C4⋊Dic47C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29C22×C4⋊Dic47C2211yescharacteristic
30C2×#13093949C2211yescharacteristic
31C2×#13093949C2211yescharacteristic
32C2×#13093949C2211yescharacteristic
33C2×#13093949C2211yescharacteristic
34#15689016—21no—
35#15689009—21no—
36#15689003—21no—
37#15688989C2211yescharacteristic
38#15688983C2211yescharacteristic
39#15688983C2211yescharacteristic
40C4×C4⋊Dic47C2211yescharacteristic
41C22⋊C4×Dic47—21no—
42#15688886C2211yescharacteristic
43#15688886C2211yescharacteristic
44#15688886C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688886C2211yescharacteristic
54C22×M16×C47C2211yescharacteristic
55C23×C8×C47C2211yescharacteristic
56C2×C4×D4×C47C2211yescharacteristic
57C47×#435—24no—
58C2×C4⋊C8×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C2×#97×C47C2211yescharacteristic
62C22×Dic94—21no—
63C22×Dic94C2311yescharacteristic
64C23×Dic47—21no—
65C23×Dic47—21no—
66C23×Dic47—21no—
67#13094024—22no—
68#13094024C2×C414yescomplemented
69#13094015—28no—
70#13094003—22no—
71#13094003—22no—
72#13094003C2×C414yes—
73#13094003C2×C414yescomplemented
74#13094001—28no—
75#13094001—28no—
76C4×Dic94—22no—
77C4×Dic94C2×C414yescomplemented
78D4×Dic47—28no—
79#13093983—22no—
80#13093983—41no—
81C2×C4⋊Dic47—22no—
82C2×C4⋊Dic47—22no—
83C2×C4⋊Dic47—21no—
84C2×C4⋊Dic47—21no—
85C2×C4⋊Dic47—21no—
86C2×C4⋊Dic47—22no—
87C2×C4⋊Dic47—21no—
88C2×C4⋊Dic47—41no—
89C2×C4⋊Dic47C2×C414yes—
90C2×C4⋊Dic47C2×C414yescomplemented
91C2×C4⋊Dic47C2311yescharacteristic
92C2×C4⋊Dic47C2311yescharacteristic
93C2×C4⋊Dic47C2311yescharacteristic
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C4⋊Dic47C2311yescharacteristic
97C2×C4⋊Dic47C2311yescharacteristic
98C2×Dic47⋊C4—21no—
99C2×Dic47⋊C4—21no—
100C2×Dic47⋊C4—21no—
101C2×C22⋊Dic47—21no—
102C2×C22⋊Dic47—21no—
103C2×C22⋊Dic47—21no—
104C2×C22⋊Dic47—21no—
105C2×C22⋊Dic47—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47—21no—
109#13093949—22no—
110#13093949—22no—
111#13093949—41no—
112#13093949—41no—
113C47⋊#95—21no—
114C47⋊#95—21no—
115C47⋊#95—21no—
116C47⋊#95—21no—
117C47⋊#95—21no—
118C22×D4×C47D411yescharacteristic
119C23×C4×C47C2311yescharacteristic
120C23×C4×C47C2311yescharacteristic
121C2×M16×C47—22no—
122C2×M16×C47—22no—
123C2×M16×C47—41no—
124C22×C8×C47—22no—
125C22×C8×C47—22no—
126C22×C8×C47—41no—
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C22×C8×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C4×D4×C47C2×C414yes—
132C4×D4×C47D414yes—
133C2×C4⋊C4×C47D411yescharacteristic
134C2×C22⋊C4×C47D411yescharacteristic
135C2×C22⋊C4×C47D411yescharacteristic
136C2×C42×C47C2311yescharacteristic
137C4⋊C8×C47—22no—
138C22⋊C8×C47—22no—
139C22⋊C8×C47—22no—
140#97×C47—22no—
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C2×D4×C47—22no—
144C2×D4×C47—22no—
145C2×D4×C47C22⋊C414yes—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47C22×C412yes—
155C22×C4×C47C22×C412yes—
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2411yescharacteristic
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—24no—
169C22×Dic47—24no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—42no—
174C22×Dic47—42no—
175C22×Dic47—81no—
176C22×Dic47—81no—
177C22×Dic47—81no—
178C22×Dic47—81no—
179C22×Dic47—81no—
180C2×Dic94—21no—
181C2×Dic94—21no—
182C2×Dic94—21no—
183C2×Dic94—21no—
184C2×Dic94—21no—
185C2×Dic94—24no—
186C2×Dic94—81no—
187C2×Dic94—81no—
188C2×Dic94C22×C412yes—
189M16×C47—44no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—44no—
202C2×C8×C47#4112yes—
203C4⋊C4×C47C22⋊C414yes—
204C22⋊C4×C47C22⋊C414yes—
205C22⋊C4×C47C22⋊C414yes—
206C42×C47C22×C412yes—
207C42×C47C2×D412yes—
208C22⋊Dic47—24no—
209C22⋊Dic47—24no—
210C22⋊Dic47—42no—
211C22⋊Dic47—42no—
212C22⋊Dic47—81no—
213C4⋊Dic47—24no—
214C4⋊Dic47—24no—
215C4⋊Dic47—24no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47—21no—
220C4⋊Dic47—21no—
221C4⋊Dic47—21no—
222C4⋊Dic47—21no—
223C4⋊Dic47—21no—
224C4⋊Dic47—21no—
225C4⋊Dic47—21no—
226C4⋊Dic47—42no—
227C4⋊Dic47C22×C412yes—
228C4⋊Dic47C22×C412yes—
229C4⋊Dic47C22×C412yes—
230C4⋊Dic47#4112yes—
231Dic47⋊C4—24no—
232Dic47⋊C4—24no—
233Dic47⋊C4—24no—
234C4×Dic47—24no—
235C4×Dic47—42no—
236C4×Dic47—81no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47C2×C22⋊C412yes—
248C23×C47C2×C22⋊C412yes—
249C23×C47#13712yes—
250C23×C47#13712yes—
251C23×C47C22×D411yescharacteristic
252D4×C47—28no—
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×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47C2×C22⋊C412yes—
270C2×C4×C47C2×C22⋊C412yes—
271C2×C4×C47C2×C22⋊C412yes—
272C2×C4×C47C2×C22⋊C412yes—
273C2×C4×C47C23×C411yescharacteristic
274C2×C4×C47C22×D411yescharacteristic
275C2×C4×C47C2×#4111yescharacteristic
276C2×C4×C47C2×#4111yescharacteristic
277C2×C4×C47H(5,𝔽2)11yescharacteristic
278C2×C4×C472−1+411yescharacteristic
279C2×Dic47—22no—
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—22no—
283C2×Dic47—22no—
284C2×Dic47—41no—
285C2×Dic47—41no—
286C2×Dic47—41no—
287C2×Dic47—41no—
288C2×Dic47—41no—
289C2×Dic47—41no—
290C2×Dic47—41no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—84no—
304C2×Dic47—84no—
305C2×Dic47—84no—
306Dic94—22no—
307Dic94—22no—
308Dic94—41no—
309Dic94—41no—
310Dic94—84no—
311C8×C47—22no—
312C8×C47—41no—
313C8×C47—41no—
314C8×C47—41no—
315#22497—471nomaximal, Sylow
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—22no—
322C22×C47—22no—
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47#41914yes—
330C22×C47C22×C22⋊C411yescharacteristic
331C22×C47#54611yescharacteristic
332C22×C47#54711yescharacteristic
333C22×C47C2×#13711yescharacteristic
334C22×C47C2×#13711yescharacteristic
335C22×C47#57611yescharacteristic
336C22×C47#57711yescharacteristic
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—22no—
340C4×C47—22no—
341C4×C47C4×#4111yescharacteristic
342C4×C47#52011yescharacteristic
343C4×C47#54611yescharacteristic
344C4×C47#54711yescharacteristic
345Dic47—42no—
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349Dic47—42no—
350Dic47—81no—
351Dic47—81no—
352Dic47—81no—
353C2×#554—471no—
354C2×#435D4711yescharacteristic
355#2352—471no—
356#1993—471no—
357#1988—471no—
358#1894—471no—
359#1892—471no—
360#1873—471no—
361#1872—471no—
362#1824—471no—
363#1823—471no—
364#1805—471no—
365#1763—471no—
366#1736—471no—
367C2×#340—471no—
368C2×C47—24no—
369C2×C47—42no—
370C2×C47#233911yescharacteristic
371C2×C47C2×#41911yescharacteristic
372C2×C47#289711yescharacteristic
373C2×C47#331411yescharacteristic
374C2×C47#331611yescharacteristic
375C2×C47#334411yescharacteristic
376C2×C47#334611yescharacteristic
377C22×M16C2×D4711yescharacteristic
378C23×C8C2×D4711yescharacteristic
379#554—478no—
380#554—944no—
381C2×C4⋊Q8—471no—
382C2×#125—941no—
383C2×C22⋊Q8—471no—
384C2×C22⋊Q8—471no—
385C2×C22⋊Q8—941no—
386C2×C22⋊Q8—941no—
387C2×C4×Q8—471no—
388C2×C4×D4—941no—
389C2×C4×D4C2×D4711yescharacteristic
390C2×#117—471no—
391C22×C4⋊C4—471no—
392C22×C4⋊C4—471no—
393C22×C4⋊C4—471no—
394#435—24no—
395C2×C4⋊C8C2×D4711yescharacteristic
396C2×#103—471no—
397C2×#103—471no—
398C2×#103—471no—
399C2×#103—471no—
400C2×C22⋊C8C2×D4711yescharacteristic
401C2×C22⋊C8C2×D4711yescharacteristic
402C2×#97C2×D4711yescharacteristic
403#388—941no—
404#387—941no—
405#386—941no—
406#382—471no—
407#380—471no—
408#380—471no—
409C4×C4⋊C4—471no—
410C4×C22⋊C4—941no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415#340—471no—
416#340—471no—
417#340—471no—
418#340—471no—
419#340—471no—
420#340—471no—
421#340—471no—
422#340—471no—
423C47#2249711yescharacteristic, complemented, Sylow
424C22×Q8—471no—
425C22×Q8—941no—
426C22×D4D18811yescharacteristic
427C23×C4—941no—
428C23×C4—941no—
429C23×C4—941no—
430C23×C4C22×D4711yescharacteristic
431C23×C4C22×D4711yescharacteristic
432C2×M16—22no—
433C2×M16—22no—
434C2×M16—41no—
435C22×C8—22no—
436C22×C8—22no—
437C22×C8—41no—
438C22×C8C22×D4711yescharacteristic
439C22×C8C22×D4711yescharacteristic
440C22×C8C22×D4711yescharacteristic
441C22×C8C22×D4711yescharacteristic
442C4⋊Q8—474no—
443C4⋊Q8—942no—
444#125—948no—
445C22⋊Q8—474no—
446C22⋊Q8—474no—
447C22⋊Q8—942no—
448C22⋊Q8—942no—
449C22⋊Q8—948no—
450C22⋊Q8—948no—
451C4×Q8—474no—
452C4×Q8—942no—
453C4×D4—948no—
454C4×D4C4×D4714yes—
455C4×D4C22⋊D4714yes—
456#117—942no—
457#117—1881no—
458C2×C4⋊C4—474no—
459C2×C4⋊C4—474no—
460C2×C4⋊C4—471no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—471no—
463C2×C4⋊C4—471no—
464C2×C4⋊C4—471no—
465C2×C4⋊C4—471no—
466C2×C4⋊C4—471no—
467C2×C4⋊C4—942no—
468C2×C4⋊C4—941no—
469C2×C4⋊C4—941no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—941no—
473C2×C4⋊C4—941no—
474C2×C4⋊C4—942no—
475C2×C4⋊C4—942no—
476C2×C4⋊C4—941no—
477C2×C4⋊C4—1881no—
478C2×C4⋊C4D18811yescharacteristic
479C2×C22⋊C4—941no—
480C2×C22⋊C4—941no—
481C2×C22⋊C4—941no—
482C2×C22⋊C4—941no—
483C2×C22⋊C4—941no—
484C2×C22⋊C4D18811yescharacteristic
485C2×C22⋊C4D18811yescharacteristic
486C2×C42—941no—
487C2×C42—941no—
488C2×C42—941no—
489C2×C42C22×D4711yescharacteristic
490C4⋊C8—22no—
491#103—942no—
492#103—942no—
493#103—1881no—
494#103—1881no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497#97—22no—
498#95—941no—
499#95—941no—
500#95—941no—
501#95—941no—
502#95—941no—
503C24C2×D18811yescharacteristic
504C24C2×D18811yescharacteristic
505C2×Q8—472no—
506C2×Q8—944no—
507C2×Q8—941no—
508C2×Q8—941no—
509C2×Q8—941no—
510C2×Q8—941no—
511C2×Q8—941no—
512C2×Q8—3761no—
513C2×Q8—3761no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4(C2×D47)⋊C414yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—944no—
526C22×C4—944no—
527C22×C4—941no—
528C22×C4—941no—
529C22×C4—941no—
530C22×C4—941no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—941no—
534C22×C4—941no—
535C22×C4—3761no—
536C22×C4—3761no—
537C22×C4—3761no—
538C22×C4—3761no—
539C22×C4—3761no—
540C22×C4—1882no—
541C22×C4—1882no—
542C22×C4C2×C4×D4712yes—
543C22×C4C2×C4×D4712yes—
544C22×C4C2×D18811yescharacteristic
545C22×C4C2×D18811yescharacteristic
546C22×C4C2×D18811yescharacteristic
547C22×C4C2×D18811yescharacteristic
548C22×C4C2×C22⋊D4712yes—
549C22×C4C2×C22⋊D4712yes—
550C22×C4C23×D4711yescharacteristic
551M16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—44no—
564C2×C8#1062535212yes—
565C4⋊C4—472no—
566C4⋊C4—472no—
567C4⋊C4—472no—
568C4⋊C4—472no—
569C4⋊C4—944no—
570C4⋊C4—944no—
571C4⋊C4—944no—
572C4⋊C4—944no—
573C4⋊C4—944no—
574C4⋊C4—944no—
575C4⋊C4—941no—
576C4⋊C4—941no—
577C4⋊C4—941no—
578C4⋊C4—941no—
579C4⋊C4—941no—
580C4⋊C4—941no—
581C4⋊C4—941no—
582C4⋊C4—941no—
583C4⋊C4—941no—
584C4⋊C4—941no—
585C4⋊C4—1882no—
586C4⋊C4(C2×D47)⋊C414yes—
587C22⋊C4—944no—
588C22⋊C4—944no—
589C22⋊C4—3761no—
590C22⋊C4—1882no—
591C22⋊C4—1882no—
592C22⋊C4(C2×D47)⋊C414yes—
593C22⋊C4(C2×D47)⋊C414yes—
594C42—944no—
595C42—3761no—
596C42—1882no—
597C42C2×C4×D4712yes—
598C42C2×C22⋊D4712yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×(C2×D47)⋊C412yes—
610C23C2×(C2×D47)⋊C412yes—
611C23#1309405712yes—
612C23#1309405712yes—
613C23C22×D18811yescharacteristic
614Q8—942no—
615Q8—942no—
616Q8—3764no—
617Q8—1881no—
618Q8—1881no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—942no—
637C2×C4—942no—
638C2×C4—942no—
639C2×C4—942no—
640C2×C4—942no—
641C2×C4—3764no—
642C2×C4—3764no—
643C2×C4—3764no—
644C2×C4—1881no—
645C2×C4—1881no—
646C2×C4—1881no—
647C2×C4—1881no—
648C2×C4—1881no—
649C2×C4—1881no—
650C2×C4—1881no—
651C2×C4—1881no—
652C2×C4—1881no—
653C2×C4—1881no—
654C2×C4—1881no—
655C2×C4—1881no—
656C2×C4—1881no—
657C2×C4—1881no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4—1881no—
661C2×C4—1881no—
662C2×C4—1881no—
663C2×C4C2×(C2×D47)⋊C412yes—
664C2×C4C2×(C2×D47)⋊C412yes—
665C2×C4C2×(C2×D47)⋊C412yes—
666C2×C4C2×(C2×D47)⋊C412yes—
667C2×C4C22×C4×D4711yescharacteristic
668C2×C4C22×C22⋊D4711yescharacteristic
669C2×C4#41×D4711yescharacteristic
670C2×C4C2×#1062535211yescharacteristic
671C2×C4#1309406911yescharacteristic
672C2×C4#1309407111yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1568913314yes—
691C22C22×(C2×D47)⋊C411yescharacteristic
692C22#1568976811yescharacteristic
693C22#1568977711yescharacteristic
694C22C2×#1309405711yescharacteristic
695C22C2×#1309405711yescharacteristic
696C22#1568992811yescharacteristic
697C22#1568993511yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—3761no—
703C4—3761no—
704C4—3761no—
705C4—1882no—
706C4—1882no—
707C4—1882no—
708C4—1882no—
709C4—1882no—
710C4C4×#1062535211yescharacteristic
711C4#1568960211yescharacteristic
712C4#1568976711yescharacteristic
713C4#1568977211yescharacteristic
714C2—24no—
715C2—42no—
716C2#2024621311yescharacteristic
717C2C2×#1568913311yescharacteristic
718C2#2025191511yescharacteristic
719C2#2025547111yescharacteristic
720C2#2025550111yescharacteristic
721C2#2025584511yescharacteristic
722C2#2025587511yescharacteristic
subgroupG/H
centerC23C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
prime radicalC22×D4×C47D4
cosocleC22×C4×C47C24
hypercenterC2×#435D47
hypocenterC47#22497
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #20244361C2semidirect
4. #20244339C2semidirect
5. #20243821C2semidirect
6. #20243811C2semidirect
7. #20243698C2semidirect
8. #20243693C2semidirect
9. #20243479C2semidirect
10. #20243475C2semidirect
11. #20243404C2semidirect
12. #20243219C2semidirect
13. #20243108C2semidirect
14. C2×#15688886C2semidirect
17. #15689830C4semidirect
68. #13094024C2×C4semidirect
73. #13094003C2×C4semidirect
77. C4×Dic94C2×C4semidirect
90. C2×C4⋊Dic47C2×C4semidirect
423. C47#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#156898302
#202463172
#202443612
#202443392
#202438212
#202438112
#202436982
#202436932
#202434792
#202434752
#202434042
#202432192
#202431082
C2×#156888862
C2×C47×#4352
#2249747