Finite Group Databasebeta

← #26232564

Subgroups — #26232564

Order 12032.

1194 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×#15689815C211yesmaximal, characteristic
2C2×#15689191C211yesmaximal, characteristic
3C4⋊C4×C22⋊D47C211yesmaximal, characteristic
4#20244355C211yesmaximal, characteristic, complemented
5#20244344C211yesmaximal, characteristic, complemented
6#20243818C211yesmaximal, characteristic, complemented
7#20243812C211yesmaximal, characteristic, complemented
8#20243692C211yesmaximal, characteristic, complemented
9#20243481C211yesmaximal, characteristic, complemented
10#20243475C211yesmaximal, characteristic, complemented
11#20243391C211yesmaximal, characteristic, complemented
12#20243220C211yesmaximal, characteristic, complemented
13#20243106C211yesmaximal, characteristic, complemented
14C2×#15688885C211yesmaximal, characteristic, complemented
15C47×#1872C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18#15689815—24no—
19#15689815C418yescomplemented
20C2×#13094019—21no—
21C2×#13094015—21no—
22C2×#13094015C2211yescharacteristic
23C2×#13094008—21no—
24C2×#13094000C2211yescharacteristic
25C2×Q8×Dic47C2211yescharacteristic
26C2×C4×C22⋊D47—21no—
27C2×C4×C22⋊D47C2211yescharacteristic
28C2×#13093982C2211yescharacteristic
29C2×#13093980—21no—
30C22×C4⋊Dic47C2211yescharacteristic
31C2×C4⋊C4×D47C2211yescharacteristic
32#15689191—24no—
33C2×Dic47⋊C8C2211yescharacteristic
34C2×#13093948C2211yescharacteristic
35C2×#13093948C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×#13093934C2211yescharacteristic
38#15689018—21no—
39#15688996—21no—
40#15688994—21no—
41#15688992C2211yescharacteristic
42#15688983C2211yescharacteristic
43#15688980C2211yescharacteristic
44C4⋊C4×Dic47C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688886C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C2×C22⋊Q8×C47C2211yescharacteristic
56C22×C4⋊C4×C47C2211yescharacteristic
57C2×#103×C47C2211yescharacteristic
58C2×#103×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×C22⋊D47D411yescharacteristic
63C23×Dic47—21no—
64C22×C4×D47—21no—
65C22×C4×D47C2311yescharacteristic
66C2×#10625324—22no—
67C2×#10625324—22no—
68C2×#10625324—41no—
69C22×C47⋊C8—22no—
70C22×C47⋊C8—22no—
71C22×C47⋊C8—41no—
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74#13094019—28no—
75#13094015—28no—
76#13094015—22no—
77#13094015C2×C414yescomplemented
78#13094008—28no—
79#13094000—22no—
80#13094000C2×C414yescomplemented
81Q8×Dic47—22no—
82Q8×Dic47C2×C414yescomplemented
83C4×C22⋊D47—44no—
84C4×C22⋊D47C2×C414yes—
85C4×C22⋊D47D414yes—
86#13093982—22no—
87#13093982C2×C414yescomplemented
88#13093980—28no—
89C2×C4⋊Dic47—22no—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47—21no—
92C2×C4⋊Dic47—21no—
93C2×C4⋊Dic47C2×C414yescomplemented
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×Dic47⋊C4—21no—
102C2×Dic47⋊C4—21no—
103C2×Dic47⋊C4D411yescharacteristic
104C4⋊C4×D47—22no—
105C4⋊C4×D47—41no—
106C2×C22⋊Dic47—21no—
107C2×C22⋊Dic47D411yescharacteristic
108C2×(C2×D47)⋊C4—21no—
109C2×(C2×D47)⋊C4—21no—
110C2×(C2×D47)⋊C4—21no—
111C2×(C2×D47)⋊C4D411yescharacteristic
112C2×C4×Dic47—21no—
113C2×C4×Dic47—21no—
114C2×C4×Dic47—21no—
115C2×C4×Dic47C2311yescharacteristic
116Dic47⋊C8—22no—
117#13093948—22no—
118#13093948—41no—
119(C2×D47)⋊C8—22no—
120#13093934—22no—
121C47⋊#95—21no—
122C47⋊#95—21no—
123C47⋊#95—21no—
124C22×Q8×C47C2311yescharacteristic
125C23×C4×C47—21no—
126C23×C4×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C22⋊Q8×C47—22no—
130C22⋊Q8×C47C2×C414yescomplemented
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—22no—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47—41no—
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47C2311yescharacteristic
138C2×C22⋊C4×C47—21no—
139#103×C47—22no—
140#103×C47—41no—
141C22⋊C8×C47—22no—
142C24×C47C2×D411yescharacteristic
143C23×D47C2×D411yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47C22×C412yes—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—42no—
159C22×C4×C47—42no—
160C22×C4×C47—81no—
161C22×C4×C47C22×C412yes—
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D412yes—
164C22×C4×C47C2411yescharacteristic
165C2×C22⋊D47—22no—
166C2×C22⋊D47—22no—
167C2×C22⋊D47C22⋊C414yes—
168C22×Dic47—24no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—42no—
174C22×Dic47—42no—
175C22×Dic47C2×D411yescharacteristic
176C22×Dic47C2×D411yescharacteristic
177C22×Dic47C2×D411yescharacteristic
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—42no—
183C2×C4×D47—42no—
184C2×C4×D47—81no—
185C2×C4×D47C22×C412yes—
186C2×C4×D47C2×D412yes—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C4⋊C4×C47—24no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—42no—
199C4⋊C4×C47C22×C412yes—
200C4⋊C4×C47#4112yes—
201C22⋊C4×C47—24no—
202C22⋊Dic47—42no—
203C22⋊Dic47C22⋊C414yes—
204(C2×D47)⋊C4—24no—
205(C2×D47)⋊C4—24no—
206(C2×D47)⋊C4—42no—
207(C2×D47)⋊C4C22⋊C414yes—
208C4⋊Dic47—24no—
209C4⋊Dic47—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—24no—
212C4⋊Dic47—24no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47C22×C412yes—
218C4⋊Dic47C22×C412yes—
219Dic47⋊C4—24no—
220Dic47⋊C4—24no—
221Dic47⋊C4—42no—
222Dic47⋊C4—42no—
223Dic47⋊C4—81no—
224Dic47⋊C4C22⋊C414yes—
225C4×Dic47—24no—
226C4×Dic47—24no—
227C4×Dic47—42no—
228C4×Dic47C22×C412yes—
229C4×Dic47C2×D412yes—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—44no—
236C2×C47⋊C8#4112yes—
237#10625324—44no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47C2×C22⋊C412yes—
243C23×C47AGL(1,ℤ/8)12yes—
244C23×C47#13712yes—
245C23×C47C22×D411yescharacteristic
246C22×D47—21no—
247C22×D47—21no—
248C22×D47—21no—
249C22×D47—21no—
250C22×D47—21no—
251C22×D47—21no—
252C22×D47C2×C22⋊C412yes—
253Q8×C47—22no—
254Q8×C47—22no—
255Q8×C47—41no—
256Q8×C47—41no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—84no—
276C2×C4×C47C2×C22⋊C412yes—
277C2×C4×C47C23×C411yescharacteristic
278C2×C4×C47C22×D411yescharacteristic
279C2×C4×C47C2×#4111yescharacteristic
280C2×C4×C47C2×#4111yescharacteristic
281C2×C4×C47H(5,𝔽2)11yescharacteristic
282C2×C4×C472−1+411yescharacteristic
283C22⋊D47—28no—
284C2×Dic47—21no—
285C2×Dic47—21no—
286C2×Dic47—21no—
287C2×Dic47—21no—
288C2×Dic47—21no—
289C2×Dic47—21no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—48no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47C2×C22⋊C412yes—
304C2×Dic47C2×C22⋊C412yes—
305C2×Dic47C2×C22⋊C412yes—
306C4×D47—22no—
307C4×D47—22no—
308C4×D47—22no—
309C4×D47—22no—
310C4×D47—84no—
311C8×C47—41no—
312C8×C47—41no—
313C47⋊C8—22no—
314C47⋊C8—41no—
315#22491—471nomaximal, Sylow
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—22no—
322C22×C47#41714yes—
323C22×C47C22×C22⋊C411yescharacteristic
324C22×C47#54611yescharacteristic
325C22×C47#54711yescharacteristic
326C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C47C2×#13711yescharacteristic
328C22×C47#57711yescharacteristic
329C22×C47#57811yescharacteristic
330C2×D47—22no—
331C2×D47—22no—
332C2×D47—22no—
333C2×D47—41no—
334C2×D47—41no—
335C2×D47—41no—
336C2×D47—41no—
337C4×C47—22no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47—81no—
342C4×C47C4×#4111yescharacteristic
343C4×C47#52011yescharacteristic
344C4×C47#54611yescharacteristic
345C4×C47#54711yescharacteristic
346Dic47—22no—
347Dic47—22no—
348Dic47—22no—
349Dic47—42no—
350Dic47—42no—
351Dic47—81no—
352Dic47—81no—
353C2×#552—471no—
354C2×#435—471no—
355D4×C4⋊C4—471no—
356#1992—471no—
357#1989—471no—
358#1894—471no—
359#1892—471no—
360#1872—471no—
361#1872D4711yescharacteristic, complemented
362#1825—471no—
363#1823—471no—
364#1803—471no—
365#1763—471no—
366#1736—471no—
367C2×#340—471no—
368C2×C47—24no—
369C2×C47#233911yescharacteristic
370C2×C47C2×#41711yescharacteristic
371C2×C47#289811yescharacteristic
372C2×C47#331011yescharacteristic
373C2×C47#331211yescharacteristic
374C2×C47#334311yescharacteristic
375C2×C47#334411yescharacteristic
376D47—42no—
377C22×M16—471no—
378C23×C8—471no—
379#552—478no—
380#552—944no—
381C2×#126—941no—
382C2×#125—471no—
383C2×#125—941no—
384C2×#123—941no—
385C2×C22⋊Q8—471no—
386C2×C22⋊Q8C2×D4711yescharacteristic
387C2×C4×Q8—471no—
388C2×C4×D4—471no—
389C2×C4×D4—941no—
390C2×#117—471no—
391C2×#117—941no—
392C22×C4⋊C4—471no—
393C22×C4⋊C4—471no—
394C22×C4⋊C4C2×D4711yescharacteristic
395#435—944no—
396C2×C4⋊C8—471no—
397C2×#103—471no—
398C2×#103—471no—
399C2×#103C2×D4711yescharacteristic
400C2×#103C2×D4711yescharacteristic
401C2×C22⋊C8—471no—
402C2×C22⋊C8C2×D4711yescharacteristic
403C2×#97—471no—
404#389—941no—
405#385—941no—
406#385—941no—
407#384—471no—
408#380—471no—
409#380—471no—
410C4×C4⋊C4—471no—
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#340C2×D4711yescharacteristic
422#340C2×D4711yescharacteristic
423C47#2249111yescharacteristic, complemented, Sylow
424C22×Q8C22×D4711yescharacteristic
425C22×D4—471no—
426C23×C4—21no—
427C23×C4—471no—
428C23×C4—941no—
429C23×C4—941no—
430C23×C4C22×D4711yescharacteristic
431C2×M16—942no—
432C2×M16—942no—
433C2×M16—1881no—
434C22×C8—471no—
435C22×C8—471no—
436C22×C8—942no—
437C22×C8—942no—
438C22×C8—1881no—
439C22×C8C22×D4711yescharacteristic
440C22×C8C22×D4711yescharacteristic
441#126—948no—
442#125—474no—
443#125—942no—
444#125—948no—
445#123—948no—
446C22⋊Q8—22no—
447C22⋊Q8—474no—
448C22⋊Q8—942no—
449C22⋊Q8C4×D4714yescomplemented
450C4×Q8—474no—
451C4×Q8—942no—
452C4×D4—474no—
453C4×D4—474no—
454C4×D4—1884no—
455#117—474no—
456#117—948no—
457#117—942no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—471no—
463C2×C4⋊C4—474no—
464C2×C4⋊C4—471no—
465C2×C4⋊C4—471no—
466C2×C4⋊C4—471no—
467C2×C4⋊C4—471no—
468C2×C4⋊C4—941no—
469C2×C4⋊C4—941no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—941no—
473C2×C4⋊C4—942no—
474C2×C4⋊C4—942no—
475C2×C4⋊C4—941no—
476C2×C4⋊C4—941no—
477C2×C4⋊C4—941no—
478C2×C4⋊C4—1881no—
479C2×C4⋊C4C22×D4711yescharacteristic
480C2×C4⋊C4C22×D4711yescharacteristic
481C2×C4⋊C4C22×D4711yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—471no—
484C2×C22⋊C4—471no—
485C2×C22⋊C4—941no—
486C2×C22⋊C4—941no—
487C2×C22⋊C4—941no—
488C2×C22⋊C4—941no—
489C2×C42—471no—
490C2×C42—941no—
491C2×C42—941no—
492C2×C42—941no—
493C4⋊C8—942no—
494#103—22no—
495#103—41no—
496#103—942no—
497#103—1881no—
498C22⋊C8—22no—
499C22⋊C8—942no—
500#97—942no—
501#95—941no—
502#95—941no—
503#95—941no—
504C24—471no—
505C24D4×D4711yescharacteristic
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8C2×C4×D4712yes—
512C2×D4—474no—
513C2×D4—942no—
514C2×D4—942no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4—471no—
527C22×C4—471no—
528C22×C4—471no—
529C22×C4—472no—
530C22×C4—472no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—941no—
534C22×C4—941no—
535C22×C4—944no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4—3761no—
541C22×C4—1882no—
542C22×C4—1882no—
543C22×C4—1882no—
544C22×C4—1882no—
545C22×C4C2×C4×D4712yes—
546C22×C4D4×D4711yescharacteristic
547C22×C4D4×D4712yes—
548C22×C4C23×D4711yescharacteristic
549M16—1884no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—472no—
557C2×C8—941no—
558C2×C8—941no—
559C2×C8—941no—
560C2×C8—941no—
561C2×C8—941no—
562C2×C8—1884no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—474no—
570C4⋊C4—472no—
571C4⋊C4—472no—
572C4⋊C4—944no—
573C4⋊C4—944no—
574C4⋊C4—944no—
575C4⋊C4—944no—
576C4⋊C4—944no—
577C4⋊C4—941no—
578C4⋊C4—941no—
579C4⋊C4—941no—
580C4⋊C4—941no—
581C4⋊C4—941no—
582C4⋊C4—941no—
583C4⋊C4—3761no—
584C4⋊C4—1882no—
585C4⋊C4—1882no—
586C4⋊C4C2×C4×D4712yes—
587C4⋊C4#1062535212yes—
588C22⋊C4—24no—
589C22⋊C4—474no—
590C22⋊C4—474no—
591C22⋊C4—944no—
592C22⋊C4—944no—
593C22⋊C4—1882no—
594C22⋊C4—1882no—
595C42—472no—
596C42—472no—
597C42—944no—
598C42—944no—
599C42—1882no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—472no—
605C23—941no—
606C23—941no—
607C23—941no—
608C23—941no—
609C23—941no—
610C23—941no—
611C23C22⋊C4×D4712yes—
612C23#1309405112yes—
613C23#1309405612yes—
614C23C2×D4×D4711yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619D4—948no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—84no—
639C2×C4—472no—
640C2×C4—472no—
641C2×C4—472no—
642C2×C4—941no—
643C2×C4—941no—
644C2×C4—941no—
645C2×C4—941no—
646C2×C4—941no—
647C2×C4—941no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—3764no—
655C2×C4—1881no—
656C2×C4—1881no—
657C2×C4—1881no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4—1881no—
661C2×C4—1888no—
662C2×C4—1881no—
663C2×C4—1881no—
664C2×C4—1881no—
665C2×C4—1881no—
666C2×C4C22⋊C4×D4712yes—
667C2×C4C22×C4×D4711yescharacteristic
668C2×C4C2×D4×D4711yescharacteristic
669C2×C4#41×D4711yescharacteristic
670C2×C4C2×#1062535211yescharacteristic
671C2×C4#1309406911yescharacteristic
672C2×C4#1309407111yescharacteristic
673C8—41no—
674C8—41no—
675C8—942no—
676C8—1881no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—942no—
684C22—942no—
685C22—942no—
686C22—1881no—
687C22—1881no—
688C22—1881no—
689C22—1881no—
690C22#1568912314yes—
691C22C2×C22⋊C4×D4711yescharacteristic
692C22#1568976011yescharacteristic
693C22#1568977111yescharacteristic
694C22C2×#1309405111yescharacteristic
695C22C2×#1309405611yescharacteristic
696C22#1568993311yescharacteristic
697C22#1568993911yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—942no—
704C4—942no—
705C4—942no—
706C4—3761no—
707C4—3761no—
708C4—1882no—
709C4—1882no—
710C4C4×#1062535211yescharacteristic
711C4#1568960211yescharacteristic
712C4#1568976211yescharacteristic
713C4#1568977311yescharacteristic
714C2—24no—
715C2—1882no—
716C2#2024621411yescharacteristic
717C2C2×#1568912311yescharacteristic
718C2#2025191911yescharacteristic
719C2#2025541311yescharacteristic
720C2#2025544311yescharacteristic
721C2#2025582611yescharacteristic
722C2#2025584111yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1872C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
cosocleC22×C4×C47C24
hypercenter#1872D47
hypocenterC47#22491
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #20244355C2semidirect
5. #20244344C2semidirect
6. #20243818C2semidirect
7. #20243812C2semidirect
8. #20243692C2semidirect
9. #20243481C2semidirect
10. #20243475C2semidirect
11. #20243391C2semidirect
12. #20243220C2semidirect
13. #20243106C2semidirect
14. C2×#15688885C2semidirect
15. C47×#1872C2semidirect
19. #15689815C4semidirect
77. #13094015C2×C4semidirect
80. #13094000C2×C4semidirect
82. Q8×Dic47C2×C4semidirect
87. #13093982C2×C4semidirect
93. C2×C4⋊Dic47C2×C4semidirect
130. C22⋊Q8×C47C2×C4semidirect
361. #1872D47semidirect
423. C47#22491semidirect
449. C22⋊Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156898152
C2×#156891912
C4⋊C4×C22⋊D472
#202443552
#202443442
#202438182
#202438122
#202436922
#202434812
#202434752
#202433912
#202432202
#202431062
C2×#156888852
C47×#18722
#2249147