Finite Group Databasebeta

← #26232563

Subgroups — #26232563

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×#15689814C211yesmaximal, characteristic
2C2×#15689193C211yesmaximal, characteristic
3#20246288C211yesmaximal, characteristic
4#20244356C211yesmaximal, characteristic, complemented
5#20244343C211yesmaximal, characteristic, complemented
6#20243818C211yesmaximal, characteristic, complemented
7#20243808C211yesmaximal, characteristic, complemented
8#20243692C211yesmaximal, characteristic, complemented
9#20243692C211yesmaximal, characteristic, complemented
10#20243482C211yesmaximal, characteristic, complemented
11#20243473C211yesmaximal, characteristic, complemented
12#20243218C211yesmaximal, characteristic, complemented
13#20243106C211yesmaximal, characteristic, complemented
14#340×D47C211yesmaximal, characteristic, complemented
15C47×#1803C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18#15689814—24no—
19#15689814C418yescomplemented
20C2×#13094018—21no—
21C2×#13094016C2211yescharacteristic
22C2×#13094014—21no—
23C2×#13094009—21no—
24C2×#13094000C2211yescharacteristic
25C2×#13094000C2211yescharacteristic
26C2×C4×D188C2211yescharacteristic
27C2×#13093986—21no—
28C2×#13093982C2211yescharacteristic
29C2×#13093981—21no—
30C2×C4⋊C4×D47C2211yescharacteristic
31C2×C4⋊C4×D47C2211yescharacteristic
32C2×C4⋊C4×D47C2211yescharacteristic
33#15689193—24no—
34C2×#13093948C2211yescharacteristic
35C2×#13093948C2211yescharacteristic
36C2×(C2×D47)⋊C8C2211yescharacteristic
37C2×(C2×D47)⋊C8C2211yescharacteristic
38C2×#13093935C2211yescharacteristic
39#15689019—21no—
40#15688994—21no—
41#15688994—21no—
42#15688980C2211yescharacteristic
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×C4×Q8×C47C2211yescharacteristic
56C2×C4⋊C8×C47C2211yescharacteristic
57C2×#103×C47C2211yescharacteristic
58C2×#103×C47C2211yescharacteristic
59C47×#384C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×D188D411yescharacteristic
63C22×C4×D47—21no—
64C22×C4×D47—21no—
65C22×C4×D47—21no—
66C22×C4×D47C2311yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C2×#10625324—22no—
69C2×#10625324—22no—
70C2×#10625324—41no—
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C2×C8×D47—22no—
74C2×C8×D47—22no—
75C2×C8×D47—41no—
76#13094018—28no—
77#13094016—22no—
78#13094016C2×C414yescomplemented
79#13094014—28no—
80#13094009—28no—
81#13094000—22no—
82#13094000—22no—
83#13094000C2×C414yescomplemented
84#13094000C2×C414yescomplemented
85C4×D188C2×C414yes—
86C4×D188D414yes—
87#13093986—44no—
88#13093982—22no—
89#13093982C2×C414yescomplemented
90#13093981—28no—
91C2×C4⋊Dic47D411yescharacteristic
92C2×C4⋊Dic47C2311yescharacteristic
93C2×C4⋊Dic47C2311yescharacteristic
94C2×C4⋊Dic47C2311yescharacteristic
95C2×C4⋊Dic47C2311yescharacteristic
96C2×Dic47⋊C4—21no—
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C2×Dic47⋊C4—21no—
100C2×Dic47⋊C4—21no—
101C2×Dic47⋊C4—21no—
102C2×Dic47⋊C4—21no—
103C4⋊C4×D47—22no—
104C4⋊C4×D47—22no—
105C4⋊C4×D47—22no—
106C4⋊C4×D47—41no—
107C4⋊C4×D47—41no—
108C4⋊C4×D47C2×C414yescomplemented
109C2×(C2×D47)⋊C4—21no—
110C2×(C2×D47)⋊C4—21no—
111C2×(C2×D47)⋊C4—21no—
112C2×(C2×D47)⋊C4—21no—
113C2×(C2×D47)⋊C4—21no—
114C2×(C2×D47)⋊C4D411yescharacteristic
115C2×(C2×D47)⋊C4D411yescharacteristic
116C2×C4×Dic47—21no—
117C2×C4×Dic47—21no—
118#13093948—22no—
119#13093948—22no—
120(C2×D47)⋊C8—22no—
121(C2×D47)⋊C8—22no—
122#13093935—22no—
123C47⋊#95—21no—
124C47⋊#95—21no—
125C47⋊#95—21no—
126C22×Q8×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C4×Q8×C47—22no—
130C4×Q8×C47C2×C414yescomplemented
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C42×C47—21no—
138C2×C42×C47C2311yescharacteristic
139C4⋊C8×C47—22no—
140#103×C47—41no—
141#103×C47—41no—
142C23×D47C2×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×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2411yescharacteristic
157C22×Dic47—21no—
158C22×Dic47—21no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47C2×D411yescharacteristic
162C22×Dic47C2×D411yescharacteristic
163C2×D188—22no—
164C2×D188—22no—
165C2×D188C22⋊C414yes—
166C2×C4×D47—21no—
167C2×C4×D47—21no—
168C2×C4×D47—21no—
169C2×C4×D47—21no—
170C2×C4×D47—21no—
171C2×C4×D47—21no—
172C2×C4×D47—21no—
173C2×C4×D47—21no—
174C2×C4×D47—24no—
175C2×C4×D47—42no—
176C2×C4×D47—42no—
177C2×C4×D47—42no—
178C2×C4×D47—42no—
179C2×C4×D47—42no—
180C2×C4×D47—42no—
181C2×C4×D47—81no—
182C2×C4×D47—81no—
183C2×C4×D47C22×C412yes—
184C2×C4×D47C22×C412yes—
185C2×C4×D47C2×D412yes—
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—21no—
199C4⋊C4×C47—42no—
200C4⋊C4×C47—81no—
201C4⋊C4×C47C22×C412yes—
202C42×C47—24no—
203C42×C47C22×C412yes—
204C42×C47C2×D412yes—
205(C2×D47)⋊C4—24no—
206(C2×D47)⋊C4—24no—
207(C2×D47)⋊C4—24no—
208(C2×D47)⋊C4—42no—
209(C2×D47)⋊C4—42no—
210(C2×D47)⋊C4C22⋊C414yes—
211(C2×D47)⋊C4C22⋊C414yes—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47C22⋊C414yes—
218C4⋊Dic47C22×C412yes—
219C4⋊Dic47C22×C412yes—
220C4⋊Dic47#4112yes—
221Dic47⋊C4—24no—
222Dic47⋊C4—24no—
223Dic47⋊C4—24no—
224Dic47⋊C4—24no—
225Dic47⋊C4—24no—
226Dic47⋊C4—42no—
227Dic47⋊C4—42no—
228C4×Dic47—24no—
229C4×Dic47—42no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8#4112yes—
236#10625324—44no—
237C8×D47—44no—
238C23×C47C22×D411yescharacteristic
239C22×D47—21no—
240C22×D47—21no—
241C22×D47—21no—
242C22×D47—21no—
243C22×D47—21no—
244C22×D47—21no—
245C22×D47—21no—
246C22×D47—21no—
247C22×D47—21no—
248C22×D47—21no—
249C22×D47C2×C22⋊C412yes—
250C22×D47C2×C22⋊C412yes—
251C22×D47AGL(1,ℤ/8)12yes—
252C22×D47#13712yes—
253Q8×C47—22no—
254Q8×C47—22no—
255Q8×C47—41no—
256Q8×C47—41no—
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—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
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×C47C2×C22⋊C412yes—
274C2×C4×C47C2×C22⋊C412yes—
275C2×C4×C47C23×C411yescharacteristic
276C2×C4×C47C22×D411yescharacteristic
277C2×C4×C47C2×#4111yescharacteristic
278C2×C4×C47C2×#4111yescharacteristic
279C2×C4×C47H(5,𝔽2)11yescharacteristic
280C2×C4×C472−1+411yescharacteristic
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—22no—
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×Dic47C2×C22⋊C412yes—
298C2×Dic47C2×C22⋊C412yes—
299D188—28no—
300C4×D47—22no—
301C4×D47—22no—
302C4×D47—22no—
303C4×D47—22no—
304C4×D47—22no—
305C4×D47—22no—
306C4×D47—22no—
307C4×D47—22no—
308C4×D47—48no—
309C4×D47—84no—
310C4×D47—84no—
311C8×C47—41no—
312C8×C47—41no—
313C47⋊C8—22no—
314C47⋊C8—41no—
315#22491—471nomaximal, Sylow
316C22×C47C22×C22⋊C411yescharacteristic
317C22×C47#54611yescharacteristic
318C22×C47#54711yescharacteristic
319C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C47C2×#13711yescharacteristic
321C22×C47#57711yescharacteristic
322C22×C47#57811yescharacteristic
323C2×D47—22no—
324C2×D47—22no—
325C2×D47—22no—
326C2×D47—22no—
327C2×D47—22no—
328C2×D47—22no—
329C2×D47—22no—
330C2×D47—22no—
331C2×D47—22no—
332C2×D47—41no—
333C2×D47—41no—
334C2×D47—41no—
335C2×D47—41no—
336C2×D47#41714yes—
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47—81no—
342C4×C47—81no—
343C4×C47C4×#4111yescharacteristic
344C4×C47#52011yescharacteristic
345C4×C47#54611yescharacteristic
346C4×C47#54711yescharacteristic
347Dic47—22no—
348Dic47—22no—
349Dic47—42no—
350Dic47—42no—
351Dic47—42no—
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#1872—471no—
362#1825—471no—
363#1823—471no—
364#1803D4711yescharacteristic, complemented
365#1763—471no—
366#1736—471no—
367C2×#340—471no—
368C2×C47#233911yescharacteristic
369C2×C47C2×#41711yescharacteristic
370C2×C47#289811yescharacteristic
371C2×C47#331011yescharacteristic
372C2×C47#331211yescharacteristic
373C2×C47#334311yescharacteristic
374C2×C47#334411yescharacteristic
375D47—24no—
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⋊Q8—471no—
387C2×C4×Q8C2×D4711yescharacteristic
388C2×C4×D4—471no—
389C2×C4×D4—941no—
390C2×#117—471no—
391C2×#117—941no—
392C22×C4⋊C4—471no—
393C22×C4⋊C4—471no—
394C22×C4⋊C4—471no—
395#435—944no—
396C2×C4⋊C8C2×D4711yescharacteristic
397C2×#103—471no—
398C2×#103—471no—
399C2×#103C2×D4711yescharacteristic
400C2×#103C2×D4711yescharacteristic
401C2×C22⋊C8—471no—
402C2×C22⋊C8—471no—
403C2×#97—471no—
404#389—941no—
405#385—941no—
406#385—941no—
407#384C2×D4711yescharacteristic
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—471no—
427C23×C4—471no—
428C23×C4—941no—
429C23×C4—941no—
430C23×C4—941no—
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—948no—
444#125—942no—
445#123—948no—
446C22⋊Q8—474no—
447C22⋊Q8—474no—
448C22⋊Q8—942no—
449C22⋊Q8—942no—
450C4×Q8—22no—
451C4×Q8C4×D4714yescomplemented
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—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—471no—
463C2×C4⋊C4—471no—
464C2×C4⋊C4—471no—
465C2×C4⋊C4—474no—
466C2×C4⋊C4—471no—
467C2×C4⋊C4—942no—
468C2×C4⋊C4—942no—
469C2×C4⋊C4—942no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—941no—
473C2×C4⋊C4—941no—
474C2×C4⋊C4—941no—
475C2×C4⋊C4—941no—
476C2×C4⋊C4—941no—
477C2×C4⋊C4—1881no—
478C2×C4⋊C4—1881no—
479C2×C4⋊C4C22×D4711yescharacteristic
480C2×C4⋊C4C22×D4711yescharacteristic
481C2×C4⋊C4C22×D4711yescharacteristic
482C2×C22⋊C4—471no—
483C2×C22⋊C4—471no—
484C2×C22⋊C4—941no—
485C2×C22⋊C4—941no—
486C2×C22⋊C4—941no—
487C2×C22⋊C4—941no—
488C2×C22⋊C4—941no—
489C2×C42—21no—
490C2×C42—941no—
491C2×C42—941no—
492C2×C42C22×D4711yescharacteristic
493C4⋊C8—22no—
494#103—41no—
495#103—41no—
496#103—942no—
497#103—942no—
498C22⋊C8—942no—
499C22⋊C8—942no—
500#97—942no—
501#95—941no—
502#95—941no—
503#95—941no—
504C24—471no—
505C24—471no—
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—471no—
520C22×C4—471no—
521C22×C4—472no—
522C22×C4—472no—
523C22×C4—472no—
524C22×C4—472no—
525C22×C4—944no—
526C22×C4—941no—
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—941no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—3761no—
539C22×C4—3761no—
540C22×C4—1882no—
541C22×C4—1882no—
542C22×C4—1882no—
543C22×C4—1882no—
544C22×C4—1882no—
545C22×C4—1882no—
546C22×C4D4×D4711yescharacteristic
547C22×C4D4×D4711yescharacteristic
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—21no—
569C4⋊C4—42no—
570C4⋊C4—81no—
571C4⋊C4—474no—
572C4⋊C4—472no—
573C4⋊C4—472no—
574C4⋊C4—472no—
575C4⋊C4—944no—
576C4⋊C4—944no—
577C4⋊C4—944no—
578C4⋊C4—944no—
579C4⋊C4—944no—
580C4⋊C4—941no—
581C4⋊C4—941no—
582C4⋊C4—941no—
583C4⋊C4—941no—
584C4⋊C4—941no—
585C4⋊C4—1882no—
586C4⋊C4—1882no—
587C4⋊C4C2×C4×D4712yes—
588C22⋊C4—474no—
589C22⋊C4—474no—
590C22⋊C4—944no—
591C22⋊C4—944no—
592C22⋊C4—944no—
593C22⋊C4—1882no—
594C22⋊C4—1882no—
595C42—24no—
596C42—944no—
597C42—1882no—
598C42C2×C4×D4712yes—
599C42D4×D4712yes—
600C23—472no—
601C23—472no—
602C23—472no—
603C23—472no—
604C23—941no—
605C23—941no—
606C23—941no—
607C23—941no—
608C23—941no—
609C23—941no—
610C23—941no—
611C23—941no—
612C23—941no—
613C23—941no—
614C23C2×D4×D4711yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619D4—948no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—472no—
637C2×C4—472no—
638C2×C4—941no—
639C2×C4—941no—
640C2×C4—941no—
641C2×C4—941no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—3764no—
654C2×C4—3764no—
655C2×C4—1888no—
656C2×C4—1881no—
657C2×C4—1881no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4—1881no—
661C2×C4—1881no—
662C2×C4—1881no—
663C2×C4—1881no—
664C2×C4—1881no—
665C2×C4C22⋊C4×D4712yes—
666C2×C4C22⋊C4×D4712yes—
667C2×C4C22×C4×D4711yescharacteristic
668C2×C4C2×D4×D4711yescharacteristic
669C2×C4#41×D4711yescharacteristic
670C2×C4#41×D4711yescharacteristic
671C2×C4#1309406911yescharacteristic
672C2×C4#1309407211yescharacteristic
673C8—41no—
674C8—41no—
675C8—942no—
676C8—1881no—
677C22—474no—
678C22—942no—
679C22—942no—
680C22—942no—
681C22—942no—
682C22—942no—
683C22—942no—
684C22—942no—
685C22—942no—
686C22—942no—
687C22—1881no—
688C22—1881no—
689C22—1881no—
690C22—1881no—
691C22C2×C22⋊C4×D4711yescharacteristic
692C22#1568977011yescharacteristic
693C22#1568977511yescharacteristic
694C22AGL(1,ℤ/8)×D4711yescharacteristic
695C22#137×D4711yescharacteristic
696C22#1568992911yescharacteristic
697C22#1568993611yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—81no—
704C4—942no—
705C4—942no—
706C4—3761no—
707C4—1882no—
708C4—1882no—
709C4—1882no—
710C4#1568959111yescharacteristic
711C4#1568960411yescharacteristic
712C4#1568977011yescharacteristic
713C4#1568977511yescharacteristic
714C2—944no—
715C2—1882no—
716C2#2024621611yescharacteristic
717C2#417×D4711yescharacteristic
718C2#2025191611yescharacteristic
719C2#2025541611yescharacteristic
720C2#2025544611yescharacteristic
721C2#2025582511yescharacteristic
722C2#2025584011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1803C2
socleC23×C47C22×D4
prime radicalC22×D188D4
cosocleC22×C4×C47C24
hypercenter#1803D47
hypocenterC47#22491
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
4. #20244356C2semidirect
5. #20244343C2semidirect
6. #20243818C2semidirect
7. #20243808C2semidirect
8. #20243692C2semidirect
9. #20243692C2semidirect
10. #20243482C2semidirect
11. #20243473C2semidirect
12. #20243218C2semidirect
13. #20243106C2semidirect
14. #340×D47C2semidirect
15. C47×#1803C2semidirect
19. #15689814C4semidirect
78. #13094016C2×C4semidirect
83. #13094000C2×C4semidirect
84. #13094000C2×C4semidirect
89. #13093982C2×C4semidirect
108. C4⋊C4×D47C2×C4semidirect
130. C4×Q8×C47C2×C4semidirect
364. #1803D47semidirect
423. C47#22491semidirect
451. C4×Q8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156898142
C2×#156891932
#202462882
#202443562
#202443432
#202438182
#202438082
#202436922
#202434822
#202434732
#202432182
#202431062
#340×D472
C47×#18032
#2249147