Finite Group Databasebeta

← #26237064

Subgroups — #26237064

Order 12032.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689240C211yesmaximal, characteristic, complemented
2#20252115C211yesmaximal, characteristic, complemented
3C2×#15689140C211yesmaximal, characteristic, complemented
4#20251837C211yesmaximal, characteristic, complemented
5#20244282C211yesmaximal, characteristic, complemented
6#20244094C211yesmaximal, characteristic, complemented
7#20244038C211yesmaximal, characteristic, complemented
8#20243837C211yesmaximal, characteristic, complemented
9#20243717C211yesmaximal, characteristic, complemented
10#20243717C211yesmaximal, characteristic, complemented
11#20243665C211yesmaximal, characteristic, complemented
12#20243595C211yesmaximal, characteristic, complemented
13#20243235C211yesmaximal, characteristic, complemented
14#20243156C211yesmaximal, characteristic, complemented
15C47×#3002C211yesmaximal, characteristic
16C2×#13094031C2211yescharacteristic
17C2×#13094031C2211yescharacteristic
18C2×#13094031C2211yescharacteristic, complemented
19C22×#10625329C2211yescharacteristic
20C2×#13093983C2211yescharacteristic
21#15689240—24no—
22#15689201—21no—
23#15689195—21no—
24#15689195—21no—
25D4×C47⋊C8—21no—
26C2×#13093960C2211yescharacteristic, complemented
27C2×#13093960C2211yescharacteristic, complemented
28#15689150C2211yescharacteristic, complemented
29#15689140—24no—
30C2×#13093951C2211yescharacteristic
31C2×#13093951C2211yescharacteristic
32C2×#13093951C2211yescharacteristic
33C2×#13093951C2211yescharacteristic
34C2×#13093951C2211yescharacteristic, complemented
35C2×#13093951C2211yescharacteristic, complemented
36#15689090—21no—
37#15689090—21no—
38#15689090C2211yescharacteristic
39#15689090C2211yescharacteristic
40#15689090C2211yescharacteristic, complemented
41#15689087—21no—
42#15689087C2211yescharacteristic
43C2×C22⋊(C47⋊C8)—21no—
44C2×C22⋊(C47⋊C8)C2211yescharacteristic
45#15689079C2211yescharacteristic, complemented
46C2×#13093934C2211yescharacteristic, complemented
47C2×C8×Dic47C2211yescharacteristic, complemented
48#15688888C2211yescharacteristic, complemented
49#15688888C2211yescharacteristic, complemented
50#15688882C2211yescharacteristic, complemented
51#15688882C2211yescharacteristic, complemented
52#15688877C2211yescharacteristic, complemented
53#15688877C2211yescharacteristic, complemented
54C22×#41×C47C2211yescharacteristic
55C2×#135×C47C2211yescharacteristic
56C2×#135×C47C2211yescharacteristic
57C47×#525C2211yescharacteristic
58C47×#452C411yescharacteristic, complemented
59C47×#452C411yescharacteristic, complemented
60C47×#451C411yescharacteristic, complemented
61C47×#450C411yescharacteristic, complemented
62C47×#449C411yescharacteristic, complemented
63C47×#449C411yescharacteristic, complemented
64C47×#448C411yescharacteristic, complemented
65C47×#447C411yescharacteristic, complemented
66C47×#416C2211yescharacteristic
67C47×#416C2211yescharacteristic
68C2×C22⋊C8×C47C2211yescharacteristic
69#13094031—22no—
70#13094031—22no—
71#13094031—22no—
72#13094031—41no—
73#13094031—41no—
74#13094031—41no—
75C2×#10625329—21no—
76C2×#10625329—21no—
77C2×#10625329—21no—
78C2×#10625329—21no—
79C2×#10625329—22no—
80C2×#10625329—41no—
81C2×#10625329C2311yescharacteristic
82C2×#10625329C2311yescharacteristic
83C2×#10625329C2311yescharacteristic
84C2×#10625329C2311yescharacteristic
85C22×C47⋊C8—21no—
86C22×C47⋊C8—21no—
87C22×C47⋊C8—21no—
88C22×C47⋊C8—21no—
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2311yescharacteristic
91#13093983—22no—
92#13093983—41no—
93C2×C4⋊Dic47—21no—
94C2×C22⋊Dic47—21no—
95C2×C4×Dic47C2311yescharacteristic
96C2×C4×Dic47C2311yescharacteristic
97#13093960—22no—
98#13093960—41no—
99C4⋊(C47⋊C8)—21no—
100C4⋊(C47⋊C8)—21no—
101#13093951—22no—
102#13093951—22no—
103#13093951—22no—
104#13093951—22no—
105#13093951—41no—
106#13093951D414yescomplemented
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)—21no—
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)—21no—
111C22⋊(C47⋊C8)—21no—
112C22⋊(C47⋊C8)—21no—
113C22⋊(C47⋊C8)—21no—
114C22⋊(C47⋊C8)—21no—
115C22⋊(C47⋊C8)D411yescharacteristic
116C22⋊(C47⋊C8)D411yescharacteristic
117C22⋊(C47⋊C8)D411yescharacteristic
118C22⋊(C47⋊C8)D411yescharacteristic
119#13093935—21no—
120#13093934—41no—
121C4×C47⋊C8—21no—
122C8×Dic47—22no—
123C2×#41×C47—21no—
124C2×#41×C47—21no—
125C2×#41×C47—22no—
126C2×#41×C47—22no—
127C2×#41×C47—41no—
128C2×#41×C47—41no—
129C2×#41×C47C2×C411yescharacteristic
130C2×#41×C47C2×C411yescharacteristic
131C2×#41×C47C2311yescharacteristic
132C2×#41×C47C2311yescharacteristic
133C2×#41×C47C2311yescharacteristic
134C22×Q8×C47C2×C411yescharacteristic
135C22×D4×C47—21no—
136C22×D4×C47C2×C411yescharacteristic
137C23×C4×C47—21no—
138C23×C4×C47C2311yescharacteristic
139#135×C47—22no—
140#135×C47—22no—
141#135×C47—41no—
142#135×C47—41no—
143C2×Q16×C47C2×C411yescharacteristic
144C2×Q16×C47C2×C411yescharacteristic
145C2×SD16×C47C2×C411yescharacteristic
146C2×SD16×C47C2×C411yescharacteristic
147C2×SD16×C47C2×C411yescharacteristic
148C2×SD16×C47C2×C411yescharacteristic
149C2×D8×C47C2×C411yescharacteristic
150C2×D8×C47C2×C411yescharacteristic
151C22×C8×C47C2311yescharacteristic
152C22×C8×C47C2311yescharacteristic
153#123×C47—21no—
154C22⋊Q8×C47C2×C411yescharacteristic
155C22⋊Q8×C47C2×C411yescharacteristic
156#121×C47C2×C411yescharacteristic
157#121×C47C2×C411yescharacteristic
158#120×C47—21no—
159C4×D4×C47—21no—
160C4×D4×C47—21no—
161#117×C47C2311yescharacteristic
162#103×C47C2×C411yescharacteristic
163#103×C47C2×C411yescharacteristic
164#103×C47C2×C411yescharacteristic
165#103×C47C2×C411yescharacteristic
166#102×C47C2×C411yescharacteristic
167#102×C47C2×C411yescharacteristic
168#102×C47C2×C411yescharacteristic
169#102×C47C2×C411yescharacteristic
170C22⋊C8×C47C2×C411yescharacteristic
171C22⋊C8×C47C2×C411yescharacteristic
172C22⋊C8×C47C2×C411yescharacteristic
173C22⋊C8×C47C2×C411yescharacteristic
174C24×C47—21no—
175C24×C47#4111yescharacteristic
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—22no—
179#41×C47—22no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—21no—
183#41×C47—21no—
184#41×C47—21no—
185#41×C47—21no—
186#41×C47—21no—
187#41×C47—21no—
188#41×C47—42no—
189#41×C47—42no—
190#41×C47—41no—
191#41×C47—41no—
192#41×C47—42no—
193#41×C47—42no—
194#41×C47C2×D412yes—
195#41×C47#4112yes—
196C2×Q8×C47—21no—
197C2×Q8×C47—22no—
198C2×Q8×C47—41no—
199C2×Q8×C47C22×C411yescharacteristic
200C2×Q8×C47C22×C411yescharacteristic
201C2×Q8×C47C22×C411yescharacteristic
202C2×D4×C47—21no—
203C2×D4×C47—22no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—21no—
207C2×D4×C47—21no—
208C2×D4×C47—21no—
209C2×D4×C47—21no—
210C2×D4×C47—21no—
211C2×D4×C47—41no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47C22×C411yescharacteristic
215C2×D4×C47C22×C411yescharacteristic
216C2×D4×C47C22×C411yescharacteristic
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—42no—
228C22×C4×C47—42no—
229C22×C4×C47C22×C411yescharacteristic
230C22×C4×C47C22×C411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47#4111yescharacteristic
234C22×C4×C47C2411yescharacteristic
235C22×Dic47—21no—
236C22×Dic47—21no—
237Q16×C47—22no—
238Q16×C47—41no—
239SD16×C47—22no—
240SD16×C47—22no—
241SD16×C47—41no—
242SD16×C47—41no—
243D8×C47—22no—
244D8×C47—41no—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47C22×C411yescharacteristic
250C2×C8×C47C22×C411yescharacteristic
251C2×C8×C47C22×C411yescharacteristic
252C2×C8×C47C22×C411yescharacteristic
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47C22×C411yescharacteristic
256C4⋊C4×C47C22×C411yescharacteristic
257C22⋊C4×C47—21no—
258C22⋊C4×C47—21no—
259C22⋊C4×C47—21no—
260C22⋊C4×C47—21no—
261C22⋊C4×C47—21no—
262C42×C47—21no—
263C22⋊Dic47—42no—
264C4⋊Dic47—42no—
265C4×Dic47—21no—
266C4×Dic47—21no—
267C4×Dic47—21no—
268C4×Dic47C2×D412yes—
269#10625329—21no—
270#10625329—21no—
271#10625329—21no—
272#10625329—21no—
273#10625329—21no—
274#10625329—21no—
275#10625329—21no—
276#10625329—42no—
277#10625329—42no—
278#10625329—42no—
279#10625329—42no—
280#10625329C2×D412yes—
281C2×C47⋊C8—21no—
282C2×C47⋊C8—21no—
283C2×C47⋊C8—21no—
284C2×C47⋊C8—21no—
285C2×C47⋊C8—21no—
286C2×C47⋊C8—21no—
287C2×C47⋊C8—21no—
288C2×C47⋊C8—21no—
289C2×C47⋊C8—42no—
290C2×C47⋊C8—42no—
291C2×C47⋊C8—42no—
292C2×C47⋊C8—42no—
293C2×C47⋊C8C2×D411yescharacteristic
294C2×C47⋊C8C2×D411yescharacteristic
295C2×C47⋊C8C2×D411yescharacteristic
296C2×C47⋊C8C2×D411yescharacteristic
297C23×C47—21no—
298C23×C47—21no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—42no—
305C23×C47—42no—
306C23×C47—81no—
307C23×C47C4×D411yescharacteristic
308C23×C47C4×D411yescharacteristic
309C23×C47C2×#4111yescharacteristic
310Q8×C47—21no—
311Q8×C47—21no—
312Q8×C47—21no—
313Q8×C47—21no—
314Q8×C47—21no—
315Q8×C47—42no—
316Q8×C47C4×D412yes—
317D4×C47—22no—
318D4×C47—22no—
319D4×C47—21no—
320D4×C47—21no—
321D4×C47—21no—
322D4×C47—21no—
323D4×C47—21no—
324D4×C47—42no—
325D4×C47—42no—
326D4×C47—42no—
327D4×C47—42no—
328D4×C47—41no—
329D4×C47—41no—
330D4×C47—41no—
331D4×C47—41no—
332D4×C47—81no—
333D4×C47C4×D412yes—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—22no—
343C2×C4×C47—21no—
344C2×C4×C47—22no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—21no—
350C2×C4×C47—21no—
351C2×C4×C47—42no—
352C2×C4×C47—42no—
353C2×C4×C47—42no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47C4×D411yescharacteristic
359C2×C4×C47C4×D411yescharacteristic
360C2×C4×C47C23×C411yescharacteristic
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C2×#4111yescharacteristic
364C2×C4×C47H(5,𝔽2)11yescharacteristic
365C2×C4×C47H(5,𝔽2)11yescharacteristic
366C2×Dic47—22no—
367C2×Dic47—41no—
368C2×Dic47—41no—
369C2×Dic47—41no—
370C2×Dic47—41no—
371C2×Dic47—41no—
372C8×C47—21no—
373C8×C47—21no—
374C8×C47—21no—
375C8×C47—21no—
376C47⋊C8—21no—
377C47⋊C8—21no—
378C47⋊C8—22no—
379C47⋊C8—21no—
380C47⋊C8—21no—
381C47⋊C8—41no—
382C47⋊C8—41no—
383C47⋊C8—41no—
384#22889—471nomaximal, Sylow
385C22×C47—21no—
386C22×C47—21no—
387C22×C47—21no—
388C22×C47—21no—
389C22×C47—22no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—21no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—41no—
398C22×C47—41no—
399C22×C47—41no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47—84no—
405C22×C47C2×C4×D411yescharacteristic
406C22×C47#54611yescharacteristic
407C22×C47#55111yescharacteristic
408C4×C47—21no—
409C4×C47—21no—
410C4×C47—22no—
411C4×C47—41no—
412C4×C47—41no—
413C4×C47—41no—
414C4×C47—41no—
415C4×C47C2×C4×D411yescharacteristic
416C4×C47#51811yescharacteristic
417C4×C47D4211yescharacteristic
418C4×C47#54611yescharacteristic
419Dic47—42no—
420Dic47—81no—
421#3002D4711yescharacteristic
422C2×#443—471no—
423#2933—471no—
424C2×#421—471no—
425#2880—471no—
426#1975—471no—
427#1937—471no—
428#1929—471no—
429#1897—471no—
430#1876—471no—
431#1876—471no—
432#1866—471no—
433#1855—471no—
434#1765—471no—
435#1750—471no—
436C2×C47—21no—
437C2×C47—21no—
438C2×C47—41no—
439C2×C47—41no—
440C2×C47—42no—
441C2×C47—81no—
442C2×C47—81no—
443C2×C47#235811yescharacteristic
444C2×C47#295511yescharacteristic
445C2×C47#295711yescharacteristic
446C22×#41C2×D4711yescharacteristic
447C2×#135C2×D4711yescharacteristic
448C2×#135C2×D4711yescharacteristic
449C2×#131—471no—
450C2×#131—471no—
451C2×#131—471no—
452C22×M16—471no—
453#525C2×D4711yescharacteristic
454C2×#117—471no—
455#452Dic4711yescharacteristic, complemented
456#452Dic4711yescharacteristic, complemented
457#451Dic4711yescharacteristic, complemented
458#450Dic4711yescharacteristic, complemented
459#449Dic4711yescharacteristic, complemented
460#449Dic4711yescharacteristic, complemented
461#448Dic4711yescharacteristic, complemented
462#447Dic4711yescharacteristic, complemented
463#443—944no—
464#436—941no—
465#435—941no—
466#435—941no—
467C8×D4—941no—
468C2×#108—471no—
469C2×#108—471no—
470#424—471no—
471#421—944no—
472C2×#104—471no—
473C2×#104—471no—
474C2×#104—471no—
475C2×#104—471no—
476C2×#104—471no—
477C2×#104—471no—
478#416C2×D4711yescharacteristic
479#416C2×D4711yescharacteristic
480#408—471no—
481#408—471no—
482#408—471no—
483#408—941no—
484#408—941no—
485#407—471no—
486#407—941no—
487C2×C22⋊C8—471no—
488C2×C22⋊C8—941no—
489C2×C22⋊C8C2×D4711yescharacteristic
490#405—471no—
491C2×#97—471no—
492C2×C4×C8—471no—
493#341—471no—
494#341—471no—
495#339—471no—
496#339—471no—
497#336—471no—
498#336—471no—
499C47#2288911yescharacteristic, complemented, Sylow
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41C2×Dic4711yescharacteristic
507C2×#41C2×Dic4711yescharacteristic
508C2×#41C22×D4711yescharacteristic
509C2×#41C22×D4711yescharacteristic
510C2×#41C22×D4711yescharacteristic
511C22×Q8C2×Dic4711yescharacteristic
512C22×D4—21no—
513C22×D4C2×Dic4711yescharacteristic
514C23×C4—21no—
515C23×C4C22×D4711yescharacteristic
516#135—22no—
517#135—22no—
518#135—41no—
519#135—41no—
520C2×Q16C2×Dic4711yescharacteristic
521C2×Q16C2×Dic4711yescharacteristic
522C2×SD16C2×Dic4711yescharacteristic
523C2×SD16C2×Dic4711yescharacteristic
524C2×SD16C2×Dic4711yescharacteristic
525C2×SD16C2×Dic4711yescharacteristic
526C2×D8C2×Dic4711yescharacteristic
527C2×D8C2×Dic4711yescharacteristic
528#131—942no—
529#131—942no—
530#131—942no—
531#131—1881no—
532#131—1881no—
533#131—1881no—
534C2×M16—471no—
535C2×M16—471no—
536C2×M16—471no—
537C2×M16—471no—
538C2×M16—941no—
539C2×M16—941no—
540C2×M16—941no—
541C2×M16—941no—
542C2×M16—942no—
543C2×M16—1881no—
544C22×C8—471no—
545C22×C8—471no—
546C22×C8—941no—
547C22×C8—941no—
548C22×C8—941no—
549C22×C8—941no—
550C22×C8C22×D4711yescharacteristic
551C22×C8C22×D4711yescharacteristic
552#123—21no—
553C22⋊Q8C2×Dic4711yescharacteristic
554C22⋊Q8C2×Dic4711yescharacteristic
555#121C2×Dic4711yescharacteristic
556#121C2×Dic4711yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—942no—
561#117—1881no—
562#117C22×D4711yescharacteristic
563C2×C4⋊C4—941no—
564C2×C22⋊C4—941no—
565C2×C42—471no—
566C2×C42—471no—
567#108—942no—
568#108—1881no—
569C4⋊C8—941no—
570C4⋊C8—941no—
571#104—474no—
572#104—942no—
573#104—942no—
574#104—942no—
575#104—942no—
576#104—1881no—
577#103C2×Dic4711yescharacteristic
578#103C2×Dic4711yescharacteristic
579#103C2×Dic4711yescharacteristic
580#103C2×Dic4711yescharacteristic
581#102C2×Dic4711yescharacteristic
582#102C2×Dic4711yescharacteristic
583#102C2×Dic4711yescharacteristic
584#102C2×Dic4711yescharacteristic
585C22⋊C8—471no—
586C22⋊C8—471no—
587C22⋊C8—471no—
588C22⋊C8—471no—
589C22⋊C8—941no—
590C22⋊C8—941no—
591C22⋊C8—941no—
592C22⋊C8—941no—
593C22⋊C8—941no—
594C22⋊C8—941no—
595C22⋊C8—941no—
596C22⋊C8—941no—
597C22⋊C8C2×Dic4711yescharacteristic
598C22⋊C8C2×Dic4711yescharacteristic
599C22⋊C8C2×Dic4711yescharacteristic
600C22⋊C8C2×Dic4711yescharacteristic
601#97—941no—
602#97—1881no—
603C4×C8—941no—
604C4×C8—942no—
605C24—21no—
606C24#1062535211yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—42no—
620#41—42no—
621#41—41no—
622#41—41no—
623#41—42no—
624#41—42no—
625#41D4×D4712yes—
626#41#1062535212yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8C22×Dic4711yescharacteristic
631C2×Q8C22×Dic4711yescharacteristic
632C2×Q8C22×Dic4711yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4C22×Dic4711yescharacteristic
646C2×D4C22×Dic4711yescharacteristic
647C2×D4C22×Dic4711yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—941no—
661C22×C4—941no—
662C22×C4D4×D4711yescharacteristic
663C22×C4D4×D4711yescharacteristic
664C22×C4#1062535211yescharacteristic
665C22×C4C22×Dic4711yescharacteristic
666C22×C4C22×Dic4711yescharacteristic
667C22×C4C23×D4711yescharacteristic
668Q16—22no—
669Q16—41no—
670SD16—22no—
671SD16—22no—
672SD16—41no—
673SD16—41no—
674D8—22no—
675D8—41no—
676M16—472no—
677M16—941no—
678M16—941no—
679M16—941no—
680M16—941no—
681M16—941no—
682M16—941no—
683M16—941no—
684M16—1882no—
685M16—1882no—
686M16—1882no—
687M16—1882no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—471no—
693C2×C8—471no—
694C2×C8—471no—
695C2×C8—471no—
696C2×C8—941no—
697C2×C8—941no—
698C2×C8—941no—
699C2×C8—941no—
700C2×C8—941no—
701C2×C8—941no—
702C2×C8—941no—
703C2×C8—941no—
704C2×C8—1882no—
705C2×C8—1882no—
706C2×C8—1882no—
707C2×C8—1882no—
708C2×C8C22×Dic4711yescharacteristic
709C2×C8C22×Dic4711yescharacteristic
710C2×C8C22×Dic4711yescharacteristic
711C2×C8C22×Dic4711yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—1882no—
715C4⋊C4C22×Dic4711yescharacteristic
716C4⋊C4C22×Dic4711yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—1882no—
723C42—21no—
724C42—472no—
725C42—941no—
726C42—941no—
727C42—941no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—81no—
738C23D4×Dic4711yescharacteristic
739C23D4×Dic4711yescharacteristic
740C23C2×#1062535211yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—42no—
747Q8D4×Dic4712yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—81no—
764D4D4×Dic4712yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—942no—
790C2×C4—1881no—
791C2×C4—1881no—
792C2×C4—1881no—
793C2×C4—1881no—
794C2×C4—1881no—
795C2×C4D4×Dic4711yescharacteristic
796C2×C4D4×Dic4711yescharacteristic
797C2×C4C23×Dic4711yescharacteristic
798C2×C4C2×D4×D4711yescharacteristic
799C2×C4C2×D4×D4711yescharacteristic
800C2×C4C2×#1062535211yescharacteristic
801C2×C4#1309406911yescharacteristic
802C2×C4#1309406911yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—941no—
808C8—941no—
809C8—942no—
810C8—941no—
811C8—941no—
812C8—1881no—
813C8—1881no—
814C8—1881no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—84no—
835C22C2×D4×Dic4711yescharacteristic
836C22#1568976011yescharacteristic
837C22#1568980411yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—3761no—
846C4—1882no—
847C4C2×D4×Dic4711yescharacteristic
848C4#1568959811yescharacteristic
849C4#1568975511yescharacteristic
850C4#1568976011yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—81no—
858C2#2024637211yescharacteristic
859C2#2025229111yescharacteristic
860C2#2025230511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC47×#3002C2
socleC22×C47C2×C4×D4
cosocleC22×C4×C47C24
hypercenter#3002D47
hypocenterC47#22889
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C2×#15689240C2semidirect
2. #20252115C2semidirect
3. C2×#15689140C2semidirect
4. #20251837C2semidirect
5. #20244282C2semidirect
6. #20244094C2semidirect
7. #20244038C2semidirect
8. #20243837C2semidirect
9. #20243717C2semidirect
10. #20243717C2semidirect
11. #20243665C2semidirect
12. #20243595C2semidirect
13. #20243235C2semidirect
14. #20243156C2semidirect
18. C2×#13094031C22semidirect
26. C2×#13093960C22semidirect
27. C2×#13093960C22semidirect
28. #15689150C22semidirect
34. C2×#13093951C22semidirect
35. C2×#13093951C22semidirect
40. #15689090C22semidirect
45. #15689079C22semidirect
46. C2×#13093934C22semidirect
47. C2×C8×Dic47C22semidirect
48. #15688888C22semidirect
49. #15688888C22semidirect
50. #15688882C22semidirect
51. #15688882C22semidirect
52. #15688877C22semidirect
53. #15688877C22semidirect
58. C47×#452C4semidirect
59. C47×#452C4semidirect
60. C47×#451C4semidirect
61. C47×#450C4semidirect
62. C47×#449C4semidirect
63. C47×#449C4semidirect
64. C47×#448C4semidirect
65. C47×#447C4semidirect
106. #13093951D4semidirect
455. #452Dic47semidirect
456. #452Dic47semidirect
457. #451Dic47semidirect
458. #450Dic47semidirect
459. #449Dic47semidirect
460. #449Dic47semidirect
461. #448Dic47semidirect
462. #447Dic47semidirect
499. C47#22889semidirect

Maximal subgroups

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

subgroupindex
C2×#156892402
#202521152
C2×#156891402
#202518372
#202442822
#202440942
#202440382
#202438372
#202437172
#202436652
#202435952
#202432352
#202431562
C47×#30022
#2288947