Finite Group Databasebeta

← #26237019

Subgroups — #26237019

Order 12032.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689245C211yesmaximal, characteristic, complemented
2#20252115C211yesmaximal, characteristic, complemented
3C22×#13093951C211yesmaximal, characteristic, complemented
4#20251837C211yesmaximal, characteristic, complemented
5#20244282C211yesmaximal, characteristic, complemented
6#20244101C211yesmaximal, characteristic, complemented
7#20244038C211yesmaximal, characteristic, complemented
8#20243832C211yesmaximal, characteristic, complemented
9#20243717C211yesmaximal, characteristic, complemented
10#20243717C211yesmaximal, characteristic, complemented
11#20243665C211yesmaximal, characteristic, complemented
12#20243595C211yesmaximal, characteristic, complemented
13#20243235C211yesmaximal, characteristic, complemented
14#20243152C211yesmaximal, characteristic, complemented
15C47×#3002C211yesmaximal, characteristic
16C2×#13094031C2211yescharacteristic
17C2×#13094031C2211yescharacteristic
18C2×#13094031C2211yescharacteristic, complemented
19C22×#10625329C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21#15689245—24no—
22#15689201—21no—
23#15689195—21no—
24#15689195—21no—
25D4×C47⋊C8—21no—
26C2×#13093960C2211yescharacteristic, complemented
27C2×#13093960C2211yescharacteristic, complemented
28#15689150C2211yescharacteristic, complemented
29C2×#13093951—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×#13093934C2211yescharacteristic, 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
69C23×Dic47—21no—
70#13094031—22no—
71#13094031—22no—
72#13094031—22no—
73#13094031—41no—
74#13094031—41no—
75#13094031—41no—
76C2×#10625329—21no—
77C2×#10625329—21no—
78C2×#10625329—21no—
79C2×#10625329—21no—
80C2×#10625329—22no—
81C2×#10625329—41no—
82C2×#10625329C2311yescharacteristic
83C2×#10625329C2311yescharacteristic
84C2×#10625329C2311yescharacteristic
85C2×#10625329C2311yescharacteristic
86C22×C47⋊C8—21no—
87C22×C47⋊C8—21no—
88C22×C47⋊C8—21no—
89C22×C47⋊C8—21no—
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92C2×C4×Dic47—22no—
93C2×C4×Dic47—21no—
94C2×C4×Dic47—41no—
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—22no—
121#13093934—41no—
122C4×C47⋊C8—21no—
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, complemented
144C2×Q16×C47C2×C411yescharacteristic, complemented
145C2×SD16×C47C2×C411yescharacteristic, complemented
146C2×SD16×C47C2×C411yescharacteristic, complemented
147C2×SD16×C47C2×C411yescharacteristic, complemented
148C2×SD16×C47C2×C411yescharacteristic, complemented
149C2×D8×C47C2×C411yescharacteristic, complemented
150C2×D8×C47C2×C411yescharacteristic, complemented
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, complemented
163#103×C47C2×C411yescharacteristic, complemented
164#103×C47C2×C411yescharacteristic, complemented
165#103×C47C2×C411yescharacteristic, complemented
166#102×C47C2×C411yescharacteristic, complemented
167#102×C47C2×C411yescharacteristic, complemented
168#102×C47C2×C411yescharacteristic, complemented
169#102×C47C2×C411yescharacteristic, complemented
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—
237C22×Dic47—42no—
238C22×Dic47—42no—
239C22×Dic47—42no—
240Q16×C47—22no—
241Q16×C47—41no—
242SD16×C47—22no—
243SD16×C47—22no—
244SD16×C47—41no—
245SD16×C47—41no—
246D8×C47—22no—
247D8×C47—41no—
248C2×C8×C47—21no—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47C22×C411yescharacteristic
253C2×C8×C47C22×C411yescharacteristic
254C2×C8×C47C22×C411yescharacteristic
255C2×C8×C47C22×C411yescharacteristic
256C4⋊C4×C47—21no—
257C4⋊C4×C47—21no—
258C4⋊C4×C47C22×C411yescharacteristic
259C4⋊C4×C47C22×C411yescharacteristic
260C22⋊C4×C47—21no—
261C22⋊C4×C47—21no—
262C22⋊C4×C47—21no—
263C22⋊C4×C47—21no—
264C22⋊C4×C47—21no—
265C42×C47—21no—
266C4×Dic47—21no—
267C4×Dic47—21no—
268C4×Dic47—21no—
269C4×Dic47—42no—
270C4×Dic47C2×D412yes—
271#10625329—21no—
272#10625329—21no—
273#10625329—21no—
274#10625329—21no—
275#10625329—21no—
276#10625329—21no—
277#10625329—21no—
278#10625329—42no—
279#10625329—42no—
280#10625329—42no—
281#10625329—42no—
282#10625329C2×D412yes—
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—21no—
290C2×C47⋊C8—21no—
291C2×C47⋊C8—42no—
292C2×C47⋊C8—42no—
293C2×C47⋊C8—42no—
294C2×C47⋊C8—42no—
295C2×C47⋊C8C2×D411yescharacteristic
296C2×C47⋊C8C2×D411yescharacteristic
297C2×C47⋊C8C2×D411yescharacteristic
298C2×C47⋊C8C2×D411yescharacteristic
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—22no—
303C23×C47—21no—
304C23×C47—21no—
305C23×C47—41no—
306C23×C47—42no—
307C23×C47—42no—
308C23×C47—81no—
309C23×C47C4×D411yescharacteristic
310C23×C47C4×D411yescharacteristic
311C23×C47C2×#4111yescharacteristic
312Q8×C47—21no—
313Q8×C47—21no—
314Q8×C47—21no—
315Q8×C47—21no—
316Q8×C47—21no—
317Q8×C47—42no—
318Q8×C47C4×D412yes—
319D4×C47—22no—
320D4×C47—22no—
321D4×C47—21no—
322D4×C47—21no—
323D4×C47—21no—
324D4×C47—21no—
325D4×C47—21no—
326D4×C47—42no—
327D4×C47—42no—
328D4×C47—42no—
329D4×C47—41no—
330D4×C47—41no—
331D4×C47—41no—
332D4×C47—41no—
333D4×C47—42no—
334D4×C47—81no—
335D4×C47C4×D412yes—
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—21no—
343C2×C4×C47—21no—
344C2×C4×C47—22no—
345C2×C4×C47—21no—
346C2×C4×C47—22no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—21no—
350C2×C4×C47—21no—
351C2×C4×C47—21no—
352C2×C4×C47—21no—
353C2×C4×C47—42no—
354C2×C4×C47—42no—
355C2×C4×C47—42no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47C4×D411yescharacteristic
361C2×C4×C47C4×D411yescharacteristic
362C2×C4×C47C23×C411yescharacteristic
363C2×C4×C47C22×D411yescharacteristic
364C2×C4×C47C22×D411yescharacteristic
365C2×C4×C47C2×#4111yescharacteristic
366C2×C4×C47H(5,𝔽2)11yescharacteristic
367C2×C4×C47H(5,𝔽2)11yescharacteristic
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—41no—
371C2×Dic47—41no—
372C2×Dic47—41no—
373C2×Dic47—48no—
374C2×Dic47—41no—
375C8×C47—21no—
376C8×C47—21no—
377C8×C47—21no—
378C8×C47—21no—
379C47⋊C8—21no—
380C47⋊C8—21no—
381C47⋊C8—22no—
382C47⋊C8—21no—
383C47⋊C8—21no—
384C47⋊C8—41no—
385C47⋊C8—41no—
386C47⋊C8—41no—
387#22886—471nomaximal, Sylow
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—22no—
394C22×C47—21no—
395C22×C47—21no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—41no—
399C22×C47—41no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—41no—
403C22×C47—41no—
404C22×C47—41no—
405C22×C47—41no—
406C22×C47—84no—
407C22×C47#44412yescomplemented
408C22×C47C2×C4×D411yescharacteristic
409C22×C47#54611yescharacteristic
410C22×C47#55111yescharacteristic
411C4×C47—21no—
412C4×C47—21no—
413C4×C47—22no—
414C4×C47—41no—
415C4×C47—41no—
416C4×C47—41no—
417C4×C47—41no—
418C4×C47C2×C4×D411yescharacteristic
419C4×C47#51811yescharacteristic
420C4×C47D4211yescharacteristic
421C4×C47#54611yescharacteristic
422Dic47—42no—
423Dic47—42no—
424#3002D4711yescharacteristic
425C2×#444—471no—
426#2933—471no—
427C22×#104—471no—
428#2880—471no—
429#1975—471no—
430#1938—471no—
431#1929—471no—
432#1896—471no—
433#1876—471no—
434#1876—471no—
435#1866—471no—
436#1855—471no—
437#1765—471no—
438#1749—471no—
439C2×C47—21no—
440C2×C47—22no—
441C2×C47—21no—
442C2×C47—41no—
443C2×C47—42no—
444C2×C47—81no—
445C2×C47—81no—
446C2×C47#235811yescharacteristic
447C2×C47C2×#44411yescharacteristic
448C2×C47#295611yescharacteristic
449C22×#41C2×D4711yescharacteristic
450C2×#135C2×D4711yescharacteristic
451C2×#135C2×D4711yescharacteristic
452C2×#131—471no—
453C2×#131—471no—
454C2×#131—471no—
455C22×M16—471no—
456#525C2×D4711yescharacteristic
457C22×C42—471no—
458#452Dic4711yescharacteristic, complemented
459#452Dic4711yescharacteristic, complemented
460#451Dic4711yescharacteristic, complemented
461#450Dic4711yescharacteristic, complemented
462#449Dic4711yescharacteristic, complemented
463#449Dic4711yescharacteristic, complemented
464#448Dic4711yescharacteristic, complemented
465#447Dic4711yescharacteristic, complemented
466#444—944no—
467#436—941no—
468#435—941no—
469#435—941no—
470C8×D4—941no—
471C2×#108—471no—
472C2×#108—471no—
473#424—471no—
474C2×#104—471no—
475C2×#104—471no—
476C2×#104—471no—
477C2×#104—471no—
478C2×#104—471no—
479C2×#104—471no—
480C2×#104—944no—
481#416C2×D4711yescharacteristic
482#416C2×D4711yescharacteristic
483#408—471no—
484#408—471no—
485#408—471no—
486#408—941no—
487#408—941no—
488#407—471no—
489#407—941no—
490C2×C22⋊C8—471no—
491C2×C22⋊C8—941no—
492C2×C22⋊C8C2×D4711yescharacteristic
493#405—471no—
494C2×#97—471no—
495C2×#97—471no—
496#341—471no—
497#341—471no—
498#339—471no—
499#339—471no—
500#336—471no—
501#336—471no—
502C47#2288611yescharacteristic, complemented, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×Dic4711yescharacteristic
510C2×#41C2×Dic4711yescharacteristic
511C2×#41C22×D4711yescharacteristic
512C2×#41C22×D4711yescharacteristic
513C2×#41C22×D4711yescharacteristic
514C22×Q8C2×Dic4711yescharacteristic
515C22×D4—21no—
516C22×D4C2×Dic4711yescharacteristic
517C23×C4—21no—
518C23×C4—941no—
519C23×C4C22×D4711yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×Dic4711yescharacteristic, complemented
525C2×Q16C2×Dic4711yescharacteristic, complemented
526C2×SD16C2×Dic4711yescharacteristic, complemented
527C2×SD16C2×Dic4711yescharacteristic, complemented
528C2×SD16C2×Dic4711yescharacteristic, complemented
529C2×SD16C2×Dic4711yescharacteristic, complemented
530C2×D8C2×Dic4711yescharacteristic, complemented
531C2×D8C2×Dic4711yescharacteristic, complemented
532#131—942no—
533#131—942no—
534#131—942no—
535#131—1881no—
536#131—1881no—
537#131—1881no—
538C2×M16—471no—
539C2×M16—471no—
540C2×M16—471no—
541C2×M16—471no—
542C2×M16—941no—
543C2×M16—941no—
544C2×M16—941no—
545C2×M16—941no—
546C2×M16—942no—
547C2×M16—1881no—
548C22×C8—471no—
549C22×C8—471no—
550C22×C8—941no—
551C22×C8—941no—
552C22×C8—941no—
553C22×C8—941no—
554C22×C8C22×D4711yescharacteristic
555C22×C8C22×D4711yescharacteristic
556#123—21no—
557C22⋊Q8C2×Dic4711yescharacteristic
558C22⋊Q8C2×Dic4711yescharacteristic
559#121C2×Dic4711yescharacteristic
560#121C2×Dic4711yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D4711yescharacteristic
565C2×C42—471no—
566C2×C42—471no—
567C2×C42—942no—
568C2×C42—941no—
569C2×C42—1881no—
570#108—942no—
571#108—1881no—
572C4⋊C8—941no—
573C4⋊C8—941no—
574#104—474no—
575#104—942no—
576#104—942no—
577#104—942no—
578#104—942no—
579#104—1881no—
580#103C2×Dic4711yescharacteristic, complemented
581#103C2×Dic4711yescharacteristic, complemented
582#103C2×Dic4711yescharacteristic, complemented
583#103C2×Dic4711yescharacteristic, complemented
584#102C2×Dic4711yescharacteristic, complemented
585#102C2×Dic4711yescharacteristic, complemented
586#102C2×Dic4711yescharacteristic, complemented
587#102C2×Dic4711yescharacteristic, complemented
588C22⋊C8—471no—
589C22⋊C8—471no—
590C22⋊C8—471no—
591C22⋊C8—471no—
592C22⋊C8—941no—
593C22⋊C8—941no—
594C22⋊C8—941no—
595C22⋊C8—941no—
596C22⋊C8—941no—
597C22⋊C8—941no—
598C22⋊C8—941no—
599C22⋊C8—941no—
600C22⋊C8C2×Dic4711yescharacteristic
601C22⋊C8C2×Dic4711yescharacteristic
602C22⋊C8C2×Dic4711yescharacteristic
603C22⋊C8C2×Dic4711yescharacteristic
604#97—941no—
605#97—942no—
606#97—1881no—
607C4×C8—941no—
608C24—21no—
609C24#1062535211yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41D4×D4712yes—
629#41#1062535212yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×Dic4711yescharacteristic
634C2×Q8C22×Dic4711yescharacteristic
635C2×Q8C22×Dic4711yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×Dic4711yescharacteristic
649C2×D4C22×Dic4711yescharacteristic
650C2×D4C22×Dic4711yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—941no—
664C22×C4—941no—
665C22×C4—1882no—
666C22×C4—1882no—
667C22×C4—1882no—
668C22×C4D4×D4711yescharacteristic
669C22×C4D4×D4711yescharacteristic
670C22×C4#1062535211yescharacteristic
671C22×C4C22×Dic4711yescharacteristic
672C22×C4C22×Dic4711yescharacteristic
673C22×C4C23×D4711yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—472no—
683M16—941no—
684M16—941no—
685M16—941no—
686M16—941no—
687M16—941no—
688M16—941no—
689M16—941no—
690M16—1882no—
691M16—1882no—
692M16—1882no—
693M16—1882no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—471no—
699C2×C8—471no—
700C2×C8—471no—
701C2×C8—471no—
702C2×C8—941no—
703C2×C8—941no—
704C2×C8—941no—
705C2×C8—941no—
706C2×C8—941no—
707C2×C8—941no—
708C2×C8—941no—
709C2×C8—941no—
710C2×C8—1882no—
711C2×C8—1882no—
712C2×C8—1882no—
713C2×C8—1882no—
714C2×C8C22×Dic4711yescharacteristic
715C2×C8C22×Dic4711yescharacteristic
716C2×C8C22×Dic4711yescharacteristic
717C2×C8C22×Dic4711yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×Dic4711yescharacteristic
721C4⋊C4C22×Dic4711yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—472no—
729C42—941no—
730C42—941no—
731C42—941no—
732C42—1882no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23D4×Dic4711yescharacteristic
744C23D4×Dic4711yescharacteristic
745C23C2×#1062535211yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8D4×Dic4712yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—81no—
769D4D4×Dic4712yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—942no—
795C2×C4—942no—
796C2×C4—1881no—
797C2×C4—1881no—
798C2×C4—1881no—
799C2×C4—1888no—
800C2×C4—1881no—
801C2×C4D4×Dic4711yescharacteristic
802C2×C4D4×Dic4711yescharacteristic
803C2×C4C23×Dic4711yescharacteristic
804C2×C4C2×D4×D4711yescharacteristic
805C2×C4C2×D4×D4711yescharacteristic
806C2×C4C2×#1062535211yescharacteristic
807C2×C4#1309406911yescharacteristic
808C2×C4#1309406911yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—941no—
814C8—941no—
815C8—942no—
816C8—941no—
817C8—941no—
818C8—1881no—
819C8—1881no—
820C8—1881no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22#1568924512yescomplemented
841C22C2×D4×Dic4711yescharacteristic
842C22#1568976011yescharacteristic
843C22#1568980411yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—1882no—
852C4—1882no—
853C4C2×D4×Dic4711yescharacteristic
854C4#1568959811yescharacteristic
855C4#1568975511yescharacteristic
856C4#1568976011yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2#2024637211yescharacteristic
865C2C2×#1568924511yescharacteristic
866C2#2025229811yescharacteristic
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#22886
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×#15689245C2semidirect
2. #20252115C2semidirect
3. C22×#13093951C2semidirect
4. #20251837C2semidirect
5. #20244282C2semidirect
6. #20244101C2semidirect
7. #20244038C2semidirect
8. #20243832C2semidirect
9. #20243717C2semidirect
10. #20243717C2semidirect
11. #20243665C2semidirect
12. #20243595C2semidirect
13. #20243235C2semidirect
14. #20243152C2semidirect
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×#13093934C22semidirect
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
143. C2×Q16×C47C2×C4semidirect
144. C2×Q16×C47C2×C4semidirect
145. C2×SD16×C47C2×C4semidirect
146. C2×SD16×C47C2×C4semidirect
147. C2×SD16×C47C2×C4semidirect
148. C2×SD16×C47C2×C4semidirect
149. C2×D8×C47C2×C4semidirect
150. C2×D8×C47C2×C4semidirect
162. #103×C47C2×C4semidirect
163. #103×C47C2×C4semidirect
164. #103×C47C2×C4semidirect
165. #103×C47C2×C4semidirect
166. #102×C47C2×C4semidirect
167. #102×C47C2×C4semidirect
168. #102×C47C2×C4semidirect
169. #102×C47C2×C4semidirect
407. C22×C47#444semidirect
458. #452Dic47semidirect
459. #452Dic47semidirect
460. #451Dic47semidirect
461. #450Dic47semidirect
462. #449Dic47semidirect
463. #449Dic47semidirect
464. #448Dic47semidirect
465. #447Dic47semidirect
502. C47#22886semidirect
524. C2×Q16C2×Dic47semidirect
525. C2×Q16C2×Dic47semidirect
526. C2×SD16C2×Dic47semidirect
527. C2×SD16C2×Dic47semidirect
528. C2×SD16C2×Dic47semidirect
529. C2×SD16C2×Dic47semidirect
530. C2×D8C2×Dic47semidirect
531. C2×D8C2×Dic47semidirect
580. #103C2×Dic47semidirect
581. #103C2×Dic47semidirect
582. #103C2×Dic47semidirect
583. #103C2×Dic47semidirect
584. #102C2×Dic47semidirect
585. #102C2×Dic47semidirect
586. #102C2×Dic47semidirect
587. #102C2×Dic47semidirect
840. C22#15689245semidirect

Maximal subgroups

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

subgroupindex
C2×#156892452
#202521152
C22×#130939512
#202518372
#202442822
#202441012
#202440382
#202438322
#202437172
#202436652
#202435952
#202432352
#202431522
C47×#30022
#2288647