Finite Group Databasebeta

← #26231788

Subgroups — #26231788

Order 12032.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689195C211yesmaximal, characteristic, complemented
2C2×#15689124C211yesmaximal, characteristic, complemented
3C22×#13093948C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic47C211yesmaximal, characteristic, complemented
5#20244321C211yesmaximal, characteristic, complemented
6#20244205C211yesmaximal, characteristic, complemented
7#20243822C211yesmaximal, characteristic, complemented
8#20243817C211yesmaximal, characteristic, complemented
9#20243706C211yesmaximal, characteristic, complemented
10#20243696C211yesmaximal, characteristic, complemented
11#20243393C211yesmaximal, characteristic, complemented
12#20243328C211yesmaximal, characteristic, complemented
13#20243323C211yesmaximal, characteristic, complemented
14#20243218C211yesmaximal, characteristic, complemented
15C2×C47×#548C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C2×D4×Dic47—21no—
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21#15689195—24no—
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23#15689124—24no—
24C2×#13093948—24no—
25C2×#13093948C2211yescharacteristic
26C2×#13093948C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093948C2211yescharacteristic
31C2×#13093948C2211yescharacteristic
32C2×#13093948C2211yescharacteristic
33C2×#13093945C2211yescharacteristic
34C2×#13093945C2211yescharacteristic
35C2×#13093945C2211yescharacteristic
36C2×#13093945C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×C22⋊(C47⋊C8)C2211yescharacteristic
39C2×#13093935C2211yescharacteristic
40#15689022—21no—
41#15688998—21no—
42#15688998—21no—
43#15688993C2211yescharacteristic
44#15688983C2211yescharacteristic
45#15688983C2211yescharacteristic
46C4×C4⋊Dic47C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C22×#41×C47C2211yescharacteristic
52C23×Q8×C47C2211yescharacteristic
53C47×#548—24no—
54C47×#548C418yescomplemented
55C2×#124×C47—21no—
56C2×#124×C47C2211yescharacteristic
57C2×C22⋊Q8×C47—21no—
58C2×C22⋊Q8×C47C2211yescharacteristic
59C2×#121×C47—21no—
60C2×#121×C47C2211yescharacteristic
61C2×C4×Q8×C47C2211yescharacteristic
62C2×C4×D4×C47—21no—
63C2×C4×D4×C47C2211yescharacteristic
64C23×Dic47—21no—
65C23×Dic47—21no—
66C2×#10625329—22no—
67C2×#10625329—22no—
68C2×#10625329—41no—
69C22×C47⋊C8—22no—
70C22×C47⋊C8—22no—
71C22×C47⋊C8—41no—
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76D4×Dic47—44no—
77C2×C4⋊Dic47—22no—
78C2×C4⋊Dic47—22no—
79C2×C4⋊Dic47—21no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47—21no—
82C2×C4⋊Dic47—21no—
83C2×C4⋊Dic47—41no—
84C2×C4⋊Dic47—41no—
85C2×C4⋊Dic47C2311yescharacteristic
86C2×C4⋊Dic47C2311yescharacteristic
87C2×C4⋊Dic47C2311yescharacteristic
88C2×C4⋊Dic47C2311yescharacteristic
89C2×C22⋊Dic47—21no—
90C2×C22⋊Dic47—21no—
91C2×C4×Dic47—21no—
92C4⋊(C47⋊C8)—22no—
93#13093948—22no—
94#13093948—22no—
95#13093948—22no—
96#13093948—22no—
97#13093948—22no—
98#13093948—41no—
99#13093948—41no—
100#13093948D414yescomplemented
101#13093945—22no—
102#13093945—22no—
103#13093945—41no—
104#13093945—41no—
105C22⋊(C47⋊C8)—22no—
106C22⋊(C47⋊C8)—22no—
107#13093935—22no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C2×#41×C47—22no—
112C2×#41×C47—22no—
113C2×#41×C47—22no—
114C2×#41×C47—41no—
115C2×#41×C47—41no—
116C2×#41×C47C2×C414yescomplemented
117C22×Q8×C47—21no—
118C22×Q8×C47—22no—
119C22×Q8×C47—22no—
120C22×Q8×C47—22no—
121C22×Q8×C47—41no—
122C22×Q8×C47—41no—
123C22×Q8×C47C2×C414yescomplemented
124C22×Q8×C47C2311yescharacteristic
125C22×Q8×C47C2311yescharacteristic
126C22×D4×C47—21no—
127C22×D4×C47—21no—
128C22×D4×C47D411yescharacteristic
129C22×D4×C47C2311yescharacteristic
130C23×C4×C47—21no—
131C23×C4×C47—21no—
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134#124×C47—28no—
135#124×C47—22no—
136#124×C47C2×C414yescomplemented
137C22⋊Q8×C47—22no—
138C22⋊Q8×C47—28no—
139C22⋊Q8×C47C2×C414yescomplemented
140#121×C47—28no—
141#121×C47—22no—
142#121×C47C2×C414yescomplemented
143C4×Q8×C47—22no—
144C4×Q8×C47C2×C414yescomplemented
145C4×D4×C47—28no—
146C4×D4×C47C2×C414yes—
147C4×D4×C47D414yes—
148C2×C4⋊C4×C47—21no—
149C2×C4⋊C4×C47—21no—
150C2×C4⋊C4×C47D411yescharacteristic
151C2×C4⋊C4×C47C2311yescharacteristic
152C2×C22⋊C4×C47—21no—
153C2×C22⋊C4×C47—21no—
154C2×C22⋊C4×C47—21no—
155C2×C22⋊C4×C47—21no—
156C2×C22⋊C4×C47D411yescharacteristic
157C2×C22⋊C4×C47D411yescharacteristic
158C2×C42×C47—21no—
159C2×C42×C47C2311yescharacteristic
160C24×C47—21no—
161C24×C47C2×D411yescharacteristic
162C24×C47C2×D411yescharacteristic
163#41×C47—28no—
164#41×C47—44no—
165#41×C47—44no—
166#41×C47—44no—
167C2×Q8×C47—24no—
168C2×Q8×C47—21no—
169C2×Q8×C47—21no—
170C2×Q8×C47—21no—
171C2×Q8×C47—21no—
172C2×Q8×C47—28no—
173C2×Q8×C47—21no—
174C2×Q8×C47—21no—
175C2×Q8×C47—21no—
176C2×Q8×C47—21no—
177C2×Q8×C47—42no—
178C2×Q8×C47—42no—
179C2×Q8×C47—44no—
180C2×Q8×C47—44no—
181C2×Q8×C47—44no—
182C2×Q8×C47C22×C412yes—
183C2×Q8×C47C22×C412yes—
184C2×Q8×C47C2×D412yes—
185C2×Q8×C47#4112yes—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—24no—
189C2×D4×C47—24no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—42no—
196C2×D4×C47—42no—
197C2×D4×C47—42no—
198C2×D4×C47—42no—
199C2×D4×C47C22⋊C414yes—
200C2×D4×C47C22×C412yes—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—24no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—24no—
214C22×C4×C47—42no—
215C22×C4×C47—42no—
216C22×C4×C47—42no—
217C22×C4×C47—42no—
218C22×C4×C47C22×C412yes—
219C22×C4×C47C22×C412yes—
220C22×C4×C47C2×D411yescharacteristic
221C22×C4×C47C2×D411yescharacteristic
222C22×C4×C47C2×D411yescharacteristic
223C22×C4×C47C2×D411yescharacteristic
224C22×C4×C47C2×D412yes—
225C22×C4×C47C2×D412yes—
226C22×C4×C47C2411yescharacteristic
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—42no—
232C22×Dic47—42no—
233C22×Dic47—42no—
234C22×Dic47—42no—
235C22×Dic47—81no—
236C22×Dic47—81no—
237C4⋊C4×C47—24no—
238C4⋊C4×C47—24no—
239C4⋊C4×C47—21no—
240C4⋊C4×C47C22⋊C414yes—
241C4⋊C4×C47C22×C412yes—
242C22⋊C4×C47—24no—
243C22⋊C4×C47—24no—
244C22⋊C4×C47—24no—
245C22⋊C4×C47—24no—
246C22⋊C4×C47C22⋊C414yes—
247C22⋊C4×C47C22⋊C414yes—
248C42×C47—24no—
249C42×C47C22×C412yes—
250C42×C47C2×D412yes—
251C22⋊Dic47—42no—
252C22⋊Dic47—42no—
253C4⋊Dic47—21no—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47—42no—
261C4⋊Dic47—42no—
262C4⋊Dic47—42no—
263C4⋊Dic47—81no—
264C4⋊Dic47C2×D412yes—
265C4×Dic47—42no—
266#10625329—44no—
267C2×C47⋊C8—21no—
268C2×C47⋊C8—21no—
269C2×C47⋊C8—21no—
270C2×C47⋊C8—21no—
271C2×C47⋊C8—21no—
272C2×C47⋊C8—21no—
273C2×C47⋊C8—21no—
274C2×C47⋊C8—21no—
275C2×C47⋊C8—21no—
276C2×C47⋊C8—21no—
277C2×C47⋊C8—21no—
278C2×C47⋊C8—44no—
279C2×C47⋊C8C2×D412yes—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—22no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47C2×C22⋊C412yes—
298C23×C47C2×C22⋊C412yes—
299C23×C47AGL(1,ℤ/8)12yes—
300C23×C47#13712yes—
301C23×C47C22×D411yescharacteristic
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47—22no—
306Q8×C47—22no—
307Q8×C47—48no—
308Q8×C47—41no—
309Q8×C47—41no—
310Q8×C47C4×D414yescomplemented
311D4×C47—28no—
312D4×C47—22no—
313D4×C47—22no—
314D4×C47—48no—
315D4×C47—48no—
316D4×C47—41no—
317D4×C47—41no—
318C2×C4×C47—22no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—22no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—22no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—22no—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—48no—
340C2×C4×C47—48no—
341C2×C4×C47—41no—
342C2×C4×C47—41no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47C2×C22⋊C412yes—
346C2×C4×C47C2×C22⋊C412yes—
347C2×C4×C47C2×C22⋊C412yes—
348C2×C4×C47C2×C22⋊C412yes—
349C2×C4×C47C23×C411yescharacteristic
350C2×C4×C47C22×D411yescharacteristic
351C2×C4×C47C22×D411yescharacteristic
352C2×C4×C47C2×#4111yescharacteristic
353C2×C4×C47H(5,𝔽2)11yescharacteristic
354C2×C4×C47H(5,𝔽2)11yescharacteristic
355C2×Dic47—22no—
356C2×Dic47—41no—
357C2×Dic47—41no—
358C2×Dic47—41no—
359C2×Dic47—41no—
360C2×Dic47—41no—
361C2×Dic47—41no—
362C2×Dic47—41no—
363C2×Dic47—41no—
364C2×Dic47—41no—
365C2×Dic47—41no—
366C2×Dic47—41no—
367C2×Dic47—84no—
368C2×Dic47—84no—
369C47⋊C8—22no—
370C47⋊C8—41no—
371C47⋊C8—41no—
372C47⋊C8—41no—
373#22421—471nomaximal, Sylow
374C22×C47—22no—
375C22×C47—22no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—22no—
379C22×C47—22no—
380C22×C47—22no—
381C22×C47—22no—
382C22×C47—22no—
383C22×C47—41no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—41no—
387C22×C47—42no—
388C22×C47—42no—
389C22×C47—42no—
390C22×C47—81no—
391C22×C47—81no—
392C22×C47—81no—
393C22×C47—81no—
394C22×C47#41714yescomplemented
395C22×C47C22×C22⋊C411yescharacteristic
396C22×C47D4211yescharacteristic
397C22×C47#54611yescharacteristic
398C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C47C2×#13711yescharacteristic
400C22×C47#57711yescharacteristic
401C22×C47#57811yescharacteristic
402C4×C47—22no—
403C4×C47—22no—
404C4×C47—24no—
405C4×C47—22no—
406C4×C47—22no—
407C4×C47—42no—
408C4×C47—42no—
409C4×C47C2×C4×D411yescharacteristic
410C4×C47#51811yescharacteristic
411C4×C47D4211yescharacteristic
412C4×C47#54611yescharacteristic
413Dic47—42no—
414Dic47—81no—
415Dic47—81no—
416Dic47—81no—
417C2×#548D4711yescharacteristic
418C2×#435—471no—
419C2×#417—471no—
420C22×#103—471no—
421D4×C4⋊C4—471no—
422#1983—471no—
423#1959—471no—
424#1894—471no—
425#1893—471no—
426#1874—471no—
427#1872—471no—
428#1803—471no—
429#1788—471no—
430#1787—471no—
431#1763—471no—
432C2×C47—24no—
433C2×C47—42no—
434C2×C47—82no—
435C2×C47D4×C22⋊C411yescharacteristic
436C2×C47C2×#41711yescharacteristic
437C2×C47#289811yescharacteristic
438C2×C47#326511yescharacteristic
439C2×C47#327011yescharacteristic
440C2×C47#330811yescharacteristic
441C2×C47#331611yescharacteristic
442C22×#41C2×D4711yescharacteristic
443C23×Q8C2×D4711yescharacteristic
444C22×M16—471no—
445C23×C8—471no—
446#548—24no—
447#548Dic4718yescomplemented
448C2×#124—21no—
449C2×#124C2×D4711yescharacteristic
450C2×C22⋊Q8—21no—
451C2×C22⋊Q8C2×D4711yescharacteristic
452C2×#121—21no—
453C2×#121C2×D4711yescharacteristic
454C2×C4×Q8C2×D4711yescharacteristic
455C2×C4×D4—21no—
456C2×C4×D4—941no—
457C2×C4×D4C2×D4711yescharacteristic
458C22×C4⋊C4—471no—
459C22×C4⋊C4—471no—
460#435—944no—
461C2×C4⋊C8—471no—
462#417—944no—
463C2×#103—471no—
464C2×#103—471no—
465C2×#103—471no—
466C2×#103—471no—
467C2×#103—471no—
468C2×#103—471no—
469C2×#103—471no—
470C2×#103—471no—
471C2×#103—944no—
472C2×#102—471no—
473C2×#102—471no—
474C2×#102—471no—
475C2×#102—471no—
476C2×C22⋊C8—471no—
477C2×C22⋊C8—471no—
478C2×#97—471no—
479#389—941no—
480#385—941no—
481#385—941no—
482#384—471no—
483#380—471no—
484#380—471no—
485C4×C4⋊C4—471no—
486#340—471no—
487#340—471no—
488#340—471no—
489#340—471no—
490C47#2242111yescharacteristic, complemented, Sylow
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41C2×Dic4714yescomplemented
497C22×Q8—21no—
498C22×Q8—22no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8C2×Dic4714yescomplemented
504C22×Q8C22×D4711yescharacteristic
505C22×Q8C22×D4711yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4C22⋊D4711yescharacteristic
509C22×D4C22×D4711yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—941no—
513C23×C4—941no—
514C23×C4C22×D4711yescharacteristic
515C23×C4C22×D4711yescharacteristic
516C2×M16—942no—
517C2×M16—942no—
518C2×M16—1881no—
519C22×C8—471no—
520C22×C8—471no—
521C22×C8—471no—
522C22×C8—471no—
523C22×C8—942no—
524C22×C8—942no—
525C22×C8—1881no—
526#124—28no—
527#124—22no—
528#124C2×Dic4714yescomplemented
529C22⋊Q8—22no—
530C22⋊Q8—28no—
531C22⋊Q8C2×Dic4714yescomplemented
532#121—28no—
533#121—22no—
534#121C2×Dic4714yescomplemented
535C4×Q8—22no—
536C4×Q8C2×Dic4714yescomplemented
537C4×D4—28no—
538C4×D4—1884no—
539C4×D4C2×Dic4714yes—
540C4×D4C22⋊D4714yes—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—471no—
545C2×C4⋊C4—471no—
546C2×C4⋊C4—471no—
547C2×C4⋊C4—942no—
548C2×C4⋊C4—942no—
549C2×C4⋊C4—941no—
550C2×C4⋊C4—941no—
551C2×C4⋊C4—941no—
552C2×C4⋊C4—941no—
553C2×C4⋊C4—1881no—
554C2×C4⋊C4—1881no—
555C2×C4⋊C4C22⋊D4711yescharacteristic
556C2×C4⋊C4C22×D4711yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—941no—
562C2×C22⋊C4—941no—
563C2×C22⋊C4C22⋊D4711yescharacteristic
564C2×C22⋊C4C22⋊D4711yescharacteristic
565C2×C42—21no—
566C2×C42—941no—
567C2×C42C22×D4711yescharacteristic
568C4⋊C8—942no—
569#103—474no—
570#103—942no—
571#103—942no—
572#103—942no—
573#103—942no—
574#103—942no—
575#103—1881no—
576#103—1881no—
577#102—942no—
578#102—942no—
579#102—1881no—
580#102—1881no—
581C22⋊C8—942no—
582C22⋊C8—942no—
583#97—942no—
584#95—941no—
585#95—941no—
586#95—941no—
587C24—21no—
588C24C2×C22⋊D4711yescharacteristic
589C24C2×C22⋊D4711yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594C2×Q8—24no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—28no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—42no—
605C2×Q8—42no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8D4×D4712yes—
610C2×Q8#1062535212yes—
611C2×Q8C22×Dic4712yes—
612C2×Q8C22×Dic4712yes—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4C22⋊Dic4714yes—
627C2×D4C22×Dic4712yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—941no—
646C22×C4—941no—
647C22×C4—941no—
648C22×C4—941no—
649C22×C4—3761no—
650C22×C4—3761no—
651C22×C4—1882no—
652C22×C4—1882no—
653C22×C4—1882no—
654C22×C4—1882no—
655C22×C4C22×Dic4712yes—
656C22×C4C22×Dic4712yes—
657C22×C4C2×C22⋊D4711yescharacteristic
658C22×C4C2×C22⋊D4711yescharacteristic
659C22×C4C2×C22⋊D4711yescharacteristic
660C22×C4C2×C22⋊D4711yescharacteristic
661C22×C4C2×C22⋊D4712yes—
662C22×C4C2×C22⋊D4712yes—
663C22×C4C23×D4711yescharacteristic
664M16—1884no—
665C2×C8—472no—
666C2×C8—941no—
667C2×C8—941no—
668C2×C8—941no—
669C2×C8—941no—
670C2×C8—941no—
671C2×C8—941no—
672C2×C8—941no—
673C2×C8—941no—
674C2×C8—941no—
675C2×C8—941no—
676C2×C8—941no—
677C2×C8—1884no—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—21no—
681C4⋊C4—472no—
682C4⋊C4—941no—
683C4⋊C4—941no—
684C4⋊C4—941no—
685C4⋊C4—941no—
686C4⋊C4—941no—
687C4⋊C4—941no—
688C4⋊C4—941no—
689C4⋊C4—3761no—
690C4⋊C4—1882no—
691C4⋊C4—1882no—
692C4⋊C4—1882no—
693C4⋊C4C22⋊Dic4714yes—
694C4⋊C4C22×Dic4712yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—1882no—
700C22⋊C4—1882no—
701C22⋊C4C22⋊Dic4714yes—
702C22⋊C4C22⋊Dic4714yes—
703C42—24no—
704C42—1882no—
705C42C22×Dic4712yes—
706C42C2×C22⋊D4712yes—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23C2×C22⋊Dic4712yes—
725C23C2×C22⋊Dic4712yes—
726C23#1309404912yes—
727C23#1309405412yes—
728C23C22×C22⋊D4711yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—48no—
735Q8—41no—
736Q8—41no—
737Q8D4×Dic4714yescomplemented
738D4—28no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—48no—
743D4—41no—
744D4—41no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—942no—
773C2×C4—3764no—
774C2×C4—3764no—
775C2×C4—1881no—
776C2×C4—1881no—
777C2×C4—1881no—
778C2×C4—1881no—
779C2×C4—1881no—
780C2×C4—1881no—
781C2×C4—1881no—
782C2×C4—1881no—
783C2×C4—1881no—
784C2×C4—1881no—
785C2×C4—1881no—
786C2×C4C2×C22⋊Dic4712yes—
787C2×C4C2×C22⋊Dic4712yes—
788C2×C4C2×C22⋊Dic4712yes—
789C2×C4C2×C22⋊Dic4712yes—
790C2×C4C23×Dic4711yescharacteristic
791C2×C4C2×D4×D4711yescharacteristic
792C2×C4C22×C22⋊D4711yescharacteristic
793C2×C4C2×#1062535211yescharacteristic
794C2×C4#1309406911yescharacteristic
795C2×C4#1309406911yescharacteristic
796C8—942no—
797C8—1881no—
798C8—1881no—
799C8—1881no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22#1568912414yescomplemented
821C22C22×C22⋊Dic4711yescharacteristic
822C22D4×C22⋊D4711yescharacteristic
823C22#1568976711yescharacteristic
824C22C2×#1309404911yescharacteristic
825C22C2×#1309405411yescharacteristic
826C22#1568993111yescharacteristic
827C22#1568993811yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—24no—
832C4—22no—
833C4—42no—
834C4—42no—
835C4—3761no—
836C4—3761no—
837C4—3761no—
838C4—1882no—
839C4C2×D4×Dic4711yescharacteristic
840C4#1568959811yescharacteristic
841C4D4×C22⋊D4711yescharacteristic
842C4#1568976711yescharacteristic
843C2—24no—
844C2—42no—
845C2—82no—
846C2D4×C22⋊Dic4711yescharacteristic
847C2C2×#1568912411yescharacteristic
848C2#2025192111yescharacteristic
849C2#2025488411yescharacteristic
850C2#2025495411yescharacteristic
851C2#2025537911yescharacteristic
852C2#2025549911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#548C2
socleC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC2×#548D47
hypocenterC47#22421
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#15689195C2semidirect
2. C2×#15689124C2semidirect
3. C22×#13093948C2semidirect
4. D4×C4⋊Dic47C2semidirect
5. #20244321C2semidirect
6. #20244205C2semidirect
7. #20243822C2semidirect
8. #20243817C2semidirect
9. #20243706C2semidirect
10. #20243696C2semidirect
11. #20243393C2semidirect
12. #20243328C2semidirect
13. #20243323C2semidirect
14. #20243218C2semidirect
54. C47×#548C4semidirect
100. #13093948D4semidirect
116. C2×#41×C47C2×C4semidirect
123. C22×Q8×C47C2×C4semidirect
136. #124×C47C2×C4semidirect
139. C22⋊Q8×C47C2×C4semidirect
142. #121×C47C2×C4semidirect
144. C4×Q8×C47C2×C4semidirect
310. Q8×C47C4×D4semidirect
394. C22×C47#417semidirect
447. #548Dic47semidirect
490. C47#22421semidirect
496. C2×#41C2×Dic47semidirect
503. C22×Q8C2×Dic47semidirect
528. #124C2×Dic47semidirect
531. C22⋊Q8C2×Dic47semidirect
534. #121C2×Dic47semidirect
536. C4×Q8C2×Dic47semidirect
737. Q8D4×Dic47semidirect
820. C22#15689124semidirect

Maximal subgroups

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

subgroupindex
C2×#156891952
C2×#156891242
C22×#130939482
D4×C4⋊Dic472
#202443212
#202442052
#202438222
#202438172
#202437062
#202436962
#202433932
#202433282
#202433232
#202432182
C2×C47×#5482
#2242147