Finite Group Databasebeta

← #26231833

Subgroups — #26231833

Order 12032.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689195C211yesmaximal, characteristic, complemented
2C2×#15689128C211yesmaximal, characteristic, complemented
3C2×#15689119C211yesmaximal, characteristic, complemented
4#20246337C211yesmaximal, characteristic, complemented
5#20244321C211yesmaximal, characteristic, complemented
6#20244205C211yesmaximal, characteristic, complemented
7#20243822C211yesmaximal, characteristic, complemented
8#20243817C211yesmaximal, characteristic, complemented
9#20243711C211yesmaximal, characteristic, complemented
10#20243701C211yesmaximal, characteristic, complemented
11#20243388C211yesmaximal, characteristic, complemented
12#20243328C211yesmaximal, characteristic, complemented
13#20243319C211yesmaximal, characteristic, complemented
14#20243213C211yesmaximal, characteristic, complemented
15C2×C47×#546C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic, complemented
18C2×#13093983C2211yescharacteristic
19C2×#13093983C2211yescharacteristic, complemented
20#15689195—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
22#15689128—24no—
23#15689119—24no—
24C2×#13093948C2211yescharacteristic, complemented
25C2×#13093948C2211yescharacteristic, complemented
26C2×#13093948C2211yescharacteristic, complemented
27C2×#13093948C2211yescharacteristic, complemented
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×#13093945C2211yescharacteristic
34C2×#13093945C2211yescharacteristic
35C2×#13093945C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
38C2×#13093935C2211yescharacteristic, complemented
39#15689026—21no—
40#15689016—21no—
41#15689016—21no—
42#15688993C2211yescharacteristic, complemented
43#15688983C2211yescharacteristic
44#15688983C2211yescharacteristic, complemented
45C4⋊C4×Dic47—21no—
46C4×C4⋊Dic47C2211yescharacteristic, complemented
47#15688885C2211yescharacteristic, complemented
48#15688885C2211yescharacteristic, complemented
49#15688885C2211yescharacteristic, complemented
50#15688885C2211yescharacteristic, complemented
51C22×#41×C47C2211yescharacteristic
52C23×D4×C47C2211yescharacteristic
53C47×#546—24no—
54C47×#546C418yescomplemented
55C2×#124×C47C2211yescharacteristic
56C2×#123×C47—21no—
57C2×C22⋊Q8×C47C2211yescharacteristic
58C2×#121×C47—21no—
59C2×#121×C47C2211yescharacteristic
60C2×#120×C47—21no—
61C2×C4×D4×C47C2211yescharacteristic
62C2×C4×D4×C47C2211yescharacteristic
63C22×C22⋊C4×C47—21no—
64C2×#10625329—22no—
65C2×#10625329—22no—
66C2×#10625329—41no—
67C22×C47⋊C8—22no—
68C22×C47⋊C8—22no—
69C22×C47⋊C8—41no—
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74#13093983—22no—
75#13093983—22no—
76#13093983—41no—
77#13093983—41no—
78C2×C4⋊Dic47—21no—
79C2×C4⋊Dic47—21no—
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C22⋊Dic47—21no—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C22⋊Dic47—21no—
88C2×C4×Dic47—21no—
89C2×C4×Dic47—21no—
90C2×C4×Dic47—21no—
91C4⋊(C47⋊C8)—22no—
92#13093948—22no—
93#13093948—22no—
94#13093948—41no—
95#13093948—41no—
96#13093945—22no—
97#13093945—22no—
98#13093945—22no—
99#13093945—22no—
100#13093945—22no—
101#13093945—41no—
102#13093945—41no—
103#13093945D414yescomplemented
104C22⋊(C47⋊C8)—22no—
105C22⋊(C47⋊C8)—22no—
106#13093935—22no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C25×C47—21no—
111C2×#41×C47—22no—
112C2×#41×C47—22no—
113C2×#41×C47—22no—
114C2×#41×C47—41no—
115C2×#41×C47—41no—
116C2×#41×C47C2×C414yes—
117C22×Q8×C47C2311yescharacteristic
118C22×D4×C47—22no—
119C22×D4×C47—22no—
120C22×D4×C47—21no—
121C22×D4×C47—21no—
122C22×D4×C47—21no—
123C22×D4×C47—22no—
124C22×D4×C47—41no—
125C22×D4×C47—41no—
126C22×D4×C47C2×C414yes—
127C22×D4×C47D411yescharacteristic
128C22×D4×C47C2311yescharacteristic
129C22×D4×C47C2311yescharacteristic
130C23×C4×C47—21no—
131C23×C4×C47—21no—
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134#124×C47—22no—
135#124×C47C2×C414yes—
136#123×C47—28no—
137C22⋊Q8×C47—22no—
138C22⋊Q8×C47C2×C414yes—
139#121×C47—22no—
140#121×C47—28no—
141#121×C47C2×C414yes—
142#120×C47—28no—
143C4×D4×C47—22no—
144C4×D4×C47C2×C414yes—
145C4×D4×C47C2×C414yes—
146C4×D4×C47D414yes—
147C2×C4⋊C4×C47—21no—
148C2×C4⋊C4×C47D411yescharacteristic
149C2×C4⋊C4×C47C2311yescharacteristic
150C2×C22⋊C4×C47—21no—
151C2×C22⋊C4×C47—21no—
152C2×C22⋊C4×C47—21no—
153C2×C22⋊C4×C47—21no—
154C2×C22⋊C4×C47—21no—
155C2×C22⋊C4×C47—28no—
156C2×C22⋊C4×C47D411yescharacteristic
157C2×C22⋊C4×C47D411yescharacteristic
158C2×C42×C47C2311yescharacteristic
159C24×C47—21no—
160C24×C47—21no—
161C24×C47—24no—
162C24×C47—42no—
163C24×C47—42no—
164C24×C47—42no—
165C24×C47—42no—
166C24×C47—81no—
167C24×C47—81no—
168C24×C47C2×D411yescharacteristic
169C24×C47C2×D411yescharacteristic
170#41×C47—28no—
171#41×C47—44no—
172#41×C47—44no—
173#41×C47—44no—
174C2×Q8×C47—21no—
175C2×Q8×C47—21no—
176C2×Q8×C47—21no—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47C22×C412yes—
180C2×D4×C47—28no—
181C2×D4×C47—24no—
182C2×D4×C47—24no—
183C2×D4×C47—24no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—44no—
193C2×D4×C47—44no—
194C2×D4×C47—44no—
195C2×D4×C47—41no—
196C2×D4×C47—41no—
197C2×D4×C47—42no—
198C2×D4×C47—42no—
199C2×D4×C47—42no—
200C2×D4×C47—42no—
201C2×D4×C47—81no—
202C2×D4×C47—81no—
203C2×D4×C47C22⋊C414yes—
204C2×D4×C47C22×C412yes—
205C2×D4×C47C22×C412yes—
206C2×D4×C47C2×D412yes—
207C2×D4×C47#4112yes—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—24no—
219C22×C4×C47—24no—
220C22×C4×C47—42no—
221C22×C4×C47—42no—
222C22×C4×C47—81no—
223C22×C4×C47—81no—
224C22×C4×C47C22×C412yes—
225C22×C4×C47C22×C412yes—
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D412yes—
231C22×C4×C47C2×D412yes—
232C22×C4×C47C2411yescharacteristic
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C4⋊C4×C47—24no—
238C4⋊C4×C47—21no—
239C4⋊C4×C47C22⋊C414yes—
240C4⋊C4×C47C22×C412yes—
241C22⋊C4×C47—24no—
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×C47C22×C412yes—
249C42×C47C2×D412yes—
250C22⋊Dic47—42no—
251C22⋊Dic47—42no—
252C22⋊Dic47—81no—
253C22⋊Dic47—81no—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47—21no—
261C4⋊Dic47—42no—
262C4⋊Dic47—81no—
263C4⋊Dic47C2×D412yes—
264C4×Dic47—42no—
265C4×Dic47—42no—
266C4×Dic47—42no—
267#10625329—44no—
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—21no—
279C2×C47⋊C8—44no—
280C2×C47⋊C8C2×D412yes—
281C23×C47—22no—
282C23×C47—21no—
283C23×C47—21no—
284C23×C47—22no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—22no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—21no—
291C23×C47—21no—
292C23×C47—21no—
293C23×C47—21no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—22no—
297C23×C47—48no—
298C23×C47—48no—
299C23×C47—41no—
300C23×C47—41no—
301C23×C47—41no—
302C23×C47—41no—
303C23×C47—41no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—84no—
310C23×C47—84no—
311C23×C47—84no—
312C23×C47—84no—
313C23×C47—84no—
314C23×C47C2×C22⋊C412yes—
315C23×C47C2×C22⋊C412yes—
316C23×C47C22×D411yescharacteristic
317Q8×C47—22no—
318Q8×C47—22no—
319Q8×C47—41no—
320Q8×C47—41no—
321D4×C47—22no—
322D4×C47—22no—
323D4×C47—22no—
324D4×C47—22no—
325D4×C47—22no—
326D4×C47—44no—
327D4×C47—48no—
328D4×C47—48no—
329D4×C47—41no—
330D4×C47—41no—
331D4×C47—84no—
332D4×C47C4×D414yes—
333C2×C4×C47—21no—
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—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—48no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—84no—
357C2×C4×C47C2×C22⋊C412yes—
358C2×C4×C47C2×C22⋊C412yes—
359C2×C4×C47C2×C22⋊C412yes—
360C2×C4×C47C2×C22⋊C412yes—
361C2×C4×C47C23×C411yescharacteristic
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C22×D411yescharacteristic
364C2×C4×C47C2×#4111yescharacteristic
365C2×C4×C47H(5,𝔽2)11yescharacteristic
366C2×C4×C47H(5,𝔽2)11yescharacteristic
367C2×Dic47—22no—
368C2×Dic47—41no—
369C2×Dic47—41no—
370C2×Dic47—41no—
371C2×Dic47—41no—
372C2×Dic47—41no—
373C2×Dic47—41no—
374C2×Dic47—41no—
375C2×Dic47—41no—
376C2×Dic47—41no—
377C2×Dic47—41no—
378C2×Dic47—41no—
379C47⋊C8—22no—
380C47⋊C8—41no—
381C47⋊C8—41no—
382C47⋊C8—41no—
383#22424—471nomaximal, Sylow
384C22×C47—22no—
385C22×C47—22no—
386C22×C47—24no—
387C22×C47—22no—
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—42no—
392C22×C47—42no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—42no—
396C22×C47—41no—
397C22×C47—41no—
398C22×C47—42no—
399C22×C47—41no—
400C22×C47—41no—
401C22×C47—42no—
402C22×C47—41no—
403C22×C47—41no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—42no—
408C22×C47—816no—
409C22×C47—81no—
410C22×C47—81no—
411C22×C47—81no—
412C22×C47—81no—
413C22×C47C22×C22⋊C411yescharacteristic
414C22×C47D4211yescharacteristic
415C22×C47#54611yescharacteristic
416C22×C47#57511yescharacteristic
417C22×C47#57511yescharacteristic
418C22×C47#57611yescharacteristic
419C22×C47#57711yescharacteristic
420C4×C47—22no—
421C4×C47—22no—
422C4×C47—22no—
423C4×C47—22no—
424C4×C47—42no—
425C4×C47—42no—
426C4×C47C2×C4×D411yescharacteristic
427C4×C47#51811yescharacteristic
428C4×C47D4211yescharacteristic
429C4×C47#54611yescharacteristic
430Dic47—42no—
431Dic47—81no—
432Dic47—81no—
433Dic47—81no—
434C2×#546D4711yescharacteristic
435C2×#435—471no—
436C2×#418—471no—
437C2×#416—471no—
438#2354—471no—
439#1983—471no—
440#1959—471no—
441#1894—471no—
442#1893—471no—
443#1875—471no—
444#1873—471no—
445#1802—471no—
446#1788—471no—
447#1786—471no—
448#1762—471no—
449C2×C47—42no—
450C2×C47—42no—
451C2×C47—44no—
452C2×C47—82no—
453C2×C47D4×C22⋊C411yescharacteristic
454C2×C47#289611yescharacteristic
455C2×C47#289711yescharacteristic
456C2×C47#326711yescharacteristic
457C2×C47#326811yescharacteristic
458C2×C47#331111yescharacteristic
459C2×C47#331911yescharacteristic
460C22×#41C2×D4711yescharacteristic
461C23×D4C2×D4711yescharacteristic
462C22×M16—471no—
463C23×C8—471no—
464#546—24no—
465#546Dic4718yescomplemented
466C2×#124C2×D4711yescharacteristic
467C2×#123—21no—
468C2×C22⋊Q8C2×D4711yescharacteristic
469C2×#121—21no—
470C2×#121C2×D4711yescharacteristic
471C2×#120—21no—
472C2×C4×D4C2×D4711yescharacteristic
473C2×C4×D4C2×D4711yescharacteristic
474C2×#117—471no—
475C2×#117—471no—
476C22×C22⋊C4—21no—
477#435—944no—
478C2×C4⋊C8—471no—
479#418—944no—
480#416—944no—
481C2×#103—471no—
482C2×#103—471no—
483C2×#103—471no—
484C2×#103—471no—
485C2×#102—471no—
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102—471no—
491C2×#102—471no—
492C2×#102—471no—
493C2×C22⋊C8—471no—
494C2×C22⋊C8—471no—
495C2×#97—471no—
496#390—941no—
497#388—941no—
498#388—941no—
499#384—471no—
500#380—471no—
501#380—471no—
502C4×C4⋊C4—471no—
503C4×C4⋊C4—941no—
504#340—471no—
505#340—471no—
506#340—471no—
507#340—471no—
508C47#2242411yescharacteristic, complemented, Sylow
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic4714yes—
516C22×Q8C22×D4711yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×Dic4714yes—
526C22×D4C22⋊D4711yescharacteristic
527C22×D4C22×D4711yescharacteristic
528C22×D4C22×D4711yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D4711yescharacteristic
532C23×C4C22×D4711yescharacteristic
533C2×M16—942no—
534C2×M16—942no—
535C2×M16—1881no—
536C22×C8—471no—
537C22×C8—471no—
538C22×C8—471no—
539C22×C8—471no—
540C22×C8—942no—
541C22×C8—942no—
542C22×C8—1881no—
543#124—22no—
544#124C2×Dic4714yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×Dic4714yes—
548#121—22no—
549#121—28no—
550#121C2×Dic4714yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×Dic4714yes—
554C4×D4C2×Dic4714yes—
555C4×D4C22⋊D4714yes—
556#117—942no—
557#117—942no—
558#117—1881no—
559#117—1881no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—471no—
562C2×C4⋊C4—471no—
563C2×C4⋊C4—471no—
564C2×C4⋊C4—471no—
565C2×C4⋊C4—941no—
566C2×C4⋊C4—941no—
567C2×C4⋊C4C22⋊D4711yescharacteristic
568C2×C4⋊C4C22×D4711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—941no—
576C2×C22⋊C4—941no—
577C2×C22⋊C4—941no—
578C2×C22⋊C4—941no—
579C2×C22⋊C4C22⋊D4711yescharacteristic
580C2×C22⋊C4C22⋊D4711yescharacteristic
581C2×C42—941no—
582C2×C42—941no—
583C2×C42—941no—
584C2×C42C22×D4711yescharacteristic
585C4⋊C8—942no—
586#103—942no—
587#103—942no—
588#103—1881no—
589#103—1881no—
590#102—474no—
591#102—942no—
592#102—942no—
593#102—942no—
594#102—942no—
595#102—942no—
596#102—1881no—
597#102—1881no—
598C22⋊C8—942no—
599C22⋊C8—942no—
600#97—942no—
601#95—941no—
602#95—941no—
603#95—941no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×C22⋊D4711yescharacteristic
614C24C2×C22⋊D4711yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×Dic4712yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic4714yes—
649C2×D4D4×D4712yes—
650C2×D4#1062535212yes—
651C2×D4C22×Dic4712yes—
652C2×D4C22×Dic4712yes—
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—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—81no—
669C22×C4—941no—
670C22×C4—941no—
671C22×C4—941no—
672C22×C4—941no—
673C22×C4C22×Dic4712yes—
674C22×C4C22×Dic4712yes—
675C22×C4C2×C22⋊D4711yescharacteristic
676C22×C4C2×C22⋊D4711yescharacteristic
677C22×C4C2×C22⋊D4711yescharacteristic
678C22×C4C2×C22⋊D4711yescharacteristic
679C22×C4C2×C22⋊D4712yes—
680C22×C4C2×C22⋊D4712yes—
681C22×C4C23×D4711yescharacteristic
682M16—1884no—
683C2×C8—472no—
684C2×C8—941no—
685C2×C8—941no—
686C2×C8—941no—
687C2×C8—941no—
688C2×C8—941no—
689C2×C8—941no—
690C2×C8—941no—
691C2×C8—941no—
692C2×C8—941no—
693C2×C8—941no—
694C2×C8—941no—
695C2×C8—1884no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—472no—
699C4⋊C4—941no—
700C4⋊C4—941no—
701C4⋊C4—941no—
702C4⋊C4—941no—
703C4⋊C4—941no—
704C4⋊C4—941no—
705C4⋊C4—941no—
706C4⋊C4—3761no—
707C4⋊C4—1882no—
708C4⋊C4C22⋊Dic4714yes—
709C4⋊C4C22×Dic4712yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—3761no—
716C22⋊C4—3761no—
717C22⋊C4—1882no—
718C22⋊C4—1882no—
719C22⋊C4C22⋊Dic4714yes—
720C22⋊C4C22⋊Dic4714yes—
721C42—1882no—
722C42—1882no—
723C42—1882no—
724C42C22×Dic4712yes—
725C42C2×C22⋊D4712yes—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊Dic4712yes—
760C23C2×C22⋊Dic4712yes—
761C23C22×C22⋊D4711yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4D4×Dic4714yes—
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—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—942no—
803C2×C4—1881no—
804C2×C4—1881no—
805C2×C4—1881no—
806C2×C4—1881no—
807C2×C4—1881no—
808C2×C4—1881no—
809C2×C4—1881no—
810C2×C4—1881no—
811C2×C4—1881no—
812C2×C4—1881no—
813C2×C4—1881no—
814C2×C4C2×C22⋊Dic4712yes—
815C2×C4C2×C22⋊Dic4712yes—
816C2×C4C2×C22⋊Dic4712yes—
817C2×C4C2×C22⋊Dic4712yes—
818C2×C4C23×Dic4711yescharacteristic
819C2×C4C2×D4×D4711yescharacteristic
820C2×C4C22×C22⋊D4711yescharacteristic
821C2×C4C2×#1062535211yescharacteristic
822C2×C4#1309406911yescharacteristic
823C2×C4#1309406911yescharacteristic
824C8—942no—
825C8—1881no—
826C8—1881no—
827C8—1881no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—24no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊Dic4711yescharacteristic
858C22D4×C22⋊D4711yescharacteristic
859C22#1568976711yescharacteristic
860C22#1568992111yescharacteristic
861C22#1568992111yescharacteristic
862C22#1568992611yescharacteristic
863C22#1568993411yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—3761no—
871C4—3761no—
872C4—3761no—
873C4—1882no—
874C4C2×D4×Dic4711yescharacteristic
875C4#1568959811yescharacteristic
876C4D4×C22⋊D4711yescharacteristic
877C4#1568976711yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊Dic4711yescharacteristic
883C2#2025190711yescharacteristic
884C2#2025191411yescharacteristic
885C2#2025490911yescharacteristic
886C2#2025492411yescharacteristic
887C2#2025542411yescharacteristic
888C2#2025554411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#546C2
socleC23×C47C22×D4
cosocleC22×C4×C47C24
hypercenterC2×#546D47
hypocenterC47#22424
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#15689195C2semidirect
2. C2×#15689128C2semidirect
3. C2×#15689119C2semidirect
4. #20246337C2semidirect
5. #20244321C2semidirect
6. #20244205C2semidirect
7. #20243822C2semidirect
8. #20243817C2semidirect
9. #20243711C2semidirect
10. #20243701C2semidirect
11. #20243388C2semidirect
12. #20243328C2semidirect
13. #20243319C2semidirect
14. #20243213C2semidirect
17. C23×C47⋊C8C22semidirect
19. C2×#13093983C22semidirect
21. C2×C4⋊(C47⋊C8)C22semidirect
24. C2×#13093948C22semidirect
25. C2×#13093948C22semidirect
26. C2×#13093948C22semidirect
27. C2×#13093948C22semidirect
37. C2×C22⋊(C47⋊C8)C22semidirect
38. C2×#13093935C22semidirect
42. #15688993C22semidirect
44. #15688983C22semidirect
46. C4×C4⋊Dic47C22semidirect
47. #15688885C22semidirect
48. #15688885C22semidirect
49. #15688885C22semidirect
50. #15688885C22semidirect
54. C47×#546C4semidirect
103. #13093945D4semidirect
465. #546Dic47semidirect
508. C47#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#156891952
C2×#156891282
C2×#156891192
#202463372
#202443212
#202442052
#202438222
#202438172
#202437112
#202437012
#202433882
#202433282
#202433192
#202432132
C2×C47×#5462
#2242447