Finite Group Databasebeta

← #26231878

Subgroups — #26231878

Order 12032.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689201C211yesmaximal, characteristic, complemented
2C2×#15689124C211yesmaximal, characteristic, complemented
3C2×#15689128C211yesmaximal, characteristic, complemented
4#20246317C211yesmaximal, characteristic, complemented
5#20244321C211yesmaximal, characteristic, complemented
6#20244200C211yesmaximal, characteristic, complemented
7#20243827C211yesmaximal, characteristic, complemented
8#20243822C211yesmaximal, characteristic, complemented
9#20243706C211yesmaximal, characteristic, complemented
10#20243701C211yesmaximal, characteristic, complemented
11#20243398C211yesmaximal, characteristic, complemented
12#20243328C211yesmaximal, characteristic, complemented
13#20243319C211yesmaximal, characteristic, complemented
14C4×#13093945C211yesmaximal, characteristic, complemented
15C2×C47×#546C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic, complemented
18C2×#13093983C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic, complemented
20#15689201—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
22#15689128—24no—
23#15689124—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×C4×C47⋊C8C2211yescharacteristic, complemented
39#15689016—21no—
40#15689009—21no—
41#15689003—21no—
42#15688989C2211yescharacteristic, complemented
43#15688983C2211yescharacteristic
44#15688983C2211yescharacteristic, complemented
45C4×C4⋊Dic47C2211yescharacteristic, complemented
46C22⋊C4×Dic47—21no—
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—
64C23×Dic47—21no—
65C2×#10625329—22no—
66C2×#10625329—22no—
67C2×#10625329—22no—
68C2×#10625329—22no—
69C2×#10625329—41no—
70C2×#10625329—41no—
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75#13093983—22no—
76#13093983—41no—
77C2×C4⋊Dic47—22no—
78C2×C4⋊Dic47—21no—
79C2×C4⋊Dic47—41no—
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×C4×Dic47—21no—
88C2×C4×Dic47—21no—
89C4⋊(C47⋊C8)—22no—
90#13093948—22no—
91#13093948—22no—
92#13093948—41no—
93#13093948—41no—
94#13093945—22no—
95#13093945—22no—
96#13093945—22no—
97#13093945—22no—
98#13093945—22no—
99#13093945—41no—
100#13093945—41no—
101#13093945D414yescomplemented
102C22⋊(C47⋊C8)—22no—
103C22⋊(C47⋊C8)—22no—
104C4×C47⋊C8—22no—
105C47⋊#95—21no—
106C47⋊#95—21no—
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×C414yescomplemented
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×C414yescomplemented
136#123×C47—28no—
137C22⋊Q8×C47—22no—
138C22⋊Q8×C47C2×C414yescomplemented
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×C414yescomplemented
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—
237C22×Dic47—42no—
238C22×Dic47—42no—
239C22×Dic47—81no—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47C22⋊C414yes—
243C4⋊C4×C47C22×C412yes—
244C22⋊C4×C47—24no—
245C22⋊C4×C47—24no—
246C22⋊C4×C47—24no—
247C22⋊C4×C47—24no—
248C22⋊C4×C47—24no—
249C22⋊C4×C47C22⋊C414yes—
250C22⋊C4×C47C22⋊C414yes—
251C42×C47C22×C412yes—
252C42×C47C2×D412yes—
253C22⋊Dic47—42no—
254C22⋊Dic47—42no—
255C22⋊Dic47—81no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47—21no—
259C4⋊Dic47—21no—
260C4⋊Dic47—21no—
261C4⋊Dic47—21no—
262C4⋊Dic47—21no—
263C4⋊Dic47—42no—
264C4⋊Dic47C2×D412yes—
265C4×Dic47—42no—
266C4×Dic47—81no—
267#10625329—44no—
268#10625329—44no—
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—21no—
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—
379C2×Dic47—84no—
380C47⋊C8—22no—
381C47⋊C8—41no—
382C47⋊C8—41no—
383C47⋊C8—41no—
384#22427—471nomaximal, Sylow
385C22×C47—22no—
386C22×C47—22no—
387C22×C47—24no—
388C22×C47—22no—
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—22no—
392C22×C47—42no—
393C22×C47—42no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—42no—
397C22×C47—41no—
398C22×C47—41no—
399C22×C47—42no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—42no—
403C22×C47—41no—
404C22×C47—41no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47—42no—
408C22×C47—42no—
409C22×C47—816no—
410C22×C47—81no—
411C22×C47—81no—
412C22×C47—81no—
413C22×C47—81no—
414C22×C47C22×C22⋊C411yescharacteristic
415C22×C47D4211yescharacteristic
416C22×C47#54611yescharacteristic
417C22×C47#57511yescharacteristic
418C22×C47#57511yescharacteristic
419C22×C47#57611yescharacteristic
420C22×C47#57711yescharacteristic
421C4×C47—22no—
422C4×C47—22no—
423C4×C47—22no—
424C4×C47—22no—
425C4×C47—42no—
426C4×C47—42no—
427C4×C47C2×C4×D411yescharacteristic
428C4×C47#51811yescharacteristic
429C4×C47D4211yescharacteristic
430C4×C47#54611yescharacteristic
431Dic47—42no—
432Dic47—81no—
433Dic47—81no—
434Dic47—81no—
435C2×#546D4711yescharacteristic
436C2×#436—471no—
437C2×#417—471no—
438C2×#418—471no—
439#2352—471no—
440#1983—471no—
441#1958—471no—
442#1895—471no—
443#1894—471no—
444#1874—471no—
445#1873—471no—
446#1804—471no—
447#1788—471no—
448#1786—471no—
449C4×#102—471no—
450C2×C47—42no—
451C2×C47—42no—
452C2×C47—44no—
453C2×C47—82no—
454C2×C47D4×C22⋊C411yescharacteristic
455C2×C47#289611yescharacteristic
456C2×C47#289711yescharacteristic
457C2×C47#327311yescharacteristic
458C2×C47#327511yescharacteristic
459C2×C47#332211yescharacteristic
460C2×C47#332311yescharacteristic
461C22×#41C2×D4711yescharacteristic
462C23×D4C2×D4711yescharacteristic
463C22×M16—471no—
464C22×M16—471no—
465#546—24no—
466#546Dic4718yescomplemented
467C2×#124C2×D4711yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C2×D4711yescharacteristic
470C2×#121—21no—
471C2×#121C2×D4711yescharacteristic
472C2×#120—21no—
473C2×C4×D4C2×D4711yescharacteristic
474C2×C4×D4C2×D4711yescharacteristic
475C2×#117—471no—
476C22×C4⋊C4—471no—
477C22×C22⋊C4—21no—
478#436—944no—
479C2×C4⋊C8—471no—
480#418—944no—
481#417—944no—
482C2×#103—471no—
483C2×#103—471no—
484C2×#103—471no—
485C2×#103—471no—
486C2×#102—471no—
487C2×#102—471no—
488C2×#102—471no—
489C2×#102—471no—
490C2×#102—471no—
491C2×#102—471no—
492C2×#102—471no—
493C2×#102—471no—
494C2×C22⋊C8—471no—
495C2×C22⋊C8—471no—
496C2×C4×C8—471no—
497#388—941no—
498#387—941no—
499#386—941no—
500#382—471no—
501#380—471no—
502#380—471no—
503C4×C4⋊C4—471no—
504C4×C22⋊C4—941no—
505#340—471no—
506#340—471no—
507#340—471no—
508#340—471no—
509C47#2242711yescharacteristic, complemented, Sylow
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×Dic4714yes—
517C22×Q8C22×D4711yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×Dic4714yescomplemented
527C22×D4C22⋊D4711yescharacteristic
528C22×D4C22×D4711yescharacteristic
529C22×D4C22×D4711yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—941no—
533C23×C4C22×D4711yescharacteristic
534C23×C4C22×D4711yescharacteristic
535C2×M16—942no—
536C2×M16—942no—
537C2×M16—942no—
538C2×M16—942no—
539C2×M16—1881no—
540C2×M16—1881no—
541C22×C8—471no—
542C22×C8—471no—
543C22×C8—471no—
544C22×C8—471no—
545#124—22no—
546#124C2×Dic4714yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×Dic4714yescomplemented
550#121—22no—
551#121—28no—
552#121C2×Dic4714yes—
553#120—28no—
554C4×D4—22no—
555C4×D4C2×Dic4714yes—
556C4×D4C2×Dic4714yescomplemented
557C4×D4C22⋊D4714yes—
558#117—942no—
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—942no—
566C2×C4⋊C4—941no—
567C2×C4⋊C4—1881no—
568C2×C4⋊C4C22⋊D4711yescharacteristic
569C2×C4⋊C4C22×D4711yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
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×C42C22×D4711yescharacteristic
584C4⋊C8—942no—
585#103—942no—
586#103—942no—
587#103—1881no—
588#103—1881no—
589#102—474no—
590#102—942no—
591#102—942no—
592#102—942no—
593#102—942no—
594#102—942no—
595#102—1881no—
596#102—1881no—
597C22⋊C8—942no—
598C22⋊C8—942no—
599C4×C8—942no—
600#95—941no—
601#95—941no—
602#95—941no—
603#95—941no—
604#95—941no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×C22⋊D4711yescharacteristic
615C24C2×C22⋊D4711yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×Dic4712yes—
626C2×D4—28no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊Dic4714yes—
650C2×D4D4×D4712yes—
651C2×D4#1062535212yes—
652C2×D4C22×Dic4712yes—
653C2×D4C22×Dic4712yes—
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—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—81no—
670C22×C4—941no—
671C22×C4—941no—
672C22×C4—941no—
673C22×C4—941no—
674C22×C4—3761no—
675C22×C4—1882no—
676C22×C4—1882no—
677C22×C4C22×Dic4712yes—
678C22×C4C22×Dic4712yes—
679C22×C4C2×C22⋊D4711yescharacteristic
680C22×C4C2×C22⋊D4711yescharacteristic
681C22×C4C2×C22⋊D4711yescharacteristic
682C22×C4C2×C22⋊D4711yescharacteristic
683C22×C4C2×C22⋊D4712yes—
684C22×C4C2×C22⋊D4712yes—
685C22×C4C23×D4711yescharacteristic
686M16—1884no—
687M16—1884no—
688C2×C8—472no—
689C2×C8—941no—
690C2×C8—941no—
691C2×C8—941no—
692C2×C8—941no—
693C2×C8—941no—
694C2×C8—941no—
695C2×C8—941no—
696C2×C8—941no—
697C2×C8—941no—
698C2×C8—941no—
699C2×C8—941no—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—472no—
703C4⋊C4—941no—
704C4⋊C4—941no—
705C4⋊C4—941no—
706C4⋊C4—941no—
707C4⋊C4—941no—
708C4⋊C4—941no—
709C4⋊C4—941no—
710C4⋊C4—1882no—
711C4⋊C4C22⋊Dic4714yes—
712C4⋊C4C22×Dic4712yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—3761no—
719C22⋊C4—1882no—
720C22⋊C4—1882no—
721C22⋊C4C22⋊Dic4714yes—
722C22⋊C4C22⋊Dic4714yes—
723C42—3761no—
724C42—1882no—
725C42C22×Dic4712yes—
726C42C2×C22⋊D4712yes—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊Dic4712yes—
761C23C2×C22⋊Dic4712yes—
762C23C22×C22⋊D4711yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4D4×Dic4714yes—
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—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—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—84no—
803C2×C4—942no—
804C2×C4—3764no—
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×C4—1881no—
815C2×C4—1881no—
816C2×C4C2×C22⋊Dic4712yes—
817C2×C4C2×C22⋊Dic4712yes—
818C2×C4C2×C22⋊Dic4712yes—
819C2×C4C2×C22⋊Dic4712yes—
820C2×C4C23×Dic4711yescharacteristic
821C2×C4C2×D4×D4711yescharacteristic
822C2×C4C22×C22⋊D4711yescharacteristic
823C2×C4C2×#1062535211yescharacteristic
824C2×C4#1309406911yescharacteristic
825C2×C4#1309406911yescharacteristic
826C8—942no—
827C8—1881no—
828C8—1881no—
829C8—1881no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—24no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C22×C22⋊Dic4711yescharacteristic
860C22D4×C22⋊D4711yescharacteristic
861C22#1568976711yescharacteristic
862C22#1568992111yescharacteristic
863C22#1568992111yescharacteristic
864C22#1568992611yescharacteristic
865C22#1568993411yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—3761no—
873C4—3761no—
874C4—3761no—
875C4—1882no—
876C4C2×D4×Dic4711yescharacteristic
877C4#1568959811yescharacteristic
878C4D4×C22⋊D4711yescharacteristic
879C4#1568976711yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊Dic4711yescharacteristic
885C2#2025190711yescharacteristic
886C2#2025191411yescharacteristic
887C2#2025499511yescharacteristic
888C2#2025501511yescharacteristic
889C2#2025558911yescharacteristic
890C2#2025560411yescharacteristic
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#22427
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×#15689201C2semidirect
2. C2×#15689124C2semidirect
3. C2×#15689128C2semidirect
4. #20246317C2semidirect
5. #20244321C2semidirect
6. #20244200C2semidirect
7. #20243827C2semidirect
8. #20243822C2semidirect
9. #20243706C2semidirect
10. #20243701C2semidirect
11. #20243398C2semidirect
12. #20243328C2semidirect
13. #20243319C2semidirect
14. C4×#13093945C2semidirect
17. C22×#10625329C22semidirect
19. C22×C4⋊Dic47C22semidirect
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×C4×C47⋊C8C22semidirect
42. #15688989C22semidirect
44. #15688983C22semidirect
45. C4×C4⋊Dic47C22semidirect
47. #15688885C22semidirect
48. #15688885C22semidirect
49. #15688885C22semidirect
50. #15688885C22semidirect
54. C47×#546C4semidirect
101. #13093945D4semidirect
126. C22×D4×C47C2×C4semidirect
135. #124×C47C2×C4semidirect
138. C22⋊Q8×C47C2×C4semidirect
145. C4×D4×C47C2×C4semidirect
466. #546Dic47semidirect
509. C47#22427semidirect
526. C22×D4C2×Dic47semidirect
546. #124C2×Dic47semidirect
549. C22⋊Q8C2×Dic47semidirect
556. C4×D4C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156892012
C2×#156891242
C2×#156891282
#202463172
#202443212
#202442002
#202438272
#202438222
#202437062
#202437012
#202433982
#202433282
#202433192
C4×#130939452
C2×C47×#5462
#2242747