Finite Group Databasebeta

← #26222057

Subgroups — #26222057

Order 12032.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689262C211yesmaximal, characteristic
2C2×#15689221C211yesmaximal, characteristic, complemented
3C2×C4×#10625336C211yesmaximal, characteristic, complemented
4#20246081C211yesmaximal, characteristic
5#20243743C211yesmaximal, characteristic, complemented
6#20243743C211yesmaximal, characteristic, complemented
7#20243710C211yesmaximal, characteristic
8#20243656C211yesmaximal, characteristic, complemented
9#20243642C211yesmaximal, characteristic, complemented
10#20243587C211yesmaximal, characteristic, complemented
11#20243323C211yesmaximal, characteristic, complemented
12#20243218C211yesmaximal, characteristic, complemented
13C4×#13093948C211yesmaximal, characteristic, complemented
14#20243154C211yesmaximal, characteristic, complemented
15C2×C47×#519C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C22×#10625336C2211yescharacteristic
18C2×#13093998C2211yescharacteristic
19C2×C4×D188C2211yescharacteristic
20#15689262C418yescomplemented
21#15689221—24no—
22C4×#10625336—24no—
23C2×#13093957C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×#13093948C2211yescharacteristic
26C2×#13093948C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093948C2211yescharacteristic
31C2×#13093944C2211yescharacteristic
32C2×#13093944C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35C2×#13093935C2211yescharacteristic
36C2×C4×C47⋊C8C2211yescharacteristic
37#15689025C2211yescharacteristic
38#15689023—21no—
39#15689021C2211yescharacteristic
40#15689013—21no—
41#15688999—21no—
42#15688994—21no—
43#15688983C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51C23×Q8×C47C2211yescharacteristic
52C47×#519—24no—
53C47×#519—24no—
54C2×C4×Q8×C47—21no—
55C2×C4×Q8×C47—21no—
56C2×C4×Q8×C47C2211yescharacteristic
57C2×C4×Q8×C47C2211yescharacteristic
58C2×C4×Q8×C47C2211yescharacteristic
59C2×C4×Q8×C47C2211yescharacteristic
60C2×#117×C47—21no—
61C2×#117×C47—21no—
62C2×#117×C47C2211yescharacteristic
63C2×#117×C47C2211yescharacteristic
64C22×D188C2311yescharacteristic
65C22×C22⋊D47—21no—
66C22×C4×D47—21no—
67C2×#10625336—22no—
68C2×#10625336—22no—
69C2×#10625336—22no—
70C2×#10625336—22no—
71C2×#10625336C2×C414yes—
72C2×#10625336C2×C414yes—
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77#13093998—22no—
78#13093998C2×C414yes—
79C4×D188—22no—
80C4×D188—22no—
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×Dic47⋊C4—21no—
85C2×C22⋊Dic47—21no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4—21no—
90C2×C4×Dic47—21no—
91#13093957—22no—
92#13093955—22no—
93#13093948—22no—
94#13093948—22no—
95#13093948—22no—
96#13093948—22no—
97#13093948C2×C414yescomplemented
98#13093948C2×C414yescomplemented
99#13093944—22no—
100#13093944—22no—
101C22⋊(C47⋊C8)—22no—
102C22⋊(C47⋊C8)C2×C414yescomplemented
103#13093935—22no—
104C4×C47⋊C8—22no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C22×Q8×C47—22no—
109C22×Q8×C47—22no—
110C22×Q8×C47—22no—
111C22×Q8×C47—22no—
112C22×Q8×C47—21no—
113C22×Q8×C47—22no—
114C22×Q8×C47C2×C414yescomplemented
115C22×Q8×C47C2311yescharacteristic
116C22×Q8×C47C2311yescharacteristic
117C23×C4×C47—21no—
118C23×C4×C47C2311yescharacteristic
119C4×Q8×C47—28no—
120C4×Q8×C47—28no—
121C4×Q8×C47—22no—
122C4×Q8×C47—22no—
123C4×Q8×C47—22no—
124C4×Q8×C47—22no—
125C4×Q8×C47—22no—
126C4×Q8×C47—22no—
127C4×Q8×C47D414yescomplemented
128C4×Q8×C47D414yescomplemented
129#117×C47—28no—
130#117×C47—28no—
131#117×C47—22no—
132#117×C47—22no—
133#117×C47—22no—
134#117×C47—22no—
135C2×C4⋊C4×C47—21no—
136C2×C4⋊C4×C47—21no—
137C2×C4⋊C4×C47—21no—
138C2×C4⋊C4×C47—21no—
139C2×C4⋊C4×C47D411yescharacteristic
140C2×C4⋊C4×C47D411yescharacteristic
141C2×C4⋊C4×C47C2311yescharacteristic
142C2×C4⋊C4×C47C2311yescharacteristic
143C2×C22⋊C4×C47—21no—
144C2×C22⋊C4×C47D411yescharacteristic
145C2×C22⋊C4×C47D411yescharacteristic
146C2×C42×C47—21no—
147C2×C42×C47—21no—
148C2×C42×C47—21no—
149C2×C42×C47—21no—
150C2×C42×C47—21no—
151C2×C42×C47C2311yescharacteristic
152C2×C42×C47C2311yescharacteristic
153C24×C47C2×D411yescharacteristic
154C23×D47—21no—
155C2×Q8×C47—24no—
156C2×Q8×C47—28no—
157C2×Q8×C47—28no—
158C2×Q8×C47—24no—
159C2×Q8×C47—28no—
160C2×Q8×C47—28no—
161C2×Q8×C47—24no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47C22×C412yes—
169C2×Q8×C47C22×C412yes—
170C2×Q8×C47C2×D412yes—
171C2×Q8×C47C2×D412yes—
172C2×Q8×C47#4112yes—
173C2×Q8×C47#4112yes—
174C22×C4×C47—24no—
175C22×C4×C47—24no—
176C22×C4×C47—24no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47C22×C412yes—
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47#4112yes—
192C22×C4×C47C2411yescharacteristic
193C2×C22⋊D47—24no—
194C2×C22⋊D47—81no—
195C2×C22⋊D47—81no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C2×D188—21no—
200C2×D188—21no—
201C2×D188—21no—
202C2×D188—21no—
203C2×D188—21no—
204C2×D188C22×C412yes—
205C2×C4×D47—42no—
206C2×C4×D47—81no—
207C2×C4×D47—81no—
208C4⋊C4×C47—24no—
209C4⋊C4×C47—24no—
210C4⋊C4×C47—24no—
211C4⋊C4×C47—24no—
212C4⋊C4×C47—22no—
213C4⋊C4×C47—22no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47C2×D412yes—
217C4⋊C4×C47C2×D412yes—
218C22⋊C4×C47—24no—
219C22⋊C4×C47—22no—
220C22⋊C4×C47—22no—
221C42×C47—24no—
222C42×C47—24no—
223C42×C47—24no—
224C42×C47—24no—
225C42×C47—24no—
226C42×C47—21no—
227C42×C47—21no—
228C42×C47C2×D412yes—
229C42×C47C2×D412yes—
230C22⋊Dic47—81no—
231#10625336—28no—
232#10625336—28no—
233(C2×D47)⋊C4—24no—
234(C2×D47)⋊C4—42no—
235(C2×D47)⋊C4—81no—
236(C2×D47)⋊C4—81no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—21no—
241C4⋊Dic47—21no—
242C4⋊Dic47C22×C412yes—
243Dic47⋊C4—81no—
244C4×Dic47—81no—
245C2×C47⋊C8—21no—
246C2×C47⋊C8—21no—
247C2×C47⋊C8—21no—
248C2×C47⋊C8—21no—
249C2×C47⋊C8—21no—
250C2×C47⋊C8—21no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8C22×C412yes—
256C2×C47⋊C8C22×C412yes—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47C4×D412yes—
264C23×C47C22×D411yescharacteristic
265C22×D47—22no—
266C22×D47—41no—
267C22×D47—41no—
268C22×D47—41no—
269C22×D47—41no—
270C22×D47—41no—
271C22×D47—41no—
272Q8×C47—216no—
273Q8×C47—22no—
274Q8×C47—22no—
275Q8×C47—22no—
276Q8×C47—22no—
277Q8×C47—22no—
278Q8×C47—22no—
279Q8×C47C4×D414yes—
280Q8×C47C4×D414yes—
281C2×C4×C47—216no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—21no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47C4×D412yes—
311C2×C4×C47#12012yes—
312C2×C4×C47#12012yes—
313C2×C4×C47C23×C411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4111yescharacteristic
317C2×C4×C47C2×#4111yescharacteristic
318C2×C4×C47C2×#4111yescharacteristic
319C22⋊D47—84no—
320C2×Dic47—22no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329D188—22no—
330D188—22no—
331D188—41no—
332D188—41no—
333C4×D47—84no—
334C47⋊C8—22no—
335C47⋊C8—22no—
336C47⋊C8—41no—
337C47⋊C8—41no—
338#21462—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47C2×C4×D411yescharacteristic
347C22×C47C2×#12011yescharacteristic
348C22×C47#52511yescharacteristic
349C22×C47#57711yescharacteristic
350C22×C47#57711yescharacteristic
351C22×C47#57711yescharacteristic
352C22×C47#57811yescharacteristic
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—81no—
357C2×D47—81no—
358C2×D47—81no—
359C2×D47—81no—
360C4×C47—22no—
361C4×C47—22no—
362C4×C47—24no—
363C4×C47—24no—
364C4×C47—22no—
365C4×C47—41no—
366C4×C47—42no—
367C4×C47—41no—
368C4×C47—42no—
369C4×C47C2×C4×D411yescharacteristic
370C4×C47C2×C4×D411yescharacteristic
371C4×C47#52511yescharacteristic
372C4×C47#52511yescharacteristic
373Dic47—42no—
374Dic47—81no—
375Dic47—81no—
376C2×#519D4711yescharacteristic, complemented
377C2×#448—471no—
378C2×#440—471no—
379C2×C4×SD16—471no—
380#2324—471no—
381#1880—471no—
382#1880—471no—
383#1875—471no—
384#1865—471no—
385#1863—471no—
386#1854—471no—
387#1787—471no—
388#1763—471no—
389C4×#103—471no—
390#1750—471no—
391C2×C47—42no—
392C2×C47C4×#12011yescharacteristic
393C2×C47#294711yescharacteristic
394C2×C47#294911yescharacteristic
395C2×C47#301011yescharacteristic
396C2×C47#301311yescharacteristic
397C2×C47#312111yescharacteristic
398C2×C47#312611yescharacteristic
399D47—82no—
400C23×Q8C2×D4711yescharacteristic
401C22×SD16—471no—
402C22×SD16—471no—
403C2×#121—471no—
404#519—24no—
405#519—24no—
406C2×C4×Q8—21no—
407C2×C4×Q8—21no—
408C2×C4×Q8C2×D4711yescharacteristic
409C2×C4×Q8C2×D4711yescharacteristic
410C2×C4×Q8C2×D4711yescharacteristic
411C2×C4×Q8C2×D4711yescharacteristic
412C2×C4×D4—471no—
413C2×#117—21no—
414C2×#117—21no—
415C2×#117C2×D4711yescharacteristic
416C2×#117C2×D4711yescharacteristic
417#448—478no—
418#440—944no—
419C4×SD16—944no—
420C2×#107—471no—
421C2×#106—471no—
422C2×#103—471no—
423C2×#103—471no—
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#102—471no—
429C2×#102—471no—
430C2×C22⋊C8—471no—
431C2×C22⋊C8—471no—
432C2×#97—471no—
433C2×C4×C8—471no—
434#390—471no—
435#390—941no—
436#389—471no—
437#388—941no—
438#386—941no—
439#385—941no—
440#380—471no—
441C4×C4⋊C4—471no—
442#340—471no—
443#340—471no—
444#340—471no—
445#340—471no—
446#336—471no—
447#336—471no—
448C47#2146211yescharacteristic, complemented, Sylow
449C22×Q8—22no—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—21no—
455C22×Q8C4×D4714yescomplemented
456C22×Q8C22×D4711yescharacteristic
457C22×Q8C22×D4711yescharacteristic
458C22×D4—471no—
459C22×D4—941no—
460C23×C4—21no—
461C23×C4—941no—
462C23×C4C22×D4711yescharacteristic
463C2×SD16—474no—
464C2×SD16—474no—
465C2×SD16—942no—
466C2×SD16—942no—
467C2×SD16—942no—
468C2×SD16—942no—
469C22×C8—471no—
470C22×C8—471no—
471C22×C8—471no—
472C22×C8—471no—
473#121—474no—
474#121—942no—
475C4×Q8—28no—
476C4×Q8—28no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8C22⋊D4714yescomplemented
484C4×Q8C22⋊D4714yescomplemented
485C4×D4—942no—
486C4×D4—942no—
487#117—28no—
488#117—28no—
489#117—22no—
490#117—22no—
491#117—22no—
492#117—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—471no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4C22⋊D4711yescharacteristic
502C2×C4⋊C4C22⋊D4711yescharacteristic
503C2×C4⋊C4C22×D4711yescharacteristic
504C2×C4⋊C4C22×D4711yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—941no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4C22⋊D4711yescharacteristic
512C2×C22⋊C4C22⋊D4711yescharacteristic
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—941no—
519C2×C42C22×D4711yescharacteristic
520C2×C42C22×D4711yescharacteristic
521#107—942no—
522#106—942no—
523#103—474no—
524#103—474no—
525#103—942no—
526#103—942no—
527#103—942no—
528#103—942no—
529#102—942no—
530#102—942no—
531C22⋊C8—474no—
532C22⋊C8—942no—
533#97—942no—
534C4×C8—942no—
535#95—941no—
536#95—941no—
537#95—941no—
538C24—941no—
539C24C2×C22⋊D4711yescharacteristic
540C2×Q8—24no—
541C2×Q8—28no—
542C2×Q8—28no—
543C2×Q8—24no—
544C2×Q8—28no—
545C2×Q8—28no—
546C2×Q8—24no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C2×C4×D4712yes—
554C2×Q8C2×C4×D4712yes—
555C2×Q8#1062535012yes—
556C2×Q8#1062535012yes—
557C2×Q8C2×C22⋊D4712yes—
558C2×Q8C2×C22⋊D4712yes—
559C2×D4—472no—
560C2×D4—944no—
561C2×D4—941no—
562C2×D4—941no—
563C2×D4—941no—
564C2×D4—941no—
565C2×D4—941no—
566C2×D4—3761no—
567C2×D4—3761no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—3761no—
583C22×C4—3761no—
584C22×C4—1882no—
585C22×C4C2×C4×D4712yes—
586C22×C4#1062535012yes—
587C22×C4C2×C22⋊D4711yescharacteristic
588C22×C4C2×C22⋊D4711yescharacteristic
589C22×C4C2×C22⋊D4711yescharacteristic
590C22×C4C2×C22⋊D4711yescharacteristic
591C22×C4C2×C22⋊D4711yescharacteristic
592C22×C4C23×D4711yescharacteristic
593SD16—948no—
594SD16—948no—
595C2×C8—472no—
596C2×C8—472no—
597C2×C8—941no—
598C2×C8—941no—
599C2×C8—941no—
600C2×C8—941no—
601C2×C8—941no—
602C2×C8—941no—
603C2×C8—941no—
604C2×C8—941no—
605C2×C8—941no—
606C2×C8—941no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—472no—
616C4⋊C4—941no—
617C4⋊C4—941no—
618C4⋊C4—941no—
619C4⋊C4—941no—
620C4⋊C4—941no—
621C4⋊C4—3761no—
622C4⋊C4C2×C22⋊D4712yes—
623C4⋊C4C2×C22⋊D4712yes—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—944no—
628C22⋊C4—3761no—
629C22⋊C4—3761no—
630C22⋊C4—3761no—
631C22⋊C4—1882no—
632C42—24no—
633C42—24no—
634C42—24no—
635C42—24no—
636C42—24no—
637C42—21no—
638C42—21no—
639C42—3761no—
640C42C2×C22⋊D4712yes—
641C42C2×C22⋊D4712yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—942no—
649C23—1881no—
650C23—1881no—
651C23—1881no—
652C23—1881no—
653C23—1881no—
654C23—1881no—
655C23C4×C22⋊D4712yes—
656C23C22×C22⋊D4711yescharacteristic
657Q8—216no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8C4×C22⋊D4714yes—
665Q8C4×C22⋊D4714yes—
666D4—942no—
667D4—942no—
668D4—3764no—
669D4—1881no—
670D4—1881no—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—942no—
701C2×C4—3764no—
702C2×C4—1881no—
703C2×C4—1881no—
704C2×C4—1881no—
705C2×C4—1881no—
706C2×C4—1881no—
707C2×C4—1881no—
708C2×C4—1881no—
709C2×C4—1881no—
710C2×C4C4×C22⋊D4712yes—
711C2×C4#1309399312yes—
712C2×C4#1309399312yes—
713C2×C4C22×C4×D4711yescharacteristic
714C2×C4C22×C22⋊D4711yescharacteristic
715C2×C4C22×C22⋊D4711yescharacteristic
716C2×C4C2×#1062535011yescharacteristic
717C2×C4C2×#1062535011yescharacteristic
718C2×C4C2×#1062535011yescharacteristic
719C8—942no—
720C8—942no—
721C8—1881no—
722C8—1881no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—3761no—
731C22—3761no—
732C22—3761no—
733C22—3761no—
734C22—1882no—
735C22—1882no—
736C22—1882no—
737C22C2×C4×C22⋊D4711yescharacteristic
738C22C2×#1309399311yescharacteristic
739C22#1568963411yescharacteristic
740C22#1568993111yescharacteristic
741C22#1568993111yescharacteristic
742C22#1568993111yescharacteristic
743C22#1568993811yescharacteristic
744C4—22no—
745C4—22no—
746C4—24no—
747C4—24no—
748C4—22no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—42no—
753C4—3761no—
754C4—3761no—
755C4—1882no—
756C4C2×C4×C22⋊D4711yescharacteristic
757C4C2×C4×C22⋊D4711yescharacteristic
758C4#1568963411yescharacteristic
759C4#1568963411yescharacteristic
760C2—42no—
761C2—3762no—
762C2C4×#1309399311yescharacteristic
763C2#2025223111yescharacteristic
764C2#2025224711yescharacteristic
765C2#2025267411yescharacteristic
766C2#2025270311yescharacteristic
767C2#2025361711yescharacteristic
768C2#2025367911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#519C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenterC2×#519D47
hypocenterC47#21462
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#15689221C2semidirect
3. C2×C4×#10625336C2semidirect
5. #20243743C2semidirect
6. #20243743C2semidirect
8. #20243656C2semidirect
9. #20243642C2semidirect
10. #20243587C2semidirect
11. #20243323C2semidirect
12. #20243218C2semidirect
13. C4×#13093948C2semidirect
14. #20243154C2semidirect
15. C2×C47×#519C2semidirect
20. #15689262C4semidirect
97. #13093948C2×C4semidirect
98. #13093948C2×C4semidirect
102. C22⋊(C47⋊C8)C2×C4semidirect
114. C22×Q8×C47C2×C4semidirect
127. C4×Q8×C47D4semidirect
128. C4×Q8×C47D4semidirect
376. C2×#519D47semidirect
448. C47#21462semidirect
455. C22×Q8C4×D47semidirect
483. C4×Q8C22⋊D47semidirect
484. C4×Q8C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156892622
C2×#156892212
C2×C4×#106253362
#202460812
#202437432
#202437102
#202436562
#202436422
#202435872
#202433232
#202432182
C4×#130939482
#202431542
C2×C47×#5192
#2146247