Finite Group Databasebeta

← #26222027

Subgroups — #26222027

Order 12032.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689268C211yesmaximal, characteristic
2C2×#15689221C211yesmaximal, characteristic, complemented
3C2×C4×#10625334C211yesmaximal, characteristic, complemented
4#20246081C211yesmaximal, characteristic, complemented
5#20243743C211yesmaximal, characteristic, complemented
6#20243736C211yesmaximal, characteristic, complemented
7#20243705C211yesmaximal, characteristic, complemented
8#20243642C211yesmaximal, characteristic, complemented
9#20243635C211yesmaximal, characteristic, complemented
10#20243576C211yesmaximal, characteristic, complemented
11#20243328C211yesmaximal, characteristic, complemented
12#20243213C211yesmaximal, characteristic, complemented
13C4×#13093948C211yesmaximal, characteristic, complemented
14#20243154C211yesmaximal, characteristic, complemented
15C2×C47×#520C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C22×#10625334C2211yescharacteristic
18C2×#13093998C2211yescharacteristic
19C2×C4×D188C2211yescharacteristic
20#15689268C418yescomplemented
21#15689221—24no—
22C4×#10625334—24no—
23C2×#13093957C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×#13093948C2211yescharacteristic
26C2×#13093948C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
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
51C22×#41×C47C2211yescharacteristic
52C47×#520—24no—
53C47×#520—24no—
54C2×C4×Q8×C47C2211yescharacteristic
55C2×C4×Q8×C47C2211yescharacteristic
56C2×C4×D4×C47—21no—
57C2×C4×D4×C47—21no—
58C2×C4×D4×C47C2211yescharacteristic
59C2×C4×D4×C47C2211yescharacteristic
60C2×#117×C47—21no—
61C2×#117×C47C2211yescharacteristic
62C22×C4⋊C4×C47—21no—
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×D188C2311yescharacteristic
65C22×C22⋊D47—21no—
66C22×C4×D47—21no—
67C2×#10625336—22no—
68C2×#10625336—22no—
69C2×#10625336C2×C414yescomplemented
70C2×#10625334—22no—
71C2×#10625334—22no—
72C2×#10625334C2×C414yescomplemented
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77#13093998—22no—
78#13093998C2×C414yescomplemented
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#13093957—22no—
93#13093948—22no—
94#13093948—22no—
95#13093948C2×C414yescomplemented
96#13093945—22no—
97#13093945—22no—
98#13093945C2×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—
108C2×#41×C47—22no—
109C2×#41×C47—22no—
110C2×#41×C47—22no—
111C2×#41×C47—22no—
112C2×#41×C47—22no—
113C2×#41×C47C2×C414yescomplemented
114C22×Q8×C47C2311yescharacteristic
115C22×D4×C47—21no—
116C22×D4×C47C2311yescharacteristic
117C23×C4×C47—21no—
118C23×C4×C47—21no—
119C23×C4×C47—21no—
120C23×C4×C47—21no—
121C23×C4×C47C2311yescharacteristic
122C4×Q8×C47—22no—
123C4×Q8×C47—22no—
124C4×Q8×C47—22no—
125C4×Q8×C47D414yescomplemented
126C4×D4×C47—28no—
127C4×D4×C47—28no—
128C4×D4×C47—22no—
129C4×D4×C47—22no—
130C4×D4×C47—22no—
131C4×D4×C47D414yescomplemented
132#117×C47—28no—
133#117×C47—22no—
134#117×C47—22no—
135C2×C4⋊C4×C47—28no—
136C2×C4⋊C4×C47—21no—
137C2×C4⋊C4×C47—21no—
138C2×C4⋊C4×C47—21no—
139C2×C4⋊C4×C47—22no—
140C2×C4⋊C4×C47—22no—
141C2×C4⋊C4×C47D411yescharacteristic
142C2×C4⋊C4×C47D411yescharacteristic
143C2×C4⋊C4×C47C2311yescharacteristic
144C2×C4⋊C4×C47C2311yescharacteristic
145C2×C22⋊C4×C47—21no—
146C2×C22⋊C4×C47—21no—
147C2×C22⋊C4×C47D411yescharacteristic
148C2×C22⋊C4×C47D411yescharacteristic
149C2×C42×C47—21no—
150C2×C42×C47—21no—
151C2×C42×C47C2311yescharacteristic
152C2×C42×C47C2311yescharacteristic
153C24×C47—21no—
154C24×C47C2×D411yescharacteristic
155C23×D47—21no—
156#41×C47—28no—
157#41×C47—28no—
158#41×C47—28no—
159#41×C47—28no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47C22×C412yes—
164C2×Q8×C47C2×D412yes—
165C2×Q8×C47#4112yes—
166C2×D4×C47—24no—
167C2×D4×C47—24no—
168C2×D4×C47—24no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47C22×C412yes—
173C2×D4×C47C2×D412yes—
174C2×D4×C47#4112yes—
175C22×C4×C47—24no—
176C22×C4×C47—24no—
177C22×C4×C47—21no—
178C22×C4×C47—24no—
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×C47—24no—
186C22×C4×C47—24no—
187C22×C4×C47—24no—
188C22×C4×C47—81no—
189C22×C4×C47—81no—
190C22×C4×C47—81no—
191C22×C4×C47—81no—
192C22×C4×C47—81no—
193C22×C4×C47—81no—
194C22×C4×C47C22×C412yes—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47#4112yes—
201C22×C4×C47C2411yescharacteristic
202C2×C22⋊D47—24no—
203C2×C22⋊D47—81no—
204C2×C22⋊D47—81no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C2×D188—21no—
209C2×D188—21no—
210C2×D188—21no—
211C2×D188—21no—
212C2×D188—21no—
213C2×D188C22×C412yes—
214C2×C4×D47—42no—
215C2×C4×D47—81no—
216C2×C4×D47—81no—
217C4⋊C4×C47—24no—
218C4⋊C4×C47—24no—
219C4⋊C4×C47—22no—
220C4⋊C4×C47—24no—
221C4⋊C4×C47—22no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47C2×D412yes—
225C4⋊C4×C47C2×D412yes—
226C22⋊C4×C47—24no—
227C22⋊C4×C47—24no—
228C22⋊C4×C47—22no—
229C22⋊C4×C47—22no—
230C42×C47—24no—
231C42×C47—24no—
232C42×C47—21no—
233C42×C47—21no—
234C42×C47C2×D412yes—
235C42×C47C2×D412yes—
236C22⋊Dic47—81no—
237#10625336—28no—
238#10625334—28no—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4—42no—
241(C2×D47)⋊C4—81no—
242(C2×D47)⋊C4—81no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47C22×C412yes—
249Dic47⋊C4—81no—
250C4×Dic47—81no—
251C2×C47⋊C8—21no—
252C2×C47⋊C8—21no—
253C2×C47⋊C8—21no—
254C2×C47⋊C8—21no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—21no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8C22×C412yes—
262C2×C47⋊C8C22×C412yes—
263C23×C47—22no—
264C23×C47—21no—
265C23×C47—22no—
266C23×C47—21no—
267C23×C47—22no—
268C23×C47—21no—
269C23×C47—21no—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47C4×D412yes—
277C23×C47C22×D411yescharacteristic
278C22×D47—22no—
279C22×D47—41no—
280C22×D47—41no—
281C22×D47—41no—
282C22×D47—41no—
283C22×D47—41no—
284C22×D47—41no—
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47C4×D414yes—
289D4×C47—216no—
290D4×C47—22no—
291D4×C47—22no—
292D4×C47—22no—
293D4×C47C4×D414yes—
294C2×C4×C47—216no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—22no—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—21no—
313C2×C4×C47—21no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—84no—
321C2×C4×C47—84no—
322C2×C4×C47—84no—
323C2×C4×C47C4×D412yes—
324C2×C4×C47#12012yes—
325C2×C4×C47#12012yes—
326C2×C4×C47C23×C411yescharacteristic
327C2×C4×C47C22×D411yescharacteristic
328C2×C4×C47C22×D411yescharacteristic
329C2×C4×C47C2×#4111yescharacteristic
330C2×C4×C47C2×#4111yescharacteristic
331C2×C4×C47C2×#4111yescharacteristic
332C22⋊D47—84no—
333C2×Dic47—22no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342D188—22no—
343D188—22no—
344D188—41no—
345D188—41no—
346C4×D47—84no—
347C47⋊C8—22no—
348C47⋊C8—22no—
349C47⋊C8—41no—
350C47⋊C8—41no—
351#21460—471nomaximal, Sylow
352C22×C47—22no—
353C22×C47—22no—
354C22×C47—22no—
355C22×C47—24no—
356C22×C47—41no—
357C22×C47—42no—
358C22×C47—41no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—41no—
363C22×C47—42no—
364C22×C47—41no—
365C22×C47—42no—
366C22×C47C2×C4×D411yescharacteristic
367C22×C47C2×#12011yescharacteristic
368C22×C47#52511yescharacteristic
369C22×C47#57611yescharacteristic
370C22×C47#57611yescharacteristic
371C22×C47#57711yescharacteristic
372C22×C47#57811yescharacteristic
373C2×D47—42no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—81no—
377C2×D47—81no—
378C2×D47—81no—
379C2×D47—81no—
380C4×C47—22no—
381C4×C47—22no—
382C4×C47—22no—
383C4×C47—24no—
384C4×C47—41no—
385C4×C47—42no—
386C4×C47—42no—
387C4×C47—41no—
388C4×C47C2×C4×D411yescharacteristic
389C4×C47C2×C4×D411yescharacteristic
390C4×C47#52511yescharacteristic
391C4×C47#52511yescharacteristic
392Dic47—42no—
393Dic47—81no—
394Dic47—81no—
395C2×#520D4711yescharacteristic, complemented
396C2×#449—471no—
397C2×#440—471no—
398C2×C4×D8—471no—
399#2324—471no—
400#1880—471no—
401#1879—471no—
402#1874—471no—
403#1863—471no—
404#1862—471no—
405#1852—471no—
406#1788—471no—
407#1762—471no—
408C4×#103—471no—
409#1750—471no—
410C2×C47—42no—
411C2×C47—44no—
412C2×C47C4×#12011yescharacteristic
413C2×C47#294611yescharacteristic
414C2×C47#295111yescharacteristic
415C2×C47#300811yescharacteristic
416C2×C47#301311yescharacteristic
417C2×C47#311911yescharacteristic
418C2×C47#312411yescharacteristic
419D47—82no—
420C22×#41C2×D4711yescharacteristic
421C22×SD16—471no—
422C22×D8—471no—
423C2×#121—471no—
424#520—24no—
425#520—24no—
426C2×C4×Q8C2×D4711yescharacteristic
427C2×C4×Q8C2×D4711yescharacteristic
428C2×C4×D4—21no—
429C2×C4×D4—21no—
430C2×C4×D4—471no—
431C2×C4×D4C2×D4711yescharacteristic
432C2×C4×D4C2×D4711yescharacteristic
433C2×#117—21no—
434C2×#117C2×D4711yescharacteristic
435C22×C4⋊C4—21no—
436C22×C4⋊C4C2×D4711yescharacteristic
437#449—478no—
438#440—944no—
439C4×D8—944no—
440C2×#107—471no—
441C2×#107—471no—
442C2×#103—471no—
443C2×#103—471no—
444C2×#103—471no—
445C2×#102—471no—
446C2×#102—471no—
447C2×#102—471no—
448C2×#102—471no—
449C2×#102—471no—
450C2×C22⋊C8—471no—
451C2×C22⋊C8—471no—
452C2×#97—471no—
453C2×C4×C8—471no—
454#390—471no—
455#390—941no—
456#389—471no—
457#388—941no—
458#386—941no—
459#385—941no—
460#380—471no—
461C4×C4⋊C4—471no—
462#340—471no—
463#340—471no—
464#340—471no—
465#340—471no—
466#336—471no—
467#336—471no—
468C47#2146011yescharacteristic, complemented, Sylow
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41C4×D4714yescomplemented
475C22×Q8C22×D4711yescharacteristic
476C22×D4—21no—
477C22×D4—471no—
478C22×D4—941no—
479C22×D4C22×D4711yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—941no—
485C23×C4C22×D4711yescharacteristic
486C2×SD16—474no—
487C2×SD16—942no—
488C2×SD16—942no—
489C2×D8—474no—
490C2×D8—942no—
491C2×D8—942no—
492C22×C8—471no—
493C22×C8—471no—
494C22×C8—471no—
495C22×C8—471no—
496#121—474no—
497#121—942no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8C22⋊D4714yescomplemented
502C4×D4—28no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—942no—
508C4×D4—942no—
509C4×D4C22⋊D4714yescomplemented
510#117—28no—
511#117—22no—
512#117—22no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4C22⋊D4711yescharacteristic
524C2×C4⋊C4C22⋊D4711yescharacteristic
525C2×C4⋊C4C22×D4711yescharacteristic
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4C22⋊D4711yescharacteristic
535C2×C22⋊C4C22⋊D4711yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—941no—
539C2×C42C22×D4711yescharacteristic
540C2×C42C22×D4711yescharacteristic
541#107—942no—
542#107—942no—
543#103—474no—
544#103—942no—
545#103—942no—
546#102—474no—
547#102—942no—
548#102—942no—
549#102—942no—
550#102—942no—
551C22⋊C8—474no—
552C22⋊C8—942no—
553#97—942no—
554C4×C8—942no—
555#95—941no—
556#95—941no—
557#95—941no—
558C24—21no—
559C24—941no—
560C24C2×C22⋊D4711yescharacteristic
561#41—28no—
562#41—28no—
563#41—28no—
564#41—28no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8C2×C4×D4712yes—
569C2×Q8#1062535012yes—
570C2×Q8C2×C22⋊D4712yes—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—472no—
578C2×D4—944no—
579C2×D4—941no—
580C2×D4—941no—
581C2×D4—941no—
582C2×D4—941no—
583C2×D4—941no—
584C2×D4—3761no—
585C2×D4—3761no—
586C2×D4C2×C4×D4712yes—
587C2×D4#1062535012yes—
588C2×D4C2×C22⋊D4712yes—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—3761no—
612C22×C4—3761no—
613C22×C4—1882no—
614C22×C4C2×C4×D4712yes—
615C22×C4#1062535012yes—
616C22×C4C2×C22⋊D4711yescharacteristic
617C22×C4C2×C22⋊D4711yescharacteristic
618C22×C4C2×C22⋊D4711yescharacteristic
619C22×C4C2×C22⋊D4711yescharacteristic
620C22×C4C2×C22⋊D4711yescharacteristic
621C22×C4C23×D4711yescharacteristic
622SD16—948no—
623D8—948no—
624C2×C8—472no—
625C2×C8—472no—
626C2×C8—941no—
627C2×C8—941no—
628C2×C8—941no—
629C2×C8—941no—
630C2×C8—941no—
631C2×C8—941no—
632C2×C8—941no—
633C2×C8—941no—
634C2×C8—941no—
635C2×C8—941no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—472no—
644C4⋊C4—941no—
645C4⋊C4—941no—
646C4⋊C4—941no—
647C4⋊C4—941no—
648C4⋊C4—941no—
649C4⋊C4—3761no—
650C4⋊C4C2×C22⋊D4712yes—
651C4⋊C4C2×C22⋊D4712yes—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—944no—
657C22⋊C4—3761no—
658C22⋊C4—3761no—
659C22⋊C4—3761no—
660C22⋊C4—1882no—
661C42—24no—
662C42—24no—
663C42—21no—
664C42—21no—
665C42—3761no—
666C42C2×C22⋊D4712yes—
667C42C2×C22⋊D4712yes—
668C23—22no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—942no—
682C23—1881no—
683C23—1881no—
684C23—1881no—
685C23—1881no—
686C23—1881no—
687C23—1881no—
688C23C4×C22⋊D4712yes—
689C23C22×C22⋊D4711yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8C4×C22⋊D4714yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—942no—
699D4—942no—
700D4—3764no—
701D4—1881no—
702D4—1881no—
703D4C4×C22⋊D4714yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—942no—
734C2×C4—3764no—
735C2×C4—1881no—
736C2×C4—1881no—
737C2×C4—1881no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1881no—
741C2×C4—1881no—
742C2×C4—1881no—
743C2×C4C4×C22⋊D4712yes—
744C2×C4#1309399312yes—
745C2×C4#1309399312yes—
746C2×C4C22×C4×D4711yescharacteristic
747C2×C4C22×C22⋊D4711yescharacteristic
748C2×C4C22×C22⋊D4711yescharacteristic
749C2×C4C2×#1062535011yescharacteristic
750C2×C4C2×#1062535011yescharacteristic
751C2×C4C2×#1062535011yescharacteristic
752C8—942no—
753C8—942no—
754C8—1881no—
755C8—1881no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—3761no—
771C22—3761no—
772C22—3761no—
773C22—3761no—
774C22—1882no—
775C22—1882no—
776C22—1882no—
777C22C2×C4×C22⋊D4711yescharacteristic
778C22C2×#1309399311yescharacteristic
779C22#1568963411yescharacteristic
780C22#1568992611yescharacteristic
781C22#1568992611yescharacteristic
782C22#1568993111yescharacteristic
783C22#1568993811yescharacteristic
784C4—22no—
785C4—22no—
786C4—24no—
787C4—22no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—42no—
792C4—3761no—
793C4—3761no—
794C4—1882no—
795C4C2×C4×C22⋊D4711yescharacteristic
796C4C2×C4×C22⋊D4711yescharacteristic
797C4#1568963411yescharacteristic
798C4#1568963411yescharacteristic
799C2—42no—
800C2—44no—
801C2—3762no—
802C2C4×#1309399311yescharacteristic
803C2#2025221611yescharacteristic
804C2#2025226111yescharacteristic
805C2#2025265611yescharacteristic
806C2#2025270311yescharacteristic
807C2#2025358711yescharacteristic
808C2#2025365011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#520C2
socleC23×C47C22×D4
prime radicalC2×#15689268C2
cosocleC22×C4×C47C24
hypercenterC2×#520D47
hypocenterC47#21460
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#15689221C2semidirect
3. C2×C4×#10625334C2semidirect
4. #20246081C2semidirect
5. #20243743C2semidirect
6. #20243736C2semidirect
7. #20243705C2semidirect
8. #20243642C2semidirect
9. #20243635C2semidirect
10. #20243576C2semidirect
11. #20243328C2semidirect
12. #20243213C2semidirect
13. C4×#13093948C2semidirect
14. #20243154C2semidirect
15. C2×C47×#520C2semidirect
20. #15689268C4semidirect
69. C2×#10625336C2×C4semidirect
72. C2×#10625334C2×C4semidirect
78. #13093998C2×C4semidirect
95. #13093948C2×C4semidirect
98. #13093945C2×C4semidirect
102. C22⋊(C47⋊C8)C2×C4semidirect
113. C2×#41×C47C2×C4semidirect
125. C4×Q8×C47D4semidirect
131. C4×D4×C47D4semidirect
395. C2×#520D47semidirect
468. C47#21460semidirect
474. C2×#41C4×D47semidirect
501. C4×Q8C22⋊D47semidirect
509. C4×D4C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156892682
C2×#156892212
C2×C4×#106253342
#202460812
#202437432
#202437362
#202437052
#202436422
#202436352
#202435762
#202433282
#202432132
C4×#130939482
#202431542
C2×C47×#5202
#2146047