Finite Group Databasebeta

← #26121667

Subgroups — #26121667

Order 12032.

1522 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689596C211yesmaximal, characteristic
2C22×#13093938C211yesmaximal, characteristic
3#20245963C211yesmaximal, characteristic
4C2×#15688890C211yesmaximal, characteristic, complemented
5C2×#15688890C211yesmaximal, characteristic, complemented
6C2×#15688889C211yesmaximal, characteristic, complemented
7C2×C47×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D47C2211yescharacteristic
9#15689596—22no—
10#15689596—22no—
11#15689596—22no—
12#15689596C414yescomplemented
13C2×C4×C22⋊D47—22no—
14C2×(C22⋊D47)⋊C4—22no—
15C2×#13093980—21no—
16C22×C22⋊Dic47C2211yescharacteristic
17C22×C22⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2211yescharacteristic
19C2×C22⋊C4×D47—21no—
20C2×#13093938—22no—
21C2×#13093938—22no—
22C2×#13093938C414yescomplemented
23#15689002C414yescomplemented
24#15689000—22no—
25#15688984—21no—
26#15688978—21no—
27#15688890—22no—
28#15688890—22no—
29#15688889—22no—
30C22×C22⋊C4×C47C2211yescharacteristic
31C22×C22⋊C4×C47C2211yescharacteristic
32C22×C22⋊C4×C47C2211yescharacteristic
33C47×#342—22no—
34C24×D47D411yescharacteristic
35C22×C22⋊D47—21no—
36C22×C22⋊D47—21no—
37C22×C22⋊D47—21no—
38C22×C22⋊D47—21no—
39C22×C22⋊D47—21no—
40C22×C22⋊D47—21no—
41C22×C22⋊D47—21no—
42C22×C22⋊D47—21no—
43C22×C22⋊D47C2×C412yes—
44C22×C22⋊D47C2×C412yes—
45C22×C22⋊D47C2×C412yes—
46C22×C22⋊D47D412yes—
47C22×C22⋊D47D412yes—
48C22×C22⋊D47Q812yes—
49C23×Dic47—21no—
50C23×Dic47—21no—
51C23×Dic47—21no—
52C23×Dic47D411yescharacteristic
53C22×C4×D47—22no—
54C4×C22⋊D47—28no—
55C4×C22⋊D47—28no—
56(C22⋊D47)⋊C4—28no—
57(C22⋊D47)⋊C4—28no—
58#13093980—24no—
59#13093980—24no—
60C2×Dic47⋊C4—22no—
61C2×C22⋊Dic47—21no—
62C2×C22⋊Dic47—21no—
63C2×C22⋊Dic47—21no—
64C2×C22⋊Dic47—21no—
65C2×C22⋊Dic47—21no—
66C2×C22⋊Dic47—21no—
67C2×C22⋊Dic47—21no—
68C2×C22⋊Dic47—21no—
69C2×C22⋊Dic47—21no—
70C2×C22⋊Dic47—21no—
71C2×C22⋊Dic47—21no—
72C2×C22⋊Dic47—21no—
73C2×C22⋊Dic47—21no—
74C2×C22⋊Dic47C2×C412yes—
75C2×C22⋊Dic47C2×C412yescomplemented
76C2×C22⋊Dic47C2×C412yescomplemented
77C2×C22⋊Dic47D412yes—
78C2×C22⋊Dic47D412yes—
79C2×(C2×D47)⋊C4—22no—
80C2×(C2×D47)⋊C4—24no—
81C22⋊C4×D47—24no—
82C22⋊C4×D47—24no—
83C2×C4×Dic47—22no—
84#13093938—28no—
85C47⋊#95—24no—
86C25×C47C2311yescharacteristic
87C23×C4×C47—21no—
88C23×C4×C47—21no—
89C23×C4×C47C2×C412yescomplemented
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C22⋊C4×C47—21no—
94C2×C22⋊C4×C47—21no—
95C2×C22⋊C4×C47—21no—
96C2×C22⋊C4×C47—21no—
97C2×C22⋊C4×C47—21no—
98C2×C22⋊C4×C47—21no—
99C2×C22⋊C4×C47—21no—
100C2×C22⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47C2×C412yes—
105C2×C22⋊C4×C47C2×C412yescomplemented
106C2×C22⋊C4×C47D412yes—
107C2×C22⋊C4×C47D412yes—
108C24×C47—82no—
109C24×C47C22×C411yescharacteristic
110C24×C47C22×C411yescharacteristic
111C24×C47C22×C411yescharacteristic
112C24×C47C2×D411yescharacteristic
113C24×C47C2×D411yescharacteristic
114C24×C47C2×D411yescharacteristic
115C24×C47C2×D411yescharacteristic
116C24×C47C2×D411yescharacteristic
117C24×C47C2×D411yescharacteristic
118C24×C47C2×D411yescharacteristic
119C24×C47C2×Q811yescharacteristic
120C24×C47#4111yescharacteristic
121C24×C47#4111yescharacteristic
122C24×C47#4111yescharacteristic
123C24×C47#4111yescharacteristic
124C23×D47—21no—
125C23×D47—21no—
126C23×D47—21no—
127C23×D47—21no—
128C23×D47—82no—
129C23×D47C22⋊C412yes—
130C23×D47C22⋊C412yes—
131C23×D47C4⋊C412yes—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—41no—
140C22×C4×C47—41no—
141C22×C4×C47—82no—
142C22×C4×C47—82no—
143C22×C4×C47—82no—
144C2×C22⋊D47—22no—
145C2×C22⋊D47—22no—
146C2×C22⋊D47—22no—
147C2×C22⋊D47—22no—
148C2×C22⋊D47—22no—
149C2×C22⋊D47—22no—
150C2×C22⋊D47—22no—
151C2×C22⋊D47—22no—
152C2×C22⋊D47—22no—
153C2×C22⋊D47—22no—
154C2×C22⋊D47—22no—
155C2×C22⋊D47—22no—
156C2×C22⋊D47—22no—
157C2×C22⋊D47—22no—
158C2×C22⋊D47—22no—
159C2×C22⋊D47—22no—
160C2×C22⋊D47—22no—
161C2×C22⋊D47—22no—
162C2×C22⋊D47—22no—
163C2×C22⋊D47—22no—
164C2×C22⋊D47—22no—
165C2×C22⋊D47—22no—
166C2×C22⋊D47—22no—
167C2×C22⋊D47—22no—
168C2×C22⋊D47C4214yes—
169C2×C22⋊D47C22⋊C414yes—
170C2×C22⋊D47C4⋊C414yes—
171C2×C22⋊D47C4⋊C414yes—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—22no—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—41no—
182C22×Dic47—41no—
183C22×Dic47—41no—
184C22×Dic47—41no—
185C22×Dic47—82no—
186C22×Dic47—82no—
187C22×Dic47—82no—
188C22×Dic47C22⋊C412yes—
189C22×Dic47C22⋊C412yes—
190C22×Dic47C4⋊C412yes—
191C2×C4×D47—28no—
192C2×C4×D47—84no—
193C22⋊C4×C47—22no—
194C22⋊C4×C47—22no—
195C22⋊C4×C47—22no—
196C22⋊C4×C47—22no—
197C22⋊C4×C47—22no—
198C22⋊C4×C47—41no—
199C22⋊C4×C47—41no—
200C22⋊C4×C47—41no—
201C22⋊C4×C47—41no—
202C22⋊C4×C47—41no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47C22⋊C414yescomplemented
205C22⋊Dic47—22no—
206C22⋊Dic47—22no—
207C22⋊Dic47—22no—
208C22⋊Dic47—22no—
209C22⋊Dic47—22no—
210C22⋊Dic47—22no—
211C22⋊Dic47—22no—
212C22⋊Dic47—41no—
213C22⋊Dic47—41no—
214C22⋊Dic47—41no—
215C22⋊Dic47—41no—
216C22⋊Dic47C22⋊C414yescomplemented
217(C2×D47)⋊C4—28no—
218(C2×D47)⋊C4—84no—
219Dic47⋊C4—28no—
220C4×Dic47—28no—
221C23×C47—42no—
222C23×C47—42no—
223C23×C47—42no—
224C23×C47—42no—
225C23×C47—42no—
226C23×C47—42no—
227C23×C47—42no—
228C23×C47—81no—
229C23×C47—81no—
230C23×C47—81no—
231C23×C47—81no—
232C23×C47—81no—
233C23×C47—81no—
234C23×C47—81no—
235C23×C47—81no—
236C23×C47C2×C4211yescharacteristic
237C23×C47C2×C22⋊C411yescharacteristic
238C23×C47C2×C22⋊C411yescharacteristic
239C23×C47C2×C22⋊C411yescharacteristic
240C23×C47C2×C22⋊C411yescharacteristic
241C23×C47C2×C22⋊C411yescharacteristic
242C23×C47C2×C4⋊C411yescharacteristic
243C23×C47C2×C4⋊C411yescharacteristic
244C23×C47C2×C4⋊C411yescharacteristic
245C23×C47#11711yescharacteristic
246C23×C47#11711yescharacteristic
247C23×C47C4×D411yescharacteristic
248C23×C47C4×D411yescharacteristic
249C23×C47C4×D411yescharacteristic
250C23×C47C4×D411yescharacteristic
251C23×C47C4×D411yescharacteristic
252C23×C47C4×D411yescharacteristic
253C23×C47C4×D411yescharacteristic
254C23×C47C4×D411yescharacteristic
255C23×C47#12011yescharacteristic
256C23×C47#12011yescharacteristic
257C23×C47#12011yescharacteristic
258C23×C47#12011yescharacteristic
259C23×C47#12111yescharacteristic
260C23×C47#12111yescharacteristic
261C23×C47#12111yescharacteristic
262C23×C47#12111yescharacteristic
263C23×C47C22⋊Q811yescharacteristic
264C23×C47C22⋊Q811yescharacteristic
265C23×C47C22⋊Q811yescharacteristic
266C23×C47C22⋊Q811yescharacteristic
267C23×C47#12311yescharacteristic
268C23×C47#12311yescharacteristic
269C23×C47#12311yescharacteristic
270C23×C47#12311yescharacteristic
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—44no—
278C22×D47—44no—
279C22×D47—82no—
280C22×D47—82no—
281C22×D47—82no—
282C22×D47—82no—
283C22×D47—82no—
284C22×D47#9514yes—
285C2×C4×C47—24no—
286C2×C4×C47—44no—
287C2×C4×C47—44no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47—82no—
291C2×C4×C47—82no—
292C2×C4×C47—82no—
293C2×C4×C47—82no—
294C2×C4×C47—82no—
295C2×C4×C47—82no—
296C2×C4×C47—82no—
297C22⋊D47—24no—
298C22⋊D47—24no—
299C22⋊D47—24no—
300C22⋊D47—24no—
301C22⋊D47—24no—
302C22⋊D47—24no—
303C22⋊D47—24no—
304C22⋊D47—24no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—24no—
312C2×Dic47—44no—
313C2×Dic47—44no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—82no—
317C2×Dic47—82no—
318C2×Dic47—82no—
319C2×Dic47—82no—
320C2×Dic47—82no—
321C2×Dic47—82no—
322C2×Dic47—82no—
323C2×Dic47#9514yes—
324C4×D47—88no—
325#10754—471nomaximal, Sylow
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47C2×#9511yescharacteristic
362C22×C47C4×C22⋊C411yescharacteristic
363C22×C47C4×C22⋊C411yescharacteristic
364C22×C47#37911yescharacteristic
365C22×C47#38011yescharacteristic
366C22×C47#38011yescharacteristic
367C22×C47#38111yescharacteristic
368C22×C47#38511yescharacteristic
369C22×C47#38511yescharacteristic
370C22×C47#38511yescharacteristic
371C22×C47#38511yescharacteristic
372C22×C47#38611yescharacteristic
373C22×C47#38611yescharacteristic
374C22×C47#38611yescharacteristic
375C22×C47#38611yescharacteristic
376C2×D47—24no—
377C2×D47—44no—
378C2×D47—44no—
379C2×D47—44no—
380C2×D47—44no—
381C2×D47—82no—
382C2×D47—82no—
383C2×D47—82no—
384C4×C47—44no—
385C4×C47—82no—
386C4×C47—82no—
387Dic47—24no—
388Dic47—44no—
389Dic47—82no—
390Dic47—82no—
391C2×#518—471no—
392C22×#99—471no—
393#2308—471no—
394C2×#342—471no—
395C2×#342—471no—
396C2×#342—471no—
397C2×#342D4711yescharacteristic, complemented
398C2×C47—21no—
399C2×C47—21no—
400C2×C47—21no—
401C2×C47—21no—
402C2×C47—21no—
403C2×C47—21no—
404C2×C47—21no—
405C2×C47—21no—
406C2×C47—21no—
407C2×C47—21no—
408C2×C47—21no—
409C2×C47—21no—
410C2×C47—21no—
411C2×C47—21no—
412C2×C47C22⋊#9511yescharacteristic
413C2×C47#191312yes—
414D47—44no—
415C23×D4—471no—
416#518—474no—
417#518—942no—
418#518—942no—
419#518—942no—
420C2×C4×D4—942no—
421C2×C4×D4—942no—
422C2×#117—941no—
423C22×C22⋊C4—471no—
424C22×C22⋊C4—471no—
425C22×C22⋊C4—471no—
426C22×C22⋊C4—941no—
427C22×C22⋊C4C2×D4711yescharacteristic
428C22×C22⋊C4C2×D4711yescharacteristic
429C22×C22⋊C4C2×D4711yescharacteristic
430C2×#99—474no—
431C2×#99—942no—
432C2×#99—942no—
433#386—474no—
434#386—942no—
435#381—941no—
436#379—941no—
437#342—22no—
438#342—942no—
439#342—942no—
440#342—942no—
441C47#1075411yescharacteristic, complemented, Sylow
442C25—471no—
443C25C22×D4711yescharacteristic
444C22×D4—472no—
445C22×D4—472no—
446C22×D4—472no—
447C22×D4—472no—
448C22×D4—472no—
449C22×D4—472no—
450C22×D4—941no—
451C22×D4—941no—
452C22×D4—941no—
453C22×D4—941no—
454C22×D4—941no—
455C22×D4—941no—
456C22×D4—941no—
457C22×D4—941no—
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—471no—
461C23×C4—942no—
462C23×C4—941no—
463C23×C4—941no—
464C23×C4—941no—
465C23×C4C4×D4712yescomplemented
466C4×D4—948no—
467C4×D4—948no—
468C4×D4—948no—
469C4×D4—948no—
470#117—944no—
471#117—944no—
472C2×C4⋊C4—942no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—472no—
488C2×C22⋊C4—472no—
489C2×C22⋊C4—472no—
490C2×C22⋊C4—472no—
491C2×C22⋊C4—472no—
492C2×C22⋊C4—944no—
493C2×C22⋊C4—944no—
494C2×C22⋊C4—942no—
495C2×C22⋊C4—941no—
496C2×C22⋊C4—941no—
497C2×C22⋊C4—941no—
498C2×C22⋊C4—941no—
499C2×C22⋊C4—941no—
500C2×C22⋊C4—941no—
501C2×C22⋊C4—941no—
502C2×C22⋊C4—941no—
503C2×C22⋊C4—941no—
504C2×C22⋊C4—941no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—944no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4C4×D4712yes—
510C2×C22⋊C4C4×D4712yescomplemented
511C2×C22⋊C4D18812yes—
512C2×C22⋊C4C22⋊D4712yes—
513C2×C42—942no—
514#99—948no—
515#95—944no—
516C24—82no—
517C24—472no—
518C24—472no—
519C24—472no—
520C24—941no—
521C24—941no—
522C24—941no—
523C24—941no—
524C24—3762no—
525C24C2×C4×D4711yescharacteristic
526C24C2×C4×D4711yescharacteristic
527C24C2×C4×D4711yescharacteristic
528C24C2×D18811yescharacteristic
529C24#1062535011yescharacteristic
530C24#1062535011yescharacteristic
531C24D4×D4711yescharacteristic
532C24D4×D4711yescharacteristic
533C24D4×D4711yescharacteristic
534C24D4×D4711yescharacteristic
535C24D4×D4711yescharacteristic
536C24#1062535211yescharacteristic
537C24Q8×D4711yescharacteristic
538C24#1062535411yescharacteristic
539C24C2×C22⋊D4711yescharacteristic
540C2×D4—474no—
541C2×D4—474no—
542C2×D4—474no—
543C2×D4—474no—
544C2×D4—942no—
545C2×D4—942no—
546C2×D4—942no—
547C2×D4—942no—
548C2×D4—942no—
549C2×D4—942no—
550C2×D4—942no—
551C2×D4—942no—
552C2×D4—942no—
553C2×D4—942no—
554C2×D4—942no—
555C2×D4—942no—
556C2×D4—942no—
557C2×D4—942no—
558C2×D4—942no—
559C2×D4—942no—
560C2×D4—942no—
561C2×D4—942no—
562C2×D4—942no—
563C2×D4—942no—
564C2×D4—942no—
565C2×D4—942no—
566C2×D4—942no—
567C2×D4—942no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—472no—
581C22×C4—472no—
582C22×C4—472no—
583C22×C4—948no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—3764no—
594C22×C4—3762no—
595C22×C4—3762no—
596C22×C4—3762no—
597C22×C4—1881no—
598C22×C4—1881no—
599C22×C4—1881no—
600C22×C4—1881no—
601C4⋊C4—948no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—474no—
614C22⋊C4—948no—
615C22⋊C4—942no—
616C22⋊C4—942no—
617C22⋊C4—942no—
618C22⋊C4—942no—
619C22⋊C4—942no—
620C22⋊C4—942no—
621C22⋊C4—942no—
622C22⋊C4—3764no—
623C22⋊C4—1881no—
624C22⋊C4—1881no—
625C22⋊C4—1881no—
626C22⋊C4—1881no—
627C22⋊C4(C2×D47)⋊C414yescomplemented
628C42—948no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—474no—
645C23—942no—
646C23—942no—
647C23—942no—
648C23—942no—
649C23—942no—
650C23—942no—
651C23—3762no—
652C23—3762no—
653C23—3762no—
654C23—3762no—
655C23—3762no—
656C23—1884no—
657C23—1884no—
658C23C42×D4711yescharacteristic
659C23C22⋊C4×D4711yescharacteristic
660C23C22⋊C4×D4711yescharacteristic
661C23C22⋊C4×D4711yescharacteristic
662C23C22⋊C4×D4711yescharacteristic
663C23C2×(C2×D47)⋊C411yescharacteristic
664C23C4⋊C4×D4711yescharacteristic
665C23C4⋊C4×D4711yescharacteristic
666C23C4⋊C4×D4711yescharacteristic
667C23#1309398111yescharacteristic
668C23#1309398211yescharacteristic
669C23(C22⋊D47)⋊C411yescharacteristic
670C23(C22⋊D47)⋊C411yescharacteristic
671C23C4×C22⋊D4711yescharacteristic
672C23C4×C22⋊D4711yescharacteristic
673C23#1309398611yescharacteristic
674C23#1309398611yescharacteristic
675C23C4×D18811yescharacteristic
676C23C4×D18811yescharacteristic
677C23#1309399211yescharacteristic
678C23#1309399211yescharacteristic
679C23#1309399411yescharacteristic
680C23#1309399411yescharacteristic
681C23#1309399511yescharacteristic
682C23#1309399711yescharacteristic
683C23#1309399711yescharacteristic
684C23#1309399911yescharacteristic
685C23#1309400011yescharacteristic
686C23#1309400211yescharacteristic
687C23#1309400211yescharacteristic
688C23#1309400411yescharacteristic
689C23#1309400611yescharacteristic
690C23#1309400611yescharacteristic
691C23#1309400911yescharacteristic
692C23#1309400911yescharacteristic
693D4—944no—
694D4—944no—
695D4—944no—
696D4—944no—
697D4—944no—
698D4—944no—
699D4—944no—
700D4—944no—
701C2×C4—24no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4—474no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—944no—
721C2×C4—3768no—
722C2×C4—3762no—
723C2×C4—3762no—
724C2×C4—3762no—
725C2×C4—3762no—
726C2×C4—3762no—
727C2×C4—3762no—
728C2×C4—3762no—
729C2×C4—1884no—
730C2×C4—1882no—
731C2×C4—1882no—
732C2×C4—1884no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—944no—
769C22—3762no—
770C22—3762no—
771C22—3762no—
772C22—1884no—
773C22—1884no—
774C22—1884no—
775C22—1884no—
776C22#95×D4711yescharacteristic
777C22#1568897011yescharacteristic
778C22C4×(C2×D47)⋊C411yescharacteristic
779C22#1568897811yescharacteristic
780C22#1568898011yescharacteristic
781C22#1568898211yescharacteristic
782C22#1568898511yescharacteristic
783C22#1568899411yescharacteristic
784C22#1568899411yescharacteristic
785C22#1568899711yescharacteristic
786C22#1568899711yescharacteristic
787C22#1568899911yescharacteristic
788C22#1568899911yescharacteristic
789C22#1568900111yescharacteristic
790C22#1568900111yescharacteristic
791C4—44no—
792C4—82no—
793C4—82no—
794C4—944no—
795C4—3762no—
796C4—3762no—
797C4—1884no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—21no—
809C2—21no—
810C2—21no—
811C2—21no—
812C2—1884no—
813C2(C2×D47)⋊#9511yescharacteristic
814C2#2024392712yes—
subgroupG/H
centerC22#15688999
commutatorC23×C47C2×C42
FrattiniC25C22×D47
FittingC2×C47×#342C2
socleC22×C47#386
prime radicalC23×C22⋊D47C22
cosocleC25×C47C23
hypercenterC2×#342D47
hypocenterC47#10754
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. C2×#15688890C2semidirect
5. C2×#15688890C2semidirect
6. C2×#15688889C2semidirect
7. C2×C47×#342C2semidirect
12. #15689596C4semidirect
22. C2×#13093938C4semidirect
23. #15689002C4semidirect
75. C2×C22⋊Dic47C2×C4semidirect
76. C2×C22⋊Dic47C2×C4semidirect
89. C23×C4×C47C2×C4semidirect
105. C2×C22⋊C4×C47C2×C4semidirect
204. C22⋊C4×C47C22⋊C4semidirect
216. C22⋊Dic47C22⋊C4semidirect
397. C2×#342D47semidirect
441. C47#10754semidirect
465. C23×C4C4×D47semidirect
510. C2×C22⋊C4C4×D47semidirect
627. C22⋊C4(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156895962
C22×#130939382
#202459632
C2×#156888902
C2×#156888892
C2×C47×#3422
#1075447