Finite Group Databasebeta

← C2×C47×#3524 #26102490

Subgroups — C2×C47×#3524 #26102490

Order 12032.

7226 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3524C2132yesmaximal, direct product factor
2C2×C47×#559C213yesmaximal, complemented
3C2×C47×#557C211yesmaximal, characteristic, complemented
4C2×C47×#555C213yesmaximal, complemented
5C2×C47×#553C213yesmaximal, complemented
6C2×C47×#552C213yesmaximal, complemented
7C2×C47×#550C211yesmaximal, characteristic, complemented
8C2×C47×#548C211yesmaximal, characteristic, complemented
9C2×C47×#548C211yesmaximal, characteristic, complemented
10C2×C47×#542C213yesmaximal, complemented
11C2×C47×#540C213yesmaximal, complemented
12C2×C47×#529C213yesmaximal, complemented
13C2×C47×#529C213yesmaximal, complemented
14C2×C47×#520C211yesmaximal, characteristic, complemented
15C2×C47×#519C211yesmaximal, characteristic, complemented
16C2×C4×#41×C47C211yesmaximal, characteristic, complemented
17C22×#41×C47C2211yescharacteristic
18C22×#41×C47C2211yescharacteristic
19C23×Q8×C47C2211yescharacteristic
20C47×#559C22148yescomplemented
21C47×#557C22116yescomplemented
22C47×#555C22148yescomplemented
23C47×#553C22148yescomplemented
24C47×#552C22148yescomplemented
25C47×#550C22116yescomplemented
26C47×#548C22116yescomplemented
27C47×#548C22116yescomplemented
28C47×#542C22148yescomplemented
29C47×#540C22148yescomplemented
30C2×C4⋊Q8×C47C2213yes—
31C2×#127×C47C2213yes—
32C47×#529C22148yescomplemented
33C47×#529C22148yescomplemented
34C2×#126×C47C2211yescharacteristic
35C2×#126×C47C2213yes—
36C2×#126×C47C2216yes—
37C2×#125×C47C2213yes—
38C2×#125×C47C2213yes—
39C2×#125×C47C2213yes—
40C2×#124×C47C2213yes—
41C2×#124×C47C2213yes—
42C2×#124×C47C2213yes—
43C2×#124×C47C2216yes—
44C2×#123×C47C2216yes—
45C2×#123×C47C2213yes—
46C2×#123×C47C2213yes—
47C2×#123×C47C2216yes—
48C2×C22⋊Q8×C47C2213yes—
49C2×C22⋊Q8×C47C2213yes—
50C2×C22⋊Q8×C47C2213yes—
51C2×#121×C47C2213yes—
52C2×#121×C47C2213yes—
53C2×#121×C47C2213yes—
54C2×#121×C47C2213yes—
55C2×#121×C47C2216yes—
56C2×#121×C47C2213yes—
57C47×#520C22116yescomplemented
58C47×#519C22116yescomplemented
59C4×#41×C47C22116yescomplemented
60C2×C4×Q8×C47C2211yescharacteristic
61C2×C4×Q8×C47C2211yescharacteristic
62C2×C4×Q8×C47C2213yes—
63C2×C4×Q8×C47C2211yescharacteristic
64C2×C4×Q8×C47C2213yes—
65C2×C4×Q8×C47C2211yescharacteristic
66C2×C4×Q8×C47C2213yes—
67C2×C4×D4×C47C2213yes—
68C2×C4×D4×C47C2213yes—
69C2×C4×D4×C47C2213yes—
70C2×C4×D4×C47C2213yes—
71C2×C4×D4×C47C2213yes—
72C2×C4×D4×C47C2213yes—
73C2×C4×D4×C47C2213yes—
74C2×C4×D4×C47C2216yes—
75C2×#117×C47C2213yes—
76C2×#117×C47C2213yes—
77C2×#117×C47C2213yes—
78C2×#117×C47C2213yes—
79C2×#117×C47C2216yes—
80C22×C4⋊C4×C47C2213yes—
81C22×C42×C47C2213yes—
82C2×#41×C47—28no—
83C2×#41×C47—28no—
84C2×#41×C47C2318yes—
85C2×#41×C47C2318yes—
86C22×Q8×C47—28no—
87C22×Q8×C47C2313yes—
88C22×Q8×C47C2318yes—
89C22×Q8×C47C2313yes—
90C22×Q8×C47C2311yescharacteristic
91C22×D4×C47C2313yes—
92C22×D4×C47C2313yes—
93C22×D4×C47C2313yes—
94C22×D4×C47C2313yes—
95C22×D4×C47C2316yes—
96C22×D4×C47C2313yes—
97C23×C4×C47C2313yes—
98C23×C4×C47C2313yes—
99C23×C4×C47C2313yes—
100C23×C4×C47C2313yes—
101C23×C4×C47C2313yes—
102C23×C4×C47C2316yes—
103C4⋊Q8×C47C23124yes—
104#127×C47C23124yes—
105#126×C47C2318yes—
106#126×C47C23124yes—
107#126×C47C23148yes—
108#125×C47C23124yes—
109#125×C47C23124yes—
110#125×C47C23124yes—
111#124×C47C23124yes—
112#124×C47C23124yes—
113#124×C47C23124yes—
114#124×C47C23148yes—
115#123×C47C23148yes—
116#123×C47C23124yes—
117#123×C47C23124yes—
118#123×C47C23148yes—
119C22⋊Q8×C47C23124yes—
120C22⋊Q8×C47C23124yes—
121C22⋊Q8×C47C23124yes—
122#121×C47C23124yes—
123#121×C47C23124yes—
124#121×C47C23124yes—
125#121×C47C23124yes—
126#121×C47C23148yes—
127#121×C47C23124yes—
128C4×Q8×C47C2318yes—
129C4×Q8×C47C2318yes—
130C4×Q8×C47C23124yes—
131C4×Q8×C47C2318yes—
132C4×Q8×C47C23124yes—
133C4×Q8×C47C2318yes—
134C4×Q8×C47C23124yes—
135C4×D4×C47C23124yes—
136C4×D4×C47C23124yes—
137C4×D4×C47C23124yes—
138C4×D4×C47C23124yes—
139C4×D4×C47C23124yes—
140C4×D4×C47C23124yes—
141C4×D4×C47C23124yes—
142C4×D4×C47C23148yes—
143#117×C47C23124yes—
144#117×C47C23124yes—
145#117×C47C23124yes—
146#117×C47C23124yes—
147#117×C47C23148yes—
148C2×C4⋊C4×C47C2313yes—
149C2×C4⋊C4×C47C2313yes—
150C2×C4⋊C4×C47C2313yes—
151C2×C4⋊C4×C47C23124yes—
152C2×C4⋊C4×C47C2311yescharacteristic
153C2×C4⋊C4×C47C2313yes—
154C2×C4⋊C4×C47C2313yes—
155C2×C4⋊C4×C47C2313yes—
156C2×C4⋊C4×C47C2313yes—
157C2×C4⋊C4×C47C2313yes—
158C2×C4⋊C4×C47C2316yes—
159C2×C4⋊C4×C47C2311yescharacteristic
160C2×C4⋊C4×C47C2313yes—
161C2×C4⋊C4×C47C2313yes—
162C2×C4⋊C4×C47C2311yescharacteristic
163C2×C4⋊C4×C47C2313yes—
164C2×C22⋊C4×C47C2311yescharacteristic
165C2×C22⋊C4×C47C2313yes—
166C2×C22⋊C4×C47C2313yes—
167C2×C22⋊C4×C47C2313yes—
168C2×C22⋊C4×C47C2316yes—
169C2×C22⋊C4×C47C2313yes—
170C2×C22⋊C4×C47C2316yes—
171C2×C22⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47C2313yes—
173C2×C22⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47C2313yes—
175C2×C22⋊C4×C47C2316yes—
176C2×C22⋊C4×C47C2313yes—
177C2×C42×C47C2311yescharacteristic
178C2×C42×C47C2313yes—
179C2×C42×C47C2313yes—
180C2×C42×C47C2313yes—
181C2×C42×C47C23124yes—
182C2×C42×C47C2316yes—
183C2×C42×C47C2313yes—
184C2×C42×C47C2313yes—
185C24×C47C2411yescharacteristic
186C24×C47C2413yes—
187C24×C47C2413yes—
188#41×C47—232no—
189#41×C47—232no—
190C2×Q8×C47—232no—
191C2×Q8×C47—212no—
192C2×Q8×C47—46no—
193C2×Q8×C47#4118yes—
194C2×Q8×C47C24112yes—
195C2×Q8×C47C24112yes—
196C2×Q8×C47C2414yes—
197C2×D4×C47—212no—
198C2×D4×C47—212no—
199C2×D4×C47—46no—
200C2×D4×C47—46no—
201C2×D4×C47—46no—
202C2×D4×C47—412no—
203C2×D4×C47C24112yes—
204C2×D4×C47C24112yes—
205C2×D4×C47C24112yes—
206C2×D4×C47C24112yes—
207C2×D4×C47C24124yes—
208C2×D4×C47C24112yes—
209C22×C4×C47—212no—
210C22×C4×C47—212no—
211C22×C4×C47—212no—
212C22×C4×C47—46no—
213C22×C4×C47—412no—
214C22×C4×C47—46no—
215C22×C4×C47C24112yes—
216C22×C4×C47C24112yes—
217C22×C4×C47C24112yes—
218C22×C4×C47C2411yescharacteristic
219C22×C4×C47C2411yescharacteristic
220C22×C4×C47C2411yescharacteristic
221C22×C4×C47C2413yes—
222C22×C4×C47C2411yescharacteristic
223C22×C4×C47C2413yes—
224C22×C4×C47C2411yescharacteristic
225C22×C4×C47C2413yes—
226C22×C4×C47C2413yes—
227C22×C4×C47C2413yes—
228C22×C4×C47C2411yescharacteristic
229C22×C4×C47C24112yes—
230C22×C4×C47C24112yes—
231C22×C4×C47C24124yes—
232C22×C4×C47C2413yes—
233C4⋊C4×C47C24112yes—
234C4⋊C4×C47C24112yes—
235C4⋊C4×C47C24112yes—
236C4⋊C4×C47C2414yes—
237C4⋊C4×C47C24112yes—
238C4⋊C4×C47C24112yes—
239C4⋊C4×C47C24112yes—
240C4⋊C4×C47C24112yes—
241C4⋊C4×C47C24112yes—
242C4⋊C4×C47C24124yes—
243C4⋊C4×C47C2414yes—
244C4⋊C4×C47C24112yes—
245C4⋊C4×C47C24112yes—
246C4⋊C4×C47C2414yes—
247C4⋊C4×C47C24112yes—
248C22⋊C4×C47C2414yes—
249C22⋊C4×C47C24112yes—
250C22⋊C4×C47C24112yes—
251C22⋊C4×C47C24112yes—
252C22⋊C4×C47C24124yes—
253C22⋊C4×C47C24112yes—
254C22⋊C4×C47C24124yes—
255C22⋊C4×C47C2414yes—
256C22⋊C4×C47C24112yes—
257C22⋊C4×C47C2414yes—
258C22⋊C4×C47C24112yes—
259C22⋊C4×C47C24124yes—
260C22⋊C4×C47C24112yes—
261C42×C47C2414yes—
262C42×C47C24112yes—
263C42×C47C24112yes—
264C42×C47C24112yes—
265C42×C47C24124yes—
266C42×C47C24112yes—
267C42×C47C24112yes—
268C23×C47—22no—
269C23×C47—26no—
270C23×C47—26no—
271C23×C47—26no—
272C23×C47—26no—
273C23×C47—26no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—26no—
277C23×C47C2512yes—
278C23×C47C2516yes—
279C23×C47C2516yes—
280C23×C47C2511yescharacteristic
281Q8×C47—224no—
282Q8×C47—412no—
283Q8×C47C2×#41116yes—
284D4×C47—224no—
285D4×C47—224no—
286D4×C47—412no—
287D4×C47—412no—
288D4×C47—412no—
289D4×C47—424no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—26no—
293C2×C4×C47—22no—
294C2×C4×C47—26no—
295C2×C4×C47—22no—
296C2×C4×C47—26no—
297C2×C4×C47—26no—
298C2×C4×C47—22no—
299C2×C4×C47—26no—
300C2×C4×C47—22no—
301C2×C4×C47—224no—
302C2×C4×C47—224no—
303C2×C4×C47—224no—
304C2×C4×C47—412no—
305C2×C4×C47—424no—
306C2×C4×C47—412no—
307C2×C4×C47C2×#41112yes—
308C2×C4×C47C2512yes—
309C2×C4×C47C2512yes—
310C2×C4×C47C2512yes—
311C2×C4×C47C2516yes—
312C2×C4×C47C2512yes—
313C2×C4×C47C2516yes—
314C2×C4×C47C2512yes—
315C2×C4×C47C2516yes—
316C2×C4×C47C2516yes—
317C2×C4×C47C2516yes—
318C2×C4×C47C2512yes—
319C2×C4×C47C2516yes—
320C2×#3524C4711yesmaximal, characteristic, direct product factor, Sylow
321C22×C47—22no—
322C22×C47—26no—
323C22×C47—26no—
324C22×C47—26no—
325C22×C47—26no—
326C22×C47—26no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—26no—
330C22×C47—44no—
331C22×C47—412no—
332C22×C47—412no—
333C22×C47C22×#4112yes—
334C22×C47#58512yes—
335C22×C47#58512yes—
336C22×C47C2611yescharacteristic
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—26no—
340C4×C47—22no—
341C4×C47—26no—
342C4×C47—22no—
343C4×C47—26no—
344C4×C47—26no—
345C4×C47—22no—
346C4×C47—26no—
347C4×C47—22no—
348C4×C47C22×#41112yes—
349#3524C2×C47132yesdirect product factor
350C2×#559C2×C4713yescomplemented
351C2×#557C2×C4711yescharacteristic, complemented
352C2×#555C2×C4713yescomplemented
353C2×#553C2×C4713yescomplemented
354C2×#552C2×C4713yescomplemented
355C2×#550C2×C4711yescharacteristic, complemented
356C2×#548C2×C4711yescharacteristic, complemented
357C2×#548C2×C4711yescharacteristic, complemented
358C2×#542C2×C4713yescomplemented
359C2×#540C2×C4713yescomplemented
360C2×#529C2×C4713yescomplemented
361C2×#529C2×C4713yescomplemented
362C2×#520C2×C4711yescharacteristic, complemented
363C2×#519C2×C4711yescharacteristic, complemented
364C2×C4×#41C2×C4711yescharacteristic, complemented
365C2×C47—42no—
366C2×C47—46no—
367C2×C47—46no—
368C2×C47#352414yesdirect product factor
369C2×C47C23×#4111yescharacteristic
370C2×C47C2×#58511yescharacteristic
371C2×C47C2×#58511yescharacteristic
372C22×#41C22×C4711yescharacteristic
373C22×#41C22×C4711yescharacteristic
374C23×Q8C22×C4711yescharacteristic
375#559C22×C47148yescomplemented
376#557C22×C47116yescomplemented
377#555C22×C47148yescomplemented
378#553C22×C47148yescomplemented
379#552C22×C47148yescomplemented
380#550C22×C47116yescomplemented
381#548C22×C47116yescomplemented
382#548C22×C47116yescomplemented
383#542C22×C47148yescomplemented
384#540C22×C47148yescomplemented
385C2×C4⋊Q8C22×C4713yes—
386C2×#127C22×C4713yes—
387#529C22×C47148yescomplemented
388#529C22×C47148yescomplemented
389C2×#126C22×C4711yescharacteristic
390C2×#126C22×C4713yes—
391C2×#126C22×C4716yes—
392C2×#125C22×C4713yes—
393C2×#125C22×C4713yes—
394C2×#125C22×C4713yes—
395C2×#124C22×C4713yes—
396C2×#124C22×C4713yes—
397C2×#124C22×C4713yes—
398C2×#124C22×C4716yes—
399C2×#123C22×C4716yes—
400C2×#123C22×C4713yes—
401C2×#123C22×C4713yes—
402C2×#123C22×C4716yes—
403C2×C22⋊Q8C22×C4713yes—
404C2×C22⋊Q8C22×C4713yes—
405C2×C22⋊Q8C22×C4713yes—
406C2×#121C22×C4713yes—
407C2×#121C22×C4713yes—
408C2×#121C22×C4713yes—
409C2×#121C22×C4713yes—
410C2×#121C22×C4716yes—
411C2×#121C22×C4713yes—
412#520C22×C47116yescomplemented
413#519C22×C47116yescomplemented
414C4×#41C22×C47116yescomplemented
415C2×C4×Q8C22×C4711yescharacteristic
416C2×C4×Q8C22×C4711yescharacteristic
417C2×C4×Q8C22×C4713yes—
418C2×C4×Q8C22×C4711yescharacteristic
419C2×C4×Q8C22×C4713yes—
420C2×C4×Q8C22×C4711yescharacteristic
421C2×C4×Q8C22×C4713yes—
422C2×C4×D4C22×C4713yes—
423C2×C4×D4C22×C4713yes—
424C2×C4×D4C22×C4713yes—
425C2×C4×D4C22×C4713yes—
426C2×C4×D4C22×C4713yes—
427C2×C4×D4C22×C4713yes—
428C2×C4×D4C22×C4713yes—
429C2×C4×D4C22×C4716yes—
430C2×#117C22×C4713yes—
431C2×#117C22×C4713yes—
432C2×#117C22×C4713yes—
433C2×#117C22×C4713yes—
434C2×#117C22×C4716yes—
435C22×C4⋊C4C22×C4713yes—
436C22×C42C22×C4713yes—
437C47C2×#352411yescharacteristic, direct product factor, Sylow
438C2×#41—28no—
439C2×#41—28no—
440C2×#41C23×C4718yes—
441C2×#41C23×C4718yes—
442C22×Q8—28no—
443C22×Q8C23×C4713yes—
444C22×Q8C23×C4718yes—
445C22×Q8C23×C4713yes—
446C22×Q8C23×C4711yescharacteristic
447C22×D4C23×C4713yes—
448C22×D4C23×C4713yes—
449C22×D4C23×C4713yes—
450C22×D4C23×C4713yes—
451C22×D4C23×C4716yes—
452C22×D4C23×C4713yes—
453C23×C4C23×C4713yes—
454C23×C4C23×C4713yes—
455C23×C4C23×C4713yes—
456C23×C4C23×C4716yes—
457C23×C4C23×C4713yes—
458C23×C4C23×C4713yes—
459C4⋊Q8C23×C47124yes—
460#127C23×C47124yes—
461#126C23×C4718yes—
462#126C23×C47124yes—
463#126C23×C47148yes—
464#125C23×C47124yes—
465#125C23×C47124yes—
466#125C23×C47124yes—
467#124C23×C47124yes—
468#124C23×C47124yes—
469#124C23×C47124yes—
470#124C23×C47148yes—
471#123C23×C47148yes—
472#123C23×C47124yes—
473#123C23×C47124yes—
474#123C23×C47148yes—
475C22⋊Q8C23×C47124yes—
476C22⋊Q8C23×C47124yes—
477C22⋊Q8C23×C47124yes—
478#121C23×C47124yes—
479#121C23×C47124yes—
480#121C23×C47124yes—
481#121C23×C47124yes—
482#121C23×C47148yes—
483#121C23×C47124yes—
484C4×Q8C23×C4718yes—
485C4×Q8C23×C4718yes—
486C4×Q8C23×C47124yes—
487C4×Q8C23×C4718yes—
488C4×Q8C23×C47124yes—
489C4×Q8C23×C4718yes—
490C4×Q8C23×C47124yes—
491C4×D4C23×C47124yes—
492C4×D4C23×C47124yes—
493C4×D4C23×C47124yes—
494C4×D4C23×C47124yes—
495C4×D4C23×C47124yes—
496C4×D4C23×C47124yes—
497C4×D4C23×C47124yes—
498C4×D4C23×C47148yes—
499#117C23×C47124yes—
500#117C23×C47124yes—
501#117C23×C47124yes—
502#117C23×C47124yes—
503#117C23×C47148yes—
504C2×C4⋊C4C23×C4713yes—
505C2×C4⋊C4C23×C4713yes—
506C2×C4⋊C4C23×C4713yes—
507C2×C4⋊C4C23×C47124yes—
508C2×C4⋊C4C23×C4711yescharacteristic
509C2×C4⋊C4C23×C4713yes—
510C2×C4⋊C4C23×C4713yes—
511C2×C4⋊C4C23×C4713yes—
512C2×C4⋊C4C23×C4713yes—
513C2×C4⋊C4C23×C4713yes—
514C2×C4⋊C4C23×C4716yes—
515C2×C4⋊C4C23×C4711yescharacteristic
516C2×C4⋊C4C23×C4713yes—
517C2×C4⋊C4C23×C4713yes—
518C2×C4⋊C4C23×C4711yescharacteristic
519C2×C4⋊C4C23×C4713yes—
520C2×C22⋊C4C23×C4711yescharacteristic
521C2×C22⋊C4C23×C4713yes—
522C2×C22⋊C4C23×C4713yes—
523C2×C22⋊C4C23×C4713yes—
524C2×C22⋊C4C23×C4716yes—
525C2×C22⋊C4C23×C4713yes—
526C2×C22⋊C4C23×C4716yes—
527C2×C22⋊C4C23×C4711yescharacteristic
528C2×C22⋊C4C23×C4713yes—
529C2×C22⋊C4C23×C4711yescharacteristic
530C2×C22⋊C4C23×C4713yes—
531C2×C22⋊C4C23×C4716yes—
532C2×C22⋊C4C23×C4713yes—
533C2×C42C23×C4713yes—
534C2×C42C23×C4713yes—
535C2×C42C23×C4716yes—
536C2×C42C23×C4713yes—
537C2×C42C23×C4713yes—
538C2×C42C23×C4713yes—
539C2×C42C23×C47124yes—
540C2×C42C23×C4711yescharacteristic
541C24C24×C4711yescharacteristic
542C24C24×C4713yes—
543C24C24×C4713yes—
544#41—232no—
545#41—232no—
546C2×Q8—232no—
547C2×Q8—212no—
548C2×Q8—46no—
549C2×Q8#41×C4718yes—
550C2×Q8C24×C47112yes—
551C2×Q8C24×C47112yes—
552C2×Q8C24×C4714yes—
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—46no—
556C2×D4—46no—
557C2×D4—46no—
558C2×D4—412no—
559C2×D4C24×C47112yes—
560C2×D4C24×C47112yes—
561C2×D4C24×C47112yes—
562C2×D4C24×C47112yes—
563C2×D4C24×C47124yes—
564C2×D4C24×C47112yes—
565C22×C4—212no—
566C22×C4—212no—
567C22×C4—212no—
568C22×C4—46no—
569C22×C4—412no—
570C22×C4—46no—
571C22×C4C24×C4711yescharacteristic
572C22×C4C24×C4713yes—
573C22×C4C24×C4711yescharacteristic
574C22×C4C24×C4711yescharacteristic
575C22×C4C24×C4711yescharacteristic
576C22×C4C24×C4713yes—
577C22×C4C24×C4711yescharacteristic
578C22×C4C24×C4713yes—
579C22×C4C24×C4713yes—
580C22×C4C24×C47112yes—
581C22×C4C24×C4713yes—
582C22×C4C24×C4711yescharacteristic
583C22×C4C24×C47112yes—
584C22×C4C24×C47112yes—
585C22×C4C24×C47112yes—
586C22×C4C24×C47112yes—
587C22×C4C24×C47124yes—
588C22×C4C24×C4713yes—
589C4⋊C4C24×C47112yes—
590C4⋊C4C24×C47112yes—
591C4⋊C4C24×C47112yes—
592C4⋊C4C24×C4714yes—
593C4⋊C4C24×C47112yes—
594C4⋊C4C24×C47112yes—
595C4⋊C4C24×C47112yes—
596C4⋊C4C24×C47112yes—
597C4⋊C4C24×C47112yes—
598C4⋊C4C24×C47124yes—
599C4⋊C4C24×C4714yes—
600C4⋊C4C24×C47112yes—
601C4⋊C4C24×C47112yes—
602C4⋊C4C24×C4714yes—
603C4⋊C4C24×C47112yes—
604C22⋊C4C24×C4714yes—
605C22⋊C4C24×C47112yes—
606C22⋊C4C24×C47112yes—
607C22⋊C4C24×C47112yes—
608C22⋊C4C24×C47124yes—
609C22⋊C4C24×C47112yes—
610C22⋊C4C24×C47124yes—
611C22⋊C4C24×C4714yes—
612C22⋊C4C24×C47112yes—
613C22⋊C4C24×C4714yes—
614C22⋊C4C24×C47112yes—
615C22⋊C4C24×C47124yes—
616C22⋊C4C24×C47112yes—
617C42C24×C4714yes—
618C42C24×C47112yes—
619C42C24×C47112yes—
620C42C24×C47112yes—
621C42C24×C47124yes—
622C42C24×C47112yes—
623C42C24×C47112yes—
624C23—22no—
625C23—26no—
626C23—26no—
627C23—26no—
628C23—26no—
629C23—26no—
630C23—22no—
631C23—22no—
632C23—26no—
633C23C25×C4712yes—
634C23C25×C4716yes—
635C23C25×C4716yes—
636C23C25×C4711yescharacteristic
637Q8—224no—
638Q8—412no—
639Q8C2×#41×C47116yes—
640D4—224no—
641D4—224no—
642D4—412no—
643D4—412no—
644D4—412no—
645D4—424no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—26no—
649C2×C4—22no—
650C2×C4—26no—
651C2×C4—22no—
652C2×C4—26no—
653C2×C4—26no—
654C2×C4—22no—
655C2×C4—26no—
656C2×C4—22no—
657C2×C4—224no—
658C2×C4—224no—
659C2×C4—224no—
660C2×C4—412no—
661C2×C4—424no—
662C2×C4—412no—
663C2×C4C2×#41×C47112yes—
664C2×C4C25×C4712yes—
665C2×C4C25×C4712yes—
666C2×C4C25×C4712yes—
667C2×C4C25×C4716yes—
668C2×C4C25×C4712yes—
669C2×C4C25×C4716yes—
670C2×C4C25×C4712yes—
671C2×C4C25×C4716yes—
672C2×C4C25×C4716yes—
673C2×C4C25×C4716yes—
674C2×C4C25×C4712yes—
675C2×C4C25×C4716yes—
676C22—22no—
677C22—26no—
678C22—26no—
679C22—26no—
680C22—26no—
681C22—26no—
682C22—22no—
683C22—22no—
684C22—26no—
685C22—44no—
686C22—412no—
687C22—412no—
688C22C22×#41×C4712yes—
689C22C47×#58512yes—
690C22C47×#58512yes—
691C22C26×C4711yescharacteristic
692C4—22no—
693C4—22no—
694C4—26no—
695C4—22no—
696C4—26no—
697C4—22no—
698C4—26no—
699C4—26no—
700C4—22no—
701C4—26no—
702C4—22no—
703C4C22×#41×C47112yes—
704C2—42no—
705C2—46no—
706C2—46no—
707C2C47×#352414yesdirect product factor
708C2C23×#41×C4711yescharacteristic
709C2C2×C47×#58511yescharacteristic
710C2C2×C47×#58511yescharacteristic
subgroupG/H
center, socleC23×C47C25
commutator, Frattini, cosocleC22C26×C47
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3524C2direct (N × H)
2. C2×C47×#559C2semidirect
3. C2×C47×#557C2semidirect
4. C2×C47×#555C2semidirect
5. C2×C47×#553C2semidirect
6. C2×C47×#552C2semidirect
7. C2×C47×#550C2semidirect
8. C2×C47×#548C2semidirect
9. C2×C47×#548C2semidirect
10. C2×C47×#542C2semidirect
11. C2×C47×#540C2semidirect
12. C2×C47×#529C2semidirect
13. C2×C47×#529C2semidirect
14. C2×C47×#520C2semidirect
15. C2×C47×#519C2semidirect
16. C2×C4×#41×C47C2semidirect
20. C47×#559C22semidirect
21. C47×#557C22semidirect
22. C47×#555C22semidirect
23. C47×#553C22semidirect
24. C47×#552C22semidirect
25. C47×#550C22semidirect
26. C47×#548C22semidirect
27. C47×#548C22semidirect
28. C47×#542C22semidirect
29. C47×#540C22semidirect
32. C47×#529C22semidirect
33. C47×#529C22semidirect
57. C47×#520C22semidirect
58. C47×#519C22semidirect
59. C4×#41×C47C22semidirect
320. C2×#3524C47direct (N × H)
349. #3524C2×C47direct (N × H)
350. C2×#559C2×C47semidirect
351. C2×#557C2×C47semidirect
352. C2×#555C2×C47semidirect
353. C2×#553C2×C47semidirect
354. C2×#552C2×C47semidirect
355. C2×#550C2×C47semidirect
356. C2×#548C2×C47semidirect
357. C2×#548C2×C47semidirect
358. C2×#542C2×C47semidirect
359. C2×#540C2×C47semidirect
360. C2×#529C2×C47semidirect
361. C2×#529C2×C47semidirect
362. C2×#520C2×C47semidirect
363. C2×#519C2×C47semidirect
364. C2×C4×#41C2×C47semidirect
368. C2×C47#3524direct (N × H)
375. #559C22×C47semidirect
376. #557C22×C47semidirect
377. #555C22×C47semidirect
378. #553C22×C47semidirect
379. #552C22×C47semidirect
380. #550C22×C47semidirect
381. #548C22×C47semidirect
382. #548C22×C47semidirect
383. #542C22×C47semidirect
384. #540C22×C47semidirect
387. #529C22×C47semidirect
388. #529C22×C47semidirect
412. #520C22×C47semidirect
413. #519C22×C47semidirect
414. C4×#41C22×C47semidirect
437. C47C2×#3524direct (N × H)
707. C2C47×#3524direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35242
C2×C47×#5592
C2×C47×#5572
C2×C47×#5552
C2×C47×#5532
C2×C47×#5522
C2×C47×#5502
C2×C47×#5482
C2×C47×#5422
C2×C47×#5402
C2×C47×#5292
C2×C47×#5202
C2×C47×#5192
C2×C4×#41×C472
C2×#352447