Finite Group Databasebeta

← C2×#20246182 #26375176

Subgroups — C2×#20246182 #26375176

Order 12032.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246182C2116yesmaximal, direct product factor
2C2×#15689026C211yesmaximal, characteristic
3C2×#15689022C211yesmaximal, characteristic, complemented
4C2×#15689016C211yesmaximal, characteristic, complemented
5C2×#15689016C211yesmaximal, characteristic, complemented
6C2×#15689016C211yesmaximal, characteristic, complemented
7C2×#15689016C211yesmaximal, characteristic, complemented
8C2×#15689009C211yesmaximal, characteristic, complemented
9C2×#15689009C211yesmaximal, characteristic, complemented
10C2×#15689003C211yesmaximal, characteristic
11C2×#15688998C211yesmaximal, characteristic, complemented
12C2×#15688983C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
16C22×#123×C47C211yesmaximal, characteristic
17C24×Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C22⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2211yescharacteristic
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×C22⋊Dic47C2211yescharacteristic
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C4×Dic47C2211yescharacteristic
31C22×C4×Dic47C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33C22×C4×Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35#15689026C2218yes—
36#15689022C2218yescomplemented
37#15689016C2218yescomplemented
38#15689016C2218yescomplemented
39#15689016C2218yescomplemented
40#15689016C2218yescomplemented
41#15689009C2218yescomplemented
42#15689009C2218yescomplemented
43#15689003C2218yes—
44#15688998C2218yescomplemented
45#15688983C2218yescomplemented
46C4⋊C4×Dic47C2218yescomplemented
47C22⋊C4×Dic47C2218yescomplemented
48C4×C22⋊Dic47C2218yescomplemented
49C2×C47⋊#95C2211yescharacteristic
50C2×C47⋊#95C2211yescharacteristic
51C2×C47⋊#95C2211yescharacteristic
52C2×C47⋊#95C2211yescharacteristic
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C23×D4×C47C2211yescharacteristic
60C24×C4×C47C2211yescharacteristic
61C2×#123×C47C4116yescomplemented
62C2×#123×C47C2218yes—
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C23×Dic47—24no—
69C23×Dic47—42no—
70C23×Dic47—42no—
71C23×Dic47C2311yescharacteristic
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2314yes—
80C2×C4⋊Dic47—24no—
81C2×C4⋊Dic47—42no—
82C2×C4⋊Dic47—42no—
83C2×C4⋊Dic47—42no—
84C2×C4⋊Dic47—42no—
85C2×C4⋊Dic47C2314yes—
86C2×C4⋊Dic47C2314yes—
87C2×C4⋊Dic47C2314yes—
88C2×C4⋊Dic47C2314yes—
89C2×C4⋊Dic47C2314yes—
90C2×C22⋊Dic47—24no—
91C2×C22⋊Dic47—24no—
92C2×C22⋊Dic47—24no—
93C2×C22⋊Dic47—42no—
94C2×C22⋊Dic47—42no—
95C2×C22⋊Dic47—42no—
96C2×C22⋊Dic47—42no—
97C2×C22⋊Dic47C2314yes—
98C2×C22⋊Dic47C2314yes—
99C2×C22⋊Dic47C2314yes—
100C2×C22⋊Dic47C2314yes—
101C2×C22⋊Dic47C2314yes—
102C2×C22⋊Dic47C2314yes—
103C2×C22⋊Dic47C2314yes—
104C2×C4×Dic47—24no—
105C2×C4×Dic47—42no—
106C2×C4×Dic47—42no—
107C2×C4×Dic47—42no—
108C2×C4×Dic47—42no—
109C2×C4×Dic47C2314yes—
110C2×C4×Dic47C2314yes—
111C2×C4×Dic47C2314yes—
112C2×C4×Dic47C2314yes—
113C2×C4×Dic47C2314yes—
114C47⋊#95C2314yes—
115C47⋊#95C2314yes—
116C47⋊#95C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C25×C47C2311yescharacteristic
125C25×C47C2311yescharacteristic
126C22×D4×C47—42no—
127C22×D4×C47—42no—
128C22×D4×C47C2×C418yes—
129C22×D4×C47C2314yes—
130C23×C4×C47—42no—
131C23×C4×C47—42no—
132C23×C4×C47C2×C418yescomplemented
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2314yes—
139#123×C47C2×C4164yescomplemented
140C2×C4⋊C4×C47C2×C418yescomplemented
141C2×C4⋊C4×C47C2×C418yescomplemented
142C2×C4⋊C4×C47C2314yes—
143C2×C4⋊C4×C47C2314yes—
144C2×C22⋊C4×C47C2×C418yes—
145C2×C22⋊C4×C47C2×C418yes—
146C2×C22⋊C4×C47C2×C418yescomplemented
147C2×C22⋊C4×C47C2314yes—
148C2×C22⋊C4×C47C2314yes—
149C2×C22⋊C4×C47C2314yes—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47—22no—
157C24×C47—22no—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47C22×C414yes—
163C24×C47C22×C414yes—
164C24×C47C2412yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C2×D4×C47—416no—
168C2×D4×C47—44no—
169C2×D4×C47—44no—
170C2×D4×C47C22×C4116yes—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—416no—
182C22×C4×C47—44no—
183C22×C4×C47—44no—
184C22×C4×C47C22×C414yes—
185C22×C4×C47C22×C414yes—
186C22×C4×C47C22×C414yes—
187C22×C4×C47C22×C414yes—
188C22×C4×C47C22×C414yes—
189C22×C4×C47C22×C4116yescomplemented
190C22×C4×C47C2412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—28no—
218C22×Dic47—44no—
219C22×Dic47—44no—
220C22×Dic47—416no—
221C22×Dic47#4114yes—
222C22×Dic47#4114yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C22×Dic47C2412yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C4⋊C4×C47C22×C4116yescomplemented
232C4⋊C4×C47C22×C4116yescomplemented
233C22⋊C4×C47C22×C4116yes—
234C22⋊C4×C47C22×C4116yes—
235C22⋊C4×C47C22×C4116yescomplemented
236C22⋊Dic47—28no—
237C22⋊Dic47—28no—
238C22⋊Dic47—28no—
239C22⋊Dic47—44no—
240C22⋊Dic47—44no—
241C22⋊Dic47—44no—
242C22⋊Dic47—44no—
243C4⋊Dic47—28no—
244C4⋊Dic47—44no—
245C4⋊Dic47—44no—
246C4⋊Dic47—44no—
247C4⋊Dic47—44no—
248C4×Dic47—28no—
249C4×Dic47—44no—
250C4×Dic47—44no—
251C4×Dic47—44no—
252C4×Dic47—44no—
253C23×C47—28no—
254C23×C47—28no—
255C23×C47—28no—
256C23×C47—28no—
257C23×C47—28no—
258C23×C47—28no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—44no—
272C23×C47—44no—
273C23×C47—44no—
274C23×C47—44no—
275C23×C47—44no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47C23×C414yes—
280C23×C47C23×C414yes—
281C23×C47C23×C412yes—
282C23×C47C2×#4112yes—
283C23×C47C2×#4112yes—
284C23×C47H(5,𝔽2)12yes—
285C23×C47H(5,𝔽2)12yes—
286C23×C47H(5,𝔽2)12yes—
287C23×C472−1+412yes—
288C23×C47C2511yescharacteristic
289D4×C47—416no—
290C2×C4×C47—28no—
291C2×C4×C47—28no—
292C2×C4×C47—28no—
293C2×C4×C47—28no—
294C2×C4×C47—28no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—416no—
306C2×C4×C47C23×C414yes—
307C2×C4×C47C23×C414yes—
308C2×C4×C47C23×C414yes—
309C2×C4×C47C23×C414yes—
310C2×C4×C47C23×C414yes—
311C2×Dic47—28no—
312C2×Dic47—28no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—416no—
336C2×Dic47—44no—
337C2×Dic47—44no—
338C2×Dic47—44no—
339C2×Dic47—44no—
340C2×Dic47—44no—
341C2×Dic47—44no—
342C2×Dic47C2×#4114yes—
343C2×Dic47C2×#4114yes—
344C2×#2335—471nomaximal, Sylow
345C22×C47—24no—
346C22×C47—24no—
347C22×C47—24no—
348C22×C47—24no—
349C22×C47—24no—
350C22×C47—24no—
351C22×C47—416no—
352C22×C47—416no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47C4×#4114yes—
362C22×C47#51814yes—
363C22×C47#52014yes—
364C22×C47#53814yes—
365C22×C47#53914yes—
366C22×C47#54014yes—
367C22×C47#54214yes—
368C22×C47C24×C411yescharacteristic
369C22×C47C22×#4111yescharacteristic
370C22×C47C22×#4111yescharacteristic
371C22×C47C2×H(5,𝔽2)11yescharacteristic
372C22×C47C2×H(5,𝔽2)11yescharacteristic
373C22×C47C2×H(5,𝔽2)11yescharacteristic
374C22×C47C2×2−1+411yescharacteristic
375C4×C47—24no—
376C4×C47—24no—
377C4×C47—24no—
378C4×C47—24no—
379C4×C47—24no—
380Dic47—24no—
381Dic47—24no—
382Dic47—42no—
383Dic47—42no—
384Dic47—42no—
385Dic47—42no—
386Dic47—42no—
387Dic47—42no—
388C22×#123D4711yescharacteristic
389#2335—4716no—
390C2×#390—471no—
391C2×#389—471no—
392C2×#388—471no—
393C2×#388—471no—
394C2×#388—471no—
395C2×#388—471no—
396C2×#387—471no—
397C2×#387—471no—
398C2×#386—471no—
399C2×#385—471no—
400C2×#380—471no—
401C2×C4×C4⋊C4—471no—
402C2×C4×C22⋊C4—471no—
403C2×C4×C22⋊C4—471no—
404C2×C47—44no—
405C2×C47—44no—
406C2×C47#233518yescomplemented
407C2×C47C2×C4×#4111yescharacteristic
408C2×C47C2×#51811yescharacteristic
409C2×C47C2×#52011yescharacteristic
410C2×C47C2×#53811yescharacteristic
411C2×C47C2×#53911yescharacteristic
412C2×C47C2×#54011yescharacteristic
413C2×C47C2×#54211yescharacteristic
414C23×D4C2×D4711yescharacteristic
415C24×C4—471no—
416C24×C4C2×D4711yescharacteristic
417C2×#123Dic47116yescomplemented
418C2×#123C2×D4718yes—
419C22×C4⋊C4—471no—
420C22×C4⋊C4—471no—
421C22×C4⋊C4—471no—
422C22×C4⋊C4—471no—
423C22×C4⋊C4—471no—
424C22×C4⋊C4C2×D4711yescharacteristic
425C22×C4⋊C4C2×D4711yescharacteristic
426C22×C22⋊C4—471no—
427C22×C22⋊C4—471no—
428C22×C22⋊C4—471no—
429C22×C22⋊C4—471no—
430C22×C22⋊C4—471no—
431C22×C22⋊C4—471no—
432C22×C22⋊C4—471no—
433C22×C22⋊C4C2×D4711yescharacteristic
434C22×C22⋊C4C2×D4711yescharacteristic
435C22×C22⋊C4C2×D4711yescharacteristic
436C22×C42—471no—
437C22×C42—471no—
438C22×C42—471no—
439C22×C42—471no—
440C22×C42—471no—
441#390—478no—
442#389—478no—
443#388—478no—
444#388—478no—
445#388—478no—
446#388—478no—
447#387—478no—
448#387—478no—
449#386—478no—
450#385—478no—
451#380—478no—
452C4×C4⋊C4—478no—
453C4×C22⋊C4—478no—
454C4×C22⋊C4—478no—
455C2×#95—471no—
456C2×#95—471no—
457C2×#95—471no—
458C2×#95—471no—
459C2×#95—471no—
460C2×#95—471no—
461C2×#95—471no—
462C2×#95—471no—
463C2×#95—471no—
464C2×#95—471no—
465C47C2×#233511yescharacteristic, complemented, Sylow
466C25C22×D4711yescharacteristic
467C25C22×D4711yescharacteristic
468C22×D4—42no—
469C22×D4—42no—
470C22×D4C2×Dic4718yes—
471C22×D4C22×D4714yes—
472C23×C4—42no—
473C23×C4—42no—
474C23×C4—471no—
475C23×C4—471no—
476C23×C4—471no—
477C23×C4—471no—
478C23×C4—471no—
479C23×C4—471no—
480C23×C4—471no—
481C23×C4—471no—
482C23×C4—474no—
483C23×C4—944no—
484C23×C4—1882no—
485C23×C4—1882no—
486C23×C4C2×Dic4718yescomplemented
487C23×C4C22×D4711yescharacteristic
488C23×C4C22×D4711yescharacteristic
489C23×C4C22×D4711yescharacteristic
490C23×C4C22×D4711yescharacteristic
491C23×C4C22×D4711yescharacteristic
492C23×C4C22×D4714yes—
493#123C2×Dic47164yescomplemented
494C2×C4⋊C4—474no—
495C2×C4⋊C4—474no—
496C2×C4⋊C4—474no—
497C2×C4⋊C4—474no—
498C2×C4⋊C4—474no—
499C2×C4⋊C4—944no—
500C2×C4⋊C4—1882no—
501C2×C4⋊C4—1882no—
502C2×C4⋊C4—1882no—
503C2×C4⋊C4—1882no—
504C2×C4⋊C4C2×Dic4718yescomplemented
505C2×C4⋊C4C2×Dic4718yescomplemented
506C2×C4⋊C4C22×D4714yes—
507C2×C4⋊C4C22×D4714yes—
508C2×C22⋊C4—474no—
509C2×C22⋊C4—474no—
510C2×C22⋊C4—474no—
511C2×C22⋊C4—474no—
512C2×C22⋊C4—474no—
513C2×C22⋊C4—474no—
514C2×C22⋊C4—474no—
515C2×C22⋊C4—944no—
516C2×C22⋊C4—944no—
517C2×C22⋊C4—944no—
518C2×C22⋊C4—1882no—
519C2×C22⋊C4—1882no—
520C2×C22⋊C4—1882no—
521C2×C22⋊C4—1882no—
522C2×C22⋊C4C2×Dic4718yes—
523C2×C22⋊C4C2×Dic4718yes—
524C2×C22⋊C4C2×Dic4718yescomplemented
525C2×C22⋊C4C22×D4714yes—
526C2×C22⋊C4C22×D4714yes—
527C2×C22⋊C4C22×D4714yes—
528C2×C42—474no—
529C2×C42—474no—
530C2×C42—474no—
531C2×C42—474no—
532C2×C42—474no—
533C2×C42—944no—
534C2×C42—1882no—
535C2×C42—1882no—
536C2×C42—1882no—
537C2×C42—1882no—
538#95—474no—
539#95—474no—
540#95—474no—
541#95—474no—
542#95—474no—
543#95—474no—
544#95—474no—
545#95—474no—
546#95—474no—
547#95—474no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24C22×Dic4714yes—
561C24C22×Dic4714yes—
562C24C23×D4712yes—
563C24C23×D4712yes—
564C24C23×D4711yescharacteristic
565C2×D4—416no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4C22×Dic47116yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—416no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—474no—
583C22×C4—474no—
584C22×C4—472no—
585C22×C4—472no—
586C22×C4—472no—
587C22×C4—472no—
588C22×C4—472no—
589C22×C4—472no—
590C22×C4—472no—
591C22×C4—472no—
592C22×C4—948no—
593C22×C4—942no—
594C22×C4—942no—
595C22×C4—942no—
596C22×C4—942no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—1884no—
616C22×C4—1884no—
617C22×C4—18816no—
618C22×C4C22×Dic4714yes—
619C22×C4C22×Dic4714yes—
620C22×C4C22×Dic4714yes—
621C22×C4C22×Dic4714yes—
622C22×C4C22×Dic4714yes—
623C22×C4C22×Dic47116yescomplemented
624C22×C4C23×D4712yes—
625C22×C4C23×D4712yes—
626C22×C4C23×D4712yes—
627C22×C4C23×D4712yes—
628C22×C4C23×D4712yes—
629C4⋊C4—948no—
630C4⋊C4—1884no—
631C4⋊C4—1884no—
632C4⋊C4—1884no—
633C4⋊C4—1884no—
634C4⋊C4C22×Dic47116yescomplemented
635C4⋊C4C22×Dic47116yescomplemented
636C22⋊C4—948no—
637C22⋊C4—948no—
638C22⋊C4—948no—
639C22⋊C4—1884no—
640C22⋊C4—1884no—
641C22⋊C4—1884no—
642C22⋊C4—1884no—
643C22⋊C4C22×Dic47116yes—
644C22⋊C4C22×Dic47116yes—
645C22⋊C4C22×Dic47116yescomplemented
646C42—948no—
647C42—1884no—
648C42—1884no—
649C42—1884no—
650C42—1884no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23C23×Dic4714yes—
678C23C23×Dic4714yes—
679C23C23×Dic4712yes—
680C23#41×D4712yes—
681C23#41×D4712yes—
682C23#1309406912yes—
683C23#1309406912yes—
684C23#1309407012yes—
685C23#1309407112yes—
686C23C24×D4711yescharacteristic
687D4—416no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—416no—
704C2×C4—474no—
705C2×C4—474no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—948no—
711C2×C4—948no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—18816no—
731C2×C4—1884no—
732C2×C4—1884no—
733C2×C4—1884no—
734C2×C4—1884no—
735C2×C4—1884no—
736C2×C4—1884no—
737C2×C4C23×Dic4714yes—
738C2×C4C23×Dic4714yes—
739C2×C4C23×Dic4714yes—
740C2×C4C23×Dic4714yes—
741C2×C4C23×Dic4714yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—416no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22#41×Dic4714yes—
759C22#1568959814yes—
760C22#1568960614yes—
761C22#1568970914yes—
762C22#1568971614yes—
763C22#1568972514yes—
764C22#1568974114yes—
765C22C24×Dic4711yescharacteristic
766C22C2×#41×D4711yescharacteristic
767C22C2×#41×D4711yescharacteristic
768C22C2×#1309406911yescharacteristic
769C22C2×#1309406911yescharacteristic
770C22C2×#1309407011yescharacteristic
771C22C2×#1309407111yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—24no—
777C4—944no—
778C4—944no—
779C4—1882no—
780C4—1882no—
781C4—1882no—
782C4—1882no—
783C4—1882no—
784C4—1882no—
785C2—44no—
786C2—44no—
787C2#2024618218yesdirect product factor
788C2C2×#41×Dic4711yescharacteristic
789C2C2×#1568959811yescharacteristic
790C2C2×#1568960611yescharacteristic
791C2C2×#1568970911yescharacteristic
792C2C2×#1568971611yescharacteristic
793C2C2×#1568972511yescharacteristic
794C2C2×#1568974111yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC22×#123×C47C2
socleC24×C47C24
prime radicalC23×D4×C47C22
cosocleC23×C47C25
hypercenterC22×#123D47
hypocenterC47C2×#2335
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #20246182C2direct (N × H)
3. C2×#15689022C2semidirect
4. C2×#15689016C2semidirect
5. C2×#15689016C2semidirect
6. C2×#15689016C2semidirect
7. C2×#15689016C2semidirect
8. C2×#15689009C2semidirect
9. C2×#15689009C2semidirect
11. C2×#15688998C2semidirect
12. C2×#15688983C2semidirect
13. C2×C4⋊C4×Dic47C2semidirect
14. C2×C22⋊C4×Dic47C2semidirect
15. C2×C4×C22⋊Dic47C2semidirect
36. #15689022C22semidirect
37. #15689016C22semidirect
38. #15689016C22semidirect
39. #15689016C22semidirect
40. #15689016C22semidirect
41. #15689009C22semidirect
42. #15689009C22semidirect
44. #15688998C22semidirect
45. #15688983C22semidirect
46. C4⋊C4×Dic47C22semidirect
47. C22⋊C4×Dic47C22semidirect
48. C4×C22⋊Dic47C22semidirect
61. C2×#123×C47C4semidirect
132. C23×C4×C47C2×C4semidirect
139. #123×C47C2×C4semidirect
140. C2×C4⋊C4×C47C2×C4semidirect
141. C2×C4⋊C4×C47C2×C4semidirect
146. C2×C22⋊C4×C47C2×C4semidirect
189. C22×C4×C47C22×C4semidirect
231. C4⋊C4×C47C22×C4semidirect
232. C4⋊C4×C47C22×C4semidirect
235. C22⋊C4×C47C22×C4semidirect
406. C2×C47#2335semidirect
417. C2×#123Dic47semidirect
465. C47C2×#2335semidirect
486. C23×C4C2×Dic47semidirect
493. #123C2×Dic47semidirect
504. C2×C4⋊C4C2×Dic47semidirect
505. C2×C4⋊C4C2×Dic47semidirect
524. C2×C22⋊C4C2×Dic47semidirect
623. C22×C4C22×Dic47semidirect
634. C4⋊C4C22×Dic47semidirect
635. C4⋊C4C22×Dic47semidirect
645. C22⋊C4C22×Dic47semidirect
787. C2#20246182direct (N × H)

Maximal subgroups

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

subgroupindex
#202461822
C2×#156890262
C2×#156890222
C2×#156890162
C2×#156890092
C2×#156890032
C2×#156889982
C2×#156889832
C2×C4⋊C4×Dic472
C2×C22⋊C4×Dic472
C2×C4×C22⋊Dic472
C22×#123×C472
C2×#233547