Finite Group Databasebeta

← C2×#20246394 #26375796

Subgroups — C2×#20246394 #26375796

Order 12032.

3614 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094001C211yesmaximal, characteristic
2C22×C4×Dic94C211yesmaximal, characteristic, complemented
3C23×Dic47⋊C4C211yesmaximal, characteristic
4#20246394C2116yesmaximal, direct product factor
5C2×#15689027C211yesmaximal, characteristic, complemented
6C2×#15689021C211yesmaximal, characteristic, complemented
7C2×#15689020C211yesmaximal, characteristic, complemented
8C2×#15689020C211yesmaximal, characteristic, complemented
9C2×#15689007C211yesmaximal, characteristic, complemented
10C2×#15689006C211yesmaximal, characteristic, complemented
11C2×#15688998C211yesmaximal, characteristic
12C2×#15688996C211yesmaximal, characteristic
13C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic47C211yesmaximal, characteristic
15C2×C22⋊C4×Dic47C211yesmaximal, characteristic
16C2×C4×C22⋊C4×C47C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20C2×#13094001C4116yescomplemented
21C2×#13094001C2218yes—
22C2×C4×Dic94—28no—
23C2×C4×Dic94C2218yescomplemented
24C22×C4⋊Dic47C2211yescharacteristic
25C22×C4⋊Dic47C2211yescharacteristic
26C22×C4⋊Dic47C2211yescharacteristic
27C22×Dic47⋊C4—28no—
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2218yes—
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C22×C22⋊Dic47C2211yescharacteristic
38C22×C22⋊Dic47C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689027C2218yescomplemented
44#15689021C2218yescomplemented
45#15689020C2218yescomplemented
46#15689020C2218yescomplemented
47#15689007C2218yescomplemented
48#15689006C2218yescomplemented
49#15688998C2218yes—
50#15688996C2218yes—
51C4×Dic47⋊C4C2218yescomplemented
52C22⋊C4×Dic47C2218yes—
53C22⋊C4×Dic47C2218yes—
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C24×C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C42×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C4×C22⋊C4×C47C2218yes—
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C22×Dic94—24no—
71C22×Dic94—24no—
72C22×Dic94C2×C418yescomplemented
73C22×Dic94C2314yes—
74C23×Dic47—24no—
75C23×Dic47—24no—
76C23×Dic47—24no—
77C23×Dic47—24no—
78C23×Dic47—42no—
79C23×Dic47C2×C418yes—
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2314yes—
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2314yes—
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90#13094001C2×C4164yescomplemented
91C4×Dic94—232no—
92C2×C4⋊Dic47—24no—
93C2×C4⋊Dic47—42no—
94C2×C4⋊Dic47C2×C418yescomplemented
95C2×C4⋊Dic47C2314yes—
96C2×C4⋊Dic47C2314yes—
97C2×C4⋊Dic47C2314yes—
98C2×Dic47⋊C4—24no—
99C2×Dic47⋊C4—24no—
100C2×Dic47⋊C4—24no—
101C2×Dic47⋊C4—24no—
102C2×Dic47⋊C4—232no—
103C2×Dic47⋊C4—42no—
104C2×Dic47⋊C4C2×C418yescomplemented
105C2×Dic47⋊C4C2×C418yescomplemented
106C2×Dic47⋊C4D418yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×C22⋊Dic47—24no—
116C2×C22⋊Dic47C2×C418yes—
117C2×C22⋊Dic47C2314yes—
118C2×C22⋊Dic47C2314yes—
119C2×C4×Dic47—24no—
120C2×C4×Dic47—24no—
121C2×C4×Dic47—24no—
122C2×C4×Dic47—42no—
123C2×C4×Dic47C2314yes—
124C2×C4×Dic47C2314yes—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C25×C47C2311yescharacteristic
136C23×C4×C47—24no—
137C23×C4×C47—24no—
138C23×C4×C47—42no—
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2314yes—
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C2×C22⋊C4×C47C2×C418yes—
147C2×C22⋊C4×C47Q818yescomplemented
148C2×C22⋊C4×C47C2314yes—
149C2×C22⋊C4×C47C2314yes—
150C2×C42×C47—24no—
151C2×C42×C47—42no—
152C2×C42×C47C2314yes—
153C2×C42×C47C2314yes—
154#95×C47C2314yes—
155#95×C47C2314yes—
156C24×C47—22no—
157C24×C47—22no—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47C22×C414yes—
161C24×C47C2×Q814yes—
162C24×C47#4114yes—
163C24×C47C2412yes—
164C24×C47C2411yescharacteristic
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—28no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—28no—
180C22×C4×C47—44no—
181C22×C4×C47—416no—
182C22×C4×C47C22×C414yes—
183C22×C4×C47C22×C414yes—
184C22×C4×C47C2×D414yes—
185C22×C4×C47C2×Q814yes—
186C22×C4×C47C2×Q814yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2412yes—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2412yes—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—232no—
202C22×Dic47—28no—
203C22×Dic47—28no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—28no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47—22no—
214C22×Dic47—28no—
215C22×Dic47—44no—
216C22×Dic47—416no—
217C22×Dic47C22×C414yes—
218C22×Dic47C22×C414yes—
219C22×Dic47C22×C414yes—
220C22×Dic47C22×C4116yes—
221C22×Dic47C22×C414yes—
222C22×Dic47C2×D414yes—
223C22×Dic47C2×D414yes—
224C22×Dic47#4114yes—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C22×Dic47C2412yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C2×Dic94—232no—
234C2×Dic94—28no—
235C2×Dic94—28no—
236C2×Dic94C22×C4116yescomplemented
237C22⋊C4×C47C22×C4116yes—
238C22⋊C4×C47C2×Q8116yescomplemented
239C42×C47—28no—
240C42×C47—44no—
241C22⋊Dic47—28no—
242C22⋊Dic47C22×C4116yes—
243C4⋊Dic47—28no—
244C4⋊Dic47—44no—
245C4⋊Dic47C22×C4116yescomplemented
246Dic47⋊C4—28no—
247Dic47⋊C4—28no—
248Dic47⋊C4—28no—
249Dic47⋊C4—28no—
250Dic47⋊C4—44no—
251Dic47⋊C4C22×C4116yescomplemented
252Dic47⋊C4C22×C4116yescomplemented
253Dic47⋊C4C2×D4116yes—
254C4×Dic47—28no—
255C4×Dic47—28no—
256C4×Dic47—28no—
257C4×Dic47—44no—
258C23×C47—28no—
259C23×C47—28no—
260C23×C47—28no—
261C23×C47—28no—
262C23×C47—28no—
263C23×C47—28no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47C4×Q8116yescomplemented
269C23×C47C23×C414yes—
270C23×C47C23×C412yes—
271C23×C47C22×D412yes—
272C23×C47C22×Q814yes—
273C23×C47C22×Q812yes—
274C23×C47C2×#4112yes—
275C23×C47C2×#4114yes—
276C23×C47C2×#4112yes—
277C23×C47H(5,𝔽2)12yes—
278C23×C472−1+412yes—
279C23×C47C2511yescharacteristic
280C2×C4×C47—28no—
281C2×C4×C47—28no—
282C2×C4×C47—28no—
283C2×C4×C47—28no—
284C2×C4×C47—28no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—416no—
299C2×C4×C47—44no—
300C2×C4×C47C23×C414yes—
301C2×C4×C47C23×C414yes—
302C2×C4×C47C22×D414yes—
303C2×C4×C47C22×Q814yes—
304C2×C4×C47C22×Q814yes—
305C2×Dic47—28no—
306C2×Dic47—28no—
307C2×Dic47—28no—
308C2×Dic47—28no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—232no—
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—416no—
328C2×Dic47—44no—
329C2×Dic47—44no—
330C2×Dic47—44no—
331C2×Dic47C4×D4116yes—
332C2×Dic47C23×C414yes—
333C2×Dic47C23×C414yes—
334C2×Dic47C23×C414yes—
335C2×Dic47C23×C414yes—
336C2×Dic47C22×D414yes—
337C2×Dic47C22×D414yes—
338C2×Dic47C2×#4114yes—
339Dic94—232no—
340C2×#2360—471nomaximal, Sylow
341C22×C47—232no—
342C22×C47—24no—
343C22×C47—24no—
344C22×C47—24no—
345C22×C47—24no—
346C22×C47—24no—
347C22×C47—24no—
348C22×C47C2×C4×D414yes—
349C22×C47C2×C4×Q814yes—
350C22×C47C2×C4×Q818yescomplemented
351C22×C47#52014yes—
352C22×C47#54614yes—
353C22×C47D4×Q814yes—
354C22×C47#55214yes—
355C22×C47#55414yes—
356C22×C47C24×C411yescharacteristic
357C22×C47C23×D411yescharacteristic
358C22×C47C23×Q811yescharacteristic
359C22×C47C22×#4111yescharacteristic
360C22×C47C22×#4111yescharacteristic
361C22×C47C2×H(5,𝔽2)11yescharacteristic
362C22×C47C2×2−1+411yescharacteristic
363C4×C47—24no—
364C4×C47—24no—
365C4×C47—24no—
366C4×C47—24no—
367C4×C47—24no—
368C4×C47—42no—
369Dic47—24no—
370Dic47—24no—
371Dic47—24no—
372Dic47—24no—
373Dic47—42no—
374Dic47—42no—
375Dic47—42no—
376Dic47C2×C4×D418yes—
377C22×C22⋊Q8—471no—
378C22×C4×Q8—471no—
379C23×C4⋊C4—471no—
380#2360—4716no—
381C2×#391—471no—
382C2×#389—471no—
383C2×#389—471no—
384C2×#389—471no—
385C2×#387—471no—
386C2×#387—471no—
387C2×#385—471no—
388C2×#385—471no—
389C2×C4×C4⋊C4—471no—
390C2×C4×C22⋊C4—471no—
391C2×C4×C22⋊C4—471no—
392C2×C4×C22⋊C4D4711yescharacteristic
393C2×C47—28no—
394C2×C47#236018yescomplemented
395C2×C47C22×C4×D411yescharacteristic
396C2×C47C22×C4×Q811yescharacteristic
397C2×C47C2×#52011yescharacteristic
398C2×C47C2×#54611yescharacteristic
399C2×C47C2×D4×Q811yescharacteristic
400C2×C47C2×#55211yescharacteristic
401C2×C47C2×#55411yescharacteristic
402C23×Q8—471no—
403C24×C4—471no—
404C24×C4—471no—
405C24×C4C2×D4711yescharacteristic
406C2×C22⋊Q8—4716no—
407C2×C22⋊Q8—478no—
408C2×C4×Q8—478no—
409C2×C4×Q8—948no—
410C22×C4⋊C4—471no—
411C22×C4⋊C4—471no—
412C22×C4⋊C4—471no—
413C22×C4⋊C4—471no—
414C22×C4⋊C4—478no—
415C22×C4⋊C4—471no—
416C22×C4⋊C4—471no—
417C22×C4⋊C4—471no—
418C22×C4⋊C4—471no—
419C22×C4⋊C4—471no—
420C22×C4⋊C4—471no—
421C22×C4⋊C4—471no—
422C22×C4⋊C4—948no—
423C22×C22⋊C4—471no—
424C22×C22⋊C4—471no—
425C22×C22⋊C4C2×D4711yescharacteristic
426C22×C22⋊C4C2×D4711yescharacteristic
427C22×C42—471no—
428C22×C42—471no—
429C22×C42—471no—
430C22×C42—471no—
431C22×C42C2×D4711yescharacteristic
432C22×C42C2×D4711yescharacteristic
433#391—478no—
434#389—478no—
435#389—478no—
436#389—478no—
437#387—478no—
438#387—478no—
439#385—478no—
440#385—478no—
441C4×C4⋊C4—478no—
442C4×C22⋊C4—478no—
443C4×C22⋊C4—478no—
444C4×C22⋊C4C2×D4718yes—
445C2×#95—471no—
446C2×#95—471no—
447C2×#95—471no—
448C2×#95—471no—
449C2×#95—471no—
450C2×#95—471no—
451C2×#95—471no—
452C2×#95—471no—
453C2×#95C2×D4711yescharacteristic
454C2×#95C2×D4711yescharacteristic
455C47C2×#236011yescharacteristic, complemented, Sylow
456C25C22×D4711yescharacteristic
457C22×Q8—478no—
458C22×Q8—474no—
459C22×Q8—944no—
460C22×Q8—944no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—42no—
464C23×C4—471no—
465C23×C4—478no—
466C23×C4—474no—
467C23×C4—471no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4—471no—
474C23×C4—474no—
475C23×C4—944no—
476C23×C4—944no—
477C23×C4—944no—
478C23×C4—944no—
479C23×C4—1882no—
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4714yes—
482C23×C4C22×D4711yescharacteristic
483C23×C4C22×D4711yescharacteristic
484C23×C4C22×D4711yescharacteristic
485C23×C4C22×D4711yescharacteristic
486C23×C4C22×D4711yescharacteristic
487C22⋊Q8—4764no—
488C4×Q8—9432no—
489C2×C4⋊C4—478no—
490C2×C4⋊C4—478no—
491C2×C4⋊C4—478no—
492C2×C4⋊C4—478no—
493C2×C4⋊C4—474no—
494C2×C4⋊C4—474no—
495C2×C4⋊C4—474no—
496C2×C4⋊C4—474no—
497C2×C4⋊C4—474no—
498C2×C4⋊C4—474no—
499C2×C4⋊C4—474no—
500C2×C4⋊C4—474no—
501C2×C4⋊C4—474no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—9432no—
505C2×C4⋊C4—944no—
506C2×C4⋊C4—944no—
507C2×C4⋊C4—944no—
508C2×C4⋊C4—944no—
509C2×C4⋊C4—944no—
510C2×C4⋊C4—1882no—
511C2×C4⋊C4—1882no—
512C2×C22⋊C4—478no—
513C2×C22⋊C4—474no—
514C2×C22⋊C4—474no—
515C2×C22⋊C4—944no—
516C2×C22⋊C4Dic9418yescomplemented
517C2×C22⋊C4C4×D4718yes—
518C2×C22⋊C4C22×D4714yes—
519C2×C22⋊C4C22×D4714yes—
520C2×C42—24no—
521C2×C42—42no—
522C2×C42—474no—
523C2×C42—474no—
524C2×C42—474no—
525C2×C42—474no—
526C2×C42—944no—
527C2×C42—944no—
528C2×C42—944no—
529C2×C42—1882no—
530C2×C42C22×D4714yes—
531C2×C42C22×D4714yes—
532#95—474no—
533#95—474no—
534#95—474no—
535#95—474no—
536#95—474no—
537#95—474no—
538#95—474no—
539#95—474no—
540#95C22×D4714yes—
541#95C22×D4714yes—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×Dic9414yes—
547C24C2×C4×D4714yes—
548C24#1062535014yes—
549C24C23×D4712yes—
550C24C23×D4711yescharacteristic
551C2×Q8—4716no—
552C2×Q8—948no—
553C2×Q8—9432no—
554C2×Q8—948no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—28no—
570C22×C4—44no—
571C22×C4—416no—
572C22×C4—474no—
573C22×C4—474no—
574C22×C4—474no—
575C22×C4—472no—
576C22×C4—474no—
577C22×C4—474no—
578C22×C4—474no—
579C22×C4—4716no—
580C22×C4—474no—
581C22×C4—472no—
582C22×C4—472no—
583C22×C4—472no—
584C22×C4—472no—
585C22×C4—472no—
586C22×C4—472no—
587C22×C4—472no—
588C22×C4—948no—
589C22×C4—9432no—
590C22×C4—948no—
591C22×C4—948no—
592C22×C4—942no—
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—948no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—1884no—
611C22×C4—18816no—
612C22×C4C2×Dic9414yes—
613C22×C4C2×Dic9414yes—
614C22×C4C2×C4×D4714yes—
615C22×C4C2×C4×D4714yes—
616C22×C4D4×D4714yes—
617C22×C4C23×D4712yes—
618C22×C4C23×D4712yes—
619C22×C4C23×D4712yes—
620C22×C4C23×D4712yes—
621C22×C4C23×D4712yes—
622C22×C4C23×D4712yes—
623C4⋊C4—4716no—
624C4⋊C4—4716no—
625C4⋊C4—4716no—
626C4⋊C4—4716no—
627C4⋊C4—948no—
628C4⋊C4—948no—
629C4⋊C4—948no—
630C4⋊C4—948no—
631C4⋊C4—948no—
632C4⋊C4—1884no—
633C4⋊C4—1884no—
634C22⋊C4—4716no—
635C22⋊C4—948no—
636C22⋊C4C2×Dic94116yescomplemented
637C22⋊C4C2×C4×D47116yes—
638C42—28no—
639C42—44no—
640C42—948no—
641C42—948no—
642C42—948no—
643C42—1884no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23C4×Dic94116yescomplemented
655C23C22×C4×D4714yes—
656C23C22×C4×D4712yes—
657C23C2×D4×D4712yes—
658C23C22×Dic9414yes—
659C23C22×Dic9412yes—
660C23#41×D4712yes—
661C23C2×#1062535014yes—
662C23C2×#1062535012yes—
663C23#1309406912yes—
664C23#1309407112yes—
665C23C24×D4711yescharacteristic
666Q8—9432no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—4716no—
688C2×C4—474no—
689C2×C4—474no—
690C2×C4—474no—
691C2×C4—474no—
692C2×C4—474no—
693C2×C4—474no—
694C2×C4—474no—
695C2×C4—9432no—
696C2×C4—948no—
697C2×C4—948no—
698C2×C4—948no—
699C2×C4—948no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—18816no—
718C2×C4—1884no—
719C2×C4—1884no—
720C2×C4—1884no—
721C2×C4C22×C4×D4714yes—
722C2×C4C22×C4×D4714yes—
723C2×C4C2×D4×D4714yes—
724C2×C4C22×Dic9414yes—
725C2×C4C22×Dic9414yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—232no—
731C22—24no—
732C22—24no—
733C22C4×D4×D4714yes—
734C22C2×C4×Dic9414yes—
735C22C2×C4×Dic9418yescomplemented
736C22#1568960214yes—
737C22#1568976314yes—
738C22D4×Dic9414yes—
739C22#1568980614yes—
740C22#1568983214yes—
741C22C23×C4×D4711yescharacteristic
742C22C22×D4×D4711yescharacteristic
743C22C23×Dic9411yescharacteristic
744C22C2×#41×D4711yescharacteristic
745C22C22×#1062535011yescharacteristic
746C22C2×#1309406911yescharacteristic
747C22C2×#1309407111yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—478no—
755C4—944no—
756C4—944no—
757C4—944no—
758C4—944no—
759C4—1882no—
760C4—1882no—
761C4—1882no—
762C2—28no—
763C2#2024639418yesdirect product factor
764C2C2×C4×D4×D4711yescharacteristic
765C2C22×C4×Dic9411yescharacteristic
766C2C2×#1568960211yescharacteristic
767C2C2×#1568976311yescharacteristic
768C2C2×D4×Dic9411yescharacteristic
769C2C2×#1568980611yescharacteristic
770C2C2×#1568983211yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C4×C22⋊C4×C47C2
socleC24×C47C24
prime radicalC25×C47C23
cosocleC23×C47C25
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C2×#2360
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic94C2semidirect
4. #20246394C2direct (N × H)
5. C2×#15689027C2semidirect
6. C2×#15689021C2semidirect
7. C2×#15689020C2semidirect
8. C2×#15689020C2semidirect
9. C2×#15689007C2semidirect
10. C2×#15689006C2semidirect
13. C2×C4×Dic47⋊C4C2semidirect
20. C2×#13094001C4semidirect
23. C2×C4×Dic94C22semidirect
43. #15689027C22semidirect
44. #15689021C22semidirect
45. #15689020C22semidirect
46. #15689020C22semidirect
47. #15689007C22semidirect
48. #15689006C22semidirect
51. C4×Dic47⋊C4C22semidirect
72. C22×Dic94C2×C4semidirect
90. #13094001C2×C4semidirect
94. C2×C4⋊Dic47C2×C4semidirect
104. C2×Dic47⋊C4C2×C4semidirect
105. C2×Dic47⋊C4C2×C4semidirect
147. C2×C22⋊C4×C47Q8semidirect
236. C2×Dic94C22×C4semidirect
238. C22⋊C4×C47C2×Q8semidirect
245. C4⋊Dic47C22×C4semidirect
251. Dic47⋊C4C22×C4semidirect
252. Dic47⋊C4C22×C4semidirect
268. C23×C47C4×Q8semidirect
350. C22×C47C2×C4×Q8semidirect
394. C2×C47#2360semidirect
455. C47C2×#2360semidirect
516. C2×C22⋊C4Dic94semidirect
636. C22⋊C4C2×Dic94semidirect
654. C23C4×Dic94semidirect
735. C22C2×C4×Dic94semidirect
763. C2#20246394direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940012
C22×C4×Dic942
C23×Dic47⋊C42
#202463942
C2×#156890272
C2×#156890212
C2×#156890202
C2×#156890072
C2×#156890062
C2×#156889982
C2×#156889962
C2×C4×Dic47⋊C42
C2×C22⋊C4×Dic472
C2×C4×C22⋊C4×C472
C2×#236047