Finite Group Databasebeta

← C2×#20246396 #26375798

Subgroups — C2×#20246396 #26375798

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×#13094002C211yesmaximal, characteristic
2C22×C4×Dic94C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D47C211yesmaximal, characteristic
4#20246396C2116yesmaximal, direct product factor
5C2×#15689027C211yesmaximal, characteristic, complemented
6C2×#15689022C211yesmaximal, characteristic, complemented
7C2×#15689020C211yesmaximal, characteristic, complemented
8C2×#15689018C211yesmaximal, characteristic, complemented
9C2×#15689010C211yesmaximal, characteristic, complemented
10C2×#15688997C211yesmaximal, characteristic
11C2×#15688997C211yesmaximal, characteristic
12C2×#15688974C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
14C2×#15688970C211yesmaximal, characteristic
15C2×#15688970C211yesmaximal, characteristic
16C2×C47×#387C211yesmaximal, characteristic, complemented
17C23×Dic94C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C2×#13094002C4116yescomplemented
22C2×#13094002C2218yes—
23C2×C4×Dic94—28no—
24C2×C4×Dic94C2218yescomplemented
25C22×C4⋊Dic47C2211yescharacteristic
26C22×C4⋊Dic47C2211yescharacteristic
27C22×C4⋊Dic47C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C2×C4⋊C4×D47—28no—
35C2×C4⋊C4×D47C2218yes—
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43C22×C4×Dic47C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45#15689027C2218yescomplemented
46#15689022C2218yescomplemented
47#15689020C2218yescomplemented
48#15689018C2218yescomplemented
49#15689010C2218yescomplemented
50#15688997C2218yes—
51#15688997C2218yes—
52#15688974C2218yescomplemented
53C4×(C2×D47)⋊C4C2218yes—
54#15688970C2218yes—
55#15688970C2218yes—
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C42×C47C2211yescharacteristic
65C47×#387C2218yescomplemented
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C22×Dic94—24no—
72C22×Dic94—24no—
73C22×Dic94C2×C418yescomplemented
74C22×Dic94C2314yes—
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C22×C4×D47—24no—
83C22×C4×D47—24no—
84C22×C4×D47—24no—
85C22×C4×D47—24no—
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—42no—
89C22×C4×D47—42no—
90C22×C4×D47C2×C418yes—
91C22×C4×D47C2314yes—
92C22×C4×D47C2314yes—
93C22×C4×D47C2314yes—
94#13094002C2×C4164yescomplemented
95C4×Dic94—232no—
96C2×C4⋊Dic47—24no—
97C2×C4⋊Dic47—24no—
98C2×C4⋊Dic47—42no—
99C2×C4⋊Dic47C2314yes—
100C2×C4⋊Dic47C2314yes—
101C2×C4⋊Dic47C2314yes—
102C2×Dic47⋊C4—24no—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—42no—
105C2×Dic47⋊C4C2×C418yescomplemented
106C2×Dic47⋊C4C2×C418yescomplemented
107C2×Dic47⋊C4D418yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C4⋊C4×D47—232no—
115C2×(C2×D47)⋊C4—24no—
116C2×(C2×D47)⋊C4C2×C418yes—
117C2×(C2×D47)⋊C4C2×C418yes—
118C2×(C2×D47)⋊C4Q818yescomplemented
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×C4×Dic47—24no—
124C2×C4×Dic47—24no—
125C2×C4×Dic47—24no—
126C2×C4×Dic47—42no—
127C2×C4×Dic47—42no—
128C2×C4×Dic47C2314yes—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2314yes—
131C2×C4×Dic47C2314yes—
132C2×C4×Dic47C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C2×C4⋊C4×C47—24no—
147C2×C4⋊C4×C47C2×C418yescomplemented
148C2×C4⋊C4×C47C2314yes—
149C2×C4⋊C4×C47C2314yes—
150C2×C42×C47—24no—
151C2×C42×C47C2314yes—
152#95×C47C2314yes—
153#95×C47C2314yes—
154#95×C47C2314yes—
155#95×C47C2314yes—
156C24×C47C2411yescharacteristic
157C23×D47—22no—
158C23×D47—22no—
159C23×D47—22no—
160C23×D47—22no—
161C23×D47C22×C414yes—
162C23×D47C2×Q814yes—
163C23×D47#4114yes—
164C23×D47C2412yes—
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—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47C22×C414yes—
182C22×C4×C47C22×C414yes—
183C22×C4×C47C22×C414yes—
184C22×C4×C47C2×D414yes—
185C22×C4×C47C2×Q814yes—
186C22×C4×C47C2412yes—
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—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47C22×C414yes—
208C22×Dic47C22×C414yes—
209C22×Dic47C22×C414yes—
210C22×Dic47C2×D414yes—
211C22×Dic47C2×D414yes—
212C22×Dic47C2×Q814yes—
213C22×Dic47#4114yes—
214C22×Dic47C2412yes—
215C22×Dic47C2412yes—
216C22×Dic47C2412yes—
217C22×Dic47C2412yes—
218C22×Dic47C2412yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C2×C4×D47—232no—
222C2×C4×D47—28no—
223C2×C4×D47—28no—
224C2×C4×D47—28no—
225C2×C4×D47—28no—
226C2×C4×D47—28no—
227C2×C4×D47—28no—
228C2×C4×D47—44no—
229C2×C4×D47—44no—
230C2×C4×D47—416no—
231C2×C4×D47—416no—
232C2×C4×D47C22×C4116yes—
233C2×Dic94—232no—
234C2×Dic94—28no—
235C2×Dic94—28no—
236C2×Dic94C22×C4116yescomplemented
237C4⋊C4×C47—28no—
238C4⋊C4×C47C22×C4116yescomplemented
239C42×C47—28no—
240(C2×D47)⋊C4—28no—
241(C2×D47)⋊C4C22×C4116yes—
242(C2×D47)⋊C4C22×C4116yes—
243(C2×D47)⋊C4C2×Q8116yescomplemented
244C4⋊Dic47—28no—
245C4⋊Dic47—28no—
246C4⋊Dic47—44no—
247Dic47⋊C4—28no—
248Dic47⋊C4—28no—
249Dic47⋊C4—44no—
250Dic47⋊C4C22×C4116yescomplemented
251Dic47⋊C4C22×C4116yescomplemented
252Dic47⋊C4C2×D4116yes—
253C4×Dic47—28no—
254C4×Dic47—28no—
255C4×Dic47—28no—
256C4×Dic47—44no—
257C4×Dic47—44no—
258C23×C47C23×C412yes—
259C23×C47C22×D412yes—
260C23×C47C22×Q812yes—
261C23×C47C2×#4112yes—
262C23×C47C2×#4112yes—
263C23×C47H(5,𝔽2)12yes—
264C23×C472−1+412yes—
265C23×C47C2511yescharacteristic
266C22×D47—28no—
267C22×D47—28no—
268C22×D47—28no—
269C22×D47—28no—
270C22×D47—28no—
271C22×D47—28no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47C4×Q8116yescomplemented
277C22×D47C23×C414yes—
278C22×D47C22×Q814yes—
279C22×D47C2×#4114yes—
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—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—44no—
302C2×C4×C47—44no—
303C2×C4×C47C23×C414yes—
304C2×C4×C47C23×C414yes—
305C2×C4×C47C23×C414yes—
306C2×C4×C47C22×D414yes—
307C2×C4×C47C22×Q814yes—
308C2×Dic47—28no—
309C2×Dic47—28no—
310C2×Dic47—28no—
311C2×Dic47—28no—
312C2×Dic47—22no—
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—44no—
327C2×Dic47—44no—
328C2×Dic47C4×D4116yes—
329C2×Dic47C23×C414yes—
330C2×Dic47C23×C414yes—
331C2×Dic47C23×C414yes—
332C2×Dic47C22×D414yes—
333C2×Dic47C22×D414yes—
334C2×Dic47C22×Q814yes—
335C2×Dic47C2×#4114yes—
336C4×D47—232no—
337C4×D47—416no—
338C4×D47—416no—
339Dic94—232no—
340C2×#2360—471nomaximal, Sylow
341C22×C47C2×C4×D414yes—
342C22×C47C2×C4×Q814yes—
343C22×C47#52014yes—
344C22×C47#54614yes—
345C22×C47D4×Q814yes—
346C22×C47#55214yes—
347C22×C47#55414yes—
348C22×C47C24×C411yescharacteristic
349C22×C47C23×D411yescharacteristic
350C22×C47C23×Q811yescharacteristic
351C22×C47C22×#4111yescharacteristic
352C22×C47C22×#4111yescharacteristic
353C22×C47C2×H(5,𝔽2)11yescharacteristic
354C22×C47C2×2−1+411yescharacteristic
355C2×D47—232no—
356C2×D47—24no—
357C2×D47—24no—
358C2×D47—24no—
359C2×D47—24no—
360C2×D47—24no—
361C2×D47—24no—
362C2×D47C2×C4×Q818yescomplemented
363C4×C47—24no—
364C4×C47—24no—
365C4×C47—24no—
366C4×C47—24no—
367C4×C47—24no—
368C4×C47—42no—
369C4×C47—42no—
370Dic47—24no—
371Dic47—24no—
372Dic47—24no—
373Dic47—24no—
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×#387D4711yescharacteristic, complemented
387C2×#385—471no—
388C2×#385—471no—
389C2×C4×C4⋊C4—471no—
390C2×C4×C22⋊C4—471no—
391C2×C4×C22⋊C4—471no—
392C2×C4×C22⋊C4—471no—
393C2×C47#236018yescomplemented
394C2×C47C22×C4×D411yescharacteristic
395C2×C47C22×C4×Q811yescharacteristic
396C2×C47C2×#52011yescharacteristic
397C2×C47C2×#54611yescharacteristic
398C2×C47C2×D4×Q811yescharacteristic
399C2×C47C2×#55211yescharacteristic
400C2×C47C2×#55411yescharacteristic
401D47—28no—
402C23×Q8—471no—
403C24×C4—471no—
404C24×C4—471no—
405C24×C4—471no—
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—471no—
415C22×C4⋊C4—471no—
416C22×C4⋊C4—471no—
417C22×C4⋊C4—471no—
418C22×C4⋊C4—471no—
419C22×C4⋊C4—478no—
420C22×C4⋊C4—948no—
421C22×C4⋊C4C2×D4711yescharacteristic
422C22×C4⋊C4C2×D4711yescharacteristic
423C22×C22⋊C4—471no—
424C22×C22⋊C4—471no—
425C22×C22⋊C4—471no—
426C22×C22⋊C4—471no—
427C22×C42—471no—
428C22×C42—471no—
429C22×C42—471no—
430C22×C42—471no—
431C22×C42—471no—
432C22×C42C2×D4711yescharacteristic
433#391—478no—
434#389—478no—
435#389—478no—
436#389—478no—
437#387—478no—
438#387C2×D4718yescomplemented
439#385—478no—
440#385—478no—
441C4×C4⋊C4—478no—
442C4×C22⋊C4—478no—
443C4×C22⋊C4—478no—
444C4×C22⋊C4—478no—
445C2×#95—471no—
446C2×#95—471no—
447C2×#95—471no—
448C2×#95—471no—
449C2×#95—471no—
450C2×#95—471no—
451C2×#95C2×D4711yescharacteristic
452C2×#95C2×D4711yescharacteristic
453C2×#95C2×D4711yescharacteristic
454C2×#95C2×D4711yescharacteristic
455C47C2×#236011yescharacteristic, complemented, Sylow
456C25—471no—
457C22×Q8—478no—
458C22×Q8—474no—
459C22×Q8—944no—
460C22×Q8—944no—
461C23×C4—471no—
462C23×C4—471no—
463C23×C4—471no—
464C23×C4—471no—
465C23×C4—471no—
466C23×C4—478no—
467C23×C4—474no—
468C23×C4—471no—
469C23×C4—471no—
470C23×C4—474no—
471C23×C4—474no—
472C23×C4—944no—
473C23×C4—944no—
474C23×C4—944no—
475C23×C4—944no—
476C23×C4—944no—
477C23×C4—944no—
478C23×C4—1882no—
479C23×C4—1882no—
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4711yescharacteristic
482C23×C4C22×D4711yescharacteristic
483C23×C4C22×D4711yescharacteristic
484C23×C4C22×D4711yescharacteristic
485C23×C4C22×D4711yescharacteristic
486C23×C4C22×D4711yescharacteristic
487C22⋊Q8—4764no—
488C4×Q8—9432no—
489C2×C4⋊C4—24no—
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—9432no—
503C2×C4⋊C4—944no—
504C2×C4⋊C4—944no—
505C2×C4⋊C4—944no—
506C2×C4⋊C4—944no—
507C2×C4⋊C4—1882no—
508C2×C4⋊C4—1882no—
509C2×C4⋊C4C4×D4718yescomplemented
510C2×C4⋊C4C22×D4714yes—
511C2×C4⋊C4C22×D4714yes—
512C2×C22⋊C4—478no—
513C2×C22⋊C4—478no—
514C2×C22⋊C4—478no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—474no—
519C2×C22⋊C4—944no—
520C2×C42—24no—
521C2×C42—474no—
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×C42—1882no—
531C2×C42C22×D4714yes—
532#95—474no—
533#95—474no—
534#95—474no—
535#95—474no—
536#95—474no—
537#95—474no—
538#95C22×D4714yes—
539#95C22×D4714yes—
540#95C22×D4714yes—
541#95C22×D4714yes—
542C24—474no—
543C24—474no—
544C24—474no—
545C24—472no—
546C24—942no—
547C24—942no—
548C24—942no—
549C24—942no—
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—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—474no—
572C22×C4—474no—
573C22×C4—474no—
574C22×C4—472no—
575C22×C4—474no—
576C22×C4—474no—
577C22×C4—474no—
578C22×C4—474no—
579C22×C4—472no—
580C22×C4—472no—
581C22×C4—472no—
582C22×C4—472no—
583C22×C4—4716no—
584C22×C4—472no—
585C22×C4—472no—
586C22×C4—948no—
587C22×C4—9432no—
588C22×C4—948no—
589C22×C4—948no—
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—942no—
606C22×C4—948no—
607C22×C4—1884no—
608C22×C4—1884no—
609C22×C4—18816no—
610C22×C4—18816no—
611C22×C4C2×C4×D4714yes—
612C22×C4C2×C4×D4714yes—
613C22×C4C2×C4×D4714yes—
614C22×C4D4×D4714yes—
615C22×C4Q8×D4714yes—
616C22×C4C23×D4712yes—
617C22×C4C23×D4712yes—
618C22×C4C23×D4712yes—
619C22×C4C23×D4712yes—
620C22×C4C23×D4712yes—
621C22×C4C23×D4712yes—
622C22×C4C23×D4712yes—
623C4⋊C4—28no—
624C4⋊C4—4716no—
625C4⋊C4—4716no—
626C4⋊C4—4716no—
627C4⋊C4—948no—
628C4⋊C4—948no—
629C4⋊C4—948no—
630C4⋊C4—948no—
631C4⋊C4—1884no—
632C4⋊C4—1884no—
633C4⋊C4C2×C4×D47116yescomplemented
634C22⋊C4—4716no—
635C22⋊C4—4716no—
636C22⋊C4—4716no—
637C22⋊C4—948no—
638C42—28no—
639C42—948no—
640C42—948no—
641C42—948no—
642C42—1884no—
643C42—1884no—
644C23—4716no—
645C23—474no—
646C23—474no—
647C23—474no—
648C23—948no—
649C23—948no—
650C23—948no—
651C23—948no—
652C23—948no—
653C23—948no—
654C23—942no—
655C23—942no—
656C23—942no—
657C23—942no—
658C23C22×C4×D4712yes—
659C23C2×D4×D4712yes—
660C23C2×Q8×D4712yes—
661C23#41×D4712yes—
662C23#41×D4712yes—
663C23#1309407012yes—
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—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—4716no—
691C2×C4—474no—
692C2×C4—474no—
693C2×C4—474no—
694C2×C4—474no—
695C2×C4—474no—
696C2×C4—474no—
697C2×C4—474no—
698C2×C4—9432no—
699C2×C4—948no—
700C2×C4—948no—
701C2×C4—948no—
702C2×C4—948no—
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—18816no—
719C2×C4—1884no—
720C2×C4—1884no—
721C2×C4C22×C4×D4714yes—
722C2×C4C22×C4×D4714yes—
723C2×C4C22×C4×D4714yes—
724C2×C4C2×D4×D4714yes—
725C2×C4C2×Q8×D4714yes—
726C22—478no—
727C22—944no—
728C22—944no—
729C22—944no—
730C22—944no—
731C22—9432no—
732C22—944no—
733C22—944no—
734C22C4×D4×D4714yes—
735C22C4×Q8×D4714yes—
736C22#1568960314yes—
737C22#1568976514yes—
738C22#1568978614yes—
739C22#1568980914yes—
740C22#1568982914yes—
741C22C23×C4×D4711yescharacteristic
742C22C22×D4×D4711yescharacteristic
743C22C22×Q8×D4711yescharacteristic
744C22C2×#41×D4711yescharacteristic
745C22C2×#41×D4711yescharacteristic
746C22C2×#1309407011yescharacteristic
747C22C2×#1309407111yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—42no—
755C4—478no—
756C4—944no—
757C4—944no—
758C4—944no—
759C4—944no—
760C4—1882no—
761C4—1882no—
762C2—948no—
763C2#2024639618yesdirect product factor
764C2C2×C4×D4×D4711yescharacteristic
765C2C2×C4×Q8×D4711yescharacteristic
766C2C2×#1568960311yescharacteristic
767C2C2×#1568976511yescharacteristic
768C2C2×#1568978611yescharacteristic
769C2C2×#1568980911yescharacteristic
770C2C2×#1568982911yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#387C2
socleC24×C47C24
prime radicalC24×D47C23
cosocleC23×C47C25
hypercenterC2×#387D47
hypocenterC47C2×#2360
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic94C2semidirect
4. #20246396C2direct (N × H)
5. C2×#15689027C2semidirect
6. C2×#15689022C2semidirect
7. C2×#15689020C2semidirect
8. C2×#15689018C2semidirect
9. C2×#15689010C2semidirect
12. C2×#15688974C2semidirect
16. C2×C47×#387C2semidirect
21. C2×#13094002C4semidirect
24. C2×C4×Dic94C22semidirect
45. #15689027C22semidirect
46. #15689022C22semidirect
47. #15689020C22semidirect
48. #15689018C22semidirect
49. #15689010C22semidirect
52. #15688974C22semidirect
65. C47×#387C22semidirect
73. C22×Dic94C2×C4semidirect
94. #13094002C2×C4semidirect
105. C2×Dic47⋊C4C2×C4semidirect
106. C2×Dic47⋊C4C2×C4semidirect
118. C2×(C2×D47)⋊C4Q8semidirect
147. C2×C4⋊C4×C47C2×C4semidirect
236. C2×Dic94C22×C4semidirect
238. C4⋊C4×C47C22×C4semidirect
243. (C2×D47)⋊C4C2×Q8semidirect
250. Dic47⋊C4C22×C4semidirect
251. Dic47⋊C4C22×C4semidirect
276. C22×D47C4×Q8semidirect
362. C2×D47C2×C4×Q8semidirect
386. C2×#387D47semidirect
393. C2×C47#2360semidirect
438. #387C2×D47semidirect
455. C47C2×#2360semidirect
509. C2×C4⋊C4C4×D47semidirect
633. C4⋊C4C2×C4×D47semidirect
763. C2#20246396direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940022
C22×C4×Dic942
C22×C4⋊C4×D472
#202463962
C2×#156890272
C2×#156890222
C2×#156890202
C2×#156890182
C2×#156890102
C2×#156889972
C2×#156889742
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×C47×#3872
C2×#236047