Finite Group Databasebeta

← C2×#20249217 #26383340

Subgroups — C2×#20249217 #26383340

Order 12032.

2614 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094014C211yesmaximal, characteristic, complemented
2C22×#13093980C211yesmaximal, characteristic
3#20249217C2116yesmaximal, direct product factor
4C2×#15689057C211yesmaximal, characteristic, complemented
5C2×#15689056C211yesmaximal, characteristic, complemented
6C2×#15689054C211yesmaximal, characteristic, complemented
7C2×#15689053C211yesmaximal, characteristic, complemented
8C2×#15689046C211yesmaximal, characteristic
9C2×#15689046C211yesmaximal, characteristic
10C2×#15689046C211yesmaximal, characteristic
11C2×#15689020C211yesmaximal, characteristic, complemented
12C2×#15689018C211yesmaximal, characteristic, complemented
13C2×#15688992C211yesmaximal, characteristic, complemented
14C2×#15688981C211yesmaximal, characteristic
15C2×#15688981C211yesmaximal, characteristic
16C2×C47×#396C211yesmaximal, characteristic
17C24×Dic47C2211yescharacteristic
18C2×#13094014—28no—
19C2×#13094014C2218yescomplemented
20C2×#13093980—28no—
21C2×#13093980C2218yes—
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×Dic47⋊C4C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C22×C22⋊Dic47C2211yescharacteristic
38C22×C22⋊Dic47C2211yescharacteristic
39C22×C22⋊Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42#15689057C2218yescomplemented
43#15689056C2218yescomplemented
44#15689054C2218yescomplemented
45#15689053C2218yescomplemented
46#15689046C2218yes—
47#15689046C2218yes—
48#15689046C2218yes—
49#15689020C2218yescomplemented
50#15689018C2218yescomplemented
51#15688992C2218yescomplemented
52#15688981C2218yes—
53#15688981C2218yes—
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C47×#396C2218yes—
68C2×#95×C47C2211yescharacteristic
69C23×Dic47—24no—
70C23×Dic47—24no—
71C23×Dic47Q818yes—
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2314yes—
80C23×Dic47C2311yescharacteristic
81#13094014—232no—
82#13093980—232no—
83C2×C4⋊Dic47—24no—
84C2×C4⋊Dic47—42no—
85C2×C4⋊Dic47—42no—
86C2×C4⋊Dic47C2314yes—
87C2×C4⋊Dic47C2314yes—
88C2×C4⋊Dic47C2314yes—
89C2×Dic47⋊C4—24no—
90C2×Dic47⋊C4—24no—
91C2×Dic47⋊C4—24no—
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4—24no—
95C2×Dic47⋊C4—24no—
96C2×Dic47⋊C4—24no—
97C2×Dic47⋊C4—42no—
98C2×Dic47⋊C4—42no—
99C2×Dic47⋊C4—42no—
100C2×Dic47⋊C4—42no—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×Dic47⋊C4C2314yes—
104C2×Dic47⋊C4C2314yes—
105C2×Dic47⋊C4C2314yes—
106C2×Dic47⋊C4C2314yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×C22⋊Dic47—24no—
114C2×C22⋊Dic47—42no—
115C2×C22⋊Dic47—42no—
116C2×C22⋊Dic47C2314yes—
117C2×C22⋊Dic47C2314yes—
118C2×C22⋊Dic47C2314yes—
119C2×C4×Dic47—24no—
120C2×C4×Dic47D418yes—
121C2×C4×Dic47C2314yes—
122C2×C4×Dic47C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C47⋊#95C2314yes—
129C47⋊#95C2314yes—
130C25×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C2×C4⋊C4×C47—24no—
138C2×C4⋊C4×C47—42no—
139C2×C4⋊C4×C47—42no—
140C2×C4⋊C4×C47C2314yes—
141C2×C4⋊C4×C47C2314yes—
142C2×C4⋊C4×C47C2314yes—
143C2×C22⋊C4×C47—24no—
144C2×C22⋊C4×C47—42no—
145C2×C22⋊C4×C47—42no—
146C2×C22⋊C4×C47C2314yes—
147C2×C22⋊C4×C47C2314yes—
148C2×C22⋊C4×C47C2314yes—
149#95×C47C2314yes—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47C2×Q814yes—
157C24×C47C2412yes—
158C24×C47C2411yescharacteristic
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
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×C47C2×D414yes—
177C22×C4×C47C2412yes—
178C22×C4×C47C2412yes—
179C22×C4×C47C2412yes—
180C22×C4×C47C2412yes—
181C22×C4×C47C2412yes—
182C22×C4×C47C2412yes—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—232no—
188C22×Dic47—28no—
189C22×Dic47—28no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
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×Dic47C2×D414yes—
206C22×Dic47C2×D414yes—
207C22×Dic47C2×Q814yes—
208C22×Dic47C2×Q8116yes—
209C22×Dic47C2×Q814yes—
210C22×Dic47#4114yes—
211C22×Dic47C2412yes—
212C22×Dic47C2412yes—
213C22×Dic47C2412yes—
214C22×Dic47C2412yes—
215C22×Dic47C2412yes—
216C22×Dic47C2412yes—
217C22×Dic47C2412yes—
218C22×Dic47C2412yes—
219C4⋊C4×C47—28no—
220C4⋊C4×C47—44no—
221C4⋊C4×C47—44no—
222C22⋊C4×C47—28no—
223C22⋊C4×C47—44no—
224C22⋊C4×C47—44no—
225C22⋊Dic47—28no—
226C22⋊Dic47—44no—
227C22⋊Dic47—44no—
228C4⋊Dic47—28no—
229C4⋊Dic47—44no—
230C4⋊Dic47—44no—
231Dic47⋊C4—28no—
232Dic47⋊C4—28no—
233Dic47⋊C4—28no—
234Dic47⋊C4—28no—
235Dic47⋊C4—28no—
236Dic47⋊C4—28no—
237Dic47⋊C4—28no—
238Dic47⋊C4—28no—
239Dic47⋊C4—44no—
240Dic47⋊C4—44no—
241Dic47⋊C4—44no—
242Dic47⋊C4—44no—
243C4×Dic47—28no—
244C4×Dic47C2×D4116yes—
245C23×C47—28no—
246C23×C47—28no—
247C23×C47—28no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—44no—
255C23×C47—44no—
256C23×C47—44no—
257C23×C47—44no—
258C23×C47C22×D412yes—
259C23×C47C22×Q814yes—
260C23×C47C22×Q812yes—
261C23×C47C2×#4112yes—
262C23×C47H(5,𝔽2)12yes—
263C23×C47H(5,𝔽2)12yes—
264C23×C472−1+412yes—
265C23×C472−1+412yes—
266C23×C47C2511yescharacteristic
267C2×C4×C47—28no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—44no—
286C2×C4×C47—44no—
287C2×C4×C47—44no—
288C2×C4×C47—44no—
289C2×C4×C47—44no—
290C2×C4×C47C22×D414yes—
291C2×Dic47—28no—
292C2×Dic47—28no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—232no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—44no—
314C2×Dic47—44no—
315C2×Dic47—44no—
316C2×Dic47—44no—
317C2×Dic47—44no—
318C2×Dic47C22⋊Q8116yes—
319C2×Dic47C22×D414yes—
320C2×Dic47C22×D414yes—
321C2×Dic47C22×Q814yes—
322C2×Dic47C22×Q814yes—
323C2×Dic47C2×#4114yes—
324C2×#2629—471nomaximal, Sylow
325C22×C47—24no—
326C22×C47—24no—
327C22×C47—24no—
328C22×C47—416no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47C2×C22⋊Q814yes—
334C22×C47#53714yes—
335C22×C47#53714yes—
336C22×C47#54014yes—
337C22×C47#54114yes—
338C22×C47#54414yes—
339C22×C47#54414yes—
340C22×C47C23×D411yescharacteristic
341C22×C47C23×Q811yescharacteristic
342C22×C47C22×#4111yescharacteristic
343C22×C47C2×H(5,𝔽2)11yescharacteristic
344C22×C47C2×H(5,𝔽2)11yescharacteristic
345C22×C47C2×2−1+411yescharacteristic
346C22×C47C2×2−1+411yescharacteristic
347C4×C47—24no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47—42no—
352C4×C47—42no—
353Dic47—24no—
354Dic47—24no—
355Dic47—42no—
356Dic47—42no—
357Dic47—42no—
358Dic47—42no—
359Dic47—42no—
360Dic47C2×C22⋊Q818yes—
361C22×#125—471no—
362C22×#117—471no—
363#2629—4716no—
364C2×#398—471no—
365C2×#398—471no—
366C2×#398—471no—
367C2×#398—471no—
368C2×#396—471no—
369C2×#396—471no—
370C2×#396—471no—
371C2×#396D4711yescharacteristic
372C2×#389—471no—
373C2×#389—471no—
374C2×#384—471no—
375C2×#380—471no—
376C2×#380—471no—
377C2×C47—44no—
378C2×C47#262918yescomplemented
379C2×C47C22×C22⋊Q811yescharacteristic
380C2×C47C2×#53711yescharacteristic
381C2×C47C2×#53711yescharacteristic
382C2×C47C2×#54011yescharacteristic
383C2×C47C2×#54111yescharacteristic
384C2×C47C2×#54411yescharacteristic
385C2×C47C2×#54411yescharacteristic
386C24×C4—471no—
387C2×#125—478no—
388C2×#125—948no—
389C2×#117—478no—
390C2×#117—948no—
391C22×C4⋊C4—471no—
392C22×C4⋊C4—471no—
393C22×C4⋊C4—471no—
394C22×C4⋊C4—471no—
395C22×C4⋊C4—471no—
396C22×C4⋊C4—471no—
397C22×C4⋊C4—471no—
398C22×C4⋊C4—471no—
399C22×C4⋊C4—471no—
400C22×C4⋊C4—471no—
401C22×C4⋊C4—471no—
402C22×C4⋊C4—471no—
403C22×C4⋊C4—471no—
404C22×C4⋊C4—471no—
405C22×C4⋊C4—471no—
406C22×C4⋊C4C2×D4711yescharacteristic
407C22×C4⋊C4C2×D4711yescharacteristic
408C22×C4⋊C4C2×D4711yescharacteristic
409C22×C22⋊C4—471no—
410C22×C22⋊C4—471no—
411C22×C22⋊C4—471no—
412C22×C22⋊C4C2×D4711yescharacteristic
413C22×C22⋊C4C2×D4711yescharacteristic
414C22×C22⋊C4C2×D4711yescharacteristic
415C22×C42—471no—
416C22×C42—471no—
417#398—478no—
418#398—478no—
419#398—478no—
420#398—478no—
421#396—478no—
422#396—478no—
423#396—478no—
424#396C2×D4718yes—
425#389—478no—
426#389—478no—
427#384—478no—
428#380—478no—
429#380—478no—
430C2×#95—471no—
431C2×#95—471no—
432C2×#95—471no—
433C2×#95—471no—
434C2×#95—471no—
435C2×#95—471no—
436C2×#95—471no—
437C2×#95C2×D4711yescharacteristic
438C47C2×#262911yescharacteristic, complemented, Sylow
439C25C22×D4711yescharacteristic
440C23×C4—471no—
441C23×C4—478no—
442C23×C4—474no—
443C23×C4—471no—
444C23×C4—471no—
445C23×C4—471no—
446C23×C4—471no—
447C23×C4—471no—
448C23×C4—471no—
449C23×C4—471no—
450C23×C4—944no—
451C23×C4—944no—
452C23×C4C22×D4711yescharacteristic
453C23×C4C22×D4711yescharacteristic
454C23×C4C22×D4711yescharacteristic
455C23×C4C22×D4711yescharacteristic
456C23×C4C22×D4711yescharacteristic
457C23×C4C22×D4711yescharacteristic
458#125—9432no—
459#117—9432no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—474no—
464C2×C4⋊C4—474no—
465C2×C4⋊C4—474no—
466C2×C4⋊C4—474no—
467C2×C4⋊C4—474no—
468C2×C4⋊C4—474no—
469C2×C4⋊C4—474no—
470C2×C4⋊C4—474no—
471C2×C4⋊C4—474no—
472C2×C4⋊C4—474no—
473C2×C4⋊C4—474no—
474C2×C4⋊C4—474no—
475C2×C4⋊C4—474no—
476C2×C4⋊C4—474no—
477C2×C4⋊C4—474no—
478C2×C4⋊C4—944no—
479C2×C4⋊C4—944no—
480C2×C4⋊C4—944no—
481C2×C4⋊C4—944no—
482C2×C4⋊C4—944no—
483C2×C4⋊C4—944no—
484C2×C4⋊C4—944no—
485C2×C4⋊C4—944no—
486C2×C4⋊C4—944no—
487C2×C4⋊C4—1882no—
488C2×C4⋊C4—1882no—
489C2×C4⋊C4—1882no—
490C2×C4⋊C4—1882no—
491C2×C4⋊C4—1882no—
492C2×C4⋊C4—1882no—
493C2×C4⋊C4C22×D4714yes—
494C2×C4⋊C4C22×D4714yes—
495C2×C4⋊C4C22×D4714yes—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—474no—
500C2×C22⋊C4—474no—
501C2×C22⋊C4—474no—
502C2×C22⋊C4—944no—
503C2×C22⋊C4—1882no—
504C2×C22⋊C4—1882no—
505C2×C22⋊C4C22×D4714yes—
506C2×C22⋊C4C22×D4714yes—
507C2×C22⋊C4C22×D4714yes—
508C2×C42—478no—
509C2×C42—474no—
510C2×C42—474no—
511C2×C42—944no—
512#95—474no—
513#95—474no—
514#95—474no—
515#95—474no—
516#95—474no—
517#95—474no—
518#95—474no—
519#95C22×D4714yes—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24Q8×D4714yes—
527C24C23×D4712yes—
528C24C23×D4711yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—474no—
547C22×C4—474no—
548C22×C4—474no—
549C22×C4—472no—
550C22×C4—474no—
551C22×C4—4716no—
552C22×C4—474no—
553C22×C4—472no—
554C22×C4—472no—
555C22×C4—472no—
556C22×C4—472no—
557C22×C4—472no—
558C22×C4—472no—
559C22×C4—472no—
560C22×C4—948no—
561C22×C4—9432no—
562C22×C4—948no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—942no—
582C22×C4D4×D4714yes—
583C22×C4C23×D4712yes—
584C22×C4C23×D4712yes—
585C22×C4C23×D4712yes—
586C22×C4C23×D4712yes—
587C22×C4C23×D4712yes—
588C22×C4C23×D4712yes—
589C4⋊C4—28no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—948no—
593C4⋊C4—948no—
594C4⋊C4—948no—
595C4⋊C4—948no—
596C4⋊C4—948no—
597C4⋊C4—948no—
598C4⋊C4—948no—
599C4⋊C4—948no—
600C4⋊C4—948no—
601C4⋊C4—1884no—
602C4⋊C4—1884no—
603C4⋊C4—1884no—
604C4⋊C4—1884no—
605C4⋊C4—1884no—
606C4⋊C4—1884no—
607C22⋊C4—28no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—948no—
611C22⋊C4—1884no—
612C22⋊C4—1884no—
613C42—4716no—
614C42—948no—
615C23—28no—
616C23—28no—
617C23—28no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23C2×D4×D4712yes—
629C23C2×Q8×D4714yes—
630C23C2×Q8×D4712yes—
631C23#41×D4712yes—
632C23#1309406912yes—
633C23#1309406912yes—
634C23#1309407112yes—
635C23#1309407112yes—
636C23C24×D4711yescharacteristic
637C2×C4—22no—
638C2×C4—28no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—4716no—
661C2×C4—474no—
662C2×C4—474no—
663C2×C4—474no—
664C2×C4—474no—
665C2×C4—474no—
666C2×C4—9432no—
667C2×C4—948no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—948no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—942no—
686C2×C4—942no—
687C2×C4—942no—
688C2×C4—1884no—
689C2×C4—1884no—
690C2×C4—1884no—
691C2×C4—1884no—
692C2×C4—1884no—
693C2×C4C2×D4×D4714yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—416no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22C22⋊Q8×D4714yes—
703C22#1568970014yes—
704C22#1568970214yes—
705C22#1568972314yes—
706C22#1568973014yes—
707C22#1568975214yes—
708C22#1568975214yes—
709C22C22×D4×D4711yescharacteristic
710C22C22×Q8×D4711yescharacteristic
711C22C2×#41×D4711yescharacteristic
712C22C2×#1309406911yescharacteristic
713C22C2×#1309406911yescharacteristic
714C22C2×#1309407111yescharacteristic
715C22C2×#1309407111yescharacteristic
716C4—24no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—478no—
723C4—944no—
724C4—944no—
725C4—1882no—
726C4—1882no—
727C4—1882no—
728C4—1882no—
729C4—1882no—
730C2—44no—
731C2#2024921718yesdirect product factor
732C2C2×C22⋊Q8×D4711yescharacteristic
733C2C2×#1568970011yescharacteristic
734C2C2×#1568970211yescharacteristic
735C2C2×#1568972311yescharacteristic
736C2C2×#1568973011yescharacteristic
737C2C2×#1568975211yescharacteristic
738C2C2×#1568975211yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#396C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#396D47
hypocenterC47C2×#2629
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#13094014C2semidirect
3. #20249217C2direct (N × H)
4. C2×#15689057C2semidirect
5. C2×#15689056C2semidirect
6. C2×#15689054C2semidirect
7. C2×#15689053C2semidirect
11. C2×#15689020C2semidirect
12. C2×#15689018C2semidirect
13. C2×#15688992C2semidirect
19. C2×#13094014C22semidirect
42. #15689057C22semidirect
43. #15689056C22semidirect
44. #15689054C22semidirect
45. #15689053C22semidirect
49. #15689020C22semidirect
50. #15689018C22semidirect
51. #15688992C22semidirect
378. C2×C47#2629semidirect
438. C47C2×#2629semidirect
731. C2#20249217direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940142
C22×#130939802
#202492172
C2×#156890572
C2×#156890562
C2×#156890542
C2×#156890532
C2×#156890462
C2×#156890202
C2×#156890182
C2×#156889922
C2×#156889812
C2×C47×#3962
C2×#262947