Finite Group Databasebeta

← C2×#20247836 #26385800

Subgroups — C2×#20247836 #26385800

Order 12032.

2702 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094001C211yesmaximal, characteristic
2C22×#13093980C211yesmaximal, characteristic
3#20247836C2116yesmaximal, direct product factor
4C2×#15689051C211yesmaximal, characteristic
5C2×#15689051C211yesmaximal, characteristic
6C2×#15689048C211yesmaximal, characteristic
7C2×#15689027C211yesmaximal, characteristic, complemented
8C2×#15689027C211yesmaximal, characteristic, complemented
9C2×#15689010C211yesmaximal, characteristic, complemented
10C2×#15689009C211yesmaximal, characteristic, complemented
11C2×#15689006C211yesmaximal, characteristic, complemented
12C2×#15689005C211yesmaximal, characteristic, complemented
13C2×#15688992C211yesmaximal, characteristic, complemented
14C2×#15688987C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic47C211yesmaximal, characteristic
16C2×C47×#397C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C2×#13094001—28no—
20C2×#13094001C2218yes—
21C2×#13093980—28no—
22C2×#13093980C2218yes—
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×C22⋊Dic47C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×C4×Dic47C2211yescharacteristic
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37C22×C4×Dic47C2211yescharacteristic
38#15689051C2218yes—
39#15689051C2218yes—
40#15689048C2218yes—
41#15689027C2218yescomplemented
42#15689027C2218yescomplemented
43#15689010C2218yescomplemented
44#15689009C2218yescomplemented
45#15689006C2218yescomplemented
46#15689005C2218yescomplemented
47#15688992C2218yescomplemented
48#15688987C2218yescomplemented
49C22⋊C4×Dic47C2218yes—
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
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C47×#397C2218yes—
66C2×#95×C47C2211yescharacteristic
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C22×Dic94—24no—
70C22×Dic94—24no—
71C22×Dic94—24no—
72C22×Dic94C2314yes—
73C23×Dic47—24no—
74C23×Dic47—24no—
75C23×Dic47D418yes—
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2314yes—
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85#13094001—232no—
86#13093980—232no—
87C2×C4⋊Dic47—24no—
88C2×C4⋊Dic47—24no—
89C2×C4⋊Dic47C2314yes—
90C2×C4⋊Dic47C2314yes—
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⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×C22⋊Dic47—24no—
104C2×C22⋊Dic47—24no—
105C2×C22⋊Dic47—24no—
106C2×C22⋊Dic47C2314yes—
107C2×C22⋊Dic47C2314yes—
108C2×C22⋊Dic47C2314yes—
109C2×C4×Dic47—24no—
110C2×C4×Dic47—24no—
111C2×C4×Dic47—24no—
112C2×C4×Dic47—24no—
113C2×C4×Dic47C2314yes—
114C2×C4×Dic47C2314yes—
115C2×C4×Dic47C2314yes—
116C2×C4×Dic47C2314yes—
117C47⋊#95C2314yes—
118C47⋊#95C2314yes—
119C47⋊#95C2314yes—
120C47⋊#95C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C47⋊#95C2314yes—
128C25×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C23×C4×C47C2311yescharacteristic
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47—24no—
136C2×C4⋊C4×C47C2314yes—
137C2×C22⋊C4×C47—24no—
138C2×C22⋊C4×C47—24no—
139C2×C22⋊C4×C47—24no—
140C2×C22⋊C4×C47C2314yes—
141C2×C22⋊C4×C47C2314yes—
142C2×C22⋊C4×C47C2314yes—
143#95×C47C2314yes—
144#95×C47C2314yes—
145#95×C47C2314yes—
146C24×C47—22no—
147C24×C47—22no—
148C24×C47—22no—
149C24×C47—22no—
150C24×C47—22no—
151C24×C47—22no—
152C24×C47C2×D414yes—
153C24×C47C2412yes—
154C24×C47C2411yescharacteristic
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
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#4114yes—
173C22×C4×C47C2412yes—
174C22×C4×C47C2412yes—
175C22×C4×C47C2412yes—
176C22×C4×C47C2412yes—
177C22×C4×C47C2412yes—
178C22×C4×C47C2412yes—
179C22×Dic47—22no—
180C22×Dic47—22no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—232no—
184C22×Dic47—28no—
185C22×Dic47—28no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
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×Dic47C2×D414yes—
202C22×Dic47C2×D4116yes—
203C22×Dic47C2×D414yes—
204C22×Dic47#4114yes—
205C22×Dic47#4114yes—
206C22×Dic47#4114yes—
207C22×Dic47C2412yes—
208C22×Dic47C2412yes—
209C22×Dic47C2412yes—
210C22×Dic47C2412yes—
211C22×Dic47C2412yes—
212C22×Dic47C2412yes—
213C22×Dic47C2412yes—
214C22×Dic47C2412yes—
215C2×Dic94—28no—
216C2×Dic94—28no—
217C2×Dic94—28no—
218C2×Dic94—416no—
219C4⋊C4×C47—28no—
220C22⋊C4×C47—28no—
221C22⋊C4×C47—28no—
222C22⋊C4×C47—28no—
223C22⋊Dic47—28no—
224C22⋊Dic47—28no—
225C22⋊Dic47—28no—
226C4⋊Dic47—28no—
227C4⋊Dic47—28no—
228Dic47⋊C4—28no—
229Dic47⋊C4—28no—
230Dic47⋊C4—28no—
231Dic47⋊C4—28no—
232Dic47⋊C4—28no—
233Dic47⋊C4—28no—
234C4×Dic47—28no—
235C4×Dic47—28no—
236C4×Dic47—28no—
237C4×Dic47—28no—
238C23×C47—28no—
239C23×C47—28no—
240C23×C47—28no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—44no—
248C23×C47—44no—
249C23×C47—44no—
250C23×C47—44no—
251C23×C47C22×D414yes—
252C23×C47C22×D412yes—
253C23×C47C2×#4112yes—
254C23×C47C2×#4112yes—
255C23×C47C2×#4112yes—
256C23×C47C2×#4112yes—
257C23×C472−1+412yes—
258C23×C472−1+412yes—
259C23×C47C2511yescharacteristic
260C2×C4×C47—28no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
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—44no—
279C2×C4×C47—44no—
280C2×C4×C47—44no—
281C2×C4×C47—44no—
282C2×C4×C47—44no—
283C2×C4×C47C2×#4114yes—
284C2×Dic47—28no—
285C2×Dic47—28no—
286C2×Dic47—22no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—232no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
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—44no—
307C2×Dic47—44no—
308C2×Dic47—44no—
309C2×Dic47—44no—
310C2×Dic47—44no—
311C2×Dic47#123116yes—
312C2×Dic47C22×D414yes—
313C2×Dic47C22×D414yes—
314C2×Dic47C2×#4114yes—
315C2×Dic47C2×#4114yes—
316C2×Dic47C2×#4114yes—
317Dic94—416no—
318C2×#2499—471nomaximal, Sylow
319C22×C47—24no—
320C22×C47—24no—
321C22×C47—24no—
322C22×C47—42no—
323C22×C47—42no—
324C22×C47—42no—
325C22×C47—42no—
326C22×C47—416no—
327C22×C47C2×#12314yes—
328C22×C47#53214yes—
329C22×C47#53614yes—
330C22×C47#55214yes—
331C22×C47#55214yes—
332C22×C47#55614yes—
333C22×C47#55614yes—
334C22×C47C23×D411yescharacteristic
335C22×C47C22×#4111yescharacteristic
336C22×C47C22×#4111yescharacteristic
337C22×C47C22×#4111yescharacteristic
338C22×C47C22×#4111yescharacteristic
339C22×C47C2×2−1+411yescharacteristic
340C22×C47C2×2−1+411yescharacteristic
341C4×C47—24no—
342C4×C47—42no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47—42no—
347Dic47—24no—
348Dic47—24no—
349Dic47—42no—
350Dic47—42no—
351Dic47—42no—
352Dic47—42no—
353Dic47—42no—
354Dic47C2×#12318yes—
355C22×C22⋊Q8—471no—
356C22×#117—471no—
357#2499—4716no—
358C2×#397—471no—
359C2×#397—471no—
360C2×#397—471no—
361C2×#397D4711yescharacteristic
362C2×#391—471no—
363C2×#391—471no—
364C2×#387—471no—
365C2×#387—471no—
366C2×#387—471no—
367C2×#387—471no—
368C2×#384—471no—
369C2×#382—471no—
370C2×C4×C22⋊C4—471no—
371C2×C47—44no—
372C2×C47#249918yescomplemented
373C2×C47C22×#12311yescharacteristic
374C2×C47C2×#53211yescharacteristic
375C2×C47C2×#53611yescharacteristic
376C2×C47C2×#55211yescharacteristic
377C2×C47C2×#55211yescharacteristic
378C2×C47C2×#55611yescharacteristic
379C2×C47C2×#55611yescharacteristic
380C23×Q8—471no—
381C24×C4—471no—
382C2×C22⋊Q8—478no—
383C2×C22⋊Q8—948no—
384C2×#117—478no—
385C2×#117—948no—
386C22×C4⋊C4—471no—
387C22×C4⋊C4—471no—
388C22×C4⋊C4—471no—
389C22×C4⋊C4—471no—
390C22×C4⋊C4—471no—
391C22×C4⋊C4—471no—
392C22×C4⋊C4—471no—
393C22×C4⋊C4—471no—
394C22×C4⋊C4C2×D4711yescharacteristic
395C22×C22⋊C4—471no—
396C22×C22⋊C4—471no—
397C22×C22⋊C4—471no—
398C22×C22⋊C4C2×D4711yescharacteristic
399C22×C22⋊C4C2×D4711yescharacteristic
400C22×C22⋊C4C2×D4711yescharacteristic
401C22×C42—471no—
402C22×C42—471no—
403C22×C42—471no—
404C22×C42—471no—
405#397—478no—
406#397—478no—
407#397—478no—
408#397C2×D4718yes—
409#391—478no—
410#391—478no—
411#387—478no—
412#387—478no—
413#387—478no—
414#387—478no—
415#384—478no—
416#382—478no—
417C4×C22⋊C4—478no—
418C2×#95—471no—
419C2×#95—471no—
420C2×#95—471no—
421C2×#95—471no—
422C2×#95—471no—
423C2×#95—471no—
424C2×#95—471no—
425C2×#95—471no—
426C2×#95—471no—
427C2×#95—471no—
428C2×#95—471no—
429C2×#95C2×D4711yescharacteristic
430C2×#95C2×D4711yescharacteristic
431C2×#95C2×D4711yescharacteristic
432C47C2×#249911yescharacteristic, complemented, Sylow
433C25C22×D4711yescharacteristic
434C22×Q8—474no—
435C22×Q8—944no—
436C22×Q8—944no—
437C22×Q8—944no—
438C23×C4—471no—
439C23×C4—478no—
440C23×C4—474no—
441C23×C4—471no—
442C23×C4—471no—
443C23×C4—471no—
444C23×C4—471no—
445C23×C4—471no—
446C23×C4—471no—
447C23×C4—471no—
448C23×C4—944no—
449C23×C4—944no—
450C23×C4C22×D4711yescharacteristic
451C23×C4C22×D4711yescharacteristic
452C23×C4C22×D4711yescharacteristic
453C23×C4C22×D4711yescharacteristic
454C23×C4C22×D4711yescharacteristic
455C23×C4C22×D4711yescharacteristic
456C22⋊Q8—9432no—
457#117—9432no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—474no—
460C2×C4⋊C4—474no—
461C2×C4⋊C4—474no—
462C2×C4⋊C4—474no—
463C2×C4⋊C4—474no—
464C2×C4⋊C4—474no—
465C2×C4⋊C4—474no—
466C2×C4⋊C4—474no—
467C2×C4⋊C4—944no—
468C2×C4⋊C4—944no—
469C2×C4⋊C4—944no—
470C2×C4⋊C4—944no—
471C2×C4⋊C4—944no—
472C2×C4⋊C4—944no—
473C2×C4⋊C4—944no—
474C2×C4⋊C4—944no—
475C2×C4⋊C4C22×D4714yes—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—474no—
480C2×C22⋊C4—474no—
481C2×C22⋊C4—474no—
482C2×C22⋊C4—944no—
483C2×C22⋊C4—944no—
484C2×C22⋊C4—944no—
485C2×C22⋊C4C22×D4714yes—
486C2×C22⋊C4C22×D4714yes—
487C2×C22⋊C4C22×D4714yes—
488C2×C42—474no—
489C2×C42—474no—
490C2×C42—474no—
491C2×C42—474no—
492C2×C42—944no—
493C2×C42—944no—
494C2×C42—944no—
495C2×C42—944no—
496#95—474no—
497#95—474no—
498#95—474no—
499#95—474no—
500#95—474no—
501#95—474no—
502#95—474no—
503#95—474no—
504#95—474no—
505#95—474no—
506#95—474no—
507#95C22×D4714yes—
508#95C22×D4714yes—
509#95C22×D4714yes—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24D4×D4714yes—
517C24C23×D4712yes—
518C24C23×D4711yescharacteristic
519C2×Q8—948no—
520C2×Q8—948no—
521C2×Q8—948no—
522C2×Q8—18816no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
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—474no—
541C22×C4—474no—
542C22×C4—474no—
543C22×C4—472no—
544C22×C4—474no—
545C22×C4—4716no—
546C22×C4—474no—
547C22×C4—472no—
548C22×C4—472no—
549C22×C4—472no—
550C22×C4—472no—
551C22×C4—472no—
552C22×C4—472no—
553C22×C4—472no—
554C22×C4—9432no—
555C22×C4—948no—
556C22×C4—948no—
557C22×C4—942no—
558C22×C4—942no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
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#1062535214yes—
577C22×C4C23×D4712yes—
578C22×C4C23×D4712yes—
579C22×C4C23×D4712yes—
580C22×C4C23×D4712yes—
581C22×C4C23×D4712yes—
582C22×C4C23×D4712yes—
583C4⋊C4—28no—
584C4⋊C4—948no—
585C4⋊C4—948no—
586C4⋊C4—948no—
587C4⋊C4—948no—
588C4⋊C4—948no—
589C4⋊C4—948no—
590C4⋊C4—948no—
591C4⋊C4—948no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—948no—
596C22⋊C4—948no—
597C22⋊C4—948no—
598C42—948no—
599C42—948no—
600C42—948no—
601C42—948no—
602C23—28no—
603C23—28no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—28no—
609C23—22no—
610C23—22no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23C2×D4×D4714yes—
616C23C2×D4×D4712yes—
617C23#41×D4712yes—
618C23#41×D4712yes—
619C23#41×D4712yes—
620C23C2×#1062535212yes—
621C23#1309407112yes—
622C23#1309407112yes—
623C23C24×D4711yescharacteristic
624Q8—18816no—
625C2×C4—28no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—4716no—
649C2×C4—474no—
650C2×C4—474no—
651C2×C4—474no—
652C2×C4—474no—
653C2×C4—474no—
654C2×C4—9432no—
655C2×C4—948no—
656C2×C4—948no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—1884no—
677C2×C4—1884no—
678C2×C4—1884no—
679C2×C4—1884no—
680C2×C4—1884no—
681C2×C4C2×#1062535214yes—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—416no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22#123×D4714yes—
691C22#1568966814yes—
692C22#1568969514yes—
693C22#1568980914yes—
694C22#1568981014yes—
695C22#1568984014yes—
696C22#1568984214yes—
697C22C22×D4×D4711yescharacteristic
698C22C2×#41×D4711yescharacteristic
699C22C2×#41×D4711yescharacteristic
700C22C2×#41×D4711yescharacteristic
701C22C22×#1062535211yescharacteristic
702C22C2×#1309407111yescharacteristic
703C22C2×#1309407111yescharacteristic
704C4—24no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—478no—
711C4—944no—
712C4—944no—
713C4—1882no—
714C4—1882no—
715C4—1882no—
716C4—1882no—
717C4—1882no—
718C2—44no—
719C2#2024783618yesdirect product factor
720C2C2×#123×D4711yescharacteristic
721C2C2×#1568966811yescharacteristic
722C2C2×#1568969511yescharacteristic
723C2C2×#1568980911yescharacteristic
724C2C2×#1568981011yescharacteristic
725C2C2×#1568984011yescharacteristic
726C2C2×#1568984211yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#397C2
socleC24×C47C24
prime radicalC25×C47C23
hypercenterC2×#397D47
hypocenterC47C2×#2499
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. #20247836C2direct (N × H)
7. C2×#15689027C2semidirect
8. C2×#15689027C2semidirect
9. C2×#15689010C2semidirect
10. C2×#15689009C2semidirect
11. C2×#15689006C2semidirect
12. C2×#15689005C2semidirect
13. C2×#15688992C2semidirect
14. C2×#15688987C2semidirect
41. #15689027C22semidirect
42. #15689027C22semidirect
43. #15689010C22semidirect
44. #15689009C22semidirect
45. #15689006C22semidirect
46. #15689005C22semidirect
47. #15688992C22semidirect
48. #15688987C22semidirect
372. C2×C47#2499semidirect
432. C47C2×#2499semidirect
719. C2#20247836direct (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×#130939802
#202478362
C2×#156890512
C2×#156890482
C2×#156890272
C2×#156890102
C2×#156890092
C2×#156890062
C2×#156890052
C2×#156889922
C2×#156889872
C2×C22⋊C4×Dic472
C2×C47×#3972
C2×#249947