Finite Group Databasebeta

← C2×#20257478 #27124497

Subgroups — C2×#20257478 #27124497

Order 12032.

7022 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257478C2132yesmaximal, direct product factor
2C2×#15689851C213yesmaximal, complemented
3C2×#15689849C211yesmaximal, characteristic, complemented
4C2×#15689841C213yesmaximal, complemented
5C2×#15689814C213yesmaximal, complemented
6C2×#15689812C213yesmaximal, complemented
7C2×Q8×D188C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
9C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
10C2×#15689735C213yesmaximal, complemented
11C2×#15689731C213yesmaximal, complemented
12C2×#15689677C213yesmaximal, complemented
13C2×#15689651C213yesmaximal
14C2×#15689599C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#519C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19#15689851C22148yescomplemented
20#15689849C22116yescomplemented
21#15689841C22148yescomplemented
22#15689814C22148yescomplemented
23#15689812C22148yescomplemented
24Q8×D188C22116yescomplemented
25Q8×C22⋊D47C22116yescomplemented
26Q8×C22⋊D47C22116yescomplemented
27#15689735C22148yescomplemented
28#15689731C22148yescomplemented
29#15689677C22148yescomplemented
30C2×#13094024C2213yes—
31C2×#13094023C2213yes—
32C2×#13094022C2213yes—
33C2×#13094022C2213yes—
34#15689651C22148yes—
35C2×#13094019C2213yes—
36C2×#13094018C2216yes—
37C2×#13094017C2216yes—
38C2×#13094017C2213yes—
39C2×#13094016C2216yes—
40C2×#13094016C2213yes—
41C2×#13094015C2213yes—
42C2×#13094014C2216yes—
43C2×#13094014C2213yes—
44C2×#13094014C2216yes—
45C2×#13094010C2213yes—
46C2×#13094009C2213yes—
47C2×#13094006C2213yes—
48C2×#13094004C2213yes—
49C2×#13094004C2213yes—
50C2×#13094003C2213yes—
51C2×#13094003C2213yes—
52C2×#13094002C2213yes—
53C2×#13094000C2213yes—
54C2×#13094000C2213yes—
55C2×#13093997C2211yescharacteristic
56#15689599C22116yescomplemented
57C2×Q8×Dic47C2211yescharacteristic
58C2×Q8×Dic47C2211yescharacteristic
59C2×C4×Dic94C2213yes—
60C2×C4×Dic94C2213yes—
61C2×C4×Dic94C2213yes—
62C2×C4×Dic94C2216yes—
63C2×#13093989C2213yes—
64C2×#13093989C2213yes—
65C4×Q8×D47C22116yescomplemented
66C2×C4×D188C2213yes—
67C2×C4×C22⋊D47C2213yes—
68C2×C4×C22⋊D47C2213yes—
69C2×#13093982C2213yes—
70C2×#13093981C2213yes—
71C2×#13093981C2216yes—
72C2×C4⋊C4×D47C2213yes—
73C2×C42×D47C2213yes—
74C23×Q8×C47C2211yescharacteristic
75C47×#519C22116yescomplemented
76C2×C4×Q8×C47C2211yescharacteristic
77C2×C4×Q8×C47C2211yescharacteristic
78C2×C4×Q8×C47C2213yes—
79C2×C4×Q8×C47C2213yes—
80C2×#117×C47C2213yes—
81C2×#117×C47C2213yes—
82C22×Dic94C2313yes—
83C22×Dic94C2313yes—
84C22×Dic94C2313yes—
85C2×Q8×D47—28no—
86C2×Q8×D47—28no—
87C2×Q8×D47C2318yes—
88C2×Q8×D47C2318yes—
89C22×D188C2311yescharacteristic
90C22×C22⋊D47C2311yescharacteristic
91C22×C22⋊D47C2311yescharacteristic
92C22×C4×D47C2311yescharacteristic
93C22×C4×D47C2313yes—
94C22×C4×D47C2313yes—
95C22×C4×D47C2313yes—
96#13094024C23124yes—
97#13094023C23124yes—
98#13094022C23124yes—
99#13094022C23124yes—
100#13094019C23124yes—
101#13094018C23148yes—
102#13094017C23124yes—
103#13094017C23148yes—
104#13094016C23148yes—
105#13094016C23124yes—
106#13094015C23124yes—
107#13094014C23148yes—
108#13094014C23148yes—
109#13094014C23124yes—
110#13094010C23124yes—
111#13094009C23124yes—
112#13094006C23124yes—
113#13094004C23124yes—
114#13094004C23124yes—
115#13094003C23124yes—
116#13094003C23124yes—
117#13094002C23124yes—
118#13094000C23124yes—
119#13094000C23124yes—
120#13093997C2318yes—
121Q8×Dic47C2318yes—
122Q8×Dic47C2318yes—
123C4×Dic94C23124yes—
124C4×Dic94C23124yes—
125C4×Dic94C23148yes—
126C4×Dic94C23124yes—
127#13093989C23124yes—
128#13093989C23124yes—
129C4×D188C23124yes—
130C4×C22⋊D47C23124yes—
131C4×C22⋊D47C23124yes—
132#13093982C23124yes—
133#13093981C23124yes—
134#13093981C23148yes—
135C2×C4⋊Dic47C2313yes—
136C2×C4⋊Dic47C2313yes—
137C2×C4⋊Dic47C2313yes—
138C2×C4⋊Dic47C2316yes—
139C2×C4⋊Dic47C2313yes—
140C2×Dic47⋊C4C2316yes—
141C2×Dic47⋊C4C2313yes—
142C2×Dic47⋊C4C2313yes—
143C2×Dic47⋊C4C2316yes—
144C2×Dic47⋊C4C2316yes—
145C2×Dic47⋊C4C2313yes—
146C2×Dic47⋊C4C2313yes—
147C2×Dic47⋊C4C2311yescharacteristic
148C2×Dic47⋊C4C2316yes—
149C2×Dic47⋊C4C2313yes—
150C4⋊C4×D47C23124yes—
151C2×C22⋊Dic47C2313yes—
152C2×C22⋊Dic47C2313yes—
153C2×(C2×D47)⋊C4C2311yescharacteristic
154C2×(C2×D47)⋊C4C2313yes—
155C2×(C2×D47)⋊C4C2313yes—
156C2×(C2×D47)⋊C4C2313yes—
157C2×(C2×D47)⋊C4C2313yes—
158C2×(C2×D47)⋊C4C2313yes—
159C2×C4×Dic47C2313yes—
160C2×C4×Dic47C2313yes—
161C2×C4×Dic47C2313yes—
162C2×C4×Dic47C2316yes—
163C2×C4×Dic47C2313yes—
164C42×D47C23124yes—
165C22×Q8×C47—28no—
166C22×Q8×C47C2318yes—
167C22×Q8×C47C2313yes—
168C22×Q8×C47C2311yescharacteristic
169C23×C4×C47C2313yes—
170C4×Q8×C47C23124yes—
171C4×Q8×C47C2318yes—
172C4×Q8×C47C23124yes—
173C4×Q8×C47C2318yes—
174#117×C47C23124yes—
175#117×C47C23124yes—
176C2×C4⋊C4×C47C2313yes—
177C2×C4⋊C4×C47C2313yes—
178C2×C4⋊C4×C47C2313yes—
179C2×C4⋊C4×C47C2313yes—
180C2×C22⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47C2313yes—
182C2×C42×C47C2313yes—
183C2×C42×C47C2316yes—
184C2×C42×C47C2313yes—
185C24×C47C2411yescharacteristic
186C23×D47C2411yescharacteristic
187C23×D47C2411yescharacteristic
188C2×Q8×C47—232no—
189C2×Q8×C47—212no—
190C2×Q8×C47#4118yes—
191C2×Q8×C47C24112yes—
192C2×Q8×C47C2414yes—
193C22×C4×C47—212no—
194C22×C4×C47C2411yescharacteristic
195C22×C4×C47C2413yes—
196C22×C4×C47C2413yes—
197C22×C4×C47C2411yescharacteristic
198C22×C4×C47C2413yes—
199C22×C4×C47C24112yes—
200C22×C4×C47C2413yes—
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47C2414yes—
204C2×C22⋊D47C2414yes—
205C22×Dic47C2413yes—
206C22×Dic47C2411yescharacteristic
207C22×Dic47C2413yes—
208C22×Dic47C2413yes—
209C22×Dic47C2413yes—
210C22×Dic47C2411yescharacteristic
211Q8×D47—232no—
212Q8×D47—232no—
213C2×D188—24no—
214C2×D188C2414yes—
215C2×C4×D47—212no—
216C2×C4×D47—212no—
217C2×C4×D47—212no—
218C2×C4×D47—24no—
219C2×C4×D47C2414yes—
220C2×C4×D47C24112yes—
221C2×C4×D47C24112yes—
222C2×C4×D47C24112yes—
223C2×Dic94—212no—
224C2×Dic94—212no—
225C2×Dic94—212no—
226C2×Dic94C24112yes—
227C2×Dic94C24112yes—
228C2×Dic94C24112yes—
229C4⋊C4×C47C24112yes—
230C4⋊C4×C47C24112yes—
231C4⋊C4×C47C24112yes—
232C4⋊C4×C47C24112yes—
233C22⋊C4×C47C2414yes—
234C22⋊C4×C47C24112yes—
235C42×C47C24112yes—
236C42×C47C24124yes—
237C42×C47C24112yes—
238C22⋊Dic47C24112yes—
239C22⋊Dic47C24112yes—
240(C2×D47)⋊C4C2414yes—
241(C2×D47)⋊C4C24112yes—
242(C2×D47)⋊C4C24112yes—
243(C2×D47)⋊C4C24112yes—
244(C2×D47)⋊C4C24112yes—
245(C2×D47)⋊C4C24112yes—
246C4⋊Dic47C24112yes—
247C4⋊Dic47C24112yes—
248C4⋊Dic47C24112yes—
249C4⋊Dic47C24124yes—
250C4⋊Dic47C24112yes—
251Dic47⋊C4C24124yes—
252Dic47⋊C4C24112yes—
253Dic47⋊C4C24112yes—
254Dic47⋊C4C24124yes—
255Dic47⋊C4C24124yes—
256Dic47⋊C4C24112yes—
257Dic47⋊C4C24112yes—
258Dic47⋊C4C2414yes—
259Dic47⋊C4C24124yes—
260Dic47⋊C4C24112yes—
261C4×Dic47C24112yes—
262C4×Dic47C24112yes—
263C4×Dic47C24112yes—
264C4×Dic47C24124yes—
265C4×Dic47C24112yes—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47C2512yes—
270C23×C47C2511yescharacteristic
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D472−1+414yes—
277C22×D47C2512yes—
278C22×D47C2512yes—
279Q8×C47—224no—
280Q8×C47C2×#41116yes—
281C2×C4×C47—26no—
282C2×C4×C47—26no—
283C2×C4×C47—26no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—224no—
287C2×C4×C47C2×#41112yes—
288C2×C4×C47C2516yes—
289C2×C4×C47C2512yes—
290C2×C4×C47C2516yes—
291C2×C4×C47C2512yes—
292C2×C4×C47C2516yes—
293C2×C4×C47C2516yes—
294C22⋊D47—28no—
295C22⋊D47—28no—
296C2×Dic47—26no—
297C2×Dic47—26no—
298C2×Dic47—26no—
299C2×Dic47—26no—
300C2×Dic47—22no—
301C2×Dic472−1+414yes—
302C2×Dic47C2512yes—
303C2×Dic47C2516yes—
304C2×Dic47C2516yes—
305C2×Dic47C2516yes—
306C2×Dic47C2516yes—
307C2×Dic47C2512yes—
308D188—28no—
309C4×D47—224no—
310C4×D47—224no—
311C4×D47—224no—
312C4×D47—28no—
313Dic94—224no—
314Dic94—224no—
315Dic94—224no—
316C2×#3523—471nomaximal, Sylow
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—44no—
321C22×C47C22×#4112yes—
322C22×C47C2×2−1+412yes—
323C22×C47C2×2−1+412yes—
324C22×C47C2611yescharacteristic
325C2×D47—22no—
326C2×D47—22no—
327C2×D47—28no—
328C2×D47—22no—
329C2×D47—22no—
330C2×D47—22no—
331C2×D47—44no—
332C2×D47C2×2−1+414yes—
333C4×C47—26no—
334C4×C47—26no—
335C4×C47—26no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47C22×#41112yes—
339Dic47—26no—
340Dic47—26no—
341Dic47—26no—
342Dic47—26no—
343Dic47—22no—
344Dic47C2×2−1+414yes—
345#3523—4732no—
346C2×#557—471no—
347C2×#557—473no—
348C2×#556—473no—
349C2×#552—473no—
350C2×#552—473no—
351C2×D4×Q8—471no—
352C2×D4×Q8—471no—
353C2×D4×Q8—471no—
354C2×#541—473no—
355C2×#541—473no—
356C2×#533—473no—
357C2×#529—473no—
358C2×#519—471no—
359C2×#519D4711yescharacteristic, complemented
360C22×C4×Q8—471no—
361C2×C47—42no—
362C2×C47#352314yescomplemented
363C2×C47C23×#4111yescharacteristic
364C2×C47C22×2−1+411yescharacteristic
365C2×C47C22×2−1+411yescharacteristic
366D47—24no—
367D47—42no—
368C23×Q8—471no—
369C23×Q8—471no—
370C23×Q8C2×D4711yescharacteristic
371#557—4716no—
372#557—4748no—
373#556—4748no—
374#552—4748no—
375#552—4748no—
376D4×Q8—4716no—
377D4×Q8—4716no—
378D4×Q8—4716no—
379#541—4748no—
380#541—4748no—
381#533—4748no—
382C2×C4⋊Q8—473no—
383C2×C4⋊Q8—473no—
384C2×C4⋊Q8—473no—
385C2×C4⋊Q8—473no—
386#529—4748no—
387C2×#126—473no—
388C2×#126—473no—
389C2×#126—476no—
390C2×#126—476no—
391C2×#125—473no—
392C2×#125—476no—
393C2×#125—476no—
394C2×#125—473no—
395C2×#125—476no—
396C2×#125—473no—
397C2×#124—473no—
398C2×#123—473no—
399C2×#123—473no—
400C2×C22⋊Q8—473no—
401C2×C22⋊Q8—473no—
402C2×C22⋊Q8—473no—
403C2×C22⋊Q8—473no—
404C2×C22⋊Q8—473no—
405C2×C22⋊Q8—473no—
406C2×C22⋊Q8—473no—
407C2×#121—471no—
408#519—4716no—
409#519C2×D47116yescomplemented
410C2×C4×Q8—471no—
411C2×C4×Q8—471no—
412C2×C4×Q8—4716no—
413C2×C4×Q8—473no—
414C2×C4×Q8—473no—
415C2×C4×Q8—473no—
416C2×C4×Q8—473no—
417C2×C4×Q8—473no—
418C2×C4×Q8—476no—
419C2×C4×Q8C2×D4711yescharacteristic
420C2×C4×Q8C2×D4713yes—
421C2×C4×Q8C2×D4711yescharacteristic
422C2×C4×Q8C2×D4713yes—
423C2×C4×D4—473no—
424C2×C4×D4—473no—
425C2×C4×D4—473no—
426C2×#117—473no—
427C2×#117—473no—
428C2×#117—476no—
429C2×#117C2×D4713yes—
430C2×#117C2×D4713yes—
431C22×C4⋊C4—473no—
432C22×C42—473no—
433C47C2×#352311yescharacteristic, complemented, Sylow
434C22×Q8—28no—
435C22×Q8—478no—
436C22×Q8—478no—
437C22×Q8—473no—
438C22×Q8—473no—
439C22×Q8—473no—
440C22×Q8—948no—
441C22×Q8—948no—
442C22×Q8C22×D4713yes—
443C22×Q8C22×D4718yes—
444C22×Q8C22×D4711yescharacteristic
445C22×D4—471no—
446C22×D4—471no—
447C22×D4—471no—
448C23×C4—473no—
449C23×C4—473no—
450C23×C4—473no—
451C23×C4—471no—
452C23×C4C22×D4713yes—
453C4⋊Q8—4724no—
454C4⋊Q8—4724no—
455C4⋊Q8—4724no—
456C4⋊Q8—4724no—
457#126—4724no—
458#126—4724no—
459#126—4748no—
460#126—4748no—
461#125—4724no—
462#125—4748no—
463#125—4748no—
464#125—4724no—
465#125—4748no—
466#125—4724no—
467#124—4724no—
468#123—4724no—
469#123—4724no—
470C22⋊Q8—4724no—
471C22⋊Q8—4724no—
472C22⋊Q8—4724no—
473C22⋊Q8—4724no—
474C22⋊Q8—4724no—
475C22⋊Q8—4724no—
476C22⋊Q8—4724no—
477#121—478no—
478C4×Q8—478no—
479C4×Q8—478no—
480C4×Q8—4724no—
481C4×Q8—4724no—
482C4×Q8—4724no—
483C4×Q8—4724no—
484C4×Q8—4724no—
485C4×Q8—4748no—
486C4×Q8C22×D4718yes—
487C4×Q8C22×D47124yes—
488C4×Q8C22×D4718yes—
489C4×Q8C22×D47124yes—
490C4×D4—4724no—
491C4×D4—4724no—
492C4×D4—4724no—
493#117—4724no—
494#117—4724no—
495#117—4748no—
496#117C22×D47124yes—
497#117C22×D47124yes—
498C2×C4⋊C4—473no—
499C2×C4⋊C4—476no—
500C2×C4⋊C4—473no—
501C2×C4⋊C4—473no—
502C2×C4⋊C4—473no—
503C2×C4⋊C4—476no—
504C2×C4⋊C4—476no—
505C2×C4⋊C4—473no—
506C2×C4⋊C4—473no—
507C2×C4⋊C4—473no—
508C2×C4⋊C4—471no—
509C2×C4⋊C4—476no—
510C2×C4⋊C4—476no—
511C2×C4⋊C4—473no—
512C2×C4⋊C4—473no—
513C2×C4⋊C4—4724no—
514C2×C4⋊C4C22×D4713yes—
515C2×C4⋊C4C22×D4713yes—
516C2×C4⋊C4C22×D4713yes—
517C2×C4⋊C4C22×D4713yes—
518C2×C22⋊C4—473no—
519C2×C22⋊C4—473no—
520C2×C22⋊C4—471no—
521C2×C22⋊C4—473no—
522C2×C22⋊C4—473no—
523C2×C22⋊C4—473no—
524C2×C22⋊C4—473no—
525C2×C22⋊C4—473no—
526C2×C22⋊C4C22×D4711yescharacteristic
527C2×C22⋊C4C22×D4713yes—
528C2×C42—476no—
529C2×C42—473no—
530C2×C42—473no—
531C2×C42—473no—
532C2×C42—473no—
533C2×C42—4724no—
534C2×C42C22×D4713yes—
535C2×C42C22×D4716yes—
536C2×C42C22×D4713yes—
537C24—471no—
538C24—471no—
539C24C23×D4711yescharacteristic
540C2×Q8—232no—
541C2×Q8—212no—
542C2×Q8—4712no—
543C2×Q8—4712no—
544C2×Q8—4712no—
545C2×Q8—9412no—
546C2×Q8—9432no—
547C2×Q8—9432no—
548C2×Q8—9412no—
549C2×Q8—9412no—
550C2×Q8#1062535018yes—
551C2×Q8C23×D47112yes—
552C2×Q8C23×D4714yes—
553C2×D4—474no—
554C2×D4—474no—
555C2×D4—474no—
556C2×D4—944no—
557C2×D4—944no—
558C2×D4—944no—
559C22×C4—212no—
560C22×C4—471no—
561C22×C4—473no—
562C22×C4—471no—
563C22×C4—473no—
564C22×C4—473no—
565C22×C4—473no—
566C22×C4—474no—
567C22×C4—4712no—
568C22×C4—4712no—
569C22×C4—4712no—
570C22×C4—944no—
571C22×C4—9412no—
572C22×C4—9412no—
573C22×C4—9412no—
574C22×C4C23×D47112yes—
575C22×C4C23×D4713yes—
576C22×C4C23×D4711yescharacteristic
577C22×C4C23×D4713yes—
578C22×C4C23×D4711yescharacteristic
579C22×C4C23×D4713yes—
580C22×C4C23×D4713yes—
581C4⋊C4—4724no—
582C4⋊C4—4712no—
583C4⋊C4—4712no—
584C4⋊C4—4724no—
585C4⋊C4—4724no—
586C4⋊C4—4712no—
587C4⋊C4—4712no—
588C4⋊C4—474no—
589C4⋊C4—4724no—
590C4⋊C4—4712no—
591C4⋊C4—4712no—
592C4⋊C4—4712no—
593C4⋊C4—4712no—
594C4⋊C4—4724no—
595C4⋊C4—4712no—
596C4⋊C4C23×D47112yes—
597C4⋊C4C23×D47112yes—
598C4⋊C4C23×D47112yes—
599C4⋊C4C23×D47112yes—
600C22⋊C4—4712no—
601C22⋊C4—4712no—
602C22⋊C4—474no—
603C22⋊C4—4712no—
604C22⋊C4—4712no—
605C22⋊C4—4712no—
606C22⋊C4—4712no—
607C22⋊C4—4712no—
608C22⋊C4C23×D4714yes—
609C22⋊C4C23×D47112yes—
610C42—4712no—
611C42—4712no—
612C42—4712no—
613C42—4724no—
614C42—4712no—
615C42C23×D47112yes—
616C42C23×D47124yes—
617C42C23×D47112yes—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—474no—
622C23—472no—
623C23—472no—
624C23—942no—
625C23—942no—
626C23—942no—
627C23—942no—
628C23—942no—
629C23C24×D4712yes—
630C23C24×D4711yescharacteristic
631Q8—224no—
632Q8—9424no—
633Q8—9424no—
634Q8—9424no—
635Q8C2×#10625350116yes—
636D4—948no—
637D4—948no—
638D4—948no—
639C2×C4—26no—
640C2×C4—22no—
641C2×C4—26no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—224no—
645C2×C4—474no—
646C2×C4—472no—
647C2×C4—476no—
648C2×C4—472no—
649C2×C4—476no—
650C2×C4—476no—
651C2×C4—476no—
652C2×C4—948no—
653C2×C4—9424no—
654C2×C4—946no—
655C2×C4—946no—
656C2×C4—946no—
657C2×C4—942no—
658C2×C4—946no—
659C2×C4—9424no—
660C2×C4—9424no—
661C2×C4C2×#10625350112yes—
662C2×C4C24×D4716yes—
663C2×C4C24×D4712yes—
664C2×C4C24×D4716yes—
665C2×C4C24×D4712yes—
666C2×C4C24×D4716yes—
667C2×C4C24×D4716yes—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—474no—
673C22—942no—
674C22—942no—
675C22—948no—
676C22—942no—
677C22—942no—
678C22—942no—
679C22—1884no—
680C22C22×#1062535012yes—
681C222−1+4×D4712yes—
682C222−1+4×D4712yes—
683C22C25×D4711yescharacteristic
684C4—26no—
685C4—22no—
686C4—26no—
687C4—22no—
688C4—26no—
689C4—474no—
690C4—946no—
691C4—946no—
692C4—946no—
693C4—942no—
694C4—946no—
695C4C22×#10625350112yes—
696C2—42no—
697C2—944no—
698C2—1882no—
699C2#2025747814yesdirect product factor
700C2C23×#1062535011yescharacteristic
701C2C2×2−1+4×D4711yescharacteristic
702C2C2×2−1+4×D4711yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#519C2
socleC23×C47C25
prime radicalC2×#13093997C22
hypercenterC2×#519D47
hypocenterC47C2×#3523
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. #20257478C2direct (N × H)
2. C2×#15689851C2semidirect
3. C2×#15689849C2semidirect
4. C2×#15689841C2semidirect
5. C2×#15689814C2semidirect
6. C2×#15689812C2semidirect
7. C2×Q8×D188C2semidirect
8. C2×Q8×C22⋊D47C2semidirect
9. C2×Q8×C22⋊D47C2semidirect
10. C2×#15689735C2semidirect
11. C2×#15689731C2semidirect
12. C2×#15689677C2semidirect
14. C2×#15689599C2semidirect
15. C2×C4×Q8×D47C2semidirect
16. C2×C47×#519C2semidirect
19. #15689851C22semidirect
20. #15689849C22semidirect
21. #15689841C22semidirect
22. #15689814C22semidirect
23. #15689812C22semidirect
24. Q8×D188C22semidirect
25. Q8×C22⋊D47C22semidirect
26. Q8×C22⋊D47C22semidirect
27. #15689735C22semidirect
28. #15689731C22semidirect
29. #15689677C22semidirect
56. #15689599C22semidirect
65. C4×Q8×D47C22semidirect
75. C47×#519C22semidirect
359. C2×#519D47semidirect
362. C2×C47#3523semidirect
409. #519C2×D47semidirect
433. C47C2×#3523semidirect
699. C2#20257478direct (N × H)

Maximal subgroups

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

subgroupindex
#202574782
C2×#156898512
C2×#156898492
C2×#156898412
C2×#156898142
C2×#156898122
C2×Q8×D1882
C2×Q8×C22⋊D472
C2×#156897352
C2×#156897312
C2×#156896772
C2×#156896512
C2×#156895992
C2×C4×Q8×D472
C2×C47×#5192
C2×#352347