Finite Group Databasebeta

← C2×#20257373 #27124469

Subgroups — C2×#20257373 #27124469

Order 12032.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257373C2132yesmaximal, direct product factor
2C2×#15689849C211yesmaximal, characteristic, complemented
3C2×#15689843C213yesmaximal, complemented
4C2×#15689828C213yesmaximal, complemented
5C2×#15689823C213yesmaximal, complemented
6C2×#15689808C213yesmaximal, complemented
7C2×Q8×D188C211yesmaximal, characteristic, complemented
8C2×#15689780C211yesmaximal, characteristic, complemented
9C2×#15689780C211yesmaximal, characteristic, complemented
10C2×#15689738C213yesmaximal, complemented
11C2×#15689735C213yesmaximal, complemented
12C2×#15689655C213yesmaximal, complemented
13C2×#15689651C213yesmaximal, complemented
14C2×#15689599C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#520C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19#15689849C22116yescomplemented
20#15689843C22148yescomplemented
21#15689828C22148yescomplemented
22#15689823C22148yescomplemented
23#15689808C22148yescomplemented
24Q8×D188C22116yescomplemented
25#15689780C22116yescomplemented
26#15689780C22116yescomplemented
27#15689738C22148yescomplemented
28#15689735C22148yescomplemented
29C2×#13094024C2213yes—
30C2×#13094023C2213yes—
31#15689655C22148yescomplemented
32#15689651C22148yescomplemented
33C2×#13094019C2213yes—
34C2×#13094017C2213yes—
35C2×#13094017C2216yes—
36C2×#13094017C2216yes—
37C2×#13094016C2213yes—
38C2×#13094015C2213yes—
39C2×#13094014C2216yes—
40C2×#13094014C2213yes—
41C2×#13094011C2213yes—
42C2×#13094011C2213yes—
43C2×#13094010C2213yes—
44C2×#13094009C2211yescharacteristic
45C2×#13094007C2216yes—
46C2×#13094006C2213yes—
47C2×#13094004C2213yes—
48C2×#13094004C2213yes—
49C2×#13094003C2213yes—
50C2×#13094003C2213yes—
51C2×#13094003C2216yes—
52C2×#13094002C2213yes—
53C2×#13093997C2213yes—
54C2×#13093995C2213yes—
55C2×#13093995C2213yes—
56#15689599C22116yescomplemented
57C2×Q8×Dic47C2211yescharacteristic
58C2×Q8×Dic47C2211yescharacteristic
59C2×C4×Dic94C2213yes—
60C2×C4×Dic94C2213yes—
61C2×C4×Dic94C2213yes—
62C2×#13093989C2213yes—
63C2×#13093989C2213yes—
64C4×Q8×D47C22116yescomplemented
65C2×C4×D188C2213yes—
66C2×C4×C22⋊D47C2213yes—
67C2×C4×C22⋊D47C2213yes—
68C2×C4×C22⋊D47C2216yes—
69C2×#13093983C2216yes—
70C2×#13093982C2213yes—
71C2×#13093981C2213yes—
72C2×C4⋊C4×D47C2213yes—
73C2×C42×D47C2213yes—
74C22×#41×C47C2211yescharacteristic
75C47×#520C22116yescomplemented
76C2×C4×Q8×C47C2211yescharacteristic
77C2×C4×Q8×C47C2211yescharacteristic
78C2×C4×D4×C47C2213yes—
79C2×C4×D4×C47C2213yes—
80C2×#117×C47C2213yes—
81C22×C4⋊C4×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⋊D47C2313yes—
91C22×C22⋊D47C2313yes—
92C22×C4×D47C2311yescharacteristic
93C22×C4×D47C2313yes—
94C22×C4×D47C2313yes—
95C22×C4×D47C2313yes—
96#13094024C23124yes—
97#13094023C23124yes—
98#13094019C23124yes—
99#13094017C23148yes—
100#13094017C23148yes—
101#13094017C23124yes—
102#13094016C23124yes—
103#13094015C23124yes—
104#13094014C23124yes—
105#13094014C23148yes—
106#13094011C23124yes—
107#13094011C23124yes—
108#13094010C23124yes—
109#13094009C2318yes—
110#13094007C23148yes—
111#13094006C23124yes—
112#13094004C23124yes—
113#13094004C23124yes—
114#13094003C23124yes—
115#13094003C23124yes—
116#13094003C23148yes—
117#13094002C23124yes—
118#13093997C23124yes—
119#13093995C23124yes—
120#13093995C23124yes—
121Q8×Dic47C2318yes—
122Q8×Dic47C2318yes—
123C4×Dic94C23124yes—
124C4×Dic94C23124yes—
125C4×Dic94C23124yes—
126#13093989C23124yes—
127#13093989C23124yes—
128C4×D188C23124yes—
129C4×C22⋊D47C23124yes—
130C4×C22⋊D47C23124yes—
131C4×C22⋊D47C23148yes—
132#13093983C23148yes—
133#13093982C23124yes—
134#13093981C23124yes—
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⋊C4C2313yes—
144C2×Dic47⋊C4C2313yes—
145C2×Dic47⋊C4C2316yes—
146C2×Dic47⋊C4C2311yescharacteristic
147C2×Dic47⋊C4C2313yes—
148C4⋊C4×D47C23124yes—
149C2×C22⋊Dic47C2313yes—
150C2×C22⋊Dic47C2316yes—
151C2×C22⋊Dic47C2316yes—
152C2×C22⋊Dic47C2313yes—
153C2×(C2×D47)⋊C4C2311yescharacteristic
154C2×(C2×D47)⋊C4C2313yes—
155C2×(C2×D47)⋊C4C2311yescharacteristic
156C2×(C2×D47)⋊C4C2311yescharacteristic
157C2×(C2×D47)⋊C4C2313yes—
158C2×(C2×D47)⋊C4C2313yes—
159C2×C4×Dic47C2313yes—
160C2×C4×Dic47C2313yes—
161C2×C4×Dic47C2313yes—
162C2×C4×Dic47C2313yes—
163C2×C4×Dic47C2316yes—
164C42×D47C23124yes—
165C2×#41×C47—28no—
166C2×#41×C47C2318yes—
167C22×Q8×C47C2311yescharacteristic
168C22×D4×C47C2313yes—
169C23×C4×C47C2313yes—
170C23×C4×C47C2316yes—
171C4×Q8×C47C2318yes—
172C4×Q8×C47C2318yes—
173C4×D4×C47C23124yes—
174C4×D4×C47C23124yes—
175#117×C47C23124yes—
176C2×C4⋊C4×C47C2313yes—
177C2×C4⋊C4×C47C2313yes—
178C2×C4⋊C4×C47C2313yes—
179C2×C4⋊C4×C47C23124yes—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47C2313yes—
182C2×C22⋊C4×C47C2313yes—
183C2×C42×C47C2313yes—
184C2×C42×C47C2313yes—
185C24×C47C2413yes—
186C23×D47C2411yescharacteristic
187C23×D47C2411yescharacteristic
188#41×C47—232no—
189C2×Q8×C47#4118yes—
190C2×Q8×C47C2414yes—
191C2×D4×C47—212no—
192C2×D4×C47C24112yes—
193C22×C4×C47—212no—
194C22×C4×C47—412no—
195C22×C4×C47C2411yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C22×C4×C47C2413yes—
198C22×C4×C47C2413yes—
199C22×C4×C47C2411yescharacteristic
200C22×C4×C47C24112yes—
201C22×C4×C47C24124yes—
202C22×C4×C47C2413yes—
203C2×C22⋊D47—212no—
204C2×C22⋊D47—46no—
205C2×C22⋊D47C24112yes—
206C2×C22⋊D47C24112yes—
207C22×Dic47C2411yescharacteristic
208C22×Dic47C2411yescharacteristic
209C22×Dic47C2413yes—
210C22×Dic47C2413yes—
211C22×Dic47C2413yes—
212C22×Dic47C2413yes—
213Q8×D47—232no—
214Q8×D47—232no—
215C2×D188—24no—
216C2×D188C2414yes—
217C2×C4×D47—24no—
218C2×C4×D47—212no—
219C2×C4×D47—212no—
220C2×C4×D47—46no—
221C2×C4×D47C2414yes—
222C2×C4×D47C24112yes—
223C2×C4×D47C24112yes—
224C2×C4×D47C24112yes—
225C2×Dic94—212no—
226C2×Dic94—212no—
227C2×Dic94—46no—
228C2×Dic94C24112yes—
229C2×Dic94C24112yes—
230C2×Dic94C24112yes—
231C4⋊C4×C47C24112yes—
232C4⋊C4×C47C24112yes—
233C4⋊C4×C47C24112yes—
234C4⋊C4×C47C2414yes—
235C22⋊C4×C47C24112yes—
236C22⋊C4×C47C24112yes—
237C42×C47C24112yes—
238C42×C47C24112yes—
239C22⋊Dic47C24112yes—
240C22⋊Dic47C24124yes—
241C22⋊Dic47C24124yes—
242C22⋊Dic47C24112yes—
243(C2×D47)⋊C4C2414yes—
244(C2×D47)⋊C4C24112yes—
245(C2×D47)⋊C4C2414yes—
246(C2×D47)⋊C4C2414yes—
247(C2×D47)⋊C4C24112yes—
248(C2×D47)⋊C4C24112yes—
249C4⋊Dic47C24112yes—
250C4⋊Dic47C24112yes—
251C4⋊Dic47C24112yes—
252C4⋊Dic47C24124yes—
253C4⋊Dic47C24112yes—
254Dic47⋊C4C24124yes—
255Dic47⋊C4C24112yes—
256Dic47⋊C4C24112yes—
257Dic47⋊C4C24112yes—
258Dic47⋊C4C24112yes—
259Dic47⋊C4C24124yes—
260Dic47⋊C4C2414yes—
261Dic47⋊C4C24112yes—
262C4×Dic47C24112yes—
263C4×Dic47C24112yes—
264C4×Dic47C24112yes—
265C4×Dic47C24112yes—
266C4×Dic47C24124yes—
267C23×C47—26no—
268C23×C47—26no—
269C23×C47—26no—
270C23×C47C2516yes—
271C23×C47C2511yescharacteristic
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D472−1+414yes—
278C22×D47C2512yes—
279C22×D47C2512yes—
280Q8×C47C2×#41116yes—
281D4×C47—224no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—26no—
286C2×C4×C47—26no—
287C2×C4×C47—224no—
288C2×C4×C47—424no—
289C2×C4×C47C2×#41112yes—
290C2×C4×C47C2512yes—
291C2×C4×C47C2516yes—
292C2×C4×C47C2512yes—
293C2×C4×C47C2512yes—
294C2×C4×C47C2516yes—
295C2×C4×C47C2516yes—
296C22⋊D47—224no—
297C22⋊D47—412no—
298C2×Dic47—26no—
299C2×Dic47—26no—
300C2×Dic47—22no—
301C2×Dic47—26no—
302C2×Dic47—22no—
303C2×Dic47—26no—
304C2×Dic47C2512yes—
305C2×Dic47C2516yes—
306C2×Dic47C2512yes—
307C2×Dic47C2516yes—
308C2×Dic47C2516yes—
309C2×Dic47C2516yes—
310D188—28no—
311C4×D47—28no—
312C4×D47—224no—
313C4×D47—224no—
314C4×D47—412no—
315Dic94—224no—
316Dic94—224no—
317Dic94—412no—
318C2×#3516—471nomaximal, Sylow
319C22×C47—26no—
320C22×C47—26no—
321C22×C47—26no—
322C22×C47—412no—
323C22×C47C22×#4112yes—
324C22×C47C2×2−1+412yes—
325C22×C47#58512yes—
326C22×C47C2611yescharacteristic
327C2×D47—22no—
328C2×D47—22no—
329C2×D47—28no—
330C2×D47—22no—
331C2×D47—22no—
332C2×D47—22no—
333C2×D47—44no—
334C2×D47C2×2−1+414yes—
335C4×C47—22no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—26no—
339C4×C47—26no—
340C4×C47C22×#41112yes—
341Dic47—26no—
342Dic47—26no—
343Dic47—22no—
344Dic47—26no—
345Dic47—22no—
346Dic47—26no—
347#3516—4732no—
348C2×#557—471no—
349C2×#556—473no—
350C2×#554—473no—
351C2×#553—473no—
352C2×#552—473no—
353C2×D4×Q8—471no—
354C2×#548—471no—
355C2×#548—471no—
356C2×#542—473no—
357C2×#541—473no—
358C2×#529—473no—
359C2×#529—473no—
360C2×#520D4711yescharacteristic, complemented
361C2×#519—471no—
362C22×C4×Q8—471no—
363C2×C47—46no—
364C2×C47#351614yescomplemented
365C2×C47C23×#4111yescharacteristic
366C2×C47C22×2−1+411yescharacteristic
367C2×C47C2×#58511yescharacteristic
368D47—24no—
369D47—42no—
370C22×#41C2×D4711yescharacteristic
371C23×Q8—471no—
372C23×Q8—471no—
373#557—4716no—
374#556—4748no—
375#554—4748no—
376#553—4748no—
377#552—4748no—
378D4×Q8—4716no—
379#548—4716no—
380#548—4716no—
381#542—4748no—
382#541—4748no—
383C2×C4⋊Q8—473no—
384C2×C4⋊Q8—473no—
385#529—4748no—
386#529—4748no—
387C2×#126—473no—
388C2×#126—476no—
389C2×#126—473no—
390C2×#126—476no—
391C2×#125—473no—
392C2×#125—473no—
393C2×#125—476no—
394C2×#125—473no—
395C2×#124—473no—
396C2×#124—473no—
397C2×#124—473no—
398C2×#123—476no—
399C2×#123—471no—
400C2×#123—473no—
401C2×C22⋊Q8—473no—
402C2×C22⋊Q8—473no—
403C2×C22⋊Q8—476no—
404C2×C22⋊Q8—473no—
405C2×C22⋊Q8—473no—
406C2×C22⋊Q8—473no—
407C2×#121—473no—
408C2×#121—473no—
409C2×#121—473no—
410#520C2×D47116yescomplemented
411#519—4716no—
412C2×C4×Q8—471no—
413C2×C4×Q8—471no—
414C2×C4×Q8—4716no—
415C2×C4×Q8—473no—
416C2×C4×Q8—473no—
417C2×C4×Q8—473no—
418C2×C4×Q8—473no—
419C2×C4×Q8—473no—
420C2×C4×Q8C2×D4711yescharacteristic
421C2×C4×Q8C2×D4711yescharacteristic
422C2×C4×D4—473no—
423C2×C4×D4—473no—
424C2×C4×D4—476no—
425C2×C4×D4—473no—
426C2×C4×D4C2×D4713yes—
427C2×C4×D4C2×D4713yes—
428C2×#117—476no—
429C2×#117—473no—
430C2×#117—473no—
431C2×#117C2×D4713yes—
432C22×C4⋊C4—473no—
433C22×C4⋊C4C2×D4713yes—
434C22×C42—473no—
435C47C2×#351611yescharacteristic, complemented, Sylow
436C2×#41—28no—
437C2×#41C22×D4718yes—
438C22×Q8—478no—
439C22×Q8—478no—
440C22×Q8—473no—
441C22×Q8—473no—
442C22×Q8—473no—
443C22×Q8—948no—
444C22×Q8—948no—
445C22×Q8C22×D4711yescharacteristic
446C22×D4—473no—
447C22×D4—473no—
448C22×D4—471no—
449C22×D4C22×D4713yes—
450C23×C4—473no—
451C23×C4—473no—
452C23×C4—471no—
453C23×C4—473no—
454C23×C4C22×D4713yes—
455C23×C4C22×D4716yes—
456C4⋊Q8—4724no—
457C4⋊Q8—4724no—
458#126—4724no—
459#126—4748no—
460#126—4724no—
461#126—4748no—
462#125—4724no—
463#125—4724no—
464#125—4748no—
465#125—4724no—
466#124—4724no—
467#124—4724no—
468#124—4724no—
469#123—4748no—
470#123—478no—
471#123—4724no—
472C22⋊Q8—4724no—
473C22⋊Q8—4724no—
474C22⋊Q8—4748no—
475C22⋊Q8—4724no—
476C22⋊Q8—4724no—
477C22⋊Q8—4724no—
478#121—4724no—
479#121—4724no—
480#121—4724no—
481C4×Q8—478no—
482C4×Q8—478no—
483C4×Q8—4724no—
484C4×Q8—4724no—
485C4×Q8—4724no—
486C4×Q8—4724no—
487C4×Q8—4724no—
488C4×Q8C22×D4718yes—
489C4×Q8C22×D4718yes—
490C4×D4—4724no—
491C4×D4—4724no—
492C4×D4—4748no—
493C4×D4—4724no—
494C4×D4C22×D47124yes—
495C4×D4C22×D47124yes—
496#117—4748no—
497#117—4724no—
498#117—4724no—
499#117C22×D47124yes—
500C2×C4⋊C4—473no—
501C2×C4⋊C4—476no—
502C2×C4⋊C4—473no—
503C2×C4⋊C4—473no—
504C2×C4⋊C4—473no—
505C2×C4⋊C4—473no—
506C2×C4⋊C4—476no—
507C2×C4⋊C4—473no—
508C2×C4⋊C4—473no—
509C2×C4⋊C4—476no—
510C2×C4⋊C4—473no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—473no—
513C2×C4⋊C4—4724no—
514C2×C4⋊C4C22×D4713yes—
515C2×C4⋊C4C22×D4713yes—
516C2×C4⋊C4C22×D4713yes—
517C2×C4⋊C4C22×D47124yes—
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C22⋊C4—473no—
520C2×C22⋊C4—476no—
521C2×C22⋊C4—476no—
522C2×C22⋊C4—473no—
523C2×C22⋊C4—473no—
524C2×C22⋊C4—471no—
525C2×C22⋊C4—471no—
526C2×C22⋊C4—473no—
527C2×C22⋊C4—471no—
528C2×C22⋊C4—473no—
529C2×C22⋊C4C22×D4713yes—
530C2×C22⋊C4C22×D4713yes—
531C2×C42—476no—
532C2×C42—473no—
533C2×C42—473no—
534C2×C42—473no—
535C2×C42—473no—
536C2×C42—4724no—
537C2×C42C22×D4713yes—
538C2×C42C22×D4713yes—
539C24—471no—
540C24—471no—
541C24C23×D4713yes—
542#41—232no—
543C2×Q8—4712no—
544C2×Q8—4712no—
545C2×Q8—4712no—
546C2×Q8—9432no—
547C2×Q8—9432no—
548C2×Q8—9412no—
549C2×Q8—9412no—
550C2×Q8—1886no—
551C2×Q8#1062535018yes—
552C2×Q8C23×D4714yes—
553C2×D4—212no—
554C2×D4—4712no—
555C2×D4—4712no—
556C2×D4—474no—
557C2×D4—944no—
558C2×D4—9412no—
559C2×D4—1886no—
560C2×D4C23×D47112yes—
561C22×C4—212no—
562C22×C4—412no—
563C22×C4—471no—
564C22×C4—471no—
565C22×C4—473no—
566C22×C4—473no—
567C22×C4—473no—
568C22×C4—473no—
569C22×C4—474no—
570C22×C4—4712no—
571C22×C4—4712no—
572C22×C4—4712no—
573C22×C4—944no—
574C22×C4—9412no—
575C22×C4—9412no—
576C22×C4—1886no—
577C22×C4C23×D47112yes—
578C22×C4C23×D4711yescharacteristic
579C22×C4C23×D4713yes—
580C22×C4C23×D4711yescharacteristic
581C22×C4C23×D4713yes—
582C22×C4C23×D4711yescharacteristic
583C22×C4C23×D47124yes—
584C22×C4C23×D4713yes—
585C4⋊C4—4724no—
586C4⋊C4—4712no—
587C4⋊C4—4712no—
588C4⋊C4—4712no—
589C4⋊C4—4712no—
590C4⋊C4—4724no—
591C4⋊C4—474no—
592C4⋊C4—4712no—
593C4⋊C4—4712no—
594C4⋊C4—4712no—
595C4⋊C4—4712no—
596C4⋊C4—4724no—
597C4⋊C4—4712no—
598C4⋊C4C23×D47112yes—
599C4⋊C4C23×D47112yes—
600C4⋊C4C23×D47112yes—
601C4⋊C4C23×D4714yes—
602C22⋊C4—4712no—
603C22⋊C4—4724no—
604C22⋊C4—4724no—
605C22⋊C4—4712no—
606C22⋊C4—4712no—
607C22⋊C4—474no—
608C22⋊C4—474no—
609C22⋊C4—4712no—
610C22⋊C4—474no—
611C22⋊C4—4712no—
612C22⋊C4C23×D47112yes—
613C22⋊C4C23×D47112yes—
614C42—4712no—
615C42—4712no—
616C42—4712no—
617C42—4724no—
618C42—4712no—
619C42C23×D47112yes—
620C42C23×D47112yes—
621C23—26no—
622C23—26no—
623C23—26no—
624C23—474no—
625C23—472no—
626C23—472no—
627C23—942no—
628C23—942no—
629C23—942no—
630C23—942no—
631C23—942no—
632C23C24×D4716yes—
633C23C24×D4711yescharacteristic
634Q8—9424no—
635Q8—9424no—
636Q8—18812no—
637Q8C2×#10625350116yes—
638D4—224no—
639D4—948no—
640D4—9424no—
641D4—18812no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—26no—
646C2×C4—26no—
647C2×C4—224no—
648C2×C4—424no—
649C2×C4—472no—
650C2×C4—472no—
651C2×C4—476no—
652C2×C4—476no—
653C2×C4—476no—
654C2×C4—476no—
655C2×C4—948no—
656C2×C4—946no—
657C2×C4—946no—
658C2×C4—942no—
659C2×C4—946no—
660C2×C4—946no—
661C2×C4—942no—
662C2×C4—9424no—
663C2×C4—9424no—
664C2×C4—18812no—
665C2×C4C2×#10625350112yes—
666C2×C4C24×D4712yes—
667C2×C4C24×D4716yes—
668C2×C4C24×D4712yes—
669C2×C4C24×D4716yes—
670C2×C4C24×D4712yes—
671C2×C4C24×D4716yes—
672C22—26no—
673C22—26no—
674C22—26no—
675C22—412no—
676C22—474no—
677C22—948no—
678C22—942no—
679C22—942no—
680C22—942no—
681C22—942no—
682C22—942no—
683C22—1884no—
684C22C22×#1062535012yes—
685C222−1+4×D4712yes—
686C22#1568995812yes—
687C22C25×D4711yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—26no—
692C4—26no—
693C4—946no—
694C4—946no—
695C4—942no—
696C4—946no—
697C4—946no—
698C4—942no—
699C4C22×#10625350112yes—
700C2—46no—
701C2—944no—
702C2—1882no—
703C2#2025737314yesdirect product factor
704C2C23×#1062535011yescharacteristic
705C2C2×2−1+4×D4711yescharacteristic
706C2C2×#1568995811yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#520C2
socleC23×C47C25
hypercenterC2×#520D47
hypocenterC47C2×#3516
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #20257373C2direct (N × H)
2. C2×#15689849C2semidirect
3. C2×#15689843C2semidirect
4. C2×#15689828C2semidirect
5. C2×#15689823C2semidirect
6. C2×#15689808C2semidirect
7. C2×Q8×D188C2semidirect
8. C2×#15689780C2semidirect
9. C2×#15689780C2semidirect
10. C2×#15689738C2semidirect
11. C2×#15689735C2semidirect
12. C2×#15689655C2semidirect
13. C2×#15689651C2semidirect
14. C2×#15689599C2semidirect
15. C2×C4×Q8×D47C2semidirect
16. C2×C47×#520C2semidirect
19. #15689849C22semidirect
20. #15689843C22semidirect
21. #15689828C22semidirect
22. #15689823C22semidirect
23. #15689808C22semidirect
24. Q8×D188C22semidirect
25. #15689780C22semidirect
26. #15689780C22semidirect
27. #15689738C22semidirect
28. #15689735C22semidirect
31. #15689655C22semidirect
32. #15689651C22semidirect
56. #15689599C22semidirect
64. C4×Q8×D47C22semidirect
75. C47×#520C22semidirect
360. C2×#520D47semidirect
364. C2×C47#3516semidirect
410. #520C2×D47semidirect
435. C47C2×#3516semidirect
703. C2#20257373direct (N × H)

Maximal subgroups

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

subgroupindex
#202573732
C2×#156898492
C2×#156898432
C2×#156898282
C2×#156898232
C2×#156898082
C2×Q8×D1882
C2×#156897802
C2×#156897382
C2×#156897352
C2×#156896552
C2×#156896512
C2×#156895992
C2×C4×Q8×D472
C2×C47×#5202
C2×#351647