Finite Group Databasebeta

← C2×#20257005 #27123370

Subgroups — C2×#20257005 #27123370

Order 12032.

7706 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257005C2132yesmaximal, direct product factor
2C2×#15689849C211yesmaximal, characteristic, complemented
3C2×#15689845C213yesmaximal, complemented
4C2×#15689814C213yesmaximal, complemented
5C2×#15689808C213yesmaximal, complemented
6C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
7C2×#15689785C211yesmaximal, characteristic, complemented
8C2×#15689784C211yesmaximal, characteristic, complemented
9C2×#15689774C213yesmaximal, complemented
10C2×#15689677C213yesmaximal, complemented
11C2×#15689660C213yesmaximal, complemented
12C2×#15689657C213yesmaximal, complemented
13C2×C4×#10625354C211yesmaximal, characteristic, complemented
14C2×C4×#10625350C213yesmaximal, complemented
15C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625350C2213yes—
19C22×Q8×D47C2211yescharacteristic
20#15689849C22116yescomplemented
21#15689845C22148yescomplemented
22#15689814C22148yescomplemented
23#15689808C22148yescomplemented
24Q8×C22⋊D47C22116yescomplemented
25#15689785C22116yescomplemented
26#15689784C22116yescomplemented
27#15689774C22148yescomplemented
28#15689677C22148yescomplemented
29C2×#13094023C2213yes—
30C2×#13094022C2213yes—
31#15689660C22148yescomplemented
32#15689657C22148yescomplemented
33C2×#13094019C2216yes—
34C2×#13094018C2216yes—
35C2×#13094016C2213yes—
36C2×#13094015C2213yes—
37C2×#13094014C2216yes—
38C2×#13094013C2213yes—
39C2×#13094012C2213yes—
40C2×#13094009C2216yes—
41C2×#13094007C2216yes—
42C2×#13094004C2213yes—
43C2×#13094003C2213yes—
44C2×#13094002C2216yes—
45C2×#13094000C2213yes—
46C2×#13094000C2213yes—
47C2×#13093999C2213yes—
48C2×#13093998C2213yes—
49C4×#10625354C22116yescomplemented
50C4×#10625350C22148yescomplemented
51C2×Q8×Dic47C2211yescharacteristic
52C2×Q8×Dic47C2211yescharacteristic
53C2×C4×Dic94C2213yes—
54C2×C4×Dic94C2213yes—
55C2×C4×Dic94C2213yes—
56C2×#13093989C2213yes—
57C4×Q8×D47C22116yescomplemented
58C2×C4×D188C2213yes—
59C2×C4×D188C2213yes—
60C2×C4×D188C2213yes—
61C2×#13093986C2213yes—
62C2×C4×C22⋊D47C2211yescharacteristic
63C2×C4×C22⋊D47C2213yes—
64C2×C4×C22⋊D47C2213yes—
65C2×C4×C22⋊D47C2213yes—
66C2×#13093983C2213yes—
67C2×#13093982C2213yes—
68C2×#13093981C2213yes—
69C2×#13093981C2213yes—
70C2×#13093981C2216yes—
71C2×C4⋊C4×D47C2213yes—
72C2×C42×D47C2213yes—
73C2×C42×D47C2213yes—
74C23×Q8×C47C2211yescharacteristic
75C2×C4×Q8×C47C2211yescharacteristic
76C2×C4×Q8×C47C2211yescharacteristic
77C2×C4×Q8×C47C2213yes—
78C2×C4×Q8×C47C2213yes—
79C2×C4×Q8×C47C22116yescomplemented
80C22×C4⋊C4×C47C2213yes—
81C22×C42×C47C2213yes—
82C2×#10625354—28no—
83C2×#10625354C2318yes—
84C2×#10625350—224no—
85C2×#10625350C23124yes—
86C22×Dic94C2313yes—
87C22×Dic94C2313yes—
88C2×Q8×D47—28no—
89C2×Q8×D47C2318yes—
90C22×D188C2313yes—
91C22×D188C2313yes—
92C22×C22⋊D47C2313yes—
93C22×C22⋊D47C2311yescharacteristic
94C22×C4×D47C2311yescharacteristic
95C22×C4×D47C2313yes—
96C22×C4×D47C2313yes—
97C22×C4×D47C2313yes—
98C22×C4×D47C2313yes—
99C22×C4×D47C2313yes—
100#13094023C23124yes—
101#13094022C23124yes—
102#13094019C23148yes—
103#13094018C23148yes—
104#13094016C23124yes—
105#13094015C23124yes—
106#13094014C23148yes—
107#13094013C23124yes—
108#13094012C23124yes—
109#13094009C23148yes—
110#13094007C23148yes—
111#13094004C23124yes—
112#13094003C23124yes—
113#13094002C23148yes—
114#13094000C23124yes—
115#13094000C23124yes—
116#13093999C23124yes—
117#13093998C23124yes—
118Q8×Dic47C2318yes—
119Q8×Dic47C2318yes—
120C4×Dic94C23124yes—
121C4×Dic94C23124yes—
122C4×Dic94C23124yes—
123#13093989C23124yes—
124C4×D188C23124yes—
125C4×D188C23124yes—
126C4×D188C23124yes—
127#13093986C23124yes—
128C4×C22⋊D47C23124yes—
129C4×C22⋊D47C23124yes—
130C4×C22⋊D47C2318yes—
131C4×C22⋊D47C23124yes—
132#13093983C23124yes—
133#13093982C23124yes—
134#13093981C23124yes—
135#13093981C23124yes—
136#13093981C23148yes—
137C2×C4⋊Dic47C2313yes—
138C2×C4⋊Dic47C2313yes—
139C2×C4⋊Dic47C2313yes—
140C2×C4⋊Dic47C2313yes—
141C2×Dic47⋊C4C2316yes—
142C2×Dic47⋊C4C2311yescharacteristic
143C2×Dic47⋊C4C2313yes—
144C2×Dic47⋊C4C2313yes—
145C2×Dic47⋊C4C2313yes—
146C2×Dic47⋊C4C2316yes—
147C2×Dic47⋊C4C2316yes—
148C4⋊C4×D47C23124yes—
149C2×C22⋊Dic47C2311yescharacteristic
150C2×C22⋊Dic47C2313yes—
151C2×(C2×D47)⋊C4C2311yescharacteristic
152C2×(C2×D47)⋊C4C2313yes—
153C2×(C2×D47)⋊C4C2313yes—
154C2×(C2×D47)⋊C4C2313yes—
155C2×(C2×D47)⋊C4C2316yes—
156C2×(C2×D47)⋊C4C2316yes—
157C2×(C2×D47)⋊C4C2316yes—
158C2×C4×Dic47C2311yescharacteristic
159C2×C4×Dic47C2313yes—
160C2×C4×Dic47C2313yes—
161C2×C4×Dic47C2313yes—
162C2×C4×Dic47C2313yes—
163C2×C4×Dic47C2313yes—
164C42×D47C23124yes—
165C42×D47C23124yes—
166C22×Q8×C47—28no—
167C22×Q8×C47C2318yes—
168C22×Q8×C47C2313yes—
169C22×Q8×C47C2311yescharacteristic
170C23×C4×C47C2311yescharacteristic
171C23×C4×C47C2313yes—
172C23×C4×C47C2313yes—
173C4×Q8×C47C2318yes—
174C4×Q8×C47C23124yes—
175C4×Q8×C47C2318yes—
176C4×Q8×C47C23124yes—
177C2×C4⋊C4×C47C23124yes—
178C2×C4⋊C4×C47C2313yes—
179C2×C4⋊C4×C47C2313yes—
180C2×C4⋊C4×C47C2316yes—
181C2×C42×C47C2313yes—
182C2×C42×C47C2313yes—
183C2×C42×C47C2313yes—
184C2×C42×C47C2313yes—
185C2×C42×C47C23124yes—
186C24×C47C2411yescharacteristic
187C23×D47C2413yes—
188C23×D47C2411yescharacteristic
189C2×Q8×C47—232no—
190C2×Q8×C47—212no—
191C2×Q8×C47#4118yescomplemented
192C2×Q8×C47C24112yes—
193C2×Q8×C47C2414yes—
194C22×C4×C47—212no—
195C22×C4×C47—212no—
196C22×C4×C47—24no—
197C22×C4×C47C2411yescharacteristic
198C22×C4×C47C2414yes—
199C22×C4×C47C2413yes—
200C22×C4×C47C2413yes—
201C22×C4×C47C24112yes—
202C22×C4×C47C2413yes—
203C22×C4×C47C24112yes—
204C22×C4×C47C2413yes—
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—212no—
207C2×C22⋊D47#4118yescomplemented
208C2×C22⋊D47C24112yes—
209C2×C22⋊D47C2414yes—
210C22×Dic47C2411yescharacteristic
211C22×Dic47C2411yescharacteristic
212C22×Dic47C2413yes—
213C22×Dic47C2413yes—
214C22×Dic47C2413yes—
215C22×Dic47C2411yescharacteristic
216#10625354—232no—
217Q8×D47—232no—
218#10625350—296no—
219C2×D188—212no—
220C2×D188—212no—
221C2×D188C24112yes—
222C2×D188C24112yes—
223C2×C4×D47—212no—
224C2×C4×D47—212no—
225C2×C4×D47—212no—
226C2×C4×D47—24no—
227C2×C4×D47—212no—
228C2×C4×D47—212no—
229C2×C4×D47C2414yes—
230C2×C4×D47C24112yes—
231C2×C4×D47C24112yes—
232C2×C4×D47C24112yes—
233C2×C4×D47C24112yes—
234C2×C4×D47C24112yes—
235C2×Dic94—212no—
236C2×Dic94—212no—
237C2×Dic94C24112yes—
238C2×Dic94C24112yes—
239C4⋊C4×C47C24112yes—
240C4⋊C4×C47C24112yes—
241C4⋊C4×C47C24124yes—
242C42×C47C24112yes—
243C42×C47C24112yes—
244C42×C47C24112yes—
245C42×C47C24112yes—
246C22⋊Dic47C2414yes—
247C22⋊Dic47C24112yes—
248(C2×D47)⋊C4C2414yes—
249(C2×D47)⋊C4C24112yes—
250(C2×D47)⋊C4C24112yes—
251(C2×D47)⋊C4C24112yes—
252(C2×D47)⋊C4C24124yes—
253(C2×D47)⋊C4C24124yes—
254(C2×D47)⋊C4C24124yes—
255C4⋊Dic47C24112yes—
256C4⋊Dic47C24112yes—
257C4⋊Dic47C24112yes—
258C4⋊Dic47C24112yes—
259Dic47⋊C4C24124yes—
260Dic47⋊C4C2414yes—
261Dic47⋊C4C24112yes—
262Dic47⋊C4C24112yes—
263Dic47⋊C4C24112yes—
264Dic47⋊C4C24124yes—
265Dic47⋊C4C24124yes—
266C4×Dic47C2414yes—
267C4×Dic47C24112yes—
268C4×Dic47C24112yes—
269C4×Dic47C24112yes—
270C4×Dic47C24112yes—
271C4×Dic47C24112yes—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47C2×#4114yes—
275C23×C47C2512yes—
276C23×C47C2511yescharacteristic
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—26no—
280C22×D47—26no—
281C22×D47—26no—
282C22×D47C2×#4114yes—
283C22×D47C2516yes—
284C22×D47C2512yes—
285Q8×C47—224no—
286Q8×C47C2×#41116yescomplemented
287C2×C4×C47—26no—
288C2×C4×C47—26no—
289C2×C4×C47—224no—
290C2×C4×C47—26no—
291C2×C4×C47—22no—
292C2×C4×C47—224no—
293C2×C4×C47—28no—
294C2×C4×C47C2×#41112yes—
295C2×C4×C472−1+414yes—
296C2×C4×C47C2516yes—
297C2×C4×C47C2512yes—
298C2×C4×C47C2516yes—
299C2×C4×C47C2516yes—
300C2×C4×C47C2516yes—
301C2×C4×C47C2512yes—
302C22⋊D47—224no—
303C22⋊D47C2×#41116yescomplemented
304C2×Dic47—26no—
305C2×Dic47—26no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—26no—
309C2×Dic47C2×#4114yes—
310C2×Dic47C2512yes—
311C2×Dic47C2512yes—
312C2×Dic47C2516yes—
313C2×Dic47C2516yes—
314C2×Dic47C2516yes—
315C2×Dic47C2512yes—
316D188—224no—
317D188—224no—
318C4×D47—224no—
319C4×D47—224no—
320C4×D47—224no—
321C4×D47—28no—
322C4×D47—224no—
323C4×D47—224no—
324Dic94—224no—
325Dic94—224no—
326C2×#3482—471nomaximal, Sylow
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—28no—
330C22×C47C22×#4114yes—
331C22×C47C22×#4112yes—
332C22×C47C22×#4112yes—
333C22×C47C2×2−1+412yes—
334C22×C47C2611yescharacteristic
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—28no—
338C2×D47—26no—
339C2×D47—26no—
340C2×D47—26no—
341C2×D47—412no—
342C2×D47C22×#4114yes—
343C4×C47—26no—
344C4×C47—26no—
345C4×C47—26no—
346C4×C47—22no—
347C4×C47C22×#41112yes—
348C4×C47C2×2−1+414yes—
349Dic47—26no—
350Dic47—26no—
351Dic47—22no—
352Dic47—22no—
353Dic47—26no—
354Dic47C22×#4114yes—
355#3482—4732no—
356C2×#557—471no—
357C2×#556—473no—
358C2×#552—473no—
359C2×#552—473no—
360C2×D4×Q8—471no—
361C2×#548—471no—
362C2×#548—471no—
363C2×#547—473no—
364C2×#533—473no—
365C2×#529—473no—
366C2×#529—473no—
367C2×C4×#41—473no—
368C2×C4×#41—471no—
369C22×C4×Q8—471no—
370C22×C4×Q8D4711yescharacteristic, complemented
371C2×C47—24no—
372C2×C47#348214yescomplemented
373C2×C47C23×#4111yescharacteristic
374C2×C47C23×#4111yescharacteristic
375C2×C47C22×2−1+411yescharacteristic
376D47—24no—
377D47—46no—
378C22×#41—471no—
379C22×#41—473no—
380C23×Q8—471no—
381C23×Q8C2×D4711yescharacteristic
382#557—4716no—
383#556—4748no—
384#552—4748no—
385#552—4748no—
386D4×Q8—4716no—
387#548—4716no—
388#548—4716no—
389#547—4748no—
390#533—4748no—
391C2×C4⋊Q8—473no—
392C2×C4⋊Q8—473no—
393#529—4748no—
394#529—4748no—
395C2×#126—476no—
396C2×#126—476no—
397C2×#125—473no—
398C2×#125—476no—
399C2×#125—473no—
400C2×#124—473no—
401C2×#124—473no—
402C2×#123—476no—
403C2×#123—476no—
404C2×C22⋊Q8—473no—
405C2×C22⋊Q8—473no—
406C2×C22⋊Q8—473no—
407C2×C22⋊Q8—476no—
408C2×C22⋊Q8—473no—
409C2×#121—473no—
410C2×#121—473no—
411C4×#41—4716no—
412C4×#41—4748no—
413C2×C4×Q8—471no—
414C2×C4×Q8—471no—
415C2×C4×Q8—4716no—
416C2×C4×Q8—473no—
417C2×C4×Q8—473no—
418C2×C4×Q8—473no—
419C2×C4×Q8—473no—
420C2×C4×Q8C2×D4711yescharacteristic
421C2×C4×Q8C2×D4713yes—
422C2×C4×Q8C2×D4711yescharacteristic
423C2×C4×Q8C2×D4713yes—
424C2×C4×Q8C2×D47116yescomplemented
425C2×C4×D4—471no—
426C2×C4×D4—473no—
427C2×C4×D4—473no—
428C2×C4×D4—473no—
429C2×C4×D4—473no—
430C2×C4×D4—473no—
431C2×C4×D4—473no—
432C2×C4×D4—473no—
433C2×#117—473no—
434C2×#117—473no—
435C2×#117—473no—
436C2×#117—473no—
437C2×#117—476no—
438C22×C4⋊C4—473no—
439C22×C4⋊C4C2×D4713yes—
440C22×C42—473no—
441C22×C42—473no—
442C22×C42C2×D4713yes—
443C47C2×#348211yescharacteristic, complemented, Sylow
444C2×#41—478no—
445C2×#41—4724no—
446C2×#41—9424no—
447C2×#41—948no—
448C22×Q8—28no—
449C22×Q8—478no—
450C22×Q8—473no—
451C22×Q8—473no—
452C22×Q8—948no—
453C22×Q8C22×D4713yes—
454C22×Q8C22×D4718yes—
455C22×Q8C22×D4711yescharacteristic
456C22×D4—471no—
457C22×D4—473no—
458C22×D4—473no—
459C22×D4—473no—
460C23×C4—473no—
461C23×C4—473no—
462C23×C4—473no—
463C23×C4—473no—
464C23×C4—473no—
465C23×C4—471no—
466C23×C4C22×D4713yes—
467C23×C4C22×D4713yes—
468C23×C4C22×D4711yescharacteristic
469C4⋊Q8—4724no—
470C4⋊Q8—4724no—
471#126—4748no—
472#126—4748no—
473#125—4724no—
474#125—4748no—
475#125—4724no—
476#124—4724no—
477#124—4724no—
478#123—4748no—
479#123—4748no—
480C22⋊Q8—4724no—
481C22⋊Q8—4724no—
482C22⋊Q8—4724no—
483C22⋊Q8—4748no—
484C22⋊Q8—4724no—
485#121—4724no—
486#121—4724no—
487C4×Q8—478no—
488C4×Q8—478no—
489C4×Q8—4724no—
490C4×Q8—4724no—
491C4×Q8—4724no—
492C4×Q8—4724no—
493C4×Q8C22×D4718yes—
494C4×Q8C22×D47124yes—
495C4×Q8C22×D4718yes—
496C4×Q8C22×D47124yes—
497C4×D4—478no—
498C4×D4—4724no—
499C4×D4—4724no—
500C4×D4—4724no—
501C4×D4—4724no—
502C4×D4—4724no—
503C4×D4—4724no—
504C4×D4—4724no—
505#117—4724no—
506#117—4724no—
507#117—4724no—
508#117—4724no—
509#117—4748no—
510C2×C4⋊C4—473no—
511C2×C4⋊C4—476no—
512C2×C4⋊C4—471no—
513C2×C4⋊C4—473no—
514C2×C4⋊C4—473no—
515C2×C4⋊C4—473no—
516C2×C4⋊C4—473no—
517C2×C4⋊C4—473no—
518C2×C4⋊C4—473no—
519C2×C4⋊C4—476no—
520C2×C4⋊C4—476no—
521C2×C4⋊C4—4724no—
522C2×C4⋊C4C22×D4713yes—
523C2×C4⋊C4C22×D4713yes—
524C2×C4⋊C4C22×D4716yes—
525C2×C4⋊C4C22×D47124yes—
526C2×C22⋊C4—471no—
527C2×C22⋊C4—473no—
528C2×C22⋊C4—471no—
529C2×C22⋊C4—473no—
530C2×C22⋊C4—476no—
531C2×C22⋊C4—473no—
532C2×C22⋊C4—473no—
533C2×C22⋊C4—476no—
534C2×C22⋊C4—476no—
535C2×C42—473no—
536C2×C42—473no—
537C2×C42—473no—
538C2×C42—473no—
539C2×C42—473no—
540C2×C42—471no—
541C2×C42—4724no—
542C2×C42—4724no—
543C2×C42C22×D4713yes—
544C2×C42C22×D4713yes—
545C2×C42C22×D47124yes—
546C2×C42C22×D4713yes—
547C2×C42C22×D4713yes—
548C24—471no—
549C24—473no—
550C24C23×D4711yescharacteristic
551#41—9496no—
552#41—9432no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—4712no—
556C2×Q8—4712no—
557C2×Q8—9412no—
558C2×Q8—9432no—
559C2×Q8—9412no—
560C2×Q8#1062535018yescomplemented
561C2×Q8C23×D47112yes—
562C2×Q8C23×D4714yes—
563C2×D4—478no—
564C2×D4—474no—
565C2×D4—4712no—
566C2×D4—4712no—
567C2×D4—4712no—
568C2×D4—9412no—
569C2×D4—9412no—
570C2×D4—9412no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—24no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—471no—
577C22×C4—473no—
578C22×C4—473no—
579C22×C4—473no—
580C22×C4—474no—
581C22×C4—4712no—
582C22×C4—4712no—
583C22×C4—4712no—
584C22×C4—4712no—
585C22×C4—4712no—
586C22×C4—9412no—
587C22×C4—9412no—
588C22×C4—9412no—
589C22×C4—9412no—
590C22×C4—944no—
591C22×C4—9412no—
592C22×C4C23×D4713yes—
593C22×C4C23×D4711yescharacteristic
594C22×C4C23×D4714yes—
595C22×C4C23×D4713yes—
596C22×C4C23×D4713yes—
597C22×C4C23×D47112yes—
598C22×C4C23×D47112yes—
599C22×C4C23×D4713yes—
600C22×C4C23×D4711yescharacteristic
601C4⋊C4—4724no—
602C4⋊C4—474no—
603C4⋊C4—4712no—
604C4⋊C4—4712no—
605C4⋊C4—4712no—
606C4⋊C4—4724no—
607C4⋊C4—4724no—
608C4⋊C4—4712no—
609C4⋊C4—4712no—
610C4⋊C4—4712no—
611C4⋊C4—4712no—
612C4⋊C4C23×D47112yes—
613C4⋊C4C23×D47112yes—
614C4⋊C4C23×D47124yes—
615C22⋊C4—474no—
616C22⋊C4—4712no—
617C22⋊C4—474no—
618C22⋊C4—4712no—
619C22⋊C4—4724no—
620C22⋊C4—4712no—
621C22⋊C4—4712no—
622C22⋊C4—4724no—
623C22⋊C4—4724no—
624C42—474no—
625C42—4712no—
626C42—4712no—
627C42—4712no—
628C42—4712no—
629C42—4712no—
630C42C23×D47112yes—
631C42C23×D47112yes—
632C42C23×D47112yes—
633C42C23×D47112yes—
634C23—22no—
635C23—22no—
636C23—474no—
637C23—472no—
638C23—476no—
639C23—942no—
640C23—942no—
641C23—946no—
642C23—946no—
643C23—946no—
644C23#41×D4714yes—
645C23C24×D4712yes—
646C23C24×D4711yescharacteristic
647Q8—224no—
648Q8—9424no—
649Q8—9424no—
650Q8C2×#10625350116yescomplemented
651D4—4716no—
652D4—9424no—
653D4—9424no—
654D4—9424no—
655C2×C4—26no—
656C2×C4—26no—
657C2×C4—224no—
658C2×C4—26no—
659C2×C4—22no—
660C2×C4—224no—
661C2×C4—28no—
662C2×C4—474no—
663C2×C4—472no—
664C2×C4—472no—
665C2×C4—472no—
666C2×C4—476no—
667C2×C4—476no—
668C2×C4—476no—
669C2×C4—9424no—
670C2×C4—9424no—
671C2×C4—946no—
672C2×C4—942no—
673C2×C4—946no—
674C2×C4—942no—
675C2×C4—946no—
676C2×C4—9424no—
677C2×C4—9424no—
678C2×C4—948no—
679C2×C4—9424no—
680C2×C4C2×#10625350112yes—
681C2×C4#1309407214yes—
682C2×C4C24×D4716yes—
683C2×C4C24×D4712yes—
684C2×C4C24×D4716yes—
685C2×C4C24×D4716yes—
686C2×C4C24×D4716yes—
687C2×C4C24×D4712yes—
688C22—22no—
689C22—22no—
690C22—28no—
691C22—474no—
692C22—942no—
693C22—942no—
694C22—948no—
695C22—946no—
696C22—946no—
697C22—946no—
698C22—18812no—
699C22C2×#41×D4714yes—
700C22C2×#41×D4712yes—
701C22C22×#1062535012yes—
702C22C2×#1309407212yes—
703C22C25×D4711yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—474no—
709C4—946no—
710C4—942no—
711C4—946no—
712C4—942no—
713C4—946no—
714C4C22×#10625350112yes—
715C4C2×#1309407214yes—
716C2—24no—
717C2—944no—
718C2—1886no—
719C2#2025700514yesdirect product factor
720C2C22×#41×D4711yescharacteristic
721C2C23×#1062535011yescharacteristic
722C2C22×#1309407211yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC22×C4×Q8×C47C2
socleC23×C47C25
hypercenterC22×C4×Q8D47
hypocenterC47C2×#3482
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #20257005C2direct (N × H)
2. C2×#15689849C2semidirect
3. C2×#15689845C2semidirect
4. C2×#15689814C2semidirect
5. C2×#15689808C2semidirect
6. C2×Q8×C22⋊D47C2semidirect
7. C2×#15689785C2semidirect
8. C2×#15689784C2semidirect
9. C2×#15689774C2semidirect
10. C2×#15689677C2semidirect
11. C2×#15689660C2semidirect
12. C2×#15689657C2semidirect
13. C2×C4×#10625354C2semidirect
14. C2×C4×#10625350C2semidirect
15. C2×C4×Q8×D47C2semidirect
16. C22×C4×Q8×C47C2semidirect
20. #15689849C22semidirect
21. #15689845C22semidirect
22. #15689814C22semidirect
23. #15689808C22semidirect
24. Q8×C22⋊D47C22semidirect
25. #15689785C22semidirect
26. #15689784C22semidirect
27. #15689774C22semidirect
28. #15689677C22semidirect
31. #15689660C22semidirect
32. #15689657C22semidirect
49. C4×#10625354C22semidirect
50. C4×#10625350C22semidirect
57. C4×Q8×D47C22semidirect
79. C2×C4×Q8×C47C22semidirect
191. C2×Q8×C47#41semidirect
207. C2×C22⋊D47#41semidirect
286. Q8×C47C2×#41semidirect
303. C22⋊D47C2×#41semidirect
370. C22×C4×Q8D47semidirect
372. C2×C47#3482semidirect
424. C2×C4×Q8C2×D47semidirect
443. C47C2×#3482semidirect
560. C2×Q8#10625350semidirect
650. Q8C2×#10625350semidirect
719. C2#20257005direct (N × H)

Maximal subgroups

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

subgroupindex
#202570052
C2×#156898492
C2×#156898452
C2×#156898142
C2×#156898082
C2×Q8×C22⋊D472
C2×#156897852
C2×#156897842
C2×#156897742
C2×#156896772
C2×#156896602
C2×#156896572
C2×C4×#106253542
C2×C4×#106253502
C2×C4×Q8×D472
C22×C4×Q8×C472
C2×#348247