Finite Group Databasebeta

← C2×#20257156 #27124452

Subgroups — C2×#20257156 #27124452

Order 12032.

11210 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094072C211yesmaximal, characteristic, complemented
2C22×#13094071C211yesmaximal, characteristic, complemented
3#20257156C2132yesmaximal, direct product factor
4C2×#15689792C211yesmaximal, characteristic, complemented
5C2×#15689791C213yesmaximal, complemented
6C2×Q8×C22⋊D47C211yesmaximal, characteristic, complemented
7C2×#15689786C213yesmaximal, complemented
8C2×#15689785C211yesmaximal, characteristic, complemented
9C2×#15689782C213yesmaximal, complemented
10C2×#15689781C213yesmaximal, complemented
11C2×#15689703C213yesmaximal, complemented
12C2×#15689702C213yesmaximal, complemented
13C2×#15689672C213yesmaximal, complemented
14C2×#15689670C213yesmaximal, complemented
15C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
16C2×C47×#548C211yesmaximal, characteristic, complemented
17C2×#13094072—216no—
18C2×#13094072C22116yescomplemented
19C2×#13094071—216no—
20C2×#13094071C22116yescomplemented
21C22×#10625354C2211yescharacteristic
22C22×#10625354C2213yes—
23C22×#10625350C2213yes—
24C22×#10625350C2213yes—
25C22×#10625350C2213yes—
26C22×#10625352C2213yes—
27C22×#10625352C2213yes—
28C23×Dic94C2213yes—
29C22×Q8×D47C2213yes—
30C22×Q8×D47C2211yescharacteristic
31C22×Q8×D47C2211yescharacteristic
32#15689792C22116yescomplemented
33#15689791C22148yescomplemented
34Q8×C22⋊D47C22116yescomplemented
35#15689786C22148yescomplemented
36#15689785C22116yescomplemented
37#15689782C22148yescomplemented
38#15689781C22148yescomplemented
39#15689703C22148yescomplemented
40#15689702C22148yescomplemented
41#15689672C22148yescomplemented
42#15689670C22148yescomplemented
43C2×#13094023C2213yes—
44C2×#13094022C2213yes—
45C2×#13094020C2213yes—
46C2×#13094020C2213yes—
47C2×#13094012C2213yes—
48C2×#13094010C2213yes—
49C2×#13094010C2213yes—
50C2×#13094004C2213yes—
51C2×#13094003C2213yes—
52C2×#13094002C2216yes—
53C2×#13094001C2216yes—
54C2×#13094000C2213yes—
55C2×#13093999C2213yes—
56C2×#13093999C2213yes—
57C2×#13093998C2213yes—
58C2×#13093997C2216yes—
59C2×#13093997C2211yescharacteristic
60C2×#13093997C2213yes—
61C2×#13093997C2216yes—
62C2×#13093996C2216yes—
63C2×#13093995C2213yes—
64C2×#13093995C2213yes—
65C2×Q8×Dic47C2211yescharacteristic
66C2×C4×Dic94C2213yes—
67C2×#13093989C2213yes—
68C4×Q8×D47C22116yescomplemented
69C2×C4×D188C2213yes—
70C2×C4×C22⋊D47C2213yes—
71C2×C4×C22⋊D47C2213yes—
72C2×(C22⋊D47)⋊C4C2216yes—
73C2×(C22⋊D47)⋊C4C2216yes—
74C2×C4⋊C4×D47C2213yes—
75C2×C42×D47C2213yes—
76C22×#41×C47C2211yescharacteristic
77C23×Q8×C47C2211yescharacteristic
78C47×#548C22116yescomplemented
79C2×#124×C47C2213yes—
80C2×C22⋊Q8×C47C2213yes—
81C2×#121×C47C2213yes—
82C2×C4×Q8×C47C2211yescharacteristic
83C2×C4×D4×C47C2213yes—
84#13094072—2128no—
85#13094071—2128no—
86C2×#10625354—28no—
87C2×#10625354—224no—
88C2×#10625354C2318yes—
89C2×#10625354C23124yes—
90C2×#10625350—224no—
91C2×#10625350—224no—
92C2×#10625350—224no—
93C2×#10625350C23124yes—
94C2×#10625350C23124yes—
95C2×#10625350C23124yes—
96C2×#10625352—224no—
97C2×#10625352—224no—
98C2×#10625352C23124yes—
99C2×#10625352C23124yes—
100C22×Dic94—224no—
101C22×Dic94C23124yes—
102C22×Dic94C2313yes—
103C22×Dic94C2313yes—
104C22×Dic94C2313yes—
105C22×Dic94C2313yes—
106C2×Q8×D47—28no—
107C2×Q8×D47—224no—
108C2×Q8×D47D4116yescomplemented
109C2×Q8×D47C23124yes—
110C2×Q8×D47C2318yes—
111C2×Q8×D47C2318yes—
112C22×D188C2313yes—
113C22×D188C2311yescharacteristic
114C22×D188C2313yes—
115C22×D188C2313yes—
116C22×C22⋊D47C2313yes—
117C22×C22⋊D47C2311yescharacteristic
118C22×C22⋊D47C2311yescharacteristic
119C22×C22⋊D47C2313yes—
120C22×C22⋊D47C2313yes—
121C22×C22⋊D47C2313yes—
122C22×C22⋊D47C2316yes—
123C23×Dic47C2316yes—
124C22×C4×D47C2311yescharacteristic
125C22×C4×D47C2316yes—
126C22×C4×D47C2313yes—
127C22×C4×D47C2313yes—
128C22×C4×D47C2313yes—
129C22×C4×D47C2313yes—
130#13094023C23124yes—
131#13094022C23124yes—
132#13094020C23124yes—
133#13094020C23124yes—
134#13094012C23124yes—
135#13094010C23124yes—
136#13094010C23124yes—
137#13094004C23124yes—
138#13094003C23124yes—
139#13094002C23148yes—
140#13094001C23148yes—
141#13094000C23124yes—
142#13093999C23124yes—
143#13093999C23124yes—
144#13093998C23124yes—
145#13093997C23148yes—
146#13093997C2318yes—
147#13093997C23124yes—
148#13093997C23148yes—
149#13093996C23148yes—
150#13093995C23124yes—
151#13093995C23124yes—
152Q8×Dic47C2318yes—
153C4×Dic94C23124yes—
154#13093989C23124yes—
155C4×D188C23124yes—
156C4×C22⋊D47C23124yes—
157C4×C22⋊D47C23124yes—
158(C22⋊D47)⋊C4C23148yes—
159(C22⋊D47)⋊C4C23148yes—
160C2×C4⋊Dic47C2313yes—
161C2×C4⋊Dic47C2313yes—
162C2×Dic47⋊C4C2316yes—
163C2×Dic47⋊C4C2313yes—
164C2×Dic47⋊C4C2316yes—
165C2×Dic47⋊C4C2311yescharacteristic
166C4⋊C4×D47C23124yes—
167C2×C22⋊Dic47C2313yes—
168C2×C22⋊Dic47C2313yes—
169C2×(C2×D47)⋊C4C2313yes—
170C2×(C2×D47)⋊C4C2316yes—
171C2×(C2×D47)⋊C4C2313yes—
172C2×(C2×D47)⋊C4C2313yes—
173C2×(C2×D47)⋊C4C2311yescharacteristic
174C2×C4×Dic47C2313yes—
175C2×C4×Dic47C2313yes—
176C2×C4×Dic47C2313yes—
177C42×D47C23124yes—
178C2×#41×C47—28no—
179C2×#41×C47C2318yes—
180C22×Q8×C47—28no—
181C22×Q8×C47C2318yes—
182C22×Q8×C47C2313yes—
183C22×Q8×C47C2311yescharacteristic
184C22×D4×C47C2313yes—
185C22×D4×C47C2313yes—
186C23×C4×C47C2313yes—
187C23×C4×C47C2313yes—
188#124×C47C23124yes—
189C22⋊Q8×C47C23124yes—
190#121×C47C23124yes—
191C4×Q8×C47C2318yes—
192C4×D4×C47C23124yes—
193C2×C4⋊C4×C47C2313yes—
194C2×C4⋊C4×C47C2313yes—
195C2×C22⋊C4×C47C2311yescharacteristic
196C2×C22⋊C4×C47C2313yes—
197C2×C22⋊C4×C47C2316yes—
198C2×C42×C47C2313yes—
199C24×C47C2413yes—
200C24×C47C2411yescharacteristic
201C23×D47C2413yes—
202C23×D47C2411yescharacteristic
203C23×D47C2411yescharacteristic
204#41×C47—232no—
205C2×Q8×C47—232no—
206C2×Q8×C47—212no—
207C2×Q8×C47C2×D418yes—
208C2×Q8×C47C24112yes—
209C2×Q8×C47C2414yes—
210C2×D4×C47—212no—
211C2×D4×C47—46no—
212C2×D4×C47C24112yes—
213C2×D4×C47C24112yes—
214C22×C4×C47—212no—
215C22×C4×C47—212no—
216C22×C4×C47C2411yescharacteristic
217C22×C4×C47C2413yes—
218C22×C4×C47C2413yes—
219C22×C4×C47C2411yescharacteristic
220C22×C4×C47C24112yes—
221C22×C4×C47C24112yes—
222C22×C4×C47C2413yes—
223C2×C22⋊D47—212no—
224C2×C22⋊D47—24no—
225C2×C22⋊D47—212no—
226C2×C22⋊D47—212no—
227C2×C22⋊D47—212no—
228C2×C22⋊D47—24no—
229C2×C22⋊D47—412no—
230C2×C22⋊D47C24112yes—
231C2×C22⋊D47C2414yes—
232C2×C22⋊D47C2414yes—
233C2×C22⋊D47C24112yes—
234C2×C22⋊D47C24112yes—
235C2×C22⋊D47C24112yes—
236C2×C22⋊D47C24124yes—
237C22×Dic47—224no—
238C22×Dic47C2413yes—
239C22×Dic47C2413yes—
240C22×Dic47C2411yescharacteristic
241C22×Dic47C24124yes—
242C22×Dic47C2413yes—
243C22×Dic47C2411yescharacteristic
244#10625354—232no—
245#10625354—296no—
246Q8×D47—232no—
247Q8×D47—296no—
248Q8×D47C2×D4164yescomplemented
249#10625352—296no—
250#10625352—296no—
251#10625350—296no—
252#10625350—296no—
253#10625350—296no—
254C2×D188—24no—
255C2×D188—212no—
256C2×D188—212no—
257C2×D188—46no—
258C2×D188C24112yes—
259C2×D188C2414yes—
260C2×D188C24112yes—
261C2×D188C24112yes—
262C2×C4×D47—212no—
263C2×C4×D47—212no—
264C2×C4×D47—224no—
265C2×C4×D47—24no—
266C2×C4×D47—46no—
267C2×C4×D47C2×D4124yes—
268C2×C4×D47C2414yes—
269C2×C4×D47C24124yes—
270C2×C4×D47C24112yes—
271C2×C4×D47C24112yes—
272C2×C4×D47C24112yes—
273C2×C4×D47C24112yes—
274C2×Dic94—212no—
275C2×Dic94—212no—
276C2×Dic94—212no—
277C2×Dic94—296no—
278C2×Dic94C2×D4124yes—
279C2×Dic94C24112yes—
280C2×Dic94C24112yes—
281C2×Dic94C24112yes—
282C2×Dic94C24112yes—
283C4⋊C4×C47C24112yes—
284C4⋊C4×C47C24112yes—
285C22⋊C4×C47C2414yes—
286C22⋊C4×C47C24112yes—
287C22⋊C4×C47C24124yes—
288C42×C47C24112yes—
289C22⋊Dic47C24112yes—
290C22⋊Dic47C24112yes—
291(C2×D47)⋊C4C24112yes—
292(C2×D47)⋊C4C24124yes—
293(C2×D47)⋊C4C24112yes—
294(C2×D47)⋊C4C24112yes—
295(C2×D47)⋊C4C2414yes—
296C4⋊Dic47C24112yes—
297C4⋊Dic47C24112yes—
298Dic47⋊C4C24124yes—
299Dic47⋊C4C24112yes—
300Dic47⋊C4C24124yes—
301Dic47⋊C4C2414yes—
302C4×Dic47C24112yes—
303C4×Dic47C24112yes—
304C4×Dic47C24112yes—
305C23×C47—26no—
306C23×C47—22no—
307C23×C47—26no—
308C23×C47—22no—
309C23×C47—26no—
310C23×C47—22no—
311C23×C47C2512yes—
312C23×C47C2516yes—
313C23×C47C2511yescharacteristic
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—26no—
317C22×D47—22no—
318C22×D47—26no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—26no—
322C22×D47C22×D414yes—
323C22×D47C2516yes—
324C22×D47C2512yes—
325C22×D47C2512yes—
326Q8×C47—224no—
327Q8×C47C22×D4116yes—
328D4×C47—224no—
329D4×C47—412no—
330C2×C4×C47—22no—
331C2×C4×C47—26no—
332C2×C4×C47—22no—
333C2×C4×C47—26no—
334C2×C4×C47—224no—
335C2×C4×C47—224no—
336C2×C4×C47C22×D4112yes—
337C2×C4×C47C2512yes—
338C2×C4×C47C2516yes—
339C2×C4×C47C2516yes—
340C2×C4×C47C2512yes—
341C2×C4×C47C2516yes—
342C22⋊D47—28no—
343C22⋊D47—224no—
344C22⋊D47—224no—
345C22⋊D47—224no—
346C22⋊D47—224no—
347C22⋊D47—28no—
348C22⋊D47—424no—
349C2×Dic47—22no—
350C2×Dic47—26no—
351C2×Dic47—26no—
352C2×Dic47—248no—
353C2×Dic47C22×D4112yes—
354C2×Dic472−1+414yescomplemented
355C2×Dic47C2516yes—
356C2×Dic47C2516yes—
357C2×Dic47C2512yes—
358C2×Dic47C2516yes—
359C2×Dic47C2512yes—
360D188—28no—
361D188—224no—
362D188—224no—
363D188—412no—
364C4×D47—224no—
365C4×D47—224no—
366C4×D47—248no—
367C4×D47—28no—
368C4×D47—412no—
369C4×D47C22×D4148yes—
370Dic94—224no—
371Dic94—224no—
372Dic94—224no—
373Dic94C22×D4148yes—
374C2×#3497—471nomaximal, Sylow
375C22×C47—26no—
376C22×C47—22no—
377C22×C47—22no—
378C22×C47—26no—
379C22×C47—26no—
380C22×C47—22no—
381C22×C47—412no—
382C22×C47—44no—
383C22×C47C23×D412yes—
384C22×C47C2×2−1+412yes—
385C22×C47#58512yes—
386C22×C47C2611yescharacteristic
387C2×D47—22no—
388C2×D47—22no—
389C2×D47—28no—
390C2×D47—26no—
391C2×D47—22no—
392C2×D47—26no—
393C2×D47—22no—
394C2×D47—22no—
395C2×D47—26no—
396C2×D47—412no—
397C2×D47—44no—
398C2×D47C23×D414yes—
399C4×C47—22no—
400C4×C47—26no—
401C4×C47—22no—
402C4×C47—26no—
403C4×C47C23×D4112yes—
404Dic47—22no—
405Dic47—26no—
406Dic47—26no—
407Dic47C23×D4112yes—
408Dic47C2×2−1+414yescomplemented
409C22×2−1+4—471no—
410C22×2−1+4—471no—
411#3497—4732no—
412C2×#550—471no—
413C2×#550—473no—
414C2×D4×Q8—471no—
415C2×D4×Q8—473no—
416C2×#548—473no—
417C2×#548—471no—
418C2×#548—473no—
419C2×#548D4711yescharacteristic, complemented
420C2×#537—473no—
421C2×#537—473no—
422C2×#532—473no—
423C2×#532—473no—
424C22×C4×Q8—471no—
425C2×C47—46no—
426C2×C47—42no—
427C2×C47#349714yescomplemented
428C2×C47C24×D411yescharacteristic
429C2×C47C22×2−1+411yescharacteristic
430C2×C47C2×#58511yescharacteristic
431D47—24no—
432D47—46no—
433D47—42no—
434C2×2−1+4—4716no—
435C2×2−1+4—4716no—
436C2×2−1+4—9416no—
437C2×2−1+4—9416no—
438C22×#41—473no—
439C22×#41—471no—
440C22×#41—473no—
441C22×#41—473no—
442C22×#41—473no—
443C22×#41—473no—
444C22×#41—473no—
445C22×#41C2×D4711yescharacteristic
446C23×Q8—471no—
447C23×Q8—473no—
448C23×Q8—471no—
449C23×Q8—473no—
450C23×Q8C2×D4711yescharacteristic
451#550—4716no—
452#550—4748no—
453D4×Q8—4716no—
454D4×Q8—4748no—
455#548—4748no—
456#548—4716no—
457#548—4748no—
458#548C2×D47116yescomplemented
459#537—4748no—
460#537—4748no—
461#532—4748no—
462#532—4748no—
463C2×C4⋊Q8—473no—
464C2×C4⋊Q8—473no—
465C2×#127—473no—
466C2×#127—473no—
467C2×#124—473no—
468C2×#124—473no—
469C2×#124—473no—
470C2×#124C2×D4713yes—
471C2×C22⋊Q8—473no—
472C2×C22⋊Q8—473no—
473C2×C22⋊Q8—476no—
474C2×C22⋊Q8—473no—
475C2×C22⋊Q8—476no—
476C2×C22⋊Q8C2×D4713yes—
477C2×#121—473no—
478C2×#121—473no—
479C2×#121—476no—
480C2×#121—473no—
481C2×#121—473no—
482C2×#121—473no—
483C2×#121—473no—
484C2×#121—471no—
485C2×#121—476no—
486C2×#121—476no—
487C2×#121C2×D4713yes—
488C2×C4×Q8—471no—
489C2×C4×Q8—4716no—
490C2×C4×Q8—473no—
491C2×C4×Q8—473no—
492C2×C4×Q8C2×D4711yescharacteristic
493C2×C4×D4—473no—
494C2×C4×D4—473no—
495C2×C4×D4—476no—
496C2×C4×D4—476no—
497C2×C4×D4—473no—
498C2×C4×D4C2×D4713yes—
499C22×C4⋊C4—473no—
500C22×C42—473no—
501C47C2×#349711yescharacteristic, complemented, Sylow
5022−1+4—94128no—
5032−1+4—94128no—
504C2×#41—28no—
505C2×#41—4724no—
506C2×#41—478no—
507C2×#41—4724no—
508C2×#41—4724no—
509C2×#41—4724no—
510C2×#41—4724no—
511C2×#41—4724no—
512C2×#41—9424no—
513C2×#41—9424no—
514C2×#41—9424no—
515C2×#41—9424no—
516C2×#41—9424no—
517C2×#41—9424no—
518C2×#41—948no—
519C2×#41C22×D4718yes—
520C22×Q8—28no—
521C22×Q8—4716no—
522C22×Q8—478no—
523C22×Q8—4724no—
524C22×Q8—478no—
525C22×Q8—473no—
526C22×Q8—473no—
527C22×Q8—473no—
528C22×Q8—473no—
529C22×Q8—4724no—
530C22×Q8—9424no—
531C22×Q8—9424no—
532C22×Q8—948no—
533C22×Q8C22×D4713yes—
534C22×Q8C22×D4718yes—
535C22×Q8C22×D4711yescharacteristic
536C22×D4—471no—
537C22×D4—473no—
538C22×D4—471no—
539C22×D4—473no—
540C22×D4—473no—
541C22×D4—473no—
542C22×D4—476no—
543C22×D4—471no—
544C22×D4—473no—
545C22×D4—473no—
546C22×D4—473no—
547C22×D4C22×D4713yes—
548C22×D4C22×D4713yes—
549C23×C4—473no—
550C23×C4—476no—
551C23×C4—476no—
552C23×C4—473no—
553C23×C4—473no—
554C23×C4—471no—
555C23×C4—473no—
556C23×C4C22×D4713yes—
557C23×C4C22×D4713yes—
558C4⋊Q8—4724no—
559C4⋊Q8—4724no—
560#127—4724no—
561#127—4724no—
562#124—4724no—
563#124—4724no—
564#124—4724no—
565#124C22×D47124yes—
566C22⋊Q8—4724no—
567C22⋊Q8—4724no—
568C22⋊Q8—4748no—
569C22⋊Q8—4724no—
570C22⋊Q8—4748no—
571C22⋊Q8C22×D47124yes—
572#121—4724no—
573#121—4724no—
574#121—4748no—
575#121—4724no—
576#121—4724no—
577#121—4724no—
578#121—4724no—
579#121—478no—
580#121—4748no—
581#121—4748no—
582#121C22×D47124yes—
583C4×Q8—478no—
584C4×Q8—4724no—
585C4×Q8—4724no—
586C4×Q8C22×D4718yes—
587C4×D4—4724no—
588C4×D4—4724no—
589C4×D4—4748no—
590C4×D4—4748no—
591C4×D4—4724no—
592C4×D4C22×D47124yes—
593C2×C4⋊C4—476no—
594C2×C4⋊C4—473no—
595C2×C4⋊C4—471no—
596C2×C4⋊C4—473no—
597C2×C4⋊C4—476no—
598C2×C4⋊C4—473no—
599C2×C4⋊C4—4724no—
600C2×C4⋊C4C22×D4713yes—
601C2×C4⋊C4C22×D4713yes—
602C2×C22⋊C4—473no—
603C2×C22⋊C4—473no—
604C2×C22⋊C4—473no—
605C2×C22⋊C4—471no—
606C2×C22⋊C4—473no—
607C2×C22⋊C4—473no—
608C2×C22⋊C4—476no—
609C2×C22⋊C4C22×D4713yes—
610C2×C22⋊C4C22×D4716yes—
611C2×C22⋊C4C22×D4711yescharacteristic
612C2×C42—473no—
613C2×C42—473no—
614C2×C42—473no—
615C2×C42—4724no—
616C2×C42C22×D4713yes—
617C24—471no—
618C24—471no—
619C24—473no—
620C24C23×D4711yescharacteristic
621C24C23×D4713yes—
622#41—232no—
623#41—9496no—
624#41—9496no—
625#41—9496no—
626#41—9496no—
627#41—9496no—
628#41—9496no—
629#41—9432no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—4764no—
633C2×Q8—4724no—
634C2×Q8—4712no—
635C2×Q8—4712no—
636C2×Q8—4712no—
637C2×Q8—4712no—
638C2×Q8—9412no—
639C2×Q8—9412no—
640C2×Q8—9496no—
641C2×Q8—9496no—
642C2×Q8—9432no—
643C2×Q8—9412no—
644C2×Q8D4×D4718yes—
645C2×Q8C23×D47112yes—
646C2×Q8C23×D4714yes—
647C2×D4—212no—
648C2×D4—46no—
649C2×D4—474no—
650C2×D4—4712no—
651C2×D4—474no—
652C2×D4—4712no—
653C2×D4—4712no—
654C2×D4—4712no—
655C2×D4—4724no—
656C2×D4—474no—
657C2×D4—4712no—
658C2×D4—4712no—
659C2×D4—4712no—
660C2×D4—944no—
661C2×D4—9412no—
662C2×D4—944no—
663C2×D4—9412no—
664C2×D4—9412no—
665C2×D4—9412no—
666C2×D4—944no—
667C2×D4—9412no—
668C2×D4—9412no—
669C2×D4—1886no—
670C2×D4—18812no—
671C2×D4C23×D47112yes—
672C2×D4C23×D47112yes—
673C22×C4—212no—
674C22×C4—212no—
675C22×C4—471no—
676C22×C4—473no—
677C22×C4—4724no—
678C22×C4—4712no—
679C22×C4—4724no—
680C22×C4—473no—
681C22×C4—473no—
682C22×C4—471no—
683C22×C4—474no—
684C22×C4—4724no—
685C22×C4—4712no—
686C22×C4—4712no—
687C22×C4—4712no—
688C22×C4—944no—
689C22×C4—9424no—
690C22×C4—9424no—
691C22×C4—9412no—
692C22×C4—9412no—
693C22×C4—1886no—
694C22×C4C23×D47112yes—
695C22×C4C23×D47112yes—
696C22×C4C23×D4711yescharacteristic
697C22×C4C23×D4713yes—
698C22×C4C23×D4711yescharacteristic
699C22×C4C23×D4713yes—
700C22×C4C23×D4713yes—
701C4⋊C4—4724no—
702C4⋊C4—474no—
703C4⋊C4—4712no—
704C4⋊C4—4724no—
705C4⋊C4—4712no—
706C4⋊C4—4712no—
707C4⋊C4C23×D47112yes—
708C4⋊C4C23×D47112yes—
709C22⋊C4—4712no—
710C22⋊C4—4712no—
711C22⋊C4—4712no—
712C22⋊C4—474no—
713C22⋊C4—4712no—
714C22⋊C4—4712no—
715C22⋊C4—4724no—
716C22⋊C4C23×D47112yes—
717C22⋊C4C23×D47124yes—
718C22⋊C4C23×D4714yes—
719C42—4712no—
720C42—4712no—
721C42—4712no—
722C42C23×D47112yes—
723C23—22no—
724C23—26no—
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—474no—
730C23—472no—
731C23—472no—
732C23—476no—
733C23—942no—
734C23—942no—
735C23—946no—
736C23—942no—
737C23—942no—
738C23—946no—
739C23—942no—
740C23—946no—
741C23C24×D4712yes—
742C23C24×D4716yes—
743C23C24×D4711yescharacteristic
744Q8—224no—
745Q8—4748no—
746Q8—9424no—
747Q8—9424no—
748Q8—9424no—
749Q8C2×D4×D47116yes—
750D4—224no—
751D4—412no—
752D4—948no—
753D4—9424no—
754D4—948no—
755D4—9424no—
756D4—9424no—
757D4—9424no—
758D4—948no—
759D4—9424no—
760D4—9424no—
761D4—18812no—
762D4—18824no—
763C2×C4—22no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—4712no—
770C2×C4—474no—
771C2×C4—472no—
772C2×C4—476no—
773C2×C4—4748no—
774C2×C4—476no—
775C2×C4—476no—
776C2×C4—472no—
777C2×C4—948no—
778C2×C4—9448no—
779C2×C4—9448no—
780C2×C4—942no—
781C2×C4—946no—
782C2×C4—946no—
783C2×C4—9424no—
784C2×C4—9424no—
785C2×C4—18812no—
786C2×C4C2×D4×D47112yes—
787C2×C4C24×D4712yes—
788C2×C4C24×D4716yes—
789C2×C4C24×D4712yes—
790C2×C4C24×D4716yes—
791C2×C4C24×D4716yes—
792C22—22no—
793C22—26no—
794C22—22no—
795C22—26no—
796C22—22no—
797C22—26no—
798C22—44no—
799C22—412no—
800C22—474no—
801C22—948no—
802C22—942no—
803C22—942no—
804C22—946no—
805C22—942no—
806C22—942no—
807C22—946no—
808C22—942no—
809C22—946no—
810C22—18812no—
811C22—1884no—
812C22C22×D4×D4712yes—
813C222−1+4×D4712yes—
814C22#1568995912yes—
815C22C25×D4711yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—4712no—
821C4—474no—
822C4—946no—
823C4—942no—
824C4—946no—
825C4C22×D4×D47112yes—
826C2—42no—
827C2—46no—
828C2—944no—
829C2—1886no—
830C2—1882no—
831C2#2025715614yesdirect product factor
832C2C23×D4×D4711yescharacteristic
833C2C2×2−1+4×D4711yescharacteristic
834C2C2×#1568995911yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#548C2
socleC23×C47C25
hypercenterC2×#548D47
hypocenterC47C2×#3497
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13094072C2semidirect
2. C22×#13094071C2semidirect
3. #20257156C2direct (N × H)
4. C2×#15689792C2semidirect
5. C2×#15689791C2semidirect
6. C2×Q8×C22⋊D47C2semidirect
7. C2×#15689786C2semidirect
8. C2×#15689785C2semidirect
9. C2×#15689782C2semidirect
10. C2×#15689781C2semidirect
11. C2×#15689703C2semidirect
12. C2×#15689702C2semidirect
13. C2×#15689672C2semidirect
14. C2×#15689670C2semidirect
15. C2×C4×Q8×D47C2semidirect
16. C2×C47×#548C2semidirect
18. C2×#13094072C22semidirect
20. C2×#13094071C22semidirect
32. #15689792C22semidirect
33. #15689791C22semidirect
34. Q8×C22⋊D47C22semidirect
35. #15689786C22semidirect
36. #15689785C22semidirect
37. #15689782C22semidirect
38. #15689781C22semidirect
39. #15689703C22semidirect
40. #15689702C22semidirect
41. #15689672C22semidirect
42. #15689670C22semidirect
68. C4×Q8×D47C22semidirect
78. C47×#548C22semidirect
108. C2×Q8×D47D4semidirect
248. Q8×D47C2×D4semidirect
354. C2×Dic472−1+4semidirect
408. Dic47C2×2−1+4semidirect
419. C2×#548D47semidirect
427. C2×C47#3497semidirect
458. #548C2×D47semidirect
501. C47C2×#3497semidirect
831. C2#20257156direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940722
C22×#130940712
#202571562
C2×#156897922
C2×#156897912
C2×Q8×C22⋊D472
C2×#156897862
C2×#156897852
C2×#156897822
C2×#156897812
C2×#156897032
C2×#156897022
C2×#156896722
C2×#156896702
C2×C4×Q8×D472
C2×C47×#5482
C2×#349747