Finite Group Databasebeta

← C2×#20255730 #27094685

Subgroups — C2×#20255730 #27094685

Order 12032.

2374 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689774C211yesmaximal, characteristic, complemented
2C2×#15689773C211yesmaximal, characteristic, complemented
3#20255730C2116yesmaximal, direct product factor
4C2×#15689527C211yesmaximal, characteristic, complemented
5C2×#15689438C211yesmaximal, characteristic, complemented
6C2×#15689437C211yesmaximal, characteristic, complemented
7C2×#15689435C211yesmaximal, characteristic, complemented
8C2×#15689402C211yesmaximal, characteristic, complemented
9C2×#15689401C211yesmaximal, characteristic, complemented
10C2×#15689358C211yesmaximal, characteristic, complemented
11C2×#15689357C211yesmaximal, characteristic, complemented
12C2×#15689203C211yesmaximal, characteristic, complemented
13C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
14C22×#13093957C211yesmaximal, characteristic, complemented
15C2×#107×D47C211yesmaximal, characteristic, complemented
16C2×C47×#480C211yesmaximal, characteristic, complemented
17C22×#10625350—21no—
18C22×#10625352—21no—
19C22×#10625334C2211yescharacteristic
20C23×C47⋊C8C2211yescharacteristic
21C22×C8×D47C2211yescharacteristic
22#15689774—24no—
23#15689774C2218yescomplemented
24#15689773—24no—
25#15689773C2218yescomplemented
26C2×#13094023C2211yescharacteristic
27C2×#13094023C2211yescharacteristic
28C2×#13094009—21no—
29C2×#13094007—21no—
30C2×#13094006—21no—
31C2×#13094005—21no—
32C2×#13094002—21no—
33C2×#13094001—21no—
34C2×#13093999C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36C2×#13093995C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C2×#13093986C2211yescharacteristic
39C2×C4×C22⋊D47C2211yescharacteristic
40C22×C4⋊Dic47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689527C2218yescomplemented
44#15689438C2218yescomplemented
45#15689437C2218yescomplemented
46#15689435C2218yescomplemented
47#15689402C2218yescomplemented
48#15689401C2218yescomplemented
49#15689358C2218yescomplemented
50#15689357C2218yescomplemented
51#15689203C2218yescomplemented
52(C22⋊D47)⋊C8C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093957C2211yescharacteristic
59C2×#13093957C2211yescharacteristic
60C2×#13093957C2218yescomplemented
61#107×D47C2218yescomplemented
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#121×C47C2211yescharacteristic
70C22×C4⋊C4×C47C2211yescharacteristic
71C47×#480C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625350—28no—
78C2×#10625350—48no—
79C2×#10625352—28no—
80C2×#10625352—48no—
81C22×Dic94—21no—
82C22×Dic94—21no—
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C22⋊D47D411yescharacteristic
88C23×Dic47—21no—
89C23×Dic47—21no—
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47C2311yescharacteristic
94C2×#10625334—24no—
95C2×#10625334C2314yes—
96C22×C47⋊C8—24no—
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2314yes—
99C22×C47⋊C8C2311yescharacteristic
100C2×C8×D47—24no—
101C2×C8×D47C2314yes—
102#13094023—22no—
103#13094023—22no—
104#13094023C2314yes—
105#13094023C2314yes—
106#13094009—28no—
107#13094007—28no—
108#13094006—28no—
109#13094005—28no—
110#13094002—28no—
111#13094001—28no—
112#13093999—22no—
113#13093999C2314yes—
114#13093998—22no—
115#13093998C2314yes—
116#13093995—22no—
117#13093995C2314yes—
118D4×Dic47—22no—
119D4×Dic47C2314yes—
120#13093986—22no—
121#13093986C2314yes—
122C4×C22⋊D47D414yes—
123C4×C22⋊D47C2314yes—
124C2×C4⋊Dic47—22no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47C2314yes—
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4D411yescharacteristic
135C4⋊C4×D47—22no—
136C4⋊C4×D47—22no—
137C4⋊C4×D47C2314yes—
138C4⋊C4×D47C2314yes—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47D411yescharacteristic
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×C4×Dic47C2311yescharacteristic
147#13093958C2314yes—
148#13093958C2314yes—
149#13093957C2314yes—
150#13093957C2314yes—
151#13093957C2314yes—
152#13093957C2314yes—
153#13093957C2314yes—
154Dic47⋊C8C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093945C2314yes—
158#13093944C2314yes—
159(C2×D47)⋊C8C2314yes—
160C8×Dic47C2314yes—
161C22×D4×C47—21no—
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C23×C4×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167#121×C47—22no—
168#121×C47C2314yes—
169C2×C4⋊C4×C47—22no—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47C2314yes—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176#107×C47C2314yes—
177#107×C47C2314yes—
178#102×C47C2314yes—
179#102×C47C2314yes—
180C22⋊C8×C47C2314yes—
181C24×C47—21no—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C23×D47C2×D411yescharacteristic
185C2×D4×C47—24no—
186C2×D4×C47—21no—
187C2×D4×C47—22no—
188C2×D4×C47—22no—
189C2×D4×C47—44no—
190C2×D4×C47C2412yes—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—24no—
197C22×C4×C47—44no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2411yescharacteristic
202C2×C22⋊D47—24no—
203C2×C22⋊D47—24no—
204C2×C22⋊D47—44no—
205C2×C22⋊D47—44no—
206C2×C22⋊D47D818yescomplemented
207C2×C22⋊D47C2×D414yes—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—24no—
212C22×Dic47—24no—
213C22×Dic47—44no—
214C22×Dic47—44no—
215C22×Dic47C2×D411yescharacteristic
216C22×Dic47C2×D411yescharacteristic
217C22×Dic47C2×D411yescharacteristic
218#10625352—432no—
219#10625350—432no—
220C2×D188—22no—
221C2×D188—22no—
222C2×D188—24no—
223C2×D188—21no—
224C2×D188—44no—
225C2×D188C2412yes—
226C2×C4×D47—22no—
227C2×C4×D47—22no—
228C2×C4×D47—24no—
229C2×C4×D47—24no—
230C2×C4×D47—24no—
231C2×C4×D47—44no—
232C2×C4×D47—44no—
233C2×C4×D47—44no—
234C2×C4×D47C2×D412yes—
235C2×C4×D47C2412yes—
236C2×Dic94—24no—
237C2×Dic94—24no—
238C2×Dic94—44no—
239C2×Dic94—44no—
240C2×C8×C47—22no—
241C2×C8×C47—22no—
242C2×C8×C47C2412yes—
243C2×C8×C47C2412yes—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47—24no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47C2412yes—
249C4⋊C4×C47C2412yes—
250C4⋊C4×C47C2412yes—
251C22⋊C4×C47—24no—
252C22⋊Dic47—24no—
253C22⋊Dic47—24no—
254C22⋊Dic47C2×D414yes—
255#10625334—28no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4C2×D414yes—
260C4⋊Dic47—21no—
261C4⋊Dic47—21no—
262C4⋊Dic47—21no—
263C4⋊Dic47—24no—
264C4⋊Dic47C2412yes—
265C4⋊Dic47C2412yes—
266C4⋊Dic47C2412yes—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269Dic47⋊C4—24no—
270Dic47⋊C4—24no—
271Dic47⋊C4C2×D414yes—
272C4×Dic47C2×D412yes—
273C4×Dic47C2412yes—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—28no—
276C2×C47⋊C8#4114yescomplemented
277C2×C47⋊C8C2412yes—
278C2×C47⋊C8C2412yes—
279C8×D47—28no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47—42no—
284C23×C47—42no—
285C23×C47—42no—
286C23×C47C2×D814yes—
287C23×C47C22×D412yes—
288C23×C47C22×D411yescharacteristic
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47C2×D814yes—
296C22×D47C22×D412yes—
297D4×C47—22no—
298D4×C47—22no—
299D4×C47—48no—
300D4×C47—42no—
301C2×C4×C47—22no—
302C2×C4×C47—24no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—48no—
312C2×C4×C47C22×D412yes—
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C2×#4112yes—
315C2×C4×C472−1+412yes—
316C2×C4×C47C2511yescharacteristic
317C22⋊D47—48no—
318C22⋊D47—48no—
319C22⋊D47C2×D8116yescomplemented
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—48no—
329C2×Dic47—48no—
330C2×Dic47C2×D814yes—
331C2×Dic47C22×D412yes—
332C2×Dic47C22×D412yes—
333C2×Dic47C22×D412yes—
334D188—22no—
335D188—22no—
336D188—48no—
337D188—42no—
338C4×D47—24no—
339C4×D47—22no—
340C4×D47—22no—
341C4×D47—48no—
342C4×D47—48no—
343C4×D47—48no—
344Dic94—48no—
345Dic94—48no—
346C8×C47—22no—
347C8×C47—22no—
348C47⋊C8—22no—
349C47⋊C8C2×#4114yescomplemented
350C2×#3334—471nomaximal, Sylow
351C22×C47—28no—
352C22×C47—22no—
353C22×C47—22no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47—42no—
357C22×C47—84no—
358C22×C47#54712yes—
359C22×C47C22×D814yes—
360C22×C47C22×D812yes—
361C22×C47#57812yes—
362C22×C47C23×D411yescharacteristic
363C2×D47—28no—
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—42no—
367C2×D47—42no—
368C2×D47—42no—
369C2×D47—84no—
370C2×D47C22×D814yes—
371C4×C47—22no—
372C4×C47—42no—
373C4×C47—42no—
374C4×C47—42no—
375C4×C47#54712yes—
376C4×C47C22×#4111yescharacteristic
377C4×C47C2×2−1+411yescharacteristic
378Dic47—22no—
379Dic47—22no—
380Dic47—42no—
381Dic47—42no—
382Dic47—42no—
383Dic47C22×D814yes—
384C2×#547—471no—
385C2×#547—471no—
386#3334—4716no—
387C2×#500—471no—
388C2×#480—471no—
389C2×#480—471no—
390C2×#480—471no—
391C2×#480D4711yescharacteristic, complemented
392C2×#474—471no—
393C2×#474—471no—
394C2×#466—471no—
395C2×#466—471no—
396C2×C4×D8—471no—
397C2×C8×D4—471no—
398C22×#107—471no—
399C22×#107—471no—
400C2×C47—24no—
401C2×C47—82no—
402C2×C47#333414yescomplemented
403C2×C47C2×#54711yescharacteristic
404C2×C47C23×D811yescharacteristic
405C2×C47C2×#57811yescharacteristic
406D47—24no—
407D47—82no—
408C22×#41—941no—
409C22×#41—941no—
410C22×D8—471no—
411C23×C8—471no—
412C23×C8—471no—
413#547—478no—
414#547—478no—
415#547—944no—
416#547—944no—
417C2×C4⋊Q8—471no—
418C2×C4⋊Q8—471no—
419C2×#123—941no—
420C2×#123—941no—
421C2×#123—941no—
422C2×#123—941no—
423C2×C22⋊Q8—941no—
424C2×C22⋊Q8—941no—
425C2×#121—471no—
426C2×#121—471no—
427C2×#121—471no—
428C2×#121C2×D4711yescharacteristic
429C2×C4×D4—471no—
430C2×C4×D4—471no—
431C2×C4×D4—471no—
432C22×C4⋊C4—471no—
433C22×C4⋊C4—471no—
434C22×C4⋊C4—471no—
435C22×C4⋊C4C2×D4711yescharacteristic
436#500—478no—
437#480—478no—
438#480—478no—
439#480—478no—
440#480C2×D4718yescomplemented
441#474—478no—
442#474—478no—
443#466—478no—
444#466—478no—
445C4×D8—478no—
446C8×D4—478no—
447C2×#107—471no—
448C2×#107—471no—
449C2×#107—478no—
450C2×#107—471no—
451C2×#107—471no—
452C2×#107—471no—
453C2×#107—471no—
454C2×#107—471no—
455C2×#107—478no—
456C2×#107C2×D4711yescharacteristic
457C2×#107C2×D4711yescharacteristic
458C2×C4⋊C8—471no—
459C2×#102—471no—
460C2×#102—471no—
461C2×#102—471no—
462C2×#102—471no—
463C2×#102C2×D4711yescharacteristic
464C2×#102C2×D4711yescharacteristic
465C2×C22⋊C8—471no—
466C2×C22⋊C8C2×D4711yescharacteristic
467C2×C4×C8—471no—
468C47C2×#333411yescharacteristic, complemented, Sylow
469C2×#41—948no—
470C2×#41—948no—
471C2×#41—1888no—
472C2×#41—1888no—
473C22×Q8—941no—
474C22×Q8—941no—
475C22×D4—21no—
476C22×D4—471no—
477C22×D4—471no—
478C22×D4—941no—
479C22×D4—941no—
480C22×D4—941no—
481C22×D4C22×D4711yescharacteristic
482C23×C4—21no—
483C23×C4—471no—
484C23×C4—941no—
485C23×C4—941no—
486C23×C4—941no—
487C23×C4—941no—
488C23×C4—941no—
489C23×C4C22×D4711yescharacteristic
490C2×D8—474no—
491C2×D8—944no—
492C22×C8—471no—
493C22×C8—471no—
494C22×C8—474no—
495C22×C8—474no—
496C22×C8—944no—
497C22×C8—944no—
498C22×C8C22×D4711yescharacteristic
499C22×C8C22×D4711yescharacteristic
500C4⋊Q8—474no—
501C4⋊Q8—474no—
502C4⋊Q8—942no—
503C4⋊Q8—942no—
504#123—948no—
505#123—948no—
506#123—948no—
507#123—948no—
508C22⋊Q8—948no—
509C22⋊Q8—948no—
510#121—22no—
511#121—474no—
512#121—474no—
513#121—474no—
514#121—942no—
515#121—942no—
516#121—942no—
517#121C22×D4714yes—
518C4×D4—474no—
519C4×D4—474no—
520C4×D4—474no—
521C4×D4—474no—
522C4×D4—942no—
523C4×D4—942no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—471no—
527C2×C4⋊C4—471no—
528C2×C4⋊C4—471no—
529C2×C4⋊C4—471no—
530C2×C4⋊C4—474no—
531C2×C4⋊C4—474no—
532C2×C4⋊C4—474no—
533C2×C4⋊C4—942no—
534C2×C4⋊C4—942no—
535C2×C4⋊C4—941no—
536C2×C4⋊C4—941no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—942no—
541C2×C4⋊C4C22×D4711yescharacteristic
542C2×C4⋊C4C22×D4711yescharacteristic
543C2×C4⋊C4C22×D4711yescharacteristic
544C2×C4⋊C4C22×D4714yes—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—471no—
547C2×C22⋊C4—471no—
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C22⋊C4—941no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C42—471no—
554#107—474no—
555#107—474no—
556#107—474no—
557#107—474no—
558#107—474no—
559#107—474no—
560#107—474no—
561#107C22×D4714yes—
562#107C22×D4714yes—
563C4⋊C8—474no—
564#102—474no—
565#102—474no—
566#102—474no—
567#102—474no—
568#102C22×D4714yes—
569#102C22×D4714yes—
570C22⋊C8—474no—
571C22⋊C8C22×D4714yes—
572C4×C8—474no—
573C24—21no—
574C24—471no—
575C24—941no—
576C24D4×D4711yescharacteristic
577#41—18832no—
578#41—18832no—
579C2×Q8—944no—
580C2×Q8—944no—
581C2×Q8—1884no—
582C2×Q8—1884no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—44no—
588C2×D4—478no—
589C2×D4—474no—
590C2×D4—472no—
591C2×D4—944no—
592C2×D4—944no—
593C2×D4—944no—
594C2×D4—941no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—1884no—
598C2×D4—1884no—
599C2×D4—1884no—
600C2×D4C23×D4712yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—44no—
608C22×C4—471no—
609C22×C4—471no—
610C22×C4—471no—
611C22×C4—472no—
612C22×C4—472no—
613C22×C4—944no—
614C22×C4—944no—
615C22×C4—944no—
616C22×C4—944no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—944no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—1884no—
624C22×C4—1884no—
625C22×C4—1884no—
626C22×C4—1884no—
627C22×C4—1884no—
628C22×C4D4×D4712yes—
629C22×C4D4×D4711yescharacteristic
630C22×C4C23×D4712yes—
631C22×C4C23×D4711yescharacteristic
632D8—948no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—474no—
636C2×C8—472no—
637C2×C8—472no—
638C2×C8—948no—
639C2×C8—948no—
640C2×C8—942no—
641C2×C8C23×D4712yes—
642C2×C8C23×D4712yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—474no—
648C4⋊C4—472no—
649C4⋊C4—472no—
650C4⋊C4—472no—
651C4⋊C4—944no—
652C4⋊C4—944no—
653C4⋊C4—944no—
654C4⋊C4—944no—
655C4⋊C4—941no—
656C4⋊C4—941no—
657C4⋊C4—941no—
658C4⋊C4—944no—
659C4⋊C4C23×D4712yes—
660C4⋊C4C23×D4712yes—
661C4⋊C4C23×D4712yes—
662C22⋊C4—24no—
663C22⋊C4—474no—
664C22⋊C4—474no—
665C22⋊C4—944no—
666C22⋊C4—944no—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C42—472no—
671C42—472no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—474no—
679C23—472no—
680C23—942no—
681C23—942no—
682C23—942no—
683C23—1882no—
684C23—1882no—
685C23—1882no—
686C23D8×D4714yes—
687C23C2×D4×D4712yes—
688C23C2×D4×D4711yescharacteristic
689Q8—1888no—
690Q8—1888no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—42no—
695D4—4716no—
696D4—942no—
697D4—942no—
698D4—1888no—
699D4—1888no—
700D4—1888no—
701D4—1882no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—474no—
714C2×C4—472no—
715C2×C4—472no—
716C2×C4—472no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—944no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—1888no—
726C2×C4—1888no—
727C2×C4—1888no—
728C2×C4—1888no—
729C2×C4—1882no—
730C2×C4—1882no—
731C2×C4—1882no—
732C2×C4—1888no—
733C2×C4C2×D4×D4712yes—
734C2×C4C2×D4×D4711yescharacteristic
735C2×C4#41×D4712yes—
736C2×C4#1309407112yes—
737C2×C4C24×D4711yescharacteristic
738C8—22no—
739C8—22no—
740C8—474no—
741C8—942no—
742C22—22no—
743C22—22no—
744C22—28no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—474no—
750C22—942no—
751C22—942no—
752C22—948no—
753C22—3764no—
754C22—1882no—
755C22—1882no—
756C22—1882no—
757C22#1568977112yes—
758C22C2×D8×D4714yes—
759C22C2×D8×D4712yes—
760C22#1568993912yes—
761C22C22×D4×D4711yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—474no—
767C4—942no—
768C4—942no—
769C4—1882no—
770C4—1882no—
771C4—1882no—
772C4#1568977112yes—
773C4C2×#41×D4711yescharacteristic
774C4C2×#1309407111yescharacteristic
775C2—24no—
776C2—82no—
777C2—944no—
778C2—3762no—
779C2#2025573014yesdirect product factor
780C2C2×#1568977111yescharacteristic
781C2C22×D8×D4711yescharacteristic
782C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#480C2
socleC23×C47C22×D4
hypercenterC2×#480D47
hypocenterC47C2×#3334
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#15689774C2semidirect
2. C2×#15689773C2semidirect
3. #20255730C2direct (N × H)
4. C2×#15689527C2semidirect
5. C2×#15689438C2semidirect
6. C2×#15689437C2semidirect
7. C2×#15689435C2semidirect
8. C2×#15689402C2semidirect
9. C2×#15689401C2semidirect
10. C2×#15689358C2semidirect
11. C2×#15689357C2semidirect
12. C2×#15689203C2semidirect
13. C2×(C22⋊D47)⋊C8C2semidirect
14. C22×#13093957C2semidirect
15. C2×#107×D47C2semidirect
16. C2×C47×#480C2semidirect
23. #15689774C22semidirect
25. #15689773C22semidirect
43. #15689527C22semidirect
44. #15689438C22semidirect
45. #15689437C22semidirect
46. #15689435C22semidirect
47. #15689402C22semidirect
48. #15689401C22semidirect
49. #15689358C22semidirect
50. #15689357C22semidirect
51. #15689203C22semidirect
52. (C22⋊D47)⋊C8C22semidirect
60. C2×#13093957C22semidirect
61. #107×D47C22semidirect
71. C47×#480C22semidirect
206. C2×C22⋊D47D8semidirect
276. C2×C47⋊C8#41semidirect
319. C22⋊D47C2×D8semidirect
349. C47⋊C8C2×#41semidirect
391. C2×#480D47semidirect
402. C2×C47#3334semidirect
440. #480C2×D47semidirect
468. C47C2×#3334semidirect
779. C2#20255730direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897742
C2×#156897732
#202557302
C2×#156895272
C2×#156894382
C2×#156894372
C2×#156894352
C2×#156894022
C2×#156894012
C2×#156893582
C2×#156893572
C2×#156892032
C2×(C22⋊D47)⋊C82
C22×#130939572
C2×#107×D472
C2×C47×#4802
C2×#333447