Finite Group Databasebeta

← C2×#20254801 #27089190

Subgroups — C2×#20254801 #27089190

Order 12032.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689744C211yesmaximal, characteristic, complemented
2C2×#15689728C211yesmaximal, characteristic, complemented
3#20254801C2116yesmaximal, direct product factor
4C2×#15689431C211yesmaximal, characteristic, complemented
5C2×#15689424C211yesmaximal, characteristic, complemented
6C2×#15689414C211yesmaximal, characteristic, complemented
7C2×#15689404C211yesmaximal, characteristic, complemented
8C2×#15689376C211yesmaximal, characteristic, complemented
9C2×#15689369C211yesmaximal, characteristic, complemented
10C2×#15689359C211yesmaximal, characteristic, complemented
11C2×#15689352C211yesmaximal, characteristic, complemented
12C2×#15689324C211yesmaximal, characteristic, complemented
13C2×#15689339C211yesmaximal, characteristic, complemented
14C2×#15689339C211yesmaximal, characteristic, complemented
15C2×#15689319C211yesmaximal, characteristic, complemented
16C2×C47×#424C211yesmaximal, characteristic, complemented
17C22×#10625325C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×D376C2211yescharacteristic
20C22×D376C2211yescharacteristic
21#15689744—24no—
22#15689744C2218yescomplemented
23#15689728—24no—
24#15689728C2218yescomplemented
25C2×#13094024C2211yescharacteristic
26C2×#13094021C2211yescharacteristic
27C2×#13094019—21no—
28C2×#13094016C2211yescharacteristic
29C2×#13094012C2211yescharacteristic
30C2×#13094010—21no—
31C2×#13094009—21no—
32C2×#13094009—21no—
33C2×#13094006—21no—
34C2×#13094003C2211yescharacteristic
35C2×#13094002—21no—
36C2×#13093998C2211yescharacteristic
37C2×#13093998C2211yescharacteristic
38C2×#13093998C2211yescharacteristic
39C2×#13093997—21no—
40C2×#13093997—21no—
41C2×C4×Dic94C2211yescharacteristic
42C2×C4×D188C2211yescharacteristic
43C2×C4×D188C2211yescharacteristic
44C2×C4×D188C2211yescharacteristic
45#15689431C2218yescomplemented
46#15689424C2218yescomplemented
47#15689414C2218yescomplemented
48#15689404C2218yescomplemented
49#15689376C2218yescomplemented
50#15689369C2218yescomplemented
51#15689359C2218yescomplemented
52#15689352C2218yescomplemented
53#15689339C2218yescomplemented
54#15689339C2218yescomplemented
55#15689324C2218yescomplemented
56#15689319C2218yescomplemented
57C2×#13093958C2211yescharacteristic
58C2×#13093958C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×#117×C47C2211yescharacteristic
72C47×#424C2218yescomplemented
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×C4⋊C8×C47C2211yescharacteristic
76C2×C4⋊C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188—21no—
80C22×D188—21no—
81C22×D188C2311yescharacteristic
82C22×D188C2311yescharacteristic
83C22×D188C2311yescharacteristic
84C22×C22⋊D47—21no—
85C22×C22⋊D47—21no—
86C22×C22⋊D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C2×#10625325—42no—
91C2×#10625325—42no—
92C2×#10625325C2314yes—
93C2×#10625325C2314yes—
94C2×D376—42no—
95C2×D376—42no—
96C2×D376C2314yes—
97C2×D376C2314yes—
98#13094024—22no—
99#13094024C2314yes—
100#13094021—22no—
101#13094021C2314yes—
102#13094019—28no—
103#13094016—22no—
104#13094016C2314yes—
105#13094012—22no—
106#13094012C2314yes—
107#13094010—28no—
108#13094009—28no—
109#13094009—28no—
110#13094006—28no—
111#13094003—22no—
112#13094003C2314yes—
113#13094002—28no—
114#13093998—22no—
115#13093998—22no—
116#13093998—22no—
117#13093998C2314yes—
118#13093998C2314yes—
119#13093998C2314yes—
120#13093997—28no—
121#13093997—28no—
122C4×Dic94—22no—
123C4×Dic94C2314yes—
124C4×D188—22no—
125C4×D188—22no—
126C4×D188—22no—
127C4×D188C2314yes—
128C4×D188C2314yes—
129C4×D188C2314yes—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×C4⋊Dic47C2311yescharacteristic
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×C22⋊Dic47—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×C4×Dic47—21no—
149#13093958C2314yes—
150#13093958C2314yes—
151#13093956C2314yes—
152#13093956C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093946C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158#13093946C2314yes—
159#13093946C2314yes—
160#13093946C2314yes—
161C23×C4×C47C2311yescharacteristic
162C2×M16×C47—42no—
163C2×M16×C47C2314yes—
164C22×C8×C47—42no—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2314yes—
170#117×C47D414yes—
171#117×C47C2314yes—
172C2×C4⋊C4×C47D411yescharacteristic
173C2×C4⋊C4×C47D411yescharacteristic
174C2×C22⋊C4×C47D411yescharacteristic
175C2×C22⋊C4×C47D411yescharacteristic
176C2×C42×C47C2311yescharacteristic
177C2×C42×C47C2311yescharacteristic
178C4⋊C8×C47C2314yes—
179C4⋊C8×C47C2314yes—
180C4⋊C8×C47C2314yes—
181C4⋊C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C23×D47—21no—
185C23×D47—21no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—24no—
197C2×C22⋊D47—24no—
198C2×C22⋊D47—24no—
199C2×C22⋊D47—82no—
200C2×C22⋊D47—82no—
201C2×C22⋊D47—82no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C2×D188—22no—
208C2×D188—22no—
209C2×D188—22no—
210C2×D188—22no—
211C2×D188—22no—
212C2×D188—22no—
213C2×D188—21no—
214C2×D188—21no—
215C2×D188—21no—
216C2×D188—24no—
217C2×D188—24no—
218C2×D188—82no—
219C2×D188—82no—
220C2×D188C2412yes—
221C2×D188C2412yes—
222C2×D188C2412yes—
223C2×C4×D47—24no—
224C2×C4×D47—24no—
225C2×C4×D47—24no—
226C2×C4×D47—82no—
227C2×C4×D47—82no—
228C2×C4×D47—82no—
229C2×Dic94—22no—
230C2×Dic94—22no—
231C2×Dic94—21no—
232C2×Dic94—24no—
233C2×Dic94—82no—
234C2×Dic94C2412yes—
235M16×C47—44no—
236C2×C8×C47—22no—
237C2×C8×C47—22no—
238C2×C8×C47—22no—
239C2×C8×C47—22no—
240C2×C8×C47—44no—
241C2×C8×C47C2412yes—
242C2×C8×C47C2412yes—
243C2×C8×C47C2412yes—
244C2×C8×C47C2412yes—
245C4⋊C4×C47C2×D414yes—
246C4⋊C4×C47C2×D414yes—
247C22⋊C4×C47C2×D414yes—
248C22⋊C4×C47C2×D414yes—
249C42×C47C2×D412yes—
250C42×C47C2×D412yes—
251C42×C47C2412yes—
252C42×C47C2412yes—
253C22⋊Dic47—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262C4⋊Dic47—24no—
263C4⋊Dic47—21no—
264C4⋊Dic47—21no—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47C2412yes—
268C4⋊Dic47C2412yes—
269C4⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275C4×Dic47—24no—
276D376—44no—
277D376—44no—
278#10625325—44no—
279#10625325—44no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47C22×D412yes—
284C23×C47C22×D411yescharacteristic
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—22no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47—42no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—24no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D412yes—
308C2×C4×C47C22×D412yes—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47H(5,𝔽2)12yes—
312C2×C4×C472−1+412yes—
313C2×C4×C47C2511yescharacteristic
314C22⋊D47—84no—
315C22⋊D47—84no—
316C22⋊D47—84no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327D188—22no—
328D188—22no—
329D188—22no—
330D188—22no—
331D188—22no—
332D188—22no—
333D188—42no—
334D188—42no—
335D188—42no—
336D188—84no—
337D188—84no—
338C4×D47—84no—
339C4×D47—84no—
340C4×D47—84no—
341Dic94—22no—
342Dic94—22no—
343Dic94—42no—
344Dic94—84no—
345C8×C47—22no—
346C8×C47—22no—
347C8×C47—22no—
348C8×C47—22no—
349C2×#3257—471nomaximal, Sylow
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—22no—
353C22×C47—44no—
354C22×C47#53712yes—
355C22×C47#57612yes—
356C22×C47#57712yes—
357C22×C47C23×D411yescharacteristic
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—42no—
363C2×D47—42no—
364C2×D47—42no—
365C2×D47—42no—
366C2×D47—42no—
367C2×D47—84no—
368C2×D47—84no—
369C2×D47—84no—
370C4×C47—22no—
371C4×C47—22no—
372C4×C47—22no—
373C4×C47—22no—
374C4×C47—22no—
375C4×C47#53712yes—
376C4×C47C2×H(5,𝔽2)11yescharacteristic
377C4×C47C2×2−1+411yescharacteristic
378Dic47—42no—
379Dic47—42no—
380Dic47—42no—
381Dic47—42no—
382Dic47—42no—
383C2×#542—471no—
384C2×#540—471no—
385#3257—4716no—
386C2×#479—471no—
387C2×#478—471no—
388C2×#476—471no—
389C2×#474—471no—
390C2×#469—471no—
391C2×#468—471no—
392C2×#466—471no—
393C2×#465—471no—
394C2×#460—471no—
395C2×#463—471no—
396C2×#463—471no—
397C2×#459—471no—
398C2×#424D4711yescharacteristic, complemented
399C2×C47—42no—
400C2×C47#325714yescomplemented
401C2×C47C2×#53711yescharacteristic
402C2×C47C2×#57611yescharacteristic
403C2×C47C2×#57711yescharacteristic
404D47—82no—
405D47—82no—
406D47—82no—
407C22×SD16—471no—
408C22×SD16—471no—
409C22×D8—471no—
410C22×D8—471no—
411C22×M16C2×D4711yescharacteristic
412C23×C8C2×D4711yescharacteristic
413#542—478no—
414#542—944no—
415#540—478no—
416#540—944no—
417C2×C4⋊Q8—471no—
418C2×#127—471no—
419C2×#126—941no—
420C2×#125—471no—
421C2×#124—471no—
422C2×#124—941no—
423C2×#123—941no—
424C2×#123—941no—
425C2×#123—941no—
426C2×C22⋊Q8—471no—
427C2×C22⋊Q8—941no—
428C2×#121—471no—
429C2×#121—471no—
430C2×#121—471no—
431C2×#121—941no—
432C2×#121—941no—
433C2×C4×Q8—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×C4×D4—471no—
437C2×#117C2×D4711yescharacteristic
438#479—478no—
439#478—478no—
440#476—478no—
441#474—478no—
442#469—478no—
443#468—478no—
444#466—478no—
445#465—478no—
446#463—478no—
447#463—478no—
448#460—478no—
449#459—478no—
450C2×#107—471no—
451C2×#107—471no—
452C2×#106—471no—
453C2×#106—471no—
454#424C2×D4718yescomplemented
455C2×C4⋊C8C2×D4711yescharacteristic
456C2×C4⋊C8C2×D4711yescharacteristic
457C2×C4⋊C8C2×D4711yescharacteristic
458C2×C4⋊C8C2×D4711yescharacteristic
459C2×#103—471no—
460C2×#103—471no—
461C2×#102—471no—
462C2×#102—471no—
463C2×#102—471no—
464C2×#102—471no—
465C2×#102—471no—
466C2×#102—471no—
467C47C2×#325711yescharacteristic, complemented, Sylow
468C22×Q8—471no—
469C22×Q8—941no—
470C22×D4—471no—
471C22×D4—471no—
472C22×D4—471no—
473C22×D4—941no—
474C22×D4—941no—
475C22×D4—941no—
476C22×D4—941no—
477C22×D4—941no—
478C23×C4—941no—
479C23×C4—941no—
480C23×C4—941no—
481C23×C4C22×D4711yescharacteristic
482C2×SD16—474no—
483C2×SD16—474no—
484C2×SD16—1882no—
485C2×SD16—1882no—
486C2×D8—474no—
487C2×D8—474no—
488C2×D8—1882no—
489C2×D8—1882no—
490C2×M16—42no—
491C2×M16C22×D4714yes—
492C22×C8—42no—
493C22×C8C22×D4711yescharacteristic
494C22×C8C22×D4711yescharacteristic
495C22×C8C22×D4711yescharacteristic
496C22×C8C22×D4711yescharacteristic
497C22×C8C22×D4714yes—
498C4⋊Q8—474no—
499C4⋊Q8—942no—
500#127—474no—
501#127—942no—
502#126—948no—
503#125—474no—
504#125—942no—
505#124—474no—
506#124—948no—
507#124—942no—
508#123—948no—
509#123—948no—
510#123—948no—
511C22⋊Q8—474no—
512C22⋊Q8—942no—
513C22⋊Q8—948no—
514#121—474no—
515#121—474no—
516#121—474no—
517#121—942no—
518#121—942no—
519#121—942no—
520#121—948no—
521#121—948no—
522C4×Q8—474no—
523C4×Q8—942no—
524C4×D4—474no—
525C4×D4—474no—
526C4×D4—474no—
527C4×D4—942no—
528C4×D4—942no—
529C4×D4—942no—
530#117D18814yes—
531#117C22×D4714yes—
532C2×C4⋊C4—471no—
533C2×C4⋊C4—471no—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—941no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4D18811yescharacteristic
542C2×C4⋊C4D18811yescharacteristic
543C2×C22⋊C4—941no—
544C2×C22⋊C4—941no—
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C22⋊C4—941no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4D18811yescharacteristic
553C2×C22⋊C4D18811yescharacteristic
554C2×C42—941no—
555C2×C42C22×D4711yescharacteristic
556C2×C42C22×D4711yescharacteristic
557#107—474no—
558#107—474no—
559#106—474no—
560#106—474no—
561C4⋊C8C22×D4714yes—
562C4⋊C8C22×D4714yes—
563C4⋊C8C22×D4714yes—
564C4⋊C8C22×D4714yes—
565#103—474no—
566#103—474no—
567#102—474no—
568#102—474no—
569#102—474no—
570#102—474no—
571#102—474no—
572#102—474no—
573C24—941no—
574C24—941no—
575C24—941no—
576C24C2×D18811yescharacteristic
577C2×Q8—472no—
578C2×Q8—944no—
579C2×Q8—941no—
580C2×Q8—942no—
581C2×Q8—942no—
582C2×Q8—3762no—
583C2×D4—472no—
584C2×D4—472no—
585C2×D4—472no—
586C2×D4—944no—
587C2×D4—944no—
588C2×D4—944no—
589C2×D4—944no—
590C2×D4—944no—
591C2×D4—941no—
592C2×D4—941no—
593C2×D4—941no—
594C2×D4—942no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—942no—
600C2×D4—3762no—
601C2×D4—3762no—
602C2×D4—3762no—
603C2×D4—3762no—
604C2×D4—3762no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—944no—
613C22×C4—944no—
614C22×C4—944no—
615C22×C4—3762no—
616C22×C4—3762no—
617C22×C4—3762no—
618C22×C4C2×D18812yes—
619C22×C4C2×D18811yescharacteristic
620C22×C4C2×D18811yescharacteristic
621C22×C4C2×D18811yescharacteristic
622C22×C4C2×D18811yescharacteristic
623C22×C4C2×D18811yescharacteristic
624C22×C4C23×D4712yes—
625C22×C4C23×D4711yescharacteristic
626SD16—1884no—
627SD16—1884no—
628D8—1884no—
629D8—1884no—
630M16—44no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—44no—
636C2×C8C23×D4712yes—
637C2×C8C23×D4712yes—
638C2×C8C23×D4712yes—
639C2×C8C23×D4712yes—
640C4⋊C4—472no—
641C4⋊C4—472no—
642C4⋊C4—472no—
643C4⋊C4—472no—
644C4⋊C4—944no—
645C4⋊C4—944no—
646C4⋊C4—944no—
647C4⋊C4—944no—
648C4⋊C4—941no—
649C4⋊C4—941no—
650C4⋊C4—941no—
651C4⋊C4—941no—
652C4⋊C4—944no—
653C4⋊C4C2×D18814yes—
654C4⋊C4C2×D18814yes—
655C22⋊C4—944no—
656C22⋊C4—944no—
657C22⋊C4—944no—
658C22⋊C4—944no—
659C22⋊C4—944no—
660C22⋊C4—944no—
661C22⋊C4—944no—
662C22⋊C4—944no—
663C22⋊C4—944no—
664C22⋊C4C2×D18814yes—
665C22⋊C4C2×D18814yes—
666C42—944no—
667C42C2×D18812yes—
668C42C2×D18812yes—
669C42C23×D4712yes—
670C42C23×D4712yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—942no—
675C23—942no—
676C23—942no—
677C23—1882no—
678C23—1882no—
679C23—1882no—
680C23—1882no—
681C23—1882no—
682C23—1882no—
683C23—1882no—
684C23—1882no—
685C23—1882no—
686C23C22×D18812yes—
687C23C22×D18811yescharacteristic
688Q8—942no—
689Q8—942no—
690Q8—3764no—
691Q8—1882no—
692D4—942no—
693D4—942no—
694D4—942no—
695D4—942no—
696D4—942no—
697D4—942no—
698D4—3764no—
699D4—3764no—
700D4—3764no—
701D4—3764no—
702D4—3764no—
703D4—1882no—
704D4—1882no—
705D4—1882no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—3764no—
720C2×C4—3764no—
721C2×C4—3764no—
722C2×C4—1882no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4C22×D18812yes—
728C2×C4C22×D18812yes—
729C2×C4C22×D18812yes—
730C2×C4C22×D18812yes—
731C2×C4C22×D18812yes—
732C2×C4C22×D18811yescharacteristic
733C2×C4#1309406912yes—
734C2×C4#1309407212yes—
735C2×C4C24×D4711yescharacteristic
736C8—22no—
737C8—22no—
738C8—22no—
739C8—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—3764no—
745C22—3764no—
746C22—3764no—
747C22—1882no—
748C22—1882no—
749C22—1882no—
750C22—1882no—
751C22—1882no—
752C22—1882no—
753C22—1882no—
754C22—1882no—
755C22—1882no—
756C22#1568970412yes—
757C22#1568992812yes—
758C22#1568993512yes—
759C22C23×D18811yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—1882no—
766C4—1882no—
767C4—1882no—
768C4—1882no—
769C4—1882no—
770C4#1568970412yes—
771C4C2×#1309406911yescharacteristic
772C4C2×#1309407211yescharacteristic
773C2—42no—
774C2—3762no—
775C2—3762no—
776C2—3762no—
777C2#2025480114yesdirect product factor
778C2C2×#1568970411yescharacteristic
779C2C2×#1568992811yescharacteristic
780C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#424C2
socleC23×C47C22×D4
hypercenterC2×#424D47
hypocenterC47C2×#3257
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#15689744C2semidirect
2. C2×#15689728C2semidirect
3. #20254801C2direct (N × H)
4. C2×#15689431C2semidirect
5. C2×#15689424C2semidirect
6. C2×#15689414C2semidirect
7. C2×#15689404C2semidirect
8. C2×#15689376C2semidirect
9. C2×#15689369C2semidirect
10. C2×#15689359C2semidirect
11. C2×#15689352C2semidirect
12. C2×#15689324C2semidirect
13. C2×#15689339C2semidirect
14. C2×#15689339C2semidirect
15. C2×#15689319C2semidirect
16. C2×C47×#424C2semidirect
22. #15689744C22semidirect
24. #15689728C22semidirect
45. #15689431C22semidirect
46. #15689424C22semidirect
47. #15689414C22semidirect
48. #15689404C22semidirect
49. #15689376C22semidirect
50. #15689369C22semidirect
51. #15689359C22semidirect
52. #15689352C22semidirect
53. #15689339C22semidirect
54. #15689339C22semidirect
55. #15689324C22semidirect
56. #15689319C22semidirect
72. C47×#424C22semidirect
398. C2×#424D47semidirect
400. C2×C47#3257semidirect
454. #424C2×D47semidirect
467. C47C2×#3257semidirect
777. C2#20254801direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897442
C2×#156897282
#202548012
C2×#156894312
C2×#156894242
C2×#156894142
C2×#156894042
C2×#156893762
C2×#156893692
C2×#156893592
C2×#156893522
C2×#156893242
C2×#156893392
C2×#156893192
C2×C47×#4242
C2×#325747