Finite Group Databasebeta

← C2×#20254798 #27089187

Subgroups — C2×#20254798 #27089187

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×#15689747C211yesmaximal, characteristic, complemented
2C2×#15689724C211yesmaximal, characteristic, complemented
3#20254798C2116yesmaximal, direct product factor
4C2×#15689433C211yesmaximal, characteristic, complemented
5C2×#15689422C211yesmaximal, characteristic, complemented
6C2×#15689400C211yesmaximal, characteristic, complemented
7C2×#15689377C211yesmaximal, characteristic, complemented
8C2×#15689368C211yesmaximal, characteristic, complemented
9C2×#15689358C211yesmaximal, characteristic, complemented
10C2×#15689353C211yesmaximal, characteristic, complemented
11C2×#15689322C211yesmaximal, characteristic, complemented
12C2×#15689339C211yesmaximal, characteristic, complemented
13C2×#15689338C211yesmaximal, characteristic, complemented
14C2×#15689317C211yesmaximal, characteristic, complemented
15C2×#15689148C211yesmaximal, characteristic, complemented
16C2×C47×#476C211yesmaximal, characteristic, complemented
17C22×#10625325C2211yescharacteristic
18C22×#10625335C2211yescharacteristic
19C22×D376C2211yescharacteristic
20C22×#10625334C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic
23#15689747—24no—
24#15689747C2218yescomplemented
25#15689724—24no—
26#15689724C2218yescomplemented
27C2×#13094020C2211yescharacteristic
28C2×#13094019—21no—
29C2×#13094015C2211yescharacteristic
30C2×#13094013—21no—
31C2×#13094012C2211yescharacteristic
32C2×#13094009—21no—
33C2×#13094007—21no—
34C2×#13094006—21no—
35C2×#13094004C2211yescharacteristic
36C2×#13094000—21no—
37C2×#13093999C2211yescharacteristic
38C2×#13093999C2211yescharacteristic
39C2×#13093998—21no—
40C2×#13093997—21no—
41C2×#13093995C2211yescharacteristic
42C2×#13093989C2211yescharacteristic
43C2×C4×D188C2211yescharacteristic
44C2×#13093986C2211yescharacteristic
45C2×#13093981C2211yescharacteristic
46#15689433C2218yescomplemented
47#15689422C2218yescomplemented
48#15689400C2218yescomplemented
49#15689377C2218yescomplemented
50#15689368C2218yescomplemented
51#15689358C2218yescomplemented
52#15689353C2218yescomplemented
53#15689339C2218yescomplemented
54#15689338C2218yescomplemented
55#15689322C2218yescomplemented
56#15689317C2218yescomplemented
57C2×#13093957C2211yescharacteristic
58C2×#13093957C2211yescharacteristic
59#15689148C2218yescomplemented
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×#13093944C2211yescharacteristic
68C2×#13093944C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#476C2218yescomplemented
72C2×#106×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×D188—21no—
79C22×D188—21no—
80C22×D188C2311yescharacteristic
81C22×D188C2311yescharacteristic
82C22×C22⋊D47—21no—
83C22×C22⋊D47—21no—
84C22×C22⋊D47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47C2311yescharacteristic
88C2×#10625325—42no—
89C2×#10625325C2314yes—
90C2×#10625335—42no—
91C2×#10625335C2314yes—
92C2×D376—42no—
93C2×D376C2314yes—
94C2×#10625334—42no—
95C2×#10625334C2314yes—
96C2×#10625324—42no—
97C2×#10625324C2314yes—
98C22×C47⋊C8C2311yescharacteristic
99C22×C47⋊C8C2311yescharacteristic
100C2×C8×D47—42no—
101C2×C8×D47C2314yes—
102#13094020—22no—
103#13094020C2314yes—
104#13094019—28no—
105#13094015—22no—
106#13094015C2314yes—
107#13094013—28no—
108#13094012—22no—
109#13094012C2314yes—
110#13094009—28no—
111#13094007—28no—
112#13094006—28no—
113#13094004—22no—
114#13094004C2314yes—
115#13094000—28no—
116#13093999—22no—
117#13093999—22no—
118#13093999C2314yes—
119#13093999C2314yes—
120#13093998—28no—
121#13093997—28no—
122#13093995—22no—
123#13093995C2314yes—
124#13093989—22no—
125#13093989C2314yes—
126C4×D188—22no—
127C4×D188C2314yes—
128#13093986—22no—
129#13093986C2314yes—
130#13093981D414yes—
131#13093981C2314yes—
132C2×C4⋊Dic47—21no—
133C2×C4⋊Dic47—21no—
134C2×C4⋊Dic47C2311yescharacteristic
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4D411yescharacteristic
138C2×Dic47⋊C4D411yescharacteristic
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)⋊C4D411yescharacteristic
148C2×(C2×D47)⋊C4D411yescharacteristic
149C2×C4×Dic47—21no—
150C2×C4×Dic47C2311yescharacteristic
151#13093957C2314yes—
152#13093957C2314yes—
153C4⋊(C47⋊C8)C2314yes—
154Dic47⋊C8C2314yes—
155Dic47⋊C8C2314yes—
156#13093949C2314yes—
157#13093947C2314yes—
158#13093946C2314yes—
159#13093944C2314yes—
160#13093944C2314yes—
161#13093944C2314yes—
162C22×Q8×C47—21no—
163C22×D4×C47C2311yescharacteristic
164C23×C4×C47—21no—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C4⋊Q8×C47—22no—
168C4⋊Q8×C47C2314yes—
169C4×D4×C47—22no—
170C4×D4×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C42×C47C2311yescharacteristic
177#106×C47C2314yes—
178#106×C47C2314yes—
179C4⋊C8×C47C2314yes—
180#102×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C23×D47—21no—
184C23×D47—21no—
185C23×D47C2×D411yescharacteristic
186C2×Q8×C47—24no—
187C2×Q8×C47—82no—
188C2×D4×C47—21no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47C2412yes—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—24no—
196C22×C4×C47—82no—
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2411yescharacteristic
200C2×C22⋊D47—24no—
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47—82no—
204C2×C22⋊D47—82no—
205C2×C22⋊D47—82no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211C2×D188—22no—
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—22no—
215C2×D188—21no—
216C2×D188—21no—
217C2×D188—24no—
218C2×D188—24no—
219C2×D188—82no—
220C2×D188—82no—
221C2×D188C2412yes—
222C2×D188C2412yes—
223C2×C4×D47—22no—
224C2×C4×D47—22no—
225C2×C4×D47—24no—
226C2×C4×D47—24no—
227C2×C4×D47—82no—
228C2×C4×D47—82no—
229C2×C4×D47C2×D412yes—
230C2×C4×D47C2412yes—
231C2×Dic94—22no—
232C2×Dic94—22no—
233C2×Dic94—21no—
234C2×Dic94C2412yes—
235C2×C8×C47—22no—
236C2×C8×C47—22no—
237C2×C8×C47C2412yes—
238C2×C8×C47C2412yes—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—21no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47C2412yes—
244C4⋊C4×C47C2412yes—
245C4⋊C4×C47C2412yes—
246C22⋊C4×C47—24no—
247C42×C47C2×D412yes—
248C42×C47C2412yes—
249C22⋊Dic47—24no—
250#10625335—44no—
251#10625334—44no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—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)⋊C4C2×D414yes—
260(C2×D47)⋊C4C2×D414yes—
261C4⋊Dic47—21no—
262C4⋊Dic47—24no—
263C4⋊Dic47—24no—
264C4⋊Dic47C2412yes—
265Dic47⋊C4—24no—
266Dic47⋊C4—24no—
267Dic47⋊C4C2×D414yes—
268Dic47⋊C4C2×D414yes—
269C4×Dic47—24no—
270C4×Dic47C2×D412yes—
271C4×Dic47C2412yes—
272C2×C47⋊C8—22no—
273C2×C47⋊C8—22no—
274C2×C47⋊C8C2412yes—
275C2×C47⋊C8C2412yes—
276D376—44no—
277#10625325—44no—
278#10625324—44no—
279C8×D47—44no—
280C23×C47—22no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D411yescharacteristic
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47C22×D412yes—
297Q8×C47—84no—
298D4×C47—22no—
299D4×C47—22no—
300D4×C47—42no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47—84no—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D412yes—
312C2×C4×C47C22×D411yescharacteristic
313C2×C4×C47H(5,𝔽2)12yes—
314C2×C4×C472−1+412yes—
315C2×C4×C47C2511yescharacteristic
316C22⋊D47—84no—
317C22⋊D47—84no—
318C22⋊D47—84no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47C22×D412yes—
327C2×Dic47C22×D412yes—
328C2×Dic47C22×D412yes—
329D188—22no—
330D188—22no—
331D188—22no—
332D188—22no—
333D188—42no—
334D188—42no—
335D188—84no—
336D188—84no—
337C4×D47—24no—
338C4×D47—22no—
339C4×D47—22no—
340C4×D47—84no—
341C4×D47—84no—
342Dic94—22no—
343Dic94—22no—
344Dic94—42no—
345C8×C47—22no—
346C8×C47—22no—
347C47⋊C8—22no—
348C47⋊C8—22no—
349C2×#3257—471nomaximal, Sylow
350C22×C47—42no—
351C22×C47—42no—
352C22×C47—42no—
353C22×C47—84no—
354C22×C47#53712yes—
355C22×C47#57612yes—
356C22×C47#57712yes—
357C22×C47C23×D411yescharacteristic
358C2×D47—22no—
359C2×D47—22no—
360C2×D47—22no—
361C2×D47—44no—
362C2×D47—42no—
363C2×D47—42no—
364C2×D47—42no—
365C2×D47—42no—
366C2×D47—42no—
367C2×D47—42no—
368C2×D47—84no—
369C2×D47—84no—
370C4×C47—22no—
371C4×C47—22no—
372C4×C47—42no—
373C4×C47—42no—
374C4×C47—42no—
375C4×C47#53712yes—
376C4×C47C2×H(5,𝔽2)11yescharacteristic
377C4×C47C2×2−1+411yescharacteristic
378Dic47—22no—
379Dic47—22no—
380Dic47—22no—
381Dic47—42no—
382Dic47—42no—
383C2×#542—471no—
384C2×#540—471no—
385#3257—4716no—
386C2×#479—471no—
387C2×#478—471no—
388C2×#476D4711yescharacteristic, complemented
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×#424—471no—
399C2×C47—82no—
400C2×C47#325714yescomplemented
401C2×C47C2×#53711yescharacteristic
402C2×C47C2×#57611yescharacteristic
403C2×C47C2×#57711yescharacteristic
404D47—42no—
405D47—82no—
406D47—82no—
407C22×SD16—471no—
408C22×SD16—471no—
409C22×D8—471no—
410C22×D8—471no—
411C22×M16—471no—
412C23×C8—471no—
413#542—478no—
414#542—944no—
415#540—478no—
416#540—944no—
417C2×C4⋊Q8C2×D4711yescharacteristic
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×D4C2×D4711yescharacteristic
437C2×#117—471no—
438#479—478no—
439#478—478no—
440#476C2×D4718yescomplemented
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×#106C2×D4711yescharacteristic
453C2×#106C2×D4711yescharacteristic
454#424—478no—
455C2×C4⋊C8—471no—
456C2×C4⋊C8—471no—
457C2×C4⋊C8—471no—
458C2×C4⋊C8C2×D4711yescharacteristic
459C2×#103—471no—
460C2×#103—471no—
461C2×#102—471no—
462C2×#102—471no—
463C2×#102—471no—
464C2×#102—471no—
465C2×#102C2×D4711yescharacteristic
466C2×#102C2×D4711yescharacteristic
467C47C2×#325711yescharacteristic, complemented, Sylow
468C22×Q8—21no—
469C22×Q8—471no—
470C22×D4—471no—
471C22×D4—471no—
472C22×D4—941no—
473C22×D4—941no—
474C22×D4—941no—
475C22×D4—941no—
476C22×D4—941no—
477C22×D4C22×D4711yescharacteristic
478C23×C4—21no—
479C23×C4—471no—
480C23×C4—941no—
481C23×C4—941no—
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—474no—
491C2×M16—1882no—
492C22×C8—471no—
493C22×C8—471no—
494C22×C8—474no—
495C22×C8—1882no—
496C22×C8C22×D4711yescharacteristic
497C22×C8C22×D4711yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8C22×D4714yes—
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—948no—
518#121—948no—
519#121—942no—
520#121—942no—
521#121—942no—
522C4×Q8—474no—
523C4×Q8—942no—
524C4×D4—22no—
525C4×D4—474no—
526C4×D4—474no—
527C4×D4—942no—
528C4×D4—942no—
529C4×D4C22×D4714yes—
530#117—474no—
531#117—474no—
532C2×C4⋊C4—21no—
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⋊C4C22×D4711yescharacteristic
541C2×C4⋊C4C22×D4711yescharacteristic
542C2×C4⋊C4C22×D4711yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—471no—
545C2×C22⋊C4—471no—
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⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C42—471no—
555C2×C42—941no—
556C2×C42C22×D4711yescharacteristic
557#107—474no—
558#107—474no—
559#106C22×D4714yes—
560#106C22×D4714yes—
561C4⋊C8—474no—
562C4⋊C8—474no—
563C4⋊C8—474no—
564C4⋊C8C22×D4714yes—
565#103—474no—
566#103—474no—
567#102—474no—
568#102—474no—
569#102—474no—
570#102—474no—
571#102C22×D4714yes—
572#102C22×D4714yes—
573C24—21no—
574C24—471no—
575C24—941no—
576C24—941no—
577C2×Q8—24no—
578C2×Q8—82no—
579C2×Q8—472no—
580C2×Q8—941no—
581C2×Q8—942no—
582C2×Q8—942no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—472no—
587C2×D4—472no—
588C2×D4—944no—
589C2×D4—944no—
590C2×D4—944no—
591C2×D4—944no—
592C2×D4—944no—
593C2×D4—941no—
594C2×D4—941no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—3762no—
600C2×D4—3762no—
601C2×D4—3762no—
602C2×D4—3762no—
603C2×D4—3762no—
604C2×D4C23×D4712yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—24no—
609C22×C4—82no—
610C22×C4—471no—
611C22×C4—471no—
612C22×C4—471no—
613C22×C4—472no—
614C22×C4—472no—
615C22×C4—944no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—944no—
621C22×C4—3762no—
622C22×C4—3762no—
623C22×C4D4×D4711yescharacteristic
624C22×C4D4×D4711yescharacteristic
625C22×C4C23×D4711yescharacteristic
626SD16—1884no—
627SD16—1884no—
628D8—1884no—
629D8—1884no—
630M16—1884no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—472no—
634C2×C8—472no—
635C2×C8—942no—
636C2×C8—942no—
637C2×C8—1884no—
638C2×C8C23×D4712yes—
639C2×C8C23×D4712yes—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—474no—
645C4⋊C4—474no—
646C4⋊C4—472no—
647C4⋊C4—944no—
648C4⋊C4—944no—
649C4⋊C4—944no—
650C4⋊C4—944no—
651C4⋊C4—941no—
652C4⋊C4C23×D4712yes—
653C4⋊C4C23×D4712yes—
654C4⋊C4C23×D4712yes—
655C22⋊C4—24no—
656C22⋊C4—474no—
657C22⋊C4—474no—
658C22⋊C4—944no—
659C22⋊C4—944no—
660C22⋊C4—944no—
661C22⋊C4—944no—
662C22⋊C4—944no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C42—472no—
667C42—472no—
668C42—944no—
669C42D4×D4712yes—
670C42C23×D4712yes—
671C23—22no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—472no—
676C23—942no—
677C23—942no—
678C23—942no—
679C23—942no—
680C23—942no—
681C23—1882no—
682C23—1882no—
683C23—1882no—
684C23—1882no—
685C23—1882no—
686C23—1882no—
687C23C2×D4×D4711yescharacteristic
688Q8—84no—
689Q8—942no—
690Q8—942no—
691Q8—1882no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—942no—
696D4—942no—
697D4—942no—
698D4—942no—
699D4—3764no—
700D4—3764no—
701D4—3764no—
702D4—3764no—
703D4—3764no—
704D4—1882no—
705D4—1882no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—84no—
715C2×C4—472no—
716C2×C4—472no—
717C2×C4—472no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—944no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—3764no—
727C2×C4—3764no—
728C2×C4—1882no—
729C2×C4—1882no—
730C2×C4C2×D4×D4712yes—
731C2×C4C2×D4×D4712yes—
732C2×C4C2×D4×D4711yescharacteristic
733C2×C4#1309407012yes—
734C2×C4#1309407212yes—
735C2×C4C24×D4711yescharacteristic
736C8—22no—
737C8—22no—
738C8—942no—
739C8—942no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—942no—
745C22—942no—
746C22—942no—
747C22—3764no—
748C22—3764no—
749C22—1882no—
750C22—1882no—
751C22—1882no—
752C22—1882no—
753C22—1882no—
754C22—1882no—
755C22—1884no—
756C22#1568970312yes—
757C22#1568992712yes—
758C22#1568992912yes—
759C22C22×D4×D4711yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—942no—
766C4—942no—
767C4—942no—
768C4—1882no—
769C4—1882no—
770C4#1568970312yes—
771C4C2×#1309407011yescharacteristic
772C4C2×#1309407211yescharacteristic
773C2—82no—
774C2—3762no—
775C2—3762no—
776C2—1882no—
777C2#2025479814yesdirect product factor
778C2C2×#1568970311yescharacteristic
779C2C2×#1568992711yescharacteristic
780C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#476C2
socleC23×C47C22×D4
hypercenterC2×#476D47
hypocenterC47C2×#3257
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#15689747C2semidirect
2. C2×#15689724C2semidirect
3. #20254798C2direct (N × H)
4. C2×#15689433C2semidirect
5. C2×#15689422C2semidirect
6. C2×#15689400C2semidirect
7. C2×#15689377C2semidirect
8. C2×#15689368C2semidirect
9. C2×#15689358C2semidirect
10. C2×#15689353C2semidirect
11. C2×#15689322C2semidirect
12. C2×#15689339C2semidirect
13. C2×#15689338C2semidirect
14. C2×#15689317C2semidirect
15. C2×#15689148C2semidirect
16. C2×C47×#476C2semidirect
24. #15689747C22semidirect
26. #15689724C22semidirect
46. #15689433C22semidirect
47. #15689422C22semidirect
48. #15689400C22semidirect
49. #15689377C22semidirect
50. #15689368C22semidirect
51. #15689358C22semidirect
52. #15689353C22semidirect
53. #15689339C22semidirect
54. #15689338C22semidirect
55. #15689322C22semidirect
56. #15689317C22semidirect
59. #15689148C22semidirect
71. C47×#476C22semidirect
388. C2×#476D47semidirect
400. C2×C47#3257semidirect
440. #476C2×D47semidirect
467. C47C2×#3257semidirect
777. C2#20254798direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897472
C2×#156897242
#202547982
C2×#156894332
C2×#156894222
C2×#156894002
C2×#156893772
C2×#156893682
C2×#156893582
C2×#156893532
C2×#156893222
C2×#156893392
C2×#156893382
C2×#156893172
C2×#156891482
C2×C47×#4762
C2×#325747