Finite Group Databasebeta

← C2×#20255346 #27092785

Subgroups — C2×#20255346 #27092785

Order 12032.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689776C211yesmaximal, characteristic, complemented
2C2×#15689768C211yesmaximal, characteristic, complemented
3#20255346C2116yesmaximal, direct product factor
4C2×#15689485C211yesmaximal, characteristic, complemented
5C2×#15689443C211yesmaximal, characteristic, complemented
6C2×#15689455C211yesmaximal, characteristic, complemented
7C2×#15689377C211yesmaximal, characteristic, complemented
8C2×#15689353C211yesmaximal, characteristic, complemented
9C2×#15689339C211yesmaximal, characteristic, complemented
10C2×#15689269C211yesmaximal, characteristic, complemented
11C2×#15689258C211yesmaximal, characteristic, complemented
12C2×#15689233C211yesmaximal, characteristic, complemented
13C2×#15689193C211yesmaximal, characteristic, complemented
14C2×#15689121C211yesmaximal, characteristic, complemented
15C2×#102×D47C211yesmaximal, characteristic, complemented
16C2×C47×#476C211yesmaximal, characteristic, complemented
17C22×#10625354—21no—
18C22×#10625352C2211yescharacteristic
19C22×D4×D47C2211yescharacteristic
20C22×#10625325C2211yescharacteristic, complemented
21C22×D376C2211yescharacteristic
22C22×#10625334C2211yescharacteristic
23C22×#10625324C2211yescharacteristic, complemented
24C22×C8×D47C2211yescharacteristic
25#15689776—24no—
26#15689776C2218yescomplemented
27#15689768—24no—
28#15689768C2218yescomplemented
29C2×#13094012C2211yescharacteristic
30C2×#13094009—21no—
31C2×#13094009—21no—
32C2×#13094008—21no—
33C2×#13094004C2211yescharacteristic
34C2×#13094000—21no—
35C2×#13093999C2211yescharacteristic
36C2×#13093999C2211yescharacteristic
37C2×#13093999C2211yescharacteristic, complemented
38C2×#13093998—21no—
39C2×#13093994—21no—
40C2×C4×D188C2211yescharacteristic
41C2×C4×D188C2211yescharacteristic, complemented
42C2×C4⋊C4×D47C2211yescharacteristic
43C2×C4⋊C4×D47C2211yescharacteristic, complemented
44C22×(C2×D47)⋊C4—21no—
45#15689485C2218yescomplemented
46#15689455C2218yescomplemented
47#15689443C2218yescomplemented
48#15689377C2218yescomplemented
49#15689353C2218yescomplemented
50#15689339C2218yescomplemented
51#15689269C2218yescomplemented
52#15689258C2218yescomplemented
53#15689233C2218yescomplemented
54#15689193C2218yescomplemented
55C2×#13093955C2211yescharacteristic, complemented
56#15689121C2218yescomplemented
57C2×#13093949C2211yescharacteristic, complemented
58C2×#13093947C2211yescharacteristic, complemented
59C2×#13093947C2211yescharacteristic, complemented
60C2×#13093946C2211yescharacteristic
61C2×#13093945C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic, complemented
65#102×D47C2218yescomplemented
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic, complemented
68C2×#13093935C2211yescharacteristic, complemented
69C2×C4⋊Q8×C47C2211yescharacteristic, complemented
70C2×C4×D4×C47C2211yescharacteristic
71C47×#476C2218yescomplemented
72C2×#106×C47C2211yescharacteristic, complemented
73C2×#106×C47C2211yescharacteristic, complemented
74C2×C4⋊C8×C47C2211yescharacteristic, complemented
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C24×D47—21no—
78C2×#10625354—28no—
79C2×#10625354—48no—
80C2×#10625352—24no—
81C2×#10625352—22no—
82C2×#10625352—42no—
83C2×#10625352C2314yes—
84C22×Dic94C2311yescharacteristic
85C22×D188—21no—
86C22×D188—21no—
87C22×D188—21no—
88C22×D188D411yescharacteristic
89C22×D188C2311yescharacteristic
90C22×D188C2311yescharacteristic
91C22×C22⋊D47—21no—
92C22×C22⋊D47—21no—
93C2×D4×D47—24no—
94C2×D4×D47—22no—
95C2×D4×D47—42no—
96C2×D4×D47C2314yes—
97C23×Dic47—21no—
98C22×C4×D47—21no—
99C22×C4×D47—21no—
100C22×C4×D47—21no—
101C22×C4×D47C2311yescharacteristic
102C22×C4×D47C2311yescharacteristic
103C2×#10625325—42no—
104C2×#10625325C2314yescomplemented
105C2×D376—42no—
106C2×D376C2314yes—
107C2×#10625334—24no—
108C2×#10625334C2314yes—
109C2×#10625324—42no—
110C2×#10625324C2314yescomplemented
111C22×C47⋊C8C2311yescharacteristic
112C22×C47⋊C8C2311yescharacteristic
113C2×C8×D47—42no—
114C2×C8×D47C2314yes—
115#13094012—22no—
116#13094012C2314yes—
117#13094009—28no—
118#13094009—28no—
119#13094008—28no—
120#13094004—22no—
121#13094004C2314yes—
122#13094000—28no—
123#13093999—22no—
124#13093999—22no—
125#13093999—22no—
126#13093999C2314yes—
127#13093999C2314yes—
128#13093999C2314yescomplemented
129#13093998—28no—
130#13093994—28no—
131C4×D188—22no—
132C4×D188D414yes—
133C4×D188C2314yes—
134C4×D188C2314yescomplemented
135C2×C4⋊Dic47—21no—
136C2×C4⋊Dic47D411yescharacteristic
137C2×C4⋊Dic47C2311yescharacteristic
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C4⋊C4×D47—22no—
141C4⋊C4×D47—22no—
142C4⋊C4×D47C2314yes—
143C4⋊C4×D47C2314yescomplemented
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4—28no—
152C2×(C2×D47)⋊C4D411yescharacteristic
153C2×(C2×D47)⋊C4D411yescharacteristic
154#13093955C2314yescomplemented
155#13093949C2314yescomplemented
156#13093947C2314yescomplemented
157#13093947C2314yescomplemented
158#13093946C2314yes—
159#13093945C2314yes—
160#13093944C2314yes—
161#13093944C2314yes—
162#13093944C2314yescomplemented
163(C2×D47)⋊C8C2314yes—
164(C2×D47)⋊C8C2314yescomplemented
165#13093935C2314yescomplemented
166C22×Q8×C47—21no—
167C22×D4×C47C2311yescharacteristic
168C23×C4×C47—21no—
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C4⋊Q8×C47—22no—
172C4⋊Q8×C47C2314yescomplemented
173C4×D4×C47—22no—
174C4×D4×C47C2314yes—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C22⋊C4×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#106×C47C2314yescomplemented
182#106×C47C2314yescomplemented
183C4⋊C8×C47C2314yescomplemented
184#102×C47C2314yes—
185#102×C47C2314yes—
186C24×C47—21no—
187C23×D47—21no—
188C23×D47—21no—
189C23×D47—24no—
190C23×D47—44no—
191C23×D47—44no—
192C23×D47—82no—
193C23×D47C2×D411yescharacteristic
194C23×D47C2×D411yescharacteristic
195C2×Q8×C47—24no—
196C2×Q8×C47—44no—
197C2×D4×C47—21no—
198C2×D4×C47—22no—
199C2×D4×C47#4114yescomplemented
200C2×D4×C47C2412yes—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—24no—
205C22×C4×C47—82no—
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2411yescharacteristic
209C2×C22⋊D47—24no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—44no—
212C2×C22⋊D47—44no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—24no—
216C22×Dic47—44no—
217C22×Dic47C2×D411yescharacteristic
218C22×Dic47C2×D411yescharacteristic
219#10625354—432no—
220#10625352—28no—
221#10625352—44no—
222#10625352—48no—
223D4×D47—28no—
224D4×D47—44no—
225D4×D47—48no—
226C2×D188—24no—
227C2×D188—22no—
228C2×D188—22no—
229C2×D188—22no—
230C2×D188—22no—
231C2×D188—24no—
232C2×D188—24no—
233C2×D188—21no—
234C2×D188—21no—
235C2×D188—24no—
236C2×D188—44no—
237C2×D188—44no—
238C2×D188—82no—
239C2×D188C2×D414yes—
240C2×D188C2412yes—
241C2×D188C2412yes—
242C2×C4×D47—22no—
243C2×C4×D47—22no—
244C2×C4×D47—22no—
245C2×C4×D47—22no—
246C2×C4×D47—24no—
247C2×C4×D47—24no—
248C2×C4×D47—24no—
249C2×C4×D47—44no—
250C2×C4×D47—44no—
251C2×C4×D47—44no—
252C2×C4×D47C2×D412yes—
253C2×C4×D47C2×D412yes—
254C2×C4×D47C2412yes—
255C2×C4×D47C2412yes—
256C2×Dic94—22no—
257C2×Dic94—22no—
258C2×Dic94—21no—
259C2×Dic94C2412yes—
260C2×C8×C47—22no—
261C2×C8×C47—22no—
262C2×C8×C47C2412yes—
263C2×C8×C47C2412yes—
264C4⋊C4×C47—24no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47C2412yes—
269C4⋊C4×C47C2412yes—
270C4⋊C4×C47C2412yes—
271C22⋊C4×C47—24no—
272C42×C47C2×D412yes—
273C42×C47C2412yes—
274#10625334—28no—
275(C2×D47)⋊C4—24no—
276(C2×D47)⋊C4—24no—
277(C2×D47)⋊C4—24no—
278(C2×D47)⋊C4—24no—
279(C2×D47)⋊C4—24no—
280(C2×D47)⋊C4—24no—
281(C2×D47)⋊C4—24no—
282(C2×D47)⋊C4C2×D414yes—
283(C2×D47)⋊C4C2×D414yes—
284C4⋊Dic47—21no—
285C4⋊Dic47—24no—
286C4⋊Dic47C2×D414yes—
287C4⋊Dic47C2412yes—
288Dic47⋊C4—24no—
289Dic47⋊C4—24no—
290C2×C47⋊C8—22no—
291C2×C47⋊C8—22no—
292C2×C47⋊C8C2412yes—
293C2×C47⋊C8C2412yes—
294D376—44no—
295#10625325—44no—
296#10625324—44no—
297C8×D47—44no—
298C23×C47—24no—
299C23×C47—22no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47C22×D411yescharacteristic
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—48no—
311C22×D47—42no—
312C22×D47—42no—
313C22×D47—42no—
314C22×D47—42no—
315C22×D47—42no—
316C22×D47—42no—
317C22×D47—48no—
318C22×D47—84no—
319C22×D47—816no—
320C22×D47AGL(1,ℤ/8)14yes—
321C22×D47C22×D412yes—
322C22×D47C22×D412yes—
323Q8×C47—48no—
324D4×C47—24no—
325D4×C47—22no—
326D4×C47C2×#4114yescomplemented
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—22no—
332C2×C4×C47—42no—
333C2×C4×C47—42no—
334C2×C4×C47—42no—
335C2×C4×C47—84no—
336C2×C4×C47C22×D412yes—
337C2×C4×C47C22×D412yes—
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C2×#4112yes—
340C2×C4×C47H(5,𝔽2)12yes—
341C2×C4×C47C2511yescharacteristic
342C22⋊D47—48no—
343C22⋊D47—48no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—48no—
349C2×Dic47—42no—
350C2×Dic47—42no—
351C2×Dic47C22×D412yes—
352C2×Dic47C22×D412yes—
353D188—28no—
354D188—22no—
355D188—22no—
356D188—22no—
357D188—22no—
358D188—48no—
359D188—48no—
360D188—42no—
361D188—42no—
362D188—84no—
363C4×D47—24no—
364C4×D47—24no—
365C4×D47—22no—
366C4×D47—22no—
367C4×D47—22no—
368C4×D47—22no—
369C4×D47—48no—
370C4×D47—48no—
371C4×D47—48no—
372Dic94—22no—
373Dic94—22no—
374Dic94—42no—
375C8×C47—22no—
376C8×C47—22no—
377C47⋊C8—22no—
378C47⋊C8—22no—
379C2×#3306—471nomaximal, Sylow
380C22×C47—24no—
381C22×C47—48no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47#54612yes—
385C22×C47C2×AGL(1,ℤ/8)12yes—
386C22×C47#57712yes—
387C22×C47C23×D411yescharacteristic
388C2×D47—22no—
389C2×D47—28no—
390C2×D47—22no—
391C2×D47—22no—
392C2×D47—22no—
393C2×D47—22no—
394C2×D47—44no—
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—816no—
402C2×D47—84no—
403C2×D47—84no—
404C2×D47C2×AGL(1,ℤ/8)14yes—
405C4×C47—22no—
406C4×C47—22no—
407C4×C47—42no—
408C4×C47—42no—
409C4×C47—42no—
410C4×C47#54612yes—
411C4×C47C22×#4111yescharacteristic
412C4×C47C2×H(5,𝔽2)11yescharacteristic
413Dic47—22no—
414Dic47—22no—
415Dic47—42no—
416Dic47—42no—
417C2×#547—471no—
418C2×#546—471no—
419#3306—4716no—
420C2×#489—471no—
421C2×#481—471no—
422C2×#483—471no—
423C2×#476D4711yescharacteristic, complemented
424C2×#469—471no—
425C2×#465—471no—
426C2×#463—471no—
427C2×#449—471no—
428C2×#447—471no—
429C2×#442—471no—
430C2×#435—471no—
431C2×#417—471no—
432C22×#102—471no—
433C2×C47—44no—
434C2×C47#330614yescomplemented
435C2×C47C2×#54611yescharacteristic
436C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
437C2×C47C2×#57711yescharacteristic
438D47—24no—
439D47—42no—
440D47—82no—
441D47—82no—
442C22×#41—471no—
443C22×#41—941no—
444C23×D4—471no—
445C22×SD16—471no—
446C22×D8—471no—
447C22×D8—471no—
448C22×M16—471no—
449C23×C8—471no—
450#547—478no—
451#547—944no—
452#546—478no—
453#546—944no—
454C2×C4⋊Q8C2×D4711yescharacteristic, complemented
455C2×#124—471no—
456C2×#123—941no—
457C2×#123—941no—
458C2×#123—941no—
459C2×C22⋊Q8—471no—
460C2×C22⋊Q8—941no—
461C2×#121—471no—
462C2×#121—471no—
463C2×#121—471no—
464C2×#121—941no—
465C2×#120—941no—
466C2×C4×D4—471no—
467C2×C4×D4—471no—
468C2×C4×D4C2×D4711yescharacteristic
469C22×C4⋊C4—471no—
470C22×C4⋊C4—471no—
471C22×C22⋊C4—941no—
472#489—478no—
473#483—478no—
474#481—478no—
475#476C2×D4718yescomplemented
476#469—478no—
477#465—478no—
478#463—478no—
479#449—478no—
480#447—478no—
481#442—478no—
482#435—478no—
483C2×#106—471no—
484C2×#106C2×D4711yescharacteristic, complemented
485C2×#106C2×D4711yescharacteristic, complemented
486C2×C4⋊C8C2×D4711yescharacteristic, complemented
487#417—478no—
488C2×#103—471no—
489C2×#103—471no—
490C2×#103—471no—
491C2×#102—471no—
492C2×#102—471no—
493C2×#102—471no—
494C2×#102—471no—
495C2×#102—471no—
496C2×#102—478no—
497C2×#102C2×D4711yescharacteristic
498C2×#102C2×D4711yescharacteristic
499C2×C22⋊C8—471no—
500C2×C22⋊C8—471no—
501C2×#97—471no—
502C47C2×#330611yescharacteristic, complemented, Sylow
503C25—941no—
504C2×#41—474no—
505C2×#41—942no—
506C2×#41—948no—
507C2×#41—944no—
508C2×#41—1882no—
509C2×#41—1888no—
510C22×Q8—21no—
511C22×Q8—471no—
512C22×D4—474no—
513C22×D4—471no—
514C22×D4—471no—
515C22×D4—471no—
516C22×D4—941no—
517C22×D4—941no—
518C22×D4—941no—
519C22×D4—942no—
520C22×D4—941no—
521C22×D4—944no—
522C22×D4—941no—
523C22×D4—1882no—
524C22×D4C22×D4711yescharacteristic
525C23×C4—21no—
526C23×C4—471no—
527C23×C4—471no—
528C23×C4—941no—
529C23×C4—941no—
530C23×C4—941no—
531C23×C4—941no—
532C2×SD16—474no—
533C2×SD16—1882no—
534C2×D8—474no—
535C2×D8—474no—
536C2×D8—944no—
537C2×D8—1882no—
538C2×M16—474no—
539C2×M16—1882no—
540C22×C8—471no—
541C22×C8—471no—
542C22×C8—474no—
543C22×C8—1882no—
544C22×C8C22×D4711yescharacteristic
545C22×C8C22×D4711yescharacteristic
546C4⋊Q8—22no—
547C4⋊Q8C22×D4714yescomplemented
548#124—474no—
549#124—942no—
550#123—948no—
551#123—948no—
552#123—948no—
553C22⋊Q8—474no—
554C22⋊Q8—942no—
555C22⋊Q8—948no—
556#121—474no—
557#121—474no—
558#121—474no—
559#121—948no—
560#121—942no—
561#121—942no—
562#121—942no—
563#120—948no—
564C4×D4—22no—
565C4×D4—474no—
566C4×D4—474no—
567C4×D4—474no—
568C4×D4—942no—
569C4×D4C22×D4714yes—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—471no—
572C2×C4⋊C4—471no—
573C2×C4⋊C4—474no—
574C2×C4⋊C4—474no—
575C2×C4⋊C4—942no—
576C2×C4⋊C4—942no—
577C2×C4⋊C4—941no—
578C2×C4⋊C4—941no—
579C2×C4⋊C4—941no—
580C2×C4⋊C4C22×D4711yescharacteristic
581C2×C4⋊C4C22×D4711yescharacteristic
582C2×C4⋊C4C22×D4711yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—471no—
585C2×C22⋊C4—471no—
586C2×C22⋊C4—948no—
587C2×C22⋊C4—941no—
588C2×C22⋊C4—941no—
589C2×C22⋊C4—941no—
590C2×C22⋊C4—941no—
591C2×C22⋊C4—941no—
592C2×C22⋊C4—941no—
593C2×C22⋊C4—941no—
594C2×C42C22×D4711yescharacteristic
595#106—474no—
596#106C22×D4714yescomplemented
597#106C22×D4714yescomplemented
598C4⋊C8C22×D4714yescomplemented
599#103—474no—
600#103—474no—
601#103—474no—
602#102—474no—
603#102—474no—
604#102—474no—
605#102—474no—
606#102—474no—
607#102C22×D4714yes—
608#102C22×D4714yes—
609C22⋊C8—474no—
610C22⋊C8—474no—
611#97—474no—
612C24—21no—
613C24—471no—
614C24—471no—
615C24—944no—
616C24—941no—
617C24—941no—
618C24—3762no—
619C24—1884no—
620C24—1884no—
621#41—948no—
622#41—1884no—
623#41—1888no—
624#41—18832no—
625C2×Q8—24no—
626C2×Q8—44no—
627C2×Q8—472no—
628C2×Q8—941no—
629C2×Q8—942no—
630C2×Q8—942no—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—474no—
634C2×D4—472no—
635C2×D4—472no—
636C2×D4—944no—
637C2×D4—944no—
638C2×D4—944no—
639C2×D4—944no—
640C2×D4—944no—
641C2×D4—948no—
642C2×D4—944no—
643C2×D4—941no—
644C2×D4—941no—
645C2×D4—942no—
646C2×D4—942no—
647C2×D4—942no—
648C2×D4—942no—
649C2×D4—3762no—
650C2×D4—1884no—
651C2×D4—1884no—
652C2×D4—1884no—
653C2×D4—1888no—
654C2×D4—1884no—
655C2×D4—1884no—
656C2×D4#1062535414yescomplemented
657C2×D4C23×D4712yes—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—82no—
663C22×C4—471no—
664C22×C4—471no—
665C22×C4—472no—
666C22×C4—472no—
667C22×C4—472no—
668C22×C4—472no—
669C22×C4—944no—
670C22×C4—944no—
671C22×C4—944no—
672C22×C4—942no—
673C22×C4—942no—
674C22×C4—942no—
675C22×C4—942no—
676C22×C4—941no—
677C22×C4—941no—
678C22×C4—944no—
679C22×C4—1884no—
680C22×C4—1884no—
681C22×C4—1884no—
682C22×C4—1884no—
683C22×C4D4×D4711yescharacteristic
684C22×C4D4×D4711yescharacteristic
685C22×C4C23×D4711yescharacteristic
686SD16—1884no—
687D8—948no—
688D8—1884no—
689M16—1884no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—472no—
693C2×C8—472no—
694C2×C8—942no—
695C2×C8—942no—
696C2×C8—1884no—
697C2×C8C23×D4712yes—
698C2×C8C23×D4712yes—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—474no—
704C4⋊C4—472no—
705C4⋊C4—944no—
706C4⋊C4—944no—
707C4⋊C4—944no—
708C4⋊C4—941no—
709C4⋊C4C23×D4712yes—
710C4⋊C4C23×D4712yes—
711C4⋊C4C23×D4712yes—
712C22⋊C4—24no—
713C22⋊C4—474no—
714C22⋊C4—474no—
715C22⋊C4—944no—
716C22⋊C4—944no—
717C22⋊C4—944no—
718C22⋊C4—944no—
719C22⋊C4—944no—
720C22⋊C4—944no—
721C22⋊C4—944no—
722C42D4×D4712yes—
723C42C23×D4712yes—
724C23—24no—
725C23—22no—
726C23—42no—
727C23—42no—
728C23—474no—
729C23—472no—
730C23—472no—
731C23—942no—
732C23—942no—
733C23—942no—
734C23—942no—
735C23—942no—
736C23—942no—
737C23—942no—
738C23—37616no—
739C23—3764no—
740C23—1888no—
741C23—1888no—
742C23—1882no—
743C23—1882no—
744C23—1882no—
745C23—1882no—
746C23—1882no—
747C23—1882no—
748C23C2×D4×D4711yescharacteristic
749Q8—48no—
750Q8—942no—
751Q8—942no—
752Q8—1882no—
753D4—24no—
754D4—22no—
755D4—948no—
756D4—942no—
757D4—942no—
758D4—942no—
759D4—942no—
760D4—3764no—
761D4—1888no—
762D4—1888no—
763D4—1888no—
764D4—1888no—
765D4—1882no—
766D4—1882no—
767D4C2×#1062535414yescomplemented
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—84no—
777C2×C4—472no—
778C2×C4—472no—
779C2×C4—942no—
780C2×C4—942no—
781C2×C4—944no—
782C2×C4—944no—
783C2×C4—942no—
784C2×C4—942no—
785C2×C4—942no—
786C2×C4—942no—
787C2×C4—942no—
788C2×C4—942no—
789C2×C4—1888no—
790C2×C4—1888no—
791C2×C4—1888no—
792C2×C4—1888no—
793C2×C4—1882no—
794C2×C4—1882no—
795C2×C4C2×D4×D4712yes—
796C2×C4C2×D4×D4712yes—
797C2×C4C2×D4×D4711yescharacteristic
798C2×C4C2×#1062535412yes—
799C2×C4#1309407012yes—
800C2×C4C24×D4711yescharacteristic
801C8—22no—
802C8—22no—
803C8—942no—
804C8—942no—
805C22—24no—
806C22—42no—
807C22—42no—
808C22—48no—
809C22—474no—
810C22—942no—
811C22—942no—
812C22—948no—
813C22—942no—
814C22—942no—
815C22—942no—
816C22—37616no—
817C22—3764no—
818C22—3764no—
819C22—1882no—
820C22—1882no—
821C22—1882no—
822C22—1882no—
823C22—1882no—
824C22—1882no—
825C22—1884no—
826C22#1568976412yes—
827C22AGL(1,ℤ/8)×D4712yes—
828C22#1568992912yes—
829C22C22×D4×D4711yescharacteristic
830C4—22no—
831C4—22no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—942no—
836C4—942no—
837C4—1882no—
838C4—1882no—
839C4#1568976412yes—
840C4C22×#1062535411yescharacteristic
841C4C2×#1309407011yescharacteristic
842C2—44no—
843C2—944no—
844C2—3762no—
845C2—3762no—
846C2—1882no—
847C2#2025534614yesdirect product factor
848C2C2×#1568976411yescharacteristic
849C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
850C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#476C2
socleC23×C47C22×D4
hypercenterC2×#476D47
hypocenterC47C2×#3306
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×#15689776C2semidirect
2. C2×#15689768C2semidirect
3. #20255346C2direct (N × H)
4. C2×#15689485C2semidirect
5. C2×#15689443C2semidirect
6. C2×#15689455C2semidirect
7. C2×#15689377C2semidirect
8. C2×#15689353C2semidirect
9. C2×#15689339C2semidirect
10. C2×#15689269C2semidirect
11. C2×#15689258C2semidirect
12. C2×#15689233C2semidirect
13. C2×#15689193C2semidirect
14. C2×#15689121C2semidirect
15. C2×#102×D47C2semidirect
16. C2×C47×#476C2semidirect
20. C22×#10625325C22semidirect
23. C22×#10625324C22semidirect
26. #15689776C22semidirect
28. #15689768C22semidirect
37. C2×#13093999C22semidirect
41. C2×C4×D188C22semidirect
43. C2×C4⋊C4×D47C22semidirect
45. #15689485C22semidirect
46. #15689455C22semidirect
47. #15689443C22semidirect
48. #15689377C22semidirect
49. #15689353C22semidirect
50. #15689339C22semidirect
51. #15689269C22semidirect
52. #15689258C22semidirect
53. #15689233C22semidirect
54. #15689193C22semidirect
55. C2×#13093955C22semidirect
56. #15689121C22semidirect
57. C2×#13093949C22semidirect
58. C2×#13093947C22semidirect
59. C2×#13093947C22semidirect
64. C2×#13093944C22semidirect
65. #102×D47C22semidirect
67. C2×(C2×D47)⋊C8C22semidirect
68. C2×#13093935C22semidirect
69. C2×C4⋊Q8×C47C22semidirect
71. C47×#476C22semidirect
72. C2×#106×C47C22semidirect
73. C2×#106×C47C22semidirect
74. C2×C4⋊C8×C47C22semidirect
104. C2×#10625325C23semidirect
110. C2×#10625324C23semidirect
128. #13093999C23semidirect
134. C4×D188C23semidirect
143. C4⋊C4×D47C23semidirect
154. #13093955C23semidirect
155. #13093949C23semidirect
156. #13093947C23semidirect
157. #13093947C23semidirect
162. #13093944C23semidirect
164. (C2×D47)⋊C8C23semidirect
165. #13093935C23semidirect
172. C4⋊Q8×C47C23semidirect
181. #106×C47C23semidirect
182. #106×C47C23semidirect
183. C4⋊C8×C47C23semidirect
199. C2×D4×C47#41semidirect
326. D4×C47C2×#41semidirect
423. C2×#476D47semidirect
434. C2×C47#3306semidirect
454. C2×C4⋊Q8C2×D47semidirect
475. #476C2×D47semidirect
484. C2×#106C2×D47semidirect
485. C2×#106C2×D47semidirect
486. C2×C4⋊C8C2×D47semidirect
502. C47C2×#3306semidirect
547. C4⋊Q8C22×D47semidirect
596. #106C22×D47semidirect
597. #106C22×D47semidirect
598. C4⋊C8C22×D47semidirect
656. C2×D4#10625354semidirect
767. D4C2×#10625354semidirect
847. C2#20255346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897762
C2×#156897682
#202553462
C2×#156894852
C2×#156894432
C2×#156894552
C2×#156893772
C2×#156893532
C2×#156893392
C2×#156892692
C2×#156892582
C2×#156892332
C2×#156891932
C2×#156891212
C2×#102×D472
C2×C47×#4762
C2×#330647