Finite Group Databasebeta

← C2×#20254491 #27087667

Subgroups — C2×#20254491 #27087667

Order 12032.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689699C211yesmaximal, characteristic, complemented
2#20254491C2116yesmaximal, direct product factor
3C2×#15689518C211yesmaximal, characteristic, complemented
4C2×#15689505C211yesmaximal, characteristic, complemented
5C2×#15689485C211yesmaximal, characteristic, complemented
6C2×#15689475C211yesmaximal, characteristic, complemented
7C2×#15689345C211yesmaximal, characteristic, complemented
8C2×#15689333C211yesmaximal, characteristic, complemented
9C2×#15689338C211yesmaximal, characteristic, complemented
10C2×#15689328C211yesmaximal, characteristic, complemented
11C2×#15689283C211yesmaximal, characteristic, complemented
12C2×#15689266C211yesmaximal, characteristic
13C2×#15689278C211yesmaximal, characteristic, complemented
14C2×#15689261C211yesmaximal, characteristic, complemented
15C2×#15689184C211yesmaximal, characteristic, complemented
16C2×C47×#542C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C23×Dic94C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625337C2211yescharacteristic
21C22×#10625337C2211yescharacteristic
22C22×#10625335C2211yescharacteristic
23C22×#10625335C2211yescharacteristic
24C22×#10625335C2211yescharacteristic
25C22×#10625336C2211yescharacteristic
26C22×#10625334C2211yescharacteristic
27#15689699—24no—
28#15689699C2218yescomplemented
29C2×#13094024C2211yescharacteristic
30C2×#13094024C2211yescharacteristic
31C2×#13094012C2211yescharacteristic
32C2×#13094012C2211yescharacteristic
33C2×#13094008—21no—
34C2×#13094008—21no—
35C2×#13094004—21no—
36C2×#13094004—21no—
37#15689518C2218yescomplemented
38#15689505C2218yescomplemented
39#15689485C2218yescomplemented
40#15689475C2218yescomplemented
41#15689345C2218yescomplemented
42#15689338C2218yescomplemented
43#15689333C2218yescomplemented
44#15689328C2218yescomplemented
45#15689283C2218yescomplemented
46#15689278C2218yescomplemented
47#15689266C2218yes—
48#15689261C2218yescomplemented
49#15689184C2218yescomplemented
50C2×C4⋊(C47⋊C8)C2211yescharacteristic
51C2×C4⋊(C47⋊C8)C2211yescharacteristic
52C2×#13093947C2211yescharacteristic
53C2×#13093947C2211yescharacteristic
54C2×#13093947C2211yescharacteristic
55C2×#13093947C2211yescharacteristic
56C2×#13093947C2211yescharacteristic
57C2×#13093947C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#542—24no—
65C47×#542C2218yescomplemented
66C2×C4⋊Q8×C47C2211yescharacteristic
67C2×#126×C47—21no—
68C2×#124×C47—21no—
69C2×#124×C47C2211yescharacteristic
70C2×#123×C47—21no—
71C2×C22⋊Q8×C47—21no—
72C2×C22⋊Q8×C47C2211yescharacteristic
73C2×#121×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C2×C4×D4×C47C2211yescharacteristic
76C2×#117×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—42no—
79C2×#10625350—42no—
80C2×#10625350C2314yes—
81C22×Dic94—21no—
82C22×Dic94—22no—
83C22×Dic94—42no—
84C22×Dic94—42no—
85C22×Dic94C2311yescharacteristic
86C22×Dic94C2311yescharacteristic
87C22×Dic94C2311yescharacteristic
88C22×Dic94C2314yes—
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C23×Dic47—21no—
92C22×C4×D47—21no—
93C2×#10625337—42no—
94C2×#10625337—42no—
95C2×#10625337—42no—
96C2×#10625337C2314yes—
97C2×#10625337C2314yes—
98C2×#10625337C2314yes—
99C2×#10625335—42no—
100C2×#10625335—42no—
101C2×#10625335—42no—
102C2×#10625335C2314yes—
103C2×#10625335C2314yes—
104C2×#10625335C2314yes—
105C2×#10625336—42no—
106C2×#10625336C2314yes—
107C2×#10625334—42no—
108C2×#10625334C2314yes—
109C22×C47⋊C8C2311yescharacteristic
110C22×C47⋊C8C2311yescharacteristic
111C22×C47⋊C8C2311yescharacteristic
112C22×C47⋊C8C2311yescharacteristic
113#13094024—22no—
114#13094024—22no—
115#13094024C2314yes—
116#13094024C2314yes—
117#13094012—22no—
118#13094012—22no—
119#13094012C2314yes—
120#13094012C2314yes—
121#13094008—28no—
122#13094008—28no—
123#13094004—28no—
124#13094004—28no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×(C2×D47)⋊C4—21no—
130C2×(C2×D47)⋊C4—21no—
131C2×(C2×D47)⋊C4—21no—
132C2×(C2×D47)⋊C4—21no—
133C4⋊(C47⋊C8)C2314yes—
134C4⋊(C47⋊C8)C2314yes—
135#13093947C2314yes—
136#13093947C2314yes—
137#13093947C2314yes—
138#13093947C2314yes—
139#13093947C2314yes—
140#13093947C2314yes—
141#13093944C2314yes—
142#13093944C2314yes—
143C22⋊(C47⋊C8)C2314yes—
144C22⋊(C47⋊C8)C2314yes—
145#13093935C2314yes—
146C4×C47⋊C8C2314yes—
147C22×Q8×C47—21no—
148C22×Q8×C47C2311yescharacteristic
149C22×D4×C47—21no—
150C22×D4×C47C2311yescharacteristic
151C23×C4×C47—21no—
152C23×C4×C47C2311yescharacteristic
153C4⋊Q8×C47—22no—
154C4⋊Q8×C47C2314yes—
155#126×C47—28no—
156#124×C47—28no—
157#124×C47—22no—
158#124×C47C2314yes—
159#123×C47—28no—
160C22⋊Q8×C47—22no—
161C22⋊Q8×C47—28no—
162C22⋊Q8×C47C2314yes—
163#121×C47—22no—
164#121×C47C2314yes—
165C4×Q8×C47—22no—
166C4×Q8×C47C2314yes—
167C4×D4×C47—22no—
168C4×D4×C47C2314yes—
169#117×C47D414yes—
170#117×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47—21no—
174C2×C4⋊C4×C47D411yescharacteristic
175C2×C4⋊C4×C47D411yescharacteristic
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182C2×C22⋊C4×C47—21no—
183C2×C22⋊C4×C47D411yescharacteristic
184C2×C22⋊C4×C47D411yescharacteristic
185C2×C42×C47—21no—
186C2×C42×C47C2311yescharacteristic
187C2×C42×C47C2311yescharacteristic
188C24×C47—21no—
189C24×C47C2×D411yescharacteristic
190C23×D47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47—24no—
193C2×Q8×C47—22no—
194C2×Q8×C47—22no—
195C2×Q8×C47—82no—
196C2×Q8×C47C2412yes—
197C2×D4×C47—24no—
198C2×D4×C47—21no—
199C2×D4×C47—22no—
200C2×D4×C47—22no—
201C2×D4×C47—82no—
202C2×D4×C47C2412yes—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—24no—
209C22×C4×C47—82no—
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D412yes—
216C22×C4×C47C2412yes—
217C22×C4×C47C2411yescharacteristic
218C2×C22⋊D47—24no—
219C2×C22⋊D47—44no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—24no—
224C22×Dic47—44no—
225#10625350—44no—
226#10625350—44no—
227#10625350—48no—
228C2×D188—22no—
229C2×D188—22no—
230C2×D188—21no—
231C2×D188C2412yes—
232C2×C4×D47—24no—
233C2×C4×D47—44no—
234C2×Dic94—22no—
235C2×Dic94—22no—
236C2×Dic94—22no—
237C2×Dic94—22no—
238C2×Dic94—22no—
239C2×Dic94—22no—
240C2×Dic94—24no—
241C2×Dic94—21no—
242C2×Dic94—21no—
243C2×Dic94—21no—
244C2×Dic94—44no—
245C2×Dic94—44no—
246C2×Dic94—44no—
247C2×Dic94—48no—
248C2×Dic94C2412yes—
249C2×Dic94C2412yes—
250C2×Dic94C2412yes—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—24no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47C2×D414yes—
257C4⋊C4×C47C2×D414yes—
258C4⋊C4×C47C2412yes—
259C4⋊C4×C47C2412yes—
260C22⋊C4×C47—24no—
261C22⋊C4×C47—24no—
262C22⋊C4×C47—24no—
263C22⋊C4×C47—24no—
264C22⋊C4×C47—24no—
265C22⋊C4×C47C2×D414yes—
266C22⋊C4×C47C2×D414yes—
267C42×C47—24no—
268C42×C47C2×D412yes—
269C42×C47C2×D412yes—
270C42×C47C2412yes—
271C42×C47C2412yes—
272#10625337—44no—
273#10625337—44no—
274#10625337—44no—
275#10625336—44no—
276#10625335—44no—
277#10625335—44no—
278#10625335—44no—
279#10625334—44no—
280(C2×D47)⋊C4—24no—
281(C2×D47)⋊C4—24no—
282(C2×D47)⋊C4—24no—
283(C2×D47)⋊C4—24no—
284C4⋊Dic47—24no—
285C4⋊Dic47—24no—
286C4⋊Dic47—24no—
287C4⋊Dic47—24no—
288C2×C47⋊C8—22no—
289C2×C47⋊C8—22no—
290C2×C47⋊C8—22no—
291C2×C47⋊C8—22no—
292C2×C47⋊C8C2412yes—
293C2×C47⋊C8C2412yes—
294C2×C47⋊C8C2412yes—
295C2×C47⋊C8C2412yes—
296C23×C47—22no—
297C23×C47—22no—
298C23×C47—22no—
299C23×C47—22no—
300C23×C47—42no—
301C23×C47—42no—
302C23×C47—42no—
303C23×C47C22×D412yes—
304C23×C47C22×D411yescharacteristic
305C22×D47—22no—
306C22×D47—42no—
307C22×D47—42no—
308C22×D47—42no—
309Q8×C47—22no—
310Q8×C47—22no—
311Q8×C47—42no—
312Q8×C47—84no—
313D4×C47—22no—
314D4×C47—22no—
315D4×C47—42no—
316D4×C47—84no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—24no—
323C2×C4×C47—22no—
324C2×C4×C47—22no—
325C2×C4×C47—22no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—42no—
329C2×C4×C47—42no—
330C2×C4×C47—42no—
331C2×C4×C47—84no—
332C2×C4×C47C22×D412yes—
333C2×C4×C47C22×D412yes—
334C2×C4×C47C22×D412yes—
335C2×C4×C47C22×D412yes—
336C2×C4×C47C22×D412yes—
337C2×C4×C47C22×D411yescharacteristic
338C2×C4×C47H(5,𝔽2)12yes—
339C2×C4×C47H(5,𝔽2)12yes—
340C2×C4×C47C2511yescharacteristic
341C22⋊D47—48no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—48no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349D188—22no—
350D188—22no—
351D188—42no—
352C4×D47—48no—
353Dic94—22no—
354Dic94—22no—
355Dic94—22no—
356Dic94—22no—
357Dic94—22no—
358Dic94—22no—
359Dic94—48no—
360Dic94—42no—
361Dic94—42no—
362Dic94—42no—
363C47⋊C8—22no—
364C47⋊C8—22no—
365C47⋊C8—22no—
366C47⋊C8—22no—
367C2×#3225—471nomaximal, Sylow
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—44no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—84no—
376C22×C47#53512yes—
377C22×C47#57712yes—
378C22×C47#57812yes—
379C22×C47C23×D411yescharacteristic
380C2×D47—42no—
381C2×D47—42no—
382C2×D47—42no—
383C2×D47—84no—
384C4×C47—22no—
385C4×C47—22no—
386C4×C47—22no—
387C4×C47—22no—
388C4×C47—22no—
389C4×C47—42no—
390C4×C47—42no—
391C4×C47—42no—
392C4×C47#53512yes—
393C4×C47C2×H(5,𝔽2)11yescharacteristic
394C4×C47C2×H(5,𝔽2)11yescharacteristic
395Dic47—42no—
396Dic47—42no—
397Dic47—42no—
398C2×#542D4711yescharacteristic, complemented
399C2×#536—471no—
400#3225—4716no—
401C2×#497—471no—
402C2×#495—471no—
403C2×#489—471no—
404C2×#487—471no—
405C2×#464—471no—
406C2×#462—471no—
407C2×#463—471no—
408C2×#461—471no—
409C2×#452—471no—
410C2×#449—471no—
411C2×#451—471no—
412C2×#448—471no—
413C2×#433—471no—
414C2×C47—42no—
415C2×C47—82no—
416C2×C47#322514yescomplemented
417C2×C47C2×#53511yescharacteristic
418C2×C47C2×#57711yescharacteristic
419C2×C47C2×#57811yescharacteristic
420D47—82no—
421C22×#41—471no—
422C23×Q8—471no—
423C22×Q16—471no—
424C22×Q16—471no—
425C22×Q16—471no—
426C22×SD16—471no—
427C22×SD16—471no—
428C22×SD16—471no—
429C22×SD16—471no—
430C22×D8—471no—
431#542—24no—
432#542C2×D4718yescomplemented
433#536—478no—
434#536—944no—
435C2×C4⋊Q8—471no—
436C2×C4⋊Q8—471no—
437C2×C4⋊Q8C2×D4711yescharacteristic
438C2×#126—21no—
439C2×#124—21no—
440C2×#124—471no—
441C2×#124—471no—
442C2×#124C2×D4711yescharacteristic
443C2×#123—21no—
444C2×#123—941no—
445C2×#123—941no—
446C2×C22⋊Q8—21no—
447C2×C22⋊Q8—941no—
448C2×C22⋊Q8—941no—
449C2×C22⋊Q8C2×D4711yescharacteristic
450C2×#121C2×D4711yescharacteristic
451C2×C4×Q8C2×D4711yescharacteristic
452C2×C4×D4C2×D4711yescharacteristic
453C2×#117C2×D4711yescharacteristic
454#497—478no—
455#495—478no—
456#489—478no—
457#487—478no—
458#464—478no—
459#463—478no—
460#462—478no—
461#461—478no—
462#452—478no—
463#451—478no—
464#449—478no—
465#448—478no—
466#433—478no—
467C2×C4⋊C8—471no—
468C2×C4⋊C8—471no—
469C2×#103—471no—
470C2×#103—471no—
471C2×#103—471no—
472C2×#103—471no—
473C2×#103—471no—
474C2×#103—471no—
475C2×#102—471no—
476C2×#102—471no—
477C2×C22⋊C8—471no—
478C2×C22⋊C8—471no—
479C2×#97—471no—
480C2×C4×C8—471no—
481C47C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—474no—
483C2×#41—942no—
484C2×#41—1882no—
485C2×#41—1882no—
486C22×Q8—21no—
487C22×Q8—471no—
488C22×Q8—471no—
489C22×Q8—471no—
490C22×Q8—474no—
491C22×Q8—941no—
492C22×Q8—942no—
493C22×Q8—1882no—
494C22×Q8—1882no—
495C22×Q8C22×D4711yescharacteristic
496C22×D4—21no—
497C22×D4—471no—
498C22×D4—941no—
499C22×D4C22×D4711yescharacteristic
500C23×C4—21no—
501C23×C4—941no—
502C23×C4—941no—
503C23×C4C22×D4711yescharacteristic
504C2×Q16—474no—
505C2×Q16—474no—
506C2×Q16—474no—
507C2×Q16—1882no—
508C2×Q16—1882no—
509C2×Q16—1882no—
510C2×SD16—474no—
511C2×SD16—474no—
512C2×SD16—474no—
513C2×SD16—474no—
514C2×SD16—1882no—
515C2×SD16—1882no—
516C2×SD16—1882no—
517C2×SD16—1882no—
518C2×D8—474no—
519C2×D8—1882no—
520C22×C8—471no—
521C22×C8—471no—
522C22×C8—471no—
523C22×C8—471no—
524C4⋊Q8—22no—
525C4⋊Q8—474no—
526C4⋊Q8—474no—
527C4⋊Q8—942no—
528C4⋊Q8—942no—
529C4⋊Q8C22×D4714yes—
530#126—28no—
531#124—28no—
532#124—22no—
533#124—474no—
534#124—474no—
535#124—942no—
536#124—942no—
537#124C22×D4714yes—
538#123—28no—
539#123—948no—
540#123—948no—
541C22⋊Q8—22no—
542C22⋊Q8—28no—
543C22⋊Q8—948no—
544C22⋊Q8—948no—
545C22⋊Q8C22×D4714yes—
546#121—22no—
547#121C22×D4714yes—
548C4×Q8—22no—
549C4×Q8C22×D4714yes—
550C4×D4—22no—
551C4×D4C22×D4714yes—
552#117C22⋊D4714yes—
553#117C22×D4714yes—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—941no—
558C2×C4⋊C4—941no—
559C2×C4⋊C4—941no—
560C2×C4⋊C4—941no—
561C2×C4⋊C4C22⋊D4711yescharacteristic
562C2×C4⋊C4C22⋊D4711yescharacteristic
563C2×C4⋊C4C22×D4711yescharacteristic
564C2×C4⋊C4C22×D4711yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—941no—
571C2×C22⋊C4—941no—
572C2×C22⋊C4—941no—
573C2×C22⋊C4—941no—
574C2×C22⋊C4C22⋊D4711yescharacteristic
575C2×C22⋊C4C22⋊D4711yescharacteristic
576C2×C42—21no—
577C2×C42C22×D4711yescharacteristic
578C2×C42C22×D4711yescharacteristic
579C4⋊C8—474no—
580C4⋊C8—474no—
581#103—474no—
582#103—474no—
583#103—474no—
584#103—474no—
585#103—474no—
586#103—474no—
587#102—474no—
588#102—474no—
589C22⋊C8—474no—
590C22⋊C8—474no—
591#97—474no—
592C4×C8—474no—
593C24—21no—
594C24—941no—
595C24C2×C22⋊D4711yescharacteristic
596#41—1884no—
597#41—1884no—
598#41—1888no—
599C2×Q8—21no—
600C2×Q8—24no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—82no—
604C2×Q8—472no—
605C2×Q8—472no—
606C2×Q8—472no—
607C2×Q8—944no—
608C2×Q8—941no—
609C2×Q8—941no—
610C2×Q8—941no—
611C2×Q8—942no—
612C2×Q8—942no—
613C2×Q8—942no—
614C2×Q8—942no—
615C2×Q8—942no—
616C2×Q8—942no—
617C2×Q8—1884no—
618C2×Q8—1884no—
619C2×Q8—1884no—
620C2×Q8—1888no—
621C2×Q8C23×D4712yes—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—82no—
627C2×D4—472no—
628C2×D4—944no—
629C2×D4—941no—
630C2×D4—942no—
631C2×D4—942no—
632C2×D4—1884no—
633C2×D4C23×D4712yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—82no—
641C22×C4—944no—
642C22×C4—941no—
643C22×C4—941no—
644C22×C4—941no—
645C22×C4—944no—
646C22×C4—1884no—
647C22×C4—1884no—
648C22×C4C2×C22⋊D4712yes—
649C22×C4C2×C22⋊D4711yescharacteristic
650C22×C4C2×C22⋊D4711yescharacteristic
651C22×C4C2×C22⋊D4711yescharacteristic
652C22×C4C2×C22⋊D4711yescharacteristic
653C22×C4C2×C22⋊D4711yescharacteristic
654C22×C4C23×D4712yes—
655C22×C4C23×D4711yescharacteristic
656Q16—1884no—
657Q16—1884no—
658Q16—1884no—
659SD16—1884no—
660SD16—1884no—
661SD16—1884no—
662SD16—1884no—
663D8—1884no—
664C2×C8—472no—
665C2×C8—472no—
666C2×C8—472no—
667C2×C8—472no—
668C2×C8—942no—
669C2×C8—942no—
670C2×C8—942no—
671C2×C8—942no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—944no—
678C4⋊C4—944no—
679C4⋊C4—944no—
680C4⋊C4—944no—
681C4⋊C4C2×C22⋊D4714yes—
682C4⋊C4C2×C22⋊D4714yes—
683C4⋊C4C23×D4712yes—
684C4⋊C4C23×D4712yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—944no—
691C22⋊C4—944no—
692C22⋊C4—944no—
693C22⋊C4—944no—
694C22⋊C4C2×C22⋊D4714yes—
695C22⋊C4C2×C22⋊D4714yes—
696C42—24no—
697C42C2×C22⋊D4712yes—
698C42C2×C22⋊D4712yes—
699C42C23×D4712yes—
700C42C23×D4712yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—942no—
709C23—1882no—
710C23—1882no—
711C23—1882no—
712C23C22×C22⋊D4712yes—
713C23C22×C22⋊D4711yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—84no—
718Q8—942no—
719Q8—942no—
720Q8—942no—
721Q8—942no—
722Q8—942no—
723Q8—942no—
724Q8—1888no—
725Q8—1882no—
726Q8—1882no—
727Q8—1882no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—84no—
732D4—942no—
733D4—942no—
734D4—1888no—
735D4—1882no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—84no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—1888no—
755C2×C4—1888no—
756C2×C4—1882no—
757C2×C4—1882no—
758C2×C4—1882no—
759C2×C4C22×C22⋊D4712yes—
760C2×C4C22×C22⋊D4712yes—
761C2×C4C22×C22⋊D4712yes—
762C2×C4C22×C22⋊D4712yes—
763C2×C4C22×C22⋊D4712yes—
764C2×C4C22×C22⋊D4711yescharacteristic
765C2×C4#1309407012yes—
766C2×C4#1309407012yes—
767C2×C4C24×D4711yescharacteristic
768C8—942no—
769C8—942no—
770C8—942no—
771C8—942no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—84no—
780C22—3764no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22#1568968712yes—
785C22#1568993412yes—
786C22#1568993812yes—
787C22C23×C22⋊D4711yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—1882no—
797C4—1882no—
798C4—1882no—
799C4#1568968712yes—
800C4C2×#1309407011yescharacteristic
801C4C2×#1309407011yescharacteristic
802C2—42no—
803C2—82no—
804C2—3762no—
805C2#2025449114yesdirect product factor
806C2C2×#1568968711yescharacteristic
807C2C2×#1568993411yescharacteristic
808C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#542C2
socleC23×C47C22×D4
prime radicalC2×#15689266C2
hypercenterC2×#542D47
hypocenterC47C2×#3225
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#15689699C2semidirect
2. #20254491C2direct (N × H)
3. C2×#15689518C2semidirect
4. C2×#15689505C2semidirect
5. C2×#15689485C2semidirect
6. C2×#15689475C2semidirect
7. C2×#15689345C2semidirect
8. C2×#15689333C2semidirect
9. C2×#15689338C2semidirect
10. C2×#15689328C2semidirect
11. C2×#15689283C2semidirect
13. C2×#15689278C2semidirect
14. C2×#15689261C2semidirect
15. C2×#15689184C2semidirect
16. C2×C47×#542C2semidirect
28. #15689699C22semidirect
37. #15689518C22semidirect
38. #15689505C22semidirect
39. #15689485C22semidirect
40. #15689475C22semidirect
41. #15689345C22semidirect
42. #15689338C22semidirect
43. #15689333C22semidirect
44. #15689328C22semidirect
45. #15689283C22semidirect
46. #15689278C22semidirect
48. #15689261C22semidirect
49. #15689184C22semidirect
65. C47×#542C22semidirect
398. C2×#542D47semidirect
416. C2×C47#3225semidirect
432. #542C2×D47semidirect
481. C47C2×#3225semidirect
805. C2#20254491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896992
#202544912
C2×#156895182
C2×#156895052
C2×#156894852
C2×#156894752
C2×#156893452
C2×#156893332
C2×#156893382
C2×#156893282
C2×#156892832
C2×#156892662
C2×#156892782
C2×#156892612
C2×#156891842
C2×C47×#5422
C2×#322547