Finite Group Databasebeta

← C2×#20256463 #27097294

Subgroups — C2×#20256463 #27097294

Order 12032.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689846C211yesmaximal, characteristic, complemented
2#20256463C2116yesmaximal, direct product factor
3C2×#15689518C211yesmaximal, characteristic, complemented
4C2×#15689515C211yesmaximal, characteristic, complemented
5C2×#15689505C211yesmaximal, characteristic
6C2×#15689345C211yesmaximal, characteristic, complemented
7C2×#15689342C211yesmaximal, characteristic, complemented
8C2×#15689333C211yesmaximal, characteristic, complemented
9C2×#15689330C211yesmaximal, characteristic, complemented
10C2×#15689338C211yesmaximal, characteristic
11C2×#15689335C211yesmaximal, characteristic
12C2×#15689254C211yesmaximal, characteristic, complemented
13C2×#15689223C211yesmaximal, characteristic, complemented
14C2×#15689221C211yesmaximal, characteristic, complemented
15C2×C4×#10625337C211yesmaximal, characteristic, complemented
16C2×C47×#556C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625337C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22C22×#10625335C2211yescharacteristic
23C22×#10625336C2211yescharacteristic
24C22×#10625336C2211yescharacteristic
25C22×#10625334C2211yescharacteristic
26#15689846—24no—
27#15689846C2218yescomplemented
28C2×#13094024C2211yescharacteristic
29C2×#13094019—21no—
30C2×#13094019—21no—
31C2×#13094012C2211yescharacteristic
32C2×#13094012C2211yescharacteristic
33C2×#13094000—21no—
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×#13093982—21no—
38#15689518C2218yescomplemented
39#15689515C2218yescomplemented
40#15689505C2218yes—
41#15689345C2218yescomplemented
42#15689342C2218yescomplemented
43#15689338C2218yes—
44#15689335C2218yes—
45#15689333C2218yescomplemented
46#15689330C2218yescomplemented
47#15689254C2218yescomplemented
48#15689223C2218yescomplemented
49#15689221C2218yescomplemented
50C4×#10625337C2218yescomplemented
51C2×#13093957C2211yescharacteristic
52C2×C4⋊(C47⋊C8)C2211yescharacteristic
53C2×C4⋊(C47⋊C8)C2211yescharacteristic
54C2×C4⋊(C47⋊C8)C2211yescharacteristic
55C2×#13093948C2211yescharacteristic
56C2×#13093948C2211yescharacteristic
57C2×#13093947C2211yescharacteristic
58C2×#13093947C2211yescharacteristic
59C2×#13093945C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×#13093935C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#556—24no—
65C47×#556C2218yescomplemented
66C2×C4⋊Q8×C47C2211yescharacteristic
67C2×#126×C47—21no—
68C2×#126×C47—21no—
69C2×#124×C47C2211yescharacteristic
70C2×#124×C47C2211yescharacteristic
71C2×C22⋊Q8×C47—21no—
72C2×C4×Q8×C47C2211yescharacteristic
73C2×C4×Q8×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C2×C4×D4×C47C2211yescharacteristic
76C2×#117×C47—21no—
77C22×Dic94C2311yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C4×D47—21no—
81C2×#10625337—24no—
82C2×#10625337—42no—
83C2×#10625337—42no—
84C2×#10625337—42no—
85C2×#10625337C2314yes—
86C2×#10625337C2314yes—
87C2×#10625337C2314yes—
88C2×#10625337C2314yes—
89C2×#10625335—24no—
90C2×#10625335—42no—
91C2×#10625335C2314yes—
92C2×#10625335C2314yes—
93C2×#10625336—24no—
94C2×#10625336—42no—
95C2×#10625336C2314yes—
96C2×#10625336C2314yes—
97C2×#10625334—42no—
98C2×#10625334C2314yes—
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103#13094024—22no—
104#13094024C2314yes—
105#13094019—28no—
106#13094019—28no—
107#13094012—22no—
108#13094012—22no—
109#13094012C2314yes—
110#13094012C2314yes—
111#13094000—28no—
112C4×Dic94—22no—
113C4×Dic94—22no—
114C4×Dic94C2314yes—
115C4×Dic94C2314yes—
116C4×D188—22no—
117C4×D188C2314yes—
118#13093982—28no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47C2311yescharacteristic
122C2×Dic47⋊C4—21no—
123C2×Dic47⋊C4—21no—
124C2×(C2×D47)⋊C4—21no—
125C2×(C2×D47)⋊C4—21no—
126C2×(C2×D47)⋊C4—21no—
127C2×(C2×D47)⋊C4—21no—
128C2×(C2×D47)⋊C4—21no—
129C2×C4×Dic47—21no—
130C2×C4×Dic47—21no—
131#13093957C2314yes—
132C4⋊(C47⋊C8)C2314yes—
133C4⋊(C47⋊C8)C2314yes—
134C4⋊(C47⋊C8)C2314yes—
135#13093948C2314yes—
136#13093948C2314yes—
137#13093947C2314yes—
138#13093947C2314yes—
139#13093945C2314yes—
140#13093944C2314yes—
141#13093935C2314yes—
142#13093935C2314yes—
143C4×C47⋊C8C2314yes—
144C22×Q8×C47D411yescharacteristic
145C22×Q8×C47C2311yescharacteristic
146C22×Q8×C47C2311yescharacteristic
147C22×D4×C47C2311yescharacteristic
148C23×C4×C47—21no—
149C4⋊Q8×C47—22no—
150C4⋊Q8×C47C2314yes—
151#126×C47—28no—
152#126×C47—28no—
153#124×C47—22no—
154#124×C47—22no—
155#124×C47C2314yes—
156#124×C47C2314yes—
157C22⋊Q8×C47—28no—
158C4×Q8×C47—22no—
159C4×Q8×C47—22no—
160C4×Q8×C47D414yes—
161C4×Q8×C47C2314yes—
162C4×Q8×C47C2314yes—
163C4×Q8×C47C2314yes—
164C4×D4×C47—22no—
165C4×D4×C47C2314yes—
166#117×C47—28no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C4⋊C4×C47D411yescharacteristic
173C2×C4⋊C4×C47D411yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47—21no—
178C2×C22⋊C4×C47—21no—
179C2×C22⋊C4×C47—21no—
180C2×C42×C47—21no—
181C2×C42×C47—21no—
182C2×C42×C47C2311yescharacteristic
183C2×C42×C47C2311yescharacteristic
184C2×C42×C47C2311yescharacteristic
185C24×C47—21no—
186C23×D47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—22no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47—42no—
194C2×Q8×C47C2×D414yes—
195C2×Q8×C47C2412yes—
196C2×Q8×C47C2412yes—
197C2×D4×C47—21no—
198C2×D4×C47—22no—
199C2×D4×C47—22no—
200C2×D4×C47C2412yes—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—24no—
205C22×C4×C47—44no—
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2411yescharacteristic
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—21no—
219C2×D188C2412yes—
220C2×C4×D47—24no—
221C2×C4×D47—44no—
222C2×Dic94—22no—
223C2×Dic94—22no—
224C2×Dic94—22no—
225C2×Dic94—22no—
226C2×Dic94—21no—
227C2×Dic94—21no—
228C2×Dic94C2412yes—
229C2×Dic94C2412yes—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—24no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C2×D414yes—
236C4⋊C4×C47C2×D414yes—
237C4⋊C4×C47C2×D414yes—
238C4⋊C4×C47C2412yes—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—24no—
241C22⋊C4×C47—24no—
242C22⋊C4×C47—24no—
243C22⋊C4×C47—24no—
244C42×C47—24no—
245C42×C47—24no—
246C42×C47C2×D412yes—
247C42×C47C2×D412yes—
248C42×C47C2×D412yes—
249C42×C47C2412yes—
250C42×C47C2412yes—
251C42×C47C2412yes—
252#10625337—28no—
253#10625337—44no—
254#10625337—44no—
255#10625337—44no—
256#10625336—28no—
257#10625336—44no—
258#10625335—28no—
259#10625335—44no—
260#10625334—44no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266C4⋊Dic47—24no—
267C4⋊Dic47—24no—
268C4⋊Dic47—21no—
269C4⋊Dic47C2412yes—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272C4×Dic47—24no—
273C4×Dic47—24no—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—22no—
276C2×C47⋊C8—22no—
277C2×C47⋊C8#4114yes—
278C2×C47⋊C8C2412yes—
279C2×C47⋊C8C2412yes—
280C2×C47⋊C8C2412yes—
281C2×C47⋊C8C2412yes—
282C23×C47—22no—
283C23×C47—42no—
284C23×C47—42no—
285C23×C47—42no—
286C23×C47C22×D411yescharacteristic
287C22×D47—22no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—42no—
291Q8×C47—22no—
292Q8×C47—22no—
293Q8×C47—22no—
294Q8×C47—22no—
295Q8×C47—44no—
296Q8×C47—42no—
297Q8×C47—42no—
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—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—48no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C22×D412yes—
319C2×C4×C47C22×D412yes—
320C2×C4×C47C22×D411yescharacteristic
321C2×C4×C47C2×#4112yes—
322C2×C4×C47H(5,𝔽2)12yes—
323C2×C4×C47C2511yescharacteristic
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330D188—22no—
331D188—22no—
332D188—42no—
333C4×D47—48no—
334Dic94—22no—
335Dic94—22no—
336Dic94—22no—
337Dic94—22no—
338Dic94—42no—
339Dic94—42no—
340C47⋊C8—22no—
341C47⋊C8—22no—
342C47⋊C8—22no—
343C47⋊C8C2×#4114yes—
344C2×#3402—471nomaximal, Sylow
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—84no—
349C22×C47#55012yes—
350C22×C47#57512yes—
351C22×C47#57812yes—
352C22×C47C23×D411yescharacteristic
353C2×D47—42no—
354C2×D47—42no—
355C2×D47—42no—
356C2×D47—84no—
357C4×C47—22no—
358C4×C47—22no—
359C4×C47—22no—
360C4×C47—22no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—42no—
364C4×C47—42no—
365C4×C47—42no—
366C4×C47#55012yes—
367C4×C47C22×#4111yescharacteristic
368C4×C47C2×H(5,𝔽2)11yescharacteristic
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#556—471no—
373C2×#556D4711yescharacteristic, complemented
374#3402—4716no—
375C2×#497—471no—
376C2×#497—471no—
377C2×#495—471no—
378C2×#464—471no—
379C2×#464—471no—
380C2×#462—471no—
381C2×#462—471no—
382C2×#463—471no—
383C2×#463—471no—
384C2×#446—471no—
385C2×#440—471no—
386C2×#440—471no—
387C2×C4×Q16—471no—
388C2×C47—82no—
389C2×C47#340214yescomplemented
390C2×C47C2×#55011yescharacteristic
391C2×C47C2×#57511yescharacteristic
392C2×C47C2×#57811yescharacteristic
393D47—82no—
394C22×Q16—471no—
395C22×Q16—471no—
396C22×Q16—471no—
397C22×Q16—471no—
398C22×SD16—471no—
399C22×SD16—471no—
400C22×SD16—471no—
401C22×SD16—471no—
402C22×D8—471no—
403#556—24no—
404#556—478no—
405#556—944no—
406#556C2×D4718yescomplemented
407C2×C4⋊Q8—471no—
408C2×C4⋊Q8C2×D4711yescharacteristic
409C2×#126—21no—
410C2×#126—21no—
411C2×#126—941no—
412C2×#126—941no—
413C2×#124—471no—
414C2×#124—471no—
415C2×#124C2×D4711yescharacteristic
416C2×#124C2×D4711yescharacteristic
417C2×C22⋊Q8—21no—
418C2×C22⋊Q8—941no—
419C2×C4×Q8—471no—
420C2×C4×Q8—471no—
421C2×C4×Q8C2×D4711yescharacteristic
422C2×C4×Q8C2×D4711yescharacteristic
423C2×C4×Q8C2×D4711yescharacteristic
424C2×C4×D4—471no—
425C2×C4×D4C2×D4711yescharacteristic
426C2×#117—21no—
427C2×#117—941no—
428#497—478no—
429#497—478no—
430#495—478no—
431#464—478no—
432#464—478no—
433#463—478no—
434#463—478no—
435#462—478no—
436#462—478no—
437#446—478no—
438#440—478no—
439#440—478no—
440C4×Q16—478no—
441C2×#107—471no—
442C2×C4⋊C8—471no—
443C2×C4⋊C8—471no—
444C2×C4⋊C8—471no—
445C2×#103—471no—
446C2×#103—471no—
447C2×#103—471no—
448C2×#103—471no—
449C2×#102—471no—
450C2×#102—471no—
451C2×#97—471no—
452C2×#97—471no—
453C2×C4×C8—471no—
454C47C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—471no—
456C22×Q8—471no—
457C22×Q8C22⋊D4711yescharacteristic
458C22×Q8C22×D4711yescharacteristic
459C22×Q8C22×D4711yescharacteristic
460C22×D4—471no—
461C22×D4C22×D4711yescharacteristic
462C23×C4—21no—
463C23×C4—941no—
464C2×Q16—474no—
465C2×Q16—474no—
466C2×Q16—474no—
467C2×Q16—474no—
468C2×Q16—944no—
469C2×Q16—1882no—
470C2×Q16—1882no—
471C2×Q16—1882no—
472C2×SD16—474no—
473C2×SD16—474no—
474C2×SD16—474no—
475C2×SD16—474no—
476C2×SD16—944no—
477C2×SD16—944no—
478C2×SD16—1882no—
479C2×SD16—1882no—
480C2×D8—474no—
481C2×D8—1882no—
482C22×C8—471no—
483C22×C8—471no—
484C22×C8—471no—
485C22×C8—471no—
486C4⋊Q8—22no—
487C4⋊Q8—474no—
488C4⋊Q8—942no—
489C4⋊Q8C22×D4714yes—
490#126—28no—
491#126—28no—
492#126—948no—
493#126—948no—
494#124—22no—
495#124—22no—
496#124—474no—
497#124—474no—
498#124—942no—
499#124—942no—
500#124C22×D4714yes—
501#124C22×D4714yes—
502C22⋊Q8—28no—
503C22⋊Q8—948no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8—474no—
507C4×Q8—474no—
508C4×Q8—942no—
509C4×Q8—942no—
510C4×Q8C22⋊D4714yes—
511C4×Q8C22×D4714yes—
512C4×Q8C22×D4714yes—
513C4×Q8C22×D4714yes—
514C4×D4—22no—
515C4×D4—474no—
516C4×D4—942no—
517C4×D4C22×D4714yes—
518#117—28no—
519#117—948no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—471no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4C22⋊D4711yescharacteristic
530C2×C4⋊C4C22⋊D4711yescharacteristic
531C2×C4⋊C4C22⋊D4711yescharacteristic
532C2×C4⋊C4C22×D4711yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—941no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C22⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—941no—
546C2×C42—941no—
547C2×C42C22×D4711yescharacteristic
548C2×C42C22×D4711yescharacteristic
549C2×C42C22×D4711yescharacteristic
550#107—474no—
551C4⋊C8—474no—
552C4⋊C8—474no—
553C4⋊C8—474no—
554#103—474no—
555#103—474no—
556#103—474no—
557#103—474no—
558#102—474no—
559#102—474no—
560#97—474no—
561#97—474no—
562C4×C8—474no—
563C24—21no—
564C24—941no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—42no—
572C2×Q8—472no—
573C2×Q8—472no—
574C2×Q8—941no—
575C2×Q8—941no—
576C2×Q8—942no—
577C2×Q8—942no—
578C2×Q8—942no—
579C2×Q8—942no—
580C2×Q8C2×C22⋊D4714yes—
581C2×Q8C23×D4712yes—
582C2×Q8C23×D4712yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—472no—
587C2×D4—941no—
588C2×D4—942no—
589C2×D4—942no—
590C2×D4C23×D4712yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—944no—
600C22×C4—1884no—
601C22×C4C2×C22⋊D4711yescharacteristic
602C22×C4C2×C22⋊D4711yescharacteristic
603C22×C4C2×C22⋊D4711yescharacteristic
604C22×C4C2×C22⋊D4711yescharacteristic
605C22×C4C2×C22⋊D4711yescharacteristic
606C22×C4C2×C22⋊D4711yescharacteristic
607C22×C4C23×D4711yescharacteristic
608Q16—948no—
609Q16—1884no—
610Q16—1884no—
611Q16—1884no—
612SD16—948no—
613SD16—948no—
614SD16—1884no—
615SD16—1884no—
616D8—1884no—
617C2×C8—474no—
618C2×C8—472no—
619C2×C8—472no—
620C2×C8—472no—
621C2×C8—472no—
622C2×C8—942no—
623C2×C8—942no—
624C2×C8—942no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—21no—
630C4⋊C4—472no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—941no—
634C4⋊C4—944no—
635C4⋊C4—944no—
636C4⋊C4C2×C22⋊D4714yes—
637C4⋊C4C2×C22⋊D4714yes—
638C4⋊C4C2×C22⋊D4714yes—
639C4⋊C4C23×D4712yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—944no—
646C22⋊C4—944no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C42—24no—
651C42—24no—
652C42—944no—
653C42—944no—
654C42C2×C22⋊D4712yes—
655C42C2×C22⋊D4712yes—
656C42C2×C22⋊D4712yes—
657C42C23×D4712yes—
658C42C23×D4712yes—
659C42C23×D4712yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—942no—
665C23—1882no—
666C23—1882no—
667C23—1882no—
668C23C22×C22⋊D4711yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—44no—
674Q8—42no—
675Q8—42no—
676Q8—942no—
677Q8—942no—
678Q8—942no—
679Q8—942no—
680Q8—1882no—
681Q8—1882no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—942no—
686D4—942no—
687D4—1882no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—1888no—
705C2×C4—1882no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4C22×C22⋊D4712yes—
709C2×C4C22×C22⋊D4712yes—
710C2×C4C22×C22⋊D4712yes—
711C2×C4C22×C22⋊D4712yes—
712C2×C4C22×C22⋊D4712yes—
713C2×C4C22×C22⋊D4712yes—
714C2×C4C22×C22⋊D4711yescharacteristic
715C2×C4#41×D4712yes—
716C2×C4#1309407012yes—
717C2×C4C24×D4711yescharacteristic
718C8—474no—
719C8—942no—
720C8—942no—
721C8—942no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—3764no—
727C22—1882no—
728C22—1882no—
729C22—1882no—
730C22#1568979212yes—
731C22#1568992112yes—
732C22#1568993812yes—
733C22C23×C22⋊D4711yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—1882no—
744C4—1882no—
745C4—1882no—
746C4#1568979212yes—
747C4C2×#41×D4711yescharacteristic
748C4C2×#1309407011yescharacteristic
749C2—82no—
750C2—3762no—
751C2#2025646314yesdirect product factor
752C2C2×#1568979211yescharacteristic
753C2C2×#1568992111yescharacteristic
754C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#556C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
hypercenterC2×#556D47
hypocenterC47C2×#3402
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#15689846C2semidirect
2. #20256463C2direct (N × H)
3. C2×#15689518C2semidirect
4. C2×#15689515C2semidirect
6. C2×#15689345C2semidirect
7. C2×#15689342C2semidirect
8. C2×#15689333C2semidirect
9. C2×#15689330C2semidirect
12. C2×#15689254C2semidirect
13. C2×#15689223C2semidirect
14. C2×#15689221C2semidirect
15. C2×C4×#10625337C2semidirect
16. C2×C47×#556C2semidirect
27. #15689846C22semidirect
38. #15689518C22semidirect
39. #15689515C22semidirect
41. #15689345C22semidirect
42. #15689342C22semidirect
45. #15689333C22semidirect
46. #15689330C22semidirect
47. #15689254C22semidirect
48. #15689223C22semidirect
49. #15689221C22semidirect
50. C4×#10625337C22semidirect
65. C47×#556C22semidirect
373. C2×#556D47semidirect
389. C2×C47#3402semidirect
406. #556C2×D47semidirect
454. C47C2×#3402semidirect
751. C2#20256463direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898462
#202564632
C2×#156895182
C2×#156895152
C2×#156895052
C2×#156893452
C2×#156893422
C2×#156893332
C2×#156893302
C2×#156893382
C2×#156893352
C2×#156892542
C2×#156892232
C2×#156892212
C2×C4×#106253372
C2×C47×#5562
C2×#340247