Finite Group Databasebeta

← C2×#20253611 #27084551

Subgroups — C2×#20253611 #27084551

Order 12032.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689600C211yesmaximal, characteristic, complemented
2#20253611C2116yesmaximal, direct product factor
3C2×#15689461C211yesmaximal, characteristic, complemented
4C2×#15689444C211yesmaximal, characteristic
5C2×#15689415C211yesmaximal, characteristic, complemented
6C2×#15689405C211yesmaximal, characteristic, complemented
7C2×#15689342C211yesmaximal, characteristic, complemented
8C2×#15689342C211yesmaximal, characteristic, complemented
9C2×#15689278C211yesmaximal, characteristic, complemented
10C2×#15689261C211yesmaximal, characteristic
11C2×#15689228C211yesmaximal, characteristic, complemented
12C2×#15689223C211yesmaximal, characteristic, complemented
13C2×C4×#10625337C211yesmaximal, characteristic, complemented
14C2×C4×#10625335C211yesmaximal, characteristic, complemented
15C2×#15689184C211yesmaximal, characteristic, complemented
16C2×C47×#542C211yesmaximal, characteristic
17C23×Dic94C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625335C2211yescharacteristic
22#15689600—24no—
23#15689600C2218yescomplemented
24C2×C4×Dic94C2211yescharacteristic
25C2×C4×Dic94C2211yescharacteristic
26C2×C4×Dic94C2211yescharacteristic
27C2×C4×Dic94C2211yescharacteristic
28C2×#13093989—21no—
29C2×#13093989—21no—
30C2×#13093983C2211yescharacteristic
31C2×#13093980—21no—
32C2×#13093980—21no—
33#15689461C2218yescomplemented
34#15689444C2218yes—
35#15689415C2218yescomplemented
36#15689405C2218yescomplemented
37#15689342C2218yescomplemented
38#15689342C2218yescomplemented
39#15689278C2218yescomplemented
40#15689261C2218yes—
41#15689228C2218yescomplemented
42#15689223C2218yescomplemented
43C4×#10625337C2218yescomplemented
44C4×#10625335C2218yescomplemented
45#15689184C2218yescomplemented
46C2×#13093957C2211yescharacteristic
47C2×#13093957C2211yescharacteristic
48C2×#13093955C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×C4⋊(C47⋊C8)C2211yescharacteristic
51C2×C4⋊(C47⋊C8)C2211yescharacteristic
52C2×#13093948C2211yescharacteristic
53C2×#13093948C2211yescharacteristic
54C2×#13093947C2211yescharacteristic
55C2×#13093947C2211yescharacteristic
56C2×#13093947C2211yescharacteristic
57C2×#13093947C2211yescharacteristic
58C2×#13093945C2211yescharacteristic
59C2×#13093945C2211yescharacteristic
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#542—24no—
65C47×#542C2218yes—
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
77C22×Dic94—21no—
78C22×Dic94—22no—
79C22×Dic94—24no—
80C22×Dic94—24no—
81C22×Dic94C2314yes—
82C22×Dic94C2311yescharacteristic
83C22×Dic94C2311yescharacteristic
84C23×Dic47—21no—
85C2×#10625337—24no—
86C2×#10625337—24no—
87C2×#10625337C2314yes—
88C2×#10625337C2314yes—
89C2×#10625335—24no—
90C2×#10625335—24no—
91C2×#10625335C2314yes—
92C2×#10625335C2314yes—
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97C4×Dic94—22no—
98C4×Dic94—22no—
99C4×Dic94—22no—
100C4×Dic94—22no—
101C4×Dic94C2314yes—
102C4×Dic94C2314yes—
103C4×Dic94C2314yes—
104C4×Dic94C2314yes—
105#13093989—28no—
106#13093989—28no—
107#13093983—22no—
108#13093983C2314yes—
109#13093980—28no—
110#13093980—28no—
111C2×C4⋊Dic47C2311yescharacteristic
112C2×C4⋊Dic47C2311yescharacteristic
113C2×Dic47⋊C4—21no—
114C2×Dic47⋊C4—21no—
115C2×Dic47⋊C4—21no—
116C2×Dic47⋊C4—21no—
117C2×C22⋊Dic47—21no—
118C2×C4×Dic47—21no—
119C2×C4×Dic47—21no—
120C2×C4×Dic47—21no—
121C2×C4×Dic47—21no—
122C2×C4×Dic47—21no—
123#13093957C2314yes—
124#13093957C2314yes—
125#13093955C2314yes—
126#13093955C2314yes—
127C4⋊(C47⋊C8)C2314yes—
128C4⋊(C47⋊C8)C2314yes—
129#13093948C2314yes—
130#13093948C2314yes—
131#13093947C2314yes—
132#13093947C2314yes—
133#13093947C2314yes—
134#13093947C2314yes—
135#13093945C2314yes—
136#13093945C2314yes—
137C22⋊(C47⋊C8)C2314yes—
138C22⋊(C47⋊C8)C2314yes—
139#13093935C2314yes—
140C4×C47⋊C8C2314yes—
141C22×Q8×C47—21no—
142C22×Q8×C47C2311yescharacteristic
143C22×D4×C47—21no—
144C22×D4×C47C2311yescharacteristic
145C23×C4×C47—21no—
146C23×C4×C47C2311yescharacteristic
147C4⋊Q8×C47—22no—
148C4⋊Q8×C47C2314yes—
149#126×C47—28no—
150#124×C47—28no—
151#124×C47—22no—
152#124×C47C2314yes—
153#123×C47—28no—
154C22⋊Q8×C47—22no—
155C22⋊Q8×C47—28no—
156C22⋊Q8×C47C2314yes—
157#121×C47—22no—
158#121×C47C2314yes—
159C4×Q8×C47—22no—
160C4×Q8×C47C2314yes—
161C4×D4×C47—22no—
162C4×D4×C47C2314yes—
163#117×C47D414yes—
164#117×C47C2314yes—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47D411yescharacteristic
169C2×C4⋊C4×C47D411yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47D411yescharacteristic
178C2×C22⋊C4×C47D411yescharacteristic
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181C2×C42×C47C2311yescharacteristic
182C24×C47—21no—
183C24×C47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—24no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—82no—
189C2×Q8×C47C2412yes—
190C2×D4×C47—24no—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47—22no—
194C2×D4×C47—82no—
195C2×D4×C47C2412yes—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—24no—
202C22×C4×C47—82no—
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D412yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2411yescharacteristic
211C22×Dic47—28no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—24no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C2×Dic94—28no—
218C2×Dic94—216no—
219C2×Dic94—24no—
220C2×Dic94—21no—
221C2×Dic94—21no—
222C2×Dic94—22no—
223C2×Dic94—22no—
224C2×Dic94—28no—
225C2×Dic94—28no—
226C2×Dic94#4114yes—
227C2×Dic94#4114yes—
228C2×Dic94C2412yes—
229C2×Dic94C2412yes—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47—21no—
235C4⋊C4×C47C2×D414yes—
236C4⋊C4×C47C2×D414yes—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—24no—
241C22⋊C4×C47—24no—
242C22⋊C4×C47—24no—
243C22⋊C4×C47—24no—
244C22⋊C4×C47C2×D414yes—
245C22⋊C4×C47C2×D414yes—
246C42×C47—24no—
247C42×C47C2×D412yes—
248C42×C47C2×D412yes—
249C42×C47C2412yes—
250C42×C47C2412yes—
251C22⋊Dic47—24no—
252#10625337—28no—
253#10625337—28no—
254#10625335—28no—
255#10625335—28no—
256C4⋊Dic47—21no—
257C4⋊Dic47—21no—
258C4⋊Dic47C2412yes—
259C4⋊Dic47C2412yes—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264C4×Dic47—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8C2412yes—
274C2×C47⋊C8C2412yes—
275C2×C47⋊C8C2412yes—
276C2×C47⋊C8C2412yes—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—42no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D412yes—
285C23×C47C22×D411yescharacteristic
286Q8×C47—22no—
287Q8×C47—22no—
288Q8×C47—42no—
289Q8×C47—84no—
290D4×C47—22no—
291D4×C47—22no—
292D4×C47—42no—
293D4×C47—84no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—24no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—84no—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D412yes—
312C2×C4×C47C22×D412yes—
313C2×C4×C47C22×D412yes—
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C2×#4112yes—
316C2×C4×C47C2×#4112yes—
317C2×C4×C47C2511yescharacteristic
318C2×Dic47—216no—
319C2×Dic47—24no—
320C2×Dic47—24no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327Dic94—216no—
328Dic94—24no—
329Dic94—24no—
330Dic94—22no—
331Dic94—22no—
332Dic94C2×#4114yes—
333Dic94C2×#4114yes—
334C47⋊C8—22no—
335C47⋊C8—22no—
336C47⋊C8—22no—
337C47⋊C8—22no—
338C2×#3121—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—44no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—84no—
347C22×C47#52512yes—
348C22×C47#57712yes—
349C22×C47#57812yes—
350C22×C47C23×D411yescharacteristic
351C4×C47—22no—
352C4×C47—22no—
353C4×C47—22no—
354C4×C47—22no—
355C4×C47—22no—
356C4×C47—42no—
357C4×C47—42no—
358C4×C47—42no—
359C4×C47#52512yes—
360C4×C47C22×#4111yescharacteristic
361C4×C47C22×#4111yescharacteristic
362Dic47—24no—
363Dic47—24no—
364Dic47—42no—
365Dic47—42no—
366C2×#542D4711yescharacteristic
367C2×#519—471no—
368#3121—4716no—
369C2×#485—471no—
370C2×#482—471no—
371C2×#477—471no—
372C2×#475—471no—
373C2×#464—471no—
374C2×#464—471no—
375C2×#451—471no—
376C2×#448—471no—
377C2×#441—471no—
378C2×#440—471no—
379C2×C4×Q16—471no—
380C2×C4×SD16—471no—
381C2×#433—471no—
382C2×C47—42no—
383C2×C47—82no—
384C2×C47#312114yescomplemented
385C2×C47C2×#52511yescharacteristic
386C2×C47C2×#57711yescharacteristic
387C2×C47C2×#57811yescharacteristic
388C23×Q8—471no—
389C22×Q16—471no—
390C22×Q16—471no—
391C22×SD16—471no—
392C22×SD16—471no—
393#542—24no—
394#542C2×D4718yes—
395C2×C4⋊Q8C2×D4711yescharacteristic
396C2×#126—21no—
397C2×#124—21no—
398C2×#124C2×D4711yescharacteristic
399C2×#123—21no—
400C2×C22⋊Q8—21no—
401C2×C22⋊Q8C2×D4711yescharacteristic
402C2×#121C2×D4711yescharacteristic
403#519—478no—
404#519—944no—
405C2×C4×Q8—471no—
406C2×C4×Q8—471no—
407C2×C4×Q8—471no—
408C2×C4×Q8—471no—
409C2×C4×Q8—941no—
410C2×C4×Q8—941no—
411C2×C4×Q8C2×D4711yescharacteristic
412C2×C4×D4C2×D4711yescharacteristic
413C2×#117—471no—
414C2×#117—941no—
415C2×#117—941no—
416C2×#117C2×D4711yescharacteristic
417#485—478no—
418#482—478no—
419#477—478no—
420#475—478no—
421#464—478no—
422#464—478no—
423#451—478no—
424#448—478no—
425#441—478no—
426#440—478no—
427C4×Q16—478no—
428C4×SD16—478no—
429#433—478no—
430C2×#107—471no—
431C2×#107—471no—
432C2×#106—471no—
433C2×#106—471no—
434C2×C4⋊C8—471no—
435C2×C4⋊C8—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#103—471no—
439C2×#103—471no—
440C2×#103—471no—
441C2×#103—471no—
442C2×#102—471no—
443C2×#102—471no—
444C2×C22⋊C8—471no—
445C2×C22⋊C8—471no—
446C2×#97—471no—
447C2×C4×C8—471no—
448C47C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—21no—
450C22×Q8—471no—
451C22×Q8—471no—
452C22×Q8—474no—
453C22×Q8—944no—
454C22×Q8—944no—
455C22×Q8—941no—
456C22×Q8—942no—
457C22×Q8C22×D4711yescharacteristic
458C22×D4—21no—
459C22×D4C22×D4711yescharacteristic
460C23×C4—21no—
461C23×C4—941no—
462C23×C4C22×D4711yescharacteristic
463C2×Q16—474no—
464C2×Q16—474no—
465C2×Q16—944no—
466C2×Q16—944no—
467C2×SD16—474no—
468C2×SD16—474no—
469C2×SD16—944no—
470C2×SD16—944no—
471C22×C8—471no—
472C22×C8—471no—
473C22×C8—471no—
474C22×C8—471no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D4714yes—
477#126—28no—
478#124—28no—
479#124—22no—
480#124C22×D4714yes—
481#123—28no—
482C22⋊Q8—22no—
483C22⋊Q8—28no—
484C22⋊Q8C22×D4714yes—
485#121—22no—
486#121C22×D4714yes—
487C4×Q8—22no—
488C4×Q8—474no—
489C4×Q8—474no—
490C4×Q8—474no—
491C4×Q8—474no—
492C4×Q8—948no—
493C4×Q8—948no—
494C4×Q8—942no—
495C4×Q8—942no—
496C4×Q8—942no—
497C4×Q8—942no—
498C4×Q8C22×D4714yes—
499C4×D4—22no—
500C4×D4C22×D4714yes—
501#117—474no—
502#117—942no—
503#117—948no—
504#117—948no—
505#117C22⋊D4714yes—
506#117C22×D4714yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—471no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4C22⋊D4711yescharacteristic
517C2×C4⋊C4C22⋊D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C4⋊C4C22×D4711yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4C22⋊D4711yescharacteristic
527C2×C22⋊C4C22⋊D4711yescharacteristic
528C2×C42—21no—
529C2×C42—941no—
530C2×C42—941no—
531C2×C42—941no—
532C2×C42—941no—
533C2×C42—941no—
534C2×C42C22×D4711yescharacteristic
535C2×C42C22×D4711yescharacteristic
536#107—474no—
537#107—474no—
538#106—474no—
539#106—474no—
540C4⋊C8—474no—
541C4⋊C8—474no—
542#103—474no—
543#103—474no—
544#103—474no—
545#103—474no—
546#103—474no—
547#103—474no—
548#102—474no—
549#102—474no—
550C22⋊C8—474no—
551C22⋊C8—474no—
552#97—474no—
553C4×C8—474no—
554C24—21no—
555C24C2×C22⋊D4711yescharacteristic
556C2×Q8—21no—
557C2×Q8—24no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—82no—
561C2×Q8—474no—
562C2×Q8—474no—
563C2×Q8—472no—
564C2×Q8—472no—
565C2×Q8—948no—
566C2×Q8—948no—
567C2×Q8—948no—
568C2×Q8—9416no—
569C2×Q8—944no—
570C2×Q8—941no—
571C2×Q8—941no—
572C2×Q8—942no—
573C2×Q8—942no—
574C2×Q8C23×D4712yes—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—82no—
580C2×D4C23×D4712yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—82no—
588C22×C4—948no—
589C22×C4—944no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4C2×C22⋊D4712yes—
595C22×C4C2×C22⋊D4711yescharacteristic
596C22×C4C2×C22⋊D4711yescharacteristic
597C22×C4C2×C22⋊D4711yescharacteristic
598C22×C4C2×C22⋊D4711yescharacteristic
599C22×C4C2×C22⋊D4711yescharacteristic
600C22×C4C23×D4712yes—
601C22×C4C23×D4711yescharacteristic
602Q16—948no—
603Q16—948no—
604SD16—948no—
605SD16—948no—
606C2×C8—472no—
607C2×C8—472no—
608C2×C8—472no—
609C2×C8—472no—
610C2×C8—942no—
611C2×C8—942no—
612C2×C8—942no—
613C2×C8—942no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—472no—
620C4⋊C4—472no—
621C4⋊C4—944no—
622C4⋊C4—944no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—941no—
626C4⋊C4—941no—
627C4⋊C4C2×C22⋊D4714yes—
628C4⋊C4C2×C22⋊D4714yes—
629C4⋊C4C23×D4712yes—
630C4⋊C4C23×D4712yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—944no—
637C22⋊C4C2×C22⋊D4714yes—
638C22⋊C4C2×C22⋊D4714yes—
639C42—24no—
640C42—944no—
641C42—944no—
642C42—944no—
643C42—944no—
644C42—944no—
645C42C2×C22⋊D4712yes—
646C42C2×C22⋊D4712yes—
647C42C23×D4712yes—
648C42C23×D4712yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C22×C22⋊D4712yes—
657C23C22×C22⋊D4711yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—84no—
662Q8—474no—
663Q8—474no—
664Q8—9416no—
665Q8—944no—
666Q8—944no—
667Q8—942no—
668Q8—942no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—84no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—9416no—
689C2×C4—944no—
690C2×C4—944no—
691C2×C4—942no—
692C2×C4—942no—
693C2×C4—942no—
694C2×C4—942no—
695C2×C4—1882no—
696C2×C4—1882no—
697C2×C4C22×C22⋊D4712yes—
698C2×C4C22×C22⋊D4712yes—
699C2×C4C22×C22⋊D4712yes—
700C2×C4C22×C22⋊D4712yes—
701C2×C4C22×C22⋊D4712yes—
702C2×C4C22×C22⋊D4711yescharacteristic
703C2×C4#41×D4712yes—
704C2×C4#41×D4712yes—
705C2×C4C24×D4711yescharacteristic
706C8—942no—
707C8—942no—
708C8—942no—
709C8—942no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22#1568963012yes—
719C22#1568993412yes—
720C22#1568993812yes—
721C22C23×C22⋊D4711yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—944no—
731C4—944no—
732C4—1882no—
733C4—1882no—
734C4#1568963012yes—
735C4C2×#41×D4711yescharacteristic
736C4C2×#41×D4711yescharacteristic
737C2—42no—
738C2—82no—
739C2#2025361114yesdirect product factor
740C2C2×#1568963011yescharacteristic
741C2C2×#1568993411yescharacteristic
742C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#542C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
hypercenterC2×#542D47
hypocenterC47C2×#3121
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×#15689600C2semidirect
2. #20253611C2direct (N × H)
3. C2×#15689461C2semidirect
5. C2×#15689415C2semidirect
6. C2×#15689405C2semidirect
7. C2×#15689342C2semidirect
8. C2×#15689342C2semidirect
9. C2×#15689278C2semidirect
11. C2×#15689228C2semidirect
12. C2×#15689223C2semidirect
13. C2×C4×#10625337C2semidirect
14. C2×C4×#10625335C2semidirect
15. C2×#15689184C2semidirect
23. #15689600C22semidirect
33. #15689461C22semidirect
35. #15689415C22semidirect
36. #15689405C22semidirect
37. #15689342C22semidirect
38. #15689342C22semidirect
39. #15689278C22semidirect
41. #15689228C22semidirect
42. #15689223C22semidirect
43. C4×#10625337C22semidirect
44. C4×#10625335C22semidirect
45. #15689184C22semidirect
384. C2×C47#3121semidirect
448. C47C2×#3121semidirect
739. C2#20253611direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896002
#202536112
C2×#156894612
C2×#156894442
C2×#156894152
C2×#156894052
C2×#156893422
C2×#156892782
C2×#156892612
C2×#156892282
C2×#156892232
C2×C4×#106253372
C2×C4×#106253352
C2×#156891842
C2×C47×#5422
C2×#312147