Finite Group Databasebeta

← C2×#20253473 #27084366

Subgroups — C2×#20253473 #27084366

Order 12032.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689658C211yesmaximal, characteristic
2C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
3#20253473C2116yesmaximal, direct product factor
4C2×#15689455C211yesmaximal, characteristic, complemented
5C2×#15689438C211yesmaximal, characteristic
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689346C211yesmaximal, characteristic, complemented
8C2×#15689345C211yesmaximal, characteristic, complemented
9C2×#15689280C211yesmaximal, characteristic, complemented
10C2×#15689263C211yesmaximal, characteristic
11C2×#15689217C211yesmaximal, characteristic, complemented
12C2×#15689215C211yesmaximal, characteristic, complemented
13C2×#15689210C211yesmaximal, characteristic, complemented
14C2×#15689208C211yesmaximal, characteristic, complemented
15C2×#15689175C211yesmaximal, characteristic, complemented
16C2×C47×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625336C2211yescharacteristic
22#15689658—24no—
23#15689658C2218yes—
24C2×#13094019—21no—
25C2×#13094012C2211yescharacteristic
26C2×#13094009—21no—
27C2×#13094004C2211yescharacteristic
28C2×#13093999C2211yescharacteristic
29C2×Q8×Dic47C2211yescharacteristic
30C2×C4×Dic94—21no—
31C2×C4×Dic94C2211yescharacteristic
32C2×#13093989—21no—
33C2×#13093989C2211yescharacteristic
34C2×#13093989C2211yescharacteristic
35C4×Q8×D47—24no—
36C4×Q8×D47C2218yescomplemented
37C2×#13093986—21no—
38C2×#13093986C2211yescharacteristic
39C2×#13093982—21no—
40C2×C4⋊C4×D47—21no—
41C2×C4⋊C4×D47C2211yescharacteristic
42C2×C42×D47—21no—
43C2×C42×D47C2211yescharacteristic
44#15689455C2218yescomplemented
45#15689438C2218yes—
46#15689427C2218yescomplemented
47#15689346C2218yescomplemented
48#15689345C2218yescomplemented
49#15689280C2218yescomplemented
50#15689263C2218yes—
51#15689217C2218yescomplemented
52#15689215C2218yescomplemented
53#15689210C2218yescomplemented
54#15689208C2218yescomplemented
55#15689175C2218yescomplemented
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C47×#479C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C2×Q8×D47—24no—
81C2×Q8×D47—22no—
82C2×Q8×D47—24no—
83C2×Q8×D47C2314yes—
84C22×D188—21no—
85C22×D188C2311yescharacteristic
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47D411yescharacteristic
90C22×C4×D47D411yescharacteristic
91C22×C4×D47C2311yescharacteristic
92C2×Dic188—24no—
93C2×Dic188C2314yes—
94C2×#10625337—24no—
95C2×#10625337C2314yes—
96C2×#10625325—24no—
97C2×#10625325C2314yes—
98C2×#10625336—24no—
99C2×#10625336C2314yes—
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102#13094019—28no—
103#13094012—22no—
104#13094012C2314yes—
105#13094009—28no—
106#13094004—22no—
107#13094004C2314yes—
108#13093999—22no—
109#13093999C2314yes—
110Q8×Dic47—22no—
111Q8×Dic47C2314yes—
112C4×Dic94—22no—
113C4×Dic94—28no—
114C4×Dic94C2314yes—
115#13093989—22no—
116#13093989—28no—
117#13093989—22no—
118#13093989C2314yes—
119#13093989C2314yes—
120#13093986—28no—
121#13093986—22no—
122#13093986C2314yes—
123#13093982—28no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C4⋊C4×D47—28no—
132C4⋊C4×D47—22no—
133C4⋊C4×D47C2314yes—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47D411yescharacteristic
144C2×C4×Dic47D411yescharacteristic
145C2×C4×Dic47C2311yescharacteristic
146C42×D47—28no—
147C42×D47D414yes—
148C42×D47C2314yes—
149#13093957C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152#13093949C2314yes—
153#13093947C2314yes—
154#13093947C2314yes—
155#13093947C2314yes—
156#13093946C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160C8×Dic47C2314yes—
161C8×Dic47C2314yes—
162C22×Q8×C47C2311yescharacteristic
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165#125×C47—22no—
166#125×C47C2314yes—
167C4×Q8×C47—22no—
168C4×Q8×C47C2314yes—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C42×C47—21no—
176C2×C42×C47C2311yescharacteristic
177#107×C47C2314yes—
178#106×C47C2314yes—
179C4⋊C8×C47C2314yes—
180#103×C47C2314yes—
181#103×C47C2314yes—
182C23×D47—21no—
183C23×D47C2×D411yescharacteristic
184C2×Q8×C47—21no—
185C2×Q8×C47—22no—
186C2×Q8×C47#4114yes—
187C2×Q8×C47C2412yes—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2411yescharacteristic
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47C2×D411yescharacteristic
199C22×Dic47C2×D411yescharacteristic
200C22×Dic47C2×D411yescharacteristic
201Q8×D47—216no—
202Q8×D47—28no—
203Q8×D47—28no—
204C2×D188—22no—
205C2×D188—22no—
206C2×D188—24no—
207C2×D188—21no—
208C2×D188—44no—
209C2×D188C2412yes—
210C2×C4×D47—28no—
211C2×C4×D47—24no—
212C2×C4×D47—24no—
213C2×C4×D47—22no—
214C2×C4×D47—22no—
215C2×C4×D47—24no—
216C2×C4×D47—24no—
217C2×C4×D47—24no—
218C2×C4×D47—44no—
219C2×C4×D47—44no—
220C2×C4×D47C2×D414yes—
221C2×C4×D47C2×D412yes—
222C2×C4×D47C2×D414yes—
223C2×C4×D47C2412yes—
224C2×Dic94—28no—
225C2×Dic94—21no—
226C2×Dic94—22no—
227C2×Dic94—24no—
228C2×Dic94—22no—
229C2×Dic94—22no—
230C2×Dic94—21no—
231C2×Dic94#4114yes—
232C2×Dic94C2412yes—
233C2×Dic94C2412yes—
234C2×C8×C47—22no—
235C2×C8×C47—22no—
236C2×C8×C47C2412yes—
237C2×C8×C47C2412yes—
238C4⋊C4×C47—24no—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—21no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47C2412yes—
245C4⋊C4×C47C2412yes—
246C4⋊C4×C47C2412yes—
247C42×C47—24no—
248C42×C47C2×D412yes—
249C42×C47C2412yes—
250#10625337—28no—
251#10625336—28no—
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—
257C4⋊Dic47—21no—
258C4⋊Dic47—24no—
259C4⋊Dic47—24no—
260C4⋊Dic47C2412yes—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265C4×Dic47—24no—
266C4×Dic47—24no—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C4×Dic47C2×D412yes—
270C4×Dic47C2×D414yes—
271C4×Dic47C2×D414yes—
272C4×Dic47C2412yes—
273C2×C47⋊C8—22no—
274C2×C47⋊C8—22no—
275C2×C47⋊C8C2412yes—
276C2×C47⋊C8C2412yes—
277Dic188—28no—
278#10625325—28no—
279C23×C47C22×D411yescharacteristic
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47#13514yes—
287C22×D47C22×D412yes—
288Q8×C47—24no—
289Q8×C47—22no—
290Q8×C47C2×#4114yes—
291C2×C4×C47—24no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—42no—
299C2×C4×C47—42no—
300C2×C4×C47—42no—
301C2×C4×C47C22×D412yes—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C2×#4112yes—
305C2×C4×C47C2×#4112yes—
306C2×C4×C47C2511yescharacteristic
307C2×Dic47—22no—
308C2×Dic47—24no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47#13714yes—
316C2×Dic47C22×D412yes—
317C2×Dic47C22×D412yes—
318C2×Dic47C22×D412yes—
319D188—22no—
320D188—22no—
321D188—48no—
322D188—42no—
323C4×D47—216no—
324C4×D47—28no—
325C4×D47—24no—
326C4×D47—22no—
327C4×D47—22no—
328C4×D47—28no—
329C4×D47—48no—
330C4×D47—48no—
331Dic94—216no—
332Dic94—24no—
333Dic94—22no—
334Dic94—22no—
335Dic94—22no—
336Dic94—42no—
337Dic94C2×#4114yes—
338C8×C47—22no—
339C8×C47—22no—
340C47⋊C8—22no—
341C47⋊C8—22no—
342C2×#3108—471nomaximal, Sylow
343C22×C47#52512yes—
344C22×C47C2×#13512yes—
345C22×C47C2×#13712yes—
346C22×C47C23×D411yescharacteristic
347C2×D47—28no—
348C2×D47—22no—
349C2×D47—22no—
350C2×D47—42no—
351C2×D47—42no—
352C2×D47—42no—
353C2×D47—84no—
354C2×D47C2×#13514yes—
355C4×C47—24no—
356C4×C47—22no—
357C4×C47—22no—
358C4×C47—42no—
359C4×C47—42no—
360C4×C47—42no—
361C4×C47#52512yes—
362C4×C47C22×#4111yescharacteristic
363C4×C47C22×#4111yescharacteristic
364Dic47—22no—
365Dic47—24no—
366Dic47—22no—
367Dic47—42no—
368Dic47—42no—
369Dic47C2×#13714yes—
370C2×#529—471no—
371C22×C4×Q8—471no—
372#3108—4716no—
373C2×#483—471no—
374C2×#480—471no—
375C2×#479—471no—
376C2×#479D4711yescharacteristic, complemented
377C2×#464—471no—
378C2×#464—471no—
379C2×#451—471no—
380C2×#448—471no—
381C2×C4×Q16—471no—
382C2×C4×Q16—471no—
383C2×C4×SD16—471no—
384C2×C4×SD16—471no—
385C2×#431—471no—
386C2×C47#310814yescomplemented
387C2×C47C2×#52511yescharacteristic
388C2×C47C22×#13511yescharacteristic
389C2×C47C22×#13711yescharacteristic
390D47—24no—
391D47—82no—
392C23×Q8—471no—
393C22×Q16—471no—
394C22×Q16—471no—
395C22×SD16—471no—
396C22×SD16—471no—
397#529—478no—
398#529—944no—
399C2×#126—941no—
400C2×#125C2×D4711yescharacteristic
401C2×#124—471no—
402C2×#123—941no—
403C2×C22⋊Q8—471no—
404C2×#121—471no—
405C2×C4×Q8—471no—
406C2×C4×Q8—478no—
407C2×C4×Q8—471no—
408C2×C4×Q8—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8—941no—
411C2×C4×Q8—941no—
412C2×C4×Q8—944no—
413C2×C4×Q8C2×D4711yescharacteristic
414C2×C4×D4—471no—
415C2×C4×D4—941no—
416C2×#117—941no—
417C22×C4⋊C4—471no—
418C22×C4⋊C4—941no—
419C22×C42—471no—
420C22×C42—941no—
421#483—478no—
422#480—478no—
423#479—478no—
424#479C2×D4718yescomplemented
425#464—478no—
426#464—478no—
427#451—478no—
428#448—478no—
429C4×Q16—478no—
430C4×Q16—478no—
431C4×SD16—478no—
432C4×SD16—478no—
433#431—478no—
434C2×#107—471no—
435C2×#107C2×D4711yescharacteristic
436C2×#106—471no—
437C2×#106C2×D4711yescharacteristic
438C2×C4⋊C8—471no—
439C2×C4⋊C8C2×D4711yescharacteristic
440C2×#103—471no—
441C2×#103—471no—
442C2×#103—471no—
443C2×#103—471no—
444C2×#103C2×D4711yescharacteristic
445C2×#103C2×D4711yescharacteristic
446C2×#102—471no—
447C2×#102—471no—
448C2×C22⋊C8—471no—
449C2×C22⋊C8—471no—
450C2×C4×C8—471no—
451C2×C4×C8—471no—
452C47C2×#310811yescharacteristic, complemented, Sylow
453C22×Q8—474no—
454C22×Q8—471no—
455C22×Q8—471no—
456C22×Q8—941no—
457C22×Q8—942no—
458C22×Q8—944no—
459C22×Q8—944no—
460C22×Q8C22×D4711yescharacteristic
461C22×D4—471no—
462C22×D4—941no—
463C23×C4—471no—
464C23×C4—471no—
465C23×C4—471no—
466C23×C4—941no—
467C23×C4—941no—
468C23×C4—941no—
469C2×Q16—474no—
470C2×Q16—474no—
471C2×Q16—944no—
472C2×Q16—944no—
473C2×SD16—474no—
474C2×SD16—474no—
475C2×SD16—944no—
476C2×SD16—944no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8C22×D4711yescharacteristic
480C22×C8C22×D4711yescharacteristic
481#126—948no—
482#125—22no—
483#125C22×D4714yes—
484#124—474no—
485#124—942no—
486#123—948no—
487C22⋊Q8—474no—
488C22⋊Q8—942no—
489#121—474no—
490#121—942no—
491C4×Q8—22no—
492C4×Q8—474no—
493C4×Q8—474no—
494C4×Q8—474no—
495C4×Q8—474no—
496C4×Q8—948no—
497C4×Q8—948no—
498C4×Q8—942no—
499C4×Q8—942no—
500C4×Q8—942no—
501C4×Q8—942no—
502C4×Q8C22×D4714yes—
503C4×D4—474no—
504C4×D4—942no—
505C4×D4—948no—
506#117—948no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—471no—
511C2×C4⋊C4—474no—
512C2×C4⋊C4—942no—
513C2×C4⋊C4—948no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4C22×D4711yescharacteristic
521C2×C4⋊C4C22×D4711yescharacteristic
522C2×C4⋊C4C22×D4711yescharacteristic
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4—941no—
527C2×C22⋊C4—941no—
528C2×C42—21no—
529C2×C42—471no—
530C2×C42—471no—
531C2×C42—471no—
532C2×C42—474no—
533C2×C42—474no—
534C2×C42—948no—
535C2×C42—941no—
536C2×C42—941no—
537C2×C42—941no—
538C2×C42—941no—
539C2×C42C22×D4711yescharacteristic
540#107—474no—
541#107C22×D4714yes—
542#106—474no—
543#106C22×D4714yes—
544C4⋊C8—474no—
545C4⋊C8C22×D4714yes—
546#103—474no—
547#103—474no—
548#103—474no—
549#103—474no—
550#103C22×D4714yes—
551#103C22×D4714yes—
552#102—474no—
553#102—474no—
554C22⋊C8—474no—
555C22⋊C8—474no—
556C4×C8—474no—
557C4×C8—474no—
558C24—471no—
559C24—941no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—474no—
563C2×Q8—472no—
564C2×Q8—472no—
565C2×Q8—944no—
566C2×Q8—948no—
567C2×Q8—948no—
568C2×Q8—9416no—
569C2×Q8—948no—
570C2×Q8—941no—
571C2×Q8—941no—
572C2×Q8—942no—
573C2×Q8—942no—
574C2×Q8—942no—
575C2×Q8#1062535414yes—
576C2×Q8C23×D4712yes—
577C2×D4—472no—
578C2×D4—944no—
579C2×D4—941no—
580C2×D4—942no—
581C2×D4—942no—
582C2×D4—1884no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—471no—
588C22×C4—471no—
589C22×C4—471no—
590C22×C4—474no—
591C22×C4—474no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—944no—
595C22×C4—944no—
596C22×C4—944no—
597C22×C4—944no—
598C22×C4—948no—
599C22×C4—944no—
600C22×C4—941no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—1884no—
606C22×C4—1884no—
607C22×C4D4×D4711yescharacteristic
608C22×C4D4×D4711yescharacteristic
609C22×C4C23×D4711yescharacteristic
610Q16—948no—
611Q16—948no—
612SD16—948no—
613SD16—948no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—472no—
617C2×C8—472no—
618C2×C8—942no—
619C2×C8—942no—
620C2×C8C23×D4712yes—
621C2×C8C23×D4712yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—472no—
629C4⋊C4—944no—
630C4⋊C4—944no—
631C4⋊C4—944no—
632C4⋊C4—944no—
633C4⋊C4—944no—
634C4⋊C4—944no—
635C4⋊C4—941no—
636C4⋊C4C23×D4712yes—
637C4⋊C4C23×D4712yes—
638C4⋊C4C23×D4712yes—
639C22⋊C4—944no—
640C22⋊C4—944no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C42—24no—
645C42—474no—
646C42—472no—
647C42—474no—
648C42—472no—
649C42—944no—
650C42—944no—
651C42—944no—
652C42—944no—
653C42D4×D4712yes—
654C42C23×D4712yes—
655C23—474no—
656C23—472no—
657C23—942no—
658C23—942no—
659C23—942no—
660C23—1882no—
661C23—1882no—
662C23—1882no—
663C23C2×D4×D4711yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—474no—
667Q8—9416no—
668Q8—944no—
669Q8—942no—
670Q8—942no—
671Q8—942no—
672Q8—1882no—
673Q8C2×#1062535414yes—
674D4—942no—
675D4—942no—
676D4—1888no—
677D4—1882no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—474no—
689C2×C4—472no—
690C2×C4—472no—
691C2×C4—472no—
692C2×C4—948no—
693C2×C4—948no—
694C2×C4—9416no—
695C2×C4—942no—
696C2×C4—944no—
697C2×C4—942no—
698C2×C4—942no—
699C2×C4—944no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—1888no—
705C2×C4—1888no—
706C2×C4—1882no—
707C2×C4—1882no—
708C2×C4C2×D4×D4712yes—
709C2×C4C2×D4×D4712yes—
710C2×C4C2×D4×D4711yescharacteristic
711C2×C4#41×D4712yes—
712C2×C4C2×#1062535412yes—
713C2×C4C24×D4711yescharacteristic
714C8—22no—
715C8—22no—
716C8—942no—
717C8—942no—
718C22—474no—
719C22—948no—
720C22—942no—
721C22—942no—
722C22—3764no—
723C22—1882no—
724C22—1882no—
725C22—1882no—
726C22#1568963612yes—
727C22#135×D4712yes—
728C22#137×D4712yes—
729C22C22×D4×D4711yescharacteristic
730C4—22no—
731C4—22no—
732C4—24no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—474no—
737C4—942no—
738C4—942no—
739C4—944no—
740C4—1882no—
741C4—1882no—
742C4#1568963612yes—
743C4C2×#41×D4711yescharacteristic
744C4C22×#1062535411yescharacteristic
745C2—944no—
746C2—3762no—
747C2#2025347314yesdirect product factor
748C2C2×#1568963611yescharacteristic
749C2C2×#135×D4711yescharacteristic
750C2C2×#137×D4711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#479C2
socleC23×C47C22×D4
prime radicalC2×#13093999C22
hypercenterC2×#479D47
hypocenterC47C2×#3108
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D47C2semidirect
3. #20253473C2direct (N × H)
4. C2×#15689455C2semidirect
6. C2×#15689427C2semidirect
7. C2×#15689346C2semidirect
8. C2×#15689345C2semidirect
9. C2×#15689280C2semidirect
11. C2×#15689217C2semidirect
12. C2×#15689215C2semidirect
13. C2×#15689210C2semidirect
14. C2×#15689208C2semidirect
15. C2×#15689175C2semidirect
16. C2×C47×#479C2semidirect
36. C4×Q8×D47C22semidirect
44. #15689455C22semidirect
46. #15689427C22semidirect
47. #15689346C22semidirect
48. #15689345C22semidirect
49. #15689280C22semidirect
51. #15689217C22semidirect
52. #15689215C22semidirect
53. #15689210C22semidirect
54. #15689208C22semidirect
55. #15689175C22semidirect
71. C47×#479C22semidirect
376. C2×#479D47semidirect
386. C2×C47#3108semidirect
424. #479C2×D47semidirect
452. C47C2×#3108semidirect
747. C2#20253473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896582
C2×C4×Q8×D472
#202534732
C2×#156894552
C2×#156894382
C2×#156894272
C2×#156893462
C2×#156893452
C2×#156892802
C2×#156892632
C2×#156892172
C2×#156892152
C2×#156892102
C2×#156892082
C2×#156891752
C2×C47×#4792
C2×#310847