Finite Group Databasebeta

← C2×#20254641 #27088467

Subgroups — C2×#20254641 #27088467

Order 12032.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689728C211yesmaximal, characteristic
2#20254641C2116yesmaximal, direct product factor
3C2×#15689529C211yesmaximal, characteristic, complemented
4C2×#15689522C211yesmaximal, characteristic, complemented
5C2×#15689489C211yesmaximal, characteristic, complemented
6C2×#15689471C211yesmaximal, characteristic, complemented
7C2×#15689441C211yesmaximal, characteristic, complemented
8C2×#15689447C211yesmaximal, characteristic, complemented
9C2×#15689447C211yesmaximal, characteristic, complemented
10C2×#15689436C211yesmaximal, characteristic, complemented
11C2×#15689420C211yesmaximal, characteristic, complemented
12C2×#15689420C211yesmaximal, characteristic, complemented
13C2×#15689410C211yesmaximal, characteristic, complemented
14C2×#15689400C211yesmaximal, characteristic, complemented
15C2×#15689184C211yesmaximal, characteristic, complemented
16C2×C47×#544C211yesmaximal, characteristic, complemented
17#15689728—24no—
18#15689728C2218yes—
19C2×#13094021C2211yescharacteristic
20C2×#13094016C2211yescharacteristic
21C2×#13094009—21no—
22C2×#13094009—21no—
23C2×#13093998C2211yescharacteristic
24C2×#13093998C2211yescharacteristic
25C2×#13093997—21no—
26C2×#13093997—21no—
27C2×C4×D188C2211yescharacteristic
28C2×C4×D188C2211yescharacteristic
29#15689529C2218yescomplemented
30#15689522C2218yescomplemented
31#15689489C2218yescomplemented
32#15689471C2218yescomplemented
33#15689447C2218yescomplemented
34#15689447C2218yescomplemented
35#15689441C2218yescomplemented
36#15689436C2218yescomplemented
37#15689420C2218yescomplemented
38#15689420C2218yescomplemented
39#15689410C2218yescomplemented
40#15689400C2218yescomplemented
41#15689184C2218yescomplemented
42C2×#13093957C2211yescharacteristic
43C2×#13093957C2211yescharacteristic
44C2×#13093957C2211yescharacteristic
45C2×#13093957C2211yescharacteristic
46C2×#13093955C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×#13093955C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×C4⋊(C47⋊C8)C2211yescharacteristic
51C2×C4⋊(C47⋊C8)C2211yescharacteristic
52C2×#13093944C2211yescharacteristic
53C2×#13093944C2211yescharacteristic
54C2×#13093944C2211yescharacteristic
55C2×#13093944C2211yescharacteristic
56C2×#13093944C2211yescharacteristic
57C2×#13093944C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#544—24no—
65C47×#544C2218yescomplemented
66C2×C4⋊Q8×C47—21no—
67C2×C4⋊Q8×C47C2211yescharacteristic
68C2×C4⋊Q8×C47C2211yescharacteristic
69C2×#125×C47—21no—
70C2×#125×C47C2211yescharacteristic
71C2×#125×C47C2211yescharacteristic
72C2×C22⋊Q8×C47—21no—
73C2×C22⋊Q8×C47—21no—
74C2×#117×C47C2211yescharacteristic
75C2×#117×C47C2211yescharacteristic
76C22×C4⋊C4×C47C2211yescharacteristic
77C22×D188—21no—
78C22×D188—21no—
79C22×D188C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C22×C4×D47—21no—
84C22×C4×D47—21no—
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87C22×C47⋊C8C2311yescharacteristic
88C22×C47⋊C8C2311yescharacteristic
89#13094021—22no—
90#13094021C2314yes—
91#13094016—22no—
92#13094016C2314yes—
93#13094009—28no—
94#13094009—28no—
95#13093998—22no—
96#13093998—22no—
97#13093998C2314yes—
98#13093998C2314yes—
99#13093997—28no—
100#13093997—28no—
101C4×D188—22no—
102C4×D188—22no—
103C4×D188C2314yes—
104C4×D188C2314yes—
105C2×C4⋊Dic47C2311yescharacteristic
106C2×C4⋊Dic47C2311yescharacteristic
107C2×Dic47⋊C4—21no—
108C2×Dic47⋊C4—21no—
109C2×(C2×D47)⋊C4—21no—
110C2×(C2×D47)⋊C4—21no—
111C2×(C2×D47)⋊C4—21no—
112C2×(C2×D47)⋊C4—21no—
113#13093957C2314yes—
114#13093957C2314yes—
115#13093957C2314yes—
116#13093957C2314yes—
117#13093955C2314yes—
118#13093955C2314yes—
119#13093955C2314yes—
120#13093955C2314yes—
121C4⋊(C47⋊C8)C2314yes—
122C4⋊(C47⋊C8)C2314yes—
123#13093944C2314yes—
124#13093944C2314yes—
125#13093944C2314yes—
126#13093944C2314yes—
127#13093944C2314yes—
128#13093944C2314yes—
129#13093944C2314yes—
130#13093944C2314yes—
131C22⋊(C47⋊C8)C2314yes—
132C22⋊(C47⋊C8)C2314yes—
133#13093935C2314yes—
134C4×C47⋊C8C2314yes—
135C22×Q8×C47—21no—
136C22×Q8×C47—21no—
137C23×C4×C47—21no—
138C23×C4×C47C2311yescharacteristic
139C4⋊Q8×C47—28no—
140C4⋊Q8×C47—22no—
141C4⋊Q8×C47—22no—
142C4⋊Q8×C47C2314yes—
143C4⋊Q8×C47C2314yes—
144#125×C47—28no—
145#125×C47—22no—
146#125×C47—22no—
147#125×C47C2314yes—
148#125×C47C2314yes—
149C22⋊Q8×C47—28no—
150C22⋊Q8×C47—28no—
151#117×C47—22no—
152#117×C47D414yes—
153#117×C47C2314yes—
154#117×C47C2314yes—
155C2×C4⋊C4×C47—21no—
156C2×C4⋊C4×C47—22no—
157C2×C4⋊C4×C47—21no—
158C2×C4⋊C4×C47—21no—
159C2×C4⋊C4×C47—21no—
160C2×C4⋊C4×C47—21no—
161C2×C4⋊C4×C47—21no—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47D411yescharacteristic
164C2×C4⋊C4×C47D411yescharacteristic
165C2×C4⋊C4×C47C2311yescharacteristic
166C2×C4⋊C4×C47C2311yescharacteristic
167C2×C4⋊C4×C47C2314yes—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C22⋊C4×C47—21no—
171C2×C22⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C42×C47—21no—
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C24×C47C2×D411yescharacteristic
177C23×D47—21no—
178C23×D47—21no—
179C2×Q8×C47—24no—
180C2×Q8×C47—24no—
181C2×Q8×C47—82no—
182C2×Q8×C47—82no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—24no—
190C22×C4×C47—82no—
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2411yescharacteristic
199C2×C22⋊D47—24no—
200C2×C22⋊D47—24no—
201C2×C22⋊D47—82no—
202C2×C22⋊D47—82no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C2×D188—22no—
206C2×D188—22no—
207C2×D188—22no—
208C2×D188—22no—
209C2×D188—21no—
210C2×D188—21no—
211C2×D188—24no—
212C2×D188—24no—
213C2×D188—82no—
214C2×D188—82no—
215C2×D188C2412yes—
216C2×D188C2412yes—
217C2×C4×D47—24no—
218C2×C4×D47—24no—
219C2×C4×D47—82no—
220C2×C4×D47—82no—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—24no—
225C4⋊C4×C47—24no—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47C2×D414yes—
233C4⋊C4×C47C2×D414yes—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C22⋊C4×C47—24no—
239C22⋊C4×C47C2×D414yes—
240C22⋊C4×C47C2×D414yes—
241C42×C47—24no—
242C42×C47C2×D412yes—
243C42×C47C2×D412yes—
244C42×C47C2412yes—
245C42×C47C2412yes—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249(C2×D47)⋊C4—24no—
250C4⋊Dic47—21no—
251C4⋊Dic47—21no—
252C4⋊Dic47C2412yes—
253C4⋊Dic47C2412yes—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256C2×C47⋊C8—22no—
257C2×C47⋊C8—22no—
258C2×C47⋊C8—22no—
259C2×C47⋊C8—22no—
260C2×C47⋊C8C2412yes—
261C2×C47⋊C8C2412yes—
262C2×C47⋊C8C2412yes—
263C2×C47⋊C8C2412yes—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47C22×D412yes—
268C23×C47C22×D411yescharacteristic
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—42no—
272C22×D47—42no—
273C22×D47—42no—
274C22×D47—42no—
275C22×D47—42no—
276C22×D47—42no—
277Q8×C47—84no—
278Q8×C47—84no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—24no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—84no—
296C2×C4×C47C22×D412yes—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D412yes—
300C2×C4×C47C22×D412yes—
301C2×C4×C47C22×D411yescharacteristic
302C2×C4×C472−1+412yes—
303C2×C4×C472−1+412yes—
304C2×C4×C47C2511yescharacteristic
305C22⋊D47—84no—
306C22⋊D47—84no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311D188—22no—
312D188—22no—
313D188—22no—
314D188—22no—
315D188—42no—
316D188—42no—
317D188—84no—
318D188—84no—
319C4×D47—84no—
320C4×D47—84no—
321C47⋊C8—22no—
322C47⋊C8—22no—
323C47⋊C8—22no—
324C47⋊C8—22no—
325C2×#3241—471nomaximal, Sylow
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—44no—
330C22×C47#53612yes—
331C22×C47#57612yes—
332C22×C47#57712yes—
333C22×C47C23×D411yescharacteristic
334C2×D47—42no—
335C2×D47—42no—
336C2×D47—42no—
337C2×D47—42no—
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—84no—
341C2×D47—84no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—22no—
346C4×C47—22no—
347C4×C47—42no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47#53612yes—
352C4×C47C2×2−1+411yescharacteristic
353C4×C47C2×2−1+411yescharacteristic
354Dic47—42no—
355Dic47—42no—
356C2×#544D4711yescharacteristic, complemented
357C2×#540—471no—
358#3241—4716no—
359C2×#501—471no—
360C2×#499—471no—
361C2×#490—471no—
362C2×#486—471no—
363C2×#481—471no—
364C2×#482—471no—
365C2×#482—471no—
366C2×#480—471no—
367C2×#478—471no—
368C2×#478—471no—
369C2×#476—471no—
370C2×#474—471no—
371C2×#433—471no—
372C2×C47—42no—
373C2×C47#324114yescomplemented
374C2×C47C2×#53611yescharacteristic
375C2×C47C2×#57611yescharacteristic
376C2×C47C2×#57711yescharacteristic
377D47—82no—
378D47—82no—
379#544—24no—
380#544C2×D4718yescomplemented
381#540—478no—
382#540—944no—
383C2×C4⋊Q8—21no—
384C2×C4⋊Q8C2×D4711yescharacteristic
385C2×C4⋊Q8C2×D4711yescharacteristic
386C2×#127—471no—
387C2×#125—21no—
388C2×#125—471no—
389C2×#125C2×D4711yescharacteristic
390C2×#125C2×D4711yescharacteristic
391C2×#123—941no—
392C2×#123—941no—
393C2×C22⋊Q8—21no—
394C2×C22⋊Q8—21no—
395C2×#121—471no—
396C2×#121—471no—
397C2×#121—941no—
398C2×#121—941no—
399C2×C4×D4—471no—
400C2×C4×D4—471no—
401C2×#117C2×D4711yescharacteristic
402C2×#117C2×D4711yescharacteristic
403C22×C4⋊C4C2×D4711yescharacteristic
404#501—478no—
405#499—478no—
406#490—478no—
407#486—478no—
408#482—478no—
409#482—478no—
410#481—478no—
411#480—478no—
412#478—478no—
413#478—478no—
414#476—478no—
415#474—478no—
416#433—478no—
417C2×#107—471no—
418C2×#107—471no—
419C2×#107—471no—
420C2×#107—471no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#106—471no—
424C2×#106—471no—
425C2×C4⋊C8—471no—
426C2×C4⋊C8—471no—
427C2×#102—471no—
428C2×#102—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×#102—471no—
435C2×C22⋊C8—471no—
436C2×C22⋊C8—471no—
437C2×#97—471no—
438C2×C4×C8—471no—
439C47C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—21no—
441C22×Q8—21no—
442C22×D4—471no—
443C22×D4—471no—
444C22×D4—941no—
445C22×D4—941no—
446C22×D4—941no—
447C22×D4—941no—
448C23×C4—21no—
449C23×C4—941no—
450C23×C4—941no—
451C23×C4C22×D4711yescharacteristic
452C22×C8—471no—
453C22×C8—471no—
454C22×C8—471no—
455C22×C8—471no—
456C4⋊Q8—28no—
457C4⋊Q8—22no—
458C4⋊Q8—22no—
459C4⋊Q8C22×D4714yes—
460C4⋊Q8C22×D4714yes—
461#127—474no—
462#127—942no—
463#125—28no—
464#125—22no—
465#125—22no—
466#125—474no—
467#125—942no—
468#125C22×D4714yes—
469#125C22×D4714yes—
470#123—948no—
471#123—948no—
472C22⋊Q8—28no—
473C22⋊Q8—28no—
474#121—474no—
475#121—474no—
476#121—942no—
477#121—942no—
478#121—948no—
479#121—948no—
480C4×D4—474no—
481C4×D4—474no—
482C4×D4—942no—
483C4×D4—942no—
484#117—22no—
485#117C22⋊D4714yes—
486#117C22×D4714yes—
487#117C22×D4714yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4C22⋊D4711yescharacteristic
501C2×C4⋊C4C22⋊D4711yescharacteristic
502C2×C4⋊C4C22×D4711yescharacteristic
503C2×C4⋊C4C22×D4711yescharacteristic
504C2×C4⋊C4C22×D4714yes—
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4C22⋊D4711yescharacteristic
513C2×C22⋊C4C22⋊D4711yescharacteristic
514C2×C42—21no—
515C2×C42C22×D4711yescharacteristic
516C2×C42C22×D4711yescharacteristic
517#107—474no—
518#107—474no—
519#107—474no—
520#107—474no—
521#106—474no—
522#106—474no—
523#106—474no—
524#106—474no—
525C4⋊C8—474no—
526C4⋊C8—474no—
527#102—474no—
528#102—474no—
529#102—474no—
530#102—474no—
531#102—474no—
532#102—474no—
533#102—474no—
534#102—474no—
535C22⋊C8—474no—
536C22⋊C8—474no—
537#97—474no—
538C4×C8—474no—
539C24—941no—
540C24—941no—
541C24C2×C22⋊D4711yescharacteristic
542C2×Q8—24no—
543C2×Q8—24no—
544C2×Q8—82no—
545C2×Q8—82no—
546C2×D4—472no—
547C2×D4—472no—
548C2×D4—944no—
549C2×D4—944no—
550C2×D4—944no—
551C2×D4—944no—
552C2×D4—941no—
553C2×D4—941no—
554C2×D4—942no—
555C2×D4—942no—
556C2×D4—942no—
557C2×D4—942no—
558C2×D4—3762no—
559C2×D4—3762no—
560C2×D4—3762no—
561C2×D4—3762no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—82no—
570C22×C4—941no—
571C22×C4—941no—
572C22×C4—944no—
573C22×C4—944no—
574C22×C4—3762no—
575C22×C4—3762no—
576C22×C4C2×C22⋊D4712yes—
577C22×C4C2×C22⋊D4711yescharacteristic
578C22×C4C2×C22⋊D4711yescharacteristic
579C22×C4C2×C22⋊D4711yescharacteristic
580C22×C4C2×C22⋊D4711yescharacteristic
581C22×C4C2×C22⋊D4711yescharacteristic
582C22×C4C23×D4712yes—
583C22×C4C23×D4711yescharacteristic
584C2×C8—472no—
585C2×C8—472no—
586C2×C8—472no—
587C2×C8—472no—
588C2×C8—942no—
589C2×C8—942no—
590C2×C8—942no—
591C2×C8—942no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—472no—
604C4⋊C4—472no—
605C4⋊C4—944no—
606C4⋊C4—944no—
607C4⋊C4—941no—
608C4⋊C4—941no—
609C4⋊C4C2×C22⋊D4714yes—
610C4⋊C4C2×C22⋊D4714yes—
611C4⋊C4C23×D4712yes—
612C4⋊C4C23×D4712yes—
613C4⋊C4C23×D4712yes—
614C4⋊C4C23×D4712yes—
615C22⋊C4—24no—
616C22⋊C4—944no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4C2×C22⋊D4714yes—
621C22⋊C4C2×C22⋊D4714yes—
622C42—24no—
623C42C2×C22⋊D4712yes—
624C42C2×C22⋊D4712yes—
625C42C23×D4712yes—
626C42C23×D4712yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—942no—
631C23—942no—
632C23—1882no—
633C23—1882no—
634C23—1882no—
635C23—1882no—
636C23—1882no—
637C23—1882no—
638C23C22×C22⋊D4712yes—
639C23C22×C22⋊D4711yescharacteristic
640Q8—84no—
641Q8—84no—
642D4—942no—
643D4—942no—
644D4—942no—
645D4—942no—
646D4—3764no—
647D4—3764no—
648D4—3764no—
649D4—3764no—
650D4—1882no—
651D4—1882no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—84no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—3764no—
672C2×C4—3764no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4C22×C22⋊D4712yes—
676C2×C4C22×C22⋊D4712yes—
677C2×C4C22×C22⋊D4712yes—
678C2×C4C22×C22⋊D4712yes—
679C2×C4C22×C22⋊D4712yes—
680C2×C4C22×C22⋊D4711yescharacteristic
681C2×C4#1309407212yes—
682C2×C4#1309407212yes—
683C2×C4C24×D4711yescharacteristic
684C8—942no—
685C8—942no—
686C8—942no—
687C8—942no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—3764no—
693C22—3764no—
694C22—1882no—
695C22—1882no—
696C22—1882no—
697C22—1882no—
698C22—1882no—
699C22—1882no—
700C22#1568969712yes—
701C22#1568992612yes—
702C22#1568993112yes—
703C22C23×C22⋊D4711yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—1882no—
714C4—1882no—
715C4#1568969712yes—
716C4C2×#1309407211yescharacteristic
717C4C2×#1309407211yescharacteristic
718C2—42no—
719C2—3762no—
720C2—3762no—
721C2#2025464114yesdirect product factor
722C2C2×#1568969711yescharacteristic
723C2C2×#1568992611yescharacteristic
724C2C2×#1568993111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#544C2
socleC23×C47C22×D4
prime radicalC2×#15689728C2
hypercenterC2×#544D47
hypocenterC47C2×#3241
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #20254641C2direct (N × H)
3. C2×#15689529C2semidirect
4. C2×#15689522C2semidirect
5. C2×#15689489C2semidirect
6. C2×#15689471C2semidirect
7. C2×#15689441C2semidirect
8. C2×#15689447C2semidirect
9. C2×#15689447C2semidirect
10. C2×#15689436C2semidirect
11. C2×#15689420C2semidirect
12. C2×#15689420C2semidirect
13. C2×#15689410C2semidirect
14. C2×#15689400C2semidirect
15. C2×#15689184C2semidirect
16. C2×C47×#544C2semidirect
29. #15689529C22semidirect
30. #15689522C22semidirect
31. #15689489C22semidirect
32. #15689471C22semidirect
33. #15689447C22semidirect
34. #15689447C22semidirect
35. #15689441C22semidirect
36. #15689436C22semidirect
37. #15689420C22semidirect
38. #15689420C22semidirect
39. #15689410C22semidirect
40. #15689400C22semidirect
41. #15689184C22semidirect
65. C47×#544C22semidirect
356. C2×#544D47semidirect
373. C2×C47#3241semidirect
380. #544C2×D47semidirect
439. C47C2×#3241semidirect
721. C2#20254641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897282
#202546412
C2×#156895292
C2×#156895222
C2×#156894892
C2×#156894712
C2×#156894412
C2×#156894472
C2×#156894362
C2×#156894202
C2×#156894102
C2×#156894002
C2×#156891842
C2×C47×#5442
C2×#324147