Finite Group Databasebeta

← C2×#20255948 #27094956

Subgroups — C2×#20255948 #27094956

Order 12032.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689819C211yesmaximal, characteristic
2#20255948C2116yesmaximal, direct product factor
3C2×#15689522C211yesmaximal, characteristic, complemented
4C2×#15689441C211yesmaximal, characteristic, complemented
5C2×#15689461C211yesmaximal, characteristic, complemented
6C2×#15689447C211yesmaximal, characteristic, complemented
7C2×#15689451C211yesmaximal, characteristic, complemented
8C2×#15689430C211yesmaximal, characteristic, complemented
9C2×#15689420C211yesmaximal, characteristic, complemented
10C2×#15689371C211yesmaximal, characteristic, complemented
11C2×#15689371C211yesmaximal, characteristic, complemented
12C2×C4×#10625336C211yesmaximal, characteristic, complemented
13C2×#15689201C211yesmaximal, characteristic, complemented
14C2×#15689166C211yesmaximal, characteristic, complemented
15C2×#15689163C211yesmaximal, characteristic, complemented
16C2×C47×#552C211yesmaximal, characteristic, complemented
17C22×#10625336C2211yescharacteristic
18C22×#10625329C2211yescharacteristic
19C22×#10625329C2211yescharacteristic
20#15689819—24no—
21#15689819C2218yes—
22C2×#13094019—21no—
23C2×#13094016C2211yescharacteristic
24C2×#13094006—21no—
25C2×#13093998C2211yescharacteristic
26C2×#13093998C2211yescharacteristic
27C2×#13093996—21no—
28C2×C4×D188C2211yescharacteristic
29C2×(C22⋊D47)⋊C4—21no—
30C2×#13093983C2211yescharacteristic
31C22×C4⋊Dic47C2211yescharacteristic
32#15689522C2218yescomplemented
33#15689461C2218yescomplemented
34#15689451C2218yescomplemented
35#15689447C2218yescomplemented
36#15689441C2218yescomplemented
37#15689430C2218yescomplemented
38#15689420C2218yescomplemented
39#15689371C2218yescomplemented
40#15689371C2218yescomplemented
41C4×#10625336C2218yescomplemented
42#15689201C2218yescomplemented
43#15689166C2218yescomplemented
44#15689163C2218yescomplemented
45C2×#13093957C2211yescharacteristic
46C2×#13093957C2211yescharacteristic
47C2×#13093957C2211yescharacteristic
48C2×#13093957C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×#13093955C2211yescharacteristic
51C2×#13093955C2211yescharacteristic
52C2×#13093955C2211yescharacteristic
53C2×#13093955C2211yescharacteristic
54C2×C4⋊(C47⋊C8)C2211yescharacteristic
55C2×#13093948C2211yescharacteristic
56C2×#13093948C2211yescharacteristic
57C2×#13093948C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#552—24no—
65C47×#552C2218yescomplemented
66C2×#126×C47—21no—
67C2×#125×C47—21no—
68C2×#125×C47C2211yescharacteristic
69C2×#123×C47—21no—
70C2×C22⋊Q8×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C2×C4×D4×C47C2211yescharacteristic
74C2×#117×C47—21no—
75C2×#117×C47C2211yescharacteristic
76C22×C4⋊C4×C47C2211yescharacteristic
77C22×D188C2311yescharacteristic
78C22×C22⋊D47—21no—
79C22×C22⋊D47—21no—
80C23×Dic47—21no—
81C22×C4×D47—21no—
82C2×#10625336—24no—
83C2×#10625336C2314yes—
84C2×#10625329—24no—
85C2×#10625329—24no—
86C2×#10625329C2314yes—
87C2×#10625329C2314yes—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92#13094019—28no—
93#13094016—22no—
94#13094016C2314yes—
95#13094006—28no—
96#13093998—22no—
97#13093998—22no—
98#13093998C2314yes—
99#13093998C2314yes—
100#13093996—28no—
101C4×D188—22no—
102C4×D188C2314yes—
103(C22⋊D47)⋊C4—28no—
104#13093983—22no—
105#13093983C2314yes—
106C2×C4⋊Dic47—22no—
107C2×C4⋊Dic47—21no—
108C2×C4⋊Dic47C2314yes—
109C2×C4⋊Dic47C2311yescharacteristic
110C2×C4⋊Dic47C2311yescharacteristic
111C2×C4⋊Dic47C2311yescharacteristic
112C2×Dic47⋊C4—21no—
113C2×Dic47⋊C4—21no—
114C2×C22⋊Dic47—21no—
115C2×(C2×D47)⋊C4—21no—
116C2×(C2×D47)⋊C4—21no—
117C2×(C2×D47)⋊C4—21no—
118C2×C4×Dic47—21no—
119#13093957C2314yes—
120#13093957C2314yes—
121#13093957C2314yes—
122#13093957C2314yes—
123#13093955C2314yes—
124#13093955C2314yes—
125#13093955C2314yes—
126#13093955C2314yes—
127#13093955C2314yes—
128C4⋊(C47⋊C8)C2314yes—
129#13093948C2314yes—
130#13093948C2314yes—
131#13093948C2314yes—
132#13093944C2314yes—
133#13093944C2314yes—
134#13093944C2314yes—
135C22⋊(C47⋊C8)C2314yes—
136C22⋊(C47⋊C8)C2314yes—
137C4×C47⋊C8C2314yes—
138C22×Q8×C47C2311yescharacteristic
139C22×D4×C47D411yescharacteristic
140C23×C4×C47—21no—
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143#126×C47—28no—
144#125×C47—28no—
145#125×C47—22no—
146#125×C47C2314yes—
147#123×C47—28no—
148C22⋊Q8×C47—22no—
149C22⋊Q8×C47—22no—
150C22⋊Q8×C47C2314yes—
151C22⋊Q8×C47C2314yes—
152C4×Q8×C47—22no—
153C4×Q8×C47C2314yes—
154C4×D4×C47D414yes—
155C4×D4×C47C2314yes—
156#117×C47—22no—
157#117×C47—28no—
158#117×C47C2314yes—
159C2×C4⋊C4×C47—21no—
160C2×C4⋊C4×C47—22no—
161C2×C4⋊C4×C47—21no—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47—21no—
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47D411yescharacteristic
167C2×C4⋊C4×C47C2311yescharacteristic
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2314yes—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C22⋊C4×C47—21no—
172C2×C22⋊C4×C47—21no—
173C2×C22⋊C4×C47—21no—
174C2×C22⋊C4×C47D411yescharacteristic
175C2×C22⋊C4×C47D411yescharacteristic
176C2×C42×C47—21no—
177C2×C42×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C24×C47C2×D411yescharacteristic
180C24×C47C2×D411yescharacteristic
181C23×D47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47C2412yes—
186C2×D4×C47—42no—
187C2×D4×C47C2×D414yes—
188C22×C4×C47—22no—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—22no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—24no—
197C22×C4×C47—44no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2412yes—
206C22×C4×C47C2411yescharacteristic
207C2×C22⋊D47—24no—
208C2×C22⋊D47—24no—
209C2×C22⋊D47—44no—
210C2×C22⋊D47—82no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—24no—
215C22×Dic47—82no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188—21no—
219C2×D188C2412yes—
220C2×C4×D47—24no—
221C2×C4×D47—82no—
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×C47C2×D414yes—
232C4⋊C4×C47C2412yes—
233C4⋊C4×C47C2412yes—
234C4⋊C4×C47C2412yes—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—24no—
237C22⋊C4×C47—24no—
238C22⋊C4×C47C2×D414yes—
239C22⋊C4×C47C2×D414yes—
240C42×C47—24no—
241C42×C47—24no—
242C42×C47C2×D412yes—
243C42×C47C2412yes—
244C22⋊Dic47—24no—
245#10625336—28no—
246(C2×D47)⋊C4—24no—
247(C2×D47)⋊C4—24no—
248(C2×D47)⋊C4—24no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47—24no—
252C4⋊Dic47—21no—
253C4⋊Dic47C2412yes—
254C4⋊Dic47C2412yes—
255C4⋊Dic47C2412yes—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258C4×Dic47—24no—
259#10625329—28no—
260#10625329—28no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8—22no—
263C2×C47⋊C8—22no—
264C2×C47⋊C8#4114yes—
265C2×C47⋊C8C2412yes—
266C2×C47⋊C8C2412yes—
267C2×C47⋊C8C2412yes—
268C2×C47⋊C8C2412yes—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47C22×D412yes—
276C23×C47C22×D412yes—
277C23×C47C22×D411yescharacteristic
278C22×D47—22no—
279C22×D47—42no—
280C22×D47—42no—
281C22×D47—42no—
282Q8×C47—22no—
283Q8×C47—22no—
284Q8×C47—42no—
285D4×C47—44no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—24no—
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—22no—
299C2×C4×C47—22no—
300C2×C4×C47—48no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D412yes—
308C2×C4×C47C22×D412yes—
309C2×C4×C47C22×D411yescharacteristic
310C2×C4×C47C2×#4112yes—
311C2×C4×C472−1+412yes—
312C2×C4×C47C2511yescharacteristic
313C22⋊D47—48no—
314C22⋊D47—84no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—84no—
322D188—22no—
323D188—22no—
324D188—42no—
325C4×D47—84no—
326C47⋊C8—22no—
327C47⋊C8—22no—
328C47⋊C8—22no—
329C47⋊C8C2×#4114yes—
330C2×#3351—471nomaximal, Sylow
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—44no—
338C22×C47—44no—
339C22×C47#54712yes—
340C22×C47#57512yes—
341C22×C47#57712yes—
342C22×C47C23×D411yescharacteristic
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—42no—
346C2×D47—84no—
347C4×C47—22no—
348C4×C47—22no—
349C4×C47—22no—
350C4×C47—22no—
351C4×C47—42no—
352C4×C47—42no—
353C4×C47—42no—
354C4×C47—42no—
355C4×C47#54712yes—
356C4×C47C22×#4111yescharacteristic
357C4×C47C2×2−1+411yescharacteristic
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361C2×#553—471no—
362C2×#552D4711yescharacteristic, complemented
363#3351—4716no—
364C2×#499—471no—
365C2×#481—471no—
366C2×#485—471no—
367C2×#482—471no—
368C2×#483—471no—
369C2×#479—471no—
370C2×#478—471no—
371C2×#468—471no—
372C2×#468—471no—
373C2×C4×SD16—471no—
374C2×#436—471no—
375C2×#428—471no—
376C2×#428—471no—
377C2×C47—42no—
378C2×C47—42no—
379C2×C47#335114yescomplemented
380C2×C47C2×#54711yescharacteristic
381C2×C47C2×#57511yescharacteristic
382C2×C47C2×#57711yescharacteristic
383D47—82no—
384C22×SD16—471no—
385C22×M16—471no—
386C22×M16—471no—
387#553—478no—
388#553—944no—
389#552—24no—
390#552C2×D4718yescomplemented
391C2×#126—21no—
392C2×#126—941no—
393C2×#125—21no—
394C2×#125—471no—
395C2×#125C2×D4711yescharacteristic
396C2×#123—21no—
397C2×#123—941no—
398C2×C22⋊Q8C2×D4711yescharacteristic
399C2×C22⋊Q8C2×D4711yescharacteristic
400C2×#121—471no—
401C2×#121—471no—
402C2×#121—941no—
403C2×C4×Q8C2×D4711yescharacteristic
404C2×C4×D4—471no—
405C2×C4×D4—941no—
406C2×C4×D4C2×D4711yescharacteristic
407C2×#117—21no—
408C2×#117—471no—
409C2×#117C2×D4711yescharacteristic
410C22×C4⋊C4—471no—
411C22×C4⋊C4C2×D4711yescharacteristic
412#499—478no—
413#485—478no—
414#483—478no—
415#482—478no—
416#481—478no—
417#479—478no—
418#478—478no—
419#468—478no—
420#468—478no—
421C4×SD16—478no—
422#436—478no—
423#428—478no—
424#428—478no—
425C2×#107—471no—
426C2×#107—471no—
427C2×#107—471no—
428C2×#107—471no—
429C2×#106—471no—
430C2×#106—471no—
431C2×#106—471no—
432C2×#106—471no—
433C2×#106—471no—
434C2×C4⋊C8—471no—
435C2×#103—471no—
436C2×#103—471no—
437C2×#103—471no—
438C2×#102—471no—
439C2×#102—471no—
440C2×#102—471no—
441C2×C22⋊C8—471no—
442C2×C22⋊C8—471no—
443C2×C4×C8—471no—
444C47C2×#335111yescharacteristic, complemented, Sylow
445C22×Q8C22×D4711yescharacteristic
446C22×D4—471no—
447C22×D4—941no—
448C22×D4—941no—
449C22×D4C22⋊D4711yescharacteristic
450C23×C4—21no—
451C23×C4—941no—
452C23×C4—941no—
453C23×C4C22×D4711yescharacteristic
454C23×C4C22×D4711yescharacteristic
455C2×SD16—474no—
456C2×SD16—944no—
457C2×M16—474no—
458C2×M16—474no—
459C2×M16—944no—
460C2×M16—944no—
461C22×C8—471no—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8—471no—
465#126—28no—
466#126—948no—
467#125—28no—
468#125—22no—
469#125—474no—
470#125—942no—
471#125C22×D4714yes—
472#123—28no—
473#123—948no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8C22×D4714yes—
477C22⋊Q8C22×D4714yes—
478#121—474no—
479#121—474no—
480#121—948no—
481#121—942no—
482#121—942no—
483C4×Q8—22no—
484C4×Q8C22×D4714yes—
485C4×D4—474no—
486C4×D4—948no—
487C4×D4—942no—
488C4×D4C22⋊D4714yes—
489C4×D4C22×D4714yes—
490#117—22no—
491#117—28no—
492#117—474no—
493#117—942no—
494#117C22×D4714yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—471no—
503C2×C4⋊C4—471no—
504C2×C4⋊C4—474no—
505C2×C4⋊C4—471no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—942no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4C22⋊D4711yescharacteristic
511C2×C4⋊C4C22×D4711yescharacteristic
512C2×C4⋊C4C22×D4711yescharacteristic
513C2×C4⋊C4C22×D4714yes—
514C2×C4⋊C4C22×D4711yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—941no—
519C2×C22⋊C4—941no—
520C2×C22⋊C4—941no—
521C2×C22⋊C4—941no—
522C2×C22⋊C4C22⋊D4711yescharacteristic
523C2×C22⋊C4C22⋊D4711yescharacteristic
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—941no—
527C2×C42C22×D4711yescharacteristic
528#107—474no—
529#107—474no—
530#107—474no—
531#107—474no—
532#106—474no—
533#106—474no—
534#106—474no—
535#106—474no—
536#106—474no—
537C4⋊C8—474no—
538#103—474no—
539#103—474no—
540#103—474no—
541#102—474no—
542#102—474no—
543#102—474no—
544C22⋊C8—474no—
545C22⋊C8—474no—
546C4×C8—474no—
547C24—941no—
548C24C2×C22⋊D4711yescharacteristic
549C24C2×C22⋊D4711yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8C23×D4712yes—
554C2×D4—42no—
555C2×D4—472no—
556C2×D4—944no—
557C2×D4—944no—
558C2×D4—941no—
559C2×D4—942no—
560C2×D4—942no—
561C2×D4—3762no—
562C2×D4—1884no—
563C2×D4C2×C22⋊D4714yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—44no—
574C22×C4—944no—
575C22×C4—941no—
576C22×C4—941no—
577C22×C4—941no—
578C22×C4—944no—
579C22×C4—3762no—
580C22×C4—3762no—
581C22×C4C2×C22⋊D4712yes—
582C22×C4C2×C22⋊D4712yes—
583C22×C4C2×C22⋊D4711yescharacteristic
584C22×C4C2×C22⋊D4711yescharacteristic
585C22×C4C2×C22⋊D4711yescharacteristic
586C22×C4C2×C22⋊D4711yescharacteristic
587C22×C4C23×D4712yes—
588C22×C4C23×D4712yes—
589C22×C4C23×D4711yescharacteristic
590SD16—948no—
591M16—948no—
592M16—948no—
593C2×C8—474no—
594C2×C8—472no—
595C2×C8—472no—
596C2×C8—472no—
597C2×C8—472no—
598C2×C8—942no—
599C2×C8—942no—
600C2×C8—942no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—21no—
610C4⋊C4—472no—
611C4⋊C4—472no—
612C4⋊C4—472no—
613C4⋊C4—944no—
614C4⋊C4—944no—
615C4⋊C4—941no—
616C4⋊C4—941no—
617C4⋊C4—944no—
618C4⋊C4—941no—
619C4⋊C4C2×C22⋊D4714yes—
620C4⋊C4C23×D4712yes—
621C4⋊C4C23×D4712yes—
622C4⋊C4C23×D4712yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—944no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C22⋊C4C2×C22⋊D4714yes—
631C22⋊C4C2×C22⋊D4714yes—
632C42—24no—
633C42—24no—
634C42—944no—
635C42C2×C22⋊D4712yes—
636C42C23×D4712yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—942no—
644C23—1882no—
645C23—1882no—
646C23—1882no—
647C23C22×C22⋊D4712yes—
648C23C22×C22⋊D4712yes—
649C23C22×C22⋊D4711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653D4—44no—
654D4—942no—
655D4—942no—
656D4—3764no—
657D4—1888no—
658D4—1882no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—48no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—942no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—3764no—
682C2×C4—3764no—
683C2×C4—1882no—
684C2×C4—1882no—
685C2×C4—1882no—
686C2×C4C22×C22⋊D4712yes—
687C2×C4C22×C22⋊D4712yes—
688C2×C4C22×C22⋊D4712yes—
689C2×C4C22×C22⋊D4712yes—
690C2×C4C22×C22⋊D4711yescharacteristic
691C2×C4#41×D4712yes—
692C2×C4#1309407112yes—
693C2×C4C24×D4711yescharacteristic
694C8—474no—
695C8—942no—
696C8—942no—
697C8—942no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—3764no—
707C22—1882no—
708C22—1882no—
709C22—1882no—
710C22#1568977212yes—
711C22#1568992112yes—
712C22#1568993112yes—
713C22C23×C22⋊D4711yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—1882no—
723C4—1882no—
724C4—1882no—
725C4#1568977212yes—
726C4C2×#41×D4711yescharacteristic
727C4C2×#1309407111yescharacteristic
728C2—42no—
729C2—42no—
730C2—3762no—
731C2#2025594814yesdirect product factor
732C2C2×#1568977211yescharacteristic
733C2C2×#1568992111yescharacteristic
734C2C2×#1568993111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#552C2
socleC23×C47C22×D4
prime radicalC2×#15689819C2
hypercenterC2×#552D47
hypocenterC47C2×#3351
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #20255948C2direct (N × H)
3. C2×#15689522C2semidirect
4. C2×#15689441C2semidirect
5. C2×#15689461C2semidirect
6. C2×#15689447C2semidirect
7. C2×#15689451C2semidirect
8. C2×#15689430C2semidirect
9. C2×#15689420C2semidirect
10. C2×#15689371C2semidirect
11. C2×#15689371C2semidirect
12. C2×C4×#10625336C2semidirect
13. C2×#15689201C2semidirect
14. C2×#15689166C2semidirect
15. C2×#15689163C2semidirect
16. C2×C47×#552C2semidirect
32. #15689522C22semidirect
33. #15689461C22semidirect
34. #15689451C22semidirect
35. #15689447C22semidirect
36. #15689441C22semidirect
37. #15689430C22semidirect
38. #15689420C22semidirect
39. #15689371C22semidirect
40. #15689371C22semidirect
41. C4×#10625336C22semidirect
42. #15689201C22semidirect
43. #15689166C22semidirect
44. #15689163C22semidirect
65. C47×#552C22semidirect
362. C2×#552D47semidirect
379. C2×C47#3351semidirect
390. #552C2×D47semidirect
444. C47C2×#3351semidirect
731. C2#20255948direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898192
#202559482
C2×#156895222
C2×#156894412
C2×#156894612
C2×#156894472
C2×#156894512
C2×#156894302
C2×#156894202
C2×#156893712
C2×C4×#106253362
C2×#156892012
C2×#156891662
C2×#156891632
C2×C47×#5522
C2×#335147