Finite Group Databasebeta

← C2×#20254058 #27086148

Subgroups — C2×#20254058 #27086148

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689744C211yesmaximal, characteristic
2#20254058C2116yesmaximal, direct product factor
3C2×#15689533C211yesmaximal, characteristic, complemented
4C2×#15689515C211yesmaximal, characteristic, complemented
5C2×#15689480C211yesmaximal, characteristic, complemented
6C2×#15689473C211yesmaximal, characteristic, complemented
7C2×#15689379C211yesmaximal, characteristic, complemented
8C2×#15689371C211yesmaximal, characteristic
9C2×#15689362C211yesmaximal, characteristic, complemented
10C2×#15689354C211yesmaximal, characteristic
11C2×#15689228C211yesmaximal, characteristic, complemented
12C2×#15689221C211yesmaximal, characteristic, complemented
13C2×C4×#10625337C211yesmaximal, characteristic, complemented
14C2×C4×#10625336C211yesmaximal, characteristic, complemented
15C2×#15689079C211yesmaximal, characteristic, complemented
16C2×C47×#541C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625337C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625329C2211yescharacteristic
22C23×C47⋊C8C2211yescharacteristic
23#15689744—24no—
24#15689744C2218yes—
25C2×#13094024C2211yescharacteristic
26C2×#13094019—21no—
27C2×#13094012C2211yescharacteristic
28C2×#13094010—21no—
29C2×#13094006—21no—
30C2×#13094003C2211yescharacteristic
31C2×#13094002—21no—
32C2×#13093998C2211yescharacteristic
33C2×C4×Dic94C2211yescharacteristic
34C2×C4×D188C2211yescharacteristic
35#15689533C2218yescomplemented
36#15689515C2218yescomplemented
37#15689480C2218yescomplemented
38#15689473C2218yescomplemented
39#15689379C2218yescomplemented
40#15689371C2218yes—
41#15689362C2218yescomplemented
42#15689354C2218yes—
43#15689228C2218yescomplemented
44#15689221C2218yescomplemented
45C4×#10625337C2218yescomplemented
46C4×#10625336C2218yescomplemented
47C2×#13093957C2211yescharacteristic
48C2×#13093957C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×#13093955C2211yescharacteristic
51C2×#13093948C2211yescharacteristic
52C2×#13093948C2211yescharacteristic
53C2×#13093948C2211yescharacteristic
54C2×#13093948C2211yescharacteristic
55C2×#13093947C2211yescharacteristic
56C2×#13093947C2211yescharacteristic
57C2×#13093944C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59#15689079C2218yescomplemented
60C2×#13093935C2211yescharacteristic
61C2×#13093935C2211yescharacteristic
62C2×C4×C47⋊C8C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#541—24no—
65C47×#541C2218yescomplemented
66C2×C4⋊Q8×C47C2211yescharacteristic
67C2×#126×C47—21no—
68C2×#126×C47—21no—
69C2×#125×C47—21no—
70C2×#125×C47—21no—
71C2×#125×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C2×C22⋊Q8×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C2×C4×Q8×C47C2211yescharacteristic
76C2×#117×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C4×D47—21no—
82C2×#10625337—24no—
83C2×#10625337—24no—
84C2×#10625337C2314yes—
85C2×#10625337C2314yes—
86C2×#10625336—24no—
87C2×#10625336—24no—
88C2×#10625336C2314yes—
89C2×#10625336C2314yes—
90C2×#10625329—24no—
91C2×#10625329C2314yes—
92C22×C47⋊C8—24no—
93C22×C47⋊C8C2311yescharacteristic
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2314yes—
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98#13094024—22no—
99#13094024C2314yes—
100#13094019—28no—
101#13094012—22no—
102#13094012C2314yes—
103#13094010—28no—
104#13094006—28no—
105#13094003—22no—
106#13094003C2314yes—
107#13094002—28no—
108#13093998—22no—
109#13093998C2314yes—
110C4×Dic94—22no—
111C4×Dic94C2314yes—
112C4×D188—22no—
113C4×D188C2314yes—
114C2×C4⋊Dic47—21no—
115C2×C4⋊Dic47C2311yescharacteristic
116C2×C4⋊Dic47C2311yescharacteristic
117C2×Dic47⋊C4—21no—
118C2×Dic47⋊C4—21no—
119C2×C22⋊Dic47—21no—
120C2×(C2×D47)⋊C4—21no—
121C2×(C2×D47)⋊C4—21no—
122C2×(C2×D47)⋊C4—21no—
123C2×(C2×D47)⋊C4—21no—
124C2×C4×Dic47—21no—
125#13093957C2314yes—
126#13093957C2314yes—
127#13093955C2314yes—
128#13093955C2314yes—
129#13093948C2314yes—
130#13093948C2314yes—
131#13093948C2314yes—
132#13093948C2314yes—
133#13093947C2314yes—
134#13093947C2314yes—
135#13093944C2314yes—
136#13093944C2314yes—
137#13093935C2314yes—
138#13093935C2314yes—
139C4×C47⋊C8C2314yes—
140C4×C47⋊C8C2314yes—
141C22×Q8×C47C2311yescharacteristic
142C22×Q8×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C4⋊Q8×C47—22no—
145C4⋊Q8×C47C2314yes—
146#126×C47—28no—
147#126×C47—28no—
148#125×C47—28no—
149#125×C47—28no—
150#125×C47—22no—
151#125×C47C2314yes—
152C22⋊Q8×C47—22no—
153C22⋊Q8×C47—22no—
154C22⋊Q8×C47C2314yes—
155C22⋊Q8×C47C2314yes—
156C4×Q8×C47—22no—
157C4×Q8×C47—22no—
158C4×Q8×C47C2314yes—
159C4×Q8×C47C2314yes—
160#117×C47D414yes—
161#117×C47C2314yes—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47—21no—
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47D411yescharacteristic
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47D411yescharacteristic
177C2×C22⋊C4×C47D411yescharacteristic
178C2×C42×C47—21no—
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181C2×C42×C47C2311yescharacteristic
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47—22no—
189C2×Q8×C47—22no—
190C2×Q8×C47C2412yes—
191C2×Q8×C47C2412yes—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—24no—
207C2×C22⋊D47—82no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C2×D188—22no—
212C2×D188—22no—
213C2×D188—21no—
214C2×D188C2412yes—
215C2×C4×D47—24no—
216C2×C4×D47—82no—
217C2×Dic94—22no—
218C2×Dic94—22no—
219C2×Dic94—21no—
220C2×Dic94—24no—
221C2×Dic94—82no—
222C2×Dic94C2412yes—
223C4⋊C4×C47—24no—
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—24no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47C2×D414yes—
234C4⋊C4×C47C2×D414yes—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C22⋊C4×C47—24no—
238C22⋊C4×C47—24no—
239C22⋊C4×C47C2×D414yes—
240C22⋊C4×C47C2×D414yes—
241C42×C47—24no—
242C42×C47—24no—
243C42×C47C2×D412yes—
244C42×C47C2×D412yes—
245C42×C47C2412yes—
246C42×C47C2412yes—
247C22⋊Dic47—24no—
248#10625337—28no—
249#10625337—28no—
250#10625336—28no—
251#10625336—28no—
252(C2×D47)⋊C4—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256C4⋊Dic47—24no—
257C4⋊Dic47—21no—
258C4⋊Dic47—21no—
259C4⋊Dic47C2412yes—
260C4⋊Dic47C2412yes—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263C4×Dic47—24no—
264#10625329—28no—
265C2×C47⋊C8—22no—
266C2×C47⋊C8—22no—
267C2×C47⋊C8—28no—
268C2×C47⋊C8#4114yes—
269C2×C47⋊C8#4114yes—
270C2×C47⋊C8C2412yes—
271C2×C47⋊C8C2412yes—
272C2×C47⋊C8C2412yes—
273C2×C47⋊C8C2412yes—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47C22×D412yes—
278C23×C47C22×D411yescharacteristic
279C22×D47—22no—
280C22×D47—42no—
281C22×D47—42no—
282C22×D47—42no—
283Q8×C47—22no—
284Q8×C47—22no—
285Q8×C47—22no—
286Q8×C47—22no—
287Q8×C47—42no—
288Q8×C47—42no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—24no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
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×D412yes—
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C2×#4112yes—
312C2×C4×C47C2×#4112yes—
313C2×C4×C47C2511yescharacteristic
314C22⋊D47—84no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—42no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321D188—22no—
322D188—22no—
323D188—42no—
324C4×D47—84no—
325Dic94—22no—
326Dic94—22no—
327Dic94—42no—
328Dic94—84no—
329C47⋊C8—22no—
330C47⋊C8—22no—
331C47⋊C8C2×#4114yes—
332C47⋊C8C2×#4114yes—
333C2×#3178—471nomaximal, Sylow
334C22×C47—22no—
335C22×C47—22no—
336C22×C47—22no—
337C22×C47—44no—
338C22×C47#53212yes—
339C22×C47#57712yes—
340C22×C47#57812yes—
341C22×C47C23×D411yescharacteristic
342C2×D47—42no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—84no—
346C4×C47—22no—
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#53212yes—
356C4×C47C22×#4111yescharacteristic
357C4×C47C22×#4111yescharacteristic
358Dic47—42no—
359Dic47—42no—
360Dic47—42no—
361C2×#542—471no—
362C2×#541D4711yescharacteristic, complemented
363#3178—4716no—
364C2×#501—471no—
365C2×#497—471no—
366C2×#488—471no—
367C2×#487—471no—
368C2×#470—471no—
369C2×#468—471no—
370C2×#467—471no—
371C2×#465—471no—
372C2×#441—471no—
373C2×#440—471no—
374C2×C4×Q16—471no—
375C2×C4×SD16—471no—
376C2×#405—471no—
377C2×C47—42no—
378C2×C47#317814yescomplemented
379C2×C47C2×#53211yescharacteristic
380C2×C47C2×#57711yescharacteristic
381C2×C47C2×#57811yescharacteristic
382D47—82no—
383C22×Q16—471no—
384C22×Q16—471no—
385C22×SD16—471no—
386C22×SD16—471no—
387C22×M16—471no—
388C23×C8—471no—
389#542—478no—
390#542—944no—
391#541—24no—
392#541C2×D4718yescomplemented
393C2×C4⋊Q8—471no—
394C2×C4⋊Q8C2×D4711yescharacteristic
395C2×#126—21no—
396C2×#126—21no—
397C2×#126—941no—
398C2×#125—21no—
399C2×#125—21no—
400C2×#125C2×D4711yescharacteristic
401C2×#124—471no—
402C2×#124—941no—
403C2×#123—941no—
404C2×C22⋊Q8—471no—
405C2×C22⋊Q8—941no—
406C2×C22⋊Q8C2×D4711yescharacteristic
407C2×C22⋊Q8C2×D4711yescharacteristic
408C2×#121—471no—
409C2×C4×Q8—471no—
410C2×C4×Q8C2×D4711yescharacteristic
411C2×C4×Q8C2×D4711yescharacteristic
412C2×C4×D4—471no—
413C2×#117C2×D4711yescharacteristic
414#501—478no—
415#497—478no—
416#488—478no—
417#487—478no—
418#470—478no—
419#468—478no—
420#467—478no—
421#465—478no—
422#441—478no—
423#440—478no—
424C4×Q16—478no—
425C4×SD16—478no—
426C2×#107—471no—
427C2×#107—471no—
428C2×#106—471no—
429C2×#106—471no—
430C2×#103—471no—
431C2×#103—471no—
432C2×#103—471no—
433C2×#103—471no—
434C2×#103—471no—
435C2×#103—471no—
436C2×#102—471no—
437C2×#102—471no—
438#405—478no—
439C2×#97—471no—
440C2×#97—471no—
441C2×C4×C8—471no—
442C2×C4×C8—471no—
443C47C2×#317811yescharacteristic, complemented, Sylow
444C22×Q8—471no—
445C22×Q8—941no—
446C22×Q8C22×D4711yescharacteristic
447C22×Q8C22×D4711yescharacteristic
448C22×D4—471no—
449C22×D4—941no—
450C23×C4—941no—
451C23×C4C22×D4711yescharacteristic
452C2×Q16—474no—
453C2×Q16—474no—
454C2×Q16—944no—
455C2×Q16—944no—
456C2×SD16—474no—
457C2×SD16—474no—
458C2×SD16—944no—
459C2×SD16—944no—
460C2×M16—474no—
461C2×M16—944no—
462C22×C8—471no—
463C22×C8—471no—
464C22×C8—471no—
465C22×C8—474no—
466C22×C8—471no—
467C22×C8—944no—
468C4⋊Q8—22no—
469C4⋊Q8—474no—
470C4⋊Q8—942no—
471C4⋊Q8C22×D4714yes—
472#126—28no—
473#126—28no—
474#126—948no—
475#125—28no—
476#125—28no—
477#125—22no—
478#125C22×D4714yes—
479#124—474no—
480#124—948no—
481#124—942no—
482#123—948no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—474no—
486C22⋊Q8—942no—
487C22⋊Q8—948no—
488C22⋊Q8C22×D4714yes—
489C22⋊Q8C22×D4714yes—
490#121—474no—
491#121—942no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—474no—
495C4×Q8—942no—
496C4×Q8C22×D4714yes—
497C4×Q8C22×D4714yes—
498C4×D4—474no—
499C4×D4—942no—
500#117C22⋊D4714yes—
501#117C22×D4714yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
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⋊C4C22⋊D4711yescharacteristic
516C2×C4⋊C4C22⋊D4711yescharacteristic
517C2×C4⋊C4C22×D4711yescharacteristic
518C2×C4⋊C4C22×D4711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—941no—
522C2×C22⋊C4—941no—
523C2×C22⋊C4—941no—
524C2×C22⋊C4—941no—
525C2×C22⋊C4—941no—
526C2×C22⋊C4C22⋊D4711yescharacteristic
527C2×C22⋊C4C22⋊D4711yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—941no—
531C2×C42C22×D4711yescharacteristic
532C2×C42C22×D4711yescharacteristic
533#107—474no—
534#107—474no—
535#106—474no—
536#106—474no—
537#103—474no—
538#103—474no—
539#103—474no—
540#103—474no—
541#103—474no—
542#103—474no—
543#102—474no—
544#102—474no—
545#97—474no—
546#97—474no—
547C4×C8—474no—
548C4×C8—474no—
549C24—941no—
550C24C2×C22⋊D4711yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—472no—
558C2×Q8—944no—
559C2×Q8—941no—
560C2×Q8—942no—
561C2×Q8—942no—
562C2×Q8—3762no—
563C2×Q8C23×D4712yes—
564C2×Q8C23×D4712yes—
565C2×D4—472no—
566C2×D4—944no—
567C2×D4—941no—
568C2×D4—942no—
569C2×D4—942no—
570C2×D4—3762no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—944no—
581C22×C4—3762no—
582C22×C4C2×C22⋊D4712yes—
583C22×C4C2×C22⋊D4711yescharacteristic
584C22×C4C2×C22⋊D4711yescharacteristic
585C22×C4C2×C22⋊D4711yescharacteristic
586C22×C4C2×C22⋊D4711yescharacteristic
587C22×C4C2×C22⋊D4711yescharacteristic
588C22×C4C23×D4712yes—
589C22×C4C23×D4711yescharacteristic
590Q16—948no—
591Q16—948no—
592SD16—948no—
593SD16—948no—
594M16—948no—
595C2×C8—474no—
596C2×C8—474no—
597C2×C8—472no—
598C2×C8—472no—
599C2×C8—472no—
600C2×C8—472no—
601C2×C8—948no—
602C2×C8—942no—
603C2×C8—942no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—472no—
615C4⋊C4—472no—
616C4⋊C4—944no—
617C4⋊C4—944no—
618C4⋊C4—941no—
619C4⋊C4—941no—
620C4⋊C4—944no—
621C4⋊C4C2×C22⋊D4714yes—
622C4⋊C4C2×C22⋊D4714yes—
623C4⋊C4C23×D4712yes—
624C4⋊C4C23×D4712yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—944no—
628C22⋊C4—944no—
629C22⋊C4—944no—
630C22⋊C4—944no—
631C22⋊C4—944no—
632C22⋊C4C2×C22⋊D4714yes—
633C22⋊C4C2×C22⋊D4714yes—
634C42—24no—
635C42—24no—
636C42—944no—
637C42C2×C22⋊D4712yes—
638C42C2×C22⋊D4712yes—
639C42C23×D4712yes—
640C42C23×D4712yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—942no—
645C23—1882no—
646C23—1882no—
647C23—1882no—
648C23C22×C22⋊D4712yes—
649C23C22×C22⋊D4711yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—42no—
655Q8—42no—
656Q8—942no—
657Q8—942no—
658Q8—3764no—
659Q8—1882no—
660D4—942no—
661D4—942no—
662D4—3764no—
663D4—1882no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—942no—
681C2×C4—942no—
682C2×C4—942no—
683C2×C4—3764no—
684C2×C4—1882no—
685C2×C4—1882no—
686C2×C4—1882no—
687C2×C4C22×C22⋊D4712yes—
688C2×C4C22×C22⋊D4712yes—
689C2×C4C22×C22⋊D4712yes—
690C2×C4C22×C22⋊D4712yes—
691C2×C4C22×C22⋊D4712yes—
692C2×C4C22×C22⋊D4711yescharacteristic
693C2×C4#41×D4712yes—
694C2×C4#41×D4712yes—
695C2×C4C24×D4711yescharacteristic
696C8—474no—
697C8—474no—
698C8—942no—
699C8—942no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—3764no—
705C22—1882no—
706C22—1882no—
707C22—1882no—
708C22#1568966912yes—
709C22#1568993112yes—
710C22#1568993812yes—
711C22C23×C22⋊D4711yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—1882no—
722C4—1882no—
723C4—1882no—
724C4#1568966912yes—
725C4C2×#41×D4711yescharacteristic
726C4C2×#41×D4711yescharacteristic
727C2—42no—
728C2—3762no—
729C2#2025405814yesdirect product factor
730C2C2×#1568966911yescharacteristic
731C2C2×#1568993111yescharacteristic
732C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#541C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenterC2×#541D47
hypocenterC47C2×#3178
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #20254058C2direct (N × H)
3. C2×#15689533C2semidirect
4. C2×#15689515C2semidirect
5. C2×#15689480C2semidirect
6. C2×#15689473C2semidirect
7. C2×#15689379C2semidirect
9. C2×#15689362C2semidirect
11. C2×#15689228C2semidirect
12. C2×#15689221C2semidirect
13. C2×C4×#10625337C2semidirect
14. C2×C4×#10625336C2semidirect
15. C2×#15689079C2semidirect
16. C2×C47×#541C2semidirect
35. #15689533C22semidirect
36. #15689515C22semidirect
37. #15689480C22semidirect
38. #15689473C22semidirect
39. #15689379C22semidirect
41. #15689362C22semidirect
43. #15689228C22semidirect
44. #15689221C22semidirect
45. C4×#10625337C22semidirect
46. C4×#10625336C22semidirect
59. #15689079C22semidirect
65. C47×#541C22semidirect
362. C2×#541D47semidirect
378. C2×C47#3178semidirect
392. #541C2×D47semidirect
443. C47C2×#3178semidirect
729. C2#20254058direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897442
#202540582
C2×#156895332
C2×#156895152
C2×#156894802
C2×#156894732
C2×#156893792
C2×#156893712
C2×#156893622
C2×#156893542
C2×#156892282
C2×#156892212
C2×C4×#106253372
C2×C4×#106253362
C2×#156890792
C2×C47×#5412
C2×#317847