Finite Group Databasebeta

← C2×#20255882 #27094867

Subgroups — C2×#20255882 #27094867

Order 12032.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689838C211yesmaximal, characteristic, complemented
2#20255882C2116yesmaximal, direct product factor
3C2×#15689533C211yesmaximal, characteristic, complemented
4C2×#15689447C211yesmaximal, characteristic, complemented
5C2×#15689444C211yesmaximal, characteristic, complemented
6C2×#15689444C211yesmaximal, characteristic, complemented
7C2×#15689436C211yesmaximal, characteristic, complemented
8C2×#15689420C211yesmaximal, characteristic, complemented
9C2×#15689403C211yesmaximal, characteristic, complemented
10C2×#15689374C211yesmaximal, characteristic, complemented
11C2×#15689357C211yesmaximal, characteristic, complemented
12C2×#15689233C211yesmaximal, characteristic, complemented
13C2×#15689195C211yesmaximal, characteristic, complemented
14C2×#15689163C211yesmaximal, characteristic, complemented
15C2×#15689159C211yesmaximal, characteristic, complemented
16C2×C47×#553C211yesmaximal, characteristic, complemented
17C22×#10625334C2211yescharacteristic
18C22×#10625329C2211yescharacteristic
19C23×C47⋊C8C2211yescharacteristic
20#15689838—24no—
21#15689838C2218yescomplemented
22C2×#13094024C2211yescharacteristic
23C2×#13094010—21no—
24C2×#13094010—21no—
25C2×#13093998C2211yescharacteristic
26C2×#13093998C2211yescharacteristic
27C2×#13093995—21no—
28C2×C4×D188C2211yescharacteristic
29C2×#13093983C2211yescharacteristic
30C2×#13093983C2211yescharacteristic
31C2×#13093982—21no—
32#15689533C2218yescomplemented
33#15689447C2218yescomplemented
34#15689444C2218yescomplemented
35#15689444C2218yescomplemented
36#15689436C2218yescomplemented
37#15689420C2218yescomplemented
38#15689403C2218yescomplemented
39#15689374C2218yescomplemented
40#15689357C2218yescomplemented
41#15689233C2218yescomplemented
42#15689195C2218yescomplemented
43#15689163C2218yescomplemented
44#15689159C2218yescomplemented
45C2×#13093957C2211yescharacteristic
46C2×#13093957C2211yescharacteristic
47C2×#13093957C2211yescharacteristic
48C2×#13093957C2211yescharacteristic
49C2×#13093957C2211yescharacteristic
50C2×#13093955C2211yescharacteristic
51C2×#13093955C2211yescharacteristic
52C2×#13093955C2211yescharacteristic
53C2×#13093955C2211yescharacteristic
54C2×C4⋊(C47⋊C8)C2211yescharacteristic
55C2×#13093945C2211yescharacteristic
56C2×#13093945C2211yescharacteristic
57C2×#13093945C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×C22⋊(C47⋊C8)C2211yescharacteristic
63C2×#13093935C2211yescharacteristic
64C47×#553—24no—
65C47×#553C2218yescomplemented
66C2×#126×C47—21no—
67C2×#125×C47C2211yescharacteristic
68C2×#123×C47—21no—
69C2×#121×C47—21no—
70C2×#121×C47C2211yescharacteristic
71C2×#121×C47C2211yescharacteristic
72C2×C4×D4×C47—21no—
73C2×C4×D4×C47C2211yescharacteristic
74C2×C4×D4×C47C2211yescharacteristic
75C2×#117×C47C2211yescharacteristic
76C22×C4⋊C4×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×D188C2311yescharacteristic
79C22×C22⋊D47—21no—
80C22×C22⋊D47—21no—
81C22×C4×D47—21no—
82C2×#10625334—24no—
83C2×#10625334C2314yes—
84C2×#10625329—24no—
85C2×#10625329C2314yes—
86C22×C47⋊C8—24no—
87C22×C47⋊C8C2311yescharacteristic
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2314yes—
91C22×C47⋊C8C2311yescharacteristic
92#13094024—22no—
93#13094024C2314yes—
94#13094010—28no—
95#13094010—28no—
96#13093998—22no—
97#13093998—22no—
98#13093998C2314yes—
99#13093998C2314yes—
100#13093995—28no—
101C4×D188—22no—
102C4×D188C2314yes—
103#13093983—22no—
104#13093983—22no—
105#13093983C2314yes—
106#13093983C2314yes—
107#13093982—28no—
108C2×C4⋊Dic47—21no—
109C2×C4⋊Dic47C2311yescharacteristic
110C2×C4⋊Dic47C2311yescharacteristic
111C2×C4⋊Dic47C2311yescharacteristic
112C2×C22⋊Dic47—21no—
113C2×C22⋊Dic47—21no—
114C2×(C2×D47)⋊C4—21no—
115C2×(C2×D47)⋊C4—21no—
116C2×(C2×D47)⋊C4—21no—
117C2×C4×Dic47—21no—
118C2×C4×Dic47—21no—
119#13093957C2314yes—
120#13093957C2314yes—
121#13093957C2314yes—
122#13093957C2314yes—
123#13093957C2314yes—
124#13093955C2314yes—
125#13093955C2314yes—
126#13093955C2314yes—
127#13093955C2314yes—
128C4⋊(C47⋊C8)C2314yes—
129#13093945C2314yes—
130#13093945C2314yes—
131#13093945C2314yes—
132#13093944C2314yes—
133#13093944C2314yes—
134#13093944C2314yes—
135C22⋊(C47⋊C8)C2314yes—
136C22⋊(C47⋊C8)C2314yes—
137#13093935C2314yes—
138C22×D4×C47—21no—
139C22×D4×C47—21no—
140C22×D4×C47D411yescharacteristic
141C22×D4×C47C2311yescharacteristic
142C23×C4×C47—21no—
143C23×C4×C47—21no—
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146#126×C47—28no—
147#125×C47—22no—
148#125×C47C2314yes—
149#123×C47—28no—
150#121×C47—28no—
151#121×C47—22no—
152#121×C47—22no—
153#121×C47C2314yes—
154#121×C47C2314yes—
155C4×D4×C47—28no—
156C4×D4×C47—22no—
157C4×D4×C47D414yes—
158C4×D4×C47C2314yes—
159C4×D4×C47C2314yes—
160#117×C47—22no—
161#117×C47C2314yes—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47—22no—
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×C47—21no—
175C2×C22⋊C4×C47D411yescharacteristic
176C2×C22⋊C4×C47D411yescharacteristic
177C2×C42×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C24×C47—21no—
180C24×C47C2×D411yescharacteristic
181C24×C47C2×D411yescharacteristic
182C23×D47—21no—
183C2×D4×C47—24no—
184C2×D4×C47—24no—
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—42no—
189C2×D4×C47—44no—
190C2×D4×C47—82no—
191C2×D4×C47C2×D414yes—
192C2×D4×C47C2412yes—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—24no—
201C22×C4×C47—24no—
202C22×C4×C47—82no—
203C22×C4×C47—82no—
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D412yes—
209C22×C4×C47C2×D412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2411yescharacteristic
213C2×C22⋊D47—24no—
214C2×C22⋊D47—24no—
215C2×C22⋊D47—82no—
216C2×C22⋊D47—82no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C2×D188—22no—
221C2×D188—22no—
222C2×D188—21no—
223C2×D188C2412yes—
224C2×C4×D47—24no—
225C2×C4×D47—44no—
226C2×Dic94—24no—
227C2×Dic94—82no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—24no—
232C4⋊C4×C47—24no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47C2×D414yes—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C22⋊C4×C47—24no—
239C22⋊C4×C47—24no—
240C22⋊C4×C47—24no—
241C22⋊C4×C47—24no—
242C22⋊C4×C47C2×D414yes—
243C22⋊C4×C47C2×D414yes—
244C42×C47—24no—
245C42×C47C2×D412yes—
246C42×C47C2412yes—
247C22⋊Dic47—24no—
248C22⋊Dic47—24no—
249#10625334—28no—
250(C2×D47)⋊C4—24no—
251(C2×D47)⋊C4—24no—
252(C2×D47)⋊C4—24no—
253C4⋊Dic47—24no—
254C4⋊Dic47—21no—
255C4⋊Dic47—21no—
256C4⋊Dic47—21no—
257C4⋊Dic47C2412yes—
258C4⋊Dic47C2412yes—
259C4⋊Dic47C2412yes—
260C4×Dic47—24no—
261C4×Dic47—24no—
262#10625329—28no—
263C2×C47⋊C8—22no—
264C2×C47⋊C8—22no—
265C2×C47⋊C8—22no—
266C2×C47⋊C8—28no—
267C2×C47⋊C8#4114yes—
268C2×C47⋊C8C2412yes—
269C2×C47⋊C8C2412yes—
270C2×C47⋊C8C2412yes—
271C2×C47⋊C8C2412yes—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—42no—
280C23×C47—42no—
281C23×C47—42no—
282C23×C47C22×D412yes—
283C23×C47C22×D412yes—
284C23×C47C22×D411yescharacteristic
285C22×D47—22no—
286C22×D47—42no—
287C22×D47—42no—
288C22×D47—42no—
289D4×C47—22no—
290D4×C47—22no—
291D4×C47—44no—
292D4×C47—48no—
293D4×C47—42no—
294D4×C47—84no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—24no—
300C2×C4×C47—24no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—84no—
312C2×C4×C47—84no—
313C2×C4×C47C22×D412yes—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C2×#4112yes—
319C2×C4×C472−1+412yes—
320C2×C4×C47C2511yescharacteristic
321C22⋊D47—84no—
322C22⋊D47—84no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329D188—22no—
330D188—22no—
331D188—42no—
332C4×D47—48no—
333Dic94—84no—
334C47⋊C8—22no—
335C47⋊C8—22no—
336C47⋊C8—22no—
337C47⋊C8C2×#4114yes—
338C2×#3347—471nomaximal, Sylow
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—44no—
346C22×C47—44no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—84no—
351C22×C47#54712yes—
352C22×C47#57512yes—
353C22×C47#57612yes—
354C22×C47C23×D411yescharacteristic
355C2×D47—42no—
356C2×D47—42no—
357C2×D47—42no—
358C2×D47—84no—
359C4×C47—22no—
360C4×C47—22no—
361C4×C47—22no—
362C4×C47—22no—
363C4×C47—42no—
364C4×C47—42no—
365C4×C47—42no—
366C4×C47#54712yes—
367C4×C47C22×#4111yescharacteristic
368C4×C47C2×2−1+411yescharacteristic
369Dic47—42no—
370Dic47—42no—
371Dic47—42no—
372C2×#555—471no—
373C2×#553D4711yescharacteristic, complemented
374#3347—4716no—
375C2×#501—471no—
376C2×#482—471no—
377C2×#482—471no—
378C2×#482—471no—
379C2×#480—471no—
380C2×#478—471no—
381C2×#474—471no—
382C2×#469—471no—
383C2×#466—471no—
384C2×#442—471no—
385C2×#435—471no—
386C2×#428—471no—
387C2×#427—471no—
388C2×C47—42no—
389C2×C47—42no—
390C2×C47—82no—
391C2×C47#334714yescomplemented
392C2×C47C2×#54711yescharacteristic
393C2×C47C2×#57511yescharacteristic
394C2×C47C2×#57611yescharacteristic
395D47—82no—
396C22×D8—471no—
397C22×M16—471no—
398C23×C8—471no—
399#555—478no—
400#555—944no—
401#553—24no—
402#553C2×D4718yescomplemented
403C2×C4⋊Q8—471no—
404C2×#126—21no—
405C2×#125C2×D4711yescharacteristic
406C2×#124—941no—
407C2×#124—941no—
408C2×#123—21no—
409C2×#121—21no—
410C2×#121—471no—
411C2×#121—471no—
412C2×#121—941no—
413C2×#121C2×D4711yescharacteristic
414C2×#121C2×D4711yescharacteristic
415C2×C4×D4—21no—
416C2×C4×D4—471no—
417C2×C4×D4C2×D4711yescharacteristic
418C2×C4×D4C2×D4711yescharacteristic
419C2×#117—471no—
420C2×#117—471no—
421C2×#117—941no—
422C2×#117C2×D4711yescharacteristic
423C22×C4⋊C4C2×D4711yescharacteristic
424#501—478no—
425#482—478no—
426#482—478no—
427#482—478no—
428#480—478no—
429#478—478no—
430#474—478no—
431#469—478no—
432#466—478no—
433#442—478no—
434#435—478no—
435#428—478no—
436#427—478no—
437C2×#107—471no—
438C2×#107—471no—
439C2×#107—471no—
440C2×#107—471no—
441C2×#107—471no—
442C2×#106—471no—
443C2×#106—471no—
444C2×#106—471no—
445C2×#106—471no—
446C2×C4⋊C8—471no—
447C2×#102—471no—
448C2×#102—471no—
449C2×#102—471no—
450C2×#102—471no—
451C2×#102—471no—
452C2×#102—471no—
453C2×C22⋊C8—471no—
454C2×C22⋊C8—471no—
455C2×#97—471no—
456C47C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—941no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—471no—
461C22×D4—941no—
462C22×D4—941no—
463C22×D4C22⋊D4711yescharacteristic
464C22×D4C22×D4711yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—941no—
468C23×C4C22×D4711yescharacteristic
469C23×C4C22×D4711yescharacteristic
470C2×D8—474no—
471C2×D8—944no—
472C2×M16—474no—
473C2×M16—944no—
474C22×C8—471no—
475C22×C8—471no—
476C22×C8—474no—
477C22×C8—471no—
478C22×C8—471no—
479C22×C8—944no—
480C4⋊Q8—474no—
481C4⋊Q8—942no—
482#126—28no—
483#125—22no—
484#125C22×D4714yes—
485#124—948no—
486#124—948no—
487#123—28no—
488#121—28no—
489#121—22no—
490#121—22no—
491#121—474no—
492#121—474no—
493#121—948no—
494#121—942no—
495#121—942no—
496#121C22×D4714yes—
497#121C22×D4714yes—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—474no—
501C4×D4—942no—
502C4×D4C22⋊D4714yes—
503C4×D4C22×D4714yes—
504C4×D4C22×D4714yes—
505#117—22no—
506#117—474no—
507#117—474no—
508#117—942no—
509#117—942no—
510#117—948no—
511#117C22×D4714yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—471no—
517C2×C4⋊C4—471no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4C22⋊D4711yescharacteristic
521C2×C4⋊C4C22×D4711yescharacteristic
522C2×C4⋊C4C22×D4711yescharacteristic
523C2×C4⋊C4C22×D4714yes—
524C2×C4⋊C4C22×D4711yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4C22⋊D4711yescharacteristic
535C2×C22⋊C4C22⋊D4711yescharacteristic
536C2×C42—21no—
537C2×C42—941no—
538C2×C42—941no—
539C2×C42C22×D4711yescharacteristic
540#107—474no—
541#107—474no—
542#107—474no—
543#107—474no—
544#107—474no—
545#106—474no—
546#106—474no—
547#106—474no—
548#106—474no—
549C4⋊C8—474no—
550#102—474no—
551#102—474no—
552#102—474no—
553#102—474no—
554#102—474no—
555#102—474no—
556C22⋊C8—474no—
557C22⋊C8—474no—
558#97—474no—
559C24—21no—
560C24—941no—
561C24C2×C22⋊D4711yescharacteristic
562C24C2×C22⋊D4711yescharacteristic
563C2×Q8—944no—
564C2×Q8—3762no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—82no—
573C2×D4—472no—
574C2×D4—944no—
575C2×D4—944no—
576C2×D4—941no—
577C2×D4—942no—
578C2×D4—942no—
579C2×D4—3762no—
580C2×D4—3762no—
581C2×D4C2×C22⋊D4714yes—
582C2×D4C23×D4712yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—944no—
598C22×C4—1884no—
599C22×C4C2×C22⋊D4712yes—
600C22×C4C2×C22⋊D4712yes—
601C22×C4C2×C22⋊D4711yescharacteristic
602C22×C4C2×C22⋊D4711yescharacteristic
603C22×C4C2×C22⋊D4711yescharacteristic
604C22×C4C2×C22⋊D4711yescharacteristic
605C22×C4C23×D4712yes—
606C22×C4C23×D4712yes—
607C22×C4C23×D4711yescharacteristic
608D8—948no—
609M16—948no—
610C2×C8—474no—
611C2×C8—472no—
612C2×C8—472no—
613C2×C8—472no—
614C2×C8—472no—
615C2×C8—948no—
616C2×C8—942no—
617C2×C8—942no—
618C2×C8—942no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—472no—
626C4⋊C4—472no—
627C4⋊C4—472no—
628C4⋊C4—941no—
629C4⋊C4—941no—
630C4⋊C4—941no—
631C4⋊C4—944no—
632C4⋊C4C2×C22⋊D4714yes—
633C4⋊C4C23×D4712yes—
634C4⋊C4C23×D4712yes—
635C4⋊C4C23×D4712yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—944no—
641C22⋊C4—944no—
642C22⋊C4—944no—
643C22⋊C4—944no—
644C22⋊C4—944no—
645C22⋊C4C2×C22⋊D4714yes—
646C22⋊C4C2×C22⋊D4714yes—
647C42—24no—
648C42—944no—
649C42—944no—
650C42C2×C22⋊D4712yes—
651C42C23×D4712yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—942no—
663C23—1882no—
664C23—1882no—
665C23—1882no—
666C23C22×C22⋊D4712yes—
667C23C22×C22⋊D4712yes—
668C23C22×C22⋊D4711yescharacteristic
669Q8—3764no—
670D4—22no—
671D4—22no—
672D4—44no—
673D4—48no—
674D4—42no—
675D4—84no—
676D4—942no—
677D4—942no—
678D4—3764no—
679D4—3764no—
680D4—1882no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—942no—
700C2×C4—942no—
701C2×C4—942no—
702C2×C4—1888no—
703C2×C4—1882no—
704C2×C4—1882no—
705C2×C4—1882no—
706C2×C4C22×C22⋊D4712yes—
707C2×C4C22×C22⋊D4712yes—
708C2×C4C22×C22⋊D4712yes—
709C2×C4C22×C22⋊D4712yes—
710C2×C4C22×C22⋊D4711yescharacteristic
711C2×C4#41×D4712yes—
712C2×C4#1309407112yes—
713C2×C4C24×D4711yescharacteristic
714C8—474no—
715C8—942no—
716C8—942no—
717C8—942no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—3764no—
731C22—1882no—
732C22—1882no—
733C22—1882no—
734C22#1568977212yes—
735C22#1568992112yes—
736C22#1568992612yes—
737C22C23×C22⋊D4711yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—1882no—
746C4—1882no—
747C4—1882no—
748C4#1568977212yes—
749C4C2×#41×D4711yescharacteristic
750C4C2×#1309407111yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—3762no—
755C2#2025588214yesdirect product factor
756C2C2×#1568977211yescharacteristic
757C2C2×#1568992111yescharacteristic
758C2C2×#1568992611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#553C2
socleC23×C47C22×D4
hypercenterC2×#553D47
hypocenterC47C2×#3347
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#15689838C2semidirect
2. #20255882C2direct (N × H)
3. C2×#15689533C2semidirect
4. C2×#15689447C2semidirect
5. C2×#15689444C2semidirect
6. C2×#15689444C2semidirect
7. C2×#15689436C2semidirect
8. C2×#15689420C2semidirect
9. C2×#15689403C2semidirect
10. C2×#15689374C2semidirect
11. C2×#15689357C2semidirect
12. C2×#15689233C2semidirect
13. C2×#15689195C2semidirect
14. C2×#15689163C2semidirect
15. C2×#15689159C2semidirect
16. C2×C47×#553C2semidirect
21. #15689838C22semidirect
32. #15689533C22semidirect
33. #15689447C22semidirect
34. #15689444C22semidirect
35. #15689444C22semidirect
36. #15689436C22semidirect
37. #15689420C22semidirect
38. #15689403C22semidirect
39. #15689374C22semidirect
40. #15689357C22semidirect
41. #15689233C22semidirect
42. #15689195C22semidirect
43. #15689163C22semidirect
44. #15689159C22semidirect
65. C47×#553C22semidirect
373. C2×#553D47semidirect
391. C2×C47#3347semidirect
402. #553C2×D47semidirect
456. C47C2×#3347semidirect
755. C2#20255882direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898382
#202558822
C2×#156895332
C2×#156894472
C2×#156894442
C2×#156894362
C2×#156894202
C2×#156894032
C2×#156893742
C2×#156893572
C2×#156892332
C2×#156891952
C2×#156891632
C2×#156891592
C2×C47×#5532
C2×#334747