Finite Group Databasebeta

← C2×#20253354 #27084114

Subgroups — C2×#20253354 #27084114

Order 12032.

2170 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689696C211yesmaximal, characteristic
2C2×#15689603C211yesmaximal, characteristic
3#20253354C2116yesmaximal, direct product factor
4C2×#15689460C211yesmaximal, characteristic, complemented
5C2×#15689456C211yesmaximal, characteristic, complemented
6C2×#15689467C211yesmaximal, characteristic, complemented
7C2×#15689464C211yesmaximal, characteristic, complemented
8C2×#15689462C211yesmaximal, characteristic, complemented
9C2×#15689454C211yesmaximal, characteristic, complemented
10C2×#15689452C211yesmaximal, characteristic, complemented
11C2×#15689164C211yesmaximal, characteristic, complemented
12C2×#15689158C211yesmaximal, characteristic, complemented
13C2×#15689130C211yesmaximal, characteristic, complemented
14C2×#103×D47C211yesmaximal, characteristic, complemented
15C2×#15689088C211yesmaximal, characteristic
16C2×C47×#485C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21#15689696—24no—
22#15689696C2218yes—
23C2×#13094023—21no—
24C2×#13094010—21no—
25C2×#13094009—21no—
26C2×#13094006—21no—
27C2×#13094004C2211yescharacteristic
28C2×#13094003C2211yescharacteristic
29C2×#13094000C2211yescharacteristic
30#15689603—24no—
31#15689603C2218yes—
32C2×C4×Dic94—21no—
33C2×C4×D188—21no—
34C2×(C22⋊D47)⋊C4—21no—
35C2×(C22⋊D47)⋊C4—21no—
36C2×#13093982C2211yescharacteristic
37C2×#13093982C2211yescharacteristic
38C2×#13093982C2211yescharacteristic
39C22×C4⋊Dic47C2211yescharacteristic
40C2×C4⋊C4×D47C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689467C2218yescomplemented
43#15689464C2218yescomplemented
44#15689462C2218yescomplemented
45#15689460C2218yescomplemented
46#15689456C2218yescomplemented
47#15689454C2218yescomplemented
48#15689452C2218yescomplemented
49#15689164C2218yescomplemented
50#15689158C2218yescomplemented
51C2×#13093957C2211yescharacteristic
52C2×#13093957C2211yescharacteristic
53C2×#13093957C2211yescharacteristic
54C2×#13093956C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57#15689130C2218yescomplemented
58C2×#13093949C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64#103×D47C2218yescomplemented
65#15689088C2218yes—
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#485C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625350—24no—
78C2×#10625350—24no—
79C2×#10625350D414yes—
80C2×#10625350C2314yes—
81C22×Dic94—21no—
82C22×Dic94D411yescharacteristic
83C22×Dic94C2311yescharacteristic
84C2×Q8×D47—22no—
85C2×Q8×D47—24no—
86C2×Q8×D47—24no—
87C2×Q8×D47C2314yes—
88C22×D188D411yescharacteristic
89C22×C22⋊D47D411yescharacteristic
90C22×C22⋊D47D411yescharacteristic
91C23×Dic47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47C2311yescharacteristic
96C22×C4×D47C2311yescharacteristic
97C2×#10625324—24no—
98C2×#10625324C2314yes—
99C22×C47⋊C8C2311yescharacteristic
100C22×C47⋊C8C2311yescharacteristic
101C2×C8×D47—24no—
102C2×C8×D47C2314yes—
103#13094023—28no—
104#13094010—28no—
105#13094009—28no—
106#13094006—28no—
107#13094004—22no—
108#13094004C2314yes—
109#13094003—22no—
110#13094003C2314yes—
111#13094000—22no—
112#13094000C2314yes—
113C4×Dic94—28no—
114C4×D188—28no—
115(C22⋊D47)⋊C4—28no—
116(C22⋊D47)⋊C4—28no—
117#13093982—22no—
118#13093982—22no—
119#13093982—22no—
120#13093982C2314yes—
121#13093982C2314yes—
122#13093982C2314yes—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—22no—
125C2×C4⋊Dic47—21no—
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2314yes—
129C2×C4⋊Dic47C2311yescharacteristic
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C4⋊C4×D47—22no—
135C4⋊C4×D47—22no—
136C4⋊C4×D47C2314yes—
137C4⋊C4×D47C2314yes—
138C2×C22⋊Dic47—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147#13093957C2314yes—
148#13093957C2314yes—
149#13093957C2314yes—
150#13093956C2314yes—
151#13093956C2314yes—
152#13093955C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093948C2314yes—
156#13093948C2314yes—
157#13093947C2314yes—
158#13093947C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160(C2×D47)⋊C8C2314yes—
161(C2×D47)⋊C8C2314yes—
162C22×Q8×C47C2311yescharacteristic
163C23×C4×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22⋊Q8×C47—22no—
167C22⋊Q8×C47C2314yes—
168#117×C47—22no—
169#117×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176C2×C42×C47—21no—
177#107×C47C2314yes—
178#106×C47C2314yes—
179#103×C47C2314yes—
180#103×C47C2314yes—
181C22⋊C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47C2×D411yescharacteristic
184C23×D47C2×D411yescharacteristic
185C2×Q8×C47—21no—
186C2×Q8×C47—22no—
187C2×Q8×C47—22no—
188C2×Q8×C47C2412yes—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2411yescharacteristic
199C2×C22⋊D47—24no—
200C2×C22⋊D47—24no—
201C2×C22⋊D47C2×D414yes—
202C2×C22⋊D47C2×D414yes—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—24no—
208C22×Dic47—82no—
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211Q8×D47—28no—
212Q8×D47—28no—
213Q8×D47—48no—
214#10625350—216no—
215#10625350—28no—
216#10625350—28no—
217C2×D188—24no—
218C2×D188C2×D414yes—
219C2×C4×D47—22no—
220C2×C4×D47—22no—
221C2×C4×D47—24no—
222C2×C4×D47—24no—
223C2×C4×D47—24no—
224C2×C4×D47—44no—
225C2×C4×D47—82no—
226C2×C4×D47—82no—
227C2×C4×D47C2×D412yes—
228C2×C4×D47C2×D412yes—
229C2×C4×D47#4114yes—
230C2×C4×D47#4114yes—
231C2×C4×D47C2412yes—
232C2×C4×D47C2412yes—
233C2×Dic94—24no—
234C2×Dic94—22no—
235C2×Dic94—22no—
236C2×Dic94—21no—
237C2×Dic94—24no—
238C2×Dic94—44no—
239C2×Dic94C2×D414yes—
240C2×Dic94C2412yes—
241C2×C8×C47—22no—
242C2×C8×C47—22no—
243C2×C8×C47C2412yes—
244C2×C8×C47C2412yes—
245C4⋊C4×C47—24no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47C2412yes—
250C4⋊C4×C47C2412yes—
251C4⋊C4×C47C2412yes—
252C22⋊C4×C47—24no—
253C22⋊C4×C47—24no—
254C42×C47—24no—
255C22⋊Dic47—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261C4⋊Dic47—21no—
262C4⋊Dic47—21no—
263C4⋊Dic47—24no—
264C4⋊Dic47—21no—
265C4⋊Dic47—24no—
266C4⋊Dic47C2412yes—
267C4⋊Dic47C2412yes—
268C4⋊Dic47C2412yes—
269Dic47⋊C4—24no—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273C4×Dic47—24no—
274C4×Dic47—24no—
275C4×Dic47—24no—
276C2×C47⋊C8—22no—
277C2×C47⋊C8—22no—
278C2×C47⋊C8C2412yes—
279C2×C47⋊C8C2412yes—
280#10625324—28no—
281C8×D47—28no—
282C23×C47—22no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47C22×D412yes—
286C23×C47C22×D411yescharacteristic
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47#12314yes—
293C22×D47C22×D412yes—
294C22×D47C22×D412yes—
295Q8×C47—22no—
296Q8×C47—22no—
297Q8×C47—42no—
298C2×C4×C47—22no—
299C2×C4×C47—24no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C2×#4112yes—
313C2×C4×C47C2×#4112yes—
314C2×C4×C47C2511yescharacteristic
315C22⋊D47—28no—
316C22⋊D47—28no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47—84no—
327C2×Dic47#12314yes—
328C2×Dic47C22×D412yes—
329C2×Dic47C22×D412yes—
330D188—28no—
331C4×D47—24no—
332C4×D47—22no—
333C4×D47—22no—
334C4×D47—48no—
335C4×D47—84no—
336C4×D47—84no—
337C4×D47#12318yes—
338C4×D47C2×#4114yes—
339C4×D47C2×#4114yes—
340Dic94—28no—
341Dic94—22no—
342Dic94—22no—
343Dic94—42no—
344Dic94—48no—
345C8×C47—22no—
346C8×C47—22no—
347C47⋊C8—22no—
348C47⋊C8—22no—
349C2×#3097—471nomaximal, Sylow
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—22no—
353C22×C47—44no—
354C22×C47C2×#12312yes—
355C22×C47#57712yes—
356C22×C47#57812yes—
357C22×C47C23×D411yescharacteristic
358C2×D47—28no—
359C2×D47—22no—
360C2×D47—22no—
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—44no—
365C2×D47C2×#12314yes—
366C4×C47—22no—
367C4×C47—42no—
368C4×C47—42no—
369C4×C47—42no—
370C4×C47—42no—
371C4×C47C2×#12312yes—
372C4×C47C22×#4111yescharacteristic
373C4×C47C22×#4111yescharacteristic
374Dic47—22no—
375Dic47—42no—
376Dic47—42no—
377Dic47—42no—
378Dic47—42no—
379Dic47C2×#12314yes—
380C2×#536—471no—
381C2×#520—471no—
382#3097—4716no—
383C2×#484—471no—
384C2×#484—471no—
385C2×#485—471no—
386C2×#485—471no—
387C2×#485—471no—
388C2×#485D4711yescharacteristic, complemented
389C2×#483—471no—
390C2×#483—471no—
391C2×#428—471no—
392C2×#427—471no—
393C2×#419—471no—
394C22×#103—471no—
395C2×#408—471no—
396C2×C47—42no—
397C2×C47#309714yescomplemented
398C2×C47C22×#12311yescharacteristic
399C2×C47C2×#57711yescharacteristic
400C2×C47C2×#57811yescharacteristic
401D47—24no—
402D47—42no—
403C22×#41—471no—
404C23×Q8—471no—
405C22×M16—471no—
406C23×C8—471no—
407#536—478no—
408#536—944no—
409C2×C4⋊Q8—941no—
410C2×#124—941no—
411C2×#123—941no—
412C2×#123—941no—
413C2×C22⋊Q8—471no—
414C2×C22⋊Q8—471no—
415C2×C22⋊Q8—471no—
416C2×C22⋊Q8C2×D4711yescharacteristic
417#520—478no—
418#520—944no—
419C2×C4×Q8—941no—
420C2×C4×D4—941no—
421C2×C4×D4—941no—
422C2×C4×D4—941no—
423C2×#117—471no—
424C2×#117—471no—
425C2×#117—471no—
426C2×#117C2×D4711yescharacteristic
427C22×C4⋊C4—471no—
428C22×C4⋊C4—471no—
429C22×C4⋊C4—471no—
430#485—478no—
431#485—478no—
432#485—478no—
433#485C2×D4718yescomplemented
434#484—478no—
435#484—478no—
436#483—478no—
437#483—478no—
438#428—478no—
439#427—478no—
440C2×#107—471no—
441C2×#107—471no—
442C2×#107—471no—
443C2×#107C2×D4711yescharacteristic
444C2×#106—471no—
445C2×#106—471no—
446C2×#106—471no—
447C2×#106C2×D4711yescharacteristic
448#419—478no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#103—471no—
453C2×#103—471no—
454C2×#103—471no—
455C2×#103—478no—
456C2×#103C2×D4711yescharacteristic
457C2×#103C2×D4711yescharacteristic
458#408—478no—
459C2×C22⋊C8—471no—
460C2×C22⋊C8—471no—
461C2×C22⋊C8—471no—
462C2×C22⋊C8C2×D4711yescharacteristic
463C47C2×#309711yescharacteristic, complemented, Sylow
464C2×#41—474no—
465C2×#41—474no—
466C2×#41—944no—
467C2×#41—944no—
468C22×Q8—471no—
469C22×Q8—474no—
470C22×Q8—471no—
471C22×Q8—941no—
472C22×Q8—942no—
473C22×Q8—944no—
474C22×Q8—944no—
475C22×Q8C22×D4711yescharacteristic
476C22×D4—471no—
477C22×D4—471no—
478C22×D4—471no—
479C23×C4—471no—
480C23×C4—471no—
481C23×C4—941no—
482C23×C4—941no—
483C23×C4—941no—
484C23×C4—941no—
485C23×C4C22×D4711yescharacteristic
486C2×M16—474no—
487C2×M16—944no—
488C22×C8—471no—
489C22×C8—471no—
490C22×C8—474no—
491C22×C8—944no—
492C22×C8C22×D4711yescharacteristic
493C22×C8C22×D4711yescharacteristic
494C4⋊Q8—948no—
495#124—948no—
496#123—948no—
497#123—948no—
498C22⋊Q8—22no—
499C22⋊Q8—474no—
500C22⋊Q8—474no—
501C22⋊Q8—474no—
502C22⋊Q8—942no—
503C22⋊Q8—942no—
504C22⋊Q8—942no—
505C22⋊Q8C22×D4714yes—
506C4×Q8—948no—
507C4×D4—948no—
508C4×D4—948no—
509C4×D4—948no—
510#117—22no—
511#117—474no—
512#117—474no—
513#117—474no—
514#117—942no—
515#117—942no—
516#117—942no—
517#117C22×D4714yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—474no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—474no—
525C2×C4⋊C4—942no—
526C2×C4⋊C4—942no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4—941no—
532C2×C4⋊C4—942no—
533C2×C4⋊C4—941no—
534C2×C4⋊C4C22×D4711yescharacteristic
535C2×C4⋊C4C22×D4711yescharacteristic
536C2×C4⋊C4C22×D4711yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C22⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C22⋊C4—941no—
544C2×C22⋊C4—941no—
545C2×C42—21no—
546C2×C42—941no—
547C2×C42—941no—
548C2×C42—941no—
549#107—474no—
550#107—474no—
551#107—474no—
552#107C22×D4714yes—
553#106—474no—
554#106—474no—
555#106—474no—
556#106C22×D4714yes—
557#103—474no—
558#103—474no—
559#103—474no—
560#103—474no—
561#103—474no—
562#103—474no—
563#103C22×D4714yes—
564#103C22×D4714yes—
565C22⋊C8—474no—
566C22⋊C8—474no—
567C22⋊C8—474no—
568C22⋊C8C22×D4714yes—
569C24—471no—
570C24—471no—
571C24D4×D4711yescharacteristic
572#41—9416no—
573#41—948no—
574#41—948no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—474no—
579C2×Q8—472no—
580C2×Q8—944no—
581C2×Q8—944no—
582C2×Q8—948no—
583C2×Q8—948no—
584C2×Q8—941no—
585C2×Q8—942no—
586C2×Q8—942no—
587C2×Q8—1884no—
588C2×Q8—1888no—
589C2×Q8C23×D4712yes—
590C2×D4—474no—
591C2×D4—474no—
592C2×D4—474no—
593C2×D4—944no—
594C2×D4—944no—
595C2×D4—944no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—471no—
603C22×C4—472no—
604C22×C4—474no—
605C22×C4—474no—
606C22×C4—472no—
607C22×C4—471no—
608C22×C4—472no—
609C22×C4—472no—
610C22×C4—944no—
611C22×C4—944no—
612C22×C4—944no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—944no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—3762no—
621C22×C4—3762no—
622C22×C4—3762no—
623C22×C4—1884no—
624C22×C4D4×D4712yes—
625C22×C4D4×D4711yescharacteristic
626C22×C4C23×D4712yes—
627C22×C4C23×D4711yescharacteristic
628M16—948no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—472no—
632C2×C8—472no—
633C2×C8—948no—
634C2×C8—942no—
635C2×C8—942no—
636C2×C8C23×D4712yes—
637C2×C8C23×D4712yes—
638C4⋊C4—24no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—472no—
643C4⋊C4—472no—
644C4⋊C4—472no—
645C4⋊C4—944no—
646C4⋊C4—944no—
647C4⋊C4—944no—
648C4⋊C4—944no—
649C4⋊C4—944no—
650C4⋊C4—941no—
651C4⋊C4—941no—
652C4⋊C4—944no—
653C4⋊C4—941no—
654C4⋊C4C23×D4712yes—
655C4⋊C4C23×D4712yes—
656C4⋊C4C23×D4712yes—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—944no—
660C22⋊C4—944no—
661C22⋊C4—944no—
662C22⋊C4—944no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C42—24no—
666C42—944no—
667C42—944no—
668C42—944no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—474no—
673C23—472no—
674C23—472no—
675C23—942no—
676C23—942no—
677C23—942no—
678C23—942no—
679C23—942no—
680C23C2×D4×D4712yes—
681C23C2×D4×D4711yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—948no—
686Q8—942no—
687Q8—942no—
688Q8—1888no—
689Q8—1882no—
690D4—948no—
691D4—948no—
692D4—948no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—474no—
706C2×C4—472no—
707C2×C4—478no—
708C2×C4—474no—
709C2×C4—474no—
710C2×C4—472no—
711C2×C4—942no—
712C2×C4—944no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—3764no—
720C2×C4—3764no—
721C2×C4—3764no—
722C2×C4—1888no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4C2×D4×D4712yes—
728C2×C4C2×D4×D4711yescharacteristic
729C2×C4#41×D4712yes—
730C2×C4#41×D4712yes—
731C2×C4C24×D4711yescharacteristic
732C8—22no—
733C8—22no—
734C8—942no—
735C8—942no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—44no—
740C22—474no—
741C22—942no—
742C22—942no—
743C22—948no—
744C22—942no—
745C22—942no—
746C22—942no—
747C22—1884no—
748C22#123×D4712yes—
749C22#1568993012yes—
750C22#1568993912yes—
751C22C22×D4×D4711yescharacteristic
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—474no—
758C4—942no—
759C4—1882no—
760C4—1882no—
761C4—1882no—
762C4—1882no—
763C4#123×D4712yes—
764C4C2×#41×D4711yescharacteristic
765C4C2×#41×D4711yescharacteristic
766C2—42no—
767C2—944no—
768C2—1882no—
769C2#2025335414yesdirect product factor
770C2C2×#123×D4711yescharacteristic
771C2C2×#1568993011yescharacteristic
772C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#485C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
hypercenterC2×#485D47
hypocenterC47C2×#3097
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #20253354C2direct (N × H)
4. C2×#15689460C2semidirect
5. C2×#15689456C2semidirect
6. C2×#15689467C2semidirect
7. C2×#15689464C2semidirect
8. C2×#15689462C2semidirect
9. C2×#15689454C2semidirect
10. C2×#15689452C2semidirect
11. C2×#15689164C2semidirect
12. C2×#15689158C2semidirect
13. C2×#15689130C2semidirect
14. C2×#103×D47C2semidirect
16. C2×C47×#485C2semidirect
42. #15689467C22semidirect
43. #15689464C22semidirect
44. #15689462C22semidirect
45. #15689460C22semidirect
46. #15689456C22semidirect
47. #15689454C22semidirect
48. #15689452C22semidirect
49. #15689164C22semidirect
50. #15689158C22semidirect
57. #15689130C22semidirect
64. #103×D47C22semidirect
71. C47×#485C22semidirect
388. C2×#485D47semidirect
397. C2×C47#3097semidirect
433. #485C2×D47semidirect
463. C47C2×#3097semidirect
769. C2#20253354direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896962
C2×#156896032
#202533542
C2×#156894602
C2×#156894562
C2×#156894672
C2×#156894642
C2×#156894622
C2×#156894542
C2×#156894522
C2×#156891642
C2×#156891582
C2×#156891302
C2×#103×D472
C2×#156890882
C2×C47×#4852
C2×#309747