Finite Group Databasebeta

← C2×#20253652 #27084595

Subgroups — C2×#20253652 #27084595

Order 12032.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689744C211yesmaximal, characteristic, complemented
2C2×#15689603C211yesmaximal, characteristic, complemented
3#20253652C2116yesmaximal, direct product factor
4C2×#15689459C211yesmaximal, characteristic, complemented
5C2×#15689437C211yesmaximal, characteristic, complemented
6C2×#15689419C211yesmaximal, characteristic, complemented
7C2×#15689404C211yesmaximal, characteristic, complemented
8C2×#15689346C211yesmaximal, characteristic, complemented
9C2×#15689339C211yesmaximal, characteristic, complemented
10C2×#15689287C211yesmaximal, characteristic, complemented
11C2×#15689270C211yesmaximal, characteristic
12C2×#15689225C211yesmaximal, characteristic, complemented
13C2×#15689225C211yesmaximal, characteristic, complemented
14C2×C4×Dic188C211yesmaximal, characteristic, complemented
15C2×C4×D376C211yesmaximal, characteristic, complemented
16C2×C47×#433C211yesmaximal, characteristic, complemented
17C22×#10625350C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×D376C2211yescharacteristic
22#15689744—24no—
23#15689744C2218yescomplemented
24C2×#13094024C2211yescharacteristic
25C2×#13094019—21no—
26C2×#13094012C2211yescharacteristic
27C2×#13094010—21no—
28C2×#13094006—21no—
29C2×#13094003C2211yescharacteristic
30C2×#13094002—21no—
31C2×#13093998C2211yescharacteristic
32#15689603—24no—
33#15689603C2218yescomplemented
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×Dic94C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×C4×D188C2211yescharacteristic
40C2×(C22⋊D47)⋊C4—21no—
41C2×(C22⋊D47)⋊C4—21no—
42C2×#13093982—21no—
43C22×C4⋊Dic47C2211yescharacteristic
44C2×C4⋊C4×D47—21no—
45#15689459C2218yescomplemented
46#15689437C2218yescomplemented
47#15689419C2218yescomplemented
48#15689404C2218yescomplemented
49#15689346C2218yescomplemented
50#15689339C2218yescomplemented
51#15689287C2218yescomplemented
52#15689270C2218yes—
53#15689225C2218yescomplemented
54#15689225C2218yescomplemented
55C4×Dic188C2218yescomplemented
56C4×D376C2218yescomplemented
57C2×#13093958C2211yescharacteristic
58C2×#13093958C2211yescharacteristic
59C2×#13093958C2211yescharacteristic
60C2×#13093958C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C2×#117×C47C2211yescharacteristic
70C47×#433C2218yescomplemented
71C2×C4⋊C8×C47C2211yescharacteristic
72C2×C4⋊C8×C47C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625350—22no—
78C2×#10625350—24no—
79C2×#10625350—24no—
80C2×#10625350C2314yes—
81C22×Dic94—21no—
82C22×Dic94C2311yescharacteristic
83C22×Dic94C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C23×Dic47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C2×Dic188—24no—
94C2×Dic188C2314yes—
95C2×#10625325—24no—
96C2×#10625325—24no—
97C2×#10625325C2314yes—
98C2×#10625325C2314yes—
99C2×D376—24no—
100C2×D376C2314yes—
101#13094024—22no—
102#13094024C2314yes—
103#13094019—28no—
104#13094012—22no—
105#13094012C2314yes—
106#13094010—28no—
107#13094006—28no—
108#13094003—22no—
109#13094003C2314yes—
110#13094002—28no—
111#13093998—22no—
112#13093998C2314yes—
113C4×Dic94—22no—
114C4×Dic94—22no—
115C4×Dic94—22no—
116C4×Dic94C2314yes—
117C4×Dic94C2314yes—
118C4×Dic94C2314yes—
119C4×D188—22no—
120C4×D188—22no—
121C4×D188—22no—
122C4×D188C2314yes—
123C4×D188C2314yes—
124C4×D188C2314yes—
125(C22⋊D47)⋊C4—28no—
126(C22⋊D47)⋊C4—28no—
127#13093982—28no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47—22no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2314yes—
134C2×C4⋊Dic47C2311yescharacteristic
135C2×C4⋊Dic47C2311yescharacteristic
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C4⋊C4×D47—28no—
141C2×C22⋊Dic47—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×C4×Dic47—21no—
149C2×C4×Dic47—21no—
150C2×C4×Dic47—21no—
151#13093958C2314yes—
152#13093958C2314yes—
153#13093958C2314yes—
154#13093958C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093949C2314yes—
158#13093949C2314yes—
159#13093946C2314yes—
160#13093946C2314yes—
161#13093946C2314yes—
162#13093946C2314yes—
163C23×C4×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168#117×C47D414yes—
169#117×C47C2314yes—
170C2×C4⋊C4×C47D411yescharacteristic
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C4⋊C8×C47C2314yes—
177C4⋊C8×C47C2314yes—
178C22⋊C8×C47C2314yes—
179C22⋊C8×C47C2314yes—
180#97×C47C2314yes—
181C4×C8×C47C2314yes—
182C24×C47C2×D411yescharacteristic
183C23×D47—21no—
184C23×D47—21no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2411yescharacteristic
195C2×C22⋊D47—28no—
196C2×C22⋊D47—24no—
197C2×C22⋊D47—24no—
198C2×C22⋊D47—82no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—24no—
206C22×Dic47—82no—
207#10625350—216no—
208#10625350—28no—
209#10625350—28no—
210C2×D188—21no—
211C2×D188—22no—
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—21no—
215C2×D188#4114yes—
216C2×D188C2412yes—
217C2×D188C2412yes—
218C2×C4×D47—28no—
219C2×C4×D47—24no—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—24no—
223C2×C4×D47—82no—
224C2×C4×D47—82no—
225C2×C4×D47—82no—
226C2×Dic94—21no—
227C2×Dic94—22no—
228C2×Dic94—22no—
229C2×Dic94—22no—
230C2×Dic94—21no—
231C2×Dic94—24no—
232C2×Dic94—82no—
233C2×Dic94#4114yes—
234C2×Dic94C2412yes—
235C2×Dic94C2412yes—
236C2×C8×C47—22no—
237C2×C8×C47—22no—
238C2×C8×C47—22no—
239C2×C8×C47—22no—
240C2×C8×C47C2412yes—
241C2×C8×C47C2412yes—
242C2×C8×C47C2412yes—
243C2×C8×C47C2412yes—
244C4⋊C4×C47C2×D414yes—
245C4⋊C4×C47C2×D414yes—
246C22⋊C4×C47C2×D414yes—
247C22⋊C4×C47C2×D414yes—
248C42×C47C2×D412yes—
249C42×C47C2×D412yes—
250C42×C47C2412yes—
251C42×C47C2412yes—
252C22⋊Dic47—24no—
253(C2×D47)⋊C4—24no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259C4⋊Dic47—24no—
260C4⋊Dic47—21no—
261C4⋊Dic47—21no—
262C4⋊Dic47—24no—
263C4⋊Dic47—21no—
264C4⋊Dic47—21no—
265C4⋊Dic47C2412yes—
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—
276Dic188—28no—
277D376—28no—
278#10625325—28no—
279#10625325—28no—
280C23×C47—22no—
281C23×C47—22no—
282C23×C47—22no—
283C23×C47C22×D412yes—
284C23×C47C22×D411yescharacteristic
285C22×D47—24no—
286C22×D47—22no—
287C22×D47—22no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—24no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47C22×D412yes—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D412yes—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D411yescharacteristic
307C2×C4×C47C2×#4112yes—
308C2×C4×C47C2×#4112yes—
309C2×C4×C47C2511yescharacteristic
310C22⋊D47—216no—
311C22⋊D47—84no—
312C2×Dic47—24no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—84no—
325D188—24no—
326D188—22no—
327D188—22no—
328D188—22no—
329D188—42no—
330D188C2×#4114yes—
331C4×D47—216no—
332C4×D47—84no—
333C4×D47—84no—
334C4×D47—84no—
335Dic94—24no—
336Dic94—22no—
337Dic94—22no—
338Dic94—22no—
339Dic94—42no—
340Dic94—84no—
341Dic94C2×#4114yes—
342C8×C47—22no—
343C8×C47—22no—
344C8×C47—22no—
345C8×C47—22no—
346C2×#3124—471nomaximal, Sylow
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—44no—
351C22×C47#52512yes—
352C22×C47#57612yes—
353C22×C47#57812yes—
354C22×C47C23×D411yescharacteristic
355C2×D47—24no—
356C2×D47—48no—
357C2×D47—42no—
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—84no—
363C4×C47—22no—
364C4×C47—22no—
365C4×C47—22no—
366C4×C47—22no—
367C4×C47—22no—
368C4×C47#52512yes—
369C4×C47C22×#4111yescharacteristic
370C4×C47C22×#4111yescharacteristic
371Dic47—24no—
372Dic47—42no—
373Dic47—42no—
374Dic47—42no—
375Dic47—42no—
376Dic47—42no—
377C2×#542—471no—
378C2×#520—471no—
379#3124—4716no—
380C2×#484—471no—
381C2×#480—471no—
382C2×#477—471no—
383C2×#474—471no—
384C2×#464—471no—
385C2×#463—471no—
386C2×#452—471no—
387C2×#449—471no—
388C2×#440—471no—
389C2×#440—471no—
390C2×C4×Q16—471no—
391C2×C4×D8—471no—
392C2×#433D4711yescharacteristic, complemented
393C2×C47—42no—
394C2×C47#312414yescomplemented
395C2×C47C2×#52511yescharacteristic
396C2×C47C2×#57611yescharacteristic
397C2×C47C2×#57811yescharacteristic
398D47—44no—
399D47—82no—
400C22×#41—471no—
401C22×Q16—471no—
402C22×SD16—471no—
403C22×SD16—471no—
404C22×D8—471no—
405#542—478no—
406#542—944no—
407C2×C4⋊Q8—471no—
408C2×#126—941no—
409C2×#124—471no—
410C2×#124—941no—
411C2×#123—941no—
412C2×C22⋊Q8—471no—
413C2×C22⋊Q8—941no—
414C2×#121—471no—
415#520—478no—
416#520—944no—
417C2×C4×Q8—471no—
418C2×C4×Q8—471no—
419C2×C4×Q8—471no—
420C2×C4×D4—471no—
421C2×C4×D4—471no—
422C2×C4×D4—471no—
423C2×C4×D4—941no—
424C2×C4×D4—941no—
425C2×#117—941no—
426C2×#117C2×D4711yescharacteristic
427C22×C4⋊C4—471no—
428C22×C4⋊C4—941no—
429#484—478no—
430#480—478no—
431#477—478no—
432#474—478no—
433#464—478no—
434#463—478no—
435#452—478no—
436#449—478no—
437#440—478no—
438#440—478no—
439C4×Q16—478no—
440C4×D8—478no—
441#433C2×D4718yescomplemented
442C2×#107—471no—
443C2×#107—471no—
444C2×#107—471no—
445C2×#107—471no—
446C2×C4⋊C8C2×D4711yescharacteristic
447C2×C4⋊C8C2×D4711yescharacteristic
448C2×#103—471no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#102—471no—
453C2×#102—471no—
454C2×#102—471no—
455C2×#102—471no—
456C2×C22⋊C8C2×D4711yescharacteristic
457C2×C22⋊C8C2×D4711yescharacteristic
458C2×#97C2×D4711yescharacteristic
459C2×C4×C8C2×D4711yescharacteristic
460C47C2×#312411yescharacteristic, complemented, Sylow
461C2×#41—474no—
462C2×#41—944no—
463C2×#41—944no—
464C2×#41—942no—
465C22×Q8—471no—
466C22×Q8—471no—
467C22×Q8—941no—
468C22×D4—471no—
469C22×D4—471no—
470C22×D4—941no—
471C22×D4—941no—
472C23×C4—941no—
473C23×C4—941no—
474C23×C4—941no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4C22×D4711yescharacteristic
478C2×Q16—474no—
479C2×Q16—944no—
480C2×SD16—474no—
481C2×SD16—474no—
482C2×SD16—944no—
483C2×SD16—944no—
484C2×D8—474no—
485C2×D8—944no—
486C22×C8C22×D4711yescharacteristic
487C22×C8C22×D4711yescharacteristic
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490C4⋊Q8—474no—
491C4⋊Q8—942no—
492#126—948no—
493#124—474no—
494#124—948no—
495#124—942no—
496#123—948no—
497C22⋊Q8—474no—
498C22⋊Q8—942no—
499C22⋊Q8—948no—
500#121—474no—
501#121—942no—
502C4×Q8—474no—
503C4×Q8—474no—
504C4×Q8—474no—
505C4×Q8—942no—
506C4×Q8—942no—
507C4×Q8—942no—
508C4×D4—474no—
509C4×D4—474no—
510C4×D4—474no—
511C4×D4—948no—
512C4×D4—948no—
513C4×D4—942no—
514C4×D4—942no—
515C4×D4—942no—
516#117—948no—
517#117D18814yes—
518#117C22×D4714yes—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—474no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—471no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—942no—
526C2×C4⋊C4—941no—
527C2×C4⋊C4—941no—
528C2×C4⋊C4—941no—
529C2×C4⋊C4—941no—
530C2×C4⋊C4—941no—
531C2×C4⋊C4—948no—
532C2×C4⋊C4D18811yescharacteristic
533C2×C4⋊C4D18811yescharacteristic
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—941no—
538C2×C22⋊C4—941no—
539C2×C22⋊C4—941no—
540C2×C22⋊C4—941no—
541C2×C22⋊C4D18811yescharacteristic
542C2×C22⋊C4D18811yescharacteristic
543C2×C42—941no—
544C2×C42—941no—
545C2×C42—941no—
546C2×C42C22×D4711yescharacteristic
547C2×C42C22×D4711yescharacteristic
548#107—474no—
549#107—474no—
550#107—474no—
551#107—474no—
552C4⋊C8C22×D4714yes—
553C4⋊C8C22×D4714yes—
554#103—474no—
555#103—474no—
556#103—474no—
557#103—474no—
558#102—474no—
559#102—474no—
560#102—474no—
561#102—474no—
562C22⋊C8C22×D4714yes—
563C22⋊C8C22×D4714yes—
564#97C22×D4714yes—
565C4×C8C22×D4714yes—
566C24—941no—
567C24—941no—
568C24C2×D18811yescharacteristic
569#41—948no—
570#41—948no—
571#41—9416no—
572C2×Q8—474no—
573C2×Q8—472no—
574C2×Q8—472no—
575C2×Q8—941no—
576C2×Q8—944no—
577C2×Q8—941no—
578C2×Q8—942no—
579C2×Q8—942no—
580C2×Q8—942no—
581C2×Q8—3762no—
582C2×D4—474no—
583C2×D4—472no—
584C2×D4—472no—
585C2×D4—948no—
586C2×D4—944no—
587C2×D4—944no—
588C2×D4—941no—
589C2×D4—941no—
590C2×D4—942no—
591C2×D4—942no—
592C2×D4—942no—
593C2×D4—3762no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—948no—
597C22×C4—941no—
598C22×C4—944no—
599C22×C4—944no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—944no—
606C22×C4—944no—
607C22×C4—944no—
608C22×C4—3762no—
609C22×C4—3762no—
610C22×C4—3762no—
611C22×C4—3762no—
612C22×C4C2×D18812yes—
613C22×C4C2×D18811yescharacteristic
614C22×C4C2×D18811yescharacteristic
615C22×C4C2×D18811yescharacteristic
616C22×C4C2×D18811yescharacteristic
617C22×C4C2×D18811yescharacteristic
618C22×C4C23×D4712yes—
619C22×C4C23×D4711yescharacteristic
620Q16—948no—
621SD16—948no—
622SD16—948no—
623D8—948no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8C23×D4712yes—
629C2×C8C23×D4712yes—
630C2×C8C23×D4712yes—
631C2×C8C23×D4712yes—
632C4⋊C4—472no—
633C4⋊C4—472no—
634C4⋊C4—472no—
635C4⋊C4—472no—
636C4⋊C4—944no—
637C4⋊C4—944no—
638C4⋊C4—944no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—941no—
642C4⋊C4—941no—
643C4⋊C4—941no—
644C4⋊C4—941no—
645C4⋊C4—944no—
646C4⋊C4C2×D18814yes—
647C4⋊C4C2×D18814yes—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C22⋊C4—944no—
651C22⋊C4—944no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C22⋊C4—944no—
655C22⋊C4C2×D18814yes—
656C22⋊C4C2×D18814yes—
657C42—944no—
658C42—944no—
659C42—944no—
660C42C2×D18812yes—
661C42C2×D18812yes—
662C42C23×D4712yes—
663C42C23×D4712yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—944no—
668C23—942no—
669C23—942no—
670C23—1882no—
671C23—1882no—
672C23—1882no—
673C23—1882no—
674C23—1882no—
675C23C22×D18812yes—
676C23C22×D18811yescharacteristic
677Q8—474no—
678Q8—944no—
679Q8—942no—
680Q8—942no—
681Q8—942no—
682Q8—3764no—
683Q8—1882no—
684D4—474no—
685D4—9416no—
686D4—944no—
687D4—942no—
688D4—942no—
689D4—942no—
690D4—3764no—
691D4—1882no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—9416no—
701C2×C4—944no—
702C2×C4—942no—
703C2×C4—942no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—3764no—
709C2×C4—3764no—
710C2×C4—3764no—
711C2×C4—3764no—
712C2×C4—1882no—
713C2×C4—1882no—
714C2×C4—1882no—
715C2×C4—1882no—
716C2×C4—1882no—
717C2×C4C22×D18812yes—
718C2×C4C22×D18812yes—
719C2×C4C22×D18812yes—
720C2×C4C22×D18812yes—
721C2×C4C22×D18812yes—
722C2×C4C22×D18811yescharacteristic
723C2×C4#41×D4712yes—
724C2×C4#41×D4712yes—
725C2×C4C24×D4711yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—944no—
735C22—3764no—
736C22—1882no—
737C22—1882no—
738C22—1882no—
739C22—1882no—
740C22—1882no—
741C22—1888no—
742C22#1568963512yes—
743C22#1568992812yes—
744C22#1568994012yes—
745C22C23×D18811yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—944no—
752C4—1882no—
753C4—1882no—
754C4—1882no—
755C4—1882no—
756C4—1882no—
757C4#1568963512yes—
758C4C2×#41×D4711yescharacteristic
759C4C2×#41×D4711yescharacteristic
760C2—42no—
761C2—3762no—
762C2—1884no—
763C2#2025365214yesdirect product factor
764C2C2×#1568963511yescharacteristic
765C2C2×#1568992811yescharacteristic
766C2C2×#1568994011yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#433C2
socleC23×C47C22×D4
prime radicalC2×#15689270C2
hypercenterC2×#433D47
hypocenterC47C2×#3124
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#15689744C2semidirect
2. C2×#15689603C2semidirect
3. #20253652C2direct (N × H)
4. C2×#15689459C2semidirect
5. C2×#15689437C2semidirect
6. C2×#15689419C2semidirect
7. C2×#15689404C2semidirect
8. C2×#15689346C2semidirect
9. C2×#15689339C2semidirect
10. C2×#15689287C2semidirect
12. C2×#15689225C2semidirect
13. C2×#15689225C2semidirect
14. C2×C4×Dic188C2semidirect
15. C2×C4×D376C2semidirect
16. C2×C47×#433C2semidirect
23. #15689744C22semidirect
33. #15689603C22semidirect
45. #15689459C22semidirect
46. #15689437C22semidirect
47. #15689419C22semidirect
48. #15689404C22semidirect
49. #15689346C22semidirect
50. #15689339C22semidirect
51. #15689287C22semidirect
53. #15689225C22semidirect
54. #15689225C22semidirect
55. C4×Dic188C22semidirect
56. C4×D376C22semidirect
70. C47×#433C22semidirect
392. C2×#433D47semidirect
394. C2×C47#3124semidirect
441. #433C2×D47semidirect
460. C47C2×#3124semidirect
763. C2#20253652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897442
C2×#156896032
#202536522
C2×#156894592
C2×#156894372
C2×#156894192
C2×#156894042
C2×#156893462
C2×#156893392
C2×#156892872
C2×#156892702
C2×#156892252
C2×C4×Dic1882
C2×C4×D3762
C2×C47×#4332
C2×#312447