Finite Group Databasebeta

← C2×#20243922 #26218273

Subgroups — C2×#20243922 #26218273

Order 12032.

1694 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×#15689694C211yesmaximal, characteristic
2C2×#15689600C211yesmaximal, characteristic, complemented
3C2×#15689140C211yesmaximal, characteristic
4C22×#13093942C211yesmaximal, characteristic, complemented
5#20243922C218yesmaximal, direct product factor
6C2×#15688880C211yesmaximal, characteristic, complemented
7C2×#15688879C211yesmaximal, characteristic, complemented
8C2×C47×#421C211yesmaximal, characteristic
9C23×Dic94C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11#15689694—22no—
12#15689694—22no—
13#15689694C414yescomplemented
14#15689694C2214yes—
15C2×#13094022C412yescomplemented
16C2×#13094011C412yescomplemented
17C2×#13094005—22no—
18C2×#13094003—22no—
19#15689600—22no—
20#15689600—22no—
21#15689600—22no—
22#15689600C2214yescomplemented
23C2×C4×Dic94—22no—
24C2×#13093989—22no—
25C2×#13093983C2211yescharacteristic
26C2×#13093983C2211yescharacteristic
27C2×#13093980—22no—
28#15689140—22no—
29#15689140C2214yes—
30C2×#13093951—22no—
31C2×#13093942—22no—
32C2×#13093942—22no—
33C2×#13093942C2214yescomplemented
34#15688880C2214yescomplemented
35#15688879C2214yescomplemented
36C22×#41×C47C2211yescharacteristic
37C22×M16×C47C2211yescharacteristic
38C2×#117×C47C2211yescharacteristic
39C47×#421—22no—
40C47×#421C2214yes—
41C2×#104×C47—22no—
42C22×Dic94—21no—
43C22×Dic94—21no—
44C22×Dic94—21no—
45C22×Dic94—21no—
46C22×Dic94—21no—
47C22×Dic94—21no—
48C22×Dic94—21no—
49C22×Dic94—21no—
50C22×Dic94C2×C412yes—
51C22×Dic94C2×C412yes—
52C22×Dic94D412yes—
53C22×Dic94D412yes—
54C22×Dic94D412yes—
55C22×Dic94C2312yes—
56C23×Dic47D412yes—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329C2312yes—
63C22×C47⋊C8—21no—
64#13094022—24no—
65#13094022C2×C418yescomplemented
66#13094011—24no—
67#13094011C2×C418yescomplemented
68#13094005—28no—
69#13094005—28no—
70#13094003—28no—
71#13094003—28no—
72C4×Dic94—28no—
73C4×Dic94—28no—
74#13093989—28no—
75#13093989—28no—
76#13093983—21no—
77#13093983—21no—
78#13093983—21no—
79#13093983—21no—
80#13093983C2×C412yes—
81#13093983D412yes—
82#13093983C2312yes—
83#13093983C2312yes—
84#13093980—28no—
85#13093980—28no—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47—21no—
88C2×Dic47⋊C4—24no—
89C2×Dic47⋊C4—24no—
90C2×C22⋊Dic47—21no—
91C2×C22⋊Dic47—21no—
92C2×C22⋊Dic47—24no—
93C2×C4×Dic47—24no—
94C2×C4×Dic47C2×C412yes—
95C2×C4×Dic47D412yes—
96#13093951—28no—
97#13093942—28no—
98C2×#41×C47—21no—
99C2×#41×C47—21no—
100C2×#41×C47—21no—
101C2×#41×C47—21no—
102C2×#41×C47—21no—
103C2×#41×C47—21no—
104C2×#41×C47—21no—
105C2×#41×C47—21no—
106C2×#41×C47—21no—
107C2×#41×C47—21no—
108C2×#41×C47C2×C412yes—
109C2×#41×C47C2312yes—
110C22×Q8×C47C2×C411yescharacteristic
111C22×D4×C47—21no—
112C22×D4×C47C2×C411yescharacteristic
113C23×C4×C47—21no—
114C23×C4×C47C2311yescharacteristic
115C2×M16×C47—21no—
116C2×M16×C47—21no—
117C2×M16×C47—21no—
118C2×M16×C47—21no—
119C2×M16×C47—21no—
120C2×M16×C47C2312yes—
121C22×C8×C47—21no—
122#117×C47—21no—
123#117×C47—21no—
124#117×C47D412yes—
125#117×C47C2312yes—
126C2×C4⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C42×C47D412yes—
129#104×C47—28no—
130C24×C47—21no—
131C24×C47C2×D411yescharacteristic
132#41×C47—22no—
133#41×C47—22no—
134#41×C47—22no—
135#41×C47—22no—
136#41×C47—22no—
137#41×C47—22no—
138#41×C47—22no—
139#41×C47—22no—
140#41×C47—41no—
141#41×C47—41no—
142#41×C47—41no—
143#41×C47—41no—
144#41×C47—41no—
145#41×C47—41no—
146#41×C47—41no—
147#41×C47—41no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47C22×C412yes—
154C2×D4×C47—22no—
155C2×D4×C47—22no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—21no—
160C2×D4×C47—21no—
161C2×D4×C47—41no—
162C2×D4×C47—41no—
163C2×D4×C47—41no—
164C2×D4×C47—41no—
165C2×D4×C47C22×C412yes—
166C22×C4×C47—21no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—41no—
171C22×C4×C47—41no—
172C22×C4×C47—41no—
173C22×C4×C47—41no—
174C22×C4×C47C22×C411yescharacteristic
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47#4111yescharacteristic
184C22×C4×C47#4111yescharacteristic
185C22×C4×C47#4111yescharacteristic
186C22×C4×C47#4111yescharacteristic
187C22×C4×C47C2411yescharacteristic
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47C22⋊C414yes—
195C22×Dic47C22⋊C414yes—
196C22×Dic47C2×D414yes—
197C2×Dic94—22no—
198C2×Dic94—22no—
199C2×Dic94—22no—
200C2×Dic94—22no—
201C2×Dic94—22no—
202C2×Dic94—22no—
203C2×Dic94—22no—
204C2×Dic94—22no—
205C2×Dic94—22no—
206C2×Dic94—22no—
207C2×Dic94—22no—
208C2×Dic94—22no—
209C2×Dic94—22no—
210C2×Dic94—22no—
211C2×Dic94—22no—
212C2×Dic94—22no—
213C2×Dic94—22no—
214C2×Dic94—22no—
215C2×Dic94—22no—
216C2×Dic94—22no—
217C2×Dic94—22no—
218C2×Dic94—22no—
219C2×Dic94—22no—
220C2×Dic94—22no—
221C2×Dic94C22⋊C414yes—
222C2×Dic94C22⋊C414yes—
223C2×Dic94C22×C414yes—
224C2×Dic94C2×D414yes—
225M16×C47—22no—
226M16×C47—22no—
227M16×C47—41no—
228M16×C47—41no—
229C2×C8×C47—22no—
230C2×C8×C47—41no—
231C2×C8×C47—41no—
232C4⋊C4×C47—22no—
233C4⋊C4×C47—22no—
234C22⋊C4×C47—22no—
235C22⋊C4×C47—22no—
236C42×C47—22no—
237C42×C47C2×D414yes—
238C22⋊Dic47—22no—
239C22⋊Dic47—22no—
240C22⋊Dic47—22no—
241C22⋊Dic47—22no—
242C22⋊Dic47—216no—
243C4⋊Dic47—22no—
244C4⋊Dic47—22no—
245C4⋊Dic47—22no—
246C4⋊Dic47—22no—
247Dic47⋊C4—216no—
248Dic47⋊C4—216no—
249C4×Dic47—216no—
250C4×Dic47—22no—
251C4×Dic47—22no—
252C4×Dic47C22×C414yes—
253C4×Dic47C2×D414yes—
254#10625329—22no—
255#10625329—22no—
256#10625329—41no—
257#10625329—41no—
258C2×C47⋊C8—22no—
259C2×C47⋊C8—41no—
260C2×C47⋊C8—41no—
261C23×C47—22no—
262C23×C47—42no—
263C23×C47—44no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47C2×C22⋊C411yescharacteristic
267C23×C47C2×C22⋊C411yescharacteristic
268C23×C47#12011yescharacteristic
269C23×C47#12011yescharacteristic
270C23×C47#12311yescharacteristic
271C23×C47#12311yescharacteristic
272C23×C47C22×D411yescharacteristic
273Q8×C47—22no—
274Q8×C47—22no—
275Q8×C47—41no—
276Q8×C47—41no—
277D4×C47—22no—
278D4×C47—22no—
279D4×C47—42no—
280D4×C47—42no—
281D4×C47—42no—
282D4×C47—42no—
283D4×C47—41no—
284D4×C47—41no—
285C2×C4×C47—22no—
286C2×C4×C47—24no—
287C2×C4×C47—44no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47C2×C22⋊C411yescharacteristic
295C2×C4×C47C2×C22⋊C411yescharacteristic
296C2×C4×C47C4×D411yescharacteristic
297C2×C4×C47C4×D411yescharacteristic
298C2×C4×C47C4×D411yescharacteristic
299C2×C4×C47C4×D411yescharacteristic
300C2×C4×C47C4×D411yescharacteristic
301C2×C4×C47C4×D411yescharacteristic
302C2×C4×C47C4×D411yescharacteristic
303C2×C4×C47C4×D411yescharacteristic
304C2×C4×C47#12011yescharacteristic
305C2×C4×C47#12011yescharacteristic
306C2×C4×C47#12111yescharacteristic
307C2×C4×C47#12111yescharacteristic
308C2×C4×C47#12111yescharacteristic
309C2×C4×C47#12111yescharacteristic
310C2×C4×C47#12111yescharacteristic
311C2×C4×C47#12111yescharacteristic
312C2×C4×C47#12111yescharacteristic
313C2×C4×C47#12111yescharacteristic
314C2×C4×C47#12311yescharacteristic
315C2×C4×C47#12311yescharacteristic
316C2×C4×C47C23×C411yescharacteristic
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47C2×#4111yescharacteristic
321C2×C4×C47C2×#4111yescharacteristic
322C2×Dic47—24no—
323C2×Dic47—24no—
324C2×Dic47—24no—
325C2×Dic47—24no—
326C2×Dic47—24no—
327C2×Dic47—24no—
328C2×Dic47—24no—
329C2×Dic47—24no—
330C2×Dic47—44no—
331C2×Dic47—44no—
332C2×Dic47C2×C22⋊C418yes—
333Dic94—24no—
334Dic94—24no—
335Dic94—24no—
336Dic94—24no—
337Dic94—24no—
338Dic94—24no—
339Dic94—24no—
340Dic94—24no—
341C8×C47—42no—
342C47⋊C8—42no—
343C2×#1912—471nomaximal, Sylow
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—44no—
352C22×C47—42no—
353C22×C47—82no—
354C22×C47—82no—
355C22×C47#38611yescharacteristic
356C22×C47#38611yescharacteristic
357C22×C47#38611yescharacteristic
358C22×C47#38611yescharacteristic
359C22×C47C22×C22⋊C411yescharacteristic
360C22×C47C2×#12011yescharacteristic
361C22×C47C2×#12311yescharacteristic
362C4×C47—44no—
363C4×C47—42no—
364C4×C47#38611yescharacteristic
365C4×C47#38611yescharacteristic
366C4×C47#38611yescharacteristic
367C4×C47#38611yescharacteristic
368C4×C47C2×C4×D411yescharacteristic
369C4×C47C2×C4×D411yescharacteristic
370C4×C47C2×#12111yescharacteristic
371C4×C47C2×#12111yescharacteristic
372Dic47—28no—
373Dic47—44no—
374Dic47—44no—
375C2×#536—471no—
376C2×#519—471no—
377C2×#421—471no—
378C2×#421D4711yescharacteristic
379C22×#101—471no—
380#1912—478no—
381C2×H(3,ℤ/4)—471no—
382C2×H(3,ℤ/4)—471no—
383C2×C47—21no—
384C2×C47—21no—
385C2×C47—21no—
386C2×C47—21no—
387C2×C47—21no—
388C2×C47—21no—
389C2×C47—82no—
390C2×C47#191212yescomplemented
391C2×C47C2×#38611yescharacteristic
392C22×#41C2×D4711yescharacteristic
393C23×Q8—471no—
394C22×M16—471no—
395C22×M16C2×D4711yescharacteristic
396#536—474no—
397#536—474no—
398#536—942no—
399#536—942no—
400C2×C4⋊Q8—472no—
401C2×#124—472no—
402C2×#123—942no—
403C2×C22⋊Q8—942no—
404#519—474no—
405#519—942no—
406#519—942no—
407#519—942no—
408C2×C4×Q8—942no—
409C2×C4×Q8—942no—
410C2×#117—471no—
411C2×#117—471no—
412C2×#117—942no—
413C2×#117C2×D4711yescharacteristic
414#421—22no—
415#421—474no—
416#421—942no—
417#421C2×D4714yes—
418C2×#104—22no—
419C2×#104—942no—
420C2×#101—474no—
421C2×#101—942no—
422C2×#101—942no—
423H(3,ℤ/4)—474no—
424H(3,ℤ/4)—474no—
425C47C2×#191211yescharacteristic, complemented, Sylow
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41C4×D4712yes—
437C2×#41C22×D4712yes—
438C22×Q8—472no—
439C22×Q8—472no—
440C22×Q8—472no—
441C22×Q8—472no—
442C22×Q8—472no—
443C22×Q8—472no—
444C22×Q8—941no—
445C22×Q8—941no—
446C22×Q8—941no—
447C22×Q8—941no—
448C22×Q8—941no—
449C22×Q8—941no—
450C22×Q8—941no—
451C22×Q8—941no—
452C22×Q8C4×D4711yescharacteristic
453C22×D4—21no—
454C22×D4C4×D4711yescharacteristic
455C23×C4—21no—
456C23×C4—472no—
457C23×C4C22×D4711yescharacteristic
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—472no—
464C2×M16—941no—
465C2×M16—941no—
466C2×M16—941no—
467C2×M16—941no—
468C2×M16—941no—
469C2×M16C22×D4712yes—
470C22×C8—21no—
471C22×C8—941no—
472C4⋊Q8—478no—
473C4⋊Q8—944no—
474#124—478no—
475#124—944no—
476#123—948no—
477#123—948no—
478C22⋊Q8—948no—
479C22⋊Q8—948no—
480C4×Q8—948no—
481C4×Q8—948no—
482C4×Q8—948no—
483C4×Q8—948no—
484#117—21no—
485#117—21no—
486#117—472no—
487#117—472no—
488#117—472no—
489#117—472no—
490#117—948no—
491#117—948no—
492#117—941no—
493#117—941no—
494#117—941no—
495#117—941no—
496#117C22⋊D4712yes—
497#117C22×D4712yes—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—944no—
500C2×C4⋊C4—944no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—944no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C42—472no—
508C2×C42—472no—
509C2×C42—944no—
510C2×C42C22⋊D4712yes—
511#104—28no—
512#104—948no—
513#101—948no—
514C24—21no—
515C24D4×D4711yescharacteristic
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—474no—
538C2×Q8—474no—
539C2×Q8—474no—
540C2×Q8—474no—
541C2×Q8—942no—
542C2×Q8—942no—
543C2×Q8—942no—
544C2×Q8—942no—
545C2×Q8—942no—
546C2×Q8—942no—
547C2×Q8—942no—
548C2×Q8—942no—
549C2×Q8—942no—
550C2×Q8—942no—
551C2×Q8—942no—
552C2×Q8—942no—
553C2×Q8—942no—
554C2×Q8—942no—
555C2×Q8—942no—
556C2×Q8—942no—
557C2×Q8—942no—
558C2×Q8—942no—
559C2×Q8—942no—
560C2×Q8—942no—
561C2×Q8—942no—
562C2×Q8—942no—
563C2×Q8—942no—
564C2×Q8—942no—
565C2×Q8C2×C4×D4712yes—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4C2×C4×D4712yes—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—474no—
587C22×C4—474no—
588C22×C4—474no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—942no—
594C22×C4—942no—
595C22×C4C2×C4×D4711yescharacteristic
596C22×C4C2×C4×D4711yescharacteristic
597C22×C4#1062535011yescharacteristic
598C22×C4#1062535011yescharacteristic
599C22×C4D4×D4711yescharacteristic
600C22×C4D4×D4711yescharacteristic
601C22×C4D4×D4711yescharacteristic
602C22×C4D4×D4711yescharacteristic
603C22×C4D4×D4711yescharacteristic
604C22×C4#1062535211yescharacteristic
605C22×C4#1062535211yescharacteristic
606C22×C4C2×C22⋊D4711yescharacteristic
607C22×C4C2×C22⋊D4711yescharacteristic
608C22×C4C23×D4711yescharacteristic
609M16—22no—
610M16—22no—
611M16—41no—
612M16—41no—
613M16—942no—
614M16—942no—
615M16—1881no—
616M16—1881no—
617C2×C8—22no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—942no—
621C2×C8—1881no—
622C2×C8—1881no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—9416no—
626C4⋊C4—9416no—
627C4⋊C4—942no—
628C4⋊C4—942no—
629C4⋊C4—942no—
630C4⋊C4—942no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—9416no—
634C22⋊C4—942no—
635C22⋊C4—942no—
636C22⋊C4—942no—
637C22⋊C4—942no—
638C42—22no—
639C42—474no—
640C42—474no—
641C42—9416no—
642C42—942no—
643C42—942no—
644C42C2×C22⋊D4714yes—
645C23—22no—
646C23—42no—
647C23—44no—
648C23—41no—
649C23—41no—
650C23C22⋊C4×D4711yescharacteristic
651C23C22⋊C4×D4711yescharacteristic
652C23#1309399211yescharacteristic
653C23#1309399211yescharacteristic
654C23#1309400611yescharacteristic
655C23#1309400611yescharacteristic
656C23C2×D4×D4711yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—944no—
662Q8—944no—
663Q8—944no—
664Q8—944no—
665Q8—944no—
666Q8—944no—
667Q8—944no—
668Q8—944no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—41no—
676D4—41no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—478no—
687C2×C4—944no—
688C2×C4—944no—
689C2×C4—944no—
690C2×C4—944no—
691C2×C4—944no—
692C2×C4—944no—
693C2×C4—944no—
694C2×C4—944no—
695C2×C4—1884no—
696C2×C4—1884no—
697C2×C4C22⋊C4×D4711yescharacteristic
698C2×C4C22⋊C4×D4711yescharacteristic
699C2×C4(C22⋊D47)⋊C411yescharacteristic
700C2×C4(C22⋊D47)⋊C411yescharacteristic
701C2×C4(C22⋊D47)⋊C411yescharacteristic
702C2×C4(C22⋊D47)⋊C411yescharacteristic
703C2×C4C4×C22⋊D4711yescharacteristic
704C2×C4C4×C22⋊D4711yescharacteristic
705C2×C4C4×C22⋊D4711yescharacteristic
706C2×C4C4×C22⋊D4711yescharacteristic
707C2×C4#1309399211yescharacteristic
708C2×C4#1309399211yescharacteristic
709C2×C4#1309399511yescharacteristic
710C2×C4#1309399511yescharacteristic
711C2×C4#1309399511yescharacteristic
712C2×C4#1309399511yescharacteristic
713C2×C4#1309399711yescharacteristic
714C2×C4#1309399711yescharacteristic
715C2×C4#1309399711yescharacteristic
716C2×C4#1309399711yescharacteristic
717C2×C4#1309400611yescharacteristic
718C2×C4#1309400611yescharacteristic
719C2×C4C22×C4×D4711yescharacteristic
720C2×C4C2×D4×D4711yescharacteristic
721C2×C4C2×D4×D4711yescharacteristic
722C2×C4C22×C22⋊D4711yescharacteristic
723C2×C4C2×#1062535211yescharacteristic
724C2×C4C2×#1062535011yescharacteristic
725C8—42no—
726C8—1882no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—44no—
735C22—42no—
736C22—82no—
737C22—82no—
738C22#1568899911yescharacteristic
739C22#1568899911yescharacteristic
740C22#1568899911yescharacteristic
741C22#1568899911yescharacteristic
742C22C2×C22⋊C4×D4711yescharacteristic
743C22C2×#1309399211yescharacteristic
744C22C2×#1309400611yescharacteristic
745C4—44no—
746C4—42no—
747C4—948no—
748C4—1884no—
749C4—1884no—
750C4#1568899911yescharacteristic
751C4#1568899911yescharacteristic
752C4#1568899911yescharacteristic
753C4#1568899911yescharacteristic
754C4C2×(C22⋊D47)⋊C411yescharacteristic
755C4C2×C4×C22⋊D4711yescharacteristic
756C4C2×#1309399511yescharacteristic
757C4C2×#1309399711yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—82no—
765C2#2024392212yesdirect product factor
766C2C2×#1568899911yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#421C2
socleC22×C47#386
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#421D47
hypocenterC47C2×#1912
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#15689600C2semidirect
4. C22×#13093942C2semidirect
5. #20243922C2direct (N × H)
6. C2×#15688880C2semidirect
7. C2×#15688879C2semidirect
13. #15689694C4semidirect
15. C2×#13094022C4semidirect
16. C2×#13094011C4semidirect
22. #15689600C22semidirect
33. C2×#13093942C22semidirect
34. #15688880C22semidirect
35. #15688879C22semidirect
65. #13094022C2×C4semidirect
67. #13094011C2×C4semidirect
390. C2×C47#1912semidirect
425. C47C2×#1912semidirect
765. C2#20243922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896942
C2×#156896002
C2×#156891402
C22×#130939422
#202439222
C2×#156888802
C2×#156888792
C2×C47×#4212
C2×#191247