Finite Group Databasebeta

← C2×#20243907 #26218248

Subgroups — C2×#20243907 #26218248

Order 12032.

1686 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×#15689889C211yesmaximal, characteristic
2C2×#15689697C211yesmaximal, characteristic
3C2×#15689132C211yesmaximal, characteristic, complemented
4C2×#15689096C211yesmaximal, characteristic
5#20243907C218yesmaximal, direct product factor
6C2×#15688880C211yesmaximal, characteristic, complemented
7C2×#15688879C211yesmaximal, characteristic, complemented
8C2×C47×#419C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689889—22no—
11#15689889—22no—
12#15689889—22no—
13#15689889C2214yes—
14C2×#13094032—22no—
15C2×#13094030—22no—
16C22×#10625329C2211yescharacteristic
17C2×M16×D47—22no—
18#15689697—22no—
19#15689697—22no—
20#15689697C414yescomplemented
21#15689697C2214yes—
22C2×#13094022C412yescomplemented
23C2×#13094013C412yescomplemented
24C2×#13094007—22no—
25C2×#13094000—22no—
26C2×#13093983C2211yescharacteristic
27C2×#13093983C2211yescharacteristic
28#15689132—22no—
29#15689132C2214yescomplemented
30C2×#13093948—22no—
31#15689096—22no—
32#15689096C2214yes—
33C2×#13093938—22no—
34#15688880C2214yescomplemented
35#15688879C2214yescomplemented
36C23×Q8×C47C2211yescharacteristic
37C22×M16×C47C2211yescharacteristic
38C2×#117×C47C2211yescharacteristic
39C47×#419—22no—
40C47×#419C2214yescomplemented
41C2×#103×C47—22no—
42C2×#10625350—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350C2×C412yes—
51C2×#10625350D412yes—
52C2×#10625350D412yes—
53C2×#10625350C2312yes—
54C22×Dic94C2×C411yescharacteristic
55C22×D188C2×C411yescharacteristic
56C22×C22⋊D47D412yes—
57C22×C4×D47D412yes—
58#13094032—28no—
59#13094032—28no—
60#13094030—28no—
61#13094030—28no—
62C2×#10625329—21no—
63C2×#10625329—21no—
64C2×#10625329—21no—
65C2×#10625329—21no—
66C2×#10625329D412yes—
67C2×#10625329C2312yes—
68C2×#10625324—24no—
69M16×D47—28no—
70M16×D47—28no—
71C22×C47⋊C8D412yes—
72C2×C8×D47—24no—
73#13094022—24no—
74#13094022C2×C418yescomplemented
75#13094013—24no—
76#13094013C2×C418yescomplemented
77#13094007—28no—
78#13094007—28no—
79#13094000—28no—
80#13094000—28no—
81#13093983—21no—
82#13093983—21no—
83#13093983—21no—
84#13093983—21no—
85#13093983—21no—
86#13093983C2×C412yes—
87#13093983C2312yes—
88#13093983C2312yes—
89C2×C4⋊Dic47—21no—
90C2×C4⋊Dic47—21no—
91C2×Dic47⋊C4—24no—
92C2×C22⋊Dic47—21no—
93C2×C22⋊Dic47—21no—
94C2×(C2×D47)⋊C4—24no—
95C2×C4×Dic47—21no—
96C2×C4×Dic47C2×C412yes—
97#13093948—28no—
98#13093938—28no—
99C22×Q8×C47—21no—
100C22×Q8×C47—21no—
101C22×Q8×C47—21no—
102C22×Q8×C47—21no—
103C22×Q8×C47—21no—
104C22×Q8×C47—21no—
105C22×Q8×C47—21no—
106C22×Q8×C47—21no—
107C22×Q8×C47—21no—
108C22×Q8×C47—21no—
109C22×Q8×C47—21no—
110C22×Q8×C47C2×C412yes—
111C22×Q8×C47C2×C412yes—
112C22×Q8×C47C2312yes—
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×C47D412yes—
120C2×M16×C47C2312yes—
121C22×C8×C47D412yes—
122#117×C47—21no—
123#117×C47—21no—
124#117×C47—21no—
125#117×C47C2312yes—
126C2×C4⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C42×C47—21no—
129#103×C47—28no—
130C24×C47C2×D411yescharacteristic
131C23×D47C22⋊C412yes—
132C2×Q8×C47—22no—
133C2×Q8×C47—22no—
134C2×Q8×C47—22no—
135C2×Q8×C47—22no—
136C2×Q8×C47—22no—
137C2×Q8×C47—22no—
138C2×Q8×C47—22no—
139C2×Q8×C47—22no—
140C2×Q8×C47—22no—
141C2×Q8×C47—22no—
142C2×Q8×C47—22no—
143C2×Q8×C47—22no—
144C2×Q8×C47—22no—
145C2×Q8×C47—22no—
146C2×Q8×C47—22no—
147C2×Q8×C47—41no—
148C2×Q8×C47—41no—
149C2×Q8×C47—41no—
150C2×Q8×C47—41no—
151C2×Q8×C47—41no—
152C2×Q8×C47—41no—
153C2×Q8×C47—41no—
154C2×Q8×C47—41no—
155C2×Q8×C47—41no—
156C2×Q8×C47—41no—
157C2×Q8×C47—41no—
158C2×Q8×C47—41no—
159C2×Q8×C47C22×C414yes—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—41no—
164C22×C4×C47—41no—
165C22×C4×C47—41no—
166C22×C4×C47—41no—
167C22×C4×C47—41no—
168C22×C4×C47C22×C411yescharacteristic
169C22×C4×C47C22×C411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47#4111yescharacteristic
178C22×C4×C47#4111yescharacteristic
179C22×C4×C47#4111yescharacteristic
180C22×C4×C47#4111yescharacteristic
181C22×C4×C47C2411yescharacteristic
182C2×C22⋊D47—22no—
183C2×C22⋊D47—22no—
184C2×C22⋊D47—22no—
185C2×C22⋊D47—22no—
186C2×C22⋊D47C22⋊C414yes—
187C2×C22⋊D47C2×D414yes—
188C22×Dic47—22no—
189C22×Dic47—41no—
190C22×Dic47C22⋊C412yes—
191#10625350—22no—
192#10625350—22no—
193#10625350—22no—
194#10625350—22no—
195#10625350—22no—
196#10625350—22no—
197#10625350—22no—
198#10625350—22no—
199#10625350—22no—
200#10625350—22no—
201#10625350—22no—
202#10625350—22no—
203#10625350—22no—
204#10625350—22no—
205#10625350—22no—
206#10625350—22no—
207C2×D188—21no—
208C2×D188—21no—
209C2×D188—21no—
210C2×D188—21no—
211C2×D188C22⋊C412yes—
212C2×D188C22×C412yes—
213C2×C4×D47—22no—
214C2×C4×D47—22no—
215C2×C4×D47—22no—
216C2×C4×D47—22no—
217C2×C4×D47C22⋊C414yes—
218C2×C4×D47C2×D414yes—
219C2×Dic94—21no—
220C2×Dic94—21no—
221C2×Dic94—21no—
222C2×Dic94—21no—
223C2×Dic94C22⋊C412yes—
224C2×Dic94C22×C412yes—
225M16×C47—22no—
226M16×C47—22no—
227M16×C47—22no—
228M16×C47—22no—
229C2×C8×C47—22no—
230C2×C8×C47—22no—
231C2×C8×C47C2×D414yes—
232C4⋊C4×C47—22no—
233C4⋊C4×C47—41no—
234C22⋊C4×C47—22no—
235C22⋊C4×C47—41no—
236C42×C47—22no—
237C42×C47—41no—
238C22⋊Dic47—22no—
239C22⋊Dic47—22no—
240C22⋊Dic47—22no—
241C22⋊Dic47—41no—
242(C2×D47)⋊C4—216no—
243C4⋊Dic47—22no—
244C4⋊Dic47—22no—
245C4⋊Dic47—22no—
246C4⋊Dic47—41no—
247Dic47⋊C4—216no—
248C4×Dic47—22no—
249C4×Dic47—22no—
250C4×Dic47—41no—
251C4×Dic47C22×C414yes—
252#10625329—22no—
253#10625329—22no—
254#10625329—22no—
255#10625329—22no—
256C2×C47⋊C8—22no—
257C2×C47⋊C8—22no—
258C2×C47⋊C8C2×D414yes—
259#10625324—216no—
260C8×D47—216no—
261C23×C47—42no—
262C23×C47C2×C22⋊C411yescharacteristic
263C23×C47C2×C22⋊C411yescharacteristic
264C23×C47#12111yescharacteristic
265C23×C47#12111yescharacteristic
266C23×C47#12111yescharacteristic
267C23×C47#12111yescharacteristic
268C23×C47C22×D411yescharacteristic
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—44no—
272C22×D47C2×C22⋊C414yes—
273Q8×C47—24no—
274Q8×C47—24no—
275Q8×C47—42no—
276Q8×C47—42no—
277Q8×C47—42no—
278Q8×C47—42no—
279Q8×C47—42no—
280Q8×C47—42no—
281C2×C4×C47—24no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—82no—
290C2×C4×C47C2×C22⋊C411yescharacteristic
291C2×C4×C47C2×C22⋊C411yescharacteristic
292C2×C4×C47C4×D411yescharacteristic
293C2×C4×C47C4×D411yescharacteristic
294C2×C4×C47C4×D411yescharacteristic
295C2×C4×C47C4×D411yescharacteristic
296C2×C4×C47C4×D411yescharacteristic
297C2×C4×C47C4×D411yescharacteristic
298C2×C4×C47C4×D411yescharacteristic
299C2×C4×C47C4×D411yescharacteristic
300C2×C4×C47#12011yescharacteristic
301C2×C4×C47#12011yescharacteristic
302C2×C4×C47#12011yescharacteristic
303C2×C4×C47#12011yescharacteristic
304C2×C4×C47#12111yescharacteristic
305C2×C4×C47#12111yescharacteristic
306C2×C4×C47#12111yescharacteristic
307C2×C4×C47#12111yescharacteristic
308C2×C4×C47#12311yescharacteristic
309C2×C4×C47#12311yescharacteristic
310C2×C4×C47#12311yescharacteristic
311C2×C4×C47#12311yescharacteristic
312C2×C4×C47C23×C411yescharacteristic
313C2×C4×C47C22×D411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4111yescharacteristic
317C2×C4×C47C2×#4111yescharacteristic
318C22⋊D47—24no—
319C22⋊D47—24no—
320C22⋊D47—24no—
321C22⋊D47—24no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—24no—
325C2×Dic47—44no—
326C2×Dic47—42no—
327C2×Dic47—82no—
328C2×Dic47C2×C22⋊C414yes—
329D188—22no—
330D188—22no—
331D188—22no—
332D188—22no—
333C4×D47—24no—
334C4×D47—24no—
335C4×D47—24no—
336C4×D47—24no—
337Dic94—22no—
338Dic94—22no—
339Dic94—22no—
340Dic94—22no—
341C8×C47—24no—
342C47⋊C8—24no—
343C2×#1909—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#38611yescharacteristic
352C22×C47#38611yescharacteristic
353C22×C47#38611yescharacteristic
354C22×C47#38611yescharacteristic
355C22×C47C22×C22⋊C411yescharacteristic
356C22×C47C2×#12111yescharacteristic
357C22×C47C2×#12111yescharacteristic
358C2×D47—24no—
359C2×D47—44no—
360C2×D47—44no—
361C2×D47—82no—
362C4×C47—44no—
363C4×C47—82no—
364C4×C47#38611yescharacteristic
365C4×C47#38611yescharacteristic
366C4×C47#38611yescharacteristic
367C4×C47#38611yescharacteristic
368C4×C47C2×C4×D411yescharacteristic
369C4×C47C2×C4×D411yescharacteristic
370C4×C47C2×#12011yescharacteristic
371C4×C47C2×#12311yescharacteristic
372Dic47—24no—
373Dic47—44no—
374Dic47—82no—
375C2×#568—471no—
376C2×#536—471no—
377C2×#419—471no—
378C2×#419D4711yescharacteristic, complemented
379C2×#410—471no—
380#1909—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#190912yescomplemented
390C2×C47C2×#38611yescharacteristic
391D47—44no—
392C22×#41—471no—
393C23×Q8C2×D4711yescharacteristic
394#568—474no—
395#568—942no—
396#568—942no—
397#568—942no—
398C2×#131—942no—
399C2×#131—942no—
400C22×M16—471no—
401C22×M16—942no—
402C22×M16C2×D4711yescharacteristic
403#536—474no—
404#536—474no—
405#536—942no—
406#536—942no—
407C2×C4⋊Q8—472no—
408C2×#124—472no—
409C2×#123—942no—
410C2×C22⋊Q8—942no—
411C2×#117—471no—
412C2×#117—471no—
413C2×#117C2×D4711yescharacteristic
414#419—22no—
415#419—474no—
416#419—942no—
417#419C2×D4714yescomplemented
418C2×#103—22no—
419C2×#103—942no—
420#410—474no—
421#410—942no—
422C2×#99—942no—
423H(3,ℤ/4)—474no—
424H(3,ℤ/4)—474no—
425C47C2×#190911yescharacteristic, complemented, Sylow
426C2×#41—472no—
427C2×#41—472no—
428C2×#41—472no—
429C2×#41—472no—
430C2×#41—941no—
431C2×#41—941no—
432C2×#41—941no—
433C2×#41—941no—
434C2×#41—941no—
435C2×#41—941no—
436C2×#41—941no—
437C2×#41—941no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—471no—
450C22×Q8C4×D4712yes—
451C22×Q8C4×D4712yes—
452C22×Q8C22×D4712yes—
453C22×D4—472no—
454C22×D4—471no—
455C23×C4—21no—
456C23×C4—472no—
457C23×C4C22×D4711yescharacteristic
458#131—948no—
459#131—948no—
460#131—948no—
461#131—948no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—472no—
467C2×M16—472no—
468C2×M16—944no—
469C2×M16—948no—
470C2×M16—948no—
471C2×M16—941no—
472C2×M16—941no—
473C2×M16—941no—
474C2×M16—941no—
475C2×M16C22⋊D4712yes—
476C2×M16C22×D4712yes—
477C22×C8—472no—
478C22×C8—944no—
479C22×C8C22⋊D4712yes—
480C4⋊Q8—478no—
481C4⋊Q8—944no—
482#124—478no—
483#124—944no—
484#123—948no—
485#123—948no—
486C22⋊Q8—948no—
487C22⋊Q8—948no—
488#117—21no—
489#117—21no—
490#117—21no—
491#117—472no—
492#117—472no—
493#117—472no—
494#117—941no—
495#117—941no—
496#117—941no—
497#117—941no—
498#117—941no—
499#117C22×D4712yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—944no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—944no—
506C2×C22⋊C4—941no—
507C2×C22⋊C4—941no—
508C2×C42—21no—
509C2×C42—472no—
510C2×C42—941no—
511#103—28no—
512#103—948no—
513#99—948no—
514C24—472no—
515C24D4×D4711yescharacteristic
516#41—942no—
517#41—942no—
518#41—942no—
519#41—942no—
520#41—942no—
521#41—942no—
522#41—942no—
523#41—942no—
524#41—942no—
525#41—942no—
526#41—942no—
527#41—942no—
528#41—942no—
529#41—942no—
530#41—942no—
531#41—942no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—472no—
560C2×Q8—472no—
561C2×Q8—941no—
562C2×Q8—941no—
563C2×Q8—941no—
564C2×Q8—941no—
565C2×Q8C2×C4×D4714yes—
566C2×D4—474no—
567C2×D4—474no—
568C2×D4—472no—
569C2×D4—472no—
570C2×D4—942no—
571C2×D4—942no—
572C2×D4—942no—
573C2×D4—942no—
574C2×D4—941no—
575C2×D4—941no—
576C2×D4—941no—
577C2×D4—941no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—472no—
587C22×C4—474no—
588C22×C4—474no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—942no—
594C22×C4—1881no—
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—22no—
612M16—22no—
613M16—9416no—
614M16—942no—
615M16—942no—
616M16—942no—
617M16—942no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—474no—
621C2×C8—9416no—
622C2×C8—942no—
623C2×C8—942no—
624C2×C8C2×C22⋊D4714yes—
625C4⋊C4—22no—
626C4⋊C4—41no—
627C4⋊C4—9416no—
628C4⋊C4—942no—
629C4⋊C4—942no—
630C4⋊C4—942no—
631C4⋊C4—1881no—
632C22⋊C4—22no—
633C22⋊C4—41no—
634C22⋊C4—9416no—
635C22⋊C4—942no—
636C22⋊C4—942no—
637C22⋊C4—942no—
638C22⋊C4—1881no—
639C42—22no—
640C42—41no—
641C42—474no—
642C42—942no—
643C42—942no—
644C42—1881no—
645C23—42no—
646C23—474no—
647C23—942no—
648C23—942no—
649C23—1884no—
650C23C22⋊C4×D4711yescharacteristic
651C23C22⋊C4×D4711yescharacteristic
652C23#1309399511yescharacteristic
653C23#1309399511yescharacteristic
654C23#1309399711yescharacteristic
655C23#1309399711yescharacteristic
656C23C2×D4×D4711yescharacteristic
657Q8—24no—
658Q8—24no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—942no—
666Q8—942no—
667Q8—942no—
668Q8—942no—
669D4—944no—
670D4—944no—
671D4—944no—
672D4—944no—
673D4—942no—
674D4—942no—
675D4—942no—
676D4—942no—
677C2×C4—24no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—82no—
686C2×C4—474no—
687C2×C4—942no—
688C2×C4—942no—
689C2×C4—944no—
690C2×C4—944no—
691C2×C4—944no—
692C2×C4—944no—
693C2×C4—944no—
694C2×C4—3762no—
695C2×C4—1882no—
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#1309399211yescharacteristic
710C2×C4#1309399211yescharacteristic
711C2×C4#1309399511yescharacteristic
712C2×C4#1309399511yescharacteristic
713C2×C4#1309399711yescharacteristic
714C2×C4#1309399711yescharacteristic
715C2×C4#1309400611yescharacteristic
716C2×C4#1309400611yescharacteristic
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—24no—
726C8—944no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—944no—
735C22—3762no—
736C22—1884no—
737C22—1884no—
738C22#1568899911yescharacteristic
739C22#1568899911yescharacteristic
740C22#1568899911yescharacteristic
741C22#1568899911yescharacteristic
742C22C2×C22⋊C4×D4711yescharacteristic
743C22C2×#1309399511yescharacteristic
744C22C2×#1309399711yescharacteristic
745C4—44no—
746C4—82no—
747C4—944no—
748C4—3762no—
749C4—1884no—
750C4#1568899911yescharacteristic
751C4#1568899911yescharacteristic
752C4#1568899911yescharacteristic
753C4#1568899911yescharacteristic
754C4C2×(C22⋊D47)⋊C411yescharacteristic
755C4C2×C4×C22⋊D4711yescharacteristic
756C4C2×#1309399211yescharacteristic
757C4C2×#1309400611yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—1884no—
765C2#2024390712yesdirect product factor
766C2C2×#1568899911yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#419C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×#419D47
hypocenterC47C2×#1909
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. C2×#15689132C2semidirect
5. #20243907C2direct (N × H)
6. C2×#15688880C2semidirect
7. C2×#15688879C2semidirect
8. C2×C47×#419C2semidirect
20. #15689697C4semidirect
22. C2×#13094022C4semidirect
23. C2×#13094013C4semidirect
29. #15689132C22semidirect
34. #15688880C22semidirect
35. #15688879C22semidirect
40. C47×#419C22semidirect
74. #13094022C2×C4semidirect
76. #13094013C2×C4semidirect
378. C2×#419D47semidirect
389. C2×C47#1909semidirect
417. #419C2×D47semidirect
425. C47C2×#1909semidirect
765. C2#20243907direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898892
C2×#156896972
C2×#156891322
C2×#156890962
#202439072
C2×#156888802
C2×#156888792
C2×C47×#4192
C2×#190947