Finite Group Databasebeta

← C2×#20243750 #26217752

Subgroups — C2×#20243750 #26217752

Order 12032.

1682 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689921C211yesmaximal, characteristic
2C2×#15689139C211yesmaximal, characteristic, complemented
3C2×#15689119C211yesmaximal, characteristic, complemented
4C2×#15689091C211yesmaximal, characteristic, complemented
5#20243750C218yesmaximal, direct product factor
6C2×#15688894C211yesmaximal, characteristic, complemented
7C2×#15688887C211yesmaximal, characteristic, complemented
8C2×C47×#568C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689921—22no—
11#15689921—22no—
12#15689921C414yescomplemented
13#15689921C2214yes—
14C2×#13094055—21no—
15C2×#13094054C412yescomplemented
16C2×#13094050—21no—
17C2×#13094049C412yescomplemented
18C2×#13094044—22no—
19C22×#10625329C2211yescharacteristic
20C23×C47⋊C8C2211yescharacteristic
21C2×#13093983C2211yescharacteristic
22#15689139—22no—
23#15689139C2214yescomplemented
24C2×#13093950—22no—
25#15689119—22no—
26#15689119C2214yescomplemented
27C2×#13093948—21no—
28C2×#13093945—21no—
29#15689091—22no—
30#15689091C2214yescomplemented
31C2×(C2×D47)⋊C8—22no—
32#15688894C2214yescomplemented
33#15688887C2214yescomplemented
34C22×#41×C47C2211yescharacteristic
35C47×#568—22no—
36C47×#568—22no—
37C47×#568—22no—
38C47×#568C2214yescomplemented
39C2×#131×C47—22no—
40C2×#131×C47—22no—
41C22×M16×C47—22no—
42C22×M16×C47C2211yescharacteristic
43C22×M16×C47C2211yescharacteristic
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350—21no—
53C2×#10625350—21no—
54C2×#10625350C2×C412yes—
55C2×#10625350C2312yes—
56C22×Dic94C2×C411yescharacteristic
57C22×D188C2×C411yescharacteristic
58C22×C22⋊D47—21no—
59C22×C4×D47—21no—
60#13094055—24no—
61#13094055—24no—
62#13094054—24no—
63#13094054C2×C418yescomplemented
64#13094050—24no—
65#13094050—24no—
66#13094049—24no—
67#13094049C2×C418yescomplemented
68#13094044—28no—
69#13094044—28no—
70C2×#10625337—22no—
71C2×#10625335—22no—
72C2×#10625336—22no—
73C2×#10625334—22no—
74C2×#10625329—21no—
75C2×#10625329—21no—
76C2×#10625329—21no—
77C2×#10625329C2×C412yes—
78C2×#10625329C2×C412yes—
79C2×#10625329C2312yes—
80C22×C47⋊C8—21no—
81C22×C47⋊C8—21no—
82C22×C47⋊C8—21no—
83C22×C47⋊C8—21no—
84C22×C47⋊C8—21no—
85C22×C47⋊C8—21no—
86C22×C47⋊C8—21no—
87C22×C47⋊C8C2312yes—
88#13093983—21no—
89#13093983—21no—
90#13093983—21no—
91#13093983C2312yes—
92C2×C4⋊Dic47—21no—
93C2×C22⋊Dic47—21no—
94C2×C4×Dic47—21no—
95#13093950—28no—
96#13093948—24no—
97#13093945—24no—
98(C2×D47)⋊C8—28no—
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×C47C2×C412yes—
106C2×#41×C47C2×C412yes—
107C2×#41×C47D412yes—
108C2×#41×C47D412yes—
109C2×#41×C47D412yes—
110C2×#41×C47C2312yes—
111C22×Q8×C47D411yescharacteristic
112C22×D4×C47—21no—
113C22×D4×C47D411yescharacteristic
114C23×C4×C47—21no—
115C23×C4×C47C2311yescharacteristic
116#131×C47—28no—
117#131×C47—28no—
118#131×C47—28no—
119#131×C47—28no—
120C2×M16×C47—24no—
121C2×M16×C47—28no—
122C2×M16×C47—21no—
123C2×M16×C47—21no—
124C2×M16×C47—21no—
125C2×M16×C47—21no—
126C2×M16×C47—21no—
127C2×M16×C47—21no—
128C2×M16×C47—21no—
129C2×M16×C47—28no—
130C2×M16×C47D412yes—
131C2×M16×C47D412yes—
132C2×M16×C47D412yes—
133C2×M16×C47C2312yes—
134C2×M16×C47C2312yes—
135C22×C8×C47—24no—
136C22×C8×C47—21no—
137C22×C8×C47D412yes—
138C24×C47—21no—
139C24×C47#4111yescharacteristic
140C23×D47—21no—
141#41×C47—22no—
142#41×C47—22no—
143#41×C47—22no—
144#41×C47—22no—
145#41×C47—22no—
146#41×C47—22no—
147#41×C47—22no—
148#41×C47—22no—
149#41×C47—22no—
150#41×C47—22no—
151#41×C47—22no—
152#41×C47—22no—
153#41×C47C22⋊C414yes—
154#41×C47C22⋊C414yes—
155#41×C47C22×C414yes—
156#41×C47C2×D414yes—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47C22⋊C412yes—
161C2×Q8×C47C22⋊C412yes—
162C2×Q8×C47C2×D412yes—
163C2×D4×C47—22no—
164C2×D4×C47—22no—
165C2×D4×C47—22no—
166C2×D4×C47—22no—
167C2×D4×C47—22no—
168C2×D4×C47—22no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47C22⋊C412yes—
173C2×D4×C47C22⋊C412yes—
174C2×D4×C47C2×D412yes—
175C22×C4×C47—21no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47#4111yescharacteristic
193C22×C4×C47#4111yescharacteristic
194C22×C4×C47#4111yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C2×C22⋊D47—22no—
197C2×C22⋊D47—22no—
198C2×C22⋊D47—41no—
199C2×C22⋊D47—41no—
200C2×C22⋊D47—41no—
201C2×C22⋊D47—41no—
202C22×Dic47—21no—
203C22×Dic47—41no—
204#10625350—22no—
205#10625350—22no—
206#10625350—22no—
207#10625350—22no—
208#10625350—22no—
209#10625350—22no—
210#10625350—22no—
211#10625350—22no—
212#10625350—41no—
213#10625350—41no—
214#10625350—41no—
215#10625350—41no—
216#10625350—41no—
217#10625350—41no—
218#10625350—41no—
219#10625350—41no—
220C2×D188—21no—
221C2×D188—21no—
222C2×D188—21no—
223C2×D188—21no—
224C2×D188—21no—
225C2×D188C22×C412yes—
226C2×C4×D47—22no—
227C2×C4×D47—22no—
228C2×C4×D47—41no—
229C2×C4×D47—41no—
230C2×C4×D47—41no—
231C2×C4×D47—41no—
232C2×Dic94—21no—
233C2×Dic94—21no—
234C2×Dic94—21no—
235C2×Dic94—21no—
236C2×Dic94—21no—
237C2×Dic94C22×C412yes—
238M16×C47—216no—
239M16×C47—22no—
240M16×C47—22no—
241M16×C47—22no—
242M16×C47—22no—
243M16×C47—22no—
244M16×C47—22no—
245M16×C47—22no—
246M16×C47C2×D414yes—
247C2×C8×C47—216no—
248C2×C8×C47—22no—
249C2×C8×C47—22no—
250C2×C8×C47—22no—
251C2×C8×C47—22no—
252C2×C8×C47—22no—
253C2×C8×C47C2×D414yes—
254C22⋊Dic47—22no—
255C22⋊Dic47—41no—
256#10625337—28no—
257#10625336—28no—
258#10625335—28no—
259#10625334—28no—
260C4⋊Dic47—22no—
261C4⋊Dic47—41no—
262C4×Dic47—22no—
263C4×Dic47—41no—
264#10625329—22no—
265#10625329—22no—
266#10625329—22no—
267#10625329C22×C414yes—
268C2×C47⋊C8—22no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8—22no—
274C2×C47⋊C8—41no—
275C2×C47⋊C8—41no—
276C2×C47⋊C8—41no—
277C2×C47⋊C8—41no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—42no—
282C23×C47—82no—
283C23×C47C4×D411yescharacteristic
284C23×C47C4×D411yescharacteristic
285C23×C47#12111yescharacteristic
286C23×C47#12111yescharacteristic
287C23×C47#12311yescharacteristic
288C23×C47#12311yescharacteristic
289C23×C47C2×#4111yescharacteristic
290C22×D47—22no—
291C22×D47—44no—
292C22×D47—41no—
293C22×D47—41no—
294Q8×C47—22no—
295Q8×C47—22no—
296Q8×C47—22no—
297Q8×C47C2×C22⋊C414yes—
298D4×C47—24no—
299D4×C47—24no—
300D4×C47—24no—
301D4×C47—24no—
302D4×C47—22no—
303D4×C47—22no—
304D4×C47—22no—
305D4×C47C2×C22⋊C414yes—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—24no—
310C2×C4×C47—24no—
311C2×C4×C47—24no—
312C2×C4×C47—24no—
313C2×C4×C47C2×C22⋊C411yescharacteristic
314C2×C4×C47C2×C22⋊C411yescharacteristic
315C2×C4×C47C2×C22⋊C411yescharacteristic
316C2×C4×C47C2×C22⋊C411yescharacteristic
317C2×C4×C47C4×D411yescharacteristic
318C2×C4×C47C4×D411yescharacteristic
319C2×C4×C47C4×D411yescharacteristic
320C2×C4×C47C4×D411yescharacteristic
321C2×C4×C47C4×D411yescharacteristic
322C2×C4×C47C4×D411yescharacteristic
323C2×C4×C47#12011yescharacteristic
324C2×C4×C47#12011yescharacteristic
325C2×C4×C47#12011yescharacteristic
326C2×C4×C47#12011yescharacteristic
327C2×C4×C47#12111yescharacteristic
328C2×C4×C47#12111yescharacteristic
329C2×C4×C47#12111yescharacteristic
330C2×C4×C47#12111yescharacteristic
331C2×C4×C47#12111yescharacteristic
332C2×C4×C47#12111yescharacteristic
333C2×C4×C47#12311yescharacteristic
334C2×C4×C47#12311yescharacteristic
335C2×C4×C47C23×C411yescharacteristic
336C2×C4×C47C22×D411yescharacteristic
337C2×C4×C47C22×D411yescharacteristic
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C2×#4111yescharacteristic
341C22⋊D47—42no—
342C22⋊D47—42no—
343C22⋊D47—42no—
344C22⋊D47—42no—
345C2×Dic47—22no—
346C2×Dic47—41no—
347C2×Dic47—41no—
348C2×Dic47—42no—
349C2×Dic47—82no—
350D188—22no—
351D188—22no—
352D188—41no—
353D188—41no—
354C4×D47—42no—
355C4×D47—42no—
356C4×D47—42no—
357C4×D47—42no—
358Dic94—22no—
359Dic94—22no—
360Dic94—41no—
361Dic94—41no—
362C8×C47—24no—
363C8×C47—24no—
364C47⋊C8—24no—
365C47⋊C8—42no—
366C2×#1881—471nomaximal, Sylow
367C22×C47—22no—
368C22×C47—22no—
369C22×C47—22no—
370C22×C47—24no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—44no—
376C22×C47—82no—
377C22×C47—82no—
378C22×C47#38611yescharacteristic
379C22×C47#38611yescharacteristic
380C22×C47#38611yescharacteristic
381C22×C47#38611yescharacteristic
382C22×C47C2×C4×D411yescharacteristic
383C22×C47C2×#12111yescharacteristic
384C22×C47C2×#12311yescharacteristic
385C2×D47—44no—
386C2×D47—42no—
387C2×D47—82no—
388C2×D47—82no—
389C4×C47—24no—
390C4×C47#38611yescharacteristic
391C4×C47#38611yescharacteristic
392C4×C47#38611yescharacteristic
393C4×C47#38611yescharacteristic
394C4×C47C22×C22⋊C411yescharacteristic
395C4×C47C2×C4×D411yescharacteristic
396C4×C47C2×#12011yescharacteristic
397C4×C47C2×#12111yescharacteristic
398Dic47—42no—
399Dic47—82no—
400C2×#575—471no—
401C2×#568D4711yescharacteristic, complemented
402C2×#421—471no—
403C2×#416—471no—
404C2×#408—471no—
405#1881—478no—
406C2×#344—471no—
407C2×#341—471no—
408C2×C47—21no—
409C2×C47—21no—
410C2×C47—21no—
411C2×C47—21no—
412C2×C47—21no—
413C2×C47—21no—
414C2×C47—44no—
415C2×C47#188112yescomplemented
416C2×C47C2×#38611yescharacteristic
417D47—82no—
418C22×#41—471no—
419C22×#41C2×D4711yescharacteristic
420#575—474no—
421#575—474no—
422#575—942no—
423#575—942no—
424C2×#137—472no—
425C2×#137—941no—
426C2×AGL(1,ℤ/8)—472no—
427C2×AGL(1,ℤ/8)—941no—
428C2×#135—942no—
429#568—22no—
430#568—22no—
431#568—22no—
432#568C2×D4714yescomplemented
433C2×#131—22no—
434C2×#131—22no—
435C22×M16—22no—
436C22×M16—471no—
437C22×M16C2×D4711yescharacteristic
438C22×M16C2×D4711yescharacteristic
439C23×C8—471no—
440C2×#117—471no—
441#421—474no—
442#421—942no—
443C2×#104—942no—
444#416—474no—
445#416—942no—
446C2×#103—941no—
447C2×#102—941no—
448#408—474no—
449#408—942no—
450C2×C22⋊C8—942no—
451#344—474no—
452#341—474no—
453C47C2×#188111yescharacteristic, complemented, Sylow
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—472no—
461C2×#41—472no—
462C2×#41—941no—
463C2×#41—941no—
464C2×#41—941no—
465C2×#41—941no—
466C2×#41—941no—
467C2×#41—941no—
468C2×#41—941no—
469C2×#41—941no—
470C2×#41—941no—
471C2×#41—941no—
472C2×#41C4×D4712yes—
473C2×#41C4×D4712yes—
474C2×#41D18812yes—
475C2×#41C22⋊D4712yes—
476C2×#41C22⋊D4712yes—
477C2×#41C22×D4712yes—
478C22×Q8—471no—
479C22×Q8D18811yescharacteristic
480C22×D4—21no—
481C22×D4—471no—
482C22×D4—941no—
483C22×D4D18811yescharacteristic
484C23×C4—21no—
485C23×C4—941no—
486C23×C4C22×D4711yescharacteristic
487#137—478no—
488#137—944no—
489#137—944no—
490#137—944no—
491AGL(1,ℤ/8)—478no—
492AGL(1,ℤ/8)—944no—
493AGL(1,ℤ/8)—944no—
494AGL(1,ℤ/8)—944no—
495#135—948no—
496#135—948no—
497C2×Q16—942no—
498C2×SD16—942no—
499C2×SD16—942no—
500C2×D8—942no—
501#131—28no—
502#131—28no—
503#131—28no—
504#131—28no—
505C2×M16—24no—
506C2×M16—28no—
507C2×M16—21no—
508C2×M16—21no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—28no—
515C2×M16—472no—
516C2×M16—472no—
517C2×M16—472no—
518C2×M16—941no—
519C2×M16—941no—
520C2×M16—941no—
521C2×M16C22⋊D4712yes—
522C2×M16C22⋊D4712yes—
523C2×M16C22⋊D4712yes—
524C2×M16C22×D4712yes—
525C2×M16C22×D4712yes—
526C22×C8—24no—
527C22×C8—21no—
528C22×C8—472no—
529C22×C8—941no—
530C22×C8—941no—
531C22×C8—941no—
532C22×C8—941no—
533C22×C8—941no—
534C22×C8—941no—
535C22×C8—941no—
536C22×C8C22⋊D4712yes—
537#117—472no—
538#117—941no—
539#117—941no—
540#117—941no—
541C2×C4⋊C4—941no—
542C2×C22⋊C4—941no—
543C2×C42—941no—
544#104—948no—
545#103—944no—
546#102—944no—
547C22⋊C8—948no—
548C24—21no—
549C24—941no—
550C24#1062535011yescharacteristic
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—942no—
564#41—942no—
565#41—942no—
566#41—942no—
567#41—942no—
568#41—942no—
569#41—942no—
570#41—942no—
571#41—1881no—
572#41—1881no—
573#41—1881no—
574#41—1881no—
575#41—1881no—
576#41—1881no—
577#41—1881no—
578#41—1881no—
579#41(C2×D47)⋊C414yes—
580#41(C2×D47)⋊C414yes—
581#41C2×C4×D4714yes—
582#41C2×C22⋊D4714yes—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—472no—
587C2×Q8—941no—
588C2×Q8—941no—
589C2×Q8—941no—
590C2×Q8—941no—
591C2×Q8—941no—
592C2×Q8(C2×D47)⋊C412yes—
593C2×Q8(C2×D47)⋊C412yes—
594C2×Q8C2×D18812yes—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—472no—
605C2×D4—942no—
606C2×D4—942no—
607C2×D4—941no—
608C2×D4—941no—
609C2×D4—941no—
610C2×D4—941no—
611C2×D4—941no—
612C2×D4—1881no—
613C2×D4—1881no—
614C2×D4—1881no—
615C2×D4—1881no—
616C2×D4(C2×D47)⋊C412yes—
617C2×D4(C2×D47)⋊C412yes—
618C2×D4C2×D18812yes—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—941no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—1881no—
630C22×C4—1881no—
631C22×C4—1881no—
632C22×C4—1881no—
633C22×C4—1881no—
634C22×C4C2×C4×D4711yescharacteristic
635C22×C4C2×C4×D4711yescharacteristic
636C22×C4C2×D18811yescharacteristic
637C22×C4C2×D18811yescharacteristic
638C22×C4#1062535011yescharacteristic
639C22×C4#1062535011yescharacteristic
640C22×C4#1062535011yescharacteristic
641C22×C4C2×C22⋊D4711yescharacteristic
642C22×C4C2×C22⋊D4711yescharacteristic
643C22×C4C2×C22⋊D4711yescharacteristic
644C22×C4C2×C22⋊D4711yescharacteristic
645C22×C4C2×C22⋊D4711yescharacteristic
646C22×C4C2×C22⋊D4711yescharacteristic
647C22×C4C23×D4711yescharacteristic
648Q16—948no—
649SD16—948no—
650SD16—948no—
651D8—948no—
652M16—216no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—22no—
657M16—22no—
658M16—22no—
659M16—22no—
660M16—474no—
661M16—942no—
662M16—942no—
663M16—942no—
664M16C2×C22⋊D4714yes—
665C2×C8—216no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—942no—
672C2×C8—942no—
673C2×C8—942no—
674C2×C8—942no—
675C2×C8—942no—
676C2×C8—942no—
677C2×C8—1881no—
678C2×C8—1881no—
679C2×C8—1881no—
680C2×C8—1881no—
681C2×C8C2×C22⋊D4714yes—
682C4⋊C4—942no—
683C4⋊C4—1881no—
684C22⋊C4—942no—
685C22⋊C4—1881no—
686C42—942no—
687C42—1881no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—82no—
693C23—942no—
694C23—1884no—
695C23—1881no—
696C23—1881no—
697C23C4×C22⋊D4711yescharacteristic
698C23C4×C22⋊D4711yescharacteristic
699C23#1309399811yescharacteristic
700C23#1309399811yescharacteristic
701C23#1309400711yescharacteristic
702C23#1309400711yescharacteristic
703C23C2×#1062535011yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—942no—
708Q8—942no—
709Q8—1881no—
710Q8—1881no—
711Q8C2×(C2×D47)⋊C414yes—
712D4—24no—
713D4—24no—
714D4—24no—
715D4—24no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—942no—
720D4—942no—
721D4—1882no—
722D4—1882no—
723D4—1882no—
724D4—1882no—
725D4—1881no—
726D4—1881no—
727D4C2×(C2×D47)⋊C414yes—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—942no—
736C2×C4—3762no—
737C2×C4—1882no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1882no—
741C2×C4—1882no—
742C2×C4—1882no—
743C2×C4—1882no—
744C2×C4C2×(C2×D47)⋊C411yescharacteristic
745C2×C4C2×(C2×D47)⋊C411yescharacteristic
746C2×C4C2×(C2×D47)⋊C411yescharacteristic
747C2×C4C2×(C2×D47)⋊C411yescharacteristic
748C2×C4C4×C22⋊D4711yescharacteristic
749C2×C4C4×C22⋊D4711yescharacteristic
750C2×C4C4×C22⋊D4711yescharacteristic
751C2×C4C4×C22⋊D4711yescharacteristic
752C2×C4C4×C22⋊D4711yescharacteristic
753C2×C4C4×C22⋊D4711yescharacteristic
754C2×C4#1309399311yescharacteristic
755C2×C4#1309399311yescharacteristic
756C2×C4#1309399311yescharacteristic
757C2×C4#1309399311yescharacteristic
758C2×C4#1309399811yescharacteristic
759C2×C4#1309399811yescharacteristic
760C2×C4#1309399811yescharacteristic
761C2×C4#1309399811yescharacteristic
762C2×C4#1309399811yescharacteristic
763C2×C4#1309399811yescharacteristic
764C2×C4#1309400711yescharacteristic
765C2×C4#1309400711yescharacteristic
766C2×C4C22×C4×D4711yescharacteristic
767C2×C4C22×C22⋊D4711yescharacteristic
768C2×C4C22×C22⋊D4711yescharacteristic
769C2×C4C22×C22⋊D4711yescharacteristic
770C2×C4C22×D18811yescharacteristic
771C2×C4C2×#1062535011yescharacteristic
772C8—24no—
773C8—24no—
774C8—944no—
775C8—1882no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—24no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—82no—
786C22—82no—
787C22—3762no—
788C22—3762no—
789C22—1884no—
790C22—1882no—
791C22#1568900211yescharacteristic
792C22#1568900211yescharacteristic
793C22#1568900211yescharacteristic
794C22#1568900211yescharacteristic
795C22C2×C4×C22⋊D4711yescharacteristic
796C22C2×#1309399811yescharacteristic
797C22C2×#1309400711yescharacteristic
798C4—24no—
799C4—3762no—
800C4—1882no—
801C4#1568900211yescharacteristic
802C4#1568900211yescharacteristic
803C4#1568900211yescharacteristic
804C4#1568900211yescharacteristic
805C4C22×(C2×D47)⋊C411yescharacteristic
806C4C2×C4×C22⋊D4711yescharacteristic
807C4C2×#1309399311yescharacteristic
808C4C2×#1309399811yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—44no—
816C2—3762no—
817C2#2024375012yesdirect product factor
818C2C2×#1568900211yescharacteristic
subgroupG/H
centerC2×C4#13093993
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#568C2
socleC22×C47#386
prime radicalC2×#15689921C2
cosocleC22×C4×C47C24
hypercenterC2×#568D47
hypocenterC47C2×#1881
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#15689139C2semidirect
3. C2×#15689119C2semidirect
4. C2×#15689091C2semidirect
5. #20243750C2direct (N × H)
6. C2×#15688894C2semidirect
7. C2×#15688887C2semidirect
8. C2×C47×#568C2semidirect
12. #15689921C4semidirect
15. C2×#13094054C4semidirect
17. C2×#13094049C4semidirect
23. #15689139C22semidirect
26. #15689119C22semidirect
30. #15689091C22semidirect
32. #15688894C22semidirect
33. #15688887C22semidirect
38. C47×#568C22semidirect
63. #13094054C2×C4semidirect
67. #13094049C2×C4semidirect
401. C2×#568D47semidirect
415. C2×C47#1881semidirect
432. #568C2×D47semidirect
453. C47C2×#1881semidirect
817. C2#20243750direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156899212
C2×#156891392
C2×#156891192
C2×#156890912
#202437502
C2×#156888942
C2×#156888872
C2×C47×#5682
C2×#188147