Finite Group Databasebeta

← #27083700

Subgroups — #27083700

Order 12032.

2628 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689921C211yesmaximal, characteristic, complemented
2C2×#15689921C211yesmaximal, characteristic, complemented
3C2×#15689890C211yesmaximal, characteristic, complemented
4#20253127C214yesmaximal, complemented
5#20253122C214yesmaximal, complemented
6#20253118C214yesmaximal, complemented
7#20253113C214yesmaximal, complemented
8#20253105C218yesmaximal, complemented
9C2×#15689171C211yesmaximal, characteristic, complemented
10C2×#15689107C211yesmaximal, characteristic, complemented
11C2×#15689105C211yesmaximal, characteristic, complemented
12C2×C47×#575C211yesmaximal, characteristic, complemented
13C22×#10625350C2211yescharacteristic
14#15689921—22no—
15#15689921—22no—
16#15689921—22no—
17#15689921—22no—
18#15689921—22no—
19#15689921—22no—
20#15689921C2214yes—
21#15689921C2214yescomplemented
22C2×#13094055—21no—
23C2×#13094055C2212yescomplemented
24C2×#13094054C2212yescomplemented
25C2×#13094054C2212yescomplemented
26C2×#13094050—21no—
27C2×#13094050C2212yescomplemented
28C2×#13094049C2212yescomplemented
29C2×#13094049C2212yescomplemented
30C2×#13094044—22no—
31C2×#13094044C2214yescomplemented
32#15689890—22no—
33#15689890—22no—
34#15689890C2214yescomplemented
35#15689890C2214yescomplemented
36C2×#13094031—22no—
37C2×#13094031C2214yescomplemented
38C22×#10625329—22no—
39C22×#10625329C2211yescharacteristic
40C22×#10625329C2211yescharacteristic
41C22×#10625329C2211yescharacteristic
42#15689396C22116yescomplemented
43#15689391C22116yescomplemented
44#15689388C22116yescomplemented
45#15689384C22116yescomplemented
46#15689171C2214yescomplemented
47#15689171C2214yescomplemented
48C2×#13093959C2214yescomplemented
49#15689107C2214yescomplemented
50#15689107C2214yescomplemented
51#15689105C2214yescomplemented
52#15689105C2214yescomplemented
53C2×#13093943C2212yescomplemented
54C2×#13093942C2212yescomplemented
55C2×#13093941C2212yescomplemented
56C2×#13093940C2212yescomplemented
57C22×#41×C47C2211yescharacteristic
58C22×#41×C47C2211yescharacteristic
59C47×#575—22no—
60C47×#575—22no—
61C47×#575C2214yes—
62C47×#575C2214yescomplemented
63C2×#137×C47—21no—
64C2×#137×C47C2212yescomplemented
65C2×AGL(1,ℤ/8)×C47—21no—
66C2×AGL(1,ℤ/8)×C47C2212yescomplemented
67C2×#135×C47—22no—
68C22×M16×C47C2211yescharacteristic
69C2×#10625350—21no—
70C2×#10625350—21no—
71C2×#10625350—21no—
72C2×#10625350—21no—
73C2×#10625350—21no—
74C2×#10625350—21no—
75C2×#10625350—21no—
76C2×#10625350—21no—
77C2×#10625350—21no—
78C2×#10625350—21no—
79C2×#10625350C2312yes—
80C2×#10625350C2312yes—
81C22×Dic94C2311yescharacteristic
82C22×D188C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C4×D47—21no—
85#13094055—24no—
86#13094055—24no—
87#13094055—24no—
88#13094055—24no—
89#13094054—24no—
90#13094054—24no—
91#13094054—24no—
92#13094054C2318yes—
93#13094050—24no—
94#13094050—24no—
95#13094050—24no—
96#13094050—24no—
97#13094049—24no—
98#13094049—24no—
99#13094049—24no—
100#13094049C2318yes—
101#13094044—28no—
102#13094044—28no—
103#13094044—28no—
104#13094044—28no—
105C2×#10625337—22no—
106C2×#10625337C2314yescomplemented
107C2×#10625335—22no—
108C2×#10625335C2314yescomplemented
109C2×#10625336—22no—
110C2×#10625336C2314yescomplemented
111C2×#10625334—22no—
112C2×#10625334C2314yescomplemented
113#13094031—28no—
114#13094031—28no—
115#13094031—28no—
116#13094031C23116yes—
117C2×#10625329—21no—
118C2×#10625329—21no—
119C2×#10625329—21no—
120C2×#10625329—21no—
121C2×#10625329—21no—
122C2×#10625329—21no—
123C2×#10625329—28no—
124C2×#10625329—28no—
125C2×#10625329—24no—
126C2×#10625329D412yes—
127C2×#10625329D412yes—
128C2×#10625329D412yes—
129C2×#10625329D412yes—
130C2×#10625329C2312yes—
131C2×#10625329C2312yes—
132C2×#10625329C2312yes—
133C2×#10625329C2312yes—
134C2×#10625329C2312yes—
135C2×#10625329C2312yes—
136C2×#10625329C2312yes—
137C2×#10625329C2312yes—
138C22×C47⋊C8—21no—
139C22×C47⋊C8—21no—
140C22×C47⋊C8—24no—
141C22×C47⋊C8C2312yes—
142#13093959C23116yescomplemented
143#13093943C2318yescomplemented
144#13093942C2318yescomplemented
145#13093941C2318yescomplemented
146#13093940C2318yescomplemented
147C2×#41×C47—21no—
148C2×#41×C47—21no—
149C2×#41×C47—21no—
150C2×#41×C47—21no—
151C2×#41×C47—21no—
152C2×#41×C47—21no—
153C2×#41×C47—21no—
154C2×#41×C47—21no—
155C2×#41×C47—21no—
156C2×#41×C47—21no—
157C2×#41×C47—21no—
158C2×#41×C47—21no—
159C2×#41×C47—21no—
160C2×#41×C47—21no—
161C2×#41×C47—21no—
162C2×#41×C47—21no—
163C2×#41×C47D412yes—
164C2×#41×C47D412yes—
165C2×#41×C47D412yes—
166C2×#41×C47C2312yes—
167C2×#41×C47C2312yes—
168C2×#41×C47C2312yes—
169C2×#41×C47C2312yes—
170C2×#41×C47C2312yes—
171C22×Q8×C47D411yescharacteristic
172C22×Q8×C47C2311yescharacteristic
173C22×D4×C47—21no—
174C22×D4×C47—21no—
175C22×D4×C47D411yescharacteristic
176C22×D4×C47C2311yescharacteristic
177C23×C4×C47—21no—
178C23×C4×C47—21no—
179C23×C4×C47C2311yescharacteristic
180#137×C47—24no—
181#137×C47—24no—
182#137×C47—24no—
183#137×C47C2318yes—
184AGL(1,ℤ/8)×C47—24no—
185AGL(1,ℤ/8)×C47—24no—
186AGL(1,ℤ/8)×C47—24no—
187AGL(1,ℤ/8)×C47C2318yes—
188#135×C47—28no—
189#135×C47—28no—
190C2×Q16×C47—22no—
191C2×SD16×C47—22no—
192C2×SD16×C47—22no—
193C2×D8×C47—22no—
194C2×M16×C47—21no—
195C2×M16×C47—21no—
196C2×M16×C47—21no—
197C2×M16×C47C2312yes—
198C2×M16×C47C2312yes—
199C2×M16×C47C2312yes—
200C22×C8×C47—21no—
201C24×C47—21no—
202C24×C47—21no—
203C24×C47#4111yescharacteristic
204C23×D47—21no—
205#41×C47—22no—
206#41×C47—22no—
207#41×C47—22no—
208#41×C47—22no—
209#41×C47—22no—
210#41×C47—22no—
211#41×C47—22no—
212#41×C47—22no—
213#41×C47—22no—
214#41×C47—22no—
215#41×C47—22no—
216#41×C47—22no—
217#41×C47—22no—
218#41×C47—22no—
219#41×C47—22no—
220#41×C47—22no—
221#41×C47—22no—
222#41×C47—22no—
223#41×C47—22no—
224#41×C47—22no—
225#41×C47—41no—
226#41×C47—41no—
227#41×C47—41no—
228#41×C47—41no—
229#41×C47—41no—
230#41×C47—41no—
231#41×C47—41no—
232#41×C47—41no—
233#41×C47C2×D414yes—
234#41×C47C2×D414yes—
235#41×C47C2×D414yes—
236#41×C47C2414yes—
237C2×Q8×C47—21no—
238C2×Q8×C47—21no—
239C2×Q8×C47—21no—
240C2×Q8×C47—21no—
241C2×Q8×C47—21no—
242C2×Q8×C47—21no—
243C2×Q8×C47—21no—
244C2×Q8×C47—21no—
245C2×Q8×C47C2×D412yes—
246C2×Q8×C47C2×D412yes—
247C2×Q8×C47C2×D412yes—
248C2×Q8×C47C2412yes—
249C2×D4×C47—22no—
250C2×D4×C47—22no—
251C2×D4×C47—22no—
252C2×D4×C47—22no—
253C2×D4×C47—22no—
254C2×D4×C47—22no—
255C2×D4×C47—22no—
256C2×D4×C47—22no—
257C2×D4×C47—21no—
258C2×D4×C47—21no—
259C2×D4×C47—21no—
260C2×D4×C47—21no—
261C2×D4×C47—21no—
262C2×D4×C47—21no—
263C2×D4×C47—21no—
264C2×D4×C47—21no—
265C2×D4×C47—41no—
266C2×D4×C47—41no—
267C2×D4×C47—41no—
268C2×D4×C47—41no—
269C2×D4×C47C2×D412yes—
270C2×D4×C47C2×D412yes—
271C2×D4×C47C2×D412yes—
272C2×D4×C47C2412yes—
273C22×C4×C47—21no—
274C22×C4×C47—22no—
275C22×C4×C47—22no—
276C22×C4×C47—22no—
277C22×C4×C47—22no—
278C22×C4×C47—22no—
279C22×C4×C47—22no—
280C22×C4×C47—21no—
281C22×C4×C47—22no—
282C22×C4×C47—22no—
283C22×C4×C47—41no—
284C22×C4×C47—41no—
285C22×C4×C47—41no—
286C22×C4×C47—41no—
287C22×C4×C47C2×D411yescharacteristic
288C22×C4×C47C2×D411yescharacteristic
289C22×C4×C47C2×D411yescharacteristic
290C22×C4×C47C2×D411yescharacteristic
291C22×C4×C47C2×D411yescharacteristic
292C22×C4×C47C2×D411yescharacteristic
293C22×C4×C47C2×D411yescharacteristic
294C22×C4×C47C2×D411yescharacteristic
295C22×C4×C47#4111yescharacteristic
296C22×C4×C47#4111yescharacteristic
297C22×C4×C47#4111yescharacteristic
298C22×C4×C47C2411yescharacteristic
299C22×C4×C47C2411yescharacteristic
300C22×C4×C47C2411yescharacteristic
301C2×C22⋊D47—22no—
302C2×C22⋊D47—22no—
303C2×C22⋊D47—41no—
304C2×C22⋊D47—41no—
305C2×C22⋊D47—41no—
306C2×C22⋊D47—41no—
307C22×Dic47—21no—
308#10625350—22no—
309#10625350—22no—
310#10625350—22no—
311#10625350—22no—
312#10625350—22no—
313#10625350—22no—
314#10625350—22no—
315#10625350—22no—
316#10625350—41no—
317#10625350—41no—
318#10625350—41no—
319#10625350—41no—
320#10625350—41no—
321#10625350—41no—
322#10625350—41no—
323#10625350—41no—
324C2×D188—21no—
325C2×D188—21no—
326C2×D188—21no—
327C2×D188—21no—
328C2×D188—21no—
329C2×D188C2412yes—
330C2×C4×D47—22no—
331C2×C4×D47—22no—
332C2×C4×D47—41no—
333C2×C4×D47—41no—
334C2×C4×D47—41no—
335C2×C4×D47—41no—
336C2×Dic94—21no—
337C2×Dic94—21no—
338C2×Dic94—21no—
339C2×Dic94—21no—
340C2×Dic94—21no—
341C2×Dic94C2412yes—
342Q16×C47—28no—
343SD16×C47—28no—
344SD16×C47—28no—
345D8×C47—28no—
346M16×C47—22no—
347M16×C47—22no—
348M16×C47—22no—
349M16×C47C2414yes—
350C2×C8×C47—22no—
351C2×C8×C47—22no—
352C2×C8×C47—22no—
353#10625337—28no—
354#10625337—28no—
355#10625336—28no—
356#10625336—28no—
357#10625335—28no—
358#10625335—28no—
359#10625334—28no—
360#10625334—28no—
361#10625329—22no—
362#10625329—22no—
363#10625329—22no—
364#10625329—22no—
365#10625329—22no—
366#10625329—22no—
367#10625329—216no—
368#10625329C2×D414yes—
369#10625329C2×D414yes—
370#10625329C2×D414yes—
371#10625329C2×D414yes—
372#10625329C2414yes—
373#10625329C2414yes—
374C2×C47⋊C8—22no—
375C2×C47⋊C8—22no—
376C2×C47⋊C8—22no—
377C2×C47⋊C8—22no—
378C2×C47⋊C8—22no—
379C2×C47⋊C8—22no—
380C2×C47⋊C8—216no—
381C2×C47⋊C8C2×D414yes—
382C2×C47⋊C8C2×D414yes—
383C2×C47⋊C8C2414yes—
384C23×C47—22no—
385C23×C47—22no—
386C23×C47—22no—
387C23×C47—22no—
388C23×C47—41no—
389C23×C47—41no—
390C23×C47—81no—
391C23×C47—82no—
392C23×C47—82no—
393C23×C47#12111yescharacteristic
394C23×C47#12111yescharacteristic
395C23×C47#12111yescharacteristic
396C23×C47#12111yescharacteristic
397C23×C47C2×#4111yescharacteristic
398C23×C47C2×#4111yescharacteristic
399C23×C47C2×#4111yescharacteristic
400C22×D47—22no—
401C22×D47—41no—
402C22×D47—41no—
403C22×D47—82no—
404Q8×C47—22no—
405Q8×C47—22no—
406Q8×C47—22no—
407Q8×C47—22no—
408Q8×C47—22no—
409Q8×C47—41no—
410Q8×C47—41no—
411Q8×C47C22×D414yes—
412D4×C47—24no—
413D4×C47—24no—
414D4×C47—24no—
415D4×C47—24no—
416D4×C47—22no—
417D4×C47—22no—
418D4×C47—22no—
419D4×C47—22no—
420D4×C47—22no—
421D4×C47—42no—
422D4×C47—42no—
423D4×C47—42no—
424D4×C47—42no—
425D4×C47—41no—
426D4×C47—41no—
427D4×C47C22×D414yes—
428C2×C4×C47—22no—
429C2×C4×C47—22no—
430C2×C4×C47—22no—
431C2×C4×C47—24no—
432C2×C4×C47—24no—
433C2×C4×C47—24no—
434C2×C4×C47—24no—
435C2×C4×C47—22no—
436C2×C4×C47—41no—
437C2×C4×C47—41no—
438C2×C4×C47—42no—
439C2×C4×C47—42no—
440C2×C4×C47—42no—
441C2×C4×C47—42no—
442C2×C4×C47#12111yescharacteristic
443C2×C4×C47#12111yescharacteristic
444C2×C4×C47#12111yescharacteristic
445C2×C4×C47#12111yescharacteristic
446C2×C4×C47#12111yescharacteristic
447C2×C4×C47#12111yescharacteristic
448C2×C4×C47#12111yescharacteristic
449C2×C4×C47#12111yescharacteristic
450C2×C4×C47#12111yescharacteristic
451C2×C4×C47#12111yescharacteristic
452C2×C4×C47#12111yescharacteristic
453C2×C4×C47#12111yescharacteristic
454C2×C4×C47C22×D411yescharacteristic
455C2×C4×C47C22×D411yescharacteristic
456C2×C4×C47C22×D411yescharacteristic
457C2×C4×C47C22×D411yescharacteristic
458C2×C4×C47C22×D411yescharacteristic
459C2×C4×C47C22×D411yescharacteristic
460C2×C4×C47C22×D411yescharacteristic
461C2×C4×C47C22×D411yescharacteristic
462C2×C4×C47C22×D411yescharacteristic
463C2×C4×C47C22×D411yescharacteristic
464C2×C4×C47C22×D411yescharacteristic
465C2×C4×C47C22×D411yescharacteristic
466C2×C4×C47C2×#4111yescharacteristic
467C2×C4×C47C2×#4111yescharacteristic
468C2×C4×C47C2×#4111yescharacteristic
469C2×C4×C47C2511yescharacteristic
470C22⋊D47—42no—
471C22⋊D47—42no—
472C22⋊D47—42no—
473C22⋊D47—42no—
474C2×Dic47—22no—
475C2×Dic47—41no—
476C2×Dic47—41no—
477D188—22no—
478D188—22no—
479D188—41no—
480D188—41no—
481C4×D47—42no—
482C4×D47—42no—
483C4×D47—42no—
484C4×D47—42no—
485Dic94—22no—
486Dic94—22no—
487Dic94—41no—
488Dic94—41no—
489C8×C47—24no—
490C47⋊C8—24no—
491C47⋊C8—24no—
492C47⋊C8C22×D418yes—
493#60469—471nomaximal, Sylow
494C22×C47—24no—
495C22×C47—41no—
496C22×C47—41no—
497C22×C47—41no—
498C22×C47—41no—
499C22×C47—41no—
500C22×C47—41no—
501C22×C47—41no—
502C22×C47—44no—
503C22×C47—42no—
504C22×C47—82no—
505C22×C47—82no—
506C22×C47—82no—
507C22×C47—82no—
508C22×C47—82no—
509C22×C47C2×#12111yescharacteristic
510C22×C47C2×#12111yescharacteristic
511C22×C47C2×#12111yescharacteristic
512C22×C47C2×#12111yescharacteristic
513C22×C47C2×#12111yescharacteristic
514C22×C47C2×#12111yescharacteristic
515C22×C47C22×#4111yescharacteristic
516C2×D47—42no—
517C2×D47—82no—
518C2×D47—82no—
519C2×D47—82no—
520C4×C47—24no—
521C4×C47—42no—
522C4×C47C2×#12111yescharacteristic
523C4×C47C2×#12111yescharacteristic
524C4×C47C2×#12111yescharacteristic
525C4×C47C2×#12111yescharacteristic
526C4×C47C2×#12111yescharacteristic
527C4×C47C2×#12111yescharacteristic
528C4×C47C23×D411yescharacteristic
529C4×C47C23×D411yescharacteristic
530Dic47—42no—
531C2×#575—471no—
532C2×#575—471no—
533C2×#575D4711yescharacteristic, complemented
534C2×#568—471no—
535#3069—474no—
536#3069—474no—
537#3068—474no—
538#3068—474no—
539#3067—478no—
540C2×#430—471no—
541C2×#413—471no—
542C2×#413—471no—
543C2×C47—21no—
544C2×C47—21no—
545C2×C47—21no—
546C2×C47—21no—
547C2×C47—21no—
548C2×C47—21no—
549C2×C47—21no—
550C2×C47—44no—
551C2×C47—82no—
552C2×C47C22×#12111yescharacteristic
553D47—82no—
554C22×#41—471no—
555C22×#41C2×D4711yescharacteristic
556C22×#41C2×D4711yescharacteristic
557#575—22no—
558#575—22no—
559#575—474no—
560#575—474no—
561#575—942no—
562#575—942no—
563#575—942no—
564#575—942no—
565#575—942no—
566#575—942no—
567#575C2×D4714yes—
568#575C2×D4714yescomplemented
569C2×#137—21no—
570C2×#137—472no—
571C2×#137—472no—
572C2×#137—472no—
573C2×#137—941no—
574C2×#137C2×D4712yescomplemented
575C2×AGL(1,ℤ/8)—21no—
576C2×AGL(1,ℤ/8)—472no—
577C2×AGL(1,ℤ/8)—472no—
578C2×AGL(1,ℤ/8)—472no—
579C2×AGL(1,ℤ/8)—941no—
580C2×AGL(1,ℤ/8)C2×D4712yescomplemented
581C2×#135—22no—
582C2×#135—474no—
583C2×#135—942no—
584#568—474no—
585#568—474no—
586#568—942no—
587#568—942no—
588C2×#131—474no—
589C2×#131—942no—
590C22×M16—471no—
591C22×M16—471no—
592C22×M16—471no—
593C22×M16—942no—
594C22×M16C2×D4711yescharacteristic
595#473—4716no—
596#472—4716no—
597#471—4716no—
598#471—4716no—
599#430—474no—
600#430—474no—
601C2×#108—474no—
602#413—474no—
603#413—474no—
604#413—474no—
605#413—474no—
606C2×#101—472no—
607C2×#101—472no—
608C2×#100—472no—
609C2×#100—472no—
610C47#6046911yescharacteristic, complemented, Sylow
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41—21no—
617C2×#41—21no—
618C2×#41—21no—
619C2×#41—21no—
620C2×#41—21no—
621C2×#41—21no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—21no—
627C2×#41—472no—
628C2×#41—472no—
629C2×#41—941no—
630C2×#41—941no—
631C2×#41—941no—
632C2×#41—941no—
633C2×#41—941no—
634C2×#41—941no—
635C2×#41—941no—
636C2×#41—941no—
637C2×#41—941no—
638C2×#41—941no—
639C2×#41C22⋊D4712yes—
640C2×#41C22⋊D4712yes—
641C2×#41C22⋊D4712yes—
642C2×#41C22×D4712yes—
643C2×#41C22×D4712yes—
644C2×#41C22×D4712yes—
645C2×#41C22×D4712yes—
646C2×#41C22×D4712yes—
647C22×Q8—471no—
648C22×Q8C22⋊D4711yescharacteristic
649C22×Q8C22×D4711yescharacteristic
650C22×D4—21no—
651C22×D4—21no—
652C22×D4—471no—
653C22×D4—941no—
654C22×D4C22⋊D4711yescharacteristic
655C22×D4C22×D4711yescharacteristic
656C23×C4—21no—
657C23×C4—21no—
658C23×C4—941no—
659C23×C4C22×D4711yescharacteristic
660#137—24no—
661#137—24no—
662#137—24no—
663#137—478no—
664#137—944no—
665#137—944no—
666#137—944no—
667#137—944no—
668#137—944no—
669#137—944no—
670#137—944no—
671#137C22×D4718yes—
672AGL(1,ℤ/8)—24no—
673AGL(1,ℤ/8)—24no—
674AGL(1,ℤ/8)—24no—
675AGL(1,ℤ/8)—478no—
676AGL(1,ℤ/8)—944no—
677AGL(1,ℤ/8)—944no—
678AGL(1,ℤ/8)—944no—
679AGL(1,ℤ/8)—944no—
680AGL(1,ℤ/8)—944no—
681AGL(1,ℤ/8)—944no—
682AGL(1,ℤ/8)—944no—
683AGL(1,ℤ/8)C22×D4718yes—
684#135—28no—
685#135—28no—
686#135—948no—
687#135—948no—
688#135—948no—
689#135—948no—
690C2×Q16—22no—
691C2×Q16—474no—
692C2×Q16—942no—
693C2×SD16—22no—
694C2×SD16—22no—
695C2×SD16—474no—
696C2×SD16—474no—
697C2×SD16—942no—
698C2×SD16—942no—
699C2×D8—22no—
700C2×D8—474no—
701C2×D8—942no—
702#131—4716no—
703#131—948no—
704#131—948no—
705#131—948no—
706C2×M16—21no—
707C2×M16—21no—
708C2×M16—21no—
709C2×M16—472no—
710C2×M16—472no—
711C2×M16—472no—
712C2×M16—472no—
713C2×M16—472no—
714C2×M16—472no—
715C2×M16—472no—
716C2×M16—472no—
717C2×M16—472no—
718C2×M16—472no—
719C2×M16—472no—
720C2×M16—472no—
721C2×M16—944no—
722C2×M16—948no—
723C2×M16—948no—
724C2×M16—941no—
725C2×M16—941no—
726C2×M16—941no—
727C2×M16—941no—
728C2×M16—941no—
729C2×M16—941no—
730C2×M16C22×D4712yes—
731C2×M16C22×D4712yes—
732C2×M16C22×D4712yes—
733C22×C8—21no—
734C22×C8—472no—
735C22×C8—944no—
736C22×C8—941no—
737C22×C8—941no—
738#108—4716no—
739#101—478no—
740#101—478no—
741#100—478no—
742#100—478no—
743C24—21no—
744C24—21no—
745C24—941no—
746C24#1062535211yescharacteristic
747#41—22no—
748#41—22no—
749#41—22no—
750#41—22no—
751#41—22no—
752#41—22no—
753#41—22no—
754#41—22no—
755#41—22no—
756#41—22no—
757#41—22no—
758#41—22no—
759#41—22no—
760#41—22no—
761#41—22no—
762#41—22no—
763#41—22no—
764#41—22no—
765#41—22no—
766#41—22no—
767#41—41no—
768#41—41no—
769#41—41no—
770#41—41no—
771#41—41no—
772#41—41no—
773#41—41no—
774#41—41no—
775#41—942no—
776#41—942no—
777#41—942no—
778#41—942no—
779#41—942no—
780#41—942no—
781#41—942no—
782#41—942no—
783#41—1881no—
784#41—1881no—
785#41—1881no—
786#41—1881no—
787#41—1881no—
788#41—1881no—
789#41—1881no—
790#41—1881no—
791#41C2×C22⋊D4714yes—
792#41C2×C22⋊D4714yes—
793#41C2×C22⋊D4714yes—
794#41C23×D4714yes—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—472no—
804C2×Q8—941no—
805C2×Q8—941no—
806C2×Q8—941no—
807C2×Q8—941no—
808C2×Q8—941no—
809C2×Q8C2×C22⋊D4712yes—
810C2×Q8C2×C22⋊D4712yes—
811C2×Q8C2×C22⋊D4712yes—
812C2×Q8C23×D4712yes—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—41no—
830C2×D4—41no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4—472no—
834C2×D4—942no—
835C2×D4—942no—
836C2×D4—941no—
837C2×D4—941no—
838C2×D4—941no—
839C2×D4—941no—
840C2×D4—941no—
841C2×D4—1881no—
842C2×D4—1881no—
843C2×D4—1881no—
844C2×D4—1881no—
845C2×D4C2×C22⋊D4712yes—
846C2×D4C2×C22⋊D4712yes—
847C2×D4C2×C22⋊D4712yes—
848C2×D4C23×D4712yes—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—941no—
864C22×C4—942no—
865C22×C4—942no—
866C22×C4—1881no—
867C22×C4—1881no—
868C22×C4—1881no—
869C22×C4—1881no—
870C22×C4D4×D4711yescharacteristic
871C22×C4D4×D4711yescharacteristic
872C22×C4D4×D4711yescharacteristic
873C22×C4D4×D4711yescharacteristic
874C22×C4#1062535211yescharacteristic
875C22×C4#1062535211yescharacteristic
876C22×C4#1062535211yescharacteristic
877C22×C4C2×C22⋊D4711yescharacteristic
878C22×C4C2×C22⋊D4711yescharacteristic
879C22×C4C2×C22⋊D4711yescharacteristic
880C22×C4C2×C22⋊D4711yescharacteristic
881C22×C4C23×D4711yescharacteristic
882C22×C4C23×D4711yescharacteristic
883C22×C4C23×D4711yescharacteristic
884Q16—28no—
885Q16—948no—
886Q16—948no—
887SD16—28no—
888SD16—28no—
889SD16—948no—
890SD16—948no—
891SD16—948no—
892SD16—948no—
893D8—28no—
894D8—948no—
895D8—948no—
896M16—22no—
897M16—22no—
898M16—22no—
899M16—474no—
900M16—474no—
901M16—474no—
902M16—474no—
903M16—474no—
904M16—474no—
905M16—9416no—
906M16—942no—
907M16—942no—
908M16—942no—
909M16—942no—
910M16—942no—
911M16—942no—
912M16C23×D4714yes—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—22no—
916C2×C8—474no—
917C2×C8—474no—
918C2×C8—474no—
919C2×C8—9416no—
920C2×C8—942no—
921C2×C8—942no—
922C2×C8—942no—
923C2×C8—942no—
924C2×C8—942no—
925C2×C8—942no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23—942no—
936C23—3762no—
937C23—1881no—
938C23—1881no—
939C23#1309399611yescharacteristic
940C23#1309399611yescharacteristic
941C23#1309399611yescharacteristic
942C23#1309399611yescharacteristic
943C23C2×#1062535211yescharacteristic
944C23C2×#1062535211yescharacteristic
945C23C2×#1062535211yescharacteristic
946Q8—22no—
947Q8—22no—
948Q8—22no—
949Q8—22no—
950Q8—22no—
951Q8—41no—
952Q8—41no—
953Q8—942no—
954Q8—942no—
955Q8—1881no—
956Q8—1881no—
957Q8C22×C22⋊D4714yes—
958D4—24no—
959D4—24no—
960D4—24no—
961D4—24no—
962D4—22no—
963D4—22no—
964D4—22no—
965D4—22no—
966D4—22no—
967D4—42no—
968D4—42no—
969D4—42no—
970D4—42no—
971D4—41no—
972D4—41no—
973D4—942no—
974D4—942no—
975D4—1882no—
976D4—1882no—
977D4—1882no—
978D4—1882no—
979D4—1881no—
980D4—1881no—
981D4C22×C22⋊D4714yes—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—942no—
997C2×C4—1881no—
998C2×C4—1881no—
999C2×C4—1882no—
1000C2×C4—1882no—
1001C2×C4—1882no—
1002C2×C4—1882no—
1003C2×C4#1309399611yescharacteristic
1004C2×C4#1309399611yescharacteristic
1005C2×C4#1309399611yescharacteristic
1006C2×C4#1309399611yescharacteristic
1007C2×C4#1309399611yescharacteristic
1008C2×C4#1309399611yescharacteristic
1009C2×C4#1309399611yescharacteristic
1010C2×C4#1309399611yescharacteristic
1011C2×C4#1309399611yescharacteristic
1012C2×C4#1309399611yescharacteristic
1013C2×C4#1309399611yescharacteristic
1014C2×C4#1309399611yescharacteristic
1015C2×C4C2×D4×D4711yescharacteristic
1016C2×C4C2×D4×D4711yescharacteristic
1017C2×C4C2×D4×D4711yescharacteristic
1018C2×C4C2×D4×D4711yescharacteristic
1019C2×C4C2×D4×D4711yescharacteristic
1020C2×C4C2×D4×D4711yescharacteristic
1021C2×C4C22×C22⋊D4711yescharacteristic
1022C2×C4C22×C22⋊D4711yescharacteristic
1023C2×C4C22×C22⋊D4711yescharacteristic
1024C2×C4C22×C22⋊D4711yescharacteristic
1025C2×C4C22×C22⋊D4711yescharacteristic
1026C2×C4C22×C22⋊D4711yescharacteristic
1027C2×C4C2×#1062535211yescharacteristic
1028C2×C4C2×#1062535211yescharacteristic
1029C2×C4C2×#1062535211yescharacteristic
1030C2×C4C24×D4711yescharacteristic
1031C8—24no—
1032C8—478no—
1033C8—944no—
1034C8—944no—
1035C22—24no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—44no—
1044C22—42no—
1045C22—82no—
1046C22—82no—
1047C22—82no—
1048C22—82no—
1049C22—82no—
1050C22—3762no—
1051C22—3762no—
1052C22—3762no—
1053C22—1882no—
1054C22C2×#1309399611yescharacteristic
1055C22C2×#1309399611yescharacteristic
1056C22C2×#1309399611yescharacteristic
1057C22C2×#1309399611yescharacteristic
1058C22C2×#1309399611yescharacteristic
1059C22C2×#1309399611yescharacteristic
1060C22C22×#1062535211yescharacteristic
1061C4—24no—
1062C4—42no—
1063C4—1882no—
1064C4C2×#1309399611yescharacteristic
1065C4C2×#1309399611yescharacteristic
1066C4C2×#1309399611yescharacteristic
1067C4C2×#1309399611yescharacteristic
1068C4C2×#1309399611yescharacteristic
1069C4C2×#1309399611yescharacteristic
1070C4C22×D4×D4711yescharacteristic
1071C4C23×C22⋊D4711yescharacteristic
1072C2—21no—
1073C2—21no—
1074C2—21no—
1075C2—21no—
1076C2—21no—
1077C2—21no—
1078C2—21no—
1079C2—44no—
1080C2—82no—
1081C2—3762no—
1082C2C22×#1309399611yescharacteristic
subgroupG/H
centerC4C2×#13093996
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#575C2
socleC2×C47C22×#121
hypercenterC2×#575D47
hypocenterC47#60469
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#15689921C2semidirect
2. C2×#15689921C2semidirect
3. C2×#15689890C2semidirect
4. #20253127C2semidirect
5. #20253122C2semidirect
6. #20253118C2semidirect
7. #20253113C2semidirect
8. #20253105C2semidirect
9. C2×#15689171C2semidirect
10. C2×#15689107C2semidirect
11. C2×#15689105C2semidirect
12. C2×C47×#575C2semidirect
21. #15689921C22semidirect
23. C2×#13094055C22semidirect
24. C2×#13094054C22semidirect
25. C2×#13094054C22semidirect
27. C2×#13094050C22semidirect
28. C2×#13094049C22semidirect
29. C2×#13094049C22semidirect
31. C2×#13094044C22semidirect
34. #15689890C22semidirect
35. #15689890C22semidirect
37. C2×#13094031C22semidirect
42. #15689396C22semidirect
43. #15689391C22semidirect
44. #15689388C22semidirect
45. #15689384C22semidirect
46. #15689171C22semidirect
47. #15689171C22semidirect
48. C2×#13093959C22semidirect
49. #15689107C22semidirect
50. #15689107C22semidirect
51. #15689105C22semidirect
52. #15689105C22semidirect
53. C2×#13093943C22semidirect
54. C2×#13093942C22semidirect
55. C2×#13093941C22semidirect
56. C2×#13093940C22semidirect
62. C47×#575C22semidirect
64. C2×#137×C47C22semidirect
66. C2×AGL(1,ℤ/8)×C47C22semidirect
106. C2×#10625337C23semidirect
108. C2×#10625335C23semidirect
110. C2×#10625336C23semidirect
112. C2×#10625334C23semidirect
142. #13093959C23semidirect
143. #13093943C23semidirect
144. #13093942C23semidirect
145. #13093941C23semidirect
146. #13093940C23semidirect
533. C2×#575D47semidirect
568. #575C2×D47semidirect
574. C2×#137C2×D47semidirect
580. C2×AGL(1,ℤ/8)C2×D47semidirect
610. C47#60469semidirect

Maximal subgroups

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

subgroupindex
C2×#156899212
C2×#156898902
#202531272
#202531222
#202531182
#202531132
#202531052
C2×#156891712
C2×#156891072
C2×#156891052
C2×C47×#5752
#6046947