Finite Group Databasebeta

← #25964019

Subgroups — #25964019

Order 11008.

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×#14583697C211yesmaximal, characteristic, complemented
2C2×#14583697C211yesmaximal, characteristic, complemented
3C2×#14583666C211yesmaximal, characteristic, complemented
4#19144334C214yesmaximal, complemented
5#19144329C214yesmaximal, complemented
6#19144325C214yesmaximal, complemented
7#19144320C214yesmaximal, complemented
8#19144312C218yesmaximal, complemented
9C2×#14582947C211yesmaximal, characteristic, complemented
10C2×#14582883C211yesmaximal, characteristic, complemented
11C2×#14582881C211yesmaximal, characteristic, complemented
12C2×C43×#575C211yesmaximal, characteristic, complemented
13C22×#10621898C2211yescharacteristic
14#14583697—22no—
15#14583697—22no—
16#14583697—22no—
17#14583697—22no—
18#14583697—22no—
19#14583697—22no—
20#14583697C2214yes—
21#14583697C2214yescomplemented
22C2×#13063356—21no—
23C2×#13063356C2212yescomplemented
24C2×#13063355C2212yescomplemented
25C2×#13063355C2212yescomplemented
26C2×#13063351—21no—
27C2×#13063351C2212yescomplemented
28C2×#13063350C2212yescomplemented
29C2×#13063350C2212yescomplemented
30C2×#13063345—22no—
31C2×#13063345C2214yescomplemented
32#14583666—22no—
33#14583666—22no—
34#14583666C2214yescomplemented
35#14583666C2214yescomplemented
36C2×#13063332—22no—
37C2×#13063332C2214yescomplemented
38C22×#10621877—22no—
39C22×#10621877C2211yescharacteristic
40C22×#10621877C2211yescharacteristic
41C22×#10621877C2211yescharacteristic
42#14583172C22116yescomplemented
43#14583167C22116yescomplemented
44#14583164C22116yescomplemented
45#14583160C22116yescomplemented
46#14582947C2214yescomplemented
47#14582947C2214yescomplemented
48C2×#13063260C2214yescomplemented
49#14582883C2214yescomplemented
50#14582883C2214yescomplemented
51#14582881C2214yescomplemented
52#14582881C2214yescomplemented
53C2×#13063244C2212yescomplemented
54C2×#13063243C2212yescomplemented
55C2×#13063242C2212yescomplemented
56C2×#13063241C2212yescomplemented
57C22×#41×C43C2211yescharacteristic
58C22×#41×C43C2211yescharacteristic
59C43×#575—22no—
60C43×#575—22no—
61C43×#575C2214yes—
62C43×#575C2214yescomplemented
63C2×#137×C43—21no—
64C2×#137×C43C2212yescomplemented
65C2×AGL(1,ℤ/8)×C43—21no—
66C2×AGL(1,ℤ/8)×C43C2212yescomplemented
67C2×#135×C43—22no—
68C22×M16×C43C2211yescharacteristic
69C2×#10621898—21no—
70C2×#10621898—21no—
71C2×#10621898—21no—
72C2×#10621898—21no—
73C2×#10621898—21no—
74C2×#10621898—21no—
75C2×#10621898—21no—
76C2×#10621898—21no—
77C2×#10621898—21no—
78C2×#10621898—21no—
79C2×#10621898C2312yes—
80C2×#10621898C2312yes—
81C22×Dic86C2311yescharacteristic
82C22×D172C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C4×D43—21no—
85#13063356—24no—
86#13063356—24no—
87#13063356—24no—
88#13063356—24no—
89#13063355—24no—
90#13063355—24no—
91#13063355—24no—
92#13063355C2318yes—
93#13063351—24no—
94#13063351—24no—
95#13063351—24no—
96#13063351—24no—
97#13063350—24no—
98#13063350—24no—
99#13063350—24no—
100#13063350C2318yes—
101#13063345—28no—
102#13063345—28no—
103#13063345—28no—
104#13063345—28no—
105C2×#10621885—22no—
106C2×#10621885C2314yescomplemented
107C2×#10621883—22no—
108C2×#10621883C2314yescomplemented
109C2×#10621884—22no—
110C2×#10621884C2314yescomplemented
111C2×#10621882—22no—
112C2×#10621882C2314yescomplemented
113#13063332—28no—
114#13063332—28no—
115#13063332—28no—
116#13063332C23116yes—
117C2×#10621877—21no—
118C2×#10621877—21no—
119C2×#10621877—21no—
120C2×#10621877—21no—
121C2×#10621877—21no—
122C2×#10621877—21no—
123C2×#10621877—28no—
124C2×#10621877—28no—
125C2×#10621877—24no—
126C2×#10621877D412yes—
127C2×#10621877D412yes—
128C2×#10621877D412yes—
129C2×#10621877D412yes—
130C2×#10621877C2312yes—
131C2×#10621877C2312yes—
132C2×#10621877C2312yes—
133C2×#10621877C2312yes—
134C2×#10621877C2312yes—
135C2×#10621877C2312yes—
136C2×#10621877C2312yes—
137C2×#10621877C2312yes—
138C22×C43⋊C8—21no—
139C22×C43⋊C8—21no—
140C22×C43⋊C8—24no—
141C22×C43⋊C8C2312yes—
142#13063260C23116yescomplemented
143#13063244C2318yescomplemented
144#13063243C2318yescomplemented
145#13063242C2318yescomplemented
146#13063241C2318yescomplemented
147C2×#41×C43—21no—
148C2×#41×C43—21no—
149C2×#41×C43—21no—
150C2×#41×C43—21no—
151C2×#41×C43—21no—
152C2×#41×C43—21no—
153C2×#41×C43—21no—
154C2×#41×C43—21no—
155C2×#41×C43—21no—
156C2×#41×C43—21no—
157C2×#41×C43—21no—
158C2×#41×C43—21no—
159C2×#41×C43—21no—
160C2×#41×C43—21no—
161C2×#41×C43—21no—
162C2×#41×C43—21no—
163C2×#41×C43D412yes—
164C2×#41×C43D412yes—
165C2×#41×C43D412yes—
166C2×#41×C43C2312yes—
167C2×#41×C43C2312yes—
168C2×#41×C43C2312yes—
169C2×#41×C43C2312yes—
170C2×#41×C43C2312yes—
171C22×Q8×C43D411yescharacteristic
172C22×Q8×C43C2311yescharacteristic
173C22×D4×C43—21no—
174C22×D4×C43—21no—
175C22×D4×C43D411yescharacteristic
176C22×D4×C43C2311yescharacteristic
177C23×C4×C43—21no—
178C23×C4×C43—21no—
179C23×C4×C43C2311yescharacteristic
180#137×C43—24no—
181#137×C43—24no—
182#137×C43—24no—
183#137×C43C2318yes—
184AGL(1,ℤ/8)×C43—24no—
185AGL(1,ℤ/8)×C43—24no—
186AGL(1,ℤ/8)×C43—24no—
187AGL(1,ℤ/8)×C43C2318yes—
188#135×C43—28no—
189#135×C43—28no—
190C2×Q16×C43—22no—
191C2×SD16×C43—22no—
192C2×SD16×C43—22no—
193C2×D8×C43—22no—
194C2×M16×C43—21no—
195C2×M16×C43—21no—
196C2×M16×C43—21no—
197C2×M16×C43C2312yes—
198C2×M16×C43C2312yes—
199C2×M16×C43C2312yes—
200C22×C8×C43—21no—
201C24×C43—21no—
202C24×C43—21no—
203C24×C43#4111yescharacteristic
204C23×D43—21no—
205#41×C43—22no—
206#41×C43—22no—
207#41×C43—22no—
208#41×C43—22no—
209#41×C43—22no—
210#41×C43—22no—
211#41×C43—22no—
212#41×C43—22no—
213#41×C43—22no—
214#41×C43—22no—
215#41×C43—22no—
216#41×C43—22no—
217#41×C43—22no—
218#41×C43—22no—
219#41×C43—22no—
220#41×C43—22no—
221#41×C43—22no—
222#41×C43—22no—
223#41×C43—22no—
224#41×C43—22no—
225#41×C43—41no—
226#41×C43—41no—
227#41×C43—41no—
228#41×C43—41no—
229#41×C43—41no—
230#41×C43—41no—
231#41×C43—41no—
232#41×C43—41no—
233#41×C43C2×D414yes—
234#41×C43C2×D414yes—
235#41×C43C2×D414yes—
236#41×C43C2414yes—
237C2×Q8×C43—21no—
238C2×Q8×C43—21no—
239C2×Q8×C43—21no—
240C2×Q8×C43—21no—
241C2×Q8×C43—21no—
242C2×Q8×C43—21no—
243C2×Q8×C43—21no—
244C2×Q8×C43—21no—
245C2×Q8×C43C2×D412yes—
246C2×Q8×C43C2×D412yes—
247C2×Q8×C43C2×D412yes—
248C2×Q8×C43C2412yes—
249C2×D4×C43—21no—
250C2×D4×C43—21no—
251C2×D4×C43—21no—
252C2×D4×C43—21no—
253C2×D4×C43—22no—
254C2×D4×C43—22no—
255C2×D4×C43—22no—
256C2×D4×C43—22no—
257C2×D4×C43—22no—
258C2×D4×C43—22no—
259C2×D4×C43—22no—
260C2×D4×C43—22no—
261C2×D4×C43—21no—
262C2×D4×C43—21no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—41no—
266C2×D4×C43—41no—
267C2×D4×C43—41no—
268C2×D4×C43—41no—
269C2×D4×C43C2×D412yes—
270C2×D4×C43C2×D412yes—
271C2×D4×C43C2×D412yes—
272C2×D4×C43C2412yes—
273C22×C4×C43—22no—
274C22×C4×C43—22no—
275C22×C4×C43—22no—
276C22×C4×C43—22no—
277C22×C4×C43—22no—
278C22×C4×C43—22no—
279C22×C4×C43—22no—
280C22×C4×C43—22no—
281C22×C4×C43—21no—
282C22×C4×C43—21no—
283C22×C4×C43—41no—
284C22×C4×C43—41no—
285C22×C4×C43—41no—
286C22×C4×C43—41no—
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2×D411yescharacteristic
290C22×C4×C43C2×D411yescharacteristic
291C22×C4×C43C2×D411yescharacteristic
292C22×C4×C43C2×D411yescharacteristic
293C22×C4×C43C2×D411yescharacteristic
294C22×C4×C43C2×D411yescharacteristic
295C22×C4×C43#4111yescharacteristic
296C22×C4×C43#4111yescharacteristic
297C22×C4×C43#4111yescharacteristic
298C22×C4×C43C2411yescharacteristic
299C22×C4×C43C2411yescharacteristic
300C22×C4×C43C2411yescharacteristic
301C2×C22⋊D43—22no—
302C2×C22⋊D43—22no—
303C2×C22⋊D43—41no—
304C2×C22⋊D43—41no—
305C2×C22⋊D43—41no—
306C2×C22⋊D43—41no—
307C22×Dic43—21no—
308#10621898—22no—
309#10621898—22no—
310#10621898—22no—
311#10621898—22no—
312#10621898—22no—
313#10621898—22no—
314#10621898—22no—
315#10621898—22no—
316#10621898—41no—
317#10621898—41no—
318#10621898—41no—
319#10621898—41no—
320#10621898—41no—
321#10621898—41no—
322#10621898—41no—
323#10621898—41no—
324C2×D172—21no—
325C2×D172—21no—
326C2×D172—21no—
327C2×D172—21no—
328C2×D172—21no—
329C2×D172C2412yes—
330C2×C4×D43—22no—
331C2×C4×D43—22no—
332C2×C4×D43—41no—
333C2×C4×D43—41no—
334C2×C4×D43—41no—
335C2×C4×D43—41no—
336C2×Dic86—21no—
337C2×Dic86—21no—
338C2×Dic86—21no—
339C2×Dic86—21no—
340C2×Dic86—21no—
341C2×Dic86C2412yes—
342Q16×C43—28no—
343SD16×C43—28no—
344SD16×C43—28no—
345D8×C43—28no—
346M16×C43—22no—
347M16×C43—22no—
348M16×C43—22no—
349M16×C43C2414yes—
350C2×C8×C43—22no—
351C2×C8×C43—22no—
352C2×C8×C43—22no—
353#10621885—28no—
354#10621885—28no—
355#10621884—28no—
356#10621884—28no—
357#10621883—28no—
358#10621883—28no—
359#10621882—28no—
360#10621882—28no—
361#10621877—22no—
362#10621877—22no—
363#10621877—22no—
364#10621877—22no—
365#10621877—22no—
366#10621877—22no—
367#10621877—216no—
368#10621877C2×D414yes—
369#10621877C2×D414yes—
370#10621877C2×D414yes—
371#10621877C2×D414yes—
372#10621877C2414yes—
373#10621877C2414yes—
374C2×C43⋊C8—22no—
375C2×C43⋊C8—22no—
376C2×C43⋊C8—22no—
377C2×C43⋊C8—22no—
378C2×C43⋊C8—22no—
379C2×C43⋊C8—22no—
380C2×C43⋊C8—216no—
381C2×C43⋊C8C2×D414yes—
382C2×C43⋊C8C2×D414yes—
383C2×C43⋊C8C2414yes—
384C23×C43—22no—
385C23×C43—22no—
386C23×C43—22no—
387C23×C43—22no—
388C23×C43—41no—
389C23×C43—41no—
390C23×C43—81no—
391C23×C43—82no—
392C23×C43—82no—
393C23×C43#12111yescharacteristic
394C23×C43#12111yescharacteristic
395C23×C43#12111yescharacteristic
396C23×C43#12111yescharacteristic
397C23×C43C2×#4111yescharacteristic
398C23×C43C2×#4111yescharacteristic
399C23×C43C2×#4111yescharacteristic
400C22×D43—22no—
401C22×D43—41no—
402C22×D43—41no—
403C22×D43—82no—
404Q8×C43—22no—
405Q8×C43—22no—
406Q8×C43—22no—
407Q8×C43—22no—
408Q8×C43—22no—
409Q8×C43—41no—
410Q8×C43—41no—
411Q8×C43C22×D414yes—
412D4×C43—24no—
413D4×C43—24no—
414D4×C43—24no—
415D4×C43—24no—
416D4×C43—22no—
417D4×C43—22no—
418D4×C43—22no—
419D4×C43—22no—
420D4×C43—22no—
421D4×C43—42no—
422D4×C43—42no—
423D4×C43—42no—
424D4×C43—42no—
425D4×C43—41no—
426D4×C43—41no—
427D4×C43C22×D414yes—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—24no—
432C2×C4×C43—24no—
433C2×C4×C43—24no—
434C2×C4×C43—24no—
435C2×C4×C43—22no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—42no—
439C2×C4×C43—42no—
440C2×C4×C43—42no—
441C2×C4×C43—42no—
442C2×C4×C43#12111yescharacteristic
443C2×C4×C43#12111yescharacteristic
444C2×C4×C43#12111yescharacteristic
445C2×C4×C43#12111yescharacteristic
446C2×C4×C43#12111yescharacteristic
447C2×C4×C43#12111yescharacteristic
448C2×C4×C43#12111yescharacteristic
449C2×C4×C43#12111yescharacteristic
450C2×C4×C43#12111yescharacteristic
451C2×C4×C43#12111yescharacteristic
452C2×C4×C43#12111yescharacteristic
453C2×C4×C43#12111yescharacteristic
454C2×C4×C43C22×D411yescharacteristic
455C2×C4×C43C22×D411yescharacteristic
456C2×C4×C43C22×D411yescharacteristic
457C2×C4×C43C22×D411yescharacteristic
458C2×C4×C43C22×D411yescharacteristic
459C2×C4×C43C22×D411yescharacteristic
460C2×C4×C43C22×D411yescharacteristic
461C2×C4×C43C22×D411yescharacteristic
462C2×C4×C43C22×D411yescharacteristic
463C2×C4×C43C22×D411yescharacteristic
464C2×C4×C43C22×D411yescharacteristic
465C2×C4×C43C22×D411yescharacteristic
466C2×C4×C43C2×#4111yescharacteristic
467C2×C4×C43C2×#4111yescharacteristic
468C2×C4×C43C2×#4111yescharacteristic
469C2×C4×C43C2511yescharacteristic
470C22⋊D43—42no—
471C22⋊D43—42no—
472C22⋊D43—42no—
473C22⋊D43—42no—
474C2×Dic43—22no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477D172—22no—
478D172—22no—
479D172—41no—
480D172—41no—
481C4×D43—42no—
482C4×D43—42no—
483C4×D43—42no—
484C4×D43—42no—
485Dic86—22no—
486Dic86—22no—
487Dic86—41no—
488Dic86—41no—
489C8×C43—24no—
490C43⋊C8—24no—
491C43⋊C8—24no—
492C43⋊C8C22×D418yes—
493#60469—431nomaximal, Sylow
494C22×C43—24no—
495C22×C43—41no—
496C22×C43—41no—
497C22×C43—41no—
498C22×C43—41no—
499C22×C43—41no—
500C22×C43—41no—
501C22×C43—41no—
502C22×C43—44no—
503C22×C43—42no—
504C22×C43—82no—
505C22×C43—82no—
506C22×C43—82no—
507C22×C43—82no—
508C22×C43—82no—
509C22×C43C2×#12111yescharacteristic
510C22×C43C2×#12111yescharacteristic
511C22×C43C2×#12111yescharacteristic
512C22×C43C2×#12111yescharacteristic
513C22×C43C2×#12111yescharacteristic
514C22×C43C2×#12111yescharacteristic
515C22×C43C22×#4111yescharacteristic
516C2×D43—42no—
517C2×D43—82no—
518C2×D43—82no—
519C2×D43—82no—
520C4×C43—24no—
521C4×C43—42no—
522C4×C43C2×#12111yescharacteristic
523C4×C43C2×#12111yescharacteristic
524C4×C43C2×#12111yescharacteristic
525C4×C43C2×#12111yescharacteristic
526C4×C43C2×#12111yescharacteristic
527C4×C43C2×#12111yescharacteristic
528C4×C43C23×D411yescharacteristic
529C4×C43C23×D411yescharacteristic
530Dic43—42no—
531C2×#575—431no—
532C2×#575—431no—
533C2×#575D4311yescharacteristic, complemented
534C2×#568—431no—
535#3069—434no—
536#3069—434no—
537#3068—434no—
538#3068—434no—
539#3067—438no—
540C2×#430—431no—
541C2×#413—431no—
542C2×#413—431no—
543C2×C43—21no—
544C2×C43—21no—
545C2×C43—21no—
546C2×C43—21no—
547C2×C43—21no—
548C2×C43—21no—
549C2×C43—21no—
550C2×C43—44no—
551C2×C43—82no—
552C2×C43C22×#12111yescharacteristic
553D43—82no—
554C22×#41—431no—
555C22×#41C2×D4311yescharacteristic
556C22×#41C2×D4311yescharacteristic
557#575—22no—
558#575—22no—
559#575—434no—
560#575—434no—
561#575—862no—
562#575—862no—
563#575—862no—
564#575—862no—
565#575—862no—
566#575—862no—
567#575C2×D4314yes—
568#575C2×D4314yescomplemented
569C2×#137—21no—
570C2×#137—432no—
571C2×#137—432no—
572C2×#137—432no—
573C2×#137—861no—
574C2×#137C2×D4312yescomplemented
575C2×AGL(1,ℤ/8)—21no—
576C2×AGL(1,ℤ/8)—432no—
577C2×AGL(1,ℤ/8)—432no—
578C2×AGL(1,ℤ/8)—432no—
579C2×AGL(1,ℤ/8)—861no—
580C2×AGL(1,ℤ/8)C2×D4312yescomplemented
581C2×#135—22no—
582C2×#135—434no—
583C2×#135—862no—
584#568—434no—
585#568—434no—
586#568—862no—
587#568—862no—
588C2×#131—434no—
589C2×#131—862no—
590C22×M16—431no—
591C22×M16—431no—
592C22×M16—431no—
593C22×M16—862no—
594C22×M16C2×D4311yescharacteristic
595#473—4316no—
596#472—4316no—
597#471—4316no—
598#471—4316no—
599#430—434no—
600#430—434no—
601C2×#108—434no—
602#413—434no—
603#413—434no—
604#413—434no—
605#413—434no—
606C2×#101—432no—
607C2×#101—432no—
608C2×#100—432no—
609C2×#100—432no—
610C43#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—432no—
628C2×#41—432no—
629C2×#41—861no—
630C2×#41—861no—
631C2×#41—861no—
632C2×#41—861no—
633C2×#41—861no—
634C2×#41—861no—
635C2×#41—861no—
636C2×#41—861no—
637C2×#41—861no—
638C2×#41—861no—
639C2×#41C22⋊D4312yes—
640C2×#41C22⋊D4312yes—
641C2×#41C22⋊D4312yes—
642C2×#41C22×D4312yes—
643C2×#41C22×D4312yes—
644C2×#41C22×D4312yes—
645C2×#41C22×D4312yes—
646C2×#41C22×D4312yes—
647C22×Q8—431no—
648C22×Q8C22⋊D4311yescharacteristic
649C22×Q8C22×D4311yescharacteristic
650C22×D4—21no—
651C22×D4—21no—
652C22×D4—431no—
653C22×D4—861no—
654C22×D4C22⋊D4311yescharacteristic
655C22×D4C22×D4311yescharacteristic
656C23×C4—21no—
657C23×C4—21no—
658C23×C4—861no—
659C23×C4C22×D4311yescharacteristic
660#137—24no—
661#137—24no—
662#137—24no—
663#137—438no—
664#137—864no—
665#137—864no—
666#137—864no—
667#137—864no—
668#137—864no—
669#137—864no—
670#137—864no—
671#137C22×D4318yes—
672AGL(1,ℤ/8)—24no—
673AGL(1,ℤ/8)—24no—
674AGL(1,ℤ/8)—24no—
675AGL(1,ℤ/8)—438no—
676AGL(1,ℤ/8)—864no—
677AGL(1,ℤ/8)—864no—
678AGL(1,ℤ/8)—864no—
679AGL(1,ℤ/8)—864no—
680AGL(1,ℤ/8)—864no—
681AGL(1,ℤ/8)—864no—
682AGL(1,ℤ/8)—864no—
683AGL(1,ℤ/8)C22×D4318yes—
684#135—28no—
685#135—28no—
686#135—868no—
687#135—868no—
688#135—868no—
689#135—868no—
690C2×Q16—22no—
691C2×Q16—434no—
692C2×Q16—862no—
693C2×SD16—22no—
694C2×SD16—22no—
695C2×SD16—434no—
696C2×SD16—434no—
697C2×SD16—862no—
698C2×SD16—862no—
699C2×D8—22no—
700C2×D8—434no—
701C2×D8—862no—
702#131—4316no—
703#131—868no—
704#131—868no—
705#131—868no—
706C2×M16—21no—
707C2×M16—21no—
708C2×M16—21no—
709C2×M16—432no—
710C2×M16—432no—
711C2×M16—432no—
712C2×M16—432no—
713C2×M16—432no—
714C2×M16—432no—
715C2×M16—432no—
716C2×M16—432no—
717C2×M16—432no—
718C2×M16—432no—
719C2×M16—432no—
720C2×M16—432no—
721C2×M16—864no—
722C2×M16—868no—
723C2×M16—868no—
724C2×M16—861no—
725C2×M16—861no—
726C2×M16—861no—
727C2×M16—861no—
728C2×M16—861no—
729C2×M16—861no—
730C2×M16C22×D4312yes—
731C2×M16C22×D4312yes—
732C2×M16C22×D4312yes—
733C22×C8—21no—
734C22×C8—432no—
735C22×C8—864no—
736C22×C8—861no—
737C22×C8—861no—
738#108—4316no—
739#101—438no—
740#101—438no—
741#100—438no—
742#100—438no—
743C24—21no—
744C24—21no—
745C24—861no—
746C24#1062190011yescharacteristic
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—862no—
776#41—862no—
777#41—862no—
778#41—862no—
779#41—862no—
780#41—862no—
781#41—862no—
782#41—862no—
783#41—1721no—
784#41—1721no—
785#41—1721no—
786#41—1721no—
787#41—1721no—
788#41—1721no—
789#41—1721no—
790#41—1721no—
791#41C2×C22⋊D4314yes—
792#41C2×C22⋊D4314yes—
793#41C2×C22⋊D4314yes—
794#41C23×D4314yes—
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—432no—
804C2×Q8—861no—
805C2×Q8—861no—
806C2×Q8—861no—
807C2×Q8—861no—
808C2×Q8—861no—
809C2×Q8C2×C22⋊D4312yes—
810C2×Q8C2×C22⋊D4312yes—
811C2×Q8C2×C22⋊D4312yes—
812C2×Q8C23×D4312yes—
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—432no—
834C2×D4—862no—
835C2×D4—862no—
836C2×D4—861no—
837C2×D4—861no—
838C2×D4—861no—
839C2×D4—861no—
840C2×D4—861no—
841C2×D4—1721no—
842C2×D4—1721no—
843C2×D4—1721no—
844C2×D4—1721no—
845C2×D4C2×C22⋊D4312yes—
846C2×D4C2×C22⋊D4312yes—
847C2×D4C2×C22⋊D4312yes—
848C2×D4C23×D4312yes—
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—861no—
864C22×C4—862no—
865C22×C4—862no—
866C22×C4—1721no—
867C22×C4—1721no—
868C22×C4—1721no—
869C22×C4—1721no—
870C22×C4D4×D4311yescharacteristic
871C22×C4D4×D4311yescharacteristic
872C22×C4D4×D4311yescharacteristic
873C22×C4D4×D4311yescharacteristic
874C22×C4#1062190011yescharacteristic
875C22×C4#1062190011yescharacteristic
876C22×C4#1062190011yescharacteristic
877C22×C4C2×C22⋊D4311yescharacteristic
878C22×C4C2×C22⋊D4311yescharacteristic
879C22×C4C2×C22⋊D4311yescharacteristic
880C22×C4C2×C22⋊D4311yescharacteristic
881C22×C4C23×D4311yescharacteristic
882C22×C4C23×D4311yescharacteristic
883C22×C4C23×D4311yescharacteristic
884Q16—28no—
885Q16—868no—
886Q16—868no—
887SD16—28no—
888SD16—28no—
889SD16—868no—
890SD16—868no—
891SD16—868no—
892SD16—868no—
893D8—28no—
894D8—868no—
895D8—868no—
896M16—22no—
897M16—22no—
898M16—22no—
899M16—434no—
900M16—434no—
901M16—434no—
902M16—434no—
903M16—434no—
904M16—434no—
905M16—8616no—
906M16—862no—
907M16—862no—
908M16—862no—
909M16—862no—
910M16—862no—
911M16—862no—
912M16C23×D4314yes—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—22no—
916C2×C8—434no—
917C2×C8—434no—
918C2×C8—434no—
919C2×C8—8616no—
920C2×C8—862no—
921C2×C8—862no—
922C2×C8—862no—
923C2×C8—862no—
924C2×C8—862no—
925C2×C8—862no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23—862no—
936C23—3442no—
937C23—1721no—
938C23—1721no—
939C23#1306329711yescharacteristic
940C23#1306329711yescharacteristic
941C23#1306329711yescharacteristic
942C23#1306329711yescharacteristic
943C23C2×#1062190011yescharacteristic
944C23C2×#1062190011yescharacteristic
945C23C2×#1062190011yescharacteristic
946Q8—22no—
947Q8—22no—
948Q8—22no—
949Q8—22no—
950Q8—22no—
951Q8—41no—
952Q8—41no—
953Q8—862no—
954Q8—862no—
955Q8—1721no—
956Q8—1721no—
957Q8C22×C22⋊D4314yes—
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—862no—
974D4—862no—
975D4—1722no—
976D4—1722no—
977D4—1722no—
978D4—1722no—
979D4—1721no—
980D4—1721no—
981D4C22×C22⋊D4314yes—
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—862no—
997C2×C4—1721no—
998C2×C4—1721no—
999C2×C4—1722no—
1000C2×C4—1722no—
1001C2×C4—1722no—
1002C2×C4—1722no—
1003C2×C4#1306329711yescharacteristic
1004C2×C4#1306329711yescharacteristic
1005C2×C4#1306329711yescharacteristic
1006C2×C4#1306329711yescharacteristic
1007C2×C4#1306329711yescharacteristic
1008C2×C4#1306329711yescharacteristic
1009C2×C4#1306329711yescharacteristic
1010C2×C4#1306329711yescharacteristic
1011C2×C4#1306329711yescharacteristic
1012C2×C4#1306329711yescharacteristic
1013C2×C4#1306329711yescharacteristic
1014C2×C4#1306329711yescharacteristic
1015C2×C4C2×D4×D4311yescharacteristic
1016C2×C4C2×D4×D4311yescharacteristic
1017C2×C4C2×D4×D4311yescharacteristic
1018C2×C4C2×D4×D4311yescharacteristic
1019C2×C4C2×D4×D4311yescharacteristic
1020C2×C4C2×D4×D4311yescharacteristic
1021C2×C4C22×C22⋊D4311yescharacteristic
1022C2×C4C22×C22⋊D4311yescharacteristic
1023C2×C4C22×C22⋊D4311yescharacteristic
1024C2×C4C22×C22⋊D4311yescharacteristic
1025C2×C4C22×C22⋊D4311yescharacteristic
1026C2×C4C22×C22⋊D4311yescharacteristic
1027C2×C4C2×#1062190011yescharacteristic
1028C2×C4C2×#1062190011yescharacteristic
1029C2×C4C2×#1062190011yescharacteristic
1030C2×C4C24×D4311yescharacteristic
1031C8—24no—
1032C8—438no—
1033C8—864no—
1034C8—864no—
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—3442no—
1051C22—3442no—
1052C22—3442no—
1053C22—1722no—
1054C22C2×#1306329711yescharacteristic
1055C22C2×#1306329711yescharacteristic
1056C22C2×#1306329711yescharacteristic
1057C22C2×#1306329711yescharacteristic
1058C22C2×#1306329711yescharacteristic
1059C22C2×#1306329711yescharacteristic
1060C22C22×#1062190011yescharacteristic
1061C4—24no—
1062C4—42no—
1063C4—1722no—
1064C4C2×#1306329711yescharacteristic
1065C4C2×#1306329711yescharacteristic
1066C4C2×#1306329711yescharacteristic
1067C4C2×#1306329711yescharacteristic
1068C4C2×#1306329711yescharacteristic
1069C4C2×#1306329711yescharacteristic
1070C4C22×D4×D4311yescharacteristic
1071C4C23×C22⋊D4311yescharacteristic
1072C2—21no—
1073C2—21no—
1074C2—21no—
1075C2—21no—
1076C2—21no—
1077C2—21no—
1078C2—21no—
1079C2—44no—
1080C2—82no—
1081C2—3442no—
1082C2C22×#1306329711yescharacteristic
subgroupG/H
centerC4C2×#13063297
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#575C2
socleC2×C43C22×#121
hypercenterC2×#575D43
hypocenterC43#60469
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#14583697C2semidirect
2. C2×#14583697C2semidirect
3. C2×#14583666C2semidirect
4. #19144334C2semidirect
5. #19144329C2semidirect
6. #19144325C2semidirect
7. #19144320C2semidirect
8. #19144312C2semidirect
9. C2×#14582947C2semidirect
10. C2×#14582883C2semidirect
11. C2×#14582881C2semidirect
12. C2×C43×#575C2semidirect
21. #14583697C22semidirect
23. C2×#13063356C22semidirect
24. C2×#13063355C22semidirect
25. C2×#13063355C22semidirect
27. C2×#13063351C22semidirect
28. C2×#13063350C22semidirect
29. C2×#13063350C22semidirect
31. C2×#13063345C22semidirect
34. #14583666C22semidirect
35. #14583666C22semidirect
37. C2×#13063332C22semidirect
42. #14583172C22semidirect
43. #14583167C22semidirect
44. #14583164C22semidirect
45. #14583160C22semidirect
46. #14582947C22semidirect
47. #14582947C22semidirect
48. C2×#13063260C22semidirect
49. #14582883C22semidirect
50. #14582883C22semidirect
51. #14582881C22semidirect
52. #14582881C22semidirect
53. C2×#13063244C22semidirect
54. C2×#13063243C22semidirect
55. C2×#13063242C22semidirect
56. C2×#13063241C22semidirect
62. C43×#575C22semidirect
64. C2×#137×C43C22semidirect
66. C2×AGL(1,ℤ/8)×C43C22semidirect
106. C2×#10621885C23semidirect
108. C2×#10621883C23semidirect
110. C2×#10621884C23semidirect
112. C2×#10621882C23semidirect
142. #13063260C23semidirect
143. #13063244C23semidirect
144. #13063243C23semidirect
145. #13063242C23semidirect
146. #13063241C23semidirect
533. C2×#575D43semidirect
568. #575C2×D43semidirect
574. C2×#137C2×D43semidirect
580. C2×AGL(1,ℤ/8)C2×D43semidirect
610. C43#60469semidirect

Maximal subgroups

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

subgroupindex
C2×#145836972
C2×#145836662
#191443342
#191443292
#191443252
#191443202
#191443122
C2×#145829472
C2×#145828832
C2×#145828812
C2×C43×#5752
#6046943