Finite Group Databasebeta

← #25964020

Subgroups — #25964020

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×#14583699C211yesmaximal, characteristic, complemented
2C2×#14583697C211yesmaximal, characteristic, complemented
3C2×#14583697C211yesmaximal, characteristic, complemented
4C2×#14583665C211yesmaximal, characteristic, complemented
5#19144335C214yesmaximal, complemented
6#19144331C214yesmaximal, complemented
7#19144326C214yesmaximal, complemented
8#19144322C214yesmaximal, complemented
9#19144314C218yesmaximal, complemented
10C2×#14582947C211yesmaximal, characteristic, complemented
11C2×#14582881C211yesmaximal, characteristic, complemented
12C2×C43×#413C211yesmaximal, characteristic, complemented
13C22×#10621898C2211yescharacteristic
14C22×#10621898C2211yescharacteristic
15#14583699—22no—
16#14583699—22no—
17#14583699C2214yes—
18#14583699C2214yescomplemented
19#14583697—22no—
20#14583697—22no—
21#14583697—22no—
22#14583697—22no—
23#14583697—22no—
24#14583697—22no—
25#14583697C2214yes—
26#14583697C2214yescomplemented
27C2×#13063358—21no—
28C2×#13063358C2212yescomplemented
29C2×#13063356C2212yescomplemented
30C2×#13063356C2212yescomplemented
31C2×#13063355—21no—
32C2×#13063355C2212yescomplemented
33C2×#13063353—21no—
34C2×#13063353C2212yescomplemented
35C2×#13063351C2212yescomplemented
36C2×#13063351C2212yescomplemented
37C2×#13063350—21no—
38C2×#13063350C2212yescomplemented
39C2×#13063347—22no—
40C2×#13063345—22no—
41C2×#13063345C2214yescomplemented
42#14583665—22no—
43#14583665—22no—
44#14583665C2214yescomplemented
45#14583665C2214yescomplemented
46C2×#13063333C2214yescomplemented
47C2×#13063331—22no—
48C22×#10621877C2211yescharacteristic
49C22×#10621877C2211yescharacteristic
50C2×M16×D43—22no—
51#14583173C22116yescomplemented
52#14583168C22116yescomplemented
53#14583165C22116yescomplemented
54#14583161C22116yescomplemented
55#14582947C2214yescomplemented
56#14582947C2214yescomplemented
57C2×#13063260C2214yescomplemented
58#14582881C2214yescomplemented
59#14582881C2214yescomplemented
60C2×#13063243C2212yescomplemented
61C2×#13063241C2212yescomplemented
62C22×#41×C43C2211yescharacteristic
63C22×M16×C43C2211yescharacteristic
64C22×M16×C43C2211yescharacteristic
65C43×#413C2214yescomplemented
66C43×#413C2214yescomplemented
67C2×#101×C43C2212yescomplemented
68C2×#100×C43C2212yescomplemented
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×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898—21no—
82C2×#10621898—21no—
83C2×#10621898—21no—
84C2×#10621898—21no—
85C2×#10621898D412yes—
86C2×#10621898D412yes—
87C2×#10621898D412yes—
88C2×#10621898C2312yes—
89C2×#10621898C2312yes—
90C2×#10621898C2312yes—
91C2×#10621898C2312yes—
92C2×#10621898C2312yes—
93C22×Dic86D411yescharacteristic
94C22×Dic86C2311yescharacteristic
95C22×D172D411yescharacteristic
96C22×D172C2311yescharacteristic
97C22×C22⋊D43—21no—
98C22×C22⋊D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43—21no—
101#13063358—24no—
102#13063358—24no—
103#13063358—24no—
104#13063358C2318yes—
105#13063356—24no—
106#13063356—24no—
107#13063356—24no—
108#13063356C2318yes—
109#13063355—24no—
110#13063355—24no—
111#13063355—24no—
112#13063355—24no—
113#13063353—24no—
114#13063353—24no—
115#13063353—24no—
116#13063353C2318yes—
117#13063351—24no—
118#13063351—24no—
119#13063351—24no—
120#13063351C2318yes—
121#13063350—24no—
122#13063350—24no—
123#13063350—24no—
124#13063350—24no—
125#13063347—28no—
126#13063347—28no—
127#13063345—28no—
128#13063345—28no—
129#13063345—28no—
130#13063345—28no—
131C2×Dic172—22no—
132C2×#10621885—22no—
133C2×#10621885C2314yescomplemented
134C2×#10621873—22no—
135C2×#10621873—22no—
136C2×#10621883—22no—
137C2×#10621883C2314yescomplemented
138C2×#10621884—22no—
139C2×#10621884C2314yescomplemented
140C2×D344—22no—
141C2×#10621882—22no—
142C2×#10621882C2314yescomplemented
143#13063333—28no—
144#13063333C23116yes—
145#13063331—28no—
146#13063331—28no—
147C2×#10621877—21no—
148C2×#10621877—21no—
149C2×#10621877—21no—
150C2×#10621877D412yes—
151C2×#10621877D412yes—
152C2×#10621877D412yes—
153C2×#10621877D412yes—
154C2×#10621877C2312yes—
155C2×#10621877C2312yes—
156C2×#10621877C2312yes—
157C2×#10621877C2312yes—
158C2×#10621877C2312yes—
159C2×#10621872—24no—
160M16×D43—28no—
161M16×D43—28no—
162C22×C43⋊C8—21no—
163C22×C43⋊C8C2312yes—
164C2×C8×D43—24no—
165#13063260C23116yescomplemented
166#13063243C2318yescomplemented
167#13063241C2318yescomplemented
168C2×#41×C43—21no—
169C2×#41×C43—21no—
170C2×#41×C43—21no—
171C2×#41×C43—21no—
172C2×#41×C43—21no—
173C2×#41×C43—21no—
174C2×#41×C43—21no—
175C2×#41×C43—21no—
176C2×#41×C43—21no—
177C2×#41×C43—21no—
178C2×#41×C43C2312yes—
179C2×#41×C43C2312yes—
180C22×Q8×C43C2311yescharacteristic
181C22×D4×C43—21no—
182C22×D4×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43C2311yescharacteristic
185C2×M16×C43—21no—
186C2×M16×C43—21no—
187C2×M16×C43—21no—
188C2×M16×C43—21no—
189C2×M16×C43—21no—
190C2×M16×C43—21no—
191C2×M16×C43C2312yes—
192C2×M16×C43C2312yes—
193C2×M16×C43C2312yes—
194C2×M16×C43C2312yes—
195C2×M16×C43C2312yes—
196C2×M16×C43C2312yes—
197C22×C8×C43—21no—
198C22×C8×C43—21no—
199#101×C43C2318yescomplemented
200#100×C43C2318yescomplemented
201C24×C43—21no—
202C24×C43#4111yescharacteristic
203C23×D43—21no—
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—41no—
214#41×C43—41no—
215#41×C43—41no—
216#41×C43—41no—
217#41×C43—41no—
218#41×C43—41no—
219#41×C43—41no—
220#41×C43—41no—
221C2×Q8×C43—21no—
222C2×Q8×C43—21no—
223C2×Q8×C43—21no—
224C2×Q8×C43—21no—
225C2×Q8×C43—21no—
226C2×Q8×C43C2412yes—
227C2×D4×C43—21no—
228C2×D4×C43—22no—
229C2×D4×C43—22no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43—21no—
233C2×D4×C43—21no—
234C2×D4×C43—41no—
235C2×D4×C43—41no—
236C2×D4×C43—41no—
237C2×D4×C43—41no—
238C2×D4×C43C2412yes—
239C22×C4×C43—22no—
240C22×C4×C43—22no—
241C22×C4×C43—21no—
242C22×C4×C43—41no—
243C22×C4×C43—41no—
244C22×C4×C43—41no—
245C22×C4×C43—41no—
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2×D411yescharacteristic
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43#4111yescharacteristic
255C22×C4×C43#4111yescharacteristic
256C22×C4×C43#4111yescharacteristic
257C22×C4×C43C2411yescharacteristic
258C22×C4×C43C2411yescharacteristic
259C22×C4×C43C2411yescharacteristic
260C2×C22⋊D43—22no—
261C2×C22⋊D43—22no—
262C2×C22⋊D43—22no—
263C2×C22⋊D43—22no—
264C2×C22⋊D43—22no—
265C2×C22⋊D43—22no—
266C2×C22⋊D43—22no—
267C2×C22⋊D43—22no—
268C2×C22⋊D43—41no—
269C2×C22⋊D43—41no—
270C2×C22⋊D43—41no—
271C2×C22⋊D43—41no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274#10621898—22no—
275#10621898—22no—
276#10621898—22no—
277#10621898—22no—
278#10621898—22no—
279#10621898—22no—
280#10621898—22no—
281#10621898—22no—
282#10621898—22no—
283#10621898—22no—
284#10621898—22no—
285#10621898—22no—
286#10621898—22no—
287#10621898—22no—
288#10621898—22no—
289#10621898—22no—
290#10621898—22no—
291#10621898—22no—
292#10621898—22no—
293#10621898—22no—
294#10621898—41no—
295#10621898—41no—
296#10621898—41no—
297#10621898—41no—
298#10621898—41no—
299#10621898—41no—
300#10621898—41no—
301#10621898—41no—
302#10621898C2×D414yes—
303#10621898C2×D414yes—
304#10621898C2×D414yes—
305#10621898C2414yes—
306C2×D172—21no—
307C2×D172—21no—
308C2×D172—21no—
309C2×D172—21no—
310C2×D172—21no—
311C2×D172—21no—
312C2×D172—21no—
313C2×D172—21no—
314C2×D172C2×D412yes—
315C2×D172C2×D412yes—
316C2×D172C2×D412yes—
317C2×D172C2412yes—
318C2×C4×D43—22no—
319C2×C4×D43—22no—
320C2×C4×D43—22no—
321C2×C4×D43—22no—
322C2×C4×D43—22no—
323C2×C4×D43—22no—
324C2×C4×D43—22no—
325C2×C4×D43—22no—
326C2×C4×D43—41no—
327C2×C4×D43—41no—
328C2×C4×D43—41no—
329C2×C4×D43—41no—
330C2×Dic86—21no—
331C2×Dic86—21no—
332C2×Dic86—21no—
333C2×Dic86—21no—
334C2×Dic86—21no—
335C2×Dic86—21no—
336C2×Dic86—21no—
337C2×Dic86—21no—
338C2×Dic86C2×D412yes—
339C2×Dic86C2×D412yes—
340C2×Dic86C2×D412yes—
341C2×Dic86C2412yes—
342M16×C43—22no—
343M16×C43—22no—
344M16×C43—22no—
345M16×C43—22no—
346M16×C43—22no—
347M16×C43—22no—
348M16×C43C2414yes—
349M16×C43C2414yes—
350C2×C8×C43—22no—
351C2×C8×C43—22no—
352C2×C8×C43—22no—
353C2×C8×C43—22no—
354C2×C8×C43—22no—
355C2×C8×C43—22no—
356#10621885—28no—
357#10621885—28no—
358#10621884—28no—
359#10621884—28no—
360#10621883—28no—
361#10621883—28no—
362#10621882—28no—
363#10621882—28no—
364#10621877—22no—
365#10621877—22no—
366#10621877—22no—
367#10621877C2×D414yes—
368#10621877C2×D414yes—
369#10621877C2×D414yes—
370#10621877C2×D414yes—
371#10621877C2414yes—
372C2×C43⋊C8—22no—
373C2×C43⋊C8—22no—
374C2×C43⋊C8—22no—
375C2×C43⋊C8C2×D414yes—
376C2×C43⋊C8C2×D414yes—
377C2×C43⋊C8C2414yes—
378Dic172—28no—
379D344—28no—
380#10621873—28no—
381#10621873—28no—
382#10621872—216no—
383C8×D43—216no—
384C23×C43—22no—
385C23×C43—41no—
386C23×C43—41no—
387C23×C43—81no—
388C23×C43—82no—
389C23×C43#12111yescharacteristic
390C23×C43#12111yescharacteristic
391C23×C43#12111yescharacteristic
392C23×C43#12111yescharacteristic
393C23×C43C2×#4111yescharacteristic
394C23×C43C2×#4111yescharacteristic
395C23×C43C2×#4111yescharacteristic
396C22×D43—22no—
397C22×D43—22no—
398C22×D43—22no—
399C22×D43—22no—
400C22×D43—41no—
401C22×D43—41no—
402C22×D43—82no—
403C22×D43—82no—
404Q8×C43—22no—
405Q8×C43—22no—
406Q8×C43—41no—
407Q8×C43—41no—
408D4×C43—22no—
409D4×C43—22no—
410D4×C43—42no—
411D4×C43—42no—
412D4×C43—42no—
413D4×C43—42no—
414D4×C43—41no—
415D4×C43—41no—
416C2×C4×C43—22no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—42no—
420C2×C4×C43—42no—
421C2×C4×C43—42no—
422C2×C4×C43—42no—
423C2×C4×C43#12111yescharacteristic
424C2×C4×C43#12111yescharacteristic
425C2×C4×C43#12111yescharacteristic
426C2×C4×C43#12111yescharacteristic
427C2×C4×C43#12111yescharacteristic
428C2×C4×C43#12111yescharacteristic
429C2×C4×C43#12111yescharacteristic
430C2×C4×C43#12111yescharacteristic
431C2×C4×C43#12111yescharacteristic
432C2×C4×C43#12111yescharacteristic
433C2×C4×C43#12111yescharacteristic
434C2×C4×C43#12111yescharacteristic
435C2×C4×C43C22×D411yescharacteristic
436C2×C4×C43C22×D411yescharacteristic
437C2×C4×C43C22×D411yescharacteristic
438C2×C4×C43C22×D411yescharacteristic
439C2×C4×C43C22×D411yescharacteristic
440C2×C4×C43C22×D411yescharacteristic
441C2×C4×C43C22×D411yescharacteristic
442C2×C4×C43C22×D411yescharacteristic
443C2×C4×C43C22×D411yescharacteristic
444C2×C4×C43C22×D411yescharacteristic
445C2×C4×C43C22×D411yescharacteristic
446C2×C4×C43C22×D411yescharacteristic
447C2×C4×C43C2×#4111yescharacteristic
448C2×C4×C43C2×#4111yescharacteristic
449C2×C4×C43C2×#4111yescharacteristic
450C2×C4×C43C2511yescharacteristic
451C22⋊D43—24no—
452C22⋊D43—24no—
453C22⋊D43—24no—
454C22⋊D43—24no—
455C22⋊D43—42no—
456C22⋊D43—42no—
457C22⋊D43—42no—
458C22⋊D43—42no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—41no—
464C2×Dic43—41no—
465D172—22no—
466D172—22no—
467D172—22no—
468D172—22no—
469D172—22no—
470D172—41no—
471D172—41no—
472D172C22×D414yes—
473C4×D43—24no—
474C4×D43—24no—
475C4×D43—24no—
476C4×D43—24no—
477C4×D43—42no—
478C4×D43—42no—
479C4×D43—42no—
480C4×D43—42no—
481Dic86—22no—
482Dic86—22no—
483Dic86—22no—
484Dic86—22no—
485Dic86—22no—
486Dic86—41no—
487Dic86—41no—
488Dic86C22×D414yes—
489C8×C43—24no—
490C8×C43—24no—
491C43⋊C8—24no—
492C43⋊C8C22×D418yes—
493#60469—431nomaximal, Sylow
494C22×C43—41no—
495C22×C43—41no—
496C22×C43—41no—
497C22×C43—41no—
498C22×C43—41no—
499C22×C43—41no—
500C22×C43—41no—
501C22×C43—42no—
502C22×C43—82no—
503C22×C43—82no—
504C22×C43—82no—
505C22×C43C2×#12111yescharacteristic
506C22×C43C2×#12111yescharacteristic
507C22×C43C2×#12111yescharacteristic
508C22×C43C2×#12111yescharacteristic
509C22×C43C2×#12111yescharacteristic
510C22×C43C2×#12111yescharacteristic
511C22×C43C22×#4111yescharacteristic
512C2×D43—24no—
513C2×D43—44no—
514C2×D43—42no—
515C2×D43—82no—
516C2×D43—82no—
517C2×D43—82no—
518C2×D43—82no—
519C2×D43—82no—
520C4×C43—42no—
521C4×C43C2×#12111yescharacteristic
522C4×C43C2×#12111yescharacteristic
523C4×C43C2×#12111yescharacteristic
524C4×C43C2×#12111yescharacteristic
525C4×C43C2×#12111yescharacteristic
526C4×C43C2×#12111yescharacteristic
527C4×C43C23×D411yescharacteristic
528C4×C43C23×D411yescharacteristic
529Dic43—24no—
530Dic43—42no—
531C2×#575—431no—
532C2×#575—431no—
533C2×#575—431no—
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×#413D4311yescharacteristic, complemented
543C2×C43—21no—
544C2×C43—21no—
545C2×C43—21no—
546C2×C43—21no—
547C2×C43—21no—
548C2×C43—21no—
549C2×C43—21no—
550C2×C43—82no—
551C2×C43C22×#12111yescharacteristic
552D43—44no—
553D43—82no—
554C22×#41—431no—
555C22×#41—431no—
556C22×#41C2×D4311yescharacteristic
557#575—434no—
558#575—434no—
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#575—862no—
568#575—862no—
569C2×#137—432no—
570C2×#137—432no—
571C2×#137—432no—
572C2×#137—432no—
573C2×#137—861no—
574C2×#137—861no—
575C2×AGL(1,ℤ/8)—432no—
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)—861no—
581C2×#135—434no—
582C2×#135—862no—
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—862no—
593C22×M16C2×D4311yescharacteristic
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#413C2×D4314yescomplemented
605#413C2×D4314yescomplemented
606C2×#101—432no—
607C2×#101C2×D4312yescomplemented
608C2×#100—432no—
609C2×#100C2×D4312yescomplemented
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—432no—
622C2×#41—432no—
623C2×#41—432no—
624C2×#41—432no—
625C2×#41—432no—
626C2×#41—432no—
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×#41—861no—
640C2×#41—861no—
641C2×#41—861no—
642C2×#41—861no—
643C2×#41—861no—
644C2×#41—861no—
645C2×#41C22×D4312yes—
646C2×#41C22×D4312yes—
647C22×Q8—431no—
648C22×Q8—431no—
649C22×Q8C22×D4311yescharacteristic
650C22×D4—21no—
651C22×D4—431no—
652C22×D4—431no—
653C22×D4—861no—
654C22×D4—861no—
655C22×D4C22×D4311yescharacteristic
656C23×C4—21no—
657C23×C4—861no—
658C23×C4—861no—
659C23×C4C22×D4311yescharacteristic
660#137—438no—
661#137—438no—
662#137—864no—
663#137—864no—
664#137—864no—
665#137—864no—
666#137—864no—
667#137—864no—
668#137—864no—
669#137—864no—
670#137—864no—
671#137—864no—
672AGL(1,ℤ/8)—438no—
673AGL(1,ℤ/8)—438no—
674AGL(1,ℤ/8)—864no—
675AGL(1,ℤ/8)—864no—
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)—864no—
684#135—868no—
685#135—868no—
686#135—868no—
687#135—868no—
688#135—868no—
689#135—868no—
690C2×Q16—434no—
691C2×Q16—862no—
692C2×Q16—862no—
693C2×SD16—434no—
694C2×SD16—434no—
695C2×SD16—862no—
696C2×SD16—862no—
697C2×SD16—862no—
698C2×SD16—862no—
699C2×D8—434no—
700C2×D8—862no—
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—21no—
710C2×M16—21no—
711C2×M16—21no—
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×M16C22×D4312yes—
728C2×M16C22×D4312yes—
729C2×M16C22×D4312yes—
730C2×M16C22×D4312yes—
731C2×M16C22×D4312yes—
732C2×M16C22×D4312yes—
733C22×C8—21no—
734C22×C8—21no—
735C22×C8—432no—
736C22×C8—864no—
737C22×C8—861no—
738#108—4316no—
739#101—438no—
740#101C22×D4318yescomplemented
741#100—438no—
742#100C22×D4318yescomplemented
743C24—21no—
744C24—861no—
745C24—861no—
746C24#1062189811yescharacteristic
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—41no—
756#41—41no—
757#41—41no—
758#41—41no—
759#41—41no—
760#41—41no—
761#41—41no—
762#41—41no—
763#41—434no—
764#41—434no—
765#41—434no—
766#41—434no—
767#41—862no—
768#41—862no—
769#41—862no—
770#41—862no—
771#41—862no—
772#41—862no—
773#41—862no—
774#41—862no—
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—862no—
784#41—862no—
785#41—862no—
786#41—862no—
787#41—1721no—
788#41—1721no—
789#41—1721no—
790#41—1721no—
791#41—1721no—
792#41—1721no—
793#41—1721no—
794#41—1721no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—432no—
801C2×Q8—432no—
802C2×Q8—432no—
803C2×Q8—432no—
804C2×Q8—861no—
805C2×Q8—861no—
806C2×Q8—861no—
807C2×Q8—861no—
808C2×Q8—861no—
809C2×Q8—861no—
810C2×Q8—861no—
811C2×Q8—861no—
812C2×Q8C23×D4312yes—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—432no—
825C2×D4—432no—
826C2×D4—432no—
827C2×D4—432no—
828C2×D4—862no—
829C2×D4—862no—
830C2×D4—862no—
831C2×D4—862no—
832C2×D4—862no—
833C2×D4—862no—
834C2×D4—862no—
835C2×D4—862no—
836C2×D4—861no—
837C2×D4—861no—
838C2×D4—861no—
839C2×D4—861no—
840C2×D4—861no—
841C2×D4—861no—
842C2×D4—861no—
843C2×D4—861no—
844C2×D4—1721no—
845C2×D4—1721no—
846C2×D4—1721no—
847C2×D4—1721no—
848C2×D4C23×D4312yes—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—861no—
857C22×C4—862no—
858C22×C4—862no—
859C22×C4—862no—
860C22×C4—862no—
861C22×C4—862no—
862C22×C4—862no—
863C22×C4—861no—
864C22×C4—862no—
865C22×C4—862no—
866C22×C4—1721no—
867C22×C4—1721no—
868C22×C4—1721no—
869C22×C4—1721no—
870C22×C4#1062189811yescharacteristic
871C22×C4#1062189811yescharacteristic
872C22×C4#1062189811yescharacteristic
873C22×C4D4×D4311yescharacteristic
874C22×C4D4×D4311yescharacteristic
875C22×C4D4×D4311yescharacteristic
876C22×C4D4×D4311yescharacteristic
877C22×C4D4×D4311yescharacteristic
878C22×C4D4×D4311yescharacteristic
879C22×C4D4×D4311yescharacteristic
880C22×C4D4×D4311yescharacteristic
881C22×C4C23×D4311yescharacteristic
882C22×C4C23×D4311yescharacteristic
883C22×C4C23×D4311yescharacteristic
884Q16—868no—
885Q16—868no—
886Q16—868no—
887SD16—868no—
888SD16—868no—
889SD16—868no—
890SD16—868no—
891SD16—868no—
892SD16—868no—
893D8—868no—
894D8—868no—
895D8—868no—
896M16—22no—
897M16—22no—
898M16—22no—
899M16—22no—
900M16—22no—
901M16—22no—
902M16—434no—
903M16—434no—
904M16—434no—
905M16—434no—
906M16—434no—
907M16—8616no—
908M16—862no—
909M16—862no—
910M16—862no—
911M16C23×D4314yes—
912M16C23×D4314yes—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—22no—
916C2×C8—22no—
917C2×C8—22no—
918C2×C8—22no—
919C2×C8—434no—
920C2×C8—434no—
921C2×C8—434no—
922C2×C8—8616no—
923C2×C8—862no—
924C2×C8—862no—
925C2×C8—862no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—81no—
930C23—82no—
931C23—862no—
932C23—862no—
933C23—862no—
934C23—862no—
935C23—3442no—
936C23—3442no—
937C23—1721no—
938C23—1721no—
939C23#1306329811yescharacteristic
940C23#1306329811yescharacteristic
941C23#1306329811yescharacteristic
942C23#1306329811yescharacteristic
943C23C2×#1062189811yescharacteristic
944C23C2×#1062189811yescharacteristic
945C23C2×#1062189811yescharacteristic
946Q8—22no—
947Q8—22no—
948Q8—41no—
949Q8—41no—
950Q8—434no—
951Q8—862no—
952Q8—862no—
953Q8—862no—
954Q8—862no—
955Q8—862no—
956Q8—1721no—
957Q8—1721no—
958D4—22no—
959D4—22no—
960D4—42no—
961D4—42no—
962D4—42no—
963D4—42no—
964D4—41no—
965D4—41no—
966D4—434no—
967D4—864no—
968D4—864no—
969D4—864no—
970D4—864no—
971D4—862no—
972D4—862no—
973D4—862no—
974D4—862no—
975D4—862no—
976D4—1722no—
977D4—1722no—
978D4—1722no—
979D4—1722no—
980D4—1721no—
981D4—1721no—
982C2×C4—22no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—862no—
990C2×C4—862no—
991C2×C4—862no—
992C2×C4—864no—
993C2×C4—864no—
994C2×C4—864no—
995C2×C4—864no—
996C2×C4—862no—
997C2×C4—1721no—
998C2×C4—1721no—
999C2×C4—1722no—
1000C2×C4—1722no—
1001C2×C4—1722no—
1002C2×C4—1722no—
1003C2×C4#1306329811yescharacteristic
1004C2×C4#1306329811yescharacteristic
1005C2×C4#1306329811yescharacteristic
1006C2×C4#1306329811yescharacteristic
1007C2×C4#1306329811yescharacteristic
1008C2×C4#1306329811yescharacteristic
1009C2×C4#1306329811yescharacteristic
1010C2×C4#1306329811yescharacteristic
1011C2×C4#1306329811yescharacteristic
1012C2×C4#1306329811yescharacteristic
1013C2×C4#1306329811yescharacteristic
1014C2×C4#1306329811yescharacteristic
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×C4C2×D4×D4311yescharacteristic
1022C2×C4C2×D4×D4311yescharacteristic
1023C2×C4C2×D4×D4311yescharacteristic
1024C2×C4C2×D4×D4311yescharacteristic
1025C2×C4C2×D4×D4311yescharacteristic
1026C2×C4C2×D4×D4311yescharacteristic
1027C2×C4C2×#1062189811yescharacteristic
1028C2×C4C2×#1062189811yescharacteristic
1029C2×C4C2×#1062189811yescharacteristic
1030C2×C4C24×D4311yescharacteristic
1031C8—24no—
1032C8—24no—
1033C8—438no—
1034C8—864no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—42no—
1043C22—82no—
1044C22—82no—
1045C22—82no—
1046C22—864no—
1047C22—3442no—
1048C22—3442no—
1049C22—3442no—
1050C22—3442no—
1051C22—3442no—
1052C22—1724no—
1053C22—1722no—
1054C22C2×#1306329811yescharacteristic
1055C22C2×#1306329811yescharacteristic
1056C22C2×#1306329811yescharacteristic
1057C22C2×#1306329811yescharacteristic
1058C22C2×#1306329811yescharacteristic
1059C22C2×#1306329811yescharacteristic
1060C22C22×#1062189811yescharacteristic
1061C4—42no—
1062C4—864no—
1063C4—1722no—
1064C4C2×#1306329811yescharacteristic
1065C4C2×#1306329811yescharacteristic
1066C4C2×#1306329811yescharacteristic
1067C4C2×#1306329811yescharacteristic
1068C4C2×#1306329811yescharacteristic
1069C4C2×#1306329811yescharacteristic
1070C4C22×D4×D4311yescharacteristic
1071C4C22×D4×D4311yescharacteristic
1072C2—21no—
1073C2—21no—
1074C2—21no—
1075C2—21no—
1076C2—21no—
1077C2—21no—
1078C2—21no—
1079C2—82no—
1080C2—3442no—
1081C2—1724no—
1082C2C22×#1306329811yescharacteristic
subgroupG/H
centerC4C2×#13063298
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#413C2
socleC2×C43C22×#121
hypercenterC2×#413D43
hypocenterC43#60469
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
1. C2×#14583699C2semidirect
2. C2×#14583697C2semidirect
3. C2×#14583697C2semidirect
4. C2×#14583665C2semidirect
5. #19144335C2semidirect
6. #19144331C2semidirect
7. #19144326C2semidirect
8. #19144322C2semidirect
9. #19144314C2semidirect
10. C2×#14582947C2semidirect
11. C2×#14582881C2semidirect
12. C2×C43×#413C2semidirect
18. #14583699C22semidirect
26. #14583697C22semidirect
28. C2×#13063358C22semidirect
29. C2×#13063356C22semidirect
30. C2×#13063356C22semidirect
32. C2×#13063355C22semidirect
34. C2×#13063353C22semidirect
35. C2×#13063351C22semidirect
36. C2×#13063351C22semidirect
38. C2×#13063350C22semidirect
41. C2×#13063345C22semidirect
44. #14583665C22semidirect
45. #14583665C22semidirect
46. C2×#13063333C22semidirect
51. #14583173C22semidirect
52. #14583168C22semidirect
53. #14583165C22semidirect
54. #14583161C22semidirect
55. #14582947C22semidirect
56. #14582947C22semidirect
57. C2×#13063260C22semidirect
58. #14582881C22semidirect
59. #14582881C22semidirect
60. C2×#13063243C22semidirect
61. C2×#13063241C22semidirect
65. C43×#413C22semidirect
66. C43×#413C22semidirect
67. C2×#101×C43C22semidirect
68. C2×#100×C43C22semidirect
133. C2×#10621885C23semidirect
137. C2×#10621883C23semidirect
139. C2×#10621884C23semidirect
142. C2×#10621882C23semidirect
165. #13063260C23semidirect
166. #13063243C23semidirect
167. #13063241C23semidirect
199. #101×C43C23semidirect
200. #100×C43C23semidirect
542. C2×#413D43semidirect
604. #413C2×D43semidirect
605. #413C2×D43semidirect
607. C2×#101C2×D43semidirect
609. C2×#100C2×D43semidirect
610. C43#60469semidirect
740. #101C22×D43semidirect
742. #100C22×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836992
C2×#145836972
C2×#145836652
#191443352
#191443312
#191443262
#191443222
#191443142
C2×#145829472
C2×#145828812
C2×C43×#4132
#6046943