Finite Group Databasebeta

← #11878845

Subgroups — #11878845

Order 1152.

1047 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595367C211yesmaximal, characteristic, complemented
2D3×#940C211yesmaximal, characteristic
3#10592874C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591620C211yesmaximal, characteristic, complemented
8#10591617C211yesmaximal, characteristic, complemented
9#10591459C211yesmaximal, characteristic, complemented
10#10591439C211yesmaximal, characteristic, complemented
11#10591402C211yesmaximal, characteristic, complemented
12#10590946C211yesmaximal, characteristic, complemented
13#10590885C211yesmaximal, characteristic, complemented
14#10590879C211yesmaximal, characteristic, complemented
15#10590656C211yesmaximal, characteristic, complemented
16#80387—31nomaximal
17#80138—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64153C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25#64149C2211yescharacteristic
26C2×#3754C2211yescharacteristic, complemented
27C2×#3744C2211yescharacteristic, complemented
28C3×#946C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic, complemented
31C2×C3×#215C2211yescharacteristic, complemented
32C3×#940C2211yescharacteristic
33#63979—21no—
34#63979—21no—
35#63919C2211yescharacteristic, complemented
36#63914C2211yescharacteristic
37#63911C2211yescharacteristic
38#63899—21no—
39#63877—21no—
40C4×D3×Dic3C2211yescharacteristic
41#63857C2211yescharacteristic
42#63847—21no—
43#63844C2211yescharacteristic, complemented
44#63837—21no—
45C2×#3716C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61C2×#940—31no—
62D3×#127—31no—
63#5622—31no—
64#5578—31no—
65C3×#460—31no—
66C3×#450—31no—
67#5218—31no—
68#5175—31no—
69#5175—31no—
70#5175—31no—
71#5175—31no—
72#5175—61no—
73#5169—31no—
74#5169D311yescharacteristic, complemented
75#5163—31no—
76#5163D311yescharacteristic, complemented
77#5075—31no—
78#5046—31no—
79#5027—31no—
80#4848—31no—
81#4833—31no—
82#4776—31no—
83#4776—31no—
84#4762—31no—
85#4762—31no—
86#4760—31no—
87#4760—31no—
88#4760—31no—
89#4760—31no—
90#4731—31no—
91#4718—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×D3×D4—41no—
104C3×D3×D4—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108D3×#67—44no—
109D3×#67—44no—
110C2×#627—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#625—21no—
115C2×#625—21no—
116C2×D3×Dic3D411yescharacteristic
117C2×D3×Dic3D411yescharacteristic
118D3×D12—41no—
119D3×D12—41no—
120C32×SD16—41no—
121C2×C32×C8C2311yescharacteristic
122#3755—41no—
123#3754—41no—
124#3750—21no—
125#3750—21no—
126C4×C3⋊Dic3C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128#3744—41no—
129C3×#215—41no—
130C3×#215—41no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140#3724—21no—
141#3724—21no—
142Dic3⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145Dic32D411yescharacteristic
146Dic32D411yescharacteristic
147#3716—41no—
148#3716—41no—
149#3208—91noSylow
150C22×C3×D4—31no—
151C22×#67—61no—
152C22×#67—61no—
153C2×D3×D4—31no—
154C2×D3×D4—61no—
155C2×D3×D4—61no—
156C2×D3×D4C2×D311yescharacteristic
157C22×D12—31no—
158C2×C3×SD16—21no—
159C2×C3×SD16—31no—
160C2×C3×SD16—31no—
161C2×C3×SD16C2×D311yescharacteristic, complemented
162C2×C3×SD16C2×D311yescharacteristic, complemented
163C3×#127—31no—
164C3×C22⋊Q8—31no—
165C3×C4×Q8—31no—
166#946C2×D311yescharacteristic
167Q8×Dic3C2×D311yescharacteristic, complemented
168#944—31no—
169#944—31no—
170#944—61no—
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—61no—
174C2×#215C2×D311yescharacteristic, complemented
175C2×#215C2×D311yescharacteristic, complemented
176#940—31no—
177#940—31no—
178#940—31no—
179#940—31no—
180#940—31no—
181#940—61no—
182#940—61no—
183#940—61no—
184#940—61no—
185#940—61no—
186#940C2×D311yescharacteristic
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—61no—
192#924—31no—
193C2×C4×Dic3—31no—
194C2×#204—31no—
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—61no—
199#897—31no—
200#896—61no—
201#889—61no—
202#889—61no—
203#888—31no—
204#888—31no—
205#887—31no—
206#887—61no—
207#878—61no—
208#877—61no—
209#874—31no—
210#872—61no—
211C42×D3—31no—
212C4×Dic6—31no—
213C4×Dic6—61no—
214C3×C4⋊C8—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×C22⋊C8—31no—
220#832—31no—
221#832—31no—
222#832C2×D311yescharacteristic, complemented
223#832C2×D311yescharacteristic, complemented
224#830—31no—
225#821—31no—
226#821—31no—
227#821C2×D311yescharacteristic, complemented
228#821C2×D311yescharacteristic, complemented
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8C2×D311yescharacteristic
231Dic3⋊C8—31no—
232Dic3⋊C8C2×D311yescharacteristic, complemented
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236C8×Dic3—31no—
237C8×Dic3—61no—
238#809—31no—
239#809—31no—
240#809—31no—
241#809—31no—
242C4⋊(C3⋊C8)—31no—
243C23×C32—21no—
244C22×C3⋊D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3—42no—
250C22×C3×D3C2×D411yescharacteristic
251C2×D32—42no—
252C2×D32—42no—
253C2×D32—42no—
254C32×Q8—21no—
255C32×Q8—21no—
256C32×D4—21no—
257C32×D4—21no—
258C2×C32×C4—21no—
259C2×C32×C4C2411yescharacteristic
260#638—42no—
261#638—42no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267#634—21no—
268#634—21no—
269C3×#67—42no—
270C3×#67—42no—
271C3×#67—42no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283#627—42no—
284#626—42no—
285#626—42no—
286#626—42no—
287#625—42no—
288#625—42no—
289D3×Dic3—22no—
290D3×Dic3SD1614yescomplemented
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295#533—91no—
296C2×#127—91no—
297#492—91no—
298#492—91no—
299#486—91no—
300#486—91no—
301#460—31no—
302#460—91no—
303#460—91no—
304#460—91no—
305#450—31no—
306#450—91no—
307#450—91no—
308#450—91no—
309#431—91no—
310C24×C3—61no—
311C23×D3—21no—
312C23×D3—61no—
313C23×D3—61no—
314C2×C3×Q8—21no—
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×D4—21no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4—121no—
324C2×C3×D4—121no—
325C2×C3×D4C22×D311yescharacteristic
326C2×C3×D4C22×D311yescharacteristic
327C22×C3×C4—31no—
328C2×#67—21no—
329C2×#67—21no—
330C2×#67—21no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—121no—
343C2×#67—121no—
344C2×#67—124no—
345C2×#67—124no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348D3×D4—41no—
349D3×D4—41no—
350D3×D4—121no—
351D3×D4—121no—
352D3×D4—124no—
353D3×D4—124no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—121no—
361C2×D12—121no—
362C2×D12C22×D311yescharacteristic
363C2×D12C22×D311yescharacteristic
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3C22×D311yescharacteristic
367C2×Dic6—31no—
368C2×Dic6—31no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—61no—
372C3×SD16—41no—
373C3×SD16—41no—
374C3×SD16—42no—
375C3×SD16—121no—
376C3×SD16—121no—
377C2×C3×C8—21no—
378C2×C3×C8—31no—
379C2×C3×C8—31no—
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C22×D311yescharacteristic
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C42—31no—
388C3×C42—61no—
389#217—61no—
390#215—41no—
391#215—41no—
392#215—121no—
393#215—121no—
394#215—122no—
395#214—121no—
396#214—121no—
397#214—121no—
398#214—121no—
399#214—122no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—61no—
402C4⋊Dic3—21no—
403C4⋊Dic3—61no—
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—121no—
417Dic3⋊C4—121no—
418C4×Dic3—21no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—31no—
424C4×Dic3—31no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3C22×D311yescharacteristic
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—61no—
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434#204—121no—
435#204—121no—
436#204—122no—
437#204—121no—
438#204—121no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—84no—
455C2×C3×D3C2×SD1612yes—
456D32—84no—
457C32×C4—41no—
458C32×C4H(5,𝔽2)11yescharacteristic
459C32×C4H(5,𝔽2)11yescharacteristic
460C3⋊Dic3—41no—
461C3⋊Dic3C2×SD1612yes—
462C3⋊Dic3AGL(1,ℤ/8)12yes—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3C2×SD1612yes—
468C22×D4—31no—
469C22×D4—91no—
470C22×D4—181no—
471C22×D4—181no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16D3211yescharacteristic, complemented
480C4⋊Q8—91no—
481C4⋊Q8—91no—
482#127—31no—
483#127—91no—
484#127—91no—
485#127—91no—
486#127—181no—
487#127—181no—
488#125—181no—
489C22⋊Q8—31no—
490C22⋊Q8—91no—
491C22⋊Q8—181no—
492C4×Q8—31no—
493C4×Q8—91no—
494C4×Q8—181no—
495#117—181no—
496C2×C42—91no—
497C4⋊C8—31no—
498C4⋊C8—91no—
499#102—31no—
500#102—31no—
501#102—31no—
502#102—31no—
503#102—91no—
504#102—91no—
505#102—91no—
506#102—91no—
507C22⋊C8—31no—
508C22⋊C8—91no—
509C4×C8—91no—
510C4×C8—91no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—31no—
514C23×C3—41no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—122no—
518C23×C3—122no—
519C23×C3—122no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—42no—
523C22×D3—42no—
524C22×D3—42no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—121no—
528C22×D3—122no—
529C22×D3—122no—
530C22×D3—122no—
531C22×D3—122no—
532C22×D3—122no—
533C22×D3—122no—
534C22×D3D3×D411yescharacteristic
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—21no—
539C3×Q8—41no—
540C3×Q8—41no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—21no—
544C3×D4—21no—
545C3×D4—41no—
546C3×D4—41no—
547C3×D4—61no—
548C3×D4—61no—
549C3×D4—61no—
550C3×D4—61no—
551C3×D4—122no—
552C3×D4—122no—
553C3×D4—122no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—41no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4C23×D311yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567#67—42no—
568#67—42no—
569#67—42no—
570#67—122no—
571#67—122no—
572#67—122no—
573#67—122no—
574#67—122no—
575#67—122no—
576#67—122no—
577#67—122no—
578#67—122no—
579#67—122no—
580#67—122no—
581#67—242no—
582#67—242no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—34no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—62no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—121no—
596C2×Dic3D3×D411yescharacteristic
597C2×Dic3D3×D411yescharacteristic
598C2×Dic3D3×D411yescharacteristic
599D12—21no—
600D12—21no—
601D12—21no—
602D12—21no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—121no—
608D12—121no—
609D12—122no—
610D12—122no—
611D12—122no—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—34no—
615C4×D3—62no—
616Dic6—61no—
617Dic6—61no—
618Dic6—61no—
619Dic6—61no—
620Dic6—121no—
621Dic6—121no—
622Dic6—122no—
623Dic6—122no—
624C3×C8—22no—
625C3×C8—21no—
626C3×C8—21no—
627C3×C8—61no—
628C3×C8—61no—
629C3⋊C8—21no—
630C3⋊C8—21no—
631C3⋊C8—62no—
632C3⋊C8—61no—
633C3⋊C8—61no—
634C2×C32—81no—
635C2×C32#53511yescharacteristic
636C2×C32C22×SD1611yescharacteristic
637C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
638C3⋊D3—81no—
639C3×D3—22no—
640C3×D3—81no—
641C3×D3—81no—
642C24—61no—
643C24—181no—
644C2×Q8—91no—
645C2×Q8—181no—
646C2×Q8C2×D3211yescharacteristic
647C2×D4—31no—
648C2×D4—31no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—61no—
652C2×D4—91no—
653C2×D4—121no—
654C2×D4—121no—
655C2×D4—181no—
656C2×D4—181no—
657C2×D4—181no—
658C2×D4—181no—
659C2×D4—181no—
660C2×D4—181no—
661C2×D4—181no—
662C2×D4—361no—
663C2×D4—361no—
664C2×D4—364no—
665C2×D4—364no—
666C2×D4C2×D3211yescharacteristic
667C22×C4—31no—
668C22×C4—91no—
669C22×C4—91no—
670SD16—41no—
671SD16—121no—
672SD16—121no—
673SD16—361no—
674SD16—361no—
675SD16—361no—
676SD16—361no—
677SD16—361no—
678C2×C8—31no—
679C2×C8—31no—
680C2×C8—91no—
681C2×C8C2×D3211yescharacteristic
682C4⋊C4—31no—
683C4⋊C4—31no—
684C4⋊C4—61no—
685C4⋊C4—61no—
686C4⋊C4—181no—
687C4⋊C4—181no—
688C4⋊C4—181no—
689C4⋊C4—181no—
690C4⋊C4—181no—
691C22⋊C4—61no—
692C22⋊C4—181no—
693C42—31no—
694C42—61no—
695C42—91no—
696C42—91no—
697C42—91no—
698C42—181no—
699C22×C3—21no—
700C22×C3—32no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—244no—
719C22×C3C2×D3×D411yescharacteristic
720C22×C3C2×D3×D411yescharacteristic
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—41no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—84no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—241no—
737C2×D3—241no—
738C2×D3—241no—
739C2×D3—244no—
740C2×D3—244no—
741C2×D3D3×SD1612yes—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—32no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—61no—
748C3×C4—61no—
749C3×C4—81no—
750C3×C4—121no—
751C3×C4—121no—
752C3×C4#100411yescharacteristic
753C3×C4#100411yescharacteristic
754C3×C4#100411yescharacteristic
755C3×C4#100911yescharacteristic
756Dic3—21no—
757Dic3—21no—
758Dic3—32no—
759Dic3—32no—
760Dic3—32no—
761Dic3—32no—
762Dic3—41no—
763Dic3—41no—
764Dic3—62no—
765Dic3—62no—
766Dic3—121no—
767Dic3—121no—
768Dic3—241no—
769Dic3D3×SD1612yes—
770C32#320811yescharacteristic, complemented, Sylow
771C23—21no—
772C23—31no—
773C23—61no—
774C23—61no—
775C23—122no—
776C23—122no—
777C23—122no—
778C23—181no—
779C23—362no—
780C23—362no—
781C23—362no—
782Q8—21no—
783Q8—21no—
784Q8—181no—
785Q8—181no—
786Q8—362no—
787D4—21no—
788D4—21no—
789D4—61no—
790D4—61no—
791D4—61no—
792D4—61no—
793D4—122no—
794D4—122no—
795D4—122no—
796D4—181no—
797D4—181no—
798D4—362no—
799D4—362no—
800D4—362no—
801D4—362no—
802D4—362no—
803D4—362no—
804D4—362no—
805C2×C4—21no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—94no—
814C2×C4—91no—
815C2×C4—91no—
816C2×C4—182no—
817C2×C4—181no—
818C2×C4C22×D3211yescharacteristic
819C8—21no—
820C8—61no—
821C8—61no—
822C8—181no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—62no—
827C2×C3—81no—
828C2×C3—81no—
829C2×C3—161no—
830C2×C3—241no—
831C2×C3—241no—
832C2×C3#559211yescharacteristic
833C2×C3#560711yescharacteristic
834C2×C3C2×D3×SD1611yescharacteristic
835C2×C3C2×D3×SD1611yescharacteristic
836C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
837C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
838D3—22no—
839D3—81no—
840D3—81no—
841D3—241no—
842D3—241no—
843D3—481no—
844C22—32no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—61no—
849C22—61no—
850C22—121no—
851C22—121no—
852C22—121no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—244no—
857C22—361no—
858C22—361no—
859C22—361no—
860C22—724no—
861C22D32×D411yescharacteristic
862C4—32no—
863C4—41no—
864C4—61no—
865C4—61no—
866C4—92no—
867C4—92no—
868C4—121no—
869C4—121no—
870C4—361no—
871C4#6431411yescharacteristic
872C4#6433011yescharacteristic
873C3—21no—
874C3#8013811yescharacteristic, complemented
875C3#8038711yescharacteristic, complemented
876C2—62no—
877C2—81no—
878C2—241no—
879C2—241no—
880C2—721no—
881C2D32×SD1611yescharacteristic
882C2#1059474011yescharacteristic
883C2#1059528511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalD3×#940C2
hypercenterC2×SD16D32
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595367C2semidirect
3. #10592874C2semidirect
4. C3×#5169C2semidirect
5. C3×#5163C2semidirect
6. #10591651C2semidirect
7. #10591620C2semidirect
8. #10591617C2semidirect
9. #10591459C2semidirect
10. #10591439C2semidirect
11. #10591402C2semidirect
12. #10590946C2semidirect
13. #10590885C2semidirect
14. #10590879C2semidirect
15. #10590656C2semidirect
22. C2×C32×SD16C22semidirect
23. #64153C22semidirect
24. C2×#3755C22semidirect
26. C2×#3754C22semidirect
27. C2×#3744C22semidirect
29. C3×Q8×Dic3C22semidirect
30. C2×C3×#215C22semidirect
31. C2×C3×#215C22semidirect
35. #63919C22semidirect
43. #63844C22semidirect
45. C2×#3716C22semidirect
46. C2×#3716C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
50. C3×#821C22semidirect
51. C3×#821C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
60. #63553C22semidirect
74. #5169D3semidirect
76. #5163D3semidirect
161. C2×C3×SD16C2×D3semidirect
162. C2×C3×SD16C2×D3semidirect
167. Q8×Dic3C2×D3semidirect
174. C2×#215C2×D3semidirect
175. C2×#215C2×D3semidirect
222. #832C2×D3semidirect
223. #832C2×D3semidirect
227. #821C2×D3semidirect
228. #821C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
290. D3×Dic3SD16semidirect
479. C2×SD16D32semidirect
770. C32#3208semidirect
874. C3#80138semidirect
875. C3#80387semidirect

Maximal subgroups

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

subgroupindex
#105953672
D3×#9402
#105928742
C3×#51692
C3×#51632
#105916512
#105916202
#105916172
#105914592
#105914392
#105914022
#105909462
#105908852
#105908792
#105906562
#803873
#801383