Finite Group Databasebeta

← #11878847

Subgroups — #11878847

Order 1152.

1040 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595368C211yesmaximal, characteristic, complemented
2D3×#940C211yesmaximal, characteristic
3#10592862C211yesmaximal, characteristic, complemented
4C3×#5175C211yesmaximal, characteristic, complemented
5C3×#5169C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591622C211yesmaximal, characteristic, complemented
8#10591618C211yesmaximal, characteristic, complemented
9#10591487C211yesmaximal, characteristic, complemented
10#10591458C211yesmaximal, characteristic, complemented
11#10591444C211yesmaximal, characteristic, complemented
12#10590942C211yesmaximal, characteristic, complemented
13#10590878C211yesmaximal, characteristic, complemented
14#10590876C211yesmaximal, characteristic, complemented
15#10590655C211yesmaximal, characteristic, complemented
16#81766—31nomaximal
17#80138—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25#64149C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#944C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#940C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#204C2211yescharacteristic, complemented
33#63979—21no—
34#63979—21no—
35#63918C2211yescharacteristic, complemented
36#63914C2211yescharacteristic
37#63911C2211yescharacteristic
38#63893—21no—
39#63878—21no—
40C4×D3×Dic3C2211yescharacteristic
41#63856C2211yescharacteristic
42#63845—21no—
43#63843C2211yescharacteristic, complemented
44#63838—21no—
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47#63659C2211yescharacteristic, complemented
48#63648C2211yescharacteristic, complemented
49#63641C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C2×#940—31no—
62#5728—31no—
63D3×#127—31no—
64#5622—31no—
65C3×#492—31no—
66C3×#450—31no—
67#5218—31no—
68#5175—31no—
69#5175D311yescharacteristic, complemented
70#5169—31no—
71#5169—31no—
72#5169—31no—
73#5169D311yescharacteristic, complemented
74#5163—31no—
75#5163—31no—
76#5163—31no—
77#5163—31no—
78#5163—31no—
79#5163—31no—
80#5163—61no—
81#5085—31no—
82#5070—31no—
83#5046—31no—
84#4762—31no—
85#4762—31no—
86#4760—31no—
87#4760—31no—
88#4731—31no—
89#4718—31no—
90#4694—31no—
91#4685—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×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×D4—41no—
103C3×D3×D4—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
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—
123C4⋊(C3⋊Dic3)—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#215—41no—
129C3×#215—41no—
130C3×#214—41no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—41no—
140#3724—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145Dic32D411yescharacteristic
146Dic32D411yescharacteristic
147#3717—41no—
148#3715—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×SD16—31no—
162C2×C3×SD16—31no—
163C2×C3×SD16C2×D311yescharacteristic, complemented
164C2×C3×SD16C2×D311yescharacteristic, complemented
165C3×C4⋊Q8—31no—
166C3×#127—31no—
167C3×C22⋊Q8—31no—
168#946—31no—
169#946C2×D311yescharacteristic
170Q8×Dic3—31no—
171Q8×Dic3—31no—
172Q8×Dic3—31no—
173Q8×Dic3—61no—
174#944C2×D311yescharacteristic, complemented
175C2×#215—31no—
176C2×#215—31no—
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—61no—
180C2×#215C2×D311yescharacteristic, complemented
181C2×#215C2×D311yescharacteristic, complemented
182#940—31no—
183#940—31no—
184#940—31no—
185#940—31no—
186#940—31no—
187#940—61no—
188#940—61no—
189#940—61no—
190#940—61no—
191#940—61no—
192#940C2×D311yescharacteristic
193C2×#214—31no—
194C2×#214C2×D311yescharacteristic, complemented
195#924—31no—
196C2×C4×Dic3—31no—
197C2×#204—31no—
198C2×#204C2×D311yescharacteristic, complemented
199#897—61no—
200#892—61no—
201#890—61no—
202#889—61no—
203#888—31no—
204#887—31no—
205#887—61no—
206#887—61no—
207#878—61no—
208#877—61no—
209#874—31no—
210C42×D3—31no—
211#869—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×C22⋊C8—31no—
215C3×C4×C8—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—61no—
222#832C2×D311yescharacteristic, complemented
223#830—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229#821—61no—
230#821C2×D311yescharacteristic, complemented
231(C2×D3)⋊C8—31no—
232(C2×D3)⋊C8C2×D311yescharacteristic
233Dic3⋊C8—31no—
234Dic3⋊C8—31no—
235Dic3⋊C8—31no—
236Dic3⋊C8—31no—
237Dic3⋊C8—61no—
238C8×Dic3—31no—
239C8×Dic3C2×D311yescharacteristic, complemented
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—
267C3×#67—42no—
268C3×#67—42no—
269C3×#67—42no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
281C3×Dic6—21no—
282C3×Dic6—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—31no—
298#492—91no—
299#486—91no—
300#486—91no—
301#460—91no—
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×Q8—31no—
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×D4—21no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—121no—
325C2×C3×D4—121no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—31no—
329C2×#67—21no—
330C2×#67—21no—
331C2×#67—21no—
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—61no—
343C2×#67—121no—
344C2×#67—121no—
345C2×#67—124no—
346C2×#67—124no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349D3×D4—41no—
350D3×D4—41no—
351D3×D4—121no—
352D3×D4—121no—
353D3×D4—124no—
354D3×D4—124no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—121no—
362C2×D12—121no—
363C2×D12C22×D311yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6C22×D311yescharacteristic
371C3×SD16—41no—
372C3×SD16—41no—
373C3×SD16—42no—
374C3×SD16—121no—
375C3×SD16—121no—
376C3×SD16—121no—
377C3×SD16—121no—
378C2×C3×C8—21no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C22×D311yescharacteristic
383C3×C4⋊C4—31no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C42—31no—
389#217—61no—
390#215—41no—
391#215—41no—
392#215—121no—
393#215—121no—
394#215—121no—
395#215—121no—
396#215—122no—
397#214—41no—
398#214—121no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—61no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—121no—
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—121no—
429C4×Dic3C22×D311yescharacteristic
430C2×C3⋊C8—31no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—61no—
433C2×C3⋊C8C22×D311yescharacteristic
434C2×C3⋊C8C22×D311yescharacteristic
435#204—41no—
436#204—121no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32C22×D411yescharacteristic
441C2×C3⋊D3—41no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3×D3—21no—
445C2×C3×D3—21no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—84no—
453C2×C3×D3C2×SD1612yes—
454D32—84no—
455C32×C4—41no—
456C32×C4H(5,𝔽2)11yescharacteristic
457C32×C4H(5,𝔽2)11yescharacteristic
458C3⋊Dic3—21no—
459C3⋊Dic3—41no—
460C3⋊Dic3C2×SD1612yes—
461C3×Dic3—21no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3C2×SD1612yes—
465C3×Dic3AGL(1,ℤ/8)12yes—
466C22×D4—31no—
467C22×D4—91no—
468C22×D4—181no—
469C22×D4—181no—
470C2×SD16—31no—
471C2×SD16—31no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16D3211yescharacteristic, complemented
478C4⋊Q8—31no—
479C4⋊Q8—91no—
480#127—31no—
481#127—91no—
482#127—91no—
483#127—91no—
484#127—181no—
485#127—181no—
486#125—181no—
487C22⋊Q8—31no—
488C22⋊Q8—91no—
489C22⋊Q8—181no—
490C4×Q8—91no—
491C4×Q8—91no—
492C4×Q8—181no—
493#117—181no—
494C2×C42—91no—
495C4⋊C8—91no—
496C4⋊C8—91no—
497#102—31no—
498#102—31no—
499#102—91no—
500#102—91no—
501#102—91no—
502#102—91no—
503#102—91no—
504#102—91no—
505C22⋊C8—31no—
506C22⋊C8—91no—
507C4×C8—31no—
508C4×C8—91no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—31no—
512C23×C3—41no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—122no—
516C23×C3—122no—
517C23×C3—122no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3—42no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—121no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—122no—
529C22×D3—122no—
530C22×D3—122no—
531C22×D3—122no—
532C22×D3D3×D411yescharacteristic
533C3×Q8—22no—
534C3×Q8—21no—
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—41no—
539C3×Q8—61no—
540C3×Q8—61no—
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—34no—
588C2×Dic3—31no—
589C2×Dic3—31no—
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—21no—
617Dic6—21no—
618Dic6—122no—
619Dic6—122no—
620C3×C8—21no—
621C3×C8—21no—
622C3×C8—41no—
623C3×C8—61no—
624C3×C8—61no—
625C3⋊C8—21no—
626C3⋊C8—21no—
627C3⋊C8—61no—
628C3⋊C8—61no—
629C3⋊C8—121no—
630C2×C32—81no—
631C2×C32#53511yescharacteristic
632C2×C32C22×SD1611yescharacteristic
633C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
634C3⋊D3—81no—
635C3×D3—22no—
636C3×D3—81no—
637C3×D3—81no—
638C24—61no—
639C24—181no—
640C2×Q8—31no—
641C2×Q8—181no—
642C2×Q8C2×D3211yescharacteristic
643C2×D4—31no—
644C2×D4—31no—
645C2×D4—61no—
646C2×D4—61no—
647C2×D4—61no—
648C2×D4—91no—
649C2×D4—121no—
650C2×D4—121no—
651C2×D4—181no—
652C2×D4—181no—
653C2×D4—181no—
654C2×D4—181no—
655C2×D4—181no—
656C2×D4—181no—
657C2×D4—181no—
658C2×D4—361no—
659C2×D4—361no—
660C2×D4—364no—
661C2×D4—364no—
662C2×D4C2×D3211yescharacteristic
663C22×C4—31no—
664C22×C4—91no—
665C22×C4—91no—
666SD16—41no—
667SD16—121no—
668SD16—121no—
669SD16—121no—
670SD16—121no—
671SD16—361no—
672SD16—361no—
673SD16—361no—
674C2×C8—31no—
675C2×C8—31no—
676C2×C8—91no—
677C2×C8C2×D3211yescharacteristic
678C4⋊C4—31no—
679C4⋊C4—61no—
680C4⋊C4—61no—
681C4⋊C4—61no—
682C4⋊C4—91no—
683C4⋊C4—181no—
684C4⋊C4—181no—
685C4⋊C4—181no—
686C4⋊C4—181no—
687C22⋊C4—61no—
688C22⋊C4—181no—
689C42—31no—
690C42—91no—
691C42—91no—
692C42—91no—
693C42—181no—
694C42—181no—
695C22×C3—21no—
696C22×C3—32no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—121no—
709C22×C3—121no—
710C22×C3—121no—
711C22×C3—121no—
712C22×C3—121no—
713C22×C3—121no—
714C22×C3—244no—
715C22×C3C2×D3×D411yescharacteristic
716C22×C3C2×D3×D411yescharacteristic
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—84no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—241no—
733C2×D3—241no—
734C2×D3—241no—
735C2×D3—244no—
736C2×D3—244no—
737C2×D3D3×SD1612yes—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—32no—
741C3×C4—32no—
742C3×C4—42no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—61no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4#100411yescharacteristic
749C3×C4#100411yescharacteristic
750C3×C4#100411yescharacteristic
751C3×C4#100411yescharacteristic
752Dic3—21no—
753Dic3—32no—
754Dic3—32no—
755Dic3—41no—
756Dic3—41no—
757Dic3—62no—
758Dic3—61no—
759Dic3—61no—
760Dic3—121no—
761Dic3—121no—
762Dic3—121no—
763Dic3—241no—
764Dic3D3×SD1612yes—
765Dic3#91412yes—
766C32#320811yescharacteristic, complemented, Sylow
767C23—21no—
768C23—31no—
769C23—61no—
770C23—61no—
771C23—122no—
772C23—122no—
773C23—122no—
774C23—181no—
775C23—362no—
776C23—362no—
777C23—362no—
778Q8—21no—
779Q8—21no—
780Q8—61no—
781Q8—61no—
782Q8—362no—
783D4—21no—
784D4—21no—
785D4—61no—
786D4—61no—
787D4—61no—
788D4—61no—
789D4—122no—
790D4—122no—
791D4—122no—
792D4—181no—
793D4—181no—
794D4—362no—
795D4—362no—
796D4—362no—
797D4—362no—
798D4—362no—
799D4—362no—
800D4—362no—
801C2×C4—21no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—94no—
810C2×C4—91no—
811C2×C4—91no—
812C2×C4—182no—
813C2×C4—181no—
814C2×C4C22×D3211yescharacteristic
815C8—21no—
816C8—61no—
817C8—61no—
818C8—181no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—62no—
823C2×C3—81no—
824C2×C3—81no—
825C2×C3—161no—
826C2×C3—241no—
827C2×C3—241no—
828C2×C3#559211yescharacteristic
829C2×C3#571511yescharacteristic
830C2×C3C2×D3×SD1611yescharacteristic
831C2×C3C2×D3×SD1611yescharacteristic
832C2×C3C2×#91411yescharacteristic
833C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
834D3—22no—
835D3—81no—
836D3—81no—
837D3—241no—
838D3—241no—
839D3—481no—
840C22—32no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—61no—
845C22—61no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22—244no—
853C22—361no—
854C22—361no—
855C22—361no—
856C22—724no—
857C22D32×D411yescharacteristic
858C4—32no—
859C4—32no—
860C4—41no—
861C4—61no—
862C4—92no—
863C4—121no—
864C4—121no—
865C4—181no—
866C4—361no—
867C4#6431311yescharacteristic
868C4#6433011yescharacteristic
869C3—21no—
870C3#8013811yescharacteristic, complemented
871C3#8176611yescharacteristic, complemented
872C2—62no—
873C2—81no—
874C2—241no—
875C2—241no—
876C2—721no—
877C2D32×SD1611yescharacteristic
878C2D3×#91411yescharacteristic
879C2#1059528611yescharacteristic
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. #10595368C2semidirect
3. #10592862C2semidirect
4. C3×#5175C2semidirect
5. C3×#5169C2semidirect
6. #10591651C2semidirect
7. #10591622C2semidirect
8. #10591618C2semidirect
9. #10591487C2semidirect
10. #10591458C2semidirect
11. #10591444C2semidirect
12. #10590942C2semidirect
13. #10590878C2semidirect
14. #10590876C2semidirect
15. #10590655C2semidirect
22. C2×C32×SD16C22semidirect
23. Q8×C3⋊Dic3C22semidirect
24. C2×#3755C22semidirect
27. C3×#944C22semidirect
28. C2×C3×#215C22semidirect
29. C2×C3×#215C22semidirect
31. C2×C3×#214C22semidirect
32. C2×C3×#204C22semidirect
35. #63918C22semidirect
43. #63843C22semidirect
45. C2×#3717C22semidirect
46. C2×#3715C22semidirect
47. #63659C22semidirect
48. #63648C22semidirect
49. #63641C22semidirect
50. C3×#832C22semidirect
51. C3×#821C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63572C22semidirect
55. #63564C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
69. #5175D3semidirect
73. #5169D3semidirect
163. C2×C3×SD16C2×D3semidirect
164. C2×C3×SD16C2×D3semidirect
174. #944C2×D3semidirect
180. C2×#215C2×D3semidirect
181. C2×#215C2×D3semidirect
194. C2×#214C2×D3semidirect
198. C2×#204C2×D3semidirect
222. #832C2×D3semidirect
230. #821C2×D3semidirect
239. C8×Dic3C2×D3semidirect
290. D3×Dic3SD16semidirect
477. C2×SD16D32semidirect
766. C32#3208semidirect
870. C3#80138semidirect
871. C3#81766semidirect

Maximal subgroups

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

subgroupindex
#105953682
D3×#9402
#105928622
C3×#51752
C3×#51692
#105916512
#105916222
#105916182
#105914872
#105914582
#105914442
#105909422
#105908782
#105908762
#105906552
#817663
#801383