Finite Group Databasebeta

← #11887022

Subgroups — #11887022

Order 1152.

1202 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#638C211yesmaximal, characteristic, complemented
2#10594928C211yesmaximal, characteristic, complemented
3C3×#5217C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591494C211yesmaximal, characteristic, complemented
6#10591456C211yesmaximal, characteristic, complemented
7#10591455C211yesmaximal, characteristic, complemented
8#10591435C211yesmaximal, characteristic, complemented
9#10591433C211yesmaximal, characteristic, complemented
10#10591417C211yesmaximal, characteristic, complemented
11#10591416C211yesmaximal, characteristic, complemented
12#10591402C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14#10591148C211yesmaximal, characteristic, complemented
15#10591133C211yesmaximal, characteristic, complemented
16#80014—31nomaximal
17#78757—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×#638—21no—
20C2×D4×C3⋊D3C2211yescharacteristic
21C2×#3804—21no—
22#64162—21no—
23#64149C2211yescharacteristic
24#64148—21no—
25#64147C2211yescharacteristic
26#64146—21no—
27D4×C3⋊Dic3C2211yescharacteristic
28#64139C2211yescharacteristic
29C4×#638C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic, complemented
32C3×#930C2211yescharacteristic, complemented
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C22×C3×C3⋊C8C2211yescharacteristic, complemented
35#63961—21no—
36#63919C2211yescharacteristic, complemented
37#63916C2211yescharacteristic, complemented
38#63900C2211yescharacteristic, complemented
39#63899—21no—
40#63898C2211yescharacteristic, complemented
41#63854—21no—
42C2×#3714C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic, complemented
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#830C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61D4×#67—31no—
62D4×#67—31no—
63D4×#67—61no—
64#5611—31no—
65#5507—31no—
66C3×#447—31no—
67C2×C3×#102—31no—
68#5217D311yescharacteristic, complemented
69C2×#832D311yescharacteristic, complemented
70#5157—31no—
71#5156—31no—
72#5150—31no—
73Dic3×D8—31no—
74#5115—31no—
75C8×#67—31no—
76#5038—31no—
77#4967—31no—
78#4786—31no—
79#4775—31no—
80#4774—31no—
81#4774—31no—
82#4773—31no—
83D3×#102—31no—
84D3×#102—31no—
85#4760—31no—
86#4760—31no—
87#4759—31no—
88#4759—31no—
89#4756—31no—
90#4736—31no—
91#67⋊C8—31no—
92C24×C32—21no—
93C23×C3⋊D3—21no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4—41no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101C2×#638—21no—
102C2×#638—21no—
103C2×#638—21no—
104C2×#638—21no—
105C2×#638—44no—
106C2×#638D411yescharacteristic
107C22×C3⋊Dic3—21no—
108D4×C3⋊D3—22no—
109D4×C3⋊D3—41no—
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C3×#67—21no—
113C22×C3×Dic3—21no—
114C2×C3×D12C2311yescharacteristic
115C2×#627—21no—
116C2×#626—21no—
117C2×#624—21no—
118#3804—44no—
119C2×D3×Dic3—21no—
120#3757—21no—
121#3757—21no—
122#3757D411yescharacteristic
123#3752—21no—
124#3752D411yescharacteristic
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750D411yescharacteristic
127C4×C3⋊Dic3C2311yescharacteristic
128C3×#213—22no—
129C3×#213—41no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—41no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140#3724—21no—
141#3724—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144#3714—41no—
145#3710—41no—
146#3294—91noSylow
147C22×C3×D4—21no—
148C22×C3×D4C2×D311yescharacteristic
149C22×C3×D4C2×D311yescharacteristic
150C22×#67—61no—
151C22×#67—61no—
152C22×#67—62no—
153C2×#237—61no—
154C2×D3×D4—31no—
155C2×D3×D4—31no—
156C2×D3×D4—61no—
157C2×#235—61no—
158C2×C3×D8—31no—
159C2×C3×D8—31no—
160C22×C3×C8—31no—
161C3×#121—31no—
162C2×C3×C4⋊C4—31no—
163#953—61no—
164#953—61no—
165#953—62no—
166#940—31no—
167#940—31no—
168#940—61no—
169#939—61no—
170#939—61no—
171#939—62no—
172#938—31no—
173#938—31no—
174#938—31no—
175#938—61no—
176#937—61no—
177#937—61no—
178#937—62no—
179#935—61no—
180D4×Dic3—31no—
181D4×Dic3—31no—
182D4×Dic3—31no—
183D4×Dic3—61no—
184C2×#213—31no—
185C2×#213C2×D311yescharacteristic
186C2×#213C2×D311yescharacteristic, complemented
187#930—31no—
188#930—31no—
189#930—61no—
190#930C2×D311yescharacteristic, complemented
191#929—61no—
192C4×#67—31no—
193C4×#67—31no—
194C4×#67—61no—
195C2×C4⋊Dic3C2×D311yescharacteristic, complemented
196C22×C3⋊C8C2×D311yescharacteristic, complemented
197C2×D24—31no—
198C2×D3×C8—31no—
199C2×D3×C8—31no—
200#896—61no—
201#895—31no—
202#894—61no—
203#893—31no—
204D3×C4⋊C4—31no—
205D3×C4⋊C4—31no—
206#888—31no—
207#888—31no—
208#883—61no—
209#878—61no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—31no—
217#832—31no—
218#832C2×D311yescharacteristic
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic
221#832C2×D311yescharacteristic, complemented
222#832C2×D311yescharacteristic, complemented
223#832C2×D311yescharacteristic, complemented
224#830C2×D311yescharacteristic, complemented
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8—31no—
231#818—31no—
232#818—31no—
233#818—31no—
234Dic3⋊C8—31no—
235Dic3⋊C8—31no—
236C8×Dic3—31no—
237C8×Dic3—31no—
238#809—31no—
239#809—31no—
240#809—31no—
241#807—31no—
242#807—31no—
243#807—31no—
244C23×C32—21no—
245C23×C32—21no—
246C23×C32—42no—
247C23×C32—42no—
248C23×C32—81no—
249C23×C32C2×D411yescharacteristic
250C22×C3⋊D3—21no—
251C22×C3⋊D3—42no—
252C22×C3⋊D3—42no—
253C22×C3⋊D3—81no—
254C22×C3⋊D3C2×D411yescharacteristic
255C22×C3×D3—21no—
256C32×D4—21no—
257C32×D4—21no—
258C32×D4—21no—
259C32×D4—42no—
260C32×D4#4112yescomplemented
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265#638—42no—
266#638—42no—
267#638—42no—
268#638—42no—
269#638—81no—
270#638D814yescomplemented
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—42no—
273C2×C3⋊Dic3C2×D411yescharacteristic
274C2×C3⋊Dic3C2×D411yescharacteristic
275C2×C3⋊Dic3C2×D411yescharacteristic
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—21no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—42no—
285C3×D12—21no—
286C3×D12—21no—
287#627—42no—
288#626—42no—
289#624—42no—
290D3×Dic3—42no—
291C3×C3⋊C8—21no—
292C3×C3⋊C8—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295#547—91no—
296D42—91no—
297#486—91no—
298#480—91no—
299#480—91no—
300#474—91no—
301#466—91no—
302#466—91no—
303#459—91no—
304#447—31no—
305#447—91no—
306C4×D8—91no—
307C8×D4—91no—
308C2×#102—31no—
309C2×#102—91no—
310C24×C3—22no—
311C24×C3—21no—
312C24×C3—21no—
313C23×D3—61no—
314C23×D3—61no—
315C23×D3—62no—
316C2×C3×D4—22no—
317C2×C3×D4—22no—
318C2×C3×D4—22no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—31no—
324C2×C3×D4—42no—
325C2×C3×D4—41no—
326C2×C3×D4—41no—
327C2×C3×D4—42no—
328C2×C3×D4—61no—
329C2×C3×D4C22×D311yescharacteristic
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C22×C3×C4—21no—
334C22×C3×C4—61no—
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C2×#67—21no—
338C2×#67—31no—
339C2×#67—31no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—62no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—62no—
357C2×#67—124no—
358C2×#67—124no—
359C2×#67—128no—
360C22×Dic3—21no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—62no—
365#237—124no—
366D3×D4—62no—
367D3×D4—62no—
368D3×D4—122no—
369D3×D4—121no—
370D3×D4—121no—
371D3×D4—122no—
372#235—124no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12C22×D311yescharacteristic
378C2×C4×D3—31no—
379C2×C4×D3—31no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×Dic6—61no—
385C2×Dic6—61no—
386C3×D8—62no—
387C3×D8—121no—
388C2×C3×C8—31no—
389C2×C3×C8—31no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C2×C3×C8—121no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—31no—
395C3×C4⋊C4—31no—
396C3×C4⋊C4—61no—
397C3×C22⋊C4—61no—
398#217—31no—
399#217—31no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—62no—
408#217—62no—
409#213—22no—
410#213—41no—
411#213—121no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—31no—
414(C2×D3)⋊C4—31no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421C4⋊Dic3—21no—
422C4⋊Dic3—31no—
423C4⋊Dic3—31no—
424C4⋊Dic3—61no—
425C4⋊Dic3C22×D311yescharacteristic
426C4⋊Dic3C22×D311yescharacteristic
427C4⋊Dic3C22×D311yescharacteristic
428Dic3⋊C4—31no—
429Dic3⋊C4—31no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435C4×Dic3—31no—
436C4×Dic3—31no—
437C4×Dic3—61no—
438C2×C3⋊C8—41no—
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443D24—121no—
444D3×C8—121no—
445D3×C8—121no—
446C22×C32—22no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—84no—
455C22×C32C2×D812yes—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—84no—
463C2×C3⋊D3C2×D812yes—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C32×C4—21no—
468C32×C4C2×#4111yescharacteristic
469C32×C4H(5,𝔽2)11yescharacteristic
470C3⋊Dic3—21no—
471C3⋊Dic3—21no—
472C3⋊Dic3—41no—
473C3⋊Dic3C2×D812yes—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C2×#41—181no—
478C22×D4—91no—
479C22×D4—181no—
480C22×D4D3211yescharacteristic
481C2×D8—31no—
482C2×D8—31no—
483C2×D8—91no—
484C22×C8—31no—
485C22×C8—91no—
486C4⋊Q8—91no—
487#127—91no—
488#123—181no—
489#123—181no—
490C22⋊Q8—181no—
491#121—31no—
492#121—91no—
493#121—91no—
494#121—91no—
495#121—181no—
496#120—181no—
497#120—181no—
498C4×D4—91no—
499C4×D4—91no—
500C4×D4—91no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—91no—
503#107—91no—
504#107—91no—
505#107—91no—
506C4⋊C8—91no—
507#102—31no—
508#102—31no—
509#102—31no—
510#102—31no—
511#102—31no—
512#102—31no—
513#102—91no—
514#102—91no—
515#102—91no—
516#102—91no—
517C22⋊C8—31no—
518C22⋊C8—91no—
519C4×C8—91no—
520C23×C3—22no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—22no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—42no—
528C23×C3—42no—
529C23×C3—44no—
530C23×C3—44no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—61no—
534C23×C3—81no—
535C23×C3—81no—
536C23×C3—82no—
537C23×C3D3×D411yescharacteristic
538C23×C3D3×D411yescharacteristic
539C22×D3—21no—
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—61no—
543C22×D3—62no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—124no—
551C22×D3—124no—
552C22×D3—241no—
553C22×D3—241no—
554C22×D3—242no—
555C3×D4—22no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—22no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—42no—
566C3×D4—42no—
567C3×D4—44no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—122no—
571C3×D4#23512yescomplemented
572C3×D4#23712yescomplemented
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—122no—
585C2×C3×C4D3×D411yescharacteristic
586C2×C3×C4D3×D411yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589#67—34no—
590#67—34no—
591#67—42no—
592#67—64no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—124no—
599#67—122no—
600#67—122no—
601#67—124no—
602#67—124no—
603#67—124no—
604#67—122no—
605#67—122no—
606#67—241no—
607#67—241no—
608#67—242no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—42no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—62no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—122no—
626C2×Dic3—122no—
627C2×Dic3—122no—
628C2×Dic3—124no—
629D12—21no—
630D12—21no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—121no—
636D12—121no—
637D12—122no—
638C4×D3—61no—
639C4×D3—61no—
640C4×D3—61no—
641C4×D3—61no—
642C4×D3—121no—
643C4×D3—121no—
644C4×D3—122no—
645C4×D3—122no—
646C4×D3—122no—
647Dic6—122no—
648Dic6—122no—
649C3×C8—61no—
650C3×C8—61no—
651C3×C8—61no—
652C3×C8—61no—
653C3⋊C8—21no—
654C3⋊C8—21no—
655C3⋊C8—21no—
656C3⋊C8—21no—
657C2×C32—22no—
658C2×C32—42no—
659C2×C32—81no—
660C2×C32#54611yescharacteristic
661C2×C32C22×D811yescharacteristic
662C2×C32#57711yescharacteristic
663C3⋊D3—22no—
664C3⋊D3—81no—
665C3×D3—81no—
666C24—21no—
667C24—181no—
668#41—364no—
669C2×Q8—181no—
670C2×D4—22no—
671C2×D4—21no—
672C2×D4—31no—
673C2×D4—41no—
674C2×D4—61no—
675C2×D4—91no—
676C2×D4—91no—
677C2×D4—181no—
678C2×D4—181no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—182no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—361no—
685C2×D4—364no—
686C2×D4C2×D3211yescharacteristic
687C2×D4C2×D3211yescharacteristic
688C22×C4—61no—
689C22×C4—91no—
690C22×C4—181no—
691C22×C4—181no—
692C22×C4—181no—
693C22×C4C2×D3211yescharacteristic
694D8—62no—
695D8—121no—
696D8—361no—
697C2×C8—31no—
698C2×C8—31no—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8—121no—
702C2×C8—361no—
703C4⋊C4—31no—
704C4⋊C4—31no—
705C4⋊C4—31no—
706C4⋊C4—61no—
707C4⋊C4—91no—
708C4⋊C4—91no—
709C4⋊C4—181no—
710C4⋊C4—181no—
711C22⋊C4—61no—
712C22⋊C4—91no—
713C22⋊C4—91no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C42—91no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—24no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—22no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—84no—
747C22×C3—84no—
748C22×C3—88no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3D3×D812yes—
753C22×C3D3×D812yes—
754C22×C3C2×D3×D411yescharacteristic
755C22×C3C2×D3×D411yescharacteristic
756C2×D3—32no—
757C2×D3—32no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—62no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—122no—
769C2×D3—122no—
770C2×D3—122no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—244no—
778C2×D3—244no—
779C2×D3—248no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—41no—
785C3×C4—121no—
786C3×C4—121no—
787C3×C4—121no—
788C3×C4C2×#23511yescharacteristic
789C3×C4C2×#23711yescharacteristic
790C3×C4#100411yescharacteristic
791C3×C4#100411yescharacteristic
792Dic3—32no—
793Dic3—32no—
794Dic3—41no—
795Dic3—41no—
796Dic3—41no—
797Dic3—62no—
798Dic3—61no—
799Dic3—61no—
800Dic3—61no—
801Dic3—61no—
802Dic3—121no—
803Dic3—121no—
804Dic3—122no—
805Dic3—121no—
806Dic3—121no—
807C32#329411yescharacteristic, complemented, Sylow
808C23—21no—
809C23—21no—
810C23—42no—
811C23—42no—
812C23—61no—
813C23—81no—
814C23—91no—
815C23—181no—
816C23—362no—
817C23—362no—
818C23—721no—
819C23#381111yescharacteristic
820Q8—362no—
821D4—21no—
822D4—21no—
823D4—21no—
824D4—42no—
825D4—61no—
826D4—61no—
827D4—94no—
828D4—122no—
829D4—181no—
830D4—181no—
831D4—362no—
832D4—362no—
833D4—362no—
834D4—362no—
835D4—362no—
836D4—721no—
837D4#380412yescomplemented
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—91no—
844C2×C4—91no—
845C2×C4—91no—
846C2×C4—122no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—362no—
851C2×C4—362no—
852C2×C4—362no—
853C2×C4#381111yescharacteristic
854C2×C4C22×D3211yescharacteristic
855C8—61no—
856C8—61no—
857C8—61no—
858C8—61no—
859C2×C3—22no—
860C2×C3—22no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—42no—
865C2×C3—44no—
866C2×C3—42no—
867C2×C3—42no—
868C2×C3—82no—
869C2×C3—81no—
870C2×C3—81no—
871C2×C3—241no—
872C2×C3#549011yescharacteristic
873C2×C3#559111yescharacteristic
874C2×C3C2×D3×D811yescharacteristic
875C2×C3C2×D3×D811yescharacteristic
876C2×C3#576211yescharacteristic
877C2×C3#577511yescharacteristic
878D3—62no—
879D3—62no—
880D3—81no—
881D3—122no—
882D3—242no—
883D3—241no—
884D3—241no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—84no—
894C22—92no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—181no—
899C22—181no—
900C22—361no—
901C22—361no—
902C22—361no—
903C22—724no—
904C22#6392612yes—
905C22C2×#381111yescharacteristic
906C4—21no—
907C4—92no—
908C4—121no—
909C4—121no—
910C4—121no—
911C4—181no—
912C4—181no—
913C4—361no—
914C4C2×#380411yescharacteristic
915C4#6433011yescharacteristic
916C3—21no—
917C3#7875711yescharacteristic, complemented
918C3#8001411yescharacteristic, complemented
919C2—22no—
920C2—42no—
921C2—81no—
922C2—182no—
923C2—241no—
924C2—721no—
925C2C2×#6392611yescharacteristic
926C2#1059511511yescharacteristic
927C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. D4×#638C2semidirect
2. #10594928C2semidirect
3. C3×#5217C2semidirect
4. C2×C3×#832C2semidirect
5. #10591494C2semidirect
6. #10591456C2semidirect
7. #10591455C2semidirect
8. #10591435C2semidirect
9. #10591433C2semidirect
10. #10591417C2semidirect
11. #10591416C2semidirect
12. #10591402C2semidirect
13. #10591164C2semidirect
14. #10591148C2semidirect
15. #10591133C2semidirect
31. C2×C3×#213C22semidirect
32. C3×#930C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C22×C3×C3⋊C8C22semidirect
36. #63919C22semidirect
37. #63916C22semidirect
38. #63900C22semidirect
40. #63898C22semidirect
42. C2×#3714C22semidirect
43. C2×#3710C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
50. C3×#830C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63575C22semidirect
54. #63572C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
57. #63564C22semidirect
58. #63563C22semidirect
59. #63557C22semidirect
60. #63553C22semidirect
68. #5217D3semidirect
69. C2×#832D3semidirect
186. C2×#213C2×D3semidirect
190. #930C2×D3semidirect
195. C2×C4⋊Dic3C2×D3semidirect
196. C22×C3⋊C8C2×D3semidirect
221. #832C2×D3semidirect
222. #832C2×D3semidirect
223. #832C2×D3semidirect
224. #830C2×D3semidirect
260. C32×D4#41semidirect
270. #638D8semidirect
571. C3×D4#235semidirect
572. C3×D4#237semidirect
807. C32#3294semidirect
837. D4#3804semidirect
917. C3#78757semidirect
918. C3#80014semidirect

Maximal subgroups

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

subgroupindex
D4×#6382
#105949282
C3×#52172
C2×C3×#8322
#105914942
#105914562
#105914552
#105914352
#105914332
#105914172
#105914162
#105914022
#105911642
#105911482
#105911332
#800143
#787573