Finite Group Databasebeta

← #11887447

Subgroups — #11887447

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594007C211yesmaximal, characteristic, complemented
2#10593925C211yesmaximal, characteristic, complemented
3C4×#3745C211yesmaximal, characteristic, complemented
4C3×#4697C211yesmaximal, characteristic, complemented
5C3×C8×D12C211yesmaximal, characteristic, complemented
6#10590967C211yesmaximal, characteristic, complemented
7#10590947C211yesmaximal, characteristic, complemented
8D3×#821C211yesmaximal, characteristic, complemented
9#10590847C211yesmaximal, characteristic, complemented
10#10590834C211yesmaximal, characteristic, complemented
11#10590826C211yesmaximal, characteristic, complemented
12#10590690C211yesmaximal, characteristic, complemented
13#10590682C211yesmaximal, characteristic, complemented
14#10590356C211yesmaximal, characteristic, complemented
15#10590308C211yesmaximal, characteristic, complemented
16#81653—31nomaximal
17#79441—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3745C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×D3×C8C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×#875C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×#870C2211yescharacteristic, complemented
28#63922—21no—
29#63921—21no—
30#63912—21no—
31#63909C2211yescharacteristic
32#63909C2211yescharacteristic, complemented
33#63908C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63886—21no—
36#63881—21no—
37#63856C2211yescharacteristic
38#63854—21no—
39#63853—21no—
40#63848—21no—
41#63841C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic, complemented
43C2×#3714C2211yescharacteristic
44C32×C4×C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5695—31no—
62#5676—31no—
63#5565—31no—
64#5550—31no—
65C3×#488—31no—
66C3×C8×D4—31no—
67#5115—31no—
68#5114—31no—
69#5113—31no—
70C2×#821—31no—
71#5066—31no—
72#5057—31no—
73#4847—31no—
74#4844—31no—
75#4811—31no—
76#4810—31no—
77#4807—31no—
78#4804—31no—
79#4784—31no—
80#4775—31no—
81#4773—31no—
82D3×#102—31no—
83#4737—31no—
84#4734—31no—
85#4732—31no—
86#4722—31no—
87#4697D311yescharacteristic, complemented
88C4×D24—31no—
89C4×D24—31no—
90C4×D24—61no—
91C8×D12D311yescharacteristic, complemented
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C3×D12D411yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—41no—
111#3799—22no—
112#3799—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3745—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133C3×D3×C8—41no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3717—41no—
143#3714—41no—
144#3297—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C22×C3×C8—31no—
150C22×C3×C8—31no—
151C3×#125—31no—
152C3×#124—31no—
153C3×C4×D4—31no—
154#946—31no—
155C2×#215—31no—
156#939—61no—
157#938—31no—
158#937—61no—
159C2×#213—31no—
160#930—31no—
161#930—31no—
162#930—31no—
163#926—31no—
164C2×C4⋊Dic3—31no—
165#924—31no—
166C2×D24—31no—
167C2×D24—31no—
168C2×D24—31no—
169C2×D24—61no—
170C2×#204—31no—
171C2×D3×C8C2×D311yescharacteristic
172C2×D3×C8C2×D311yescharacteristic, complemented
173#898—61no—
174#898—61no—
175#895—31no—
176#895—31no—
177#895—61no—
178#894—61no—
179#894—61no—
180#893—61no—
181#892—31no—
182D3×C4⋊C4—31no—
183#884—61no—
184#884—61no—
185#883—61no—
186#883—61no—
187#882—61no—
188#67⋊C4—61no—
189D3×C22⋊C4—61no—
190D3×C22⋊C4—61no—
191#875C2×D311yescharacteristic
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199#870C2×D311yescharacteristic, complemented
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
207C3×C4×C8—21no—
208C3×C4×C8C2×D311yescharacteristic, complemented
209C3×C4×C8C2×D311yescharacteristic, complemented
210#835—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821—61no—
221#821C2×D311yescharacteristic
222#821C2×D311yescharacteristic
223(C2×D3)⋊C8C2×D311yescharacteristic
224(C2×D3)⋊C8C2×D311yescharacteristic, complemented
225#818—31no—
226#818—31no—
227#818—31no—
228#818—61no—
229#817—31no—
230#816—31no—
231#816C2×D311yescharacteristic, complemented
232#816C2×D311yescharacteristic, complemented
233#809—31no—
234#809—31no—
235#808—31no—
236#807—31no—
237C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—81no—
256C4×C3⋊D3—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—22no—
263C3×D12—21no—
264C3×D12—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—42no—
273#626—42no—
274#626—81no—
275#625—81no—
276#624—42no—
277D3×Dic3—81no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—31no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—31no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×Q8—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311#239—62no—
312#239—121no—
313D3×D4—62no—
314D3×D4—121no—
315#235—62no—
316#235—121no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—62no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—121no—
329C2×D12D1211yescharacteristic
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—121no—
339C2×C4×D3—121no—
340C2×C4×D3C22×D311yescharacteristic
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—121no—
348C2×C3×C8—121no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—21no—
363C3×C42C22×D311yescharacteristic
364C3×C42C22×D311yescharacteristic
365#217—61no—
366#217—61no—
367#217—61no—
368#215—121no—
369#213—121no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—121no—
384(C2×D3)⋊C4—121no—
385(C2×D3)⋊C4D1211yescharacteristic
386(C2×D3)⋊C4D1211yescharacteristic
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3D1211yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406D24—62no—
407D24—62no—
408D24—64no—
409D24—121no—
410#204—121no—
411D3×C8—41no—
412D3×C8—41no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—22no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3#13512yes—
429D32—84no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—91no—
442C22×D4—91no—
443C2×SD16—91no—
444C2×D8—91no—
445C2×D8—91no—
446C22×C8—31no—
447C22×C8—31no—
448#126—181no—
449#125—31no—
450#124—31no—
451#123—181no—
452#123—181no—
453C22⋊Q8—91no—
454#121—91no—
455#121—91no—
456#121—91no—
457#121—181no—
458#121—181no—
459#120—181no—
460C4×D4—31no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—181no—
464#117—91no—
465C2×C4⋊C4—91no—
466C2×C22⋊C4—181no—
467#107—91no—
468#107—91no—
469#106—91no—
470C4⋊C8—31no—
471#103—31no—
472#103—31no—
473#103—91no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—31no—
482C22⋊C8—31no—
483C4×C8D3211yescharacteristic, complemented
484C23×C3—31no—
485C23×C3—31no—
486C23×C3—61no—
487C22×D3—21no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—61no—
492C22×D3—121no—
493C22×D3—121no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3C2×D1211yescharacteristic
501C22×D3C2×D1211yescharacteristic
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—62no—
505C3×D4—61no—
506C3×D4—61no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4C2×D1211yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—122no—
526#67—122no—
527#67—122no—
528#67—241no—
529#67—241no—
530#67—241no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—241no—
541C2×Dic3C2×D1211yescharacteristic
542C2×Dic3C2×D1211yescharacteristic
543D12—22no—
544D12—21no—
545D12—21no—
546D12—32no—
547D12—32no—
548D12—62no—
549D12—62no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—121no—
557D12—121no—
558D12—122no—
559D12—122no—
560D12—122no—
561D12—241no—
562C4×D3—21no—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—122no—
567C4×D3—122no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—242no—
574C4×D3—242no—
575Dic6—21no—
576Dic6—21no—
577C3×C8—22no—
578C3×C8—21no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—41no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C2×C32#54611yescharacteristic
588C2×C32C2×#13511yescharacteristic
589C2×C32#57611yescharacteristic
590C3⋊D3—42no—
591C3⋊D3—81no—
592C3×D3—22no—
593C3×D3—41no—
594C3×D3—81no—
595C24—181no—
596#41—182no—
597#41—361no—
598C2×Q8—31no—
599C2×D4—31no—
600C2×D4—31no—
601C2×D4—91no—
602C2×D4—91no—
603C2×D4—181no—
604C2×D4—182no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4—181no—
608C2×D4—181no—
609C2×D4—361no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4—181no—
616SD16—361no—
617D8—182no—
618D8—361no—
619C2×C8—31no—
620C2×C8—31no—
621C2×C8—121no—
622C2×C8—121no—
623C2×C8C2×D3211yescharacteristic
624C2×C8C2×D3211yescharacteristic
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—91no—
631C4⋊C4—91no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C22⋊C4—31no—
635C22⋊C4—31no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C42—181no—
646C42C2×D3211yescharacteristic
647C22×C3—21no—
648C22×C3—32no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3C22×D1211yescharacteristic
658C22×C3C2×D3×D411yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—122no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—122no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—241no—
682C2×D3—241no—
683C2×D3—241no—
684C2×D3—241no—
685C2×D3—244no—
686C2×D3—244no—
687C2×D3#90412yes—
688C3×C4—22no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—41no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4#100411yescharacteristic
702C3×C4D3×#4111yescharacteristic
703C3×C4D3×#4111yescharacteristic
704C3×C4#100911yescharacteristic
705Dic3—21no—
706Dic3—21no—
707Dic3—41no—
708Dic3—41no—
709Dic3—41no—
710Dic3—121no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—241no—
715Dic3—241no—
716C32#329711yescharacteristic, complemented, Sylow
717C23—31no—
718C23—31no—
719C23—61no—
720C23—181no—
721C23—181no—
722C23—362no—
723C23—362no—
724C23—721no—
725Q8—61no—
726Q8—61no—
727D4—62no—
728D4—61no—
729D4—61no—
730D4—92no—
731D4—181no—
732D4—181no—
733D4—181no—
734D4—362no—
735D4—362no—
736D4—362no—
737D4—721no—
738D4—721no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—362no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4D3×D1211yescharacteristic
755C2×C4D3×D1211yescharacteristic
756C2×C4C22×D3211yescharacteristic
757C8—21no—
758C8—21no—
759C8—61no—
760C8—61no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—62no—
765C2×C3—121no—
766C2×C3—241no—
767C2×C3#555411yescharacteristic
768C2×C3#567611yescharacteristic
769C2×C3C2×#90411yescharacteristic
770C2×C3#575211yescharacteristic
771C2×C3D3×#13511yescharacteristic
772C2×C3#576911yescharacteristic
773D3—22no—
774D3—41no—
775D3—81no—
776D3—122no—
777D3—122no—
778D3—242no—
779D3—242no—
780D3—241no—
781D3—241no—
782C22—32no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—61no—
787C22—61no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—182no—
792C22—361no—
793C22—361no—
794C22—361no—
795C22—361no—
796C22—361no—
797C22—724no—
798C22C2×D3×D1211yescharacteristic
799C4—21no—
800C4—21no—
801C4—61no—
802C4—61no—
803C4—121no—
804C4—121no—
805C4—121no—
806C4—361no—
807C4—361no—
808C4#6430611yescharacteristic
809C4#6430711yescharacteristic
810C3—21no—
811C3#7944111yescharacteristic, complemented
812C3#8165311yescharacteristic, complemented
813C2—62no—
814C2—121no—
815C2—241no—
816C2—362no—
817C2—721no—
818C2#1059400511yescharacteristic
819C2D3×#90411yescharacteristic
820C2#1059468011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10594007C2semidirect
2. #10593925C2semidirect
3. C4×#3745C2semidirect
4. C3×#4697C2semidirect
5. C3×C8×D12C2semidirect
6. #10590967C2semidirect
7. #10590947C2semidirect
8. D3×#821C2semidirect
9. #10590847C2semidirect
10. #10590834C2semidirect
11. #10590826C2semidirect
12. #10590690C2semidirect
13. #10590682C2semidirect
14. #10590356C2semidirect
15. #10590308C2semidirect
22. C4×C4⋊(C3⋊D3)C22semidirect
24. C2×C3×D3×C8C22semidirect
27. C3×#870C22semidirect
32. #63909C22semidirect
41. #63841C22semidirect
42. C2×#3717C22semidirect
44. C32×C4×C8C22semidirect
46. #63648C22semidirect
47. #63645C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#816C22semidirect
53. C3×#816C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
87. #4697D3semidirect
91. C8×D12D3semidirect
172. C2×D3×C8C2×D3semidirect
199. #870C2×D3semidirect
208. C3×C4×C8C2×D3semidirect
209. C3×C4×C8C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
231. #816C2×D3semidirect
232. #816C2×D3semidirect
237. C4⋊(C3⋊C8)C2×D3semidirect
483. C4×C8D32semidirect
716. C32#3297semidirect
811. C3#79441semidirect
812. C3#81653semidirect

Maximal subgroups

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

subgroupindex
#105940072
#105939252
C4×#37452
C3×#46972
C3×C8×D122
#105909672
#105909472
D3×#8212
#105908472
#105908342
#105908262
#105906902
#105906822
#105903562
#105903082
#816533
#794413