Finite Group Databasebeta

← #11887380

Subgroups — #11887380

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595067C211yesmaximal, characteristic, complemented
2#10594945C211yesmaximal, characteristic, complemented
3#10592436C211yesmaximal, characteristic, complemented
4C3×#4734C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic, complemented
6#10591164C211yesmaximal, characteristic, complemented
7#10591084C211yesmaximal, characteristic, complemented
8#10590944C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590872C211yesmaximal, characteristic, complemented
11#10590829C211yesmaximal, characteristic, complemented
12#10590772C211yesmaximal, characteristic, complemented
13Dic3×D24C211yesmaximal, characteristic, complemented
14#10590754C211yesmaximal, characteristic, complemented
15#10590682C211yesmaximal, characteristic, complemented
16#80102—31nomaximal
17#79441—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20#64139C2211yescharacteristic
21#64135C2211yescharacteristic, complemented
22C3×#930C2211yescharacteristic, complemented
23C3×C4×#67C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic, complemented
25C2×C3×D24C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic, complemented
27C2×C3×D3×C8C2211yescharacteristic
28#63983—21no—
29#63971—21no—
30#63970—21no—
31#63969—21no—
32D3×(C2×D3)⋊C4—21no—
33#63908C2211yescharacteristic
34#63902—21no—
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic, complemented
37D3×C4⋊Dic3C2211yescharacteristic
38#63869C2211yescharacteristic, complemented
39#63864C2211yescharacteristic
40#63862—21no—
41#63856C2211yescharacteristic
42#63850—21no—
43C2×#3714C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63645C2211yescharacteristic, complemented
48#63644C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#5829—31no—
62#5614—31no—
63#5565—31no—
64#5550—31no—
65C3×#449—31no—
66C3×C8×D4—31no—
67#5233—31no—
68#5171—31no—
69#5165—31no—
70#5156—31no—
71Dic3×D8—31no—
72#5115—31no—
73#5114—31no—
74#5113—31no—
75C2×#821—31no—
76#5038—31no—
77#4847—31no—
78#4844—31no—
79#4811—31no—
80#4800—31no—
81D3×#102—31no—
82#4763—31no—
83#4737—31no—
84#4737—31no—
85#4737—61no—
86#4734D311yescharacteristic, complemented
87#4732—31no—
88#67⋊C8D311yescharacteristic, complemented
89#4722—31no—
90#4697—31no—
91C4×D24—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C3×#235—22no—
100C3×#235—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3757—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4×C3⋊Dic3—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8—41no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D24—22no—
131C3×#204—41no—
132C3×D3×C8—41no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3714—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C2×D3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12—31no—
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C22×C3×C8—31no—
152C22×C3×C8—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155#947—31no—
156#946—31no—
157#939—61no—
158#939—61no—
159#938—31no—
160#938—61no—
161#937—61no—
162#937—61no—
163#935—61no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166C2×#213—31no—
167#930—31no—
168#930—31no—
169#930—31no—
170#930—61no—
171#930C2×D311yescharacteristic, complemented
172#929—61no—
173C4×#67C2×D311yescharacteristic
174C2×(C2×D3)⋊C4—61no—
175#926—31no—
176#926—31no—
177#926—61no—
178C2×C4⋊Dic3—31no—
179#924—31no—
180C22×C3⋊C8C2×D311yescharacteristic, complemented
181C2×D24—31no—
182C2×D24C2×D311yescharacteristic
183C2×#204C2×D311yescharacteristic, complemented
184C2×D3×C8C2×D311yescharacteristic
185#898—61no—
186#894—61no—
187D3×C4⋊C4—31no—
188#890—31no—
189#884—61no—
190#883—61no—
191#67⋊C4—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194#879—61no—
195#875—31no—
196C4×D12—31no—
197C4×D12—31no—
198#870—31no—
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C22⋊C8—21no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8C2×D311yescharacteristic, complemented
205C3×C22⋊C8C2×D311yescharacteristic, complemented
206C3×C4×C8—31no—
207#835—31no—
208#835—31no—
209#832—31no—
210#832—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—31no—
220#821—61no—
221#821—61no—
222#821C2×D311yescharacteristic
223(C2×D3)⋊C8C2×D311yescharacteristic
224#818—31no—
225#818—31no—
226#818—31no—
227#818—61no—
228#817—31no—
229#817—31no—
230#817—61no—
231#816—31no—
232#816—31no—
233#816C2×D311yescharacteristic, complemented
234Dic3⋊C8C2×D311yescharacteristic, complemented
235C8×Dic3C2×D311yescharacteristic, complemented
236#809—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—81no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C3×#67—22no—
257C3×#67—42no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#626—42no—
274#625—42no—
275D3×Dic3—81no—
276D3×Dic3—81no—
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—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—31no—
292#447—91no—
293C4×D8—91no—
294C8×D4—31no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—121no—
320C2×#67D1211yescharacteristic
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324D3×D4—62no—
325D3×D4—121no—
326#235—22no—
327#235—41no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—61no—
333C2×D12—121no—
334C2×D12C22×D311yescharacteristic
335C2×D12C22×D311yescharacteristic
336C2×C4×D3—21no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3C22×D311yescharacteristic
341C2×Dic6C22×D311yescharacteristic
342C3×SD16—121no—
343C3×D8—62no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—121no—
349C2×C3×C8—121no—
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—61no—
359C3×C42—31no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—121no—
367#217D1211yescharacteristic
368#213—121no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
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—121no—
381(C2×D3)⋊C4D1211yescharacteristic
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4D1211yescharacteristic
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—121no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—41no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—22no—
409D24—121no—
410#204—41no—
411D3×C8—41no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—22no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3#13512yes—
428D32—84no—
429C32×C4—21no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—31no—
441C22×D4—91no—
442C2×SD16—31no—
443C2×D8—31no—
444C2×D8—91no—
445C22×C8—31no—
446C22×C8—31no—
447#126—181no—
448#125—91no—
449#124—91no—
450#123—181no—
451#123—181no—
452C22⋊Q8—91no—
453#121—31no—
454#121—91no—
455#121—91no—
456#121—181no—
457#121—181no—
458#120—181no—
459C4×D4—31no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463#117—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—181no—
466#107—91no—
467#107—91no—
468#106—91no—
469C4⋊C8—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—31no—
481C22⋊C8D3211yescharacteristic, complemented
482C4×C8—31no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3C2×D1211yescharacteristic
488C23×C3D3×D411yescharacteristic
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—121no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3C2×D1211yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×D4—32no—
504C3×D4—62no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—122no—
509C3×D4—241no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—122no—
526C2×C3×C4C2×D1211yescharacteristic
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—22no—
531#67—42no—
532#67—81no—
533#67—122no—
534#67—122no—
535#67—122no—
536#67—241no—
537#67—241no—
538#67—242no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552C2×Dic3—241no—
553C2×Dic3C2×D1211yescharacteristic
554C2×Dic3C2×D1211yescharacteristic
555C2×Dic3C2×D1211yescharacteristic
556D12—21no—
557D12—21no—
558D12—21no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—121no—
564D12—121no—
565D12—122no—
566D12#23712yes—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—42no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573Dic6—21no—
574Dic6—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—41no—
580C3×C8—41no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C2×C32—41no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57611yescharacteristic
589C3⋊D3—81no—
590C3×D3—22no—
591C3×D3—42no—
592C3×D3—81no—
593C24—181no—
594#41—62no—
595#41—121no—
596C2×Q8—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—91no—
603C2×D4—181no—
604C2×D4—182no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4—361no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4C2×D3211yescharacteristic
614SD16—121no—
615D8—62no—
616D8—361no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—121no—
620C2×C8—121no—
621C2×C8C2×D3211yescharacteristic
622C2×C8C2×D3211yescharacteristic
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C42—31no—
644C42—181no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—62no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3C22×D1211yescharacteristic
665C22×C3C2×D3×D411yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—22no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—241no—
681C2×D3—241no—
682C2×D3—241no—
683C2×D3—244no—
684C2×D3—244no—
685C2×D3#90412yes—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—41no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4C2×#23711yescharacteristic
697C3×C4#100411yescharacteristic
698C3×C4#100411yescharacteristic
699C3×C4D3×#4111yescharacteristic
700Dic3—21no—
701Dic3—21no—
702Dic3—21no—
703Dic3—41no—
704Dic3—41no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—121no—
711Dic3—241no—
712Dic3—241no—
713Dic3—241no—
714C32#329711yescharacteristic, complemented, Sylow
715C23—31no—
716C23—61no—
717C23—61no—
718C23—181no—
719C23—362no—
720C23—362no—
721C23—721no—
722C23D3×D1211yescharacteristic
723Q8—61no—
724Q8—61no—
725D4—32no—
726D4—62no—
727D4—61no—
728D4—61no—
729D4—61no—
730D4—122no—
731D4—181no—
732D4—181no—
733D4—241no—
734D4—362no—
735D4—362no—
736D4—721no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—122no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4D3×D1211yescharacteristic
754C2×C4C22×D3211yescharacteristic
755C8—21no—
756C8—21no—
757C8—61no—
758C8—61no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—41no—
763C2×C3—41no—
764C2×C3—62no—
765C2×C3—81no—
766C2×C3—122no—
767C2×C3—241no—
768C2×C3#555411yescharacteristic
769C2×C3#559111yescharacteristic
770C2×C3C2×#90411yescharacteristic
771C2×C3#575211yescharacteristic
772C2×C3D3×#13511yescharacteristic
773C2×C3#577411yescharacteristic
774D3—22no—
775D3—42no—
776D3—81no—
777D3—241no—
778D3—241no—
779D3—481no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—32no—
784C22—61no—
785C22—61no—
786C22—62no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—361no—
793C22—361no—
794C22—361no—
795C22—724no—
796C22C2×D3×D1211yescharacteristic
797C4—21no—
798C4—61no—
799C4—61no—
800C4—61no—
801C4—121no—
802C4—121no—
803C4—361no—
804C4—361no—
805C4—361no—
806C4D3×#23711yescharacteristic
807C4#6431311yescharacteristic
808C3—21no—
809C3#7944111yescharacteristic, complemented
810C3#8010211yescharacteristic, complemented
811C2—41no—
812C2—62no—
813C2—122no—
814C2—241no—
815C2—721no—
816C2#1059429211yescharacteristic
817C2D3×#90411yescharacteristic
818C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595067C2semidirect
2. #10594945C2semidirect
3. #10592436C2semidirect
4. C3×#4734C2semidirect
5. C3×#67⋊C8C2semidirect
6. #10591164C2semidirect
7. #10591084C2semidirect
8. #10590944C2semidirect
9. D3×#821C2semidirect
10. #10590872C2semidirect
11. #10590829C2semidirect
12. #10590772C2semidirect
13. Dic3×D24C2semidirect
14. #10590754C2semidirect
15. #10590682C2semidirect
21. #64135C22semidirect
22. C3×#930C22semidirect
24. C22×C3×C3⋊C8C22semidirect
26. C2×C3×#204C22semidirect
36. Dic3×D12C22semidirect
38. #63869C22semidirect
44. C32×C22⋊C8C22semidirect
47. #63645C22semidirect
48. #63644C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63575C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
60. #63563C22semidirect
86. #4734D3semidirect
88. #67⋊C8D3semidirect
171. #930C2×D3semidirect
180. C22×C3⋊C8C2×D3semidirect
183. C2×#204C2×D3semidirect
204. C3×C22⋊C8C2×D3semidirect
205. C3×C22⋊C8C2×D3semidirect
233. #816C2×D3semidirect
234. Dic3⋊C8C2×D3semidirect
235. C8×Dic3C2×D3semidirect
481. C22⋊C8D32semidirect
714. C32#3297semidirect
809. C3#79441semidirect
810. C3#80102semidirect

Maximal subgroups

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

subgroupindex
#105950672
#105949452
#105924362
C3×#47342
C3×#67⋊C82
#105911642
#105910842
#105909442
D3×#8212
#105908722
#105908292
#105907722
Dic3×D242
#105907542
#105906822
#801023
#794413