Finite Group Databasebeta

← #11887418

Subgroups — #11887418

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595018C211yesmaximal, characteristic, complemented
2#10594995C211yesmaximal, characteristic, complemented
3C2×#63648C211yesmaximal, characteristic, complemented
4C3×#5114C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591168C211yesmaximal, characteristic, complemented
7#10591103C211yesmaximal, characteristic, complemented
8#10590872C211yesmaximal, characteristic, complemented
9#10590826C211yesmaximal, characteristic, complemented
10#10590823C211yesmaximal, characteristic, complemented
11#10590769C211yesmaximal, characteristic, complemented
12#10590754C211yesmaximal, characteristic, complemented
13#10590745C211yesmaximal, characteristic, complemented
14#10590704C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#80681—31nomaximal
17#79441—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C3×#924C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27#63981—21no—
28#63980—21no—
29#63974—21no—
30#67⋊Dic3—21no—
31#63910—21no—
32#63909C2211yescharacteristic
33#63908C2211yescharacteristic, complemented
34#63897—21no—
35#63894C2211yescharacteristic
36Dic3×D12C2211yescharacteristic, complemented
37#63891—21no—
38#63869C2211yescharacteristic, complemented
39#63864C2211yescharacteristic
40#63861—21no—
41#63841C2211yescharacteristic, complemented
42C2×#3714C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63648C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5630—31no—
62#5618—31no—
63#5565—31no—
64#5550—31no—
65C3×#465—31no—
66C3×C8×D4—31no—
67#5172—31no—
68#5165—31no—
69#5115—31no—
70#5114D311yescharacteristic, complemented
71#5113—31no—
72C2×#821—31no—
73C2×#821—31no—
74C2×#821—61no—
75C8×#67D311yescharacteristic, complemented
76#5044—31no—
77#5036—31no—
78#4871—31no—
79#4866—31no—
80#4847—31no—
81#4844—31no—
82#4804—31no—
83#4800—31no—
84#4775—31no—
85#4756—31no—
86#4737—31no—
87#4734—31no—
88#4732—31no—
89#4722—31no—
90#4697—31no—
91C4×D24—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111#3799—22no—
112#3799—41no—
113C2×C32×C8—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×#204—41no—
131C3×D3×C8—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—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#3714—22no—
143#3714—41no—
144#3297—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C2×C3×SD16—31no—
151C22×C3×C8—21no—
152C22×C3×C8—31no—
153C22×C3×C8C2×D311yescharacteristic
154C22×C3×C8C2×D311yescharacteristic
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158#947—31no—
159#939—61no—
160#939—61no—
161#938—31no—
162#937—61no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165C2×#213—31no—
166C2×#213—31no—
167#930—31no—
168#930—31no—
169#930C2×D311yescharacteristic
170C4×#67C2×D311yescharacteristic
171#926—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—61no—
175#924C2×D311yescharacteristic
176C2×D24—31no—
177C2×D24—31no—
178C2×#204C2×D311yescharacteristic, complemented
179C2×D3×C8C2×D311yescharacteristic, complemented
180#898—61no—
181#895—31no—
182#895—61no—
183#894—61no—
184#894—61no—
185#893—31no—
186#892—31no—
187#890—31no—
188#886—61no—
189#884—61no—
190#883—61no—
191#882—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#875—31no—
197C4×D12—31no—
198C4×D12—31no—
199#870—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×C4×C8—31no—
207#835—31no—
208#835—31no—
209#830C2×D311yescharacteristic
210#821—31no—
211#821—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#821—61no—
223#821—61no—
224#821C2×D311yescharacteristic, complemented
225(C2×D3)⋊C8C2×D311yescharacteristic, complemented
226#818—31no—
227#818—31no—
228#817C2×D311yescharacteristic, complemented
229#816—31no—
230#816—31no—
231#816C2×D311yescharacteristic, complemented
232Dic3⋊C8C2×D311yescharacteristic, complemented
233C8×Dic3C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#807—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—81no—
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—81no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—42no—
257C4⋊(C3⋊D3)#4112yes—
258C3×#67—22no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#626—42no—
273#626—81no—
274#625—81no—
275#624—42no—
276#624—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—31no—
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—
299C23×D3—121no—
300C2×C3×Q8—31no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—21no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67D1211yescharacteristic
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—121no—
318#239—62no—
319#239—121no—
320#235—62no—
321#235—121no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—62no—
330C2×D12—64no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—121no—
336C2×D12—121no—
337C2×D12—121no—
338C2×D12—122no—
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6C22×D311yescharacteristic
347C3×SD16—121no—
348C2×C3×C8—21no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—41no—
353C2×C3×C8—41no—
354C2×C3×C8—42no—
355C2×C3×C8—121no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—31no—
369#217—21no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217D1211yescharacteristic
374#213—62no—
375#213—121no—
376(C2×D3)⋊C4—21no—
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—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4D1211yescharacteristic
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—121no—
399C4⋊Dic3C22×D311yescharacteristic
400C4⋊Dic3C22×D311yescharacteristic
401Dic3⋊C4—21no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4D1211yescharacteristic
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—62no—
412D24—121no—
413#204—41no—
414D3×C8—41no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32#13512yes—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—84no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C32×C4—21no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41—91no—
444C22×D4—91no—
445C2×SD16—31no—
446C2×D8—91no—
447C2×D8—91no—
448C22×C8—31no—
449C22×C8D3211yescharacteristic
450#126—181no—
451#125—91no—
452#124—91no—
453#123—181no—
454#123—181no—
455C22⋊Q8—31no—
456#121—31no—
457#121—91no—
458#121—91no—
459#121—181no—
460#121—181no—
461#120—181no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—181no—
466#117—91no—
467C2×C4⋊C4—91no—
468C2×C22⋊C4—181no—
469#107—91no—
470#107—91no—
471#106—31no—
472C4⋊C8—31no—
473#103—31no—
474#103—91no—
475#103—91no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483C22⋊C8—31no—
484C22⋊C8—31no—
485C4×C8—31no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—61no—
489C23×C3C2×D1211yescharacteristic
490C23×C3D3×D411yescharacteristic
491C22×D3—21no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—121no—
497C22×D3—121no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—124no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—242no—
504C22×D3—241no—
505C22×D3—241no—
506C22×D3—242no—
507C22×D3C2×D1211yescharacteristic
508C3×Q8—61no—
509C3×Q8—61no—
510C3×D4—62no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—122no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4C2×D1211yescharacteristic
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534#67—22no—
535#67—42no—
536#67—122no—
537#67—241no—
538#67—241no—
539#67—241no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—241no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552C2×Dic3—242no—
553C2×Dic3C2×D1211yescharacteristic
554C2×Dic3C2×D1211yescharacteristic
555C2×Dic3C2×D1211yescharacteristic
556D12—21no—
557D12—21no—
558D12—32no—
559D12—32no—
560D12—62no—
561D12—62no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—61no—
568D12—121no—
569D12—121no—
570D12—122no—
571D12—122no—
572D12—124no—
573D12—122no—
574D12—241no—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—241no—
580C4×D3—241no—
581C4×D3—241no—
582Dic6—21no—
583Dic6—21no—
584C3×C8—21no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—21no—
588C3×C8—41no—
589C3×C8—41no—
590C3×C8—61no—
591C3×C8—61no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C2×C32—22no—
595C2×C32#54611yescharacteristic
596C2×C32C2×#13511yescharacteristic
597C2×C32#57611yescharacteristic
598C3⋊D3—42no—
599C3⋊D3—81no—
600C3×D3—41no—
601C3×D3—81no—
602C24—181no—
603#41—182no—
604#41—361no—
605C2×Q8—31no—
606C2×D4—31no—
607C2×D4—31no—
608C2×D4—61no—
609C2×D4—91no—
610C2×D4—91no—
611C2×D4—182no—
612C2×D4—181no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—361no—
617C22×C4—31no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4C2×D3211yescharacteristic
623SD16—121no—
624D8—182no—
625D8—361no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—41no—
629C2×C8—121no—
630C2×C8C2×D3211yescharacteristic
631C2×C8C2×D3211yescharacteristic
632C4⋊C4—31no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—61no—
636C4⋊C4—91no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C22⋊C4—31no—
642C22⋊C4—31no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C42—31no—
653C42—181no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—22no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3#90412yes—
669C22×C3#91612yes—
670C22×C3C22×D1211yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—62no—
679C2×D3—62no—
680C2×D3—122no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—122no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—241no—
693C2×D3—241no—
694C2×D3—241no—
695C2×D3—241no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3—248no—
699C3×C4—22no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—61no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4#100411yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4D3×#4111yescharacteristic
713C3×C4D3×#4111yescharacteristic
714Dic3—21no—
715Dic3—21no—
716Dic3—21no—
717Dic3—41no—
718Dic3—41no—
719Dic3—41no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723Dic3—121no—
724Dic3—241no—
725Dic3—241no—
726C32#329711yescharacteristic, complemented, Sylow
727C23—31no—
728C23—61no—
729C23—181no—
730C23—181no—
731C23—362no—
732C23—362no—
733C23—721no—
734C23D3×D1211yescharacteristic
735Q8—61no—
736Q8—61no—
737D4—62no—
738D4—61no—
739D4—61no—
740D4—92no—
741D4—122no—
742D4—181no—
743D4—181no—
744D4—181no—
745D4—362no—
746D4—362no—
747D4—721no—
748D4—721no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—362no—
762C2×C4—721no—
763C2×C4—721no—
764C2×C4—721no—
765C2×C4D3×D1211yescharacteristic
766C2×C4C22×D3211yescharacteristic
767C8—21no—
768C8—21no—
769C8—61no—
770C8—61no—
771C2×C3—24no—
772C2×C3—22no—
773C2×C3—22no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—121no—
778C2×C3—241no—
779C2×C3#555411yescharacteristic
780C2×C3#561011yescharacteristic
781C2×C3C2×#90411yescharacteristic
782C2×C3#575211yescharacteristic
783C2×C3C2×#91611yescharacteristic
784C2×C3#576911yescharacteristic
785D3—41no—
786D3—81no—
787D3—122no—
788D3—122no—
789D3—242no—
790D3—242no—
791D3—241no—
792D3—241no—
793C22—21no—
794C22—21no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—182no—
802C22—361no—
803C22—361no—
804C22—361no—
805C22—361no—
806C22—361no—
807C22—724no—
808C22#6380612yes—
809C22C2×D3×D1211yescharacteristic
810C4—21no—
811C4—61no—
812C4—61no—
813C4—61no—
814C4—121no—
815C4—121no—
816C4—121no—
817C4—361no—
818C4—361no—
819C4#6430611yescharacteristic
820C4#6433011yescharacteristic
821C3—21no—
822C3#7944111yescharacteristic, complemented
823C3#8068111yescharacteristic, complemented
824C2—22no—
825C2—121no—
826C2—241no—
827C2—362no—
828C2—721no—
829C2#1059468011yescharacteristic
830C2C2×#6380611yescharacteristic
831C2#1059507511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×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. #10595018C2semidirect
2. #10594995C2semidirect
3. C2×#63648C2semidirect
4. C3×#5114C2semidirect
5. C3×C8×#67C2semidirect
6. #10591168C2semidirect
7. #10591103C2semidirect
8. #10590872C2semidirect
9. #10590826C2semidirect
10. #10590823C2semidirect
11. #10590769C2semidirect
12. #10590754C2semidirect
13. #10590745C2semidirect
14. #10590704C2semidirect
15. #10590690C2semidirect
25. C2×C3×#204C22semidirect
26. C2×C3×D3×C8C22semidirect
33. #63908C22semidirect
36. Dic3×D12C22semidirect
38. #63869C22semidirect
41. #63841C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#817C22semidirect
52. C3×#816C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
70. #5114D3semidirect
75. C8×#67D3semidirect
178. C2×#204C2×D3semidirect
179. C2×D3×C8C2×D3semidirect
224. #821C2×D3semidirect
225. (C2×D3)⋊C8C2×D3semidirect
228. #817C2×D3semidirect
231. #816C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
233. C8×Dic3C2×D3semidirect
726. C32#3297semidirect
822. C3#79441semidirect
823. C3#80681semidirect

Maximal subgroups

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

subgroupindex
#105950182
#105949952
C2×#636482
C3×#51142
C3×C8×#672
#105911682
#105911032
#105908722
#105908262
#105908232
#105907692
#105907542
#105907452
#105907042
#105906902
#806813
#794413