Finite Group Databasebeta

← #11887419

Subgroups — #11887419

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594886C211yesmaximal, characteristic, complemented
2#10594843C211yesmaximal, characteristic, complemented
3#10592813C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591162C211yesmaximal, characteristic, complemented
7#10591135C211yesmaximal, characteristic, complemented
8#10590968C211yesmaximal, characteristic, complemented
9#10590954C211yesmaximal, characteristic, complemented
10#10590863C211yesmaximal, characteristic, complemented
11#10590860C211yesmaximal, characteristic, complemented
12#10590837C211yesmaximal, characteristic, complemented
13#10590826C211yesmaximal, characteristic, complemented
14#10590772C211yesmaximal, characteristic, complemented
15#10590745C211yesmaximal, characteristic, complemented
16#79441—31nomaximal
17#78760—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21#64139C2211yescharacteristic
22#64133C2211yescharacteristic
23C2×#3744C2211yescharacteristic, complemented
24C3×C4×#67C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic, complemented
27#63978—21no—
28#63976—21no—
29D3×#217—21no—
30#63952—21no—
31#63909C2211yescharacteristic, complemented
32#63908C2211yescharacteristic
33#63894C2211yescharacteristic, complemented
34Dic3×D12C2211yescharacteristic
35#63885—21no—
36#63884—21no—
37#63869C2211yescharacteristic, complemented
38#63860C2211yescharacteristic
39#63854—21no—
40#63848—21no—
41#63841C2211yescharacteristic, complemented
42C2×#3714C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44#63648C2211yescharacteristic, complemented
45#63644C2211yescharacteristic, complemented
46#63643C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5806—31no—
62#5565—31no—
63#5550—31no—
64#5514—31no—
65C3×C8×D4—31no—
66C2×C3×#102—31no—
67#5217—31no—
68#5115—31no—
69#5114—31no—
70#5114—31no—
71#5114—61no—
72#5113—31no—
73C2×#821D311yescharacteristic, complemented
74C8×#67D311yescharacteristic, complemented
75#4970—31no—
76#4847—31no—
77#4844—31no—
78#4787—31no—
79#4781—31no—
80#4779—31no—
81#4775—31no—
82#4772—31no—
83#4768—31no—
84#4763—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
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67D411yescharacteristic
98C22×C3×Dic3—21no—
99C2×C3×D12—22no—
100C2×C3×D12—21no—
101C2×C3×D12—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3795—22no—
112#3795—41no—
113C2×C32×C8—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116#3757—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3744—41no—
122C3×#217D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—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
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C22×C3×C8—21no—
150C22×C3×C8—31no—
151C22×C3×C8C2×D311yescharacteristic
152C22×C3×C8C2×D311yescharacteristic
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#953—61no—
156C2×#217—61no—
157#939—61no—
158#939—61no—
159#938—31no—
160#937—61no—
161#936—31no—
162#935—61no—
163D4×Dic3—31no—
164C2×#213—31no—
165C2×#213—31no—
166#930—31no—
167#930—31no—
168#930—31no—
169#930—31no—
170#930—61no—
171#930—61no—
172C4×#67—61no—
173C4×#67C2×D311yescharacteristic
174#926—31no—
175C2×C4⋊Dic3C2×D311yescharacteristic
176#924—31no—
177#924—31no—
178#924—61no—
179C2×D24—31no—
180C2×D24—31no—
181C2×#204—31no—
182C2×#204—31no—
183C2×#204—61no—
184C2×D3×C8C2×D311yescharacteristic, complemented
185#898—61no—
186#898—61no—
187#895—31no—
188#894—61no—
189#894—61no—
190#893—31no—
191#892—31no—
192#890—31no—
193#884—61no—
194#883—61no—
195#67⋊C4—61no—
196D3×C22⋊C4—61no—
197#875—31no—
198C4×D12—31no—
199C4×D12—31no—
200#870—31no—
201C3×C4⋊C8—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208C3×C4×C8—31no—
209#832—31no—
210#832—31no—
211#830C2×D311yescharacteristic
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—61no—
217#821C2×D311yescharacteristic
218#821C2×D311yescharacteristic
219#821C2×D311yescharacteristic
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic, complemented
222#818—31no—
223#818—31no—
224#817—31no—
225#817—31no—
226#817—61no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—61no—
232Dic3⋊C8C2×D311yescharacteristic, complemented
233C8×Dic3C2×D311yescharacteristic, complemented
234#810—31no—
235#810—31no—
236#807—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256#634—21no—
257#634—21no—
258C3×#67—22no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12#4112yes—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272#626—81no—
273#625—42no—
274#625—81no—
275#624—81no—
276D3×Dic3—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—91no—
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—31no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4—121no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—121no—
318C2×#67D1211yescharacteristic
319C22×Dic3—21no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322#237—62no—
323#237—121no—
324#235—62no—
325#235—121no—
326C2×D12—22no—
327C2×D12—21no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—41no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6—31no—
341C2×Dic6—31no—
342C2×Dic6—61no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—41no—
348C2×C3×C8—41no—
349C2×C3×C8—42no—
350C2×C3×C8—121no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C42—31no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—121no—
370#217D1211yescharacteristic
371#213—62no—
372#213—121no—
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—61no—
384(C2×D3)⋊C4—121no—
385(C2×D3)⋊C4D1211yescharacteristic
386C4⋊Dic3—21no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—121no—
402Dic3⋊C4D1211yescharacteristic
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—62no—
409D24—121no—
410#204—121no—
411#204—121no—
412#204—122no—
413D3×C8—41no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32#13512yes—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—22no—
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—41no—
429C2×C3×D3—41no—
430C2×C3×D3—84no—
431C32×C4—21no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—91no—
443C22×D4—31no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447C22×C8—31no—
448C22×C8D3211yescharacteristic
449#126—181no—
450#125—91no—
451#124—91no—
452#123—181no—
453#123—181no—
454C22⋊Q8—91no—
455#121—91no—
456#121—91no—
457#121—91no—
458#121—181no—
459#121—181no—
460#120—181no—
461C4×D4—31no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—181no—
465#117—91no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—181no—
468#107—91no—
469#107—91no—
470#106—91no—
471C4⋊C8—31no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—31no—
483C22⋊C8—31no—
484C4×C8—31no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—122no—
490C23×C3—122no—
491C23×C3—241no—
492C23×C3C2×D1211yescharacteristic
493C23×C3D3×D411yescharacteristic
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—81no—
501C22×D3—121no—
502C22×D3C2×D1211yescharacteristic
503C3×D4—32no—
504C3×D4—62no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—122no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—241no—
525C2×C3×C4C2×D1211yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—22no—
530#67—122no—
531#67—122no—
532#67—122no—
533#67—122no—
534#67—242no—
535#67—241no—
536#67—241no—
537#67—241no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—81no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—122no—
551C2×Dic3—241no—
552C2×Dic3C2×D1211yescharacteristic
553C2×Dic3C2×D1211yescharacteristic
554C2×Dic3C2×D1211yescharacteristic
555D12—21no—
556D12—21no—
557D12—21no—
558D12—42no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—121no—
564D12—121no—
565D12—241no—
566D12#23512yes—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—122no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573Dic6—61no—
574Dic6—61no—
575Dic6—61no—
576Dic6—61no—
577Dic6—121no—
578Dic6—121no—
579C3×C8—22no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—21no—
584C3×C8—41no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C2×C32—22no—
590C2×C32#54611yescharacteristic
591C2×C32C2×#13511yescharacteristic
592C2×C32#57611yescharacteristic
593C3⋊D3—81no—
594C3×D3—41no—
595C3×D3—42no—
596C3×D3—81no—
597C24—61no—
598#41—182no—
599#41—361no—
600C2×Q8—91no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—62no—
605C2×D4—61no—
606C2×D4—91no—
607C2×D4—121no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—181no—
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4C2×D3211yescharacteristic
618SD16—361no—
619D8—182no—
620D8—361no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—41no—
624C2×C8—121no—
625C2×C8C2×D3211yescharacteristic
626C2×C8C2×D3211yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—91no—
632C4⋊C4—91no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C42—31no—
648C42—181no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—22no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—62no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—244no—
667C22×C3#90412yes—
668C22×C3#91612yes—
669C22×C3C22×D1211yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C2×D3—21no—
672C2×D3—22no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—84no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—241no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C2×#23511yescharacteristic
701C3×C4#100411yescharacteristic
702C3×C4#100411yescharacteristic
703C3×C4D3×#4111yescharacteristic
704Dic3—21no—
705Dic3—21no—
706Dic3—21no—
707Dic3—41no—
708Dic3—41no—
709Dic3—121no—
710Dic3—121no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716Dic3—241no—
717Dic3—241no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—31no—
720C23—61no—
721C23—61no—
722C23—122no—
723C23—122no—
724C23—181no—
725C23—241no—
726C23D3×D1211yescharacteristic
727Q8—181no—
728Q8—181no—
729D4—32no—
730D4—62no—
731D4—61no—
732D4—61no—
733D4—61no—
734D4—122no—
735D4—181no—
736D4—181no—
737D4—362no—
738D4—362no—
739D4—721no—
740D4—721no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—31no—
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—241no—
754C2×C4—362no—
755C2×C4—721no—
756C2×C4—721no—
757C2×C4D3×D1211yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C8—21no—
760C8—21no—
761C8—61no—
762C8—61no—
763C2×C3—22no—
764C2×C3—22no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—122no—
770C2×C3—121no—
771C2×C3—241no—
772C2×C3#549011yescharacteristic
773C2×C3#555411yescharacteristic
774C2×C3C2×#90411yescharacteristic
775C2×C3#575211yescharacteristic
776C2×C3#575711yescharacteristic
777C2×C3C2×#91611yescharacteristic
778D3—41no—
779D3—42no—
780D3—81no—
781D3—241no—
782D3—241no—
783D3—481no—
784C22—21no—
785C22—21no—
786C22—61no—
787C22—62no—
788C22—61no—
789C22—61no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—244no—
796C22—361no—
797C22—361no—
798C22—361no—
799C22#6380612yes—
800C22C2×D3×D1211yescharacteristic
801C4—21no—
802C4—61no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—121no—
807C4—361no—
808C4—361no—
809C4—361no—
810C4D3×#23511yescharacteristic
811C4#6433011yescharacteristic
812C3—21no—
813C3#7876011yescharacteristic, complemented
814C3#7944111yescharacteristic, complemented
815C2—22no—
816C2—121no—
817C2—122no—
818C2—241no—
819C2—721no—
820C2#1059467811yescharacteristic
821C2C2×#6380611yescharacteristic
822C2#1059507311yescharacteristic
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. #10594886C2semidirect
2. #10594843C2semidirect
3. #10592813C2semidirect
4. C2×C3×#821C2semidirect
5. C3×C8×#67C2semidirect
6. #10591162C2semidirect
7. #10591135C2semidirect
8. #10590968C2semidirect
9. #10590954C2semidirect
10. #10590863C2semidirect
11. #10590860C2semidirect
12. #10590837C2semidirect
13. #10590826C2semidirect
14. #10590772C2semidirect
15. #10590745C2semidirect
23. C2×#3744C22semidirect
26. C2×C3×D3×C8C22semidirect
31. #63909C22semidirect
33. #63894C22semidirect
37. #63869C22semidirect
41. #63841C22semidirect
44. #63648C22semidirect
45. #63644C22semidirect
46. #63643C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
73. C2×#821D3semidirect
74. C8×#67D3semidirect
184. C2×D3×C8C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
233. C8×Dic3C2×D3semidirect
718. C32#3297semidirect
813. C3#78760semidirect
814. C3#79441semidirect

Maximal subgroups

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

subgroupindex
#105948862
#105948432
#105928132
C2×C3×#8212
C3×C8×#672
#105911622
#105911352
#105909682
#105909542
#105908632
#105908602
#105908372
#105908262
#105907722
#105907452
#794413
#787603