Finite Group Databasebeta

← #13164743

Subgroups — #13164743

Order 1728.

3309 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11722664C211yesmaximal, characteristic, complemented
2#64361⋊C3C211yesmaximal, characteristic, complemented
3C2×D4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
4#11722545C214yesmaximal, complemented
5C2×#88676C214yesmaximal, complemented
6#11722507C214yesmaximal, complemented
7#11722506C214yesmaximal, complemented
8#11722504C214yesmaximal, complemented
9D4×((C3⋊D3)⋊C3)⋊C2C214yesmaximal, complemented
10#11722492C212yesmaximal, complemented
11#11722490C212yesmaximal, complemented
12#10596675—31nomaximal
13D3×#1004—31nomaximal
14C23×(C3⋊D3)⋊C3C2212yescomplemented
15C22×((C3⋊D3)⋊C3)⋊C2C2214yescomplemented
16C2×D4×H(3,𝔽3)C2211yescharacteristic, complemented
17C2×#6235C2214yescomplemented
18#88744C2214yescomplemented
19D4×#272C2214yescomplemented
20#88740C2212yescomplemented
21C2×#638⋊C3C2214yescomplemented
22C2×#638⋊C3C2212yescomplemented
23#3830⋊C3C2214yescomplemented
24D4×(C3⋊D3)⋊C3C2214yescomplemented
25D4×(C3⋊D3)⋊C3C2214yescomplemented
26D4×(C3⋊D3)⋊C3C2214yescomplemented
27#3828⋊C3C2212yescomplemented
28C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
29C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
30#88677C2218yescomplemented
31#88676C2218yescomplemented
32#88676C2214yescomplemented
33#88676C2218yescomplemented
34#88676C2218yescomplemented
35#88676C2218yescomplemented
36C2×#6200C2214yescomplemented
37C2×#6198C2214yescomplemented
38#88672C2218yescomplemented
39#88671C2218yescomplemented
40#88671C2214yescomplemented
41C2×((C3⋊D3)⋊C3)⋊C4C2214yescomplemented
42#88655C2214yescomplemented
43#88654C2212yescomplemented
44#88654C2214yescomplemented
45C4×((C3⋊D3)⋊C3)⋊C2C2214yescomplemented
46#88652C2212yescomplemented
47#88650C2214yescomplemented
48#88649C2214yescomplemented
49#88648C2214yescomplemented
50#88648C2212yescomplemented
51((C3⋊D3)⋊C3)⋊Q8C2212yescomplemented
52#64361D311yescharacteristic, complemented
53C2×D4×C3⋊D3D311yescharacteristic, complemented
54C3×#1004—31no—
55C3×#1004—31no—
56C3×#1004—31no—
57C3×#1004—61no—
58C2×C3×D3×D4—31no—
59#64330—34no—
60#64330—34no—
61C2×#3811—34no—
62C2×D3×#67—34no—
63#64314—34no—
64#64314—34no—
65#64314—34no—
66#64313—34no—
67#64312—34no—
68D3×#237—34no—
69D32×D4—34no—
70D32×D4—34no—
71#64308—32no—
72#64307—32no—
73#64306—32no—
74D3×#235—32no—
75C23×H(3,𝔽3)C2312yescomplemented
76C22×#272C2314yescomplemented
77C22×(C3⋊D3)⋊C3—44no—
78C22×(C3⋊D3)⋊C3C2314yes—
79C22×(C3⋊D3)⋊C3C2311yescharacteristic
80C22×(C3⋊D3)⋊C3C2314yescomplemented
81C22×(C3⋊D3)⋊C3C2314yescomplemented
82C22×(C3⋊D3)⋊C3C2312yescomplemented
83C2×((C3⋊D3)⋊C3)⋊C2—48no—
84C2×((C3⋊D3)⋊C3)⋊C2C2314yes—
85C2×((C3⋊D3)⋊C3)⋊C2C2318yescomplemented
86D4×H(3,𝔽3)C2314yescomplemented
87C2×C4×H(3,𝔽3)C2311yescharacteristic, complemented
88#6235C2314yescomplemented
89#6235C2318yescomplemented
90C2×#1084C2314yescomplemented
91C4⋊#272C2312yescomplemented
92C4×#272C2314yescomplemented
93#6229C2312yescomplemented
94#638⋊C3C2318yescomplemented
95#638⋊C3C2314yescomplemented
96#638⋊C3C2318yescomplemented
97C2×(C3⋊Dic3)⋊C3C2314yescomplemented
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic, complemented
99C4⋊((C3⋊D3)⋊C3)C2314yescomplemented
100C4⋊((C3⋊D3)⋊C3)C2312yescomplemented
101C4×(C3⋊D3)⋊C3C2312yes—
102C4×(C3⋊D3)⋊C3C2312yescomplemented
103C4×(C3⋊D3)⋊C3C2314yescomplemented
104#634⋊C3C2312yescomplemented
105#6200C2318yescomplemented
106#6200C2314yescomplemented
107#6200C2314yescomplemented
108#6199C2314yescomplemented
109#6198C2314yescomplemented
110#6198C2318yescomplemented
111((C3⋊D3)⋊C3)⋊C4C2314yes—
112((C3⋊D3)⋊C3)⋊C4C2318yescomplemented
113((C3⋊D3)⋊C3)⋊C4C2314yescomplemented
114#6196C2314yescomplemented
115D3×H(5,𝔽2)—91no—
116D3×H(5,𝔽2)—91no—
117C2×#1004—91no—
118C23×C3⋊D3C2×D312yescomplemented
119C23×C3×D3—32no—
120C22×D32—34no—
121C22×D32—34no—
122C2×C32×D4—21no—
123C2×C32×D4C2×D311yescharacteristic, complemented
124C2×C32×D4C2×D311yescharacteristic, complemented
125C2×#638C2×D314yescomplemented
126C2×#638C2×D312yescomplemented
127#3830C2×D314yescomplemented
128D4×C3⋊D3C2×D314yescomplemented
129D4×C3⋊D3C2×D314yescomplemented
130D4×C3⋊D3C2×D314yescomplemented
131#3828C2×D312yescomplemented
132C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
133C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
134C2×C3×#67—34no—
135C2×C3×#67—34no—
136C2×C3×#67—34no—
137C2×C3×#67—32no—
138C2×C3×#67—64no—
139C3×#237—34no—
140C3×#237—34no—
141C3×#237—34no—
142C3×#237—64no—
143C3×D3×D4—34no—
144C3×D3×D4—34no—
145C3×D3×D4—34no—
146C3×D3×D4—34no—
147C3×D3×D4—34no—
148C3×D3×D4—64no—
149C3×#235—32no—
150C3×#235—32no—
151C3×#235—32no—
152C3×#235—62no—
153C2×C3×D12—31no—
154C2×C3×C4×D3—31no—
155#3811—34no—
156#3811—38no—
157#3811—38no—
158#3811—38no—
159#3811—38no—
160D3×#67—34no—
161D3×#67—38no—
162D3×#67—38no—
163D3×#67—38no—
164D3×#67—38no—
165D3×#67—38no—
166D3×#67—38no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#626—34no—
170C2×#625—34no—
171C2×#624—34no—
172#3805—34no—
173#3805—38no—
174#3804—34no—
175#3804—38no—
176#3804—38no—
177#3804—38no—
178C2×D3×Dic3—34no—
179#3802—32no—
180#3802—34no—
181D3×D12—32no—
182D3×D12—34no—
183D3×D12—34no—
184D3×D12—34no—
185C4×D32—34no—
186C4×D32—34no—
187#3799—32no—
188#3799—34no—
189#3799—34no—
190#3798—34no—
191#3798—34no—
192#3797—32no—
193#3796—32no—
194#3796—32no—
195#3796—34no—
196#3795—32no—
197#3795—34no—
198D3×Dic6—32no—
199C22×H(3,𝔽3)—42no—
200C22×H(3,𝔽3)C2414yes—
201C22×H(3,𝔽3)C2411yescharacteristic
202C2×#272—44no—
203C2×#272C2414yes—
204C2×(C3⋊D3)⋊C3—28no—
205C2×(C3⋊D3)⋊C3—22no—
206C2×(C3⋊D3)⋊C3—44no—
207C2×(C3⋊D3)⋊C3—42no—
208C2×(C3⋊D3)⋊C3—44no—
209C2×(C3⋊D3)⋊C3C2414yes—
210C2×(C3⋊D3)⋊C3C2414yes—
211C2×(C3⋊D3)⋊C3C2411yescharacteristic
212C2×(C3⋊D3)⋊C3C2411yescharacteristic
213((C3⋊D3)⋊C3)⋊C2—28no—
214((C3⋊D3)⋊C3)⋊C2—48no—
215C4×H(3,𝔽3)C2412yes—
216#1084C2414yes—
217(C3⋊Dic3)⋊C3C2412yes—
218(C3⋊Dic3)⋊C3C2414yes—
219C3×H(5,𝔽2)—91no—
220C3×H(5,𝔽2)—91no—
221C22×C3×D4—91no—
222C22×#67—94no—
223#1009—92no—
224#1009—92no—
225#1009—94no—
226#1009—94no—
227D3×#41—92no—
228D3×#41—92no—
229D3×#41—94no—
230D3×#41—94no—
231#1004—31no—
232#1004—31no—
233#1004—31no—
234#1004—61no—
235#1004—91no—
236#1004—92no—
237#1004—94no—
238#1004—94no—
239#1004—94no—
240#1004—94no—
241#1004—94no—
242#1004—94no—
243#1004—94no—
244C2×#237—94no—
245C2×D3×D4—31no—
246C2×D3×D4—91no—
247C2×D3×D4—94no—
248C2×D3×D4—94no—
249C2×D3×D4—94no—
250C2×D3×D4—94no—
251C2×D3×D4—94no—
252C2×#235—92no—
253C23×C32—22no—
254C23×C32C22×D312yescomplemented
255C23×C32C22×D312yescomplemented
256C22×C3⋊D3—44no—
257C22×C3⋊D3C22×D314yes—
258C22×C3⋊D3C22×D311yescharacteristic
259C22×C3⋊D3C22×D314yescomplemented
260C22×C3⋊D3C22×D314yescomplemented
261C22×C3⋊D3C22×D312yescomplemented
262C22×C3×D3—34no—
263C22×C3×D3—31no—
264C22×C3×D3—34no—
265C22×C3×D3—34no—
266C22×C3×D3—34no—
267C22×C3×D3—34no—
268C22×C3×D3—32no—
269C22×C3×D3—64no—
270C22×C3×D3—124no—
271C2×D32—34no—
272C2×D32—34no—
273C2×D32—38no—
274C2×D32—38no—
275C2×D32—128no—
276C2×D32—128no—
277C32×D4—24no—
278C32×D4C22×D314yescomplemented
279C32×D4C22×D314yescomplemented
280C2×C32×C4—21no—
281C2×C32×C4C22×D311yescharacteristic, complemented
282C2×C32×C4C22×D311yescharacteristic, complemented
283#638C22×D318yescomplemented
284#638C22×D314yescomplemented
285#638C22×D318yescomplemented
286C2×C3⋊Dic3C22×D314yescomplemented
287C2×C3⋊Dic3C22×D311yescharacteristic, complemented
288C4⋊(C3⋊D3)C22×D314yescomplemented
289C4⋊(C3⋊D3)C22×D312yescomplemented
290C4×C3⋊D3C22×D312yes—
291C4×C3⋊D3C22×D312yescomplemented
292C4×C3⋊D3C22×D314yescomplemented
293#634C22×D312yescomplemented
294C3×#67—38no—
295C3×#67—38no—
296C3×#67—34no—
297C3×#67—34no—
298C3×#67—38no—
299C3×#67—38no—
300C3×#67—34no—
301C3×#67—64no—
302C3×#67—68no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—34no—
305C2×C3×Dic3—34no—
306C2×C3×Dic3—34no—
307C2×C3×Dic3—64no—
308C3×D12—34no—
309C3×D12—32no—
310C3×D12—32no—
311C3×D12—32no—
312C3×D12—62no—
313C3×C4×D3—32no—
314C3×C4×D3—32no—
315C3×C4×D3—34no—
316C3×C4×D3—34no—
317C3×C4×D3—34no—
318C3×C4×D3—64no—
319C3×Dic6—32no—
320C3×Dic6—32no—
321C3×Dic6—32no—
322C3×Dic6—62no—
323#627—34no—
324#627—34no—
325#626—34no—
326#626—38no—
327#626—34no—
328#626—38no—
329#626—34no—
330#626—34no—
331#626—38no—
332#625—34no—
333#625—38no—
334#625—34no—
335#624—34no—
336#624—38no—
337#624—34no—
338D3×Dic3—34no—
339D3×Dic3—38no—
340D3×Dic3—34no—
341D3×Dic3—34no—
342D3×Dic3—34no—
343C2×H(5,𝔽2)—271noSylow
344C2×H(3,𝔽3)—24no—
345C2×H(3,𝔽3)—21no—
346C2×H(3,𝔽3)C2511yescharacteristic
347#272—24no—
348(C3⋊D3)⋊C3—24no—
349(C3⋊D3)⋊C3—24no—
350(C3⋊D3)⋊C3—21no—
351(C3⋊D3)⋊C3H(5,𝔽2)12yescomplemented
352C24×C3—92no—
353C23×D3—32no—
354C23×D3—92no—
355C23×D3—94no—
356C23×D3—94no—
357C23×D3—94no—
358C3×#41—92no—
359C3×#41—94no—
360C3×#41—94no—
361C3×#41—92no—
362C2×C3×D4—31no—
363C2×C3×D4—31no—
364C2×C3×D4—61no—
365C2×C3×D4—91no—
366C2×C3×D4—94no—
367C2×C3×D4—94no—
368C2×C3×D4—94no—
369C2×C3×D4—94no—
370C2×C3×D4—92no—
371C2×C3×D4—94no—
372C2×C3×D4—94no—
373C2×C3×D4D3211yescharacteristic
374C22×C3×C4—91no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—32no—
378C2×#67—34no—
379C2×#67—64no—
380C2×#67—92no—
381C2×#67—94no—
382C2×#67—94no—
383C2×#67—94no—
384C2×#67—94no—
385C2×#67—98no—
386C2×#67—94no—
387C2×#67—98no—
388C2×#67—98no—
389C2×#67—98no—
390C2×#67—98no—
391C2×#67—94no—
392C22×Dic3—94no—
393#239—92no—
394#239—94no—
395#239—94no—
396#239—92no—
397D3×Q8—92no—
398D3×Q8—92no—
399#237—34no—
400#237—34no—
401#237—34no—
402#237—64no—
403#237—94no—
404#237—92no—
405#237—94no—
406#237—92no—
407#237—94no—
408#237—94no—
409#237—98no—
410#237—98no—
411#237—98no—
412#237—98no—
413#237—94no—
414D3×D4—34no—
415D3×D4—34no—
416D3×D4—34no—
417D3×D4—34no—
418D3×D4—34no—
419D3×D4—64no—
420D3×D4—94no—
421D3×D4—94no—
422D3×D4—94no—
423D3×D4—92no—
424D3×D4—94no—
425D3×D4—94no—
426D3×D4—94no—
427D3×D4—92no—
428D3×D4—94no—
429D3×D4—94no—
430D3×D4—98no—
431D3×D4—98no—
432D3×D4—98no—
433D3×D4—98no—
434D3×D4—94no—
435D3×D4—98no—
436D3×D4—98no—
437D3×D4—98no—
438D3×D4—98no—
439D3×D4—98no—
440D3×D4—98no—
441#235—32no—
442#235—32no—
443#235—32no—
444#235—62no—
445#235—92no—
446#235—94no—
447#235—92no—
448#235—94no—
449#235—94no—
450#235—94no—
451#235—94no—
452#235—92no—
453#235—98no—
454#235—94no—
455#235—98no—
456C2×D12—31no—
457C2×D12—91no—
458C2×D12—94no—
459C2×D12—92no—
460C2×D12—94no—
461C2×D12—94no—
462C2×D12—94no—
463C2×C4×D3—31no—
464C2×C4×D3—91no—
465C2×C4×D3—94no—
466C2×C4×D3—94no—
467C2×C4×D3—94no—
468C2×C4×D3—94no—
469C2×C4×D3—94no—
470C2×Dic6—92no—
471C22×C32—24no—
472C22×C32—21no—
473C22×C32—42no—
474C22×C32—42no—
475C22×C32—82no—
476C22×C32C23×D314yes—
477C22×C32C23×D314yes—
478C22×C32C23×D311yescharacteristic
479C22×C32C23×D311yescharacteristic
480C2×C3⋊D3—28no—
481C2×C3⋊D3—22no—
482C2×C3⋊D3—44no—
483C2×C3⋊D3—42no—
484C2×C3⋊D3—44no—
485C2×C3⋊D3C23×D314yes—
486C2×C3⋊D3C23×D314yes—
487C2×C3⋊D3C23×D311yescharacteristic
488C2×C3⋊D3C23×D311yescharacteristic
489C2×C3×D3—31no—
490C2×C3×D3—34no—
491C2×C3×D3—34no—
492C2×C3×D3—31no—
493C2×C3×D3—34no—
494C2×C3×D3—34no—
495C2×C3×D3—64no—
496C2×C3×D3—68no—
497C2×C3×D3—62no—
498C2×C3×D3—124no—
499C2×C3×D3—122no—
500C2×C3×D3—124no—
501C2×C3×D3—124no—
502C2×C3×D3—124no—
503C2×C3×D3—244no—
504D32—68no—
505D32—68no—
506D32—128no—
507D32—128no—
508C32×C4—22no—
509C32×C4C23×D312yes—
510C32×C4C23×D312yes—
511C3⋊Dic3C23×D314yes—
512C3⋊Dic3C23×D312yes—
513C3×Dic3—32no—
514C3×Dic3—34no—
515C3×Dic3—34no—
516C3×Dic3—34no—
517C3×Dic3—64no—
518H(5,𝔽2)—91no—
519H(5,𝔽2)—91no—
520H(5,𝔽2)—274no—
521H(5,𝔽2)—274no—
522H(5,𝔽2)—274no—
523H(5,𝔽2)—272no—
524C2×#41—272no—
525C2×#41—274no—
526C22×D4—91no—
527C22×D4—274no—
528C22×D4—274no—
529H(3,𝔽3)C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
530C23×C3—32no—
531C23×C3—32no—
532C23×C3—62no—
533C23×C3—94no—
534C23×C3—91no—
535C23×C3—94no—
536C23×C3—92no—
537C23×C3—94no—
538C23×C3—94no—
539C23×C3—364no—
540C23×C3C2×D3212yes—
541C22×D3—31no—
542C22×D3—34no—
543C22×D3—34no—
544C22×D3—34no—
545C22×D3—32no—
546C22×D3—34no—
547C22×D3—34no—
548C22×D3—64no—
549C22×D3—91no—
550C22×D3—94no—
551C22×D3—94no—
552C22×D3—92no—
553C22×D3—94no—
554C22×D3—94no—
555C22×D3—98no—
556C22×D3—94no—
557C22×D3—94no—
558C22×D3—98no—
559C22×D3—98no—
560C22×D3—124no—
561C22×D3—364no—
562C22×D3—368no—
563C22×D3—368no—
564C22×D3—368no—
565C3×Q8—92no—
566C3×Q8—92no—
567C3×D4—34no—
568C3×D4—34no—
569C3×D4—64no—
570C3×D4—92no—
571C3×D4—94no—
572C3×D4—98no—
573C3×D4—94no—
574C3×D4—98no—
575C3×D4—98no—
576C3×D4—94no—
577C3×D4—92no—
578C3×D4C2×D3214yes—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—61no—
582C2×C3×C4—92no—
583C2×C3×C4—94no—
584C2×C3×C4—92no—
585C2×C3×C4—94no—
586C2×C3×C4—91no—
587C2×C3×C4—94no—
588C2×C3×C4—94no—
589C2×C3×C4C2×D3211yescharacteristic
590#67—34no—
591#67—34no—
592#67—38no—
593#67—38no—
594#67—34no—
595#67—38no—
596#67—38no—
597#67—64no—
598#67—68no—
599#67—94no—
600#67—98no—
601#67—98no—
602#67—94no—
603#67—98no—
604#67—94no—
605#67—94no—
606#67—94no—
607#67—98no—
608#67—98no—
609#67—94no—
610#67—94no—
611#67—98no—
612C2×Dic3—34no—
613C2×Dic3—34no—
614C2×Dic3—31no—
615C2×Dic3—34no—
616C2×Dic3—64no—
617C2×Dic3—91no—
618C2×Dic3—94no—
619C2×Dic3—94no—
620C2×Dic3—94no—
621C2×Dic3—94no—
622C2×Dic3—98no—
623D12—32no—
624D12—32no—
625D12—34no—
626D12—32no—
627D12—62no—
628D12—94no—
629D12—92no—
630D12—94no—
631D12—98no—
632D12—94no—
633D12—98no—
634D12—94no—
635C4×D3—34no—
636C4×D3—34no—
637C4×D3—32no—
638C4×D3—32no—
639C4×D3—34no—
640C4×D3—64no—
641C4×D3—92no—
642C4×D3—94no—
643C4×D3—92no—
644C4×D3—94no—
645C4×D3—98no—
646C4×D3—94no—
647C4×D3—94no—
648C4×D3—94no—
649C4×D3—98no—
650C4×D3—94no—
651C4×D3—94no—
652Dic6—32no—
653Dic6—32no—
654Dic6—32no—
655Dic6—62no—
656Dic6—92no—
657Dic6—94no—
658Dic6—94no—
659Dic6—94no—
660C2×C32—24no—
661C2×C32—21no—
662C2×C32—24no—
663C2×C32—21no—
664C2×C32—21no—
665C2×C32—44no—
666C2×C32—41no—
667C2×C32C24×D311yescharacteristic
668C2×C32C24×D311yescharacteristic
669C3⋊D3—24no—
670C3⋊D3—21no—
671C3⋊D3—24no—
672C3⋊D3#100412yescomplemented
673C3×D3—32no—
674C3×D3—64no—
675C3×D3—64no—
676C3×D3—64no—
677C3×D3—61no—
678C3×D3—64no—
679C3×D3—124no—
680C24—92no—
681C24—274no—
682#41—94no—
683#41—94no—
684#41—92no—
685#41—92no—
686#41—274no—
687#41—274no—
688#41—278no—
689#41—278no—
690#41—272no—
691#41—272no—
692#41—274no—
693#41—274no—
694C2×Q8—272no—
695C2×D4—92no—
696C2×D4—94no—
697C2×D4—94no—
698C2×D4—94no—
699C2×D4—94no—
700C2×D4—94no—
701C2×D4—94no—
702C2×D4—91no—
703C2×D4—272no—
704C2×D4—274no—
705C2×D4—274no—
706C2×D4—274no—
707C2×D4—274no—
708C2×D4—274no—
709C2×D4—278no—
710C2×D4—278no—
711C2×D4—278no—
712C2×D4—278no—
713C2×D4—278no—
714C2×D4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
715C22×C4—91no—
716C22×C4—274no—
717C22×C4—274no—
718C22×C3—34no—
719C22×C3—34no—
720C22×C3—31no—
721C22×C3—31no—
722C22×C3—42no—
723C22×C3—64no—
724C22×C3—61no—
725C22×C3—91no—
726C22×C3—94no—
727C22×C3—94no—
728C22×C3—91no—
729C22×C3—94no—
730C22×C3—122no—
731C22×C3—122no—
732C22×C3—188no—
733C22×C3—182no—
734C22×C3—242no—
735C22×C3—364no—
736C22×C3—364no—
737C22×C3—364no—
738C22×C3—362no—
739C22×C3C22×D3214yes—
740C22×C3C22×D3211yescharacteristic
741C2×D3—31no—
742C2×D3—34no—
743C2×D3—34no—
744C2×D3—31no—
745C2×D3—34no—
746C2×D3—34no—
747C2×D3—64no—
748C2×D3—62no—
749C2×D3—68no—
750C2×D3—91no—
751C2×D3—91no—
752C2×D3—94no—
753C2×D3—94no—
754C2×D3—124no—
755C2×D3—122no—
756C2×D3—124no—
757C2×D3—124no—
758C2×D3—124no—
759C2×D3—182no—
760C2×D3—188no—
761C2×D3—188no—
762C2×D3—188no—
763C2×D3—188no—
764C2×D3—244no—
765C2×D3—364no—
766C2×D3—362no—
767C2×D3—364no—
768C2×D3—368no—
769C2×D3—368no—
770C2×D3—368no—
771C3×C4—32no—
772C3×C4—32no—
773C3×C4—62no—
774C3×C4—92no—
775C3×C4—94no—
776C3×C4—94no—
777C3×C4C22×D3212yes—
778Dic3—34no—
779Dic3—34no—
780Dic3—34no—
781Dic3—32no—
782Dic3—64no—
783Dic3—92no—
784Dic3—94no—
785C32—21no—
786C32C2×#100411yescharacteristic, complemented
787C32D3×H(5,𝔽2)11yescharacteristic, complemented
788C23—91no—
789C23—94no—
790C23—94no—
791C23—94no—
792C23—94no—
793C23—92no—
794C23—274no—
795C23—278no—
796C23—364no—
797C23—1088no—
798C23C2×((C3⋊D3)⋊C3)⋊C212yescomplemented
799Q8—92no—
800Q8—92no—
801Q8—274no—
802D4—98no—
803D4—98no—
804D4—94no—
805D4—98no—
806D4—94no—
807D4—94no—
808D4—92no—
809D4—92no—
810D4—274no—
811D4—274no—
812D4—278no—
813D4—274no—
814D4—278no—
815D4C2×((C3⋊D3)⋊C3)⋊C214yescomplemented
816C2×C4—91no—
817C2×C4—94no—
818C2×C4—94no—
819C2×C4—92no—
820C2×C4—92no—
821C2×C4—94no—
822C2×C4—94no—
823C2×C4—274no—
824C2×C4—274no—
825C2×C4—274no—
826C2×C4—278no—
827C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
828C2×C3—21no—
829C2×C3—24no—
830C2×C3—31no—
831C2×C3—31no—
832C2×C3—64no—
833C2×C3—64no—
834C2×C3—61no—
835C2×C3—61no—
836C2×C3—61no—
837C2×C3—92no—
838C2×C3—124no—
839C2×C3—121no—
840C2×C3—184no—
841C2×C3—184no—
842C2×C3—181no—
843C2×C3—184no—
844C2×C3C23×D3211yescharacteristic
845D3—32no—
846D3—64no—
847D3—64no—
848D3—61no—
849D3—64no—
850D3—64no—
851D3—92no—
852D3—124no—
853D3—181no—
854D3—184no—
855D3—184no—
856C22—42no—
857C22—91no—
858C22—91no—
859C22—94no—
860C22—94no—
861C22—94no—
862C22—182no—
863C22—188no—
864C22—362no—
865C22—364no—
866C22—364no—
867C22—364no—
868C22—548no—
869C22—1088no—
870C22C22×((C3⋊D3)⋊C3)⋊C214yes—
871C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
872C4—92no—
873C4—94no—
874C4—94no—
875C4C22×((C3⋊D3)⋊C3)⋊C212yes—
876C3—31no—
877C3—31no—
878C3—61no—
879C3D3×#100411yescharacteristic
880C2—21no—
881C2—24no—
882C2—92no—
883C2—181no—
884C2—184no—
885C2—184no—
886C2—184no—
887C2C23×((C3⋊D3)⋊C3)⋊C211yescharacteristic
subgroupG/H
centerC2C23×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC2×H(3,𝔽3)C25
Frattini, socleC2×C3C23×D32
FittingC2×D4×H(3,𝔽3)C22
hypercenterC2×D4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×H(5,𝔽2)
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11722664C2semidirect
2. #64361⋊C3C2semidirect
3. C2×D4×(C3⋊D3)⋊C3C2semidirect
4. #11722545C2semidirect
5. C2×#88676C2semidirect
6. #11722507C2semidirect
7. #11722506C2semidirect
8. #11722504C2semidirect
9. D4×((C3⋊D3)⋊C3)⋊C2C2semidirect
10. #11722492C2semidirect
11. #11722490C2semidirect
14. C23×(C3⋊D3)⋊C3C22semidirect
15. C22×((C3⋊D3)⋊C3)⋊C2C22semidirect
16. C2×D4×H(3,𝔽3)C22semidirect
17. C2×#6235C22semidirect
18. #88744C22semidirect
19. D4×#272C22semidirect
20. #88740C22semidirect
21. C2×#638⋊C3C22semidirect
22. C2×#638⋊C3C22semidirect
23. #3830⋊C3C22semidirect
24. D4×(C3⋊D3)⋊C3C22semidirect
25. D4×(C3⋊D3)⋊C3C22semidirect
26. D4×(C3⋊D3)⋊C3C22semidirect
27. #3828⋊C3C22semidirect
28. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
29. C2×C4×(C3⋊D3)⋊C3C22semidirect
30. #88677C22semidirect
31. #88676C22semidirect
32. #88676C22semidirect
33. #88676C22semidirect
34. #88676C22semidirect
35. #88676C22semidirect
36. C2×#6200C22semidirect
37. C2×#6198C22semidirect
38. #88672C22semidirect
39. #88671C22semidirect
40. #88671C22semidirect
41. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
42. #88655C22semidirect
43. #88654C22semidirect
44. #88654C22semidirect
45. C4×((C3⋊D3)⋊C3)⋊C2C22semidirect
46. #88652C22semidirect
47. #88650C22semidirect
48. #88649C22semidirect
49. #88648C22semidirect
50. #88648C22semidirect
51. ((C3⋊D3)⋊C3)⋊Q8C22semidirect
52. #64361D3semidirect
53. C2×D4×C3⋊D3D3semidirect
75. C23×H(3,𝔽3)C23semidirect
76. C22×#272C23semidirect
80. C22×(C3⋊D3)⋊C3C23semidirect
81. C22×(C3⋊D3)⋊C3C23semidirect
82. C22×(C3⋊D3)⋊C3C23semidirect
85. C2×((C3⋊D3)⋊C3)⋊C2C23semidirect
86. D4×H(3,𝔽3)C23semidirect
87. C2×C4×H(3,𝔽3)C23semidirect
88. #6235C23semidirect
89. #6235C23semidirect
90. C2×#1084C23semidirect
91. C4⋊#272C23semidirect
92. C4×#272C23semidirect
93. #6229C23semidirect
94. #638⋊C3C23semidirect
95. #638⋊C3C23semidirect
96. #638⋊C3C23semidirect
97. C2×(C3⋊Dic3)⋊C3C23semidirect
98. C2×(C3⋊Dic3)⋊C3C23semidirect
99. C4⋊((C3⋊D3)⋊C3)C23semidirect
100. C4⋊((C3⋊D3)⋊C3)C23semidirect
102. C4×(C3⋊D3)⋊C3C23semidirect
103. C4×(C3⋊D3)⋊C3C23semidirect
104. #634⋊C3C23semidirect
105. #6200C23semidirect
106. #6200C23semidirect
107. #6200C23semidirect
108. #6199C23semidirect
109. #6198C23semidirect
110. #6198C23semidirect
112. ((C3⋊D3)⋊C3)⋊C4C23semidirect
113. ((C3⋊D3)⋊C3)⋊C4C23semidirect
114. #6196C23semidirect
118. C23×C3⋊D3C2×D3semidirect
123. C2×C32×D4C2×D3semidirect
124. C2×C32×D4C2×D3semidirect
125. C2×#638C2×D3semidirect
126. C2×#638C2×D3semidirect
127. #3830C2×D3semidirect
128. D4×C3⋊D3C2×D3semidirect
129. D4×C3⋊D3C2×D3semidirect
130. D4×C3⋊D3C2×D3semidirect
131. #3828C2×D3semidirect
132. C2×C4⋊(C3⋊D3)C2×D3semidirect
133. C2×C4×C3⋊D3C2×D3semidirect
254. C23×C32C22×D3semidirect
255. C23×C32C22×D3semidirect
259. C22×C3⋊D3C22×D3semidirect
260. C22×C3⋊D3C22×D3semidirect
261. C22×C3⋊D3C22×D3semidirect
278. C32×D4C22×D3semidirect
279. C32×D4C22×D3semidirect
281. C2×C32×C4C22×D3semidirect
282. C2×C32×C4C22×D3semidirect
283. #638C22×D3semidirect
284. #638C22×D3semidirect
285. #638C22×D3semidirect
286. C2×C3⋊Dic3C22×D3semidirect
287. C2×C3⋊Dic3C22×D3semidirect
288. C4⋊(C3⋊D3)C22×D3semidirect
289. C4⋊(C3⋊D3)C22×D3semidirect
291. C4×C3⋊D3C22×D3semidirect
292. C4×C3⋊D3C22×D3semidirect
293. #634C22×D3semidirect
351. (C3⋊D3)⋊C3H(5,𝔽2)semidirect
529. H(3,𝔽3)C2×H(5,𝔽2)semidirect
672. C3⋊D3#1004semidirect
714. C2×D4((C3⋊D3)⋊C3)⋊C2semidirect
786. C32C2×#1004semidirect
787. C32D3×H(5,𝔽2)semidirect
798. C23C2×((C3⋊D3)⋊C3)⋊C2semidirect
815. D4C2×((C3⋊D3)⋊C3)⋊C2semidirect
827. C2×C4C2×((C3⋊D3)⋊C3)⋊C2semidirect

Maximal subgroups

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

subgroupindex
#117226642
#64361⋊C32
C2×D4×(C3⋊D3)⋊C32
#117225452
C2×#886762
#117225072
#117225062
#117225042
D4×((C3⋊D3)⋊C3)⋊C22
#117224922
#117224902
#105966753
D3×#10043