Finite Group Databasebeta

← #11898307

Subgroups — #11898307

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5567C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic
3#10592726C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591618C212yesmaximal, complemented
6#10591565C212yesmaximal, complemented
7#10590549C212yesmaximal, complemented
8#10590458C212yesmaximal, complemented
9#10590373C211yesmaximal, characteristic, complemented
10#10590363C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83685—31nomaximal
13#79637—31nomaximal
14C2×#3799—21no—
15C32×C4×Q8C2211yescharacteristic
16C2×#3755C2212yes—
17#64083C2211yescharacteristic
18C3×#944C2212yes—
19C2×C3×#215C2211yescharacteristic
20C3×#889—22no—
21C3×#887C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×#870—21no—
24C3×#869C2211yescharacteristic
25C3×C4×Dic6—21no—
26C3×C4×Dic6C2211yescharacteristic
27#63911C2212yes—
28#63910—22no—
29#63909—21no—
30#63894C2212yes—
31C2×#3717C2212yes—
32C2×#3717C2212yes—
33C2×#3715C2212yes—
34#63636C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
36C3×#835C2211yescharacteristic
37C3×#809C2211yescharacteristic
38C3×#808C2211yescharacteristic
39C3×C4×C3⋊C8C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2212yes—
41#63565C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5577—31no—
45#5567D311yescharacteristic, complemented
46#5553—31no—
47C3×C4×SD16—31no—
48#5175—32no—
49#5085—32no—
50#5085—31no—
51#5083—31no—
52#5083—32no—
53#5027—31no—
54#5027—31no—
55#5027—32no—
56#5027—61no—
57C4×#215—32no—
58C4×#215D311yescharacteristic, complemented
59Q8×C3⋊C8—31no—
60#5019—31no—
61#4852—32no—
62#4818—32no—
63#4762—32no—
64#4693—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×#626—22no—
75C2×#626—22no—
76C2×#624—22no—
77#3799—44no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C42—21no—
81C32×C42C2311yescharacteristic
82#3755—42no—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×#215—22no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4D412yes—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3722—22no—
99#3717—24no—
100#3717—42no—
101#3715—42no—
102#3392—91noSylow
103C2×#239—61no—
104C2×#235—61no—
105C2×C3×SD16—31no—
106C3×C4⋊Q8—32no—
107C3×C4⋊Q8—31no—
108C3×#125—61no—
109C3×#125—62no—
110C3×C4×Q8—21no—
111C3×C4×Q8—31no—
112C3×C4×Q8—32no—
113C3×C4×Q8—61no—
114C3×C4×Q8C2×D311yescharacteristic
115C3×C4×Q8C2×D311yescharacteristic
116C3×C4×D4—31no—
117#944C2×D312yes—
118C2×#215—32no—
119C2×#215—32no—
120C2×#215—32no—
121C2×#215—32no—
122C2×#215—32no—
123C2×#215—62no—
124C2×#215C2×D311yescharacteristic
125#940—32no—
126C2×#214—32no—
127#930—61no—
128C2×#204—32no—
129C2×#204—32no—
130#895—62no—
131#895—61no—
132#893—32no—
133#889—22no—
134#887C2×D312yes—
135#884—62no—
136#874—32no—
137#874—31no—
138#874—31no—
139#874—61no—
140C4×D12—32no—
141C4×D12C2×D311yescharacteristic
142#870—21no—
143#869C2×D311yescharacteristic
144C4×Dic6—21no—
145C4×Dic6C2×D311yescharacteristic
146C3×#106—31no—
147C3×#103—31no—
148C3×#102—31no—
149C3×C4×C8—31no—
150#835—32no—
151#835C2×D311yescharacteristic
152Dic3⋊C8—32no—
153C8×Dic3—32no—
154#810—32no—
155#809—32no—
156#809—32no—
157#809—62no—
158#809C2×D311yescharacteristic
159#808C2×D311yescharacteristic
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—32no—
163C4⋊(C3⋊C8)—61no—
164C4×C3⋊C8—32no—
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊D3—22no—
167C22×C3×D3—21no—
168C32×Q8—21no—
169C32×Q8—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C4⋊(C3⋊D3)—22no—
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)—42no—
178C4⋊(C3⋊D3)—81no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—21no—
184C3×D12—21no—
185C3×C4×D3—42no—
186C3×Dic6—22no—
187C3×Dic6—22no—
188C3×Dic6SD1614yescomplemented
189#626—44no—
190#626—82no—
191#624—44no—
192C3⋊(C3⋊C8)—22no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8#4112yescomplemented
195#557—31no—
196#550—91no—
197#492—91no—
198#492—92no—
199#461—92no—
200#461—91no—
201#460—92no—
202#460—91no—
203C8×Q8—91no—
204C4×SD16—31no—
205C4×SD16—92no—
206C2×C3×Q8—21no—
207C2×C3×Q8—31no—
208C2×C3×Q8—32no—
209C2×C3×Q8C22×D311yescharacteristic
210C2×C3×Q8C22×D311yescharacteristic
211C2×C3×D4—31no—
212C22×C3×C4—61no—
213C2×#67—62no—
214C2×#67—62no—
215#239—124no—
216#235—124no—
217C2×D12—32no—
218C2×D12—32no—
219C2×D12—62no—
220C2×D12—62no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—62no—
224C2×D12—61no—
225C2×D12—61no—
226C2×D12—121no—
227C2×D12—121no—
228C2×D12C22×D311yescharacteristic
229C2×C4×D3—21no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×Dic6#6711yescharacteristic
233C2×Dic6C22×D312yes—
234C3×SD16—62no—
235C2×C3×C8—31no—
236C2×C3×C8—31no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—41no—
244C3×C4⋊C4—62no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C22⋊C4—61no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—21no—
255C3×C42—32no—
256C3×C42—41no—
257C3×C42—62no—
258C3×C42C22×D311yescharacteristic
259C3×C42C22×D311yescharacteristic
260#215—22no—
261#215—64no—
262#215—122no—
263#215—122no—
264#215—122no—
265#215—122no—
266#215—124no—
267#214—122no—
268(C2×D3)⋊C4—21no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—62no—
271C4⋊Dic3—21no—
272C4⋊Dic3—21no—
273C4⋊Dic3#6711yescharacteristic
274C4⋊Dic3C22×D311yescharacteristic
275Dic3⋊C4—22no—
276Dic3⋊C4—22no—
277Dic3⋊C4—22no—
278Dic3⋊C4#6712yes—
279C4×Dic3—22no—
280C4×Dic3C22×D312yes—
281C2×C3⋊C8—32no—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—62no—
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D311yescharacteristic
286#204—64no—
287#204—122no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—42no—
290C2×C3⋊D3—42no—
291C2×C3⋊D3—42no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C2×C3×D3—41no—
295C32×C4—21no—
296C32×C4—41no—
297C32×C4—41no—
298C32×C4C2×SD1612yes—
299C32×C4C2×#4111yescharacteristic
300C32×C4H(5,𝔽2)11yescharacteristic
301C3×Dic3—22no—
302C3×Dic3—42no—
303C3×Dic3—41no—
304C3×Dic3C2×SD1614yes—
305C2×#41—181no—
306C2×SD16—31no—
307C2×SD16—92no—
308C2×SD16—92no—
309C2×SD16—92no—
310C2×SD16—92no—
311C4⋊Q8—32no—
312C4⋊Q8—31no—
313#127—92no—
314#127—91no—
315#125—61no—
316#125—62no—
317#121—182no—
318#121—181no—
319C4×Q8—31no—
320C4×Q8—32no—
321C4×Q8—61no—
322C4×Q8D3211yescharacteristic
323C4×D4—31no—
324C4×D4—92no—
325#106—31no—
326C4⋊C8—92no—
327C4⋊C8—91no—
328#103—31no—
329#103—92no—
330#102—31no—
331#102—92no—
332C4×C8—31no—
333C4×C8—92no—
334C23×C3—61no—
335C22×D3—21no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—122no—
339C3×Q8—22no—
340C3×Q8—21no—
341C3×Q8—21no—
342C3×Q8—21no—
343C3×Q8—21no—
344C3×Q8—34no—
345C3×Q8—41no—
346C3×Q8—62no—
347C3×Q8—62no—
348C3×D4—61no—
349C3×D4—61no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—32no—
358C2×C3×C4—32no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—62no—
362C2×C3×C4—61no—
363C2×C3×C4—122no—
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370#67—124no—
371#67—242no—
372C2×Dic3—21no—
373C2×Dic3—22no—
374C2×Dic3C2×#6712yes—
375C2×Dic3C2×#6712yes—
376D12—21no—
377D12—21no—
378D12—62no—
379D12—62no—
380D12—62no—
381D12—62no—
382D12—122no—
383D12—122no—
384D12—124no—
385D12—122no—
386D12—122no—
387D12—242no—
388D12—241no—
389D12—241no—
390D12—242no—
391D12—242no—
392C4×D3—42no—
393C4×D3—124no—
394C4×D3—124no—
395Dic6—22no—
396Dic6—22no—
397Dic6#21514yescomplemented
398C3×C8—32no—
399C3×C8—61no—
400C3⋊C8—21no—
401C3⋊C8—62no—
402C3⋊C8—62no—
403C3⋊C8—122no—
404C3⋊C8#23512yescomplemented
405C2×C32#55011yescharacteristic
406C2×C32C22×SD1611yescharacteristic
407C2×C32#57711yescharacteristic
408C3⋊D3—82no—
409C3×D3—81no—
410#41—364no—
411C2×Q8—31no—
412C2×Q8—32no—
413C2×Q8C2×D3211yescharacteristic
414C2×D4—31no—
415C2×D4—92no—
416C2×D4—182no—
417C2×D4—182no—
418C2×D4—181no—
419C2×D4—181no—
420C22×C4—61no—
421C22×C4—182no—
422SD16—62no—
423SD16—184no—
424SD16—362no—
425SD16—362no—
426SD16—362no—
427C2×C8—31no—
428C2×C8—31no—
429C2×C8—92no—
430C4⋊C4—21no—
431C4⋊C4—32no—
432C4⋊C4—31no—
433C4⋊C4—31no—
434C4⋊C4—62no—
435C4⋊C4—62no—
436C4⋊C4—62no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4C2×D3211yescharacteristic
440C22⋊C4—61no—
441C22⋊C4—182no—
442C42—21no—
443C42—32no—
444C42—62no—
445C42C2×D3211yescharacteristic
446C22×C3—21no—
447C22×C3—121no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3C2×D3×D411yescharacteristic
451C22×C3C22×#6711yescharacteristic
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—41no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—242no—
462C2×D3—242no—
463C2×D3—242no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—22no—
469C3×C4—34no—
470C3×C4—41no—
471C3×C4—42no—
472C3×C4—41no—
473C3×C4—41no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—62no—
477C3×C4—81no—
478C3×C4—121no—
479C3×C4—122no—
480C3×C4D3×SD1612yes—
481C3×C4C2×#21512yes—
482C3×C4C2×#23511yescharacteristic
483C3×C4D3×#4111yescharacteristic
484C3×C4#100911yescharacteristic
485C3×C4#100911yescharacteristic
486Dic3—22no—
487Dic3—41no—
488Dic3—42no—
489Dic3C2×#21514yes—
490C32#339211yescharacteristic, complemented, Sylow
491C23—61no—
492C23—182no—
493Q8—21no—
494Q8—21no—
495Q8—34no—
496Q8—62no—
497Q8—62no—
498D4—61no—
499D4—61no—
500D4—182no—
501D4—182no—
502D4—364no—
503D4—362no—
504D4—721no—
505D4—722no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—62no—
511C2×C4—61no—
512C2×C4—122no—
513C2×C4—364no—
514C2×C4D3×#6711yescharacteristic
515C2×C4D3×#6711yescharacteristic
516C2×C4C22×D3211yescharacteristic
517C8—32no—
518C8—61no—
519C8—182no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—241no—
524C2×C3#555311yescharacteristic
525C2×C3C2×D3×SD1611yescharacteristic
526C2×C3#577011yescharacteristic
527C2×C3C22×#21511yescharacteristic
528C2×C3#583411yescharacteristic
529C2×C3#583711yescharacteristic
530D3—81no—
531D3—242no—
532D3—242no—
533D3—482no—
534C22—121no—
535C22—121no—
536C22—121no—
537C22—362no—
538C22—362no—
539C22—362no—
540C22C2×D3×#6711yescharacteristic
541C4—21no—
542C4—34no—
543C4—41no—
544C4—41no—
545C4—62no—
546C4—122no—
547C4—121no—
548C4D3×#21512yes—
549C4D3×#23511yescharacteristic
550C4#6430811yescharacteristic
551C3—21no—
552C3#7963711yescharacteristic, complemented
553C3#8368511yescharacteristic, complemented
554C2—241no—
555C2—722no—
556C2#1059500711yescharacteristic
557C2C2×D3×#21511yescharacteristic
558C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10593902C2
hypercenterC4×Q8D32
hypocenterC32#3392
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5567C2semidirect
3. #10592726C2semidirect
4. C3×C4×#215C2semidirect
5. #10591618C2semidirect
6. #10591565C2semidirect
7. #10590549C2semidirect
8. #10590458C2semidirect
9. #10590373C2semidirect
10. #10590363C2semidirect
11. C3⋊C8×Dic6C2semidirect
45. #5567D3semidirect
58. C4×#215D3semidirect
188. C3×Dic6SD16semidirect
194. C3×C3⋊C8#41semidirect
397. Dic6#215semidirect
404. C3⋊C8#235semidirect
490. C32#3392semidirect
552. C3#79637semidirect
553. C3#83685semidirect

Maximal subgroups

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

subgroupindex
C3×#55672
#105939022
#105927262
C3×C4×#2152
#105916182
#105915652
#105905492
#105904582
#105903732
#105903632
C3⋊C8×Dic62
#836853
#796373