Finite Group Databasebeta

← #11887571

Subgroups — #11887571

Order 1152.

889 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic6×D12C211yesmaximal, characteristic, complemented
2#10593895C211yesmaximal, characteristic
3#10592380C211yesmaximal, characteristic, complemented
4C3×C4×#204C211yesmaximal, characteristic, complemented
5C3×C8×D12C211yesmaximal, characteristic, complemented
6#10590825C212yesmaximal, complemented
7#10590822C212yesmaximal, complemented
8#10590674C212yesmaximal, complemented
9D3×#816C212yesmaximal, complemented
10#10590365C211yesmaximal, characteristic, complemented
11#10590301C211yesmaximal, characteristic, complemented
12#79678—31nomaximal
13#79447—31nomaximal
14C2×#3795—21no—
15C2×D3×Dic6C2212yes—
16#64078C2211yescharacteristic
17#64078C2211yescharacteristic
18C2×C3×#204C2211yescharacteristic
19C2×C3×D3×C8C2212yes—
20C3×C4×D12C2211yescharacteristic
21C3×C4×D12C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23#63918—21no—
24#63908C2212yes—
25#63893—22no—
26Dic3×D12—21no—
27#63891—22no—
28D3×C4⋊Dic3C2212yes—
29#63857—21no—
30#63857C2212yes—
31C2×#3716C2212yes—
32C32×C4×C8C2211yescharacteristic
33#63643C2212yes—
34#63643C2212yes—
35C3×#821C2211yescharacteristic
36C3×(C2×D3)⋊C8C2212yes—
37C3×#817C2211yescharacteristic
38C3×#816C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63573C2212yes—
41#63567C2212yes—
42#63566C2212yes—
43Q8×D12—31no—
44#5555—31no—
45#5551—31no—
46D4×Dic6—31no—
47C3×C4×SD16—31no—
48C3×C8×D4—31no—
49#5170—32no—
50#5114—32no—
51C2×#816—32no—
52#5020—31no—
53#5019—31no—
54#4862—32no—
55#4851—31no—
56#4841—31no—
57D3×#103—32no—
58#4778—32no—
59#4738—32no—
60#4721—32no—
61C4×#204D311yescharacteristic, complemented
62C8×D12D311yescharacteristic, complemented
63#4681—31no—
64#4681—31no—
65#4681—61no—
66C2×#634—21no—
67C2×#634C2312yes—
68C2×C3×D12D411yescharacteristic
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×C4×D3C2312yes—
72C2×C3×Dic6C2311yescharacteristic
73C2×#627—22no—
74C2×#625—22no—
75C2×D3×Dic3—22no—
76C2×D3×Dic3—22no—
77#3795—44no—
78D3×Dic6—24no—
79D3×Dic6—42no—
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C32×C42C2311yescharacteristic
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87C3×(C2×D3)⋊C4—21no—
88C3×(C2×D3)⋊C4D412yes—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×C4×Dic3—21no—
94C2×C3×C3⋊C8C2312yes—
95C3×#204—22no—
96C3×D3×C8—42no—
97Dic3⋊Dic3—22no—
98Dic3⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101#3716—42no—
102#3298—91noSylow
103C2×D3×Q8—32no—
104C2×#237—61no—
105C2×#235—61no—
106C22×Dic6—32no—
107C2×C3×SD16—31no—
108C22×C3×C8—32no—
109C3×C4×Q8—31no—
110C3×C4×D4—31no—
111C3×C4×D4—31no—
112#938—32no—
113D4×Dic3—61no—
114C2×#214—32no—
115#930—32no—
116C2×C4⋊Dic3—32no—
117#924—32no—
118#924—61no—
119C2×#204—32no—
120C2×#204C2×D311yescharacteristic
121C2×D3×C8C2×D312yes—
122#897—32no—
123#897—61no—
124#897—62no—
125D3×C4⋊C4—32no—
126#888—61no—
127#886—62no—
128#883—62no—
129#878—62no—
130C4×D12—61no—
131C4×D12C2×D311yescharacteristic
132C4×D12C2×D311yescharacteristic
133#869—31no—
134#869—31no—
135#869—31no—
136#869—31no—
137#869—61no—
138#869—61no—
139#869—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×#106—31no—
142C3×C4⋊C8—31no—
143C3×#103—31no—
144C3×#102—31no—
145C3×C22⋊C8—32no—
146C3×C4×C8—21no—
147C3×C4×C8C2×D311yescharacteristic
148C3×C4×C8C2×D311yescharacteristic
149#835—32no—
150#821C2×D311yescharacteristic
151(C2×D3)⋊C8C2×D312yes—
152#817—32no—
153#817C2×D311yescharacteristic
154#816—32no—
155#816—32no—
156#816—32no—
157#816—32no—
158#816—32no—
159#816—32no—
160#816—62no—
161#816—62no—
162#816C2×D311yescharacteristic
163#810—32no—
164#808—32no—
165C4⋊(C3⋊C8)C2×D311yescharacteristic
166C22×C3×D3—21no—
167C22×C3×D3C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173#634—22no—
174#634—22no—
175#634—42no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3C2×D412yes—
180C3×D12—21no—
181C3×D12—21no—
182C3×D12SD1614yescomplemented
183C3×C4×D3—22no—
184C3×C4×D3—22no—
185C3×C4×D3—42no—
186C3×Dic6—21no—
187C3×Dic6#4112yescomplemented
188#627—44no—
189#625—44no—
190D3×Dic3—44no—
191D3×Dic3—44no—
192C32×C8—21no—
193C32×C8—21no—
194C3×C3⋊C8—22no—
195D4×Q8—91no—
196#547—91no—
197#487—91no—
198#483—92no—
199#475—91no—
200#465—92no—
201#461—91no—
202#448—92no—
203C4×SD16—31no—
204C8×D4—31no—
205C2×#103—92no—
206C2×C3×Q8—31no—
207C2×C3×D4—31no—
208C2×C3×D4—31no—
209C22×C3×C4—32no—
210C22×C3×C4—61no—
211C2×#67—62no—
212C2×#67—62no—
213C22×Dic3—62no—
214C22×Dic3—62no—
215D3×Q8—64no—
216D3×Q8—122no—
217#237—124no—
218#235—124no—
219C2×D12D1211yescharacteristic
220C2×D12C22×D311yescharacteristic
221C2×C4×D3—21no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3C22×D312yes—
225C2×Dic6—32no—
226C2×Dic6—32no—
227C2×Dic6—62no—
228C2×Dic6—64no—
229C2×Dic6—62no—
230C2×Dic6—61no—
231C2×Dic6—61no—
232C2×Dic6—62no—
233C2×Dic6—121no—
234C2×Dic6—122no—
235C2×Dic6C22×D311yescharacteristic
236C3×SD16—62no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—32no—
240C2×C3×C8—122no—
241C2×C3×C8C22×D311yescharacteristic
242C2×C3×C8C22×D311yescharacteristic
243C2×C3×C8C22×D311yescharacteristic
244C2×C3×C8C22×D311yescharacteristic
245C3×C4⋊C4—31no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—31no—
248C3×C4⋊C4—61no—
249C3×C22⋊C4—32no—
250C3×C22⋊C4—61no—
251C3×C42—21no—
252C3×C42—61no—
253C3×C42C22×D311yescharacteristic
254C3×C42C22×D311yescharacteristic
255#217—62no—
256#217—62no—
257#214—122no—
258(C2×D3)⋊C4—21no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4D1212yes—
262C4⋊Dic3—32no—
263C4⋊Dic3—32no—
264C4⋊Dic3—62no—
265C4⋊Dic3—62no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272C4⋊Dic3—62no—
273C4⋊Dic3—121no—
274C4⋊Dic3—121no—
275C4⋊Dic3—121no—
276C4⋊Dic3D1211yescharacteristic
277C4⋊Dic3C22×D311yescharacteristic
278C4⋊Dic3C22×D311yescharacteristic
279Dic3⋊C4—21no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282C4×Dic3—21no—
283C2×C3⋊C8C22×D312yes—
284#204—22no—
285#204—122no—
286D3×C8—42no—
287C22×C32C22×D411yescharacteristic
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3C2×SD1614yes—
294C32×C4—21no—
295C32×C4C2×SD1612yes—
296C32×C4C2×#4111yescharacteristic
297C32×C4H(5,𝔽2)11yescharacteristic
298C3⋊Dic3—42no—
299C3⋊Dic3—42no—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3—41no—
303C3×Dic3—41no—
304C2×#41—181no—
305C22×Q8—92no—
306C2×SD16—31no—
307C2×SD16—92no—
308C22×C8—32no—
309C4⋊Q8—91no—
310C4⋊Q8—91no—
311C4⋊Q8—181no—
312#123—182no—
313C22⋊Q8—92no—
314C22⋊Q8—182no—
315C22⋊Q8—181no—
316#121—92no—
317C4×Q8—31no—
318C4×D4—31no—
319C4×D4—31no—
320C4×D4—181no—
321C2×C4⋊C4—92no—
322#106—31no—
323#106—92no—
324C4⋊C8—31no—
325#103—31no—
326#103—92no—
327#103—92no—
328#103—92no—
329#103—92no—
330#102—31no—
331C22⋊C8—32no—
332C4×C8D3211yescharacteristic
333C23×C3—32no—
334C23×C3—61no—
335C22×D3—21no—
336C22×D3C2×D1212yes—
337C3×Q8—32no—
338C3×Q8—61no—
339C3×D4—34no—
340C3×D4—61no—
341C3×D4—61no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—32no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—122no—
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—124no—
359#67—124no—
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—122no—
368C2×Dic3—122no—
369C2×Dic3—124no—
370C2×Dic3—124no—
371C2×Dic3C2×D1212yes—
372D12—21no—
373D12—21no—
374D12#20414yescomplemented
375C4×D3—22no—
376C4×D3—22no—
377C4×D3—42no—
378C4×D3—124no—
379C4×D3—124no—
380Dic6—21no—
381Dic6—62no—
382Dic6—62no—
383Dic6—62no—
384Dic6—62no—
385Dic6—122no—
386Dic6—122no—
387Dic6—124no—
388Dic6—124no—
389Dic6—122no—
390Dic6—122no—
391Dic6—242no—
392Dic6#23512yescomplemented
393C3×C8—21no—
394C3×C8—21no—
395C3×C8—21no—
396C3×C8—21no—
397C3×C8—41no—
398C3×C8—41no—
399C3×C8—62no—
400C3⋊C8—22no—
401C2×C32#54611yescharacteristic
402C2×C32C22×SD1611yescharacteristic
403C2×C32#57811yescharacteristic
404C3×D3—24no—
405C3×D3—81no—
406#41—364no—
407C2×Q8—31no—
408C2×Q8—92no—
409C2×Q8—182no—
410C2×Q8—184no—
411C2×Q8—181no—
412C2×Q8—362no—
413C2×D4—31no—
414C2×D4—31no—
415C2×D4—182no—
416C22×C4—32no—
417C22×C4—61no—
418C22×C4—182no—
419C22×C4—182no—
420SD16—62no—
421SD16—362no—
422C2×C8—32no—
423C2×C8—122no—
424C2×C8C2×D3211yescharacteristic
425C2×C8C2×D3211yescharacteristic
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—31no—
429C4⋊C4—61no—
430C4⋊C4—92no—
431C4⋊C4—182no—
432C4⋊C4—182no—
433C4⋊C4—181no—
434C4⋊C4—181no—
435C4⋊C4—181no—
436C22⋊C4—32no—
437C22⋊C4—61no—
438C22⋊C4—182no—
439C22⋊C4—182no—
440C42—61no—
441C42C2×D3211yescharacteristic
442C22×C3—21no—
443C22×C3—34no—
444C22×C3—62no—
445C22×C3—62no—
446C22×C3—121no—
447C22×C3—121no—
448C22×C3—121no—
449C22×C3C22×D1211yescharacteristic
450C22×C3C2×D3×D411yescharacteristic
451C2×D3—22no—
452C2×D3—22no—
453C2×D3—41no—
454C2×D3—41no—
455C2×D3—41no—
456C2×D3C2×#20414yes—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—62no—
464C3×C4—62no—
465C3×C4—121no—
466C3×C4—121no—
467C3×C4C2×#20412yes—
468C3×C4D3×SD1612yes—
469C3×C4C2×#23511yescharacteristic
470C3×C4#100411yescharacteristic
471C3×C4D3×#4111yescharacteristic
472C3×C4#100911yescharacteristic
473Dic3—22no—
474Dic3—22no—
475Dic3—41no—
476Dic3—41no—
477Dic3—122no—
478Dic3—122no—
479Dic3—122no—
480Dic3—122no—
481Dic3—242no—
482Dic3—242no—
483C32#329811yescharacteristic, complemented, Sylow
484C23—32no—
485C23—61no—
486Q8—32no—
487Q8—61no—
488Q8—182no—
489Q8—182no—
490Q8—364no—
491Q8—362no—
492D4—34no—
493D4—61no—
494D4—61no—
495D4—364no—
496C2×C4—32no—
497C2×C4—61no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—122no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—364no—
506C2×C4—364no—
507C2×C4D3×D1211yescharacteristic
508C2×C4D3×D1211yescharacteristic
509C2×C4C22×D3211yescharacteristic
510C8—21no—
511C8—21no—
512C8—62no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—64no—
517C2×C3—241no—
518C2×C3#555011yescharacteristic
519C2×C3#555411yescharacteristic
520C2×C3C22×#20411yescharacteristic
521C2×C3#575311yescharacteristic
522C2×C3C2×D3×SD1611yescharacteristic
523C2×C3#577111yescharacteristic
524D3—24no—
525D3—81no—
526C22—34no—
527C22—62no—
528C22—62no—
529C22—121no—
530C22—121no—
531C22—121no—
532C22C2×D3×D1211yescharacteristic
533C4—21no—
534C4—62no—
535C4—62no—
536C4—121no—
537C4—121no—
538C4—362no—
539C4—362no—
540C4D3×#20412yes—
541C4D3×#23511yescharacteristic
542C4#6430711yescharacteristic
543C3—21no—
544C3#7944711yescharacteristic, complemented
545C3#7967811yescharacteristic, complemented
546C2—64no—
547C2—241no—
548C2#1059400311yescharacteristic
549C2C2×D3×#20411yescharacteristic
550C2#1059469211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593895C2
hypercenterC4×C8D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. Dic6×D12C2semidirect
3. #10592380C2semidirect
4. C3×C4×#204C2semidirect
5. C3×C8×D12C2semidirect
6. #10590825C2semidirect
7. #10590822C2semidirect
8. #10590674C2semidirect
9. D3×#816C2semidirect
10. #10590365C2semidirect
11. #10590301C2semidirect
61. C4×#204D3semidirect
62. C8×D12D3semidirect
182. C3×D12SD16semidirect
187. C3×Dic6#41semidirect
374. D12#204semidirect
392. Dic6#235semidirect
483. C32#3298semidirect
544. C3#79447semidirect
545. C3#79678semidirect

Maximal subgroups

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

subgroupindex
Dic6×D122
#105938952
#105923802
C3×C4×#2042
C3×C8×D122
#105908252
#105908222
#105906742
D3×#8162
#105903652
#105903012
#796783
#794473