Finite Group Databasebeta

← #11796864

Subgroups — #11796864

Order 1152.

493 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 493 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594684C211yesmaximal, characteristic
2C3⋊D3×M32C211yesmaximal, characteristic, complemented
3#10590712C211yesmaximal, characteristic, complemented
4C3×#4518C212yesmaximal, complemented
5#10589123C212yesmaximal, complemented
6#69251—32nomaximal
7#64306—21no—
8C2×C8×C3⋊D3C2211yescharacteristic
9C3×#904C2212yes—
10#63849—21no—
11#63822—21no—
12#63810C412yescomplemented
13#63809—21no—
14#63802C411yescharacteristic, complemented
15#63797C411yescharacteristic, complemented
16#63796—21no—
17C32×M32C2211yescharacteristic, complemented
18#63639C2211yescharacteristic, complemented
19#63625—21no—
20C16×C3⋊D3—21no—
21C3×#817C2212yescomplemented
22#63576—21no—
23D3×#135—32no—
24D3×M32—32no—
25D3×M32—61no—
26#4860—32no—
27C3×#360—32no—
28#4566—32no—
29#4518D312yescomplemented
30#4488—32no—
31C2×C4×C3⋊D3D411yescharacteristic
32C3×#235—22no—
33#3811—41no—
34#3805—41no—
35#3802—21no—
36C4×D32—41no—
37#3798—41no—
38#3797—21no—
39#3796—22no—
40C2×C32×C8C2311yescharacteristic
41C2×C3⋊(C3⋊C8)D411yescharacteristic
42C8×C3⋊D3C2×C411yescharacteristic
43C8×C3⋊D3C2×C411yescharacteristic
44C8×C3⋊D3D411yescharacteristic
45C8×C3⋊D3D411yescharacteristic
46C3×C4⋊Dic3—22no—
47C3×Dic12C2×C412yes—
48C3×D24C2×C412yes—
49C3×#204—22no—
50#3722—41no—
51Dic32—41no—
52#3718—21no—
53#3715—22no—
54#3713—21no—
55C32×C16—21no—
56C3⋊(C3⋊C16)—21no—
57#2145—91noSylow
58D3×#41—62no—
59C3×#135—32no—
60#950—62no—
61#919—32no—
62D3×Q16—32no—
63#916—62no—
64D3×SD16—62no—
65#912—32no—
66D3×D8—32no—
67#904C2×D312yes—
68C2×D3×C8—32no—
69C2×D3×C8—61no—
70#892—62no—
71C3×M32—21no—
72C3×M32C2×D312yescomplemented
73C3×#106—32no—
74#817C2×D312yescomplemented
75#812—32no—
76#812—61no—
77#807—62no—
78#798—62no—
79#798—62no—
80D3×C16—62no—
81D3×C16—62no—
82C22×C3⋊D3D811yescharacteristic
83C2×D32—41no—
84C2×C32×C4C2×D411yescharacteristic
85C2×C3⋊Dic3D811yescharacteristic
86C4×C3⋊D3C22⋊C411yescharacteristic
87C4×C3⋊D3C22⋊C411yescharacteristic
88C4×C3⋊D3SD1611yescharacteristic
89C4×C3⋊D3SD1611yescharacteristic
90C3×#67—42no—
91C2×C3×Dic3—42no—
92C3×D12—22no—
93C3×C4×D3—42no—
94C3×Dic6—22no—
95#627—41no—
96#626—42no—
97#625—41no—
98#624—41no—
99D3×Dic3—42no—
100C32×C8C22×C411yescharacteristic
101C32×C8C2×D411yescharacteristic
102C3⋊(C3⋊C8)C22⋊C411yescharacteristic
103C3⋊(C3⋊C8)C22⋊C411yescharacteristic
104C2×#135—91no—
105C2×M32—91no—
106#427—91no—
107#360—32no—
108#360—92no—
109C3×#41—62no—
110#239—62no—
111D3×Q8—62no—
112#237—62no—
113#237—122no—
114D3×D4—62no—
115D3×D4—122no—
116#235—22no—
117#235—122no—
118C2×C4×D3—32no—
119C2×C4×D3—61no—
120C2×C4×D3—122no—
121C3×Q16—32no—
122C3×SD16—62no—
123C3×D8—32no—
124C2×C3×C8—21no—
125C2×C3×C8C22×D312yes—
126C3×C4⋊C4—62no—
127#216—62no—
128#215—62no—
129#214—62no—
130#213—62no—
131(C2×D3)⋊C4—122no—
132C4⋊Dic3—22no—
133C4×Dic3—122no—
134C2×C3⋊C8—32no—
135C2×C3⋊C8—61no—
136Dic12C4×D312yes—
137D24C4×D312yes—
138#204—22no—
139D3×C8—32no—
140D3×C8—32no—
141D3×C8—32no—
142D3×C8—32no—
143D3×C8—61no—
144D3×C8—61no—
145D3×C8—61no—
146D3×C8—61no—
147C3×C16—22no—
148C3×C16—22no—
149C3⋊C16—62no—
150C3⋊C16—62no—
151C22×C32C2×D811yescharacteristic
152C2×C3⋊D3—41no—
153C2×C3⋊D3#10211yescharacteristic
154C2×C3⋊D3#10211yescharacteristic
155C2×C3×D3—42no—
156D32—82no—
157C32×C4C2×C22⋊C411yescharacteristic
158C32×C4C2×SD1611yescharacteristic
159C3⋊Dic3#10211yescharacteristic
160C3⋊Dic3#10211yescharacteristic
161C3×Dic3—42no—
162C3×Dic3—82no—
163C2×#41—181no—
164#135—32no—
165#135—92no—
166#135—181no—
167#135—181no—
168C2×Q16—91no—
169C2×SD16—181no—
170C2×D8—91no—
171C22×C8—91no—
172#117—181no—
173M32—91no—
174M32—181no—
175M32D3211yescharacteristic, complemented
176C2×C16—181no—
177#107—181no—
178#106—32no—
179C22×D3—32no—
180C22×D3—61no—
181C22×D3—122no—
182C3×Q8—62no—
183C3×D4—62no—
184C3×D4—122no—
185C2×C3×C4—21no—
186C2×C3×C4—122no—
187C2×C3×C4—122no—
188C2×C3×C4D3×D412yes—
189#67—42no—
190#67—122no—
191#67—122no—
192C2×Dic3—32no—
193C2×Dic3—42no—
194C2×Dic3—61no—
195C2×Dic3—122no—
196D12—22no—
197D12—122no—
198C4×D3—32no—
199C4×D3—32no—
200C4×D3—32no—
201C4×D3—32no—
202C4×D3—42no—
203C4×D3—61no—
204C4×D3—61no—
205C4×D3—61no—
206C4×D3—61no—
207C4×D3—122no—
208C4×D3—122no—
209Dic6—22no—
210Dic6—122no—
211C3×C8—21no—
212C3×C8—21no—
213C3×C8C2×C4×D312yes—
214C3×C8D3×D412yes—
215C3⋊C8—32no—
216C3⋊C8—32no—
217C3⋊C8—61no—
218C3⋊C8—61no—
219C2×C32—21no—
220C2×C32C2×#10211yescharacteristic
221C3⋊D3—21no—
222C3⋊D3—21no—
223C3×D3—82no—
224#41—62no—
225#41—182no—
226#41—361no—
227#41—361no—
228C2×Q8—181no—
229C2×D4—181no—
230C2×D4—361no—
231C22×C4—91no—
232C22×C4—361no—
233Q16—32no—
234Q16—181no—
235SD16—62no—
236SD16—182no—
237D8—32no—
238D8—181no—
239C2×C8—91no—
240C2×C8—91no—
241C2×C8—91no—
242C2×C8—91no—
243C2×C8—91no—
244C2×C8C2×D3211yescharacteristic
245C4⋊C4—62no—
246C22⋊C4—361no—
247C42—361no—
248C16—21no—
249C16—181no—
250C22×C3—21no—
251C22×C3—122no—
252C22×C3D3×D812yes—
253C2×D3—32no—
254C2×D3—32no—
255C2×D3—42no—
256C2×D3—61no—
257C2×D3—61no—
258C2×D3—122no—
259C2×D3—122no—
260C2×D3—244no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—122no—
264C3×C4—242no—
265C3×C4D3×C22⋊C412yes—
266C3×C4D3×SD1612yes—
267Dic3—32no—
268Dic3—32no—
269Dic3—42no—
270Dic3—61no—
271Dic3—61no—
272Dic3—82no—
273C32#214511yescharacteristic, complemented, Sylow
274C23—91no—
275C23—361no—
276Q8—62no—
277Q8—361no—
278D4—62no—
279D4—122no—
280D4—361no—
281D4—362no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—122no—
288C2×C4—122no—
289C2×C4—362no—
290C2×C4—361no—
291C2×C4#380211yescharacteristic
292C8—91no—
293C8—91no—
294C8C4×D3211yescharacteristic
295C8#381111yescharacteristic
296C2×C3—22no—
297C2×C3—21no—
298C2×C3—41no—
299C2×C3—242no—
300C2×C3D3×#10212yes—
301D3—62no—
302D3—62no—
303D3—62no—
304D3—82no—
305D3—121no—
306C22—91no—
307C22—91no—
308C22—122no—
309C22—361no—
310C22—722no—
311C22#6379711yescharacteristic
312C4—91no—
313C4—91no—
314C4—122no—
315C4—242no—
316C4#6379611yescharacteristic
317C4#6392111yescharacteristic
318C3—21no—
319C3#6925112yescomplemented
320C2—21no—
321C2—181no—
322C2—181no—
323C2—242no—
324C2#1059094011yescharacteristic
subgroupG/H
centerC2#10590940
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32C2×#102
prime radical#10594684C2
cosocleC2×C32×C8C23
hypercenterM32D32
hypocenterC32#2145
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×M32C2semidirect
3. #10590712C2semidirect
4. C3×#4518C2semidirect
5. #10589123C2semidirect
12. #63810C4semidirect
14. #63802C4semidirect
15. #63797C4semidirect
17. C32×M32C22semidirect
18. #63639C22semidirect
21. C3×#817C22semidirect
29. #4518D3semidirect
72. C3×M32C2×D3semidirect
74. #817C2×D3semidirect
175. M32D32semidirect
273. C32#2145semidirect
319. C3#69251semidirect

Maximal subgroups

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

subgroupindex
#105946842
C3⋊D3×M322
#105907122
C3×#45182
#105891232
#692513