Finite Group Databasebeta

← #11796827

Subgroups — #11796827

Order 1152.

529 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 529 conjugacy classes of subgroups — too many to draw. Only its 92 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×#106C211yesmaximal, characteristic, complemented
3#10590625C211yesmaximal, characteristic, complemented
4C3×#4488C212yesmaximal, complemented
5#10589124C212yesmaximal, complemented
6D3×#360—32nomaximal
7#64306—21no—
8C2×C8×C3⋊D3C2211yescharacteristic
9C4⋊C4×C3⋊D3—21no—
10C3×#904C2212yes—
11#63822—21no—
12#63810C412yescomplemented
13#63809—21no—
14#63802C411yescharacteristic, complemented
15#63797C411yescharacteristic, complemented
16#63796—21no—
17C32×#106C2211yescharacteristic, complemented
18#63644C2211yescharacteristic, complemented
19#63635—21no—
20C3×#812C2212yescomplemented
21#63544—21no—
22#63542—21no—
23D3×#135—32no—
24D3×M32—32no—
25D3×#106—32no—
26D3×#106—61no—
27C3×#360—32no—
28#4566—32no—
29#4518—32no—
30#4488D312yescomplemented
31C2×C4×C3⋊D3—41no—
32C2×C4×C3⋊D3D411yescharacteristic
33C3×#235—22no—
34#3811—41no—
35#3805—41no—
36#3802—21no—
37C4×D32—41no—
38#3798—41no—
39#3797—21no—
40#3796—22no—
41C2×C32×C8C2311yescharacteristic
42C32×C4⋊C4—21no—
43C4⋊(C3⋊Dic3)—21no—
44#3750—41no—
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C8×C3⋊D3C2×C411yescharacteristic
47C8×C3⋊D3C2×C411yescharacteristic
48C8×C3⋊D3D411yescharacteristic
49C8×C3⋊D3D411yescharacteristic
50C3×Dic12C2×C412yescomplemented
51C3×D24C2×C412yescomplemented
52C3×#204—22no—
53#3718—21no—
54#3715—22no—
55#3713—21no—
56C3×C3⋊C16—22no—
57C2×#360—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—
70D3×C4⋊C4—62no—
71D3×C4⋊C4—62no—
72C3×M32—32no—
73C3×#106—21no—
74C3×#106C2×D312yescomplemented
75#817—32no—
76#817—61no—
77#812C2×D312yescomplemented
78#808—62no—
79#808—62no—
80#798—62no—
81D3×C16—62no—
82C22×C3⋊D3D811yescharacteristic
83C2×D32—41no—
84C2×C32×C4—41no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3D811yescharacteristic
88C4×C3⋊D3—82no—
89C4×C3⋊D3C22⋊C411yescharacteristic
90C4×C3⋊D3C22⋊C411yescharacteristic
91C4×C3⋊D3SD1611yescharacteristic
92C4×C3⋊D3SD1611yescharacteristic
93C3×#67—42no—
94C3×D12—22no—
95C3×C4×D3—42no—
96C3×Dic6—22no—
97#627—41no—
98#626—42no—
99#625—41no—
100#624—41no—
101D3×Dic3—42no—
102C32×C8C22×C411yescharacteristic
103C32×C8C2×D411yescharacteristic
104C3⋊(C3⋊C8)C22⋊C411yescharacteristic
105C3⋊(C3⋊C8)C22⋊C411yescharacteristic
106C2×#135—91no—
107C2×M32—91no—
108C2×#106—91no—
109#360—32no—
110#360—92no—
111C3×#41—62no—
112#239—62no—
113D3×Q8—62no—
114#237—62no—
115#237—122no—
116D3×D4—62no—
117D3×D4—122no—
118#235—22no—
119#235—122no—
120C2×C4×D3—32no—
121C2×C4×D3—61no—
122C2×C4×D3—122no—
123C2×C4×D3—122no—
124C2×C4×D3—122no—
125C3×Q16—32no—
126C3×SD16—62no—
127C3×D8—32no—
128C2×C3×C8—21no—
129C2×C3×C8C22×D312yes—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—22no—
132#216—62no—
133#215—62no—
134#214—62no—
135#213—62no—
136C4⋊Dic3—62no—
137C4⋊Dic3—62no—
138Dic3⋊C4—122no—
139Dic3⋊C4—122no—
140C2×C3⋊C8—32no—
141C2×C3⋊C8—61no—
142Dic12C4×D312yescomplemented
143D24C4×D312yescomplemented
144#204—22no—
145D3×C8—32no—
146D3×C8—32no—
147D3×C8—32no—
148D3×C8—32no—
149D3×C8—61no—
150D3×C8—61no—
151D3×C8—61no—
152D3×C8—61no—
153C3×C16—62no—
154C3⋊C16—22no—
155C22×C32C2×D811yescharacteristic
156C2×C3⋊D3—22no—
157C2×C3⋊D3#10211yescharacteristic
158C2×C3⋊D3#10211yescharacteristic
159C2×C3×D3—42no—
160D32—82no—
161C32×C4—81no—
162C32×C4C2×C22⋊C411yescharacteristic
163C32×C4C2×SD1611yescharacteristic
164C3⋊Dic3—81no—
165C3⋊Dic3#10211yescharacteristic
166C3⋊Dic3#10211yescharacteristic
167C3×Dic3—42no—
168C2×#41—181no—
169#135—32no—
170#135—92no—
171#135—181no—
172#135—181no—
173C2×Q16—91no—
174C2×SD16—181no—
175C2×D8—91no—
176C22×C8—91no—
177C2×C4⋊C4—181no—
178M32—32no—
179M32—181no—
180C2×C16—181no—
181#106—91no—
182#106—181no—
183#106D3211yescharacteristic, complemented
184C22×D3—32no—
185C22×D3—61no—
186C22×D3—122no—
187C3×Q8—62no—
188C3×D4—62no—
189C3×D4—122no—
190C2×C3×C4—21no—
191C2×C3×C4—42no—
192C2×C3×C4—42no—
193C2×C3×C4—122no—
194C2×C3×C4D3×D412yes—
195#67—42no—
196#67—122no—
197#67—122no—
198C2×Dic3—32no—
199C2×Dic3—61no—
200C2×Dic3—122no—
201C2×Dic3—122no—
202C2×Dic3—122no—
203D12—22no—
204D12—122no—
205C4×D3—32no—
206C4×D3—32no—
207C4×D3—32no—
208C4×D3—32no—
209C4×D3—42no—
210C4×D3—61no—
211C4×D3—61no—
212C4×D3—61no—
213C4×D3—61no—
214C4×D3—122no—
215C4×D3—122no—
216C4×D3—244no—
217C4×D3—244no—
218Dic6—22no—
219Dic6—122no—
220C3×C8—21no—
221C3×C8—21no—
222C3×C8C2×C4×D312yes—
223C3×C8D3×D412yes—
224C3⋊C8—32no—
225C3⋊C8—32no—
226C3⋊C8—61no—
227C3⋊C8—61no—
228C2×C32—21no—
229C2×C32C2×#10211yescharacteristic
230C3⋊D3—21no—
231C3⋊D3#36012yescomplemented
232C3×D3—82no—
233#41—62no—
234#41—182no—
235#41—361no—
236#41—361no—
237C2×Q8—181no—
238C2×D4—181no—
239C2×D4—361no—
240C22×C4—91no—
241C22×C4—361no—
242C22×C4—361no—
243Q16—32no—
244Q16—181no—
245SD16—62no—
246SD16—182no—
247D8—32no—
248D8—181no—
249C2×C8—91no—
250C2×C8—91no—
251C2×C8—91no—
252C2×C8—91no—
253C2×C8—91no—
254C2×C8C2×D3211yescharacteristic
255C4⋊C4—21no—
256C4⋊C4—181no—
257C4⋊C4—361no—
258C16—62no—
259C22×C3—21no—
260C22×C3—122no—
261C22×C3D3×D812yes—
262C2×D3—32no—
263C2×D3—32no—
264C2×D3—42no—
265C2×D3—61no—
266C2×D3—61no—
267C2×D3—64no—
268C2×D3—64no—
269C2×D3—244no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—82no—
273C3×C4—82no—
274C3×C4—122no—
275C3×C4D3×C22⋊C412yes—
276C3×C4D3×SD1612yes—
277Dic3—32no—
278Dic3—32no—
279Dic3—42no—
280Dic3—61no—
281Dic3—61no—
282Dic3—242no—
283Dic3—242no—
284C32C2×#36011yescharacteristic, complemented, Sylow
285C23—91no—
286C23—361no—
287Q8—62no—
288Q8—361no—
289D4—62no—
290D4—122no—
291D4—361no—
292D4—362no—
293C2×C4—41no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—122no—
300C2×C4—362no—
301C2×C4—361no—
302C2×C4—361no—
303C2×C4—722no—
304C2×C4#381111yescharacteristic
305C8—91no—
306C8—91no—
307C8C4×D3211yescharacteristic
308C8#380211yescharacteristic
309C2×C3—22no—
310C2×C3—22no—
311C2×C3—21no—
312C2×C3—242no—
313C2×C3D3×#10212yes—
314D3—34no—
315D3—62no—
316D3—62no—
317D3—62no—
318D3—82no—
319C22—91no—
320C22—91no—
321C22—122no—
322C22—182no—
323C22—722no—
324C22#6392611yescharacteristic
325C4—81no—
326C4—91no—
327C4—91no—
328C4—122no—
329C4—721no—
330C4#6392111yescharacteristic
331C4#6394011yescharacteristic
332C3—21no—
333C3D3×#36012yescomplemented
334C2—21no—
335C2—92no—
336C2—181no—
337C2—242no—
338C2#1059059311yescharacteristic
subgroupG/H
centerC2#10590593
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#106C22
socleC2×C32C2×#102
prime radical#10594684C2
cosocleC2×C32×C8C23
hypercenter#106D32
hypocenterC32C2×#360
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#106C2semidirect
3. #10590625C2semidirect
4. C3×#4488C2semidirect
5. #10589124C2semidirect
12. #63810C4semidirect
14. #63802C4semidirect
15. #63797C4semidirect
17. C32×#106C22semidirect
18. #63644C22semidirect
20. C3×#812C22semidirect
30. #4488D3semidirect
50. C3×Dic12C2×C4semidirect
51. C3×D24C2×C4semidirect
74. C3×#106C2×D3semidirect
77. #812C2×D3semidirect
142. Dic12C4×D3semidirect
143. D24C4×D3semidirect
183. #106D32semidirect
231. C3⋊D3#360semidirect
284. C32C2×#360semidirect
333. C3D3×#360semidirect

Maximal subgroups

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

subgroupindex
#105946842
C3⋊D3×#1062
#105906252
C3×#44882
#105891242
D3×#3603