Finite Group Databasebeta

← #11796838

Subgroups — #11796838

Order 1152.

410 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 61 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
2C2×#63768C211yesmaximal, characteristic, complemented
3#10590625C211yesmaximal, characteristic, complemented
4#10590019C214yesmaximal, complemented
5#64306—21no—
6C2×C4⋊#157—21no—
7C2×C8×C3⋊D3C2211yescharacteristic
8C3×#904—21no—
9#63822C412yescomplemented
10#63810—21no—
11#63809C2212yes—
12#63802C411yescharacteristic, complemented
13#63797C411yescharacteristic, complemented
14#63796—21no—
15#63768—21no—
16#63768C2212yescomplemented
17C3×#812—21no—
18#63544C2212yescomplemented
19#63542—21no—
20D3×#135—61no—
21D3×M32—61no—
22C22×#157—41no—
23C2×C4×C3⋊D3D411yescharacteristic
24C3×#235—22no—
25#3811—41no—
26#3805—41no—
27#3802—21no—
28C4×D32—41no—
29#3798—41no—
30#3797—21no—
31#3796—22no—
32C4⋊#157—22no—
33C4⋊#157—41no—
34C2×C32×C8D411yescharacteristic
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36C8×C3⋊D3C2×C411yescharacteristic
37C8×C3⋊D3D411yescharacteristic
38C8×C3⋊D3D411yescharacteristic
39C8×C3⋊D3C2311yescharacteristic
40C3×Dic12—21no—
41C3×D24—21no—
42C3×#204—22no—
43#3718C2×C412yescomplemented
44#3715—22no—
45#3713C2×C412yescomplemented
46C3×C3⋊C16—22no—
47C2×#360—91nomaximal, Sylow
48D3×#41—62no—
49C3×#135—61no—
50#950—62no—
51#919—61no—
52D3×Q16—61no—
53#916—62no—
54D3×SD16—62no—
55#912—61no—
56D3×D8—61no—
57#904—21no—
58C2×D3×C8—61no—
59C2×D3×C8—61no—
60C3×M32—61no—
61#812—21no—
62#798—62no—
63D3×C16—62no—
64C22×C3⋊D3D811yescharacteristic
65C2×D32—41no—
66C2×#157—42no—
67C2×#157—82no—
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C3⋊Dic3SD1611yescharacteristic
70C4×C3⋊D3C22⋊C411yescharacteristic
71C4×C3⋊D3D811yescharacteristic
72C4×C3⋊D3SD1611yescharacteristic
73C4×C3⋊D3C2×D411yescharacteristic
74C3×#67—42no—
75C3×D12—22no—
76C3×C4×D3—42no—
77C3×Dic6—22no—
78#627—41no—
79#626—42no—
80#625—41no—
81#624—41no—
82D3×Dic3—42no—
83C32×C8C22⋊C411yescharacteristic
84C32×C8C2×D411yescharacteristic
85C3⋊(C3⋊C8)C22⋊C411yescharacteristic
86C3⋊(C3⋊C8)C22×C411yescharacteristic
87C2×#135—91no—
88C2×M32—91no—
89C2×#106—91no—
90#360—94no—
91C3×#41—62no—
92#239—62no—
93D3×Q8—62no—
94#237—62no—
95#237—122no—
96D3×D4—62no—
97D3×D4—122no—
98#235—22no—
99#235—122no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—122no—
103C3×Q16—61no—
104C3×SD16—62no—
105C3×D8—61no—
106C2×C3×C8—21no—
107C2×C3×C8—21no—
108#216—62no—
109#215—62no—
110#214—62no—
111#213—62no—
112C2×C3⋊C8—61no—
113C2×C3⋊C8—61no—
114Dic12—21no—
115D24—21no—
116#204—22no—
117D3×C8—61no—
118D3×C8—61no—
119D3×C8—61no—
120D3×C8—61no—
121D3×C8—61no—
122D3×C8—61no—
123D3×C8—61no—
124D3×C8—61no—
125C3×C16—62no—
126C3⋊C16—22no—
127C22×C32#10211yescharacteristic
128C2×C3⋊D3—22no—
129C2×C3⋊D3#10211yescharacteristic
130C2×C3⋊D3C2×D811yescharacteristic
131C2×C3×D3—42no—
132D32—82no—
133#157—82no—
134C32×C4#10211yescharacteristic
135C32×C4C2×C22⋊C411yescharacteristic
136C3⋊Dic3#10211yescharacteristic
137C3⋊Dic3C2×SD1611yescharacteristic
138C3×Dic3—42no—
139C2×#41—181no—
140#135—61no—
141#135—92no—
142#135—92no—
143#135—181no—
144C2×Q16—91no—
145C2×SD16—181no—
146C2×D8—91no—
147C22×C8—91no—
148C2×C4⋊C4—181no—
149M32—61no—
150M32—92no—
151C2×C16—181no—
152#106—92no—
153#106—181no—
154C22×D3—61no—
155C22×D3—61no—
156C22×D3—122no—
157C3×Q8—62no—
158C3×D4—62no—
159C3×D4—122no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—122no—
163#67—42no—
164#67—122no—
165#67—122no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—122no—
169D12—22no—
170D12—122no—
171C4×D3—42no—
172C4×D3—61no—
173C4×D3—61no—
174C4×D3—61no—
175C4×D3—61no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—61no—
179C4×D3—61no—
180C4×D3—122no—
181C4×D3—122no—
182Dic6—22no—
183Dic6—122no—
184C3×C8—21no—
185C3×C8—21no—
186C3×C8—21no—
187C3×C8—21no—
188C3⋊C8—61no—
189C3⋊C8—61no—
190C3⋊C8—61no—
191C3⋊C8—61no—
192C2×C32—21no—
193C2×C32C2×#10211yescharacteristic
194C3⋊D3—21no—
195C3⋊D3#36012yescomplemented
196C3×D3—82no—
197#41—62no—
198#41—182no—
199#41—361no—
200#41—361no—
201C2×Q8—181no—
202C2×D4—181no—
203C2×D4—361no—
204C22×C4—91no—
205C22×C4—361no—
206C22×C4—361no—
207Q16—61no—
208Q16—92no—
209SD16—62no—
210SD16—182no—
211D8—61no—
212D8—92no—
213C2×C8—91no—
214C2×C8—91no—
215C2×C8—91no—
216C2×C8—91no—
217C2×C8—91no—
218C2×C8GO+(4,𝔽2)11yescharacteristic
219C4⋊C4—182no—
220C4⋊C4—361no—
221C16—62no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—122no—
225C2×D3—42no—
226C2×D3—61no—
227C2×D3—61no—
228C2×D3—61no—
229C2×D3—61no—
230C2×D3—122no—
231C2×D3—122no—
232C2×D3—244no—
233C3×C4—21no—
234C3×C4—21no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—122no—
238Dic3—42no—
239Dic3—61no—
240Dic3—61no—
241Dic3—61no—
242Dic3—61no—
243C32C2×#36011yescharacteristic, complemented, Sylow
244C23—91no—
245C23—361no—
246Q8—62no—
247Q8—361no—
248D4—62no—
249D4—122no—
250D4—361no—
251D4—362no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—122no—
258C2×C4—362no—
259C2×C4—361no—
260C2×C4—362no—
261C2×C4—722no—
262C2×C4D32⋊C411yescharacteristic
263C8—91no—
264C8—91no—
265C8D32⋊C411yescharacteristic
266C8C2×GO+(4,𝔽2)11yescharacteristic
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—41no—
270C2×C3—41no—
271C2×C3—242no—
272D3—62no—
273D3—62no—
274D3—82no—
275D3—121no—
276D3—121no—
277C22—91no—
278C22—91no—
279C22—122no—
280C22—182no—
281C22—722no—
282C22#6372911yescharacteristic
283C4—91no—
284C4—91no—
285C4—122no—
286C4—722no—
287C4#6372911yescharacteristic
288C4C2×D32⋊C411yescharacteristic
289C3—21no—
290C3—21no—
291C2—21no—
292C2—92no—
293C2—181no—
294C2—242no—
295C2C2×#6372911yescharacteristic
subgroupG/H
centerC2C2×#63729
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC8C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32C2×#102
prime radical#10594684C2
cosocleC8×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32C2×#360
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63768C2semidirect
3. #10590625C2semidirect
4. #10590019C2semidirect
9. #63822C4semidirect
12. #63802C4semidirect
13. #63797C4semidirect
16. #63768C22semidirect
18. #63544C22semidirect
43. #3718C2×C4semidirect
45. #3713C2×C4semidirect
195. C3⋊D3#360semidirect
243. C32C2×#360semidirect

Maximal subgroups

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

subgroupindex
#105946842
C2×#637682
#105906252
#105900192
C2×#3609