Finite Group Databasebeta

← #11796867

Subgroups — #11796867

Order 1152.

402 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 59 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
2#10593768C211yesmaximal, characteristic, complemented
3C2×#63544C211yesmaximal, characteristic, complemented
4#10590019C214yesmaximal, complemented
5#64306—21no—
6#64286—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#63769—21no—
16#63768C2212yescomplemented
17C2×C3×C3⋊C16—21no—
18#63544—21no—
19#63544C2212yescomplemented
20D3×#135—61no—
21C2×#798—61no—
22C2×C4×C3⋊D3D411yescharacteristic
23C3×#235—22no—
24#3811—41no—
25#3805—41no—
26#3802—21no—
27C4×D32—41no—
28#3798—41no—
29#3797—21no—
30#3796—22no—
31C22⋊#157—41no—
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×C412yes—
44#3715—22no—
45#3713C2×C412yes—
46C3×C3⋊C16—22no—
47#2145—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—
60C2×C3×C16—61no—
61C2×C3⋊C16—21no—
62#798—62no—
63#798—62no—
64C22×C3⋊D3D811yescharacteristic
65C2×D32—41no—
66C2×#157—42no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C3⋊Dic3SD1611yescharacteristic
69C4×C3⋊D3C22⋊C411yescharacteristic
70C4×C3⋊D3D811yescharacteristic
71C4×C3⋊D3SD1611yescharacteristic
72C4×C3⋊D3C2×D411yescharacteristic
73C3×#67—42no—
74C3×D12—22no—
75C3×C4×D3—42no—
76C3×Dic6—22no—
77#627—41no—
78#626—42no—
79#625—41no—
80#624—41no—
81D3×Dic3—42no—
82C32×C8C22⋊C411yescharacteristic
83C32×C8C2×D411yescharacteristic
84C3⋊(C3⋊C8)C22⋊C411yescharacteristic
85C3⋊(C3⋊C8)C22×C411yescharacteristic
86C2×#135—91no—
87C2×M32—91no—
88#427—91no—
89#360—94no—
90C3×#41—62no—
91#239—62no—
92D3×Q8—62no—
93#237—62no—
94#237—122no—
95D3×D4—62no—
96D3×D4—122no—
97#235—22no—
98#235—122no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—122no—
102C3×Q16—61no—
103C3×SD16—62no—
104C3×D8—61no—
105C2×C3×C8—21no—
106C2×C3×C8—21no—
107#216—62no—
108#215—62no—
109#214—62no—
110#213—62no—
111C2×C3⋊C8—61no—
112C2×C3⋊C8—61no—
113Dic12—21no—
114D24—21no—
115#204—22no—
116D3×C8—61no—
117D3×C8—61no—
118D3×C8—61no—
119D3×C8—61no—
120D3×C8—61no—
121D3×C8—61no—
122D3×C8—61no—
123D3×C8—61no—
124C3×C16—62no—
125C3⋊C16—22no—
126C22×C32#10211yescharacteristic
127C2×C3⋊D3—41no—
128C2×C3⋊D3#10211yescharacteristic
129C2×C3⋊D3C2×D811yescharacteristic
130C2×C3×D3—42no—
131D32—82no—
132#157—82no—
133C32×C4#10211yescharacteristic
134C32×C4C2×C22⋊C411yescharacteristic
135C3⋊Dic3#10211yescharacteristic
136C3⋊Dic3C2×SD1611yescharacteristic
137C3×Dic3—42no—
138C2×#41—181no—
139#135—61no—
140#135—92no—
141#135—92no—
142#135—181no—
143C2×Q16—91no—
144C2×SD16—181no—
145C2×D8—91no—
146C22×C8—91no—
147#117—181no—
148M32—92no—
149M32—181no—
150C2×C16—61no—
151#107—181no—
152#106—92no—
153C22×D3—61no—
154C22×D3—61no—
155C22×D3—122no—
156C3×Q8—62no—
157C3×D4—62no—
158C3×D4—122no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—122no—
162#67—42no—
163#67—122no—
164#67—122no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—122no—
168D12—22no—
169D12—122no—
170C4×D3—42no—
171C4×D3—61no—
172C4×D3—61no—
173C4×D3—61no—
174C4×D3—61no—
175C4×D3—61no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—61no—
179C4×D3—122no—
180C4×D3—122no—
181Dic6—22no—
182Dic6—122no—
183C3×C8—21no—
184C3×C8—21no—
185C3×C8—21no—
186C3×C8—21no—
187C3⋊C8—61no—
188C3⋊C8—61no—
189C3⋊C8—61no—
190C3⋊C8—61no—
191C2×C32—21no—
192C2×C32C2×#10211yescharacteristic
193C3⋊D3—21no—
194C3⋊D3—21no—
195C3×D3—82no—
196#41—62no—
197#41—182no—
198#41—361no—
199#41—361no—
200C2×Q8—181no—
201C2×D4—181no—
202C2×D4—361no—
203C22×C4—91no—
204C22×C4—361no—
205Q16—61no—
206Q16—92no—
207SD16—62no—
208SD16—182no—
209D8—61no—
210D8—92no—
211C2×C8—91no—
212C2×C8—91no—
213C2×C8—91no—
214C2×C8—91no—
215C2×C8—91no—
216C2×C8GO+(4,𝔽2)11yescharacteristic
217C4⋊C4—182no—
218C22⋊C4—361no—
219C42—361no—
220C16—62no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—122no—
224C2×D3—42no—
225C2×D3—61no—
226C2×D3—61no—
227C2×D3—61no—
228C2×D3—61no—
229C2×D3—122no—
230C2×D3—122no—
231C2×D3—244no—
232C3×C4—21no—
233C3×C4—21no—
234C3×C4—21no—
235C3×C4—21no—
236C3×C4—122no—
237Dic3—42no—
238Dic3—61no—
239Dic3—61no—
240Dic3—61no—
241Dic3—61no—
242C32#214511yescharacteristic, complemented, Sylow
243C23—91no—
244C23—361no—
245Q8—62no—
246Q8—361no—
247D4—62no—
248D4—122no—
249D4—361no—
250D4—362no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—122no—
257C2×C4—362no—
258C2×C4—361no—
259C2×C4—362no—
260C2×C4D32⋊C411yescharacteristic
261C8—91no—
262C8—91no—
263C8D32⋊C411yescharacteristic
264C8C2×GO+(4,𝔽2)11yescharacteristic
265C2×C3—22no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—41no—
269C2×C3—242no—
270D3—62no—
271D3—82no—
272D3—121no—
273D3—121no—
274D3—121no—
275C22—91no—
276C22—91no—
277C22—122no—
278C22—361no—
279C22—722no—
280C22#6372911yescharacteristic
281C4—91no—
282C4—91no—
283C4—122no—
284C4—722no—
285C4#6372911yescharacteristic
286C4C2×D32⋊C411yescharacteristic
287C3—21no—
288C3—21no—
289C2—21no—
290C2—181no—
291C2—181no—
292C2—242no—
293C2C2×#6372911yescharacteristic
subgroupG/H
centerC4#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)
hypocenterC32#2145
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10593768C2semidirect
3. C2×#63544C2semidirect
4. #10590019C2semidirect
9. #63822C4semidirect
12. #63802C4semidirect
13. #63797C4semidirect
16. #63768C22semidirect
19. #63544C22semidirect
242. C32#2145semidirect

Maximal subgroups

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

subgroupindex
#105946842
#105937682
C2×#635442
#105900192
#21459