Finite Group Databasebeta

← #11776588

Subgroups — #11776588

Order 1152.

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

normal subgroups only

This group has 636 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#10594008C211yesmaximal, characteristic
2#10593730C211yesmaximal, characteristic, complemented
3#10590299C211yesmaximal, characteristic, complemented
4#10590037C214yesmaximal, complemented
5C2×#3802—21no—
6C2×#3802—21no—
7C2×#3802C412yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×#874—21no—
10#63914—21no—
11#63914C412yes—
12#63914C2212yes—
13#63778—21no—
14#63777—21no—
15C4⋊#622C2212yescomplemented
16C3×#803—21no—
17#63572C2212yescomplemented
18#63557—21no—
19D3×#127—61no—
20#4705—61no—
21C22×D32—22no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×D12—22no—
26C2×C3×D12—22no—
27C2×C3×D12—22no—
28C2×#625—22no—
29C2×#625—22no—
30C2×#625C2×C414yes—
31#3802—44no—
32#3802—44no—
33#3802—44no—
34C2×#622—22no—
35C32×C42D411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C2×C3×C3⋊C8—22no—
40#1555—91nomaximal, Sylow
41C2×D3×D4—62no—
42C2×D3×D4—62no—
43C2×D3×D4—62no—
44C3×#127—61no—
45#940—62no—
46#940—62no—
47#940—62no—
48#874—21no—
49C42×D3—61no—
50C42×D3—61no—
51C3×#97—61no—
52(C2×D3)⋊C8—62no—
53Dic3⋊C8—62no—
54#803—21no—
55C22×C3⋊D3C22⋊C411yescharacteristic
56C22×C3×D3—24no—
57C2×D32—44no—
58C2×D32—44no—
59C2×D32—44no—
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C4×C3⋊D3—22no—
67C4×C3⋊D3—22no—
68C4×C3⋊D3—22no—
69C3×D12—44no—
70C3×D12—44no—
71C3×D12—44no—
72#625—44no—
73#625—44no—
74#625—44no—
75#622—42no—
76C3×C3⋊C8—42no—
77C2×#127—91no—
78#432—91no—
79#432—91no—
80#331—94no—
81C23×D3—64no—
82C2×C3×D4—62no—
83C2×C3×D4—62no—
84C2×C3×D4—62no—
85C2×#67—64no—
86C2×#67—64no—
87C2×#67—64no—
88D3×D4—128no—
89D3×D4—128no—
90D3×D4—128no—
91C2×D12—22no—
92C2×D12—22no—
93C2×D12—22no—
94C2×C4×D3—61no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×C3×C8—62no—
101C3×C42—21no—
102C3×C42—21no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C2×C3⋊C8—22no—
110C22×C32C2×C22⋊C411yescharacteristic
111C2×C3⋊D3—21no—
112C2×C3⋊D3—21no—
113C2×C3⋊D3#10012yes—
114C2×C3×D3—44no—
115C2×C3×D3—44no—
116C2×C3×D3—44no—
117D32—88no—
118C32×C4—21no—
119C32×C4—21no—
120C32×C4AGL(1,ℤ/8)12yes—
121C3⋊Dic3—21no—
122C3⋊Dic3—21no—
123C3⋊Dic3AGL(1,ℤ/8)12yes—
124C22×D4—92no—
125C22×D4—181no—
126C22×D4—181no—
127#127—61no—
128#127—92no—
129#127—92no—
130#127—181no—
131C2×C42—91no—
132C4⋊C8—92no—
133C4⋊C8—92no—
134C22⋊C8—181no—
135C22⋊C8—181no—
136#97—61no—
137#97—181no—
138C23×C3—64no—
139C22×D3—24no—
140C22×D3—61no—
141C22×D3—61no—
142C22×D3—128no—
143C22×D3—128no—
144C22×D3—128no—
145C3×D4—124no—
146C3×D4—124no—
147C3×D4—124no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154#67—128no—
155#67—128no—
156#67—128no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163D12—44no—
164D12—44no—
165D12—44no—
166C4×D3—64no—
167C4×D3—64no—
168C4×D3—64no—
169C4×D3—122no—
170C4×D3—122no—
171C4×D3—122no—
172C3×C8—122no—
173C3⋊C8—42no—
174C2×C32C2×#10011yescharacteristic
175C2×C32#41811yescharacteristic
176C2×C32#41811yescharacteristic
177C3⋊D3—22no—
178C3×D3—84no—
179C24—182no—
180C2×D4—62no—
181C2×D4—62no—
182C2×D4—62no—
183C2×D4—94no—
184C2×D4—182no—
185C2×D4—182no—
186C2×D4—364no—
187C2×D4—364no—
188C2×D4—364no—
189C22×C4—91no—
190C22×C4—91no—
191C22×C4—91no—
192C2×C8—62no—
193C2×C8—182no—
194C42—91no—
195C42—91no—
196C42—91no—
197C42GO+(4,𝔽2)11yescharacteristic
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—124no—
201C22×C3—124no—
202C22×C3—124no—
203C2×D3—44no—
204C2×D3—44no—
205C2×D3—44no—
206C2×D3—62no—
207C2×D3—62no—
208C2×D3—62no—
209C2×D3—62no—
210C2×D3—121no—
211C2×D3—121no—
212C2×D3—2416no—
213C3×C4—22no—
214C3×C4—22no—
215C3×C4—22no—
216C3×C4—22no—
217C3×C4—41no—
218C3×C4—41no—
219Dic3—62no—
220Dic3—62no—
221Dic3—62no—
222Dic3—62no—
223Dic3—121no—
224Dic3—121no—
225C32#155511yescharacteristic, complemented, Sylow
226C23—64no—
227C23—91no—
228C23—364no—
229C23—364no—
230C23—364no—
231D4—124no—
232D4—124no—
233D4—124no—
234D4—364no—
235D4—364no—
236D4—364no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4—91no—
240C2×C4—182no—
241C2×C4—182no—
242C2×C4—182no—
243C2×C4D32⋊C411yescharacteristic
244C2×C4D32⋊C411yescharacteristic
245C2×C4C2×GO+(4,𝔽2)11yescharacteristic
246C8—122no—
247C8—362no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—244no—
255D3—64no—
256D3—84no—
257D3—122no—
258C22—92no—
259C22—124no—
260C22—124no—
261C22—124no—
262C22—181no—
263C22—181no—
264C22—728no—
265C22C2×D32⋊C411yescharacteristic
266C4—21no—
267C4—21no—
268C4—92no—
269C4—181no—
270C4—181no—
271C4#6422412yes—
272C3—21no—
273C3—21no—
274C2—182no—
275C2—244no—
276C2#1059331211yescharacteristic
277C2#1059331811yescharacteristic
278C2#1059336311yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10594008C2
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1555
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593730C2semidirect
3. #10590299C2semidirect
4. #10590037C2semidirect
15. C4⋊#622C22semidirect
17. #63572C22semidirect
225. C32#1555semidirect

Maximal subgroups

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

subgroupindex
#105940082
#105937302
#105902992
#105900372
#15559