Finite Group Databasebeta

← #11796366

Subgroups — #11796366

Order 1152.

568 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 54 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#10595948C211yesmaximal, characteristic
2#10593792C212yesmaximal, complemented
3#10590143C212yesmaximal, complemented
4#10590142C212yesmaximal, complemented
5C2×#3828C411yescharacteristic, complemented
6C2×#3828C2211yescharacteristic
7#64286—22no—
8C2×C32×C42C411yescharacteristic, complemented
9#64139—22no—
10#64084C411yescharacteristic, complemented
11#64084C2211yescharacteristic
12#64083C2211yescharacteristic
13C4×C4⋊(C3⋊D3)—22no—
14#64078C411yescharacteristic, complemented
15#63786—22no—
16#63774C2214yes—
17#5477—62no—
18C22×C32×C4—21no—
19C22×C32×C4C2×C411yescharacteristic
20C2×#638—21no—
21C2×#638D412yes—
22#3828—41no—
23#3828—41no—
24#3828—41no—
25#3828—41no—
26C2×C4⋊(C3⋊D3)—22no—
27C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
28C2×C4⋊(C3⋊D3)C2311yescharacteristic
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3D412yes—
31C2×#634C2×C411yescharacteristic
32C2×#634C2×C411yescharacteristic
33C22⋊#157—24no—
34C4⋊#157—42no—
35C4×#157—42no—
36C32×C42—21no—
37C32×C42C2×C411yescharacteristic
38C32×C42C2×C411yescharacteristic
39#3752—22no—
40#3752—22no—
41C4⋊(C3⋊Dic3)—22no—
42#2126—91nomaximal, Sylow
43C2×#235—62no—
44C2×#235—62no—
45C2×C3×C42—22no—
46#930—68no—
47#875—62no—
48#875—62no—
49#874—62no—
50C4×D12—68no—
51#869—62no—
52C23×C32C22⋊C411yescharacteristic
53C22×C3⋊D3—21no—
54C22×C3⋊D3C2×D412yes—
55C2×#157—44no—
56C2×C32×C4—21no—
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—42no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22×C411yescharacteristic
63#638—42no—
64#638—42no—
65C2×C3⋊Dic3—21no—
66C2×C3⋊Dic3C22⋊C412yes—
67C4⋊(C3⋊D3)—41no—
68C4⋊(C3⋊D3)—41no—
69C4⋊(C3⋊D3)—44no—
70C4×C3⋊D3—22no—
71C4×C3⋊D3—22no—
72C4×C3⋊D3—41no—
73C4×C3⋊D3—41no—
74#634—41no—
75#634—41no—
76#532—91no—
77#410—92no—
78#354—92no—
79#353—92no—
80C22×C3×C4—24no—
81C22×C3×C4—22no—
82C2×#67—64no—
83C2×#67—64no—
84#235—124no—
85#235—124no—
86#235—124no—
87#235—124no—
88C2×D12—62no—
89C2×D12—62no—
90C2×D12—68no—
91C2×C4×D3—64no—
92C2×C4×D3—64no—
93C2×Dic6—62no—
94C2×Dic6—62no—
95C3×C42—24no—
96C3×C42—22no—
97C3×C42—22no—
98(C2×D3)⋊C4—68no—
99(C2×D3)⋊C4—68no—
100C4⋊Dic3—68no—
101C22×C32—21no—
102C22×C32—41no—
103C22×C32C2×C22⋊C411yescharacteristic
104C2×C3⋊D3—22no—
105C2×C3⋊D3—42no—
106C2×C3⋊D3—42no—
107C2×C3⋊D3—41no—
108#157—84no—
109C32×C4—22no—
110C32×C4—21no—
111C32×C4—41no—
112C32×C4#9911yescharacteristic
113C32×C4#9911yescharacteristic
114C3⋊Dic3—22no—
115C3⋊Dic3—41no—
116C2×#41—91no—
117C2×#41—91no—
118C4⋊Q8—91no—
119#127—91no—
120#124—91no—
121#124—91no—
122#121—182no—
123C4×D4—182no—
124#117—182no—
125C2×C42#15711yescharacteristic, complemented
126#99—94no—
127#99—182no—
128C23×C3—22no—
129C22×D3—64no—
130C22×D3—64no—
131C2×C3×C4—24no—
132C2×C3×C4—24no—
133C2×C3×C4—24no—
134C2×C3×C4—24no—
135C2×C3×C4—22no—
136C2×C3×C4—22no—
137C2×C3×C4—48no—
138#67—128no—
139#67—128no—
140C2×Dic3—64no—
141C2×Dic3—64no—
142D12—1216no—
143D12—124no—
144D12—124no—
145C4×D3—124no—
146C4×D3—124no—
147C4×D3—124no—
148C4×D3—124no—
149Dic6—124no—
150Dic6—124no—
151C2×C32—21no—
152C2×C32—41no—
153C2×C32C2×#9911yescharacteristic
154C3⋊D3—42no—
155C3⋊D3—81no—
156#41—361no—
157#41—361no—
158#41—361no—
159#41—361no—
160C2×Q8—91no—
161C2×Q8—91no—
162C2×D4—92no—
163C2×D4—91no—
164C2×D4—91no—
165C2×D4—182no—
166C2×D4—181no—
167C22×C4—21no—
168C22×C4—92no—
169C22×C4—181no—
170C22×C4C2×#15711yescharacteristic
171C4⋊C4—182no—
172C4⋊C4—362no—
173C22⋊C4—182no—
174C22⋊C4—182no—
175C22⋊C4—184no—
176C42—21no—
177C42—362no—
178C42C2×#15711yescharacteristic
179C42C2×#15711yescharacteristic
180C22×C3—24no—
181C22×C3—22no—
182C22×C3—44no—
183C2×D3—124no—
184C2×D3—124no—
185C2×D3—128no—
186C2×D3—128no—
187C3×C4—24no—
188C3×C4—28no—
189C3×C4—22no—
190C3×C4—22no—
191C3×C4—44no—
192Dic3—124no—
193Dic3—124no—
194C32#212611yescharacteristic, complemented, Sylow
195C23—92no—
196C23—181no—
197C23C22⋊#15711yescharacteristic
198Q8—361no—
199Q8—361no—
200D4—361no—
201D4—361no—
202D4—364no—
203D4—362no—
204D4—362no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—92no—
211C2×C4—182no—
212C2×C4—182no—
213C2×C4—181no—
214C2×C4—361no—
215C2×C4—361no—
216C2×C4—364no—
217C2×C4C22⋊#15711yescharacteristic
218C2×C4C22×#15711yescharacteristic
219C2×C3—24no—
220C2×C3—22no—
221C2×C3—44no—
222D3—244no—
223D3—244no—
224C22—21no—
225C22—41no—
226C22—182no—
227C22—362no—
228C22—362no—
229C22—361no—
230C22C2×C22⋊#15711yescharacteristic
231C4—22no—
232C4—21no—
233C4—41no—
234C4—182no—
235C4—361no—
236C4—724no—
237C4#6377411yescharacteristic
238C4#6377411yescharacteristic
239C3—22no—
240C2—21no—
241C2—41no—
242C2—362no—
243C2—721no—
244C2C2×#6377411yescharacteristic
subgroupG/H
centerC4#63774
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×C42C4
socleC2×C32C2×#99
prime radical#10595948C2
cosocleC2×C4⋊(C3⋊D3)C23
hypercenterC2×C42#157
hypocenterC32#2126
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10593792C2semidirect
3. #10590143C2semidirect
4. #10590142C2semidirect
5. C2×#3828C4semidirect
8. C2×C32×C42C4semidirect
10. #64084C4semidirect
14. #64078C4semidirect
125. C2×C42#157semidirect
194. C32#2126semidirect

Maximal subgroups

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

subgroupindex
#105959482
#105937922
#105901432
#105901422
#21269