Finite Group Databasebeta

← #11796365

Subgroups — #11796365

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#10596303C211yesmaximal, characteristic
2#10593792C212yesmaximal, complemented
3#10590217C212yesmaximal, complemented
4#10590211C212yesmaximal, complemented
5C2×C32×#41C411yescharacteristic, complemented
6C2×#3828C2211yescharacteristic
7#64286—22no—
8#64156C2211yescharacteristic
9#64153C411yescharacteristic, complemented
10#64149C2211yescharacteristic
11#64148—22no—
12#64145C411yescharacteristic, complemented
13C4×#638—22no—
14C2×C4×C3⋊Dic3C411yescharacteristic, complemented
15#63786—22no—
16#63774C2214yes—
17#5832—62no—
18C32×#41—41no—
19C32×#41—41no—
20C2×C32×Q8C2×C411yescharacteristic
21C2×C32×D4—21no—
22C2×C32×D4C2×C411yescharacteristic
23C22×C32×C4—21no—
24C22×C32×C4C2×C411yescharacteristic
25C2×#638—22no—
26C2×#638D412yes—
27C22×C3⋊Dic3—21no—
28#3828—41no—
29#3828—41no—
30C2×C4⋊(C3⋊D3)C2311yescharacteristic
31C2×C4×C3⋊D3D412yes—
32C2×#634C2×C411yescharacteristic
33C22⋊#157—24no—
34C4⋊#157—42no—
35C4×#157—42no—
36#3757—22no—
37#3752—22no—
38#3750—22no—
39C4×C3⋊Dic3—21no—
40C4×C3⋊Dic3C2×C411yescharacteristic
41C4×C3⋊Dic3C2×C411yescharacteristic
42#2126—91nomaximal, Sylow
43C2×C3×#41—22no—
44C2×#235—62no—
45#947—62no—
46#944—62no—
47#940—62no—
48#939—68no—
49#936—62no—
50C4×#67—68no—
51C2×C4×Dic3—62no—
52C23×C32—21no—
53C23×C32C22⋊C411yescharacteristic
54C22×C3⋊D3C2×D412yes—
55C2×#157—44no—
56C32×Q8—41no—
57C32×D4—41no—
58C32×D4—42no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—41no—
63C2×C32×C4—41no—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22×C411yescharacteristic
66#638—42no—
67#638—44no—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—42no—
71C2×C3⋊Dic3C22⋊C412yes—
72C4⋊(C3⋊D3)—41no—
73C4×C3⋊D3—22no—
74C4×C3⋊D3—22no—
75#634—41no—
76#532—91no—
77#410—92no—
78#354—92no—
79#353—92no—
80C3×#41—44no—
81C3×#41—44no—
82C2×C3×Q8—22no—
83C2×C3×D4—24no—
84C2×C3×D4—22no—
85C22×C3×C4—24no—
86C22×C3×C4—22no—
87C2×#67—64no—
88C2×#67—68no—
89C22×Dic3—64no—
90#235—124no—
91#235—124no—
92C2×D12—62no—
93C2×C4×D3—64no—
94C2×Dic6—62no—
95#217—68no—
96(C2×D3)⋊C4—68no—
97Dic3⋊C4—68no—
98C4×Dic3—62no—
99C4×Dic3—62no—
100C4×Dic3—64no—
101C22×C32—21no—
102C22×C32—41no—
103C22×C32—42no—
104C22×C32—41no—
105C22×C32C2×C22⋊C411yescharacteristic
106C2×C3⋊D3—22no—
107C2×C3⋊D3—42no—
108#157—84no—
109C32×C4—21no—
110C32×C4—41no—
111C32×C4#9911yescharacteristic
112C32×C4#9911yescharacteristic
113C3⋊Dic3—22no—
114C3⋊Dic3—22no—
115C3⋊Dic3—41no—
116C2×#41—91no—
117C2×#41#15711yescharacteristic, complemented
118C4⋊Q8—91no—
119#127—91no—
120#124—91no—
121#124—91no—
122#121—182no—
123C4×D4—182no—
124#117—182no—
125C2×C42—91no—
126#99—94no—
127#99—182no—
128C23×C3—24no—
129C23×C3—22no—
130C22×D3—64no—
131C3×Q8—44no—
132C3×D4—44no—
133C3×D4—48no—
134C2×C3×C4—24no—
135C2×C3×C4—24no—
136C2×C3×C4—24no—
137C2×C3×C4—22no—
138C2×C3×C4—22no—
139C2×C3×C4—44no—
140C2×C3×C4—44no—
141#67—1216no—
142#67—128no—
143C2×Dic3—64no—
144C2×Dic3—64no—
145C2×Dic3—64no—
146C2×Dic3—128no—
147D12—124no—
148C4×D3—124no—
149C4×D3—124no—
150Dic6—124no—
151C2×C32—21no—
152C2×C32—41no—
153C2×C32—81no—
154C2×C32C2×#9911yescharacteristic
155C3⋊D3—42no—
156#41—41no—
157#41—41no—
158#41—361no—
159#41—361no—
160C2×Q8—91no—
161C2×Q8C2×#15711yescharacteristic
162C2×D4—21no—
163C2×D4—92no—
164C2×D4—91no—
165C2×D4—182no—
166C2×D4C2×#15711yescharacteristic
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—91no—
177C42—91no—
178C42—181no—
179C42—362no—
180C22×C3—24no—
181C22×C3—22no—
182C22×C3—44no—
183C22×C3—48no—
184C22×C3—44no—
185C2×D3—124no—
186C2×D3—128no—
187C3×C4—24no—
188C3×C4—22no—
189C3×C4—22no—
190C3×C4—44no—
191Dic3—68no—
192Dic3—124no—
193Dic3—124no—
194C32#212611yescharacteristic, complemented, Sylow
195C23—21no—
196C23—92no—
197C23C22⋊#15711yescharacteristic
198Q8—41no—
199Q8—361no—
200D4—41no—
201D4—42no—
202D4—361no—
203D4—362no—
204D4—364no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—92no—
211C2×C4—181no—
212C2×C4—182no—
213C2×C4—182no—
214C2×C4—181no—
215C2×C4—362no—
216C2×C4—364no—
217C2×C4C22⋊#15711yescharacteristic
218C2×C4C22×#15711yescharacteristic
219C2×C3—24no—
220C2×C3—22no—
221C2×C3—44no—
222C2×C3—84no—
223D3—244no—
224C22—21no—
225C22—41no—
226C22—42no—
227C22—41no—
228C22—182no—
229C22—362no—
230C22C2×C22⋊#15711yescharacteristic
231C4—21no—
232C4—41no—
233C4—182no—
234C4—182no—
235C4—361no—
236C4—724no—
237C4#6378611yescharacteristic
238C4#6378611yescharacteristic
239C3—22no—
240C2—21no—
241C2—41no—
242C2—81no—
243C2—362no—
244C2C2×#6378611yescharacteristic
subgroupG/H
centerC4#63786
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×#41C4
socleC2×C32C2×#99
prime radical#10596303C2
cosocleC2×C4⋊(C3⋊D3)C23
hypercenterC2×#41#157
hypocenterC32#2126
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10593792C2semidirect
3. #10590217C2semidirect
4. #10590211C2semidirect
5. C2×C32×#41C4semidirect
9. #64153C4semidirect
12. #64145C4semidirect
14. C2×C4×C3⋊Dic3C4semidirect
117. C2×#41#157semidirect
194. C32#2126semidirect

Maximal subgroups

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

subgroupindex
#105963032
#105937922
#105902172
#105902112
#21269