Finite Group Databasebeta

← #11796695

Subgroups — #11796695

Order 1152.

430 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×#63822C211yesmaximal, characteristic
2C2×#63773C211yesmaximal, characteristic, complemented
3C2×#63576C211yesmaximal, characteristic, complemented
4#10590062C212yesmaximal, complemented
5#10590061C212yesmaximal, complemented
6C2×C3×#235—21no—
7C22×C3⋊(C3⋊C8)C2211yescharacteristic
8C2×C3×C4⋊Dic3—21no—
9C2×#3718C2211yescharacteristic
10C2×#3715—21no—
11#63822—22no—
12#63822C414yescomplemented
13C2×#3713C2211yescharacteristic
14#63773—22no—
15C2×#3708C2212yes—
16#63576—21no—
17#63576C2212yes—
18C2×#950—61no—
19C2×#807—61no—
20C22×C32×C4D411yescharacteristic
21C2×C3×#67—41no—
22C22×C3×Dic3—41no—
23C3×#235—24no—
24C3×#235—42no—
25C2×C3×D12—21no—
26C2×C3×C4×D3—41no—
27C2×C3×Dic6—21no—
28C2×C3⋊(C3⋊C8)C2×C412yes—
29C2×C3⋊(C3⋊C8)D411yescharacteristic
30C2×C3⋊(C3⋊C8)D412yes—
31C2×C3⋊(C3⋊C8)C2311yescharacteristic
32C3×C4⋊Dic3—22no—
33C3×C4⋊Dic3—41no—
34#3718—21no—
35#3718C2×C412yescomplemented
36#3715—24no—
37#3713—21no—
38#3713C2×C412yescomplemented
39#3708—22no—
40#2139—91nomaximal, Sylow
41C2×C3×#41—61no—
42C2×#235—21no—
43C2×C3×C4⋊C4—61no—
44#950—64no—
45#950—64no—
46C2×#216—61no—
47C2×#215—61no—
48C2×#214—61no—
49C2×#213—61no—
50C2×C4⋊Dic3—21no—
51C22×C3⋊C8—61no—
52C22×C3⋊C8—61no—
53#807—62no—
54#807—62no—
55C23×C32D811yescharacteristic
56C22×C3×D3—41no—
57C2×C32×C4C22⋊C412yes—
58C2×C32×C4D811yescharacteristic
59C2×C32×C4SD1612yes—
60C2×C32×C4C2×D411yescharacteristic
61C3×#67—44no—
62C2×C3×Dic3—41no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—82no—
65C3×D12—22no—
66C3×D12—41no—
67C3×C4×D3—44no—
68C3×Dic6—22no—
69C3×Dic6—41no—
70C3⋊(C3⋊C8)C22⋊C412yes—
71C3⋊(C3⋊C8)C22×C411yescharacteristic
72C3⋊(C3⋊C8)C2×D411yescharacteristic
73C2×#135—91no—
74C2×M32—91no—
75C2×#107—91no—
76#358—92no—
77#357—92no—
78C3×#41—64no—
79C3×#41—122no—
80C2×C3×Q8—61no—
81C2×C3×D4—61no—
82C2×C3×D4—121no—
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C22×C3×C4—121no—
86C22×C3×C4—121no—
87C2×#67—41no—
88C22×Dic3—41no—
89#235—24no—
90#235—42no—
91C2×D12—21no—
92C2×C4×D3—41no—
93C2×Dic6—21no—
94C3×C4⋊C4—62no—
95C3×C4⋊C4—121no—
96#216—62no—
97#216—62no—
98#215—64no—
99#214—64no—
100#213—62no—
101#213—62no—
102C4⋊Dic3—22no—
103C4⋊Dic3—41no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C2×C3⋊C8—61no—
107C2×C3⋊C8—62no—
108C2×C3⋊C8—62no—
109C2×C3⋊C8—62no—
110C2×C3⋊C8—61no—
111C2×C3⋊C8—62no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32#10212yes—
115C22×C32C2×D811yescharacteristic
116C2×C3×D3—42no—
117C2×C3×D3—81no—
118C2×C3×D3—81no—
119C32×C4#10212yes—
120C32×C4C2×C22⋊C411yescharacteristic
121C32×C4C2×SD1611yescharacteristic
122C3×Dic3—42no—
123C3×Dic3—82no—
124C2×#41—61no—
125#135—94no—
126#135—182no—
127C2×Q16—91no—
128C2×SD16—181no—
129C2×D8—91no—
130C22×C8—91no—
131C2×C4⋊C4—61no—
132M32—182no—
133C2×C16—92no—
134#107—92no—
135#107—181no—
136C23×C3—21no—
137C23×C3—21no—
138C23×C3—121no—
139C22×D3—41no—
140C3×Q8—62no—
141C3×Q8—121no—
142C3×D4—62no—
143C3×D4—121no—
144C3×D4—124no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—124no—
154C2×C3×C4—121no—
155C2×C3×C4—122no—
156C2×C3×C4—242no—
157#67—44no—
158C2×Dic3—41no—
159C2×Dic3—42no—
160C2×Dic3—82no—
161D12—22no—
162D12—41no—
163C4×D3—44no—
164Dic6—22no—
165Dic6—41no—
166C3⋊C8—62no—
167C3⋊C8—62no—
168C3⋊C8—61no—
169C3⋊C8—61no—
170C3⋊C8—61no—
171C3⋊C8—61no—
172C2×C32—22no—
173C2×C32C2×#10211yescharacteristic
174C2×C32#50911yescharacteristic
175C2×C32#51011yescharacteristic
176C3×D3—82no—
177#41—64no—
178#41—122no—
179C2×Q8—61no—
180C2×D4—61no—
181C2×D4—121no—
182C22×C4—121no—
183C22×C4—121no—
184C22×C4GO+(4,𝔽2)11yescharacteristic
185Q16—92no—
186Q16—181no—
187SD16—184no—
188D8—92no—
189D8—181no—
190C2×C8—91no—
191C2×C8—91no—
192C2×C8—92no—
193C2×C8—92no—
194C4⋊C4—62no—
195C4⋊C4—121no—
196C16—182no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—21no—
200C22×C3—21no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—41no—
204C22×C3—41no—
205C22×C3—122no—
206C22×C3—241no—
207C22×C3—241no—
208C2×D3—42no—
209C2×D3—81no—
210C2×D3—81no—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—21no—
215C3×C4—22no—
216C3×C4—22no—
217C3×C4—122no—
218C3×C4—242no—
219Dic3—42no—
220Dic3—82no—
221C32#213911yescharacteristic, complemented, Sylow
222C23—121no—
223C23#377411yescharacteristic
224Q8—62no—
225Q8—121no—
226D4—62no—
227D4—124no—
228D4—121no—
229C2×C4—121no—
230C2×C4—124no—
231C2×C4—122no—
232C2×C4—242no—
233C2×C4D32⋊C412yes—
234C2×C4#377411yescharacteristic
235C2×C4#377512yes—
236C2×C4C2×GO+(4,𝔽2)11yescharacteristic
237C8—91no—
238C8—91no—
239C8—92no—
240C2×C3—24no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—42no—
248C2×C3—242no—
249D3—82no—
250C22—21no—
251C22—21no—
252C22—122no—
253C22—241no—
254C22—241no—
255C22#6373912yes—
256C22C2×#377411yescharacteristic
257C4—122no—
258C4—242no—
259C4#6373912yes—
260C4C2×D32⋊C411yescharacteristic
261C4C2×#377511yescharacteristic
262C3—21no—
263C3—21no—
264C2—22no—
265C2—242no—
266C2#1059333411yescharacteristic
267C2#1059333611yescharacteristic
268C2C2×#6373911yescharacteristic
subgroupG/H
centerC22C2×#3774
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×D8
prime radicalC2×#63822C2
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2139
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63773C2semidirect
3. C2×#63576C2semidirect
4. #10590062C2semidirect
5. #10590061C2semidirect
12. #63822C4semidirect
35. #3718C2×C4semidirect
38. #3713C2×C4semidirect
221. C32#2139semidirect

Maximal subgroups

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

subgroupindex
C2×#638222
C2×#637732
C2×#635762
#105900622
#105900612
#21399