Finite Group Databasebeta

← C2×#10590065 #11796894

Subgroups — C2×#10590065 #11796894

Order 1152.

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

normal subgroups only

This group has 478 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
1C22×#3713C211yesmaximal, characteristic
2C2×#63773C211yesmaximal, characteristic, complemented
3C2×#63578C211yesmaximal, characteristic, complemented
4#10590065C214yesmaximal, direct product factor
5C22×C3×D12—21no—
6C22×C3⋊(C3⋊C8)C2211yescharacteristic
7C2×C3×#208—21no—
8C2×#3713—21no—
9C2×#3713—21no—
10C2×#3713—21no—
11C2×#3713C412yes—
12C2×#3713C412yes—
13C2×#3713C2212yes—
14#63773—21no—
15#63773C2212yescomplemented
16C2×#3708—21no—
17#63578—21no—
18#63578C2212yescomplemented
19C22×#213—61no—
20C2×#822—61no—
21C23×C3×D3—41no—
22C22×C32×C4D411yescharacteristic
23C2×C3×D12—22no—
24C2×C3×D12—22no—
25C2×C3×D12—22no—
26C2×C3×D12—41no—
27C2×C3×D12—41no—
28C2×C3×D12—41no—
29C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
30C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
31C2×C3⋊(C3⋊C8)D411yescharacteristic
32C2×C3⋊(C3⋊C8)D411yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C2×C3⋊(C3⋊C8)C2311yescharacteristic
35C3×#208—22no—
36C3×#208—41no—
37C2×C3×C3⋊C8—41no—
38#3713—22no—
39#3713—22no—
40#3713—22no—
41#3713C2×C414yes—
42#3708—22no—
43C2×#361—91nomaximal, Sylow
44C22×C3×D4—61no—
45C22×D12—21no—
46C2×C3×M16—61no—
47C2×#213—62no—
48C2×#213—62no—
49C2×#213—62no—
50C2×#213—62no—
51C2×#213—62no—
52C2×#213—62no—
53C2×#208—21no—
54C22×C3⋊C8—61no—
55C22×C3⋊C8—61no—
56#822—62no—
57#822—62no—
58C23×C32SD1611yescharacteristic
59C22×C3×D3—42no—
60C22×C3×D3—42no—
61C22×C3×D3—42no—
62C22×C3×D3—84no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4D811yescharacteristic
66C2×C32×C4D811yescharacteristic
67C2×C32×C4SD1611yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C3×D12—24no—
70C3×D12—42no—
71C3×D12—42no—
72C3×D12—42no—
73C3⋊(C3⋊C8)C22⋊C411yescharacteristic
74C3⋊(C3⋊C8)C22⋊C411yescharacteristic
75C3⋊(C3⋊C8)C22×C411yescharacteristic
76C3⋊(C3⋊C8)C2×D411yescharacteristic
77C3×C3⋊C8—42no—
78C22×D8—91no—
79C2×M32—91no—
80C2×#108—91no—
81#361—94no—
82C24×C3—121no—
83C23×D3—41no—
84C2×C3×D4—62no—
85C2×C3×D4—62no—
86C2×C3×D4—62no—
87C2×C3×D4—121no—
88C2×C3×D4—121no—
89C2×C3×D4—121no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C2×D12—22no—
93C2×D12—22no—
94C2×D12—22no—
95C2×D12—41no—
96C2×D12—41no—
97C2×D12—41no—
98C3×M16—62no—
99C3×M16—121no—
100C2×C3×C8—121no—
101#213—64no—
102#213—64no—
103#213—64no—
104#213—64no—
105#208—22no—
106#208—41no—
107C2×C3⋊C8—41no—
108C2×C3⋊C8—61no—
109C2×C3⋊C8—61no—
110C2×C3⋊C8—61no—
111C2×C3⋊C8—61no—
112C2×C3⋊C8—61no—
113C2×C3⋊C8—61no—
114C2×C3⋊C8—61no—
115C2×C3⋊C8—61no—
116C2×C3⋊C8—61no—
117C2×C3⋊C8—61no—
118C2×C3⋊C8—61no—
119C2×C3⋊C8—61no—
120C22×C32—22no—
121C22×C32#10211yescharacteristic
122C22×C32#10211yescharacteristic
123C22×C32C2×SD1611yescharacteristic
124C2×C3×D3—44no—
125C2×C3×D3—84no—
126C2×C3×D3—84no—
127C2×C3×D3—84no—
128C32×C4#10211yescharacteristic
129C32×C4#10211yescharacteristic
130C32×C4C2×C22⋊C411yescharacteristic
131C32×C4C2×D811yescharacteristic
132C22×D4—61no—
133C2×D8—92no—
134C2×D8—92no—
135C2×D8—92no—
136C2×D8—181no—
137C2×D8—181no—
138C2×D8—181no—
139C2×M16—61no—
140C22×C8—91no—
141M32—92no—
142M32—181no—
143C2×C16—181no—
144#108—92no—
145#108—181no—
146C23×C3—21no—
147C23×C3—21no—
148C23×C3—122no—
149C23×C3—122no—
150C23×C3—122no—
151C23×C3—244no—
152C22×D3—42no—
153C22×D3—42no—
154C22×D3—42no—
155C22×D3—84no—
156C3×D4—64no—
157C3×D4—122no—
158C3×D4—122no—
159C3×D4—122no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172D12—24no—
173D12—42no—
174D12—42no—
175D12—42no—
176C3×C8—122no—
177C3⋊C8—42no—
178C3⋊C8—61no—
179C3⋊C8—61no—
180C3⋊C8—61no—
181C3⋊C8—61no—
182C3⋊C8—61no—
183C3⋊C8—61no—
184C3⋊C8—61no—
185C3⋊C8—61no—
186C2×C32—21no—
187C2×C32—21no—
188C2×C32#36112yescomplemented
189C2×C32C2×#10211yescharacteristic
190C3×D3—84no—
191C24—121no—
192C2×D4—62no—
193C2×D4—62no—
194C2×D4—62no—
195C2×D4—121no—
196C2×D4—121no—
197C2×D4—121no—
198C22×C4GO+(4,𝔽2)11yescharacteristic
199D8—94no—
200D8—182no—
201D8—182no—
202D8—182no—
203M16—62no—
204M16—121no—
205C2×C8—91no—
206C2×C8—91no—
207C2×C8—91no—
208C2×C8—91no—
209C2×C8—91no—
210C2×C8—91no—
211C2×C8—121no—
212C16—182no—
213C22×C3—24no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—42no—
221C22×C3—124no—
222C22×C3—244no—
223C22×C3—244no—
224C22×C3—244no—
225C2×D3—44no—
226C2×D3—84no—
227C2×D3—84no—
228C2×D3—84no—
229C3×C4—21no—
230C3×C4—21no—
231C3×C4—21no—
232C3×C4—21no—
233C3×C4—21no—
234C3×C4—21no—
235C3×C4—21no—
236C3×C4—21no—
237C32C2×#36111yescharacteristic, complemented, Sylow
238C23—122no—
239C23—122no—
240C23—122no—
241C23—244no—
242C23#377511yescharacteristic
243D4—64no—
244D4—122no—
245D4—122no—
246D4—122no—
247C2×C4D32⋊C411yescharacteristic
248C2×C4D32⋊C411yescharacteristic
249C2×C4#377411yescharacteristic
250C2×C4#377411yescharacteristic
251C2×C4#377511yescharacteristic
252C2×C4C2×GO+(4,𝔽2)11yescharacteristic
253C8—91no—
254C8—91no—
255C8—91no—
256C8—91no—
257C8—122no—
258C2×C3—22no—
259C2×C3—22no—
260C2×C3—22no—
261C2×C3—22no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—41no—
265C2×C3—41no—
266C2×C3—244no—
267D3—84no—
268C22—22no—
269C22—124no—
270C22—244no—
271C22—244no—
272C22—244no—
273C22#6373911yescharacteristic
274C22#6373911yescharacteristic
275C22C2×#377511yescharacteristic
276C4#6373911yescharacteristic
277C4#6373911yescharacteristic
278C4C2×D32⋊C411yescharacteristic
279C4C2×#377411yescharacteristic
280C3—21no—
281C3—21no—
282C2—21no—
283C2—21no—
284C2—244no—
285C2#1059006512yesdirect product factor
286C2C2×#6373911yescharacteristic
subgroupG/H
centerC22#63739
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#102
prime radicalC22×#3713C2
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#361
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×#63578C2semidirect
4. #10590065C2direct (N × H)
15. #63773C22semidirect
18. #63578C22semidirect
188. C2×C32#361semidirect
237. C32C2×#361semidirect
285. C2#10590065direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37132
C2×#637732
C2×#635782
#105900652
C2×#3619