Finite Group Databasebeta

← C2×#10590066 #11796923

Subgroups — C2×#10590066 #11796923

Order 1152.

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

normal subgroups only

This group has 398 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×#3718C211yesmaximal, characteristic
2C2×#63773C211yesmaximal, characteristic
3C2×#63578C211yesmaximal, characteristic
4#10590066C214yesmaximal, direct product factor
5C22×C3×Dic6—21no—
6C22×C3⋊(C3⋊C8)C2211yescharacteristic
7C2×C3×#208—21no—
8C2×#3718—21no—
9C2×#3718—21no—
10C2×#3718—21no—
11C2×#3718C412yes—
12C2×#3718C412yes—
13C2×#3718C2212yes—
14#63773—21no—
15#63773C2212yes—
16C2×#3708—21no—
17#63578—21no—
18#63578C2212yes—
19C22×#216—61no—
20C2×#822—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3×Dic3—41no—
23C2×C3×Dic6—22no—
24C2×C3×Dic6—22no—
25C2×C3×Dic6—22no—
26C2×C3×Dic6—41no—
27C2×C3×Dic6—41no—
28C2×C3×Dic6—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#3718—22no—
39#3718—22no—
40#3718—22no—
41#3718C2×C414yes—
42#3708—22no—
43C2×#362—91nomaximal, Sylow
44C22×C3×Q8—61no—
45C22×Dic6—21no—
46C2×C3×M16—61no—
47C2×#216—62no—
48C2×#216—62no—
49C2×#216—62no—
50C2×#216—62no—
51C2×#216—62no—
52C2×#216—62no—
53C2×#208—21no—
54C22×C3⋊C8—61no—
55C22×C3⋊C8—61no—
56#822—62no—
57#822—62no—
58C23×C32SD1611yescharacteristic
59C2×C32×C4C22⋊C411yescharacteristic
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C32×C4D811yescharacteristic
62C2×C32×C4D811yescharacteristic
63C2×C32×C4SD1611yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C3×Dic3—42no—
66C2×C3×Dic3—42no—
67C2×C3×Dic3—42no—
68C3×Dic6—24no—
69C3×Dic6—42no—
70C3×Dic6—42no—
71C3×Dic6—42no—
72C3⋊(C3⋊C8)C22⋊C411yescharacteristic
73C3⋊(C3⋊C8)C22⋊C411yescharacteristic
74C3⋊(C3⋊C8)C22×C411yescharacteristic
75C3⋊(C3⋊C8)C2×D411yescharacteristic
76C3×C3⋊C8—42no—
77C22×Q16—91no—
78C2×M32—91no—
79C2×#108—91no—
80#362—94no—
81C2×C3×Q8—62no—
82C2×C3×Q8—62no—
83C2×C3×Q8—62no—
84C2×C3×Q8—121no—
85C2×C3×Q8—121no—
86C2×C3×Q8—121no—
87C22×C3×C4—21no—
88C22×C3×C4—21no—
89C22×C3×C4—121no—
90C22×Dic3—41no—
91C2×Dic6—22no—
92C2×Dic6—22no—
93C2×Dic6—22no—
94C2×Dic6—41no—
95C2×Dic6—41no—
96C2×Dic6—41no—
97C3×M16—62no—
98C3×M16—121no—
99C2×C3×C8—121no—
100#216—64no—
101#216—64no—
102#216—64no—
103#216—64no—
104#208—22no—
105#208—41no—
106C2×C3⋊C8—41no—
107C2×C3⋊C8—61no—
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—
119C22×C32—22no—
120C22×C32#10211yescharacteristic
121C22×C32#10211yescharacteristic
122C22×C32C2×SD1611yescharacteristic
123C32×C4#10211yescharacteristic
124C32×C4#10211yescharacteristic
125C32×C4C2×C22⋊C411yescharacteristic
126C32×C4C2×D811yescharacteristic
127C3×Dic3—44no—
128C22×Q8—61no—
129C2×Q16—92no—
130C2×Q16—92no—
131C2×Q16—92no—
132C2×Q16—181no—
133C2×Q16—181no—
134C2×Q16—181no—
135C2×M16—61no—
136C22×C8—91no—
137M32—92no—
138M32—181no—
139C2×C16—181no—
140#108—92no—
141#108—181no—
142C23×C3—21no—
143C23×C3—21no—
144C3×Q8—64no—
145C3×Q8—122no—
146C3×Q8—122no—
147C3×Q8—122no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—122no—
161C2×C3×C4—122no—
162C2×C3×C4—122no—
163C2×Dic3—42no—
164C2×Dic3—42no—
165C2×Dic3—42no—
166Dic6—24no—
167Dic6—42no—
168Dic6—42no—
169Dic6—42no—
170C3×C8—122no—
171C3⋊C8—42no—
172C3⋊C8—61no—
173C3⋊C8—61no—
174C3⋊C8—61no—
175C3⋊C8—61no—
176C3⋊C8—61no—
177C3⋊C8—61no—
178C3⋊C8—61no—
179C3⋊C8—61no—
180C2×C32—21no—
181C2×C32—21no—
182C2×C32#36212yescomplemented
183C2×C32C2×#10211yescharacteristic
184C2×Q8—62no—
185C2×Q8—62no—
186C2×Q8—62no—
187C2×Q8—121no—
188C2×Q8—121no—
189C2×Q8—121no—
190C22×C4—121no—
191C22×C4GO+(4,𝔽2)11yescharacteristic
192Q16—94no—
193Q16—182no—
194Q16—182no—
195Q16—182no—
196M16—62no—
197M16—121no—
198C2×C8—91no—
199C2×C8—91no—
200C2×C8—91no—
201C2×C8—91no—
202C2×C8—91no—
203C2×C8—91no—
204C2×C8—121no—
205C16—182no—
206C22×C3—24no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—42no—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—21no—
220C3×C4—21no—
221C3×C4—21no—
222C3×C4—124no—
223Dic3—44no—
224C32C2×#36211yescharacteristic, complemented, Sylow
225C23#377511yescharacteristic
226Q8—64no—
227Q8—122no—
228Q8—122no—
229Q8—122no—
230C2×C4—122no—
231C2×C4—122no—
232C2×C4—122no—
233C2×C4D32⋊C411yescharacteristic
234C2×C4D32⋊C411yescharacteristic
235C2×C4#377411yescharacteristic
236C2×C4#377411yescharacteristic
237C2×C4#377511yescharacteristic
238C2×C4C2×GO+(4,𝔽2)11yescharacteristic
239C8—91no—
240C8—91no—
241C8—91no—
242C8—91no—
243C8—122no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—22no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—41no—
251C2×C3—41no—
252C22—22no—
253C22#6373911yescharacteristic
254C22#6373911yescharacteristic
255C22C2×#377511yescharacteristic
256C4—124no—
257C4#6373911yescharacteristic
258C4#6373911yescharacteristic
259C4C2×D32⋊C411yescharacteristic
260C4C2×#377411yescharacteristic
261C3—21no—
262C3—21no—
263C2—21no—
264C2—21no—
265C2#1059006612yesdirect product factor
266C2C2×#6373911yescharacteristic
subgroupG/H
centerC22#63739
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#102
prime radicalC23×C32SD16
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#362
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
4. #10590066C2direct (N × H)
182. C2×C32#362semidirect
224. C32C2×#362semidirect
265. C2#10590066direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37182
C2×#637732
C2×#635782
#105900662
C2×#3629