Finite Group Databasebeta

← C2×#7361 #149591

Subgroups — C2×#7361 #149591

Order 512.

434 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 82 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×#1994C211yesmaximal, characteristic
2C2×#1327C212yesmaximal
3#7361C214yesmaximal, direct product factor
4C2×#533C411yescharacteristic
5C2×#423C2211yescharacteristic
6C2×C43C411yescharacteristic
7C2×#349—22no—
8#1994—22no—
9#1994C412yes—
10#1994C2212yes—
11C2×#339—22no—
12#1327—22no—
13#1327C2214yes—
14C22×M16D412yes—
15#533—21no—
16#533—21no—
17#533—41no—
18#533—41no—
19#533C812yes—
20#533C2×C412yes—
21C2×C4⋊Q8—21no—
22C2×#125C812yes—
23C2×C22⋊Q8—41no—
24C2×C4×Q8—41no—
25C2×#117—21no—
26C22×C42—21no—
27C22×C42—41no—
28C22×C42C2×C411yescharacteristic
29C2×M32—42no—
30#423—41no—
31#423C2×C411yescharacteristic
32#423D412yes—
33#423C2311yescharacteristic
34C2×C4⋊C8—41no—
35C43—21no—
36C43—41no—
37C43C2×C412yes—
38#349—24no—
39#349—42no—
40#339—24no—
41#339—24no—
42C22×Q8—41no—
43C23×C4—21no—
44C23×C4—41no—
45C23×C4C22⋊C411yescharacteristic
46C2×M16—22no—
47C2×M16—42no—
48C2×M16—42no—
49C2×M16C22⋊C412yes—
50C2×M16C2×D412yes—
51C22×C8—22no—
52C4⋊Q8—22no—
53C4⋊Q8—22no—
54C4⋊Q8—41no—
55C4⋊Q8—41no—
56#125—22no—
57#125—42no—
58#125C2×C814yes—
59C22⋊Q8—42no—
60C22⋊Q8—42no—
61C22⋊Q8—42no—
62C22⋊Q8—42no—
63C4×Q8—42no—
64C4×Q8—42no—
65C4×Q8—42no—
66C4×Q8—42no—
67#117—22no—
68#117—22no—
69#117—41no—
70#117—41no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—42no—
73C2×C4⋊C4—41no—
74C2×C22⋊C4—41no—
75C2×C42—21no—
76C2×C42—21no—
77C2×C42—21no—
78C2×C42—22no—
79C2×C42—22no—
80C2×C42—22no—
81C2×C42—42no—
82C2×C42—42no—
83C2×C42—41no—
84C2×C42—41no—
85C2×C42—48no—
86C2×C42—41no—
87C2×C42—41no—
88C2×C42C22⋊C411yescharacteristic
89C2×C42C2×C811yescharacteristic
90C2×C42C2×C811yescharacteristic
91C2×C42M1611yescharacteristic
92C2×C42M1611yescharacteristic
93C2×C42C22×C411yescharacteristic
94M32—44no—
95M32—82no—
96C2×C16—82no—
97C4⋊C8—41no—
98C4⋊C8—42no—
99C4⋊C8—41no—
100C24#10011yescharacteristic
101C2×Q8—42no—
102C2×Q8—42no—
103C2×Q8—84no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—44no—
115C22×C4—42no—
116C22×C4—42no—
117C22×C4—48no—
118C22×C4—42no—
119C22×C4—42no—
120C22×C4C22⋊C811yescharacteristic
121C22×C4C22⋊C811yescharacteristic
122C22×C4#9911yescharacteristic
123C22×C4#9911yescharacteristic
124C22×C4#10011yescharacteristic
125C22×C4C2×C22⋊C411yescharacteristic
126M16—42no—
127M16—42no—
128M16—82no—
129C2×C8—22no—
130C2×C8—22no—
131C2×C8—42no—
132C2×C8—42no—
133C4⋊C4—24no—
134C4⋊C4—44no—
135C4⋊C4—44no—
136C4⋊C4—42no—
137C4⋊C4—42no—
138C4⋊C4—42no—
139C22⋊C4—42no—
140C22⋊C4—42no—
141C42—21no—
142C42—21no—
143C42—21no—
144C42—21no—
145C42—21no—
146C42—21no—
147C42—24no—
148C42—42no—
149C42—42no—
150C42—42no—
151C42—48no—
152C42—48no—
153C42—42no—
154C42—42no—
155C42C22⋊C811yescharacteristic
156C42C22⋊C811yescharacteristic
157C42C22×C811yescharacteristic
158C42C2×M1611yescharacteristic
159C16—84no—
160C23—21no—
161C23—21no—
162C23—42no—
163C23#32311yescharacteristic
164C23#32311yescharacteristic
165C23C2×#10011yescharacteristic
166Q8—84no—
167Q8—84no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—48no—
190C2×C4—48no—
191C2×C4—48no—
192C2×C4—44no—
193C2×C4—84no—
194C2×C4#32311yescharacteristic
195C2×C4#32311yescharacteristic
196C2×C4#35411yescharacteristic
197C2×C4#35411yescharacteristic
198C2×C4#35611yescharacteristic
199C2×C4#35611yescharacteristic
200C2×C4C2×C22⋊C811yescharacteristic
201C2×C4C2×#9911yescharacteristic
202C8—42no—
203C8—42no—
204C22—22no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—42no—
210C22—42no—
211C22#131911yescharacteristic
212C22#131911yescharacteristic
213C22C2×#32311yescharacteristic
214C4—22no—
215C4—22no—
216C4—21no—
217C4—21no—
218C4—41no—
219C4—41no—
220C4—48no—
221C4—84no—
222C4#131911yescharacteristic
223C4#131911yescharacteristic
224C4C2×#35411yescharacteristic
225C4C2×#35611yescharacteristic
226C2—21no—
227C2—21no—
228C2—41no—
229C2—41no—
230C2#736112yesdirect product factor
231C2C2×#131911yescharacteristic
subgroupG/H
centerC2×C4#354
commutatorC42C22×C8
Frattini, cosocle#423C23
socleC22#1319
prime radicalC24#100
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×#423 ◁ G
LECSG ▷ #423 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #7361C2direct (N × H)
230. C2#7361direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#19942
C2×#13272
#73612