Finite Group Databasebeta

← C2×#10593546 #11858627

Subgroups — C2×#10593546 #11858627

Order 1152.

598 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 199 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×#64283C212yesmaximal
2C22×#3787C211yesmaximal, characteristic
3C2×#63748C214yesmaximal, complemented
4#10593546C218yesmaximal, direct product factor
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3792C2214yes—
7C22×#622C2212yes—
8#64283—24no—
9#64283C2218yes—
10C2×#3788—22no—
11C2×#3787—22no—
12C2×#3787C414yes—
13C2×#3787C412yes—
14C2×#3787C412yes—
15C2×#3787C2214yes—
16#63748C22116yescomplemented
17C23×C3⋊D3Q811yescharacteristic
18C22×C32×C4Q811yescharacteristic
19C22×C3⋊Dic3C2311yescharacteristic
20C2×C4×C3⋊D3C2×C412yes—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D412yes—
26C2×C4×C3⋊D3Q812yes—
27C2×C4×C3⋊D3C2312yes—
28#3792—24no—
29#3792C2318yes—
30C2×#622—24no—
31C2×#622C2×C414yes—
32C2×#622C2×C414yes—
33C2×#622C2314yes—
34#3788—28no—
35#3787—28no—
36#3787C2×C418yes—
37#3787C2×C418yes—
38C22×#108—91nomaximal, Sylow
39C22×C4×D3—121no—
40C23×C32C2×Q811yescharacteristic
41C22×C3⋊D3—24no—
42C22×C3⋊D3C4⋊C411yescharacteristic
43C22×C3⋊D3C4⋊C412yes—
44C22×C3⋊D3C4⋊C411yescharacteristic
45C22×C3⋊D3C2×Q812yes—
46C2×C32×C4C4⋊C412yes—
47C2×C32×C4C4⋊C411yescharacteristic
48C2×C32×C4C4⋊C411yescharacteristic
49C2×C32×C4C2×Q812yes—
50C2×C3⋊Dic3C22×C411yescharacteristic
51C2×C3⋊Dic3C22×C411yescharacteristic
52C2×C3⋊Dic3C2×D411yescharacteristic
53C2×C3⋊Dic3C2×D411yescharacteristic
54C2×C3⋊Dic3C2×Q811yescharacteristic
55C2×C3⋊Dic3C2411yescharacteristic
56C4×C3⋊D3C4⋊C412yes—
57C4×C3⋊D3C4⋊C412yes—
58C4×C3⋊D3C4⋊C412yes—
59C4×C3⋊D3C4⋊C412yes—
60C4×C3⋊D3C22×C412yes—
61C4×C3⋊D3C22×C412yes—
62C4×C3⋊D3C2×D412yes—
63C4×C3⋊D3C2×D412yes—
64#622—28no—
65#622C22×C418yes—
66C22×M16—92no—
67C23×C8—91no—
68C2×#108—98no—
69C2×#108—94no—
70C23×D3—121no—
71C22×C3×C4—41no—
72C22×Dic3—121no—
73C2×C4×D3—121no—
74C2×C4×D3—122no—
75C2×C4×D3—121no—
76C2×C4×D3—121no—
77C2×C4×D3—122no—
78C2×C4×D3—121no—
79C2×C4×D3—122no—
80C2×C4×D3—122no—
81C22×C32—22no—
82C22×C32C2×C4⋊C411yescharacteristic
83C22×C32C2×C4⋊C411yescharacteristic
84C22×C32C22×Q811yescharacteristic
85C2×C3⋊D3—22no—
86C2×C3⋊D3—24no—
87C2×C3⋊D3—24no—
88C2×C3⋊D3#10814yescomplemented
89C2×C3⋊D3C2×C4⋊C412yes—
90C2×C3⋊D3C2×C4⋊C412yes—
91C32×C4C2×C4⋊C412yes—
92C32×C4C2×C4⋊C412yes—
93C3⋊Dic3C2×C4⋊C411yescharacteristic
94C3⋊Dic3C2×C4⋊C411yescharacteristic
95C3⋊Dic3C23×C411yescharacteristic
96C3⋊Dic3C22×D411yescharacteristic
97C23×C4—91no—
98C2×M16—98no—
99C2×M16—94no—
100C2×M16—182no—
101C2×M16—184no—
102C22×C8—92no—
103C22×C8—94no—
104C22×C8—92no—
105C22×C8—94no—
106C22×C8—92no—
107C22×C8—182no—
108#108—916no—
109C23×C3—41no—
110C22×D3—121no—
111C22×D3—122no—
112C22×D3—121no—
113C22×D3—122no—
114C22×D3—128no—
115C2×C3×C4—42no—
116C2×C3×C4—41no—
117C2×C3×C4—42no—
118C2×C3×C4—41no—
119C2×Dic3—121no—
120C2×Dic3—121no—
121C2×Dic3—121no—
122C2×Dic3—121no—
123C2×Dic3—121no—
124C2×Dic3—121no—
125C4×D3—122no—
126C4×D3—122no—
127C4×D3—122no—
128C4×D3—122no—
129C4×D3—122no—
130C4×D3—122no—
131C4×D3—122no—
132C4×D3—122no—
133C2×C32—21no—
134C2×C32—21no—
135C2×C32C2×#10812yescomplemented
136C2×C32C22×C4⋊C411yescharacteristic
137C3⋊D3—22no—
138C3⋊D3C2×#10814yescomplemented
139C24—91no—
140C22×C4—91no—
141C22×C4—92no—
142C22×C4—92no—
143C22×C4—91no—
144C22×C4—92no—
145C22×C4—91no—
146C22×C4—92no—
147C22×C4—91no—
148C22×C4—91no—
149C22×C4PSU(3,𝔽2)11yescharacteristic
150M16—98no—
151M16—188no—
152M16—184no—
153C2×C8—94no—
154C2×C8—98no—
155C2×C8—98no—
156C2×C8—94no—
157C2×C8—94no—
158C2×C8—188no—
159C2×C8—184no—
160C22×C3—44no—
161C22×C3—41no—
162C22×C3—41no—
163C22×C3—41no—
164C2×D3—122no—
165C2×D3—122no—
166C2×D3—124no—
167C2×D3—128no—
168C2×D3—128no—
169C2×D3—124no—
170C3×C4—42no—
171C3×C4—42no—
172Dic3—121no—
173Dic3—121no—
174Dic3—121no—
175Dic3—121no—
176C32C22×#10811yescharacteristic, complemented, Sylow
177C23—91no—
178C23—92no—
179C23—92no—
180C23—91no—
181C23—184no—
182C23C2×PSU(3,𝔽2)11yescharacteristic
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—92no—
190C2×C4—92no—
191C2×C4—92no—
192C2×C4—92no—
193C2×C4—92no—
194C2×C4—92no—
195C2×C4—92no—
196C2×C4—92no—
197C2×C4#377711yescharacteristic
198C2×C4#377712yes—
199C2×C4#377711yescharacteristic
200C2×C4C2×PSU(3,𝔽2)12yes—
201C8—98no—
202C8—188no—
203C2×C3—42no—
204C2×C3—42no—
205C2×C3—42no—
206C2×C3—41no—
207D3—124no—
208D3—124no—
209C22—22no—
210C22—94no—
211C22—92no—
212C22—92no—
213C22—184no—
214C22—184no—
215C22—182no—
216C22C2×#377711yescharacteristic
217C22C2×#377711yescharacteristic
218C22C22×PSU(3,𝔽2)11yescharacteristic
219C4—91no—
220C4—91no—
221C4—91no—
222C4—91no—
223C4C2×#377712yes—
224C4C2×#377712yes—
225C3—41no—
226C2—21no—
227C2—21no—
228C2—94no—
229C2—182no—
230C2#1059354612yesdirect product factor
231C2C22×#377711yescharacteristic
subgroupG/H
centerC2×C4#3777
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4PSU(3,𝔽2)
hypocenterC32C22×#108
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63748C2semidirect
4. #10593546C2direct (N × H)
16. #63748C22semidirect
88. C2×C3⋊D3#108semidirect
135. C2×C32C2×#108semidirect
138. C3⋊D3C2×#108semidirect
176. C32C22×#108semidirect
230. C2#10593546direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642832
C22×#37872
C2×#637482
#105935462
C22×#1089