Finite Group Databasebeta

← C2×#10593755 #11858277

Subgroups — C2×#10593755 #11858277

Order 1152.

842 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 218 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×#3788C211yesmaximal, characteristic
2C22×#3787C211yesmaximal, characteristic
3C2×#64101C211yesmaximal, characteristic
4C2×#63779C212yesmaximal, complemented
5C2×C4⋊#622C212yesmaximal, complemented
6#10593755C218yesmaximal, direct product factor
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#622C2211yescharacteristic
9C22×#622C2212yes—
10C22×#622C2211yescharacteristic
11C2×#3788—24no—
12C2×#3788C2214yes—
13C2×#3787—24no—
14C2×#3787C2214yes—
15C2×C32×C4⋊C4C411yescharacteristic
16C2×#3752C412yes—
17C2×C4⋊(C3⋊Dic3)C411yescharacteristic
18C2×C4×C3⋊Dic3C2212yes—
19#64101C414yes—
20#64101C2214yes—
21#63779C2218yescomplemented
22C4⋊#622C2218yescomplemented
23C2×#892—62no—
24C23×C3⋊D3C2×C411yescharacteristic
25C22×C32×C4C2×C412yes—
26C22×C32×C4C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C412yes—
28C22×C3⋊Dic3C2311yescharacteristic
29C2×C4×C3⋊D3C2×C412yes—
30C2×C4×C3⋊D3D414yes—
31C2×C4×C3⋊D3Q814yes—
32C2×C4×C3⋊D3C2312yes—
33C2×#622—22no—
34C2×#622—22no—
35C2×#622—24no—
36C2×#622C2312yes—
37C2×#622C2312yes—
38C2×#622C2314yes—
39#3788—28no—
40#3787—28no—
41C32×C4⋊C4C2×C414yes—
42#3752C2×C418yes—
43C4⋊(C3⋊Dic3)C2×C414yes—
44C4×C3⋊Dic3C2×C414yes—
45C4×C3⋊Dic3C2314yes—
46C2×#424—91nomaximal, Sylow
47C22×C4×D3—62no—
48C2×C3×C4⋊C4—22no—
49C2×(C2×D3)⋊C4—64no—
50C2×C4⋊Dic3—62no—
51C2×C4×Dic3—64no—
52#892—68no—
53#892—68no—
54C23×C32C22×C411yescharacteristic
55C22×C3⋊D3—22no—
56C22×C3⋊D3—22no—
57C22×C3⋊D3C4⋊C414yes—
58C22×C3⋊D3C22×C412yes—
59C2×C32×C4—24no—
60C2×C32×C4C4⋊C414yes—
61C2×C32×C4C22×C414yes—
62C2×C32×C4C22×C412yes—
63C2×C3⋊Dic3—24no—
64C2×C3⋊Dic3C22×C414yes—
65C2×C3⋊Dic3C22×C411yescharacteristic
66C2×C3⋊Dic3C2×D412yes—
67C2×C3⋊Dic3C2×Q812yes—
68C2×C3⋊Dic3C2411yescharacteristic
69C4×C3⋊D3C4⋊C418yes—
70C4×C3⋊D3C2×D414yes—
71C4×C3⋊D3C2×Q814yes—
72#622—22no—
73#622—22no—
74#622—24no—
75C22×M16—91no—
76C23×C8—91no—
77C2×#117—91no—
78#424—98no—
79C2×C4⋊C8—92no—
80C2×C4⋊C8—92no—
81C23×D3—62no—
82C22×C3×C4—22no—
83C22×C3×C4—24no—
84C22×Dic3—62no—
85C22×Dic3—64no—
86C2×C4×D3—64no—
87C2×C4×D3—64no—
88C2×C4×D3—68no—
89C2×C4×D3—68no—
90C3×C4⋊C4—28no—
91(C2×D3)⋊C4—616no—
92C4⋊Dic3—68no—
93C4×Dic3—68no—
94C4×Dic3—68no—
95C22×C32C2×C4⋊C412yes—
96C22×C32#13112yes—
97C22×C32#13112yes—
98C22×C32C23×C411yescharacteristic
99C2×C3⋊D3—22no—
100C2×C3⋊D3—22no—
101C2×C3⋊D3—28no—
102C2×C3⋊D3C2×C4⋊C414yes—
103C32×C4—24no—
104C32×C4C2×C4⋊C414yes—
105C3⋊Dic3—24no—
106C3⋊Dic3C2×C4⋊C412yes—
107C3⋊Dic3C22×D411yescharacteristic
108C3⋊Dic3C22×Q811yescharacteristic
109C23×C4—91no—
110C2×M16—94no—
111C2×M16—184no—
112C22×C8—94no—
113C22×C8—91no—
114C22×C8—91no—
115C22×C8—92no—
116C22×C8—184no—
117#117—94no—
118#117—94no—
119C2×C4⋊C4—91no—
120C2×C4⋊C4#15711yescharacteristic
121C2×C22⋊C4—92no—
122C2×C42—92no—
123C4⋊C8—98no—
124C4⋊C8—98no—
125C23×C3—22no—
126C22×D3—68no—
127C22×D3—64no—
128C22×D3—124no—
129C22×D3—124no—
130C2×C3×C4—24no—
131C2×C3×C4—28no—
132C2×C3×C4—28no—
133C2×C3×C4—48no—
134C2×Dic3—62no—
135C2×Dic3—64no—
136C2×Dic3—64no—
137C2×Dic3—62no—
138C2×Dic3—68no—
139C2×Dic3—128no—
140C4×D3—616no—
141C4×D3—68no—
142C4×D3—68no—
143C2×C32#42414yescomplemented
144C2×C32C22×C4⋊C411yescharacteristic
145C2×C32C2×#13111yescharacteristic
146C2×C32C2×#13111yescharacteristic
147C3⋊D3—24no—
148C24—91no—
149C22×C4—91no—
150C22×C4—92no—
151C22×C4—92no—
152C22×C4—94no—
153C22×C4—94no—
154C22×C4—92no—
155C22×C4C2×#15712yes—
156C22×C4C2×#15711yescharacteristic
157M16—188no—
158C2×C8—92no—
159C2×C8—92no—
160C2×C8—94no—
161C2×C8—188no—
162C2×C8—182no—
163C2×C8—182no—
164C2×C8—184no—
165C4⋊C4—94no—
166C4⋊C4C2×#15714yes—
167C22⋊C4—98no—
168C42—94no—
169C42—94no—
170C22×C3—24no—
171C22×C3—24no—
172C22×C3—24no—
173C22×C3—22no—
174C2×D3—68no—
175C2×D3—124no—
176C2×D3—124no—
177C2×D3—1216no—
178C3×C4—28no—
179C3×C4—48no—
180Dic3—64no—
181Dic3—62no—
182Dic3—62no—
183Dic3—128no—
184C32C2×#42411yescharacteristic, complemented, Sylow
185C23—94no—
186C23—92no—
187C23—182no—
188C23—182no—
189C23C22×#15711yescharacteristic
190C2×C4—24no—
191C2×C4—92no—
192C2×C4—92no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—94no—
196C2×C4—94no—
197C2×C4—98no—
198C2×C4—94no—
199C2×C4—184no—
200C2×C4C4⋊#15714yes—
201C2×C4C22×#15714yes—
202C2×C4C22×#15712yes—
203C8—182no—
204C8—182no—
205C8—184no—
206C2×C3—22no—
207C2×C3—22no—
208C2×C3—22no—
209C2×C3—28no—
210D3—128no—
211C22—94no—
212C22—182no—
213C22—182no—
214C22—188no—
215C22C2×C4⋊#15712yes—
216C22#6428712yes—
217C22#6428912yes—
218C22C23×#15711yescharacteristic
219C4—24no—
220C4—91no—
221C4—92no—
222C4—91no—
223C4—184no—
224C4C2×C4⋊#15714yes—
225C3—22no—
226C2—184no—
227C2#1059375514yesdirect product factor
228C2C22×C4⋊#15711yescharacteristic
229C2C2×#6428711yescharacteristic
230C2C2×#6428911yescharacteristic
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC2×C32×C4⋊C4C4
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C3⋊Dic3C24
hypercenterC2×C4⋊C4#157
hypocenterC32C2×#424
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#63779C2semidirect
5. C2×C4⋊#622C2semidirect
6. #10593755C2direct (N × H)
21. #63779C22semidirect
22. C4⋊#622C22semidirect
143. C2×C32#424semidirect
184. C32C2×#424semidirect
227. C2#10593755direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37882
C22×#37872
C2×#641012
C2×#637792
C2×C4⋊#6222
#105937552
C2×#4249