Finite Group Databasebeta

← C2×#10593804 #11858741

Subgroups — C2×#10593804 #11858741

Order 1152.

986 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 986 conjugacy classes of subgroups — too many to draw. Only its 194 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×C4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C22⋊#622C212yesmaximal
3#10593804C218yesmaximal, direct product factor
4C2×#63779C212yesmaximal, complemented
5C2×#63777C212yesmaximal, complemented
6C23×C32×C4C411yescharacteristic
7C23×C3⋊Dic3C411yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C22×#622C2214yes—
10C2×C4×C3⋊Dic3C411yescharacteristic
11C2×C4×C3⋊Dic3C414yes—
12C2×C4×C3⋊Dic3C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2214yes—
16C22⋊#622C2218yes—
17#63779C2218yescomplemented
18#63777C2218yescomplemented
19C22×C4×Dic3—62no—
20C24×C32C2×C411yescharacteristic
21C22×C32×C4—24no—
22C22×C32×C4C2×C414yes—
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3—24no—
26C22×C3⋊Dic3—24no—
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C414yes—
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C412yes—
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2312yes—
33C22×C3⋊Dic3C2311yescharacteristic
34C2×#622—28no—
35C2×#622C2318yes—
36C4×C3⋊Dic3C2×C414yes—
37C4×C3⋊Dic3C2×C414yes—
38C4×C3⋊Dic3C2×C412yes—
39C4×C3⋊Dic3C2×C412yes—
40C4×C3⋊Dic3C2312yes—
41C4×C3⋊Dic3C2312yes—
42C2×#432—91nomaximal, Sylow
43C23×C3×C4—22no—
44C23×Dic3—62no—
45C23×Dic3—62no—
46C2×C4×Dic3—62no—
47C2×C4×Dic3—68no—
48C2×C4×Dic3—62no—
49C2×C4×Dic3—62no—
50C2×C4×Dic3—62no—
51C2×C4×Dic3—68no—
52C23×C32—22no—
53C23×C32—22no—
54C23×C32M1614yes—
55C23×C32C22×C412yes—
56C23×C32C22×C411yescharacteristic
57C2×C32×C4—28no—
58C2×C32×C4—22no—
59C2×C32×C4—22no—
60C2×C32×C4C22×C412yes—
61C2×C32×C4C22×C412yes—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—24no—
65C2×C3⋊Dic3—28no—
66C2×C3⋊Dic3—24no—
67C2×C3⋊Dic3M1614yes—
68C2×C3⋊Dic3C22×C412yes—
69C2×C3⋊Dic3C22×C412yes—
70C2×C3⋊Dic3C22×C411yescharacteristic
71C2×C3⋊Dic3C22×C412yes—
72C2×C3⋊Dic3#4114yes—
73C2×C3⋊Dic3C2411yescharacteristic
74#622—28no—
75C22×C42—91no—
76#432—98no—
77C2×C4⋊C8—92no—
78C2×C22⋊C8—92no—
79C2×#97—92no—
80C24×C3—22no—
81C22×C3×C4—216no—
82C22×C3×C4—28no—
83C22×C3×C4—22no—
84C22×C3×C4—22no—
85C22×Dic3—62no—
86C22×Dic3—64no—
87C22×Dic3—68no—
88C22×Dic3—62no—
89C22×Dic3—62no—
90C22×Dic3—62no—
91C22×Dic3—64no—
92C22×Dic3—616no—
93C22×Dic3—616no—
94C4×Dic3—64no—
95C4×Dic3—64no—
96C4×Dic3—68no—
97C4×Dic3—68no—
98C4×Dic3—64no—
99C4×Dic3—64no—
100C22×C32—22no—
101C22×C32—22no—
102C22×C32—28no—
103C22×C32#11712yes—
104C22×C32C2×M1614yes—
105C22×C32C2×M1612yes—
106C22×C32C2×M1612yes—
107C22×C32C23×C411yescharacteristic
108C32×C4—22no—
109C32×C4—22no—
110C3⋊Dic3—22no—
111C3⋊Dic3—22no—
112C3⋊Dic3#11712yes—
113C3⋊Dic3C2×M1614yes—
114C3⋊Dic3C2×#4112yes—
115C23×C4—91no—
116C23×C4—91no—
117C23×C4#15711yescharacteristic
118C22×C8—94no—
119C2×C42—91no—
120C2×C42—91no—
121C2×C42—94no—
122C2×C42—91no—
123C2×C42—94no—
124C2×C42—91no—
125C4⋊C8—98no—
126C22⋊C8—98no—
127#97—98no—
128C23×C3—28no—
129C23×C3—28no—
130C23×C3—24no—
131C23×C3—22no—
132C23×C3—28no—
133C2×C3×C4—232no—
134C2×C3×C4—28no—
135C2×C3×C4—28no—
136C2×C3×C4—24no—
137C2×C3×C4—24no—
138C2×Dic3—68no—
139C2×Dic3—62no—
140C2×Dic3—64no—
141C2×Dic3—64no—
142C2×Dic3—64no—
143C2×Dic3—68no—
144C2×Dic3—62no—
145C2×Dic3—616no—
146C2×Dic3—632no—
147C2×Dic3—616no—
148C2×Dic3—68no—
149C2×Dic3—68no—
150C2×C32—24no—
151C2×C32#43214yescomplemented
152C2×C32C2×#11711yescharacteristic
153C2×C32C22×M1611yescharacteristic
154C2×C32C22×M1611yescharacteristic
155C24C2×#15711yescharacteristic
156C22×C4—24no—
157C22×C4—91no—
158C22×C4—91no—
159C22×C4—92no—
160C22×C4—94no—
161C22×C4—92no—
162C22×C4—91no—
163C22×C4—91no—
164C22×C4—184no—
165C22×C4—184no—
166C22×C4C2×#15714yes—
167C22×C4C2×#15711yescharacteristic
168C22×C4C2×#15711yescharacteristic
169C2×C8—98no—
170C2×C8—188no—
171C42—92no—
172C42—92no—
173C42—92no—
174C42—92no—
175C42—94no—
176C42—94no—
177C22×C3—28no—
178C22×C3—28no—
179C22×C3—232no—
180C22×C3—24no—
181C22×C3—24no—
182C22×C3—28no—
183C22×C3—24no—
184C22×C3—22no—
185C3×C4—28no—
186C3×C4—28no—
187Dic3—64no—
188Dic3—68no—
189Dic3—64no—
190Dic3—68no—
191Dic3—68no—
192C32C2×#43211yescharacteristic, complemented, Sylow
193C23—22no—
194C23—22no—
195C23#379214yes—
196C23C22×#15712yes—
197C23C22×#15711yescharacteristic
198C2×C4—28no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—94no—
202C2×C4—94no—
203C2×C4—91no—
204C2×C4—92no—
205C2×C4—91no—
206C2×C4—92no—
207C2×C4—92no—
208C2×C4—188no—
209C2×C4—184no—
210C2×C4—184no—
211C2×C4—182no—
212C2×C4—182no—
213C2×C4C22×#15712yes—
214C2×C4C22×#15712yes—
215C8—188no—
216C2×C3—216no—
217C2×C3—28no—
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—22no—
221C22—28no—
222C22—22no—
223C22—22no—
224C22#6428312yes—
225C22#6428612yes—
226C22C2×#379214yes—
227C22C2×#379212yes—
228C22C23×#15711yescharacteristic
229C4—22no—
230C4—22no—
231C4—94no—
232C4—92no—
233C4—92no—
234C4—182no—
235C4—182no—
236C3—22no—
237C2—24no—
238C2#1059380414yesdirect product factor
239C2C2×#6428311yescharacteristic
240C2C2×#6428611yescharacteristic
241C2C22×#379211yescharacteristic
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC23×C32×C4C4
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC2×C3⋊Dic3C24
hypercenterC23×C4#157
hypocenterC32C2×#432
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10593804C2direct (N × H)
4. C2×#63779C2semidirect
5. C2×#63777C2semidirect
17. #63779C22semidirect
18. #63777C22semidirect
151. C2×C32#432semidirect
192. C32C2×#432semidirect
238. C2#10593804direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C2×C22⋊#6222
#105938042
C2×#637792
C2×#637772
C2×#4329