Finite Group Databasebeta

← C2×#10593731 #11858744

Subgroups — C2×#10593731 #11858744

Order 1152.

986 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 986 conjugacy classes of subgroups — too many to draw. Only its 186 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×C42×C3⋊D3C211yesmaximal, characteristic
2C2×#63779C212yesmaximal, complemented
3C2×#63778C212yesmaximal
4C2×#63777C212yesmaximal, complemented
5#10593731C218yesmaximal, direct product factor
6C22×C4×C3⋊D3C411yescharacteristic
7C22×C4×C3⋊D3C411yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#622C2214yes—
10C2×C32×C42C411yescharacteristic
11C2×C4×C3⋊Dic3C411yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C42×C3⋊D3C414yes—
15C42×C3⋊D3C2214yes—
16#63779C2218yescomplemented
17#63778C2218yes—
18#63777C2218yescomplemented
19C2×C42×D3—62no—
20C23×C3⋊D3C2×C411yescharacteristic
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2311yescharacteristic
27C2×C4×C3⋊D3—24no—
28C2×C4×C3⋊D3—24no—
29C2×C4×C3⋊D3—24no—
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3C2×C414yes—
32C2×C4×C3⋊D3C2×C414yes—
33C2×C4×C3⋊D3C2312yes—
34C2×#622—28no—
35C2×#622C2318yes—
36C32×C42C2×C414yes—
37C4×C3⋊Dic3C2×C412yes—
38C4×C3⋊Dic3C2×C412yes—
39C4×C3⋊Dic3C2×C414yes—
40C4×C3⋊Dic3C2312yes—
41C4×C3⋊Dic3C2312yes—
42C2×#432—91nomaximal, Sylow
43C22×C4×D3—62no—
44C22×C4×D3—62no—
45C22×C4×D3—62no—
46C2×C3×C42—22no—
47C2×C4×Dic3—62no—
48C2×C4×Dic3—62no—
49C2×C4×Dic3—62no—
50C42×D3—68no—
51C42×D3—68no—
52C23×C32C22×C411yescharacteristic
53C22×C3⋊D3—22no—
54C22×C3⋊D3—22no—
55C22×C3⋊D3M1614yes—
56C22×C3⋊D3C22×C412yes—
57C2×C32×C4—22no—
58C2×C32×C4—22no—
59C2×C32×C4—22no—
60C2×C32×C4C22×C412yes—
61C2×C32×C4C22×C412yes—
62C2×C32×C4C22×C412yes—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3M1614yes—
65C2×C3⋊Dic3C22×C412yes—
66C2×C3⋊Dic3C22×C411yescharacteristic
67C2×C3⋊Dic3C22×C412yes—
68C2×C3⋊Dic3#4114yes—
69C2×C3⋊Dic3C2411yescharacteristic
70C4×C3⋊D3—28no—
71C4×C3⋊D3—24no—
72C4×C3⋊D3—28no—
73C4×C3⋊D3—24no—
74#622—28no—
75C22×C42—91no—
76#432—98no—
77C2×C4⋊C8—92no—
78C2×C22⋊C8—92no—
79C2×#97—92no—
80C23×D3—62no—
81C22×C3×C4—22no—
82C22×C3×C4—22no—
83C22×C3×C4—22no—
84C22×Dic3—62no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87C2×C4×D3—64no—
88C2×C4×D3—68no—
89C2×C4×D3—68no—
90C2×C4×D3—64no—
91C2×C4×D3—616no—
92C2×C4×D3—616no—
93C2×C4×D3—616no—
94C3×C42—28no—
95C4×Dic3—64no—
96C4×Dic3—64no—
97C4×Dic3—68no—
98C4×Dic3—64no—
99C4×Dic3—64no—
100C22×C32#11712yes—
101C22×C32C2×M1612yes—
102C22×C32C2×M1612yes—
103C22×C32C23×C411yescharacteristic
104C2×C3⋊D3—22no—
105C2×C3⋊D3—22no—
106C2×C3⋊D3—28no—
107C2×C3⋊D3C2×M1614yes—
108C32×C4—22no—
109C32×C4—22no—
110C32×C4—22no—
111C3⋊Dic3—22no—
112C3⋊Dic3#11712yes—
113C3⋊Dic3C2×M1614yes—
114C3⋊Dic3C2×#4112yes—
115C23×C4—91no—
116C23×C4—91no—
117C23×C4—91no—
118C22×C8—94no—
119C2×C42—91no—
120C2×C42—91no—
121C2×C42—91no—
122C2×C42—94no—
123C2×C42—94no—
124C2×C42#15711yescharacteristic
125C4⋊C8—98no—
126C22⋊C8—98no—
127#97—98no—
128C23×C3—22no—
129C22×D3—68no—
130C22×D3—64no—
131C22×D3—68no—
132C22×D3—68no—
133C2×C3×C4—28no—
134C2×C3×C4—28no—
135C2×C3×C4—28no—
136C2×C3×C4—24no—
137C2×C3×C4—24no—
138C2×C3×C4—24no—
139C2×Dic3—68no—
140C2×Dic3—62no—
141C2×Dic3—64no—
142C2×Dic3—64no—
143C2×Dic3—68no—
144C2×Dic3—62no—
145C2×Dic3—68no—
146C4×D3—616no—
147C4×D3—632no—
148C4×D3—616no—
149C4×D3—632no—
150C2×C32#43214yescomplemented
151C2×C32C2×#11711yescharacteristic
152C2×C32C22×M1611yescharacteristic
153C2×C32C22×M1611yescharacteristic
154C3⋊D3—24no—
155C24—91no—
156C22×C4—91no—
157C22×C4—91no—
158C22×C4—91no—
159C22×C4—92no—
160C22×C4—94no—
161C22×C4—92no—
162C22×C4—94no—
163C22×C4—184no—
164C22×C4—184no—
165C22×C4—184no—
166C22×C4C2×#15711yescharacteristic
167C22×C4C2×#15711yescharacteristic
168C22×C4C2×#15711yescharacteristic
169C2×C8—98no—
170C2×C8—188no—
171C42—92no—
172C42—92no—
173C42—92no—
174C42—92no—
175C42—94no—
176C42C2×#15714yes—
177C22×C3—24no—
178C22×C3—24no—
179C22×C3—24no—
180C22×C3—22no—
181C2×D3—68no—
182C2×D3—68no—
183C2×D3—68no—
184C2×D3—632no—
185C3×C4—28no—
186C3×C4—28no—
187C3×C4—28no—
188Dic3—64no—
189Dic3—68no—
190Dic3—64no—
191Dic3—68no—
192C32C2×#43211yescharacteristic, complemented, Sylow
193C23—94no—
194C23—92no—
195C23—182no—
196C23—182no—
197C23C22×#15711yescharacteristic
198C2×C4—22no—
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—188no—
208C2×C4—184no—
209C2×C4—184no—
210C2×C4—188no—
211C2×C4—182no—
212C2×C4C22×#15712yes—
213C2×C4C22×#15712yes—
214C2×C4C22×#15712yes—
215C8—188no—
216C2×C3—22no—
217C2×C3—22no—
218C2×C3—22no—
219C2×C3—28no—
220D3—616no—
221C22—94no—
222C22—182no—
223C22—182no—
224C22—188no—
225C22#6428312yes—
226C22#6428312yes—
227C22#6428612yes—
228C22C23×#15711yescharacteristic
229C4—22no—
230C4—22no—
231C4—22no—
232C4—94no—
233C4—92no—
234C4—92no—
235C4—182no—
236C3—22no—
237C2—184no—
238C2#1059373114yesdirect product factor
239C2C2×#6428311yescharacteristic
240C2C2×#6428311yescharacteristic
241C2C2×#6428611yescharacteristic
subgroupG/H
centerC23C22×#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC2×C32×C42C4
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C3⋊Dic3C24
hypercenterC2×C42#157
hypocenterC32C2×#432
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63779C2semidirect
4. C2×#63777C2semidirect
5. #10593731C2direct (N × H)
16. #63779C22semidirect
18. #63777C22semidirect
150. C2×C32#432semidirect
192. C32C2×#432semidirect
238. C2#10593731direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C2×#637792
C2×#637782
C2×#637772
#105937312
C2×#4329