Finite Group Databasebeta

← C2×#10593384 #11874896

Subgroups — C2×#10593384 #11874896

Order 1152.

714 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 159 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×#63919C211yesmaximal, characteristic
2C2×#63873C211yesmaximal, characteristic
3C2×C4×#622C211yesmaximal, characteristic
4C2×#63742C214yesmaximal
5#10593384C218yesmaximal, direct product factor
6C22×C3×Dic6—21no—
7C22×#627—21no—
8C22×#622C2212yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C3×C4⋊Dic3—21no—
11C2×#3724—21no—
12C2×#3724C2212yes—
13C2×#3724C2212yes—
14#63919—22no—
15#63919C2214yes—
16#63873—22no—
17#63873C2214yes—
18C4×#622C2214yes—
19#63742C22116yes—
20C2×#944—61no—
21C2×#888—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C22×C3×Dic3—22no—
26C22×C3×Dic3—22no—
27C2×C3×Dic6—24no—
28C2×C3×Dic6—44no—
29C2×#627—24no—
30C2×#627—44no—
31C2×#622Q818yescomplemented
32C2×#622C2314yes—
33C4×C3⋊Dic3D412yes—
34C4×C3⋊Dic3C2312yes—
35C3×C4⋊Dic3—24no—
36#3724—22no—
37#3724—24no—
38#3724—22no—
39#3724C2314yes—
40#3724C2314yes—
41C2×#498—91nomaximal, Sylow
42C22×C3×Q8—61no—
43C22×Dic6—21no—
44C22×Dic6—62no—
45C2×C3×C4⋊C4—61no—
46#944—64no—
47#944—64no—
48C2×C4⋊Dic3—21no—
49C2×Dic3⋊C4—62no—
50C2×Dic3⋊C4—62no—
51C2×Dic3⋊C4—62no—
52C2×C4×Dic3—61no—
53C2×C4×Dic3—61no—
54#888—64no—
55#888—64no—
56C23×C32C2×D411yescharacteristic
57C2×C32×C4SD1614yes—
58C2×C32×C4C2×D412yes—
59C2×C3⋊Dic3SD1614yes—
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3C2×D412yes—
62C2×C3⋊Dic3C2×Q814yes—
63C2×C3⋊Dic3C2411yescharacteristic
64C2×C3×Dic3—24no—
65C2×C3×Dic3—24no—
66C2×C3×Dic3—44no—
67C2×C3×Dic3—44no—
68C3×Dic6—48no—
69#627—48no—
70#622C2×Q818yescomplemented
71C2×C4⋊Q8—91no—
72C2×C4⋊Q8—91no—
73#498—98no—
74C2×#106—94no—
75C2×C4×C8—91no—
76C2×C3×Q8—64no—
77C2×C3×Q8—124no—
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C22×C3×C4—62no—
81C22×C3×C4—62no—
82C22×Dic3—22no—
83C22×Dic3—22no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C22×Dic3—61no—
88C2×Dic6—24no—
89C2×Dic6—44no—
90C2×Dic6—68no—
91C2×Dic6—128no—
92C3×C4⋊C4—64no—
93C4⋊Dic3—24no—
94Dic3⋊C4—64no—
95Dic3⋊C4—64no—
96Dic3⋊C4—64no—
97Dic3⋊C4—64no—
98Dic3⋊C4—68no—
99C4×Dic3—62no—
100C4×Dic3—62no—
101C4×Dic3—62no—
102C4×Dic3—62no—
103C22×C32C4⋊Q812yes—
104C22×C32C2×SD1612yes—
105C22×C32C2×SD1612yes—
106C22×C32C22×D411yescharacteristic
107C32×C4C2×SD1614yes—
108C3⋊Dic3C4⋊Q812yes—
109C3⋊Dic3C2×SD1614yes—
110C3⋊Dic3C22×Q812yes—
111C3×Dic3—44no—
112C3×Dic3—44no—
113C22×Q8—61no—
114C22×Q8—181no—
115C22×C8—92no—
116C4⋊Q8—94no—
117C4⋊Q8—94no—
118C4⋊Q8—182no—
119C4⋊Q8—182no—
120C2×C4⋊C4—61no—
121C2×C4⋊C4—92no—
122C2×C4⋊C4—92no—
123C2×C4⋊C4—181no—
124C2×C42—91no—
125#106—916no—
126C4×C8—94no—
127C23×C3—21no—
128C23×C3—21no—
129C3×Q8—128no—
130C2×C3×C4—22no—
131C2×C3×C4—22no—
132C2×C3×C4—24no—
133C2×C3×C4—24no—
134C2×C3×C4—64no—
135C2×C3×C4—64no—
136C2×C3×C4—124no—
137C2×C3×C4—124no—
138C2×Dic3—24no—
139C2×Dic3—24no—
140C2×Dic3—44no—
141C2×Dic3—44no—
142C2×Dic3—64no—
143C2×Dic3—64no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C2×Dic3—64no—
149C2×Dic3—64no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152Dic6—48no—
153Dic6—1216no—
154C2×C32#49814yescomplemented
155C2×C32C2×C4⋊Q811yescharacteristic
156C2×C32C22×SD1611yescharacteristic
157C2×C32C22×SD1611yescharacteristic
158C2×Q8—64no—
159C2×Q8—124no—
160C2×Q8—184no—
161C2×Q8—364no—
162C22×C4—62no—
163C22×C4—62no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4GO+(4,𝔽2)11yescharacteristic
167C2×C8—94no—
168C2×C8—98no—
169C4⋊C4—64no—
170C4⋊C4—94no—
171C4⋊C4—94no—
172C4⋊C4—182no—
173C4⋊C4—182no—
174C4⋊C4—184no—
175C42—92no—
176C42—92no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—22no—
180C22×C3—22no—
181C22×C3—22no—
182C22×C3—22no—
183C22×C3—22no—
184C22×C3—22no—
185C3×C4—24no—
186C3×C4—24no—
187C3×C4—124no—
188C3×C4—124no—
189Dic3—44no—
190Dic3—44no—
191Dic3—64no—
192Dic3—62no—
193Dic3—62no—
194Dic3—64no—
195Dic3—62no—
196Dic3—62no—
197C32C2×#49811yescharacteristic, complemented, Sylow
198C23C2×GO+(4,𝔽2)11yescharacteristic
199Q8—128no—
200Q8—368no—
201C2×C4—64no—
202C2×C4—64no—
203C2×C4—91no—
204C2×C4—91no—
205C2×C4—92no—
206C2×C4—94no—
207C2×C4—94no—
208C2×C4—124no—
209C2×C4—124no—
210C2×C4#377514yes—
211C2×C4C2×GO+(4,𝔽2)12yes—
212C8—98no—
213C2×C3—24no—
214C2×C3—24no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C22#6422212yes—
222C22#6422712yes—
223C22C2×#377512yes—
224C22C22×GO+(4,𝔽2)11yescharacteristic
225C4—92no—
226C4—92no—
227C4—94no—
228C4—124no—
229C4—124no—
230C4C2×#377514yes—
231C3—21no—
232C3—21no—
233C2#1059338414yesdirect product factor
234C2C2×#6422211yescharacteristic
235C2C2×#6422711yescharacteristic
236C2C22×#377511yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#498
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
5. #10593384C2direct (N × H)
31. C2×#622Q8semidirect
70. #622C2×Q8semidirect
154. C2×C32#498semidirect
197. C32C2×#498semidirect
233. C2#10593384direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#638732
C2×C4×#6222
C2×#637422
#105933842
C2×#4989