Finite Group Databasebeta

← C2×#10593378 #11873626

Subgroups — C2×#10593378 #11873626

Order 1152.

642 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 119 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×#63870C211yesmaximal, characteristic
3C2×#63777C211yesmaximal, characteristic
4C2×#63740C212yesmaximal
5C2×#63740C212yesmaximal
6#10593378C218yesmaximal, direct product factor
7C22×#627C2212yes—
8C22×#622C2212yes—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C3×C4⋊Dic3—21no—
11C2×C3×Dic3⋊C4—21no—
12C2×#3724—21no—
13C2×#3724C2211yescharacteristic
14C2×#3724C2211yescharacteristic
15C2×Dic3⋊Dic3—21no—
16#63919—22no—
17#63919C2214yes—
18#63870—22no—
19#63870C2214yes—
20#63777C2214yes—
21#63740C2218yes—
22#63740C2218yes—
23C2×#889—61no—
24C2×#888—61no—
25C22×C32×C4D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C22×C3×Dic3—21no—
29C22×C3×Dic3—21no—
30C22×C3×Dic3—22no—
31C2×#627—28no—
32C2×#627—22no—
33C2×#627C2314yes—
34C2×#622—24no—
35C2×#622C2314yes—
36C4×C3⋊Dic3D412yes—
37C4×C3⋊Dic3C2312yes—
38C3×C4⋊Dic3—24no—
39C3×Dic3⋊C4—24no—
40#3724—21no—
41#3724—21no—
42#3724—24no—
43#3724C2312yes—
44#3724C2312yes—
45Dic3⋊Dic3—24no—
46C2×#491—91nomaximal, Sylow
47C22×Dic6—62no—
48C2×C3×C4⋊C4—61no—
49C2×C3×C4⋊C4—61no—
50C2×C4⋊Dic3—21no—
51C2×C4⋊Dic3—61no—
52C2×Dic3⋊C4—21no—
53C2×Dic3⋊C4—61no—
54C2×Dic3⋊C4—61no—
55C2×Dic3⋊C4—62no—
56C2×Dic3⋊C4—61no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—61no—
59#889—64no—
60#889—64no—
61#888—64no—
62#888—64no—
63C23×C32C2×D411yescharacteristic
64C2×C32×C4—22no—
65C2×C32×C4C2×D412yes—
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3C2×D412yes—
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3⋊Dic3#4114yes—
70C2×C3⋊Dic3C2411yescharacteristic
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C2×C3×Dic3—24no—
74C2×C3×Dic3—44no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—42no—
77#627—28no—
78#627—44no—
79#622—24no—
80C2×C4⋊Q8—91no—
81C2×#125—91no—
82#491—98no—
83C2×#103—92no—
84C2×#103—92no—
85C2×#97—91no—
86C22×C3×C4—21no—
87C22×C3×C4—21no—
88C22×C3×C4—61no—
89C22×C3×C4—61no—
90C22×C3×C4—62no—
91C22×Dic3—21no—
92C22×Dic3—21no—
93C22×Dic3—22no—
94C22×Dic3—61no—
95C22×Dic3—61no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C2×Dic6—64no—
99C2×Dic6—64no—
100C2×Dic6—128no—
101C3×C4⋊C4—64no—
102C3×C4⋊C4—64no—
103C4⋊Dic3—24no—
104C4⋊Dic3—64no—
105Dic3⋊C4—24no—
106Dic3⋊C4—62no—
107Dic3⋊C4—62no—
108Dic3⋊C4—68no—
109Dic3⋊C4—64no—
110Dic3⋊C4—62no—
111Dic3⋊C4—62no—
112C4×Dic3—62no—
113C4×Dic3—62no—
114C4×Dic3—62no—
115C4×Dic3—62no—
116C22×C32#12412yes—
117C22×C32#13712yes—
118C22×C32#13712yes—
119C22×C32C22×D411yescharacteristic
120C32×C4—22no—
121C3⋊Dic3—22no—
122C3⋊Dic3#12412yes—
123C3⋊Dic3C2×#4112yes—
124C3×Dic3—44no—
125C3×Dic3—42no—
126C3×Dic3—42no—
127C22×Q8—92no—
128C22×C8—92no—
129C4⋊Q8—94no—
130C4⋊Q8—182no—
131#125—94no—
132#125—182no—
133C2×C4⋊C4—61no—
134C2×C4⋊C4—61no—
135C2×C4⋊C4—91no—
136C2×C4⋊C4—91no—
137C2×C4⋊C4—181no—
138C2×C4⋊C4—181no—
139C2×C42—91no—
140#103—98no—
141#103—98no—
142#97—94no—
143C23×C3—21no—
144C23×C3—21no—
145C2×C3×C4—24no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—42no—
149C2×C3×C4—62no—
150C2×C3×C4—62no—
151C2×C3×C4—64no—
152C2×C3×C4—124no—
153C2×C3×C4—122no—
154C2×C3×C4—122no—
155C2×Dic3—22no—
156C2×Dic3—22no—
157C2×Dic3—24no—
158C2×Dic3—44no—
159C2×Dic3—42no—
160C2×Dic3—42no—
161C2×Dic3—61no—
162C2×Dic3—62no—
163C2×Dic3—61no—
164C2×Dic3—64no—
165C2×Dic3—64no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—62no—
169C2×Dic3—64no—
170C2×Dic3—122no—
171Dic6—128no—
172Dic6—128no—
173C2×C32#49114yescomplemented
174C2×C32C2×#12411yescharacteristic
175C2×C32C2×#13711yescharacteristic
176C2×C32C2×#13711yescharacteristic
177C2×Q8—94no—
178C2×Q8—182no—
179C2×Q8—188no—
180C22×C4—61no—
181C22×C4—61no—
182C22×C4—62no—
183C22×C4—91no—
184C22×C4—91no—
185C22×C4GO+(4,𝔽2)11yescharacteristic
186C2×C8—94no—
187C2×C8—184no—
188C4⋊C4—64no—
189C4⋊C4—64no—
190C4⋊C4—92no—
191C4⋊C4—92no—
192C4⋊C4—181no—
193C4⋊C4—181no—
194C4⋊C4—184no—
195C4⋊C4—184no—
196C42—92no—
197C42—92no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—22no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—22no—
205C22×C3—22no—
206C3×C4—24no—
207C3×C4—42no—
208C3×C4—124no—
209C3×C4—122no—
210C3×C4—122no—
211Dic3—44no—
212Dic3—42no—
213Dic3—42no—
214Dic3—62no—
215Dic3—62no—
216Dic3—62no—
217Dic3—62no—
218Dic3—64no—
219Dic3—122no—
220C32C2×#49111yescharacteristic, complemented, Sylow
221C23C2×GO+(4,𝔽2)11yescharacteristic
222Q8—188no—
223Q8—364no—
224C2×C4—22no—
225C2×C4—62no—
226C2×C4—62no—
227C2×C4—64no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—94no—
231C2×C4—92no—
232C2×C4—124no—
233C2×C4—122no—
234C2×C4—122no—
235C2×C4—182no—
236C2×C4C2×GO+(4,𝔽2)12yes—
237C8—184no—
238C2×C3—24no—
239C2×C3—24no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C22#6422112yes—
247C22#6422612yes—
248C22#6423912yes—
249C22C22×GO+(4,𝔽2)11yescharacteristic
250C4—22no—
251C4—92no—
252C4—92no—
253C4—124no—
254C4—122no—
255C4—122no—
256C4—182no—
257C3—21no—
258C3—21no—
259C2#1059337814yesdirect product factor
260C2C2×#6422111yescharacteristic
261C2C2×#6422611yescharacteristic
262C2C2×#6423911yescharacteristic
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×#491
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
6. #10593378C2direct (N × H)
173. C2×C32#491semidirect
220. C32C2×#491semidirect
259. C2#10593378direct (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×#638702
C2×#637772
C2×#637402
#105933782
C2×#4919