Finite Group Databasebeta

← C2×#10590040 #11776169

Subgroups — C2×#10590040 #11776169

Order 1152.

470 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 95 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×C4⋊#622C211yesmaximal, characteristic
3C2×#63572C211yesmaximal, characteristic
4#10590040C214yesmaximal, direct product factor
5C22×#627C412yes—
6C22×#622—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4⋊Dic3—21no—
9C22×C3×C3⋊C8—21no—
10C2×#3724—21no—
11#63919—21no—
12#63919—21no—
13#63919C412yes—
14#63919C2212yes—
15C4⋊#622—21no—
16C4⋊#622C2212yes—
17#63572—21no—
18#63572C2212yes—
19C2×#888—61no—
20C2×Dic3⋊C8—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3C2×C411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3×Dic3—22no—
25C2×#627—22no—
26C2×#627—44no—
27C2×#627C2×C414yes—
28C2×#622—22no—
29C2×#622—42no—
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C4×C3⋊Dic3C2311yescharacteristic
34C3×C4⋊Dic3—22no—
35C3×C4⋊Dic3—22no—
36C2×C3×C3⋊C8—22no—
37C2×C3×C3⋊C8—42no—
38#3724—22no—
39#3724—22no—
40C2×#333—91nomaximal, Sylow
41C22×Dic6—62no—
42C22×C3×C8—61no—
43C2×C3×C4⋊C4—61no—
44C2×C4⋊Dic3—21no—
45C2×Dic3⋊C4—62no—
46C2×C4×Dic3—61no—
47C2×C4×Dic3—61no—
48C22×C3⋊C8—21no—
49#888—62no—
50#888—62no—
51#888—62no—
52#888—62no—
53Dic3⋊C8—62no—
54Dic3⋊C8—62no—
55C23×C32C22⋊C411yescharacteristic
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4SD1612yes—
58C2×C32×C4Q1612yes—
59C2×C32×C4C2×D411yescharacteristic
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3C22⋊C411yescharacteristic
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3SD1612yes—
64C2×C3⋊Dic3Q1612yes—
65C2×C3⋊Dic3C22×C411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3×Dic3—24no—
68C2×C3×Dic3—44no—
69#627—44no—
70#627—44no—
71#622—42no—
72C3×C3⋊C8—42no—
73C2×C4⋊Q8—91no—
74C2×C4⋊C8—91no—
75C2×C4⋊C8—91no—
76#333—94no—
77C22×C3×C4—21no—
78C22×C3×C4—21no—
79C22×C3×C4—62no—
80C22×Dic3—22no—
81C22×Dic3—61no—
82C22×Dic3—61no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C2×Dic6—64no—
86C2×Dic6—64no—
87C2×Dic6—128no—
88C2×C3×C8—62no—
89C2×C3×C8—122no—
90C3×C4⋊C4—62no—
91C3×C4⋊C4—62no—
92C4⋊Dic3—22no—
93C4⋊Dic3—22no—
94Dic3⋊C4—64no—
95Dic3⋊C4—64no—
96C4×Dic3—61no—
97C4×Dic3—61no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C2×C3⋊C8—22no—
105C2×C3⋊C8—42no—
106C22×C32#10012yes—
107C22×C32#10312yes—
108C22×C32#10312yes—
109C22×C32C2×C22⋊C411yescharacteristic
110C32×C4#10312yes—
111C32×C4C2×SD1611yescharacteristic
112C32×C4C2×Q1611yescharacteristic
113C3⋊Dic3—21no—
114C3⋊Dic3—21no—
115C3⋊Dic3#10312yes—
116C3⋊Dic3C2×SD1611yescharacteristic
117C3⋊Dic3C2×Q1611yescharacteristic
118C3×Dic3—44no—
119C22×Q8—92no—
120C22×C8—61no—
121C22×C8—181no—
122C4⋊Q8—92no—
123C4⋊Q8—92no—
124C4⋊Q8—181no—
125C4⋊Q8—181no—
126C2×C4⋊C4—61no—
127C2×C4⋊C4—181no—
128C2×C42—91no—
129C4⋊C8—92no—
130C4⋊C8—92no—
131C4⋊C8—181no—
132C4⋊C8—181no—
133C23×C3—21no—
134C23×C3—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—22no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—22no—
143C2×C3×C4—64no—
144C2×C3×C4—124no—
145C2×Dic3—24no—
146C2×Dic3—44no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—62no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—64no—
160C2×Dic3—122no—
161Dic6—128no—
162Dic6—128no—
163C3×C8—122no—
164C3⋊C8—42no—
165C2×C32#33314yescomplemented
166C2×C32C2×#10011yescharacteristic
167C2×C32C2×#10311yescharacteristic
168C2×C32C2×#10311yescharacteristic
169C2×Q8—94no—
170C2×Q8—182no—
171C2×Q8—364no—
172C22×C4—62no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4GO+(4,𝔽2)11yescharacteristic
176C2×C8—62no—
177C2×C8—122no—
178C2×C8—182no—
179C2×C8—362no—
180C4⋊C4—62no—
181C4⋊C4—62no—
182C4⋊C4—182no—
183C4⋊C4—182no—
184C42—91no—
185C42—91no—
186C42—91no—
187C42—91no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—22no—
191C22×C3—22no—
192C22×C3—22no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—22no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—21no—
199C3×C4—21no—
200C3×C4—22no—
201C3×C4—22no—
202C3×C4—124no—
203Dic3—44no—
204Dic3—62no—
205Dic3—62no—
206Dic3—61no—
207Dic3—61no—
208Dic3—61no—
209Dic3—61no—
210Dic3—62no—
211Dic3—62no—
212Dic3—121no—
213Dic3—121no—
214C32C2×#33311yescharacteristic, complemented, Sylow
215C23D32⋊C411yescharacteristic
216Q8—364no—
217Q8—364no—
218C2×C4—64no—
219C2×C4—91no—
220C2×C4—91no—
221C2×C4—92no—
222C2×C4—92no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—124no—
226C2×C4—182no—
227C2×C4D32⋊C411yescharacteristic
228C2×C4#377512yes—
229C2×C4#377612yes—
230C2×C4C2×GO+(4,𝔽2)11yescharacteristic
231C8—122no—
232C8—362no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—24no—
238C2×C3—24no—
239C2×C3—21no—
240C2×C3—21no—
241C22#6372712yes—
242C22#6373012yes—
243C22#6374012yes—
244C22C2×D32⋊C411yescharacteristic
245C4—91no—
246C4—91no—
247C4—92no—
248C4—124no—
249C4—181no—
250C4—181no—
251C4#6374012yes—
252C4C2×#377511yescharacteristic
253C4C2×#377611yescharacteristic
254C3—21no—
255C3—21no—
256C2#1059004014yesdirect product factor
257C2C2×#6372711yescharacteristic
258C2C2×#6373011yescharacteristic
259C2C2×#6374011yescharacteristic
subgroupG/H
centerC23D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socle, prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#333
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590040C2direct (N × H)
165. C2×C32#333semidirect
214. C32C2×#333semidirect
256. C2#10590040direct (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×C4⋊#6222
C2×#635722
#105900402
C2×#3339