Finite Group Databasebeta

← #11791084

Subgroups — #11791084

Order 1152.

490 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 81 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×#3776C211yesmaximal, characteristic
2C2×#63777C211yesmaximal, characteristic
3C2×#63742C211yesmaximal, characteristic
4C2×#63740C212yesmaximal
5#10591396C212yesmaximal
6C22×#627C2212yes—
7C22×#622C2211yescharacteristic
8C22×#622C2211yescharacteristic
9C2×#3776—22no—
10C2×#3776—22no—
11C2×#3776C414yescomplemented
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3724C2212yes—
14#63777—22no—
15#63742—22no—
16#63740—24no—
17C3×C3⋊#95—22no—
18#63579—22no—
19#4646—62no—
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3D411yescharacteristic
22C22×C3⋊Dic3C2311yescharacteristic
23C22×C3×Dic3—22no—
24C22×C3×Dic3—22no—
25C2×#627—22no—
26C2×#627—22no—
27C2×#627—22no—
28C2×#627—22no—
29C2×#627—22no—
30C2×#627C2×C414yes—
31C2×#622—21no—
32C2×#622—21no—
33C2×#622C2×C412yes—
34C2×#622D412yes—
35C2×#622D412yes—
36C2×#622D412yes—
37#3776—28no—
38C4×C3⋊Dic3—21no—
39C4×C3⋊Dic3—21no—
40#3724—22no—
41#3724—22no—
42#1971—91nomaximal, Sylow
43C22×Dic6—62no—
44C2×Dic3⋊C4—62no—
45C2×C4×Dic3—62no—
46C3×#95—62no—
47C3⋊#95—22no—
48C3⋊#95—62no—
49C3⋊#95—62no—
50C23×C32C2×D411yescharacteristic
51C2×C32×C4—22no—
52C2×C32×C4—21no—
53C2×C3⋊Dic3—22no—
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3C22×C411yescharacteristic
56C2×C3⋊Dic3C2×D411yescharacteristic
57C2×C3⋊Dic3C2×D411yescharacteristic
58C2×C3⋊Dic3C2×D411yescharacteristic
59C2×C3⋊Dic3#4111yescharacteristic
60C2×C3⋊Dic3#4111yescharacteristic
61C2×C3×Dic3—24no—
62C2×C3×Dic3—42no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—42no—
65C2×C3×Dic3—42no—
66C2×C3×Dic3—42no—
67#627—24no—
68#627—24no—
69#627—42no—
70#627—42no—
71#622—22no—
72#622C22⋊C414yes—
73C22×Q16—91no—
74C2×#106—91no—
75C2×#103—92no—
76C2×#97—91no—
77#391—92no—
78C22×C3×C4—22no—
79C22×C3×C4—62no—
80C22×C3×C4—62no—
81C22×Dic3—22no—
82C22×Dic3—22no—
83C22×Dic3—62no—
84C22×Dic3—62no—
85C2×Dic6—64no—
86C2×Dic6—64no—
87C2×Dic6—122no—
88C2×Dic6—122no—
89C2×Dic6—122no—
90C2×Dic6—122no—
91Dic3⋊C4—122no—
92Dic3⋊C4—122no—
93C4×Dic3—122no—
94C4×Dic3—122no—
95C22×C32C4×D411yescharacteristic
96C22×C32#12111yescharacteristic
97C22×C32#12711yescharacteristic
98C22×C32#13712yes—
99C22×C32#13712yes—
100C32×C4—41no—
101C3⋊Dic3—41no—
102C3⋊Dic3C2×C22⋊C411yescharacteristic
103C3⋊Dic3C4×D411yescharacteristic
104C3⋊Dic3#12111yescharacteristic
105C3⋊Dic3#12411yescharacteristic
106C3×Dic3—44no—
107C3×Dic3—82no—
108C22×Q8—92no—
109C2×Q16—94no—
110C2×Q16—182no—
111C2×Q16—182no—
112C22×C8—91no—
113C22×C8—91no—
114C2×C4⋊C4—92no—
115C2×C42—91no—
116#106—182no—
117#103—184no—
118#97—182no—
119#95—62no—
120#95—182no—
121C23×C3—22no—
122C2×C3×C4—24no—
123C2×C3×C4—42no—
124C2×C3×C4—42no—
125C2×C3×C4—64no—
126C2×C3×C4—122no—
127C2×C3×C4—122no—
128C2×C3×C4—122no—
129C2×C3×C4—122no—
130C2×C3×C4—122no—
131C2×Dic3—24no—
132C2×Dic3—42no—
133C2×Dic3—42no—
134C2×Dic3—42no—
135C2×Dic3—42no—
136C2×Dic3—42no—
137C2×Dic3—62no—
138C2×Dic3—62no—
139C2×Dic3—62no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—64no—
144C2×Dic3—122no—
145C2×Dic3—122no—
146Dic6—124no—
147Dic6—124no—
148Dic6—124no—
149Dic6—124no—
150C2×C32#39011yescharacteristic
151C2×C32#44112yes—
152C2×C32#47011yescharacteristic
153C2×C32#47011yescharacteristic
154C2×C32#49712yes—
155C2×Q8—94no—
156C2×Q8—182no—
157C2×Q8—182no—
158C2×Q8—182no—
159C2×Q8—182no—
160C2×Q8—182no—
161C22×C4—62no—
162C22×C4—62no—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4GO+(4,𝔽2)11yescharacteristic
166Q16—188no—
167C2×C8—92no—
168C2×C8—92no—
169C2×C8—92no—
170C2×C8—92no—
171C2×C8—181no—
172C2×C8—181no—
173C4⋊C4—182no—
174C4⋊C4—182no—
175C42—181no—
176C42—181no—
177C22×C3—22no—
178C22×C3—22no—
179C22×C3—22no—
180C22×C3—22no—
181C22×C3—22no—
182C22×C3—22no—
183C22×C3—22no—
184C3×C4—44no—
185C3×C4—124no—
186C3×C4—242no—
187Dic3—44no—
188Dic3—62no—
189Dic3—62no—
190Dic3—62no—
191Dic3—62no—
192Dic3—82no—
193Dic3—124no—
194C32#197111yescharacteristic, complemented, Sylow
195C23C2×GO+(4,𝔽2)11yescharacteristic
196Q8—184no—
197Q8—184no—
198Q8—362no—
199Q8—362no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—64no—
203C2×C4—91no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—91no—
207C2×C4—91no—
208C2×C4—91no—
209C2×C4—122no—
210C2×C4—122no—
211C2×C4—122no—
212C2×C4—122no—
213C2×C4—122no—
214C2×C4—182no—
215C2×C4—181no—
216C8—94no—
217C8—182no—
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—22no—
221C2×C3—22no—
222C2×C3—22no—
223C2×C3—22no—
224C2×C3—22no—
225C22#6422612yes—
226C22C4×GO+(4,𝔽2)11yescharacteristic
227C22#6423111yescharacteristic
228C22#6423912yes—
229C22#6424211yescharacteristic
230C4—41no—
231C4—91no—
232C4—91no—
233C4—91no—
234C4—91no—
235C4—124no—
236C4—242no—
237C4—361no—
238C3—22no—
239C2#1059336912yes—
240C2#1059344312yes—
241C2#1059344911yescharacteristic
242C2#1059345411yescharacteristic
243C2#1059350811yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1971
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
11. C2×#3776C4semidirect
194. C32#1971semidirect

Maximal subgroups

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

subgroupindex
C22×#37762
C2×#637772
C2×#637422
C2×#637402
#105913962
#19719