Finite Group Databasebeta

← #11791018

Subgroups — #11791018

Order 1152.

498 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4×#622C211yesmaximal, characteristic
3C2×#63743C211yesmaximal, 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—
14C4×#622—22no—
15#63743—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#1969—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—21no—
52C2×C32×C4—21no—
53C2×C32×C4Q1612yescomplemented
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3Q1612yescomplemented
57C2×C3⋊Dic3C22×C411yescharacteristic
58C2×C3⋊Dic3C2×D411yescharacteristic
59C2×C3⋊Dic3C2×D411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3#4111yescharacteristic
62C2×C3⋊Dic3#4111yescharacteristic
63C2×C3×Dic3—24no—
64C2×C3×Dic3—42no—
65C2×C3×Dic3—42no—
66C2×C3×Dic3—42no—
67C2×C3×Dic3—42no—
68C2×C3×Dic3—42no—
69#627—24no—
70#627—24no—
71#627—42no—
72#627—42no—
73#622—22no—
74#622C22⋊C414yes—
75C22×Q16—91no—
76C2×#107—91no—
77C2×#103—92no—
78C2×C4×C8—91no—
79#391—92no—
80C22×C3×C4—22no—
81C22×C3×C4—62no—
82C22×C3×C4—62no—
83C22×Dic3—22no—
84C22×Dic3—22no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87C2×Dic6—64no—
88C2×Dic6—64no—
89C2×Dic6—122no—
90C2×Dic6—122no—
91C2×Dic6—122no—
92C2×Dic6—122no—
93Dic3⋊C4—122no—
94Dic3⋊C4—122no—
95C4×Dic3—122no—
96C4×Dic3—122no—
97C22×C32C4×D411yescharacteristic
98C22×C32#12111yescharacteristic
99C22×C32#12711yescharacteristic
100C22×C32C2×Q1611yescharacteristic
101C22×C32C2×Q1611yescharacteristic
102C22×C32#13511yescharacteristic
103C22×C32#13511yescharacteristic
104C32×C4—22no—
105C3⋊Dic3—22no—
106C3⋊Dic3C2×C22⋊C411yescharacteristic
107C3⋊Dic3C4×D411yescharacteristic
108C3⋊Dic3#12111yescharacteristic
109C3⋊Dic3#12411yescharacteristic
110C3×Dic3—44no—
111C3×Dic3—82no—
112C22×Q8—92no—
113C2×Q16—94no—
114C2×Q16—182no—
115C2×Q16—182no—
116C22×C8—91no—
117C22×C8—91no—
118C2×C4⋊C4—92no—
119C2×C42—91no—
120#107—182no—
121#103—184no—
122C4×C8—182no—
123#95—62no—
124#95—182no—
125C23×C3—22no—
126C2×C3×C4—24no—
127C2×C3×C4—42no—
128C2×C3×C4—42no—
129C2×C3×C4—64no—
130C2×C3×C4—122no—
131C2×C3×C4—122no—
132C2×C3×C4—122no—
133C2×C3×C4—122no—
134C2×C3×C4—122no—
135C2×Dic3—24no—
136C2×Dic3—42no—
137C2×Dic3—42no—
138C2×Dic3—42no—
139C2×Dic3—42no—
140C2×Dic3—42no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—64no—
148C2×Dic3—122no—
149C2×Dic3—122no—
150Dic6—124no—
151Dic6—124no—
152Dic6—124no—
153Dic6—124no—
154C2×C32#39011yescharacteristic
155C2×C32C4×Q1611yescharacteristic
156C2×C32C4×Q1611yescharacteristic
157C2×C32#46711yescharacteristic
158C2×C32#46711yescharacteristic
159C2×C32#49411yescharacteristic
160C2×C32#49511yescharacteristic
161C2×Q8—94no—
162C2×Q8—182no—
163C2×Q8—182no—
164C2×Q8—182no—
165C2×Q8—182no—
166C2×Q8—182no—
167C22×C4—62no—
168C22×C4—62no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4GO+(4,𝔽2)11yescharacteristic
172Q16—188no—
173C2×C8—92no—
174C2×C8—92no—
175C2×C8—92no—
176C2×C8—92no—
177C2×C8—181no—
178C2×C8—181no—
179C4⋊C4—182no—
180C4⋊C4—182no—
181C42—181no—
182C42—181no—
183C22×C3—22no—
184C22×C3—22no—
185C22×C3—22no—
186C22×C3—22no—
187C22×C3—22no—
188C22×C3—22no—
189C22×C3—22no—
190C3×C4—44no—
191C3×C4—124no—
192C3×C4—242no—
193Dic3—44no—
194Dic3—62no—
195Dic3—62no—
196Dic3—62no—
197Dic3—62no—
198Dic3—82no—
199Dic3—124no—
200C32#196911yescharacteristic, complemented, Sylow
201C23C2×GO+(4,𝔽2)11yescharacteristic
202Q8—184no—
203Q8—184no—
204Q8—362no—
205Q8—362no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—64no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—91no—
214C2×C4—91no—
215C2×C4—92no—
216C2×C4—122no—
217C2×C4—122no—
218C2×C4—122no—
219C2×C4—122no—
220C2×C4—122no—
221C2×C4—181no—
222C2×C4—181no—
223C2×C4#377612yescomplemented
224C8—94no—
225C8—182no—
226C2×C3—22no—
227C2×C3—22no—
228C2×C3—22no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—22no—
232C2×C3—22no—
233C22#6422311yescharacteristic
234C22#6422811yescharacteristic
235C22C4×GO+(4,𝔽2)11yescharacteristic
236C22#6423111yescharacteristic
237C22#6423711yescharacteristic
238C22C2×#377611yescharacteristic
239C22#6424211yescharacteristic
240C4—22no—
241C4—91no—
242C4—91no—
243C4—91no—
244C4—91no—
245C4—124no—
246C4—182no—
247C4—242no—
248C3—22no—
249C2#1059342411yescharacteristic
250C2C4×#377611yescharacteristic
251C2#1059344511yescharacteristic
252C2#1059344611yescharacteristic
253C2#1059345011yescharacteristic
254C2#1059345411yescharacteristic
255C2#1059352711yescharacteristic
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#1969
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
53. C2×C32×C4Q16semidirect
56. C2×C3⋊Dic3Q16semidirect
200. C32#1969semidirect
223. C2×C4#3776semidirect

Maximal subgroups

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

subgroupindex
C22×#37762
C2×C4×#6222
C2×#637432
C2×#637402
#105913962
#19699