Finite Group Databasebeta

← #11790509

Subgroups — #11790509

Order 1152.

326 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 67 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×#63771C211yesmaximal, characteristic
2#10593394C212yesmaximal
3#10590700C211yesmaximal, characteristic
4#10590687C211yesmaximal, characteristic
5#10590052C212yesmaximal
6C2×#3788C2212yes—
7C2×C8×C3⋊D3C2211yescharacteristic
8#63900C2212yes—
9#63874C2211yescharacteristic
10C2×#3712C2211yescharacteristic
11#63771C414yescomplemented
12#63743—22no—
13#63742—22no—
14C3×#818—21no—
15C3×C8×Dic3—21no—
16#63576—21no—
17#63554—21no—
18D3×#107—61no—
19#4689—61no—
20C2×C4×C3⋊D3C2311yescharacteristic
21C2×#624—22no—
22C2×#622—22no—
23#3788—22no—
24#3788C2×C414yes—
25C2×C32×C8D411yescharacteristic
26C2×C3⋊(C3⋊C8)D411yescharacteristic
27C8×C3⋊D3C2×C412yes—
28C8×C3⋊D3Q812yes—
29C3×C4⋊Dic3—22no—
30C3×C4×Dic3—21no—
31C2×C3×C3⋊C8—21no—
32#3724—22no—
33#3724D411yescharacteristic
34#3724D411yescharacteristic
35#3722—21no—
36#3712—21no—
37#3712Q812yes—
38#1952—91nomaximal, Sylow
39C2×ΓL(1,𝔽25)—61no—
40C2×D3×C8—61no—
41C2×D3×C8—61no—
42D3×C4⋊C4—62no—
43#872—61no—
44C3×#107—61no—
45C3×C4×C8—61no—
46#818—21no—
47#815—61no—
48C8×Dic3—21no—
49#807—62no—
50#803—61no—
51C22×C3⋊D3#4111yescharacteristic
52C2×C32×C4C2×D411yescharacteristic
53C2×C3⋊Dic3C2×D411yescharacteristic
54C4×C3⋊D3C22×C411yescharacteristic
55C4×C3⋊D3C2×Q811yescharacteristic
56C4×C3⋊D3C2×Q811yescharacteristic
57C4×C3⋊D3#4111yescharacteristic
58C2×C3×Dic3—21no—
59C2×C3×Dic3—21no—
60C2×C3×Dic3—42no—
61#624—82no—
62#622—24no—
63C32×C8C4⋊C412yes—
64C3⋊(C3⋊C8)C4⋊C412yes—
65C3×C3⋊C8—22no—
66C2×#108—91no—
67#428—92no—
68C2×#107—91no—
69#405—91no—
70#343—92no—
71C2×C4×D3—61no—
72C2×C4×D3—61no—
73C2×C4×D3—122no—
74C2×C3×C8—21no—
75C2×C3×C8—21no—
76C2×C3×C8—61no—
77C3×C4⋊C4—62no—
78C3×C42—61no—
79(C2×D3)⋊C4—61no—
80(C2×D3)⋊C4—61no—
81C4⋊Dic3—22no—
82Dic3⋊C4—61no—
83Dic3⋊C4—61no—
84Dic3⋊C4—122no—
85C4×Dic3—21no—
86C2×C3⋊C8—21no—
87C2×C3⋊C8—61no—
88C2×C3⋊C8—61no—
89ΓL(1,𝔽25)—62no—
90ΓL(1,𝔽25)—62no—
91D3×C8—62no—
92D3×C8—62no—
93D3×C8—62no—
94D3×C8—62no—
95C22×C32#12111yescharacteristic
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3C4×Q811yescharacteristic
99C2×C3⋊D3#12511yescharacteristic
100C32×C4C2×C4⋊C411yescharacteristic
101C32×C4C22⋊Q811yescharacteristic
102C3⋊Dic3C4×D411yescharacteristic
103C3⋊Dic3C4⋊Q811yescharacteristic
104C3×Dic3—41no—
105C3×Dic3—41no—
106C3×Dic3—82no—
107C2×M16—91no—
108C2×M16—92no—
109C22×C8—91no—
110#117—91no—
111C2×C4⋊C4—92no—
112#108—94no—
113#107—61no—
114#107—181no—
115#107—182no—
116#106—182no—
117#97—181no—
118C4×C8—61no—
119C22×D3—61no—
120C22×D3—61no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4—61no—
124C2×C3×C4—61no—
125C2×C3×C4—122no—
126C2×Dic3—21no—
127C2×Dic3—21no—
128C2×Dic3—42no—
129C2×Dic3—61no—
130C2×Dic3—61no—
131C4×D3—61no—
132C4×D3—61no—
133C4×D3—61no—
134C4×D3—61no—
135C4×D3—61no—
136C4×D3—61no—
137C4×D3—61no—
138C4×D3—61no—
139C4×D3—244no—
140C3×C8—22no—
141C3×C8—22no—
142C3×C8—62no—
143C3⋊C8—22no—
144C3⋊C8—62no—
145C3⋊C8—62no—
146C2×C32#38911yescharacteristic
147C2×C32#47211yescharacteristic
148C2×C32#47311yescharacteristic
149C3⋊D3—21no—
150C3⋊D3—21no—
151C22×C4—91no—
152C22×C4—182no—
153M16—92no—
154M16—94no—
155M16—181no—
156M16—182no—
157C2×C8—61no—
158C2×C8—91no—
159C2×C8—92no—
160C2×C8—92no—
161C2×C8—182no—
162C2×C8GO+(4,𝔽2)11yescharacteristic
163C4⋊C4—62no—
164C4⋊C4—91no—
165C4⋊C4—91no—
166C4⋊C4—182no—
167C22⋊C4—181no—
168C42—61no—
169C22×C3—21no—
170C22×C3—21no—
171C2×D3—61no—
172C2×D3—61no—
173C2×D3—61no—
174C2×D3—61no—
175C2×D3—62no—
176C2×D3—62no—
177C2×D3—121no—
178C2×D3—121no—
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—121no—
184C3×C4—121no—
185C3×C4—242no—
186Dic3—41no—
187Dic3—41no—
188Dic3—61no—
189Dic3—61no—
190Dic3—61no—
191Dic3—61no—
192Dic3—82no—
193C32#195211yescharacteristic, complemented, Sylow
194C23—91no—
195C2×C4—61no—
196C2×C4—61no—
197C2×C4—91no—
198C2×C4—91no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—91no—
202C2×C4—122no—
203C2×C4—722no—
204C2×C4C2×GO+(4,𝔽2)11yescharacteristic
205C8—62no—
206C8—92no—
207C8—184no—
208C8#377312yes—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—21no—
215D3—62no—
216D3—62no—
217D3—121no—
218D3—121no—
219C22—91no—
220C22—91no—
221C22—181no—
222C22—181no—
223C22#6423011yescharacteristic
224C4—91no—
225C4—91no—
226C4—121no—
227C4—121no—
228C4—242no—
229C4D32⋊Q811yescharacteristic
230C4C2×#377311yescharacteristic
231C3—21no—
232C3—21no—
233C2—181no—
234C2—181no—
235C2#1059330111yescharacteristic
236C2#1059330411yescharacteristic
237C2#1059341211yescharacteristic
subgroupG/H
centerC22#64230
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1952
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
11. #63771C4semidirect
193. C32#1952semidirect

Maximal subgroups

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

subgroupindex
C2×#637712
#105933942
#105907002
#105906872
#105900522
#19529