Finite Group Databasebeta

← #11781754

Subgroups — #11781754

Order 1152.

312 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 43 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
1#10593439C212yesmaximal, complemented
2#10590886C211yesmaximal, characteristic
3#10590788C211yesmaximal, characteristic, complemented
4#10590172C211yesmaximal, characteristic, complemented
5#10590037C212yesmaximal, complemented
6C2×#3775—22no—
7C2×C3×D24—21no—
8C4×#627C2211yescharacteristic
9#63914C2212yes—
10C2×#3713—21no—
11C4⋊#622C2212yes—
12#63739—22no—
13C8×C3⋊Dic3C2211yescharacteristic
14C3×Dic3⋊C8—21no—
15#63572C2211yescharacteristic
16#63554—21no—
17#5151—61no—
18#4828—61no—
19C2×C3×D12—22no—
20C2×#627D411yescharacteristic
21C2×#625—22no—
22C2×#625—22no—
23C2×#622—22no—
24#3775—44no—
25C2×C32×C8D411yescharacteristic
26C4×C3⋊Dic3C2311yescharacteristic
27C2×C3⋊(C3⋊C8)D411yescharacteristic
28C3×C4×Dic3—21no—
29C2×C3×C3⋊C8—21no—
30C3×D24—42no—
31#3724D411yescharacteristic
32Dic3⋊Dic3—21no—
33#3713—42no—
34#1688—91nomaximal, Sylow
35C2×C3×D8—61no—
36#940—62no—
37C2×#213—62no—
38C2×D24—21no—
39C4×Dic6—61no—
40C3×C4⋊C8—61no—
41#815—61no—
42Dic3⋊C8—21no—
43Dic3⋊C8—61no—
44C8×Dic3—61no—
45C8×Dic3—61no—
46#803—61no—
47C22×C3×D3—42no—
48C2×C32×C4C2×D411yescharacteristic
49C2×C3⋊Dic3C2×D411yescharacteristic
50C2×C3⋊Dic3#4111yescharacteristic
51C2×C3×Dic3—21no—
52C2×C3×Dic3—21no—
53C3×D12—42no—
54C3×D12—42no—
55#627—22no—
56#625—42no—
57#625—42no—
58#625—82no—
59#622—42no—
60C32×C8—21no—
61C3⋊(C3⋊C8)SD1612yescomplemented
62C3×C3⋊C8—41no—
63#493—91no—
64#460—92no—
65#446—91no—
66#334—91no—
67#331—92no—
68C2×C3×D4—62no—
69C2×#67—122no—
70C2×#67—122no—
71C2×D12—22no—
72C2×Dic6—61no—
73C3×D8—122no—
74C2×C3×C8—21no—
75C2×C3×C8—21no—
76C2×C3×C8—61no—
77C3×C42—61no—
78#213—124no—
79C4⋊Dic3—61no—
80Dic3⋊C4—61no—
81Dic3⋊C4—61no—
82C4×Dic3—21no—
83C4×Dic3—61no—
84C4×Dic3—61no—
85C2×C3⋊C8—21no—
86C2×C3⋊C8—61no—
87C2×C3⋊C8—61no—
88D24—42no—
89C22×C32#12111yescharacteristic
90C2×C3×D3—82no—
91C2×C3×D3—82no—
92C2×C3×D3—82no—
93C32×C4C2×SD1611yescharacteristic
94C32×C4AGL(1,ℤ/8)11yescharacteristic
95C3⋊Dic3—21no—
96C3⋊Dic3AGL(1,ℤ/8)12yes—
97C3×Dic3—41no—
98C3×Dic3—41no—
99C2×SD16—182no—
100C2×D8—61no—
101C2×D8—181no—
102#127—92no—
103C4×Q8—91no—
104C4⋊C8—61no—
105C4⋊C8—91no—
106C4⋊C8—92no—
107#102—182no—
108#97—181no—
109C4×C8—91no—
110C23×C3—122no—
111C22×D3—42no—
112C3×D4—122no—
113C3×D4—122no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—61no—
117C2×C3×C4—61no—
118#67—242no—
119#67—242no—
120#67—244no—
121C2×Dic3—21no—
122C2×Dic3—21no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—61no—
127D12—42no—
128D12—42no—
129Dic6—122no—
130C3×C8—22no—
131C3×C8—41no—
132C3×C8—121no—
133C3⋊C8—41no—
134C3⋊C8—62no—
135C3⋊C8—62no—
136C2×C32#46011yescharacteristic
137C2×C32#46911yescharacteristic
138C2×C32#47211yescharacteristic
139C3×D3—162no—
140C2×Q8—91no—
141C2×D4—62no—
142C2×D4—182no—
143C2×D4—182no—
144SD16—364no—
145D8—122no—
146D8—362no—
147C2×C8—61no—
148C2×C8—91no—
149C2×C8—182no—
150C2×C8GO+(4,𝔽2)11yescharacteristic
151C4⋊C4—91no—
152C4⋊C4—181no—
153C42—61no—
154C42—91no—
155C22×C3—21no—
156C22×C3—21no—
157C22×C3—242no—
158C22×C3—242no—
159C22×C3—242no—
160C2×D3—82no—
161C2×D3—82no—
162C2×D3—82no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—121no—
168C3×C4—121no—
169Dic3—41no—
170Dic3—41no—
171Dic3—62no—
172Dic3—62no—
173Dic3—62no—
174Dic3—121no—
175C32#168811yescharacteristic, complemented, Sylow
176C23—122no—
177Q8—182no—
178D4—122no—
179D4—122no—
180D4—362no—
181D4—362no—
182D4—722no—
183C2×C4—61no—
184C2×C4—61no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4C2×GO+(4,𝔽2)11yescharacteristic
188C8—21no—
189C8—92no—
190C8—121no—
191C8—362no—
192C2×C3—21no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—482no—
199D3—162no—
200C22—242no—
201C22—242no—
202C22—242no—
203C22#6423011yescharacteristic
204C4—92no—
205C4—121no—
206C4—121no—
207C4—181no—
208C4#6422711yescharacteristic
209C4#6423611yescharacteristic
210C3—21no—
211C3—21no—
212C2—482no—
213C2#1059328711yescharacteristic
214C2#1059330111yescharacteristic
215C2#1059335511yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radical#10590886C2
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1688
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #10593439C2semidirect
3. #10590788C2semidirect
4. #10590172C2semidirect
5. #10590037C2semidirect
61. C3⋊(C3⋊C8)SD16semidirect
175. C32#1688semidirect

Maximal subgroups

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

subgroupindex
#105934392
#105908862
#105907882
#105901722
#105900372
#16889