Finite Group Databasebeta

← #11781819

Subgroups — #11781819

Order 1152.

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

normal subgroups only

This group has 260 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#10593376C212yesmaximal
2#10590905C211yesmaximal, characteristic
3#10590788C211yesmaximal, characteristic
4#10590172C211yesmaximal, characteristic
5#10590038C212yesmaximal
6C2×C3×Dic12—21no—
7C4×#627C2211yescharacteristic
8#63873C2212yes—
9C2×#3718—21no—
10C4⋊#622C2212yes—
11#63742—22no—
12#63740—22no—
13C8×C3⋊Dic3C2211yescharacteristic
14C3×Dic3⋊C8—21no—
15#63572C2211yescharacteristic
16#63554—21no—
17#5183—61no—
18#4828—61no—
19C2×C3×Dic6—22no—
20C2×#627D411yescharacteristic
21C2×#622—22no—
22C2×C32×C8D411yescharacteristic
23C4×C3⋊Dic3C2311yescharacteristic
24C2×C3⋊(C3⋊C8)D411yescharacteristic
25C3×C4×Dic3—21no—
26C2×C3×C3⋊C8—21no—
27C3×Dic12—42no—
28#3724—22no—
29#3724—22no—
30#3724D411yescharacteristic
31Dic3⋊Dic3—21no—
32#3718—42no—
33#1690—91nomaximal, Sylow
34C2×C3×Q16—61no—
35#944—62no—
36C2×#216—62no—
37C2×Dic12—21no—
38C4×Dic6—61no—
39C3×C4⋊C8—61no—
40#815—61no—
41Dic3⋊C8—21no—
42Dic3⋊C8—61no—
43C8×Dic3—61no—
44C8×Dic3—61no—
45#803—61no—
46C2×C32×C4C2×D411yescharacteristic
47C2×C3⋊Dic3C2×D411yescharacteristic
48C2×C3⋊Dic3#4111yescharacteristic
49C2×C3×Dic3—21no—
50C2×C3×Dic3—21no—
51C2×C3×Dic3—42no—
52C3×Dic6—42no—
53C3×Dic6—42no—
54#627—22no—
55#622—42no—
56C32×C8—21no—
57C3⋊(C3⋊C8)SD1612yes—
58C3×C3⋊C8—41no—
59#494—91no—
60#475—92no—
61#446—91no—
62#334—91no—
63#332—92no—
64C2×C3×Q8—62no—
65C2×Dic6—22no—
66C2×Dic6—61no—
67C3×Q16—122no—
68C2×C3×C8—21no—
69C2×C3×C8—21no—
70C2×C3×C8—61no—
71C3×C42—61no—
72#216—124no—
73C4⋊Dic3—61no—
74Dic3⋊C4—61no—
75Dic3⋊C4—61no—
76Dic3⋊C4—122no—
77Dic3⋊C4—122no—
78C4×Dic3—21no—
79C4×Dic3—61no—
80C4×Dic3—61no—
81C2×C3⋊C8—21no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8—61no—
84Dic12—42no—
85C22×C32#12111yescharacteristic
86C32×C4C2×SD1611yescharacteristic
87C32×C4AGL(1,ℤ/8)11yescharacteristic
88C3⋊Dic3—21no—
89C3⋊Dic3#13712yes—
90C3×Dic3—41no—
91C3×Dic3—41no—
92C3×Dic3—82no—
93C2×Q16—61no—
94C2×Q16—181no—
95C4⋊Q8—92no—
96C4×Q8—91no—
97#106—182no—
98C4⋊C8—61no—
99C4⋊C8—91no—
100C4⋊C8—92no—
101#103—182no—
102#97—181no—
103C4×C8—91no—
104C3×Q8—122no—
105C3×Q8—122no—
106C2×C3×C4—21no—
107C2×C3×C4—21no—
108C2×C3×C4—61no—
109C2×C3×C4—61no—
110C2×C3×C4—122no—
111C2×Dic3—21no—
112C2×Dic3—21no—
113C2×Dic3—42no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118Dic6—42no—
119Dic6—42no—
120Dic6—122no—
121C3×C8—22no—
122C3×C8—41no—
123C3×C8—121no—
124C3⋊C8—41no—
125C3⋊C8—62no—
126C3⋊C8—62no—
127C2×C32#46011yescharacteristic
128C2×C32#47011yescharacteristic
129C2×C32#47311yescharacteristic
130C2×Q8—62no—
131C2×Q8—91no—
132Q16—122no—
133Q16—362no—
134C2×C8—61no—
135C2×C8—91no—
136C2×C8—182no—
137C2×C8GO+(4,𝔽2)11yescharacteristic
138C4⋊C4—91no—
139C4⋊C4—181no—
140C4⋊C4—182no—
141C4⋊C4—182no—
142C42—61no—
143C42—91no—
144C22×C3—21no—
145C22×C3—21no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—21no—
150C3×C4—121no—
151C3×C4—121no—
152C3×C4—242no—
153Dic3—41no—
154Dic3—41no—
155Dic3—62no—
156Dic3—62no—
157Dic3—62no—
158Dic3—82no—
159Dic3—121no—
160C32#169011yescharacteristic, complemented, Sylow
161Q8—122no—
162Q8—122no—
163Q8—182no—
164C2×C4—61no—
165C2×C4—61no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—122no—
169C2×C4C2×GO+(4,𝔽2)11yescharacteristic
170C8—21no—
171C8—92no—
172C8—121no—
173C8—362no—
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—21no—
180C22#6423011yescharacteristic
181C4—92no—
182C4—121no—
183C4—121no—
184C4—181no—
185C4—242no—
186C4#6422711yescharacteristic
187C4#6423611yescharacteristic
188C3—21no—
189C3—21no—
190C2#1059328911yescharacteristic
191C2#1059330411yescharacteristic
192C2#1059335511yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32#121
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1690
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
160. C32#1690semidirect

Maximal subgroups

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

subgroupindex
#105933762
#105909052
#105907882
#105901722
#105900382
#16909