Finite Group Databasebeta

← #11771912

Subgroups — #11771912

Order 1152.

206 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 31 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#10591188C211yesmaximal, characteristic
2C22⋊#3708C211yesmaximal, characteristic
3#10589165C211yesmaximal, characteristic
4C22×C3⋊(C3⋊C8)C2211yescharacteristic
5C3×#924—21no—
6C2×C3×#208—21no—
7C2×#3718C411yescharacteristic
8C2×#3708—21no—
9#63576C411yescharacteristic
10#63565—21no—
11#5051—61no—
12#4558—61no—
13C22×C32×C4D411yescharacteristic
14C2×C3×Dic6—21no—
15C2×C3⋊(C3⋊C8)—41no—
16C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
17C2×C3⋊(C3⋊C8)D411yescharacteristic
18C3×#217—41no—
19C3×C4⋊Dic3—21no—
20C3×Dic3⋊C4—41no—
21C3×#208—22no—
22C3×#208—41no—
23C2×C3×C3⋊C8—41no—
24#3718—41no—
25#3708—41no—
26#1350—91nomaximal, Sylow
27C2×C3×M16—61no—
28C3×C22⋊Q8—61no—
29C2×#216—61no—
30#924—21no—
31C2×#208—21no—
32C22×C3⋊C8—61no—
33C22×C3⋊C8—61no—
34#835—61no—
35#810—61no—
36#807—61no—
37C23×C32SD1611yescharacteristic
38C2×C32×C4—21no—
39C2×C32×C4—21no—
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C32×C4D811yescharacteristic
42C2×C3×Dic3—41no—
43C2×C3×Dic3—41no—
44C3×Dic6—41no—
45C3×Dic6—41no—
46C3⋊(C3⋊C8)—21no—
47C3⋊(C3⋊C8)—21no—
48C3×C3⋊C8—42no—
49#467—91no—
50C22⋊C16—91no—
51#341—91no—
52C2×C3×Q8—61no—
53C22×C3×C4—21no—
54C22×C3×C4—21no—
55C2×Dic6—21no—
56C3×M16—62no—
57C3×M16—121no—
58C2×C3×C8—121no—
59C3×C4⋊C4—61no—
60C3×C4⋊C4—121no—
61C3×C22⋊C4—121no—
62#217—41no—
63#216—122no—
64C4⋊Dic3—21no—
65Dic3⋊C4—41no—
66#208—22no—
67#208—41no—
68C2×C3⋊C8—41no—
69C2×C3⋊C8—61no—
70C2×C3⋊C8—61no—
71C2×C3⋊C8—61no—
72C2×C3⋊C8—61no—
73C2×C3⋊C8—122no—
74C2×C3⋊C8—121no—
75C2×C3⋊C8—121no—
76C22×C32—21no—
77C22×C32—21no—
78C22×C32—21no—
79C22×C32#10211yescharacteristic
80C32×C4—21no—
81C32×C4#9911yescharacteristic
82C32×C4#10411yescharacteristic
83C3×Dic3—81no—
84C3×Dic3—81no—
85C2×Q16—91no—
86C2×M16—61no—
87C22×C8—91no—
88C22⋊Q8—61no—
89C2×C16—181no—
90#107—91no—
91#103—181no—
92C23×C3—21no—
93C23×C3—21no—
94C3×Q8—121no—
95C3×Q8—121no—
96C2×C3×C4—21no—
97C2×C3×C4—21no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—41no—
105C2×C3×C4—41no—
106C2×C3×C4—121no—
107C2×C3×C4—121no—
108C2×Dic3—41no—
109C2×Dic3—41no—
110Dic6—41no—
111Dic6—41no—
112C3×C8—122no—
113C3⋊C8—42no—
114C3⋊C8—62no—
115C3⋊C8—121no—
116C3⋊C8—121no—
117C3⋊C8—121no—
118C2×C32—41no—
119C2×C32#32711yescharacteristic
120C2×C32#35911yescharacteristic
121C2×C32#36211yescharacteristic
122C2×Q8—61no—
123C22×C4GO+(4,𝔽2)11yescharacteristic
124Q16—361no—
125M16—62no—
126M16—121no—
127C2×C8—91no—
128C2×C8—91no—
129C2×C8—121no—
130C2×C8—361no—
131C4⋊C4—61no—
132C4⋊C4—121no—
133C22⋊C4—121no—
134C16—361no—
135C22×C3—21no—
136C22×C3—21no—
137C22×C3—22no—
138C22×C3—21no—
139C22×C3—21no—
140C22×C3—41no—
141C22×C3—41no—
142C22×C3—41no—
143C22×C3—41no—
144C3×C4—21no—
145C3×C4—21no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—21no—
150C3×C4—41no—
151C3×C4—241no—
152C3×C4—241no—
153Dic3—81no—
154Dic3—81no—
155C32#135011yescharacteristic, complemented, Sylow
156C23#377511yescharacteristic
157Q8—121no—
158Q8—121no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—121no—
162C2×C4—121no—
163C2×C4D32⋊C411yescharacteristic
164C2×C4#377411yescharacteristic
165C8—122no—
166C8—181no—
167C8—181no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—21no—
174C2×C3—41no—
175C2×C3—41no—
176C2×C3—42no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22#6373911yescharacteristic
181C4—21no—
182C4—241no—
183C4—241no—
184C4#6373811yescharacteristic
185C4#6374111yescharacteristic
186C3—21no—
187C3—21no—
188C2—41no—
189C2#1059006311yescharacteristic
190C2#1059006611yescharacteristic
191C2#1059007111yescharacteristic
subgroupG/H
centerC22#63739
commutatorC2×C3⋊(C3⋊C8)C2×C4
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#102
prime radicalC23×C32SD16
cosocleC22×C3⋊(C3⋊C8)C22
hypocenterC32#1350
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
155. C32#1350semidirect

Maximal subgroups

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

subgroupindex
#105911882
C22⋊#37082
#105891652
#13509