Finite Group Databasebeta

← #11771482

Subgroups — #11771482

Order 1152.

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

normal subgroups only

This group has 266 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#10591244C211yesmaximal, characteristic
2#10590203C211yesmaximal, characteristic
3#10589148C211yesmaximal, characteristic
4C2×#3750C2211yescharacteristic
5C2×C3×Dic3⋊C4—21no—
6C2×#3724C411yescharacteristic
7C2×Dic3⋊Dic3—21no—
8C2×Dic32C411yescharacteristic
9C22⋊#622—21no—
10C3×#830—21no—
11#4975—61no—
12#4469—61no—
13C22×C32×C4D411yescharacteristic
14C22×C3⋊Dic3C2×C411yescharacteristic
15C22×C3⋊Dic3D411yescharacteristic
16C22×C3×Dic3—21no—
17C22×C3×Dic3—21no—
18C2×#622—41no—
19#3750—41no—
20C3×Dic3⋊C4—42no—
21C2×C3×C3⋊C8—41no—
22#3724—41no—
23Dic3⋊Dic3—42no—
24Dic32—21no—
25Dic32C812yescomplemented
26#1325—91nomaximal, Sylow
27C2×C3×C4⋊C4—61no—
28C2×C4⋊Dic3—61no—
29C2×Dic3⋊C4—21no—
30C2×Dic3⋊C4—61no—
31C2×Dic3⋊C4—61no—
32C2×Dic3⋊C4—61no—
33C2×Dic3⋊C4—61no—
34C2×C4×Dic3—61no—
35C3×C22⋊C8—61no—
36#830—21no—
37C23×C32C22⋊C411yescharacteristic
38C2×C32×C4—21no—
39C2×C32×C4—41no—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3—41no—
44C2×C3⋊Dic3C2×C811yescharacteristic
45C2×C3⋊Dic3M1611yescharacteristic
46C2×C3×Dic3—22no—
47C2×C3×Dic3—22no—
48C2×C3×Dic3—22no—
49C2×C3×Dic3—41no—
50C2×C3×Dic3—41no—
51C2×C3×Dic3—41no—
52#622—81no—
53C3×C3⋊C8—81no—
54#384—91no—
55#324—91no—
56#324—91no—
57C22×C3×C4—21no—
58C22×C3×C4—21no—
59C22×C3×C4—61no—
60C22×C3×C4—61no—
61C22×Dic3—21no—
62C22×Dic3—21no—
63C22×Dic3—61no—
64C22×Dic3—61no—
65C22×Dic3—61no—
66C22×Dic3—61no—
67C2×C3×C8—121no—
68C3×C4⋊C4—122no—
69C4⋊Dic3—122no—
70Dic3⋊C4—42no—
71Dic3⋊C4—122no—
72Dic3⋊C4—122no—
73Dic3⋊C4—122no—
74Dic3⋊C4—121no—
75Dic3⋊C4—121no—
76C4×Dic3—62no—
77C4×Dic3—62no—
78C2×C3⋊C8—41no—
79C22×C32—21no—
80C22×C32—21no—
81C22×C32C22⋊C811yescharacteristic
82C22×C32#9911yescharacteristic
83C22×C32#10111yescharacteristic
84C32×C4—41no—
85C3⋊Dic3—21no—
86C3⋊Dic3—21no—
87C3⋊Dic3—41no—
88C3×Dic3—24no—
89C3×Dic3—81no—
90C2×C4⋊C4—61no—
91C2×C4⋊C4—91no—
92C2×C4⋊C4—91no—
93C2×C4⋊C4—181no—
94C2×C42—91no—
95C22⋊C8—61no—
96C22⋊C8—181no—
97C23×C3—21no—
98C23×C3—21no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—41no—
102C2×C3×C4—41no—
103C2×C3×C4—41no—
104C2×C3×C4—62no—
105C2×C3×C4—62no—
106C2×C3×C4—62no—
107C2×C3×C4—81no—
108C2×C3×C4—121no—
109C2×C3×C4—121no—
110C2×C3×C4—121no—
111C2×Dic3—22no—
112C2×Dic3—22no—
113C2×Dic3—22no—
114C2×Dic3—41no—
115C2×Dic3—41no—
116C2×Dic3—41no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123C2×Dic3—121no—
124C2×Dic3—121no—
125C2×Dic3—121no—
126C2×Dic3—121no—
127C2×Dic3—121no—
128C2×Dic3—121no—
129C2×Dic3—241no—
130C3×C8—241no—
131C3⋊C8—81no—
132C2×C32—21no—
133C2×C32—21no—
134C2×C32#32411yescharacteristic
135C2×C32#35311yescharacteristic
136C2×C32#35611yescharacteristic
137C22×C4—61no—
138C22×C4—61no—
139C22×C4—91no—
140C22×C4—91no—
141C22×C4GO+(4,𝔽2)11yescharacteristic
142C2×C8—121no—
143C2×C8—361no—
144C4⋊C4—122no—
145C4⋊C4—361no—
146C4⋊C4—362no—
147C4⋊C4—361no—
148C42—92no—
149C42—181no—
150C22×C3—21no—
151C22×C3—21no—
152C22×C3—21no—
153C22×C3—21no—
154C22×C3—21no—
155C22×C3—21no—
156C22×C3—21no—
157C22×C3—21no—
158C22×C3—21no—
159C22×C3—21no—
160C22×C3—41no—
161C22×C3—41no—
162C3×C4—41no—
163C3×C4—41no—
164C3×C4—64no—
165C3×C4—81no—
166C3×C4—241no—
167Dic3—24no—
168Dic3—62no—
169Dic3—62no—
170Dic3—81no—
171Dic3—121no—
172Dic3—121no—
173Dic3—241no—
174Dic3—241no—
175C32#132511yescharacteristic, complemented, Sylow
176C23D32⋊C411yescharacteristic
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—62no—
180C2×C4—62no—
181C2×C4—62no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—121no—
185C2×C4—121no—
186C2×C4—121no—
187C2×C4—181no—
188C2×C4—181no—
189C2×C4—181no—
190C2×C4—361no—
191C8—241no—
192C8—721no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3—41no—
204C2×C3—41no—
205C22—21no—
206C22—21no—
207C22D32⋊C811yescharacteristic
208C22#6372811yescharacteristic
209C22#6373811yescharacteristic
210C4—41no—
211C4—64no—
212C4—181no—
213C4—181no—
214C4—241no—
215C4—361no—
216C3—21no—
217C3—21no—
218C2—21no—
219C2—21no—
220C2#1059002811yescharacteristic
221C2#1059006011yescharacteristic
222C2#1059008011yescharacteristic
subgroupG/H
centerC22#63738
commutatorC2×C3⋊Dic3C2×C8
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×#3750C22
hypocenterC32#1325
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
25. Dic32C8semidirect
175. C32#1325semidirect

Maximal subgroups

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

subgroupindex
#105912442
#105902032
#105891482
#13259