Finite Group Databasebeta

← #11776368

Subgroups — #11776368

Order 1152.

448 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 75 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×#63919C211yesmaximal, characteristic
2#10593795C211yesmaximal, characteristic
3#10591120C211yesmaximal, characteristic
4#10590040C214yesmaximal, complemented
5C22×#627C412yes—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C2×C3×C4⋊Dic3—21no—
8C2×C3×#208—21no—
9C2×#3724—21no—
10#63919—21no—
11#63919—21no—
12#63919C412yes—
13#63919C2212yes—
14C22⋊#622—21no—
15C4⋊#622C2212yes—
16C4×#622—21no—
17#63572—21no—
18#63572C2212yes—
19C2×#888—61no—
20#5118—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3C2×C411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3×Dic3—22no—
25C2×#627—22no—
26C2×#627—44no—
27C2×#627C2×C414yes—
28C2×#622—22no—
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C3×C4⋊Dic3—22no—
34C3×C4⋊Dic3—22no—
35C3×#208—42no—
36C2×C3×C3⋊C8—22no—
37#3724—22no—
38#3724—22no—
39#1548—91nomaximal, Sylow
40C22×Dic6—62no—
41C2×C3×M16—61no—
42C2×C3×C4⋊C4—61no—
43C2×C4⋊Dic3—21no—
44C2×Dic3⋊C4—62no—
45C2×C4×Dic3—61no—
46C2×C4×Dic3—61no—
47C2×#208—21no—
48#888—62no—
49#888—62no—
50#888—62no—
51#888—62no—
52Dic3⋊C8—62no—
53Dic3⋊C8—62no—
54C23×C32C22⋊C411yescharacteristic
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4SD1612yes—
57C2×C32×C4Q1612yes—
58C2×C32×C4C2×D411yescharacteristic
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3C22⋊C411yescharacteristic
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3C22×C411yescharacteristic
64C2×C3⋊Dic3C2×D411yescharacteristic
65C2×C3×Dic3—24no—
66C2×C3×Dic3—44no—
67#627—44no—
68#627—44no—
69#622—42no—
70C3×C3⋊C8—42no—
71C2×C4⋊Q8—91no—
72#431—91no—
73#423—91no—
74#333—94no—
75C22×C3×C4—21no—
76C22×C3×C4—21no—
77C22×C3×C4—62no—
78C22×Dic3—22no—
79C22×Dic3—61no—
80C22×Dic3—61no—
81C22×Dic3—61no—
82C22×Dic3—61no—
83C2×Dic6—64no—
84C2×Dic6—64no—
85C2×Dic6—128no—
86C3×M16—122no—
87C2×C3×C8—62no—
88C3×C4⋊C4—62no—
89C3×C4⋊C4—62no—
90C4⋊Dic3—22no—
91C4⋊Dic3—22no—
92Dic3⋊C4—64no—
93Dic3⋊C4—64no—
94C4×Dic3—61no—
95C4×Dic3—61no—
96C4×Dic3—61no—
97C4×Dic3—61no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C4×Dic3—61no—
102#208—42no—
103C2×C3⋊C8—22no—
104C22×C32—21no—
105C22×C32—21no—
106C22×C32#10312yes—
107C22×C32C2×C22⋊C411yescharacteristic
108C32×C4#10312yes—
109C32×C4C2×SD1611yescharacteristic
110C32×C4C2×Q1611yescharacteristic
111C3⋊Dic3—21no—
112C3⋊Dic3—21no—
113C3⋊Dic3#10012yes—
114C3⋊Dic3#13712yes—
115C3×Dic3—44no—
116C22×Q8—92no—
117C2×M16—61no—
118C4⋊Q8—92no—
119C4⋊Q8—92no—
120C4⋊Q8—181no—
121C4⋊Q8—181no—
122C2×C4⋊C4—61no—
123C2×C4⋊C4—181no—
124C2×C42—91no—
125C4⋊C8—92no—
126C4⋊C8—92no—
127C4⋊C8—181no—
128C22⋊C8—181no—
129C4×C8—181no—
130C23×C3—21no—
131C23×C3—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—22no—
137C2×C3×C4—22no—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×C3×C4—64no—
141C2×C3×C4—124no—
142C2×Dic3—24no—
143C2×Dic3—44no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—64no—
153C2×Dic3—64no—
154C2×Dic3—122no—
155C2×Dic3—122no—
156Dic6—128no—
157Dic6—128no—
158C3×C8—122no—
159C3⋊C8—42no—
160C2×C32—22no—
161C2×C32C2×#10011yescharacteristic
162C2×C32C2×#10311yescharacteristic
163C2×C32#41911yescharacteristic
164C2×Q8—94no—
165C2×Q8—182no—
166C2×Q8—364no—
167C22×C4—62no—
168C22×C4—91no—
169C22×C4—91no—
170C22×C4GO+(4,𝔽2)11yescharacteristic
171M16—122no—
172C2×C8—62no—
173C2×C8—182no—
174C4⋊C4—62no—
175C4⋊C4—62no—
176C4⋊C4—182no—
177C4⋊C4—182no—
178C42—91no—
179C42—91no—
180C42—91no—
181C42—91no—
182C22×C3—22no—
183C22×C3—22no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—22no—
187C22×C3—22no—
188C22×C3—41no—
189C22×C3—41no—
190C3×C4—21no—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—22no—
196C3×C4—124no—
197Dic3—44no—
198Dic3—62no—
199Dic3—62no—
200Dic3—62no—
201Dic3—62no—
202Dic3—62no—
203Dic3—62no—
204Dic3—121no—
205Dic3—121no—
206C32#154811yescharacteristic, complemented, Sylow
207C23D32⋊C411yescharacteristic
208Q8—364no—
209Q8—364no—
210C2×C4—64no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—91no—
214C2×C4—91no—
215C2×C4—124no—
216C2×C4—182no—
217C2×C4—182no—
218C2×C4D32⋊C411yescharacteristic
219C2×C4#377512yes—
220C2×C4#377612yes—
221C2×C4C2×GO+(4,𝔽2)11yescharacteristic
222C8—122no—
223C8—362no—
224C2×C3—24no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—21no—
230C2×C3—21no—
231C2×C3—42no—
232C22—21no—
233C22—21no—
234C22#6374012yes—
235C22C2×D32⋊C411yescharacteristic
236C4—92no—
237C4—92no—
238C4—124no—
239C4—181no—
240C4—181no—
241C4#6374012yes—
242C4C2×#377511yescharacteristic
243C4C2×#377611yescharacteristic
244C3—21no—
245C3—21no—
246C2—22no—
247C2#1059331211yescharacteristic
248C2#1059332111yescharacteristic
249C2C2×#6374011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1548
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590040C2semidirect
206. C32#1548semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
#105937952
#105911202
#105900402
#15489