Finite Group Databasebeta

← #11776367

Subgroups — #11776367

Order 1152.

444 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 71 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#10593909C211yesmaximal, characteristic
2#10593728C211yesmaximal, characteristic
3#10590297C211yesmaximal, characteristic
4#10590040C214yesmaximal, complemented
5C2×#3797C412yes—
6C2×#3788—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×#869—21no—
9#63919C412yes—
10#63919C2212yes—
11#63900—21no—
12#63900—21no—
13#63873—21no—
14C4⋊#622—21no—
15C4⋊#622C2212yes—
16C3×C4×C3⋊C8—21no—
17#63572C2212yes—
18#63557—21no—
19D3×C4⋊Q8—61no—
20#4685—61no—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C3×Dic6—22no—
25C2×#627C2×C414yes—
26C2×#624—22no—
27#3797—44no—
28C2×#622—22no—
29#3788—42no—
30C32×C42D411yescharacteristic
31C4×C3⋊Dic3C2×C411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C4×C3⋊Dic3C2311yescharacteristic
34C3×C4⋊Dic3—22no—
35C3×C4⋊Dic3—22no—
36C2×C3×C3⋊C8—22no—
37#3724—22no—
38#3724—22no—
39#1548—91nomaximal, Sylow
40C2×D3×Q8—62no—
41C3×C4⋊Q8—61no—
42#944—62no—
43D3×C4⋊C4—62no—
44D3×C4⋊C4—62no—
45#888—62no—
46#888—62no—
47C42×D3—61no—
48C42×D3—61no—
49#869—21no—
50C3×C4×C8—61no—
51(C2×D3)⋊C8—62no—
52Dic3⋊C8—62no—
53C4×C3⋊C8—21no—
54C22×C3⋊D3C22⋊C411yescharacteristic
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3C22⋊C411yescharacteristic
59C2×C3⋊Dic3C22×C411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C4×C3⋊D3—22no—
62C4×C3⋊D3—22no—
63C4×C3⋊D3SD1612yes—
64C4×C3⋊D3Q1612yes—
65C2×C3×Dic3—24no—
66C3×Dic6—44no—
67#627—44no—
68#624—44no—
69#622—42no—
70C3×C3⋊C8—42no—
71C2×C4⋊Q8—91no—
72#431—91no—
73#423—91no—
74#333—94no—
75C2×C3×Q8—62no—
76D3×Q8—128no—
77C2×C4×D3—61no—
78C2×C4×D3—61no—
79C2×C4×D3—61no—
80C2×C4×D3—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—64no—
84C2×Dic6—22no—
85C2×Dic6—64no—
86C2×C3×C8—62no—
87C3×C4⋊C4—62no—
88C3×C4⋊C4—62no—
89C3×C42—21no—
90C3×C42—21no—
91C4⋊Dic3—22no—
92C4⋊Dic3—22no—
93Dic3⋊C4—64no—
94Dic3⋊C4—64no—
95C4×Dic3—61no—
96C4×Dic3—61no—
97C4×Dic3—61no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C2×C3⋊C8—22no—
102C22×C32C2×C22⋊C411yescharacteristic
103C2×C3⋊D3—21no—
104C2×C3⋊D3—21no—
105C2×C3⋊D3#10312yes—
106C32×C4#10012yes—
107C32×C4#10312yes—
108C32×C4#13712yes—
109C3⋊Dic3—21no—
110C3⋊Dic3—21no—
111C3⋊Dic3C2×SD1611yescharacteristic
112C3⋊Dic3C2×Q1611yescharacteristic
113C3×Dic3—44no—
114C22×Q8—92no—
115C2×M16—181no—
116C4⋊Q8—61no—
117C4⋊Q8—92no—
118C4⋊Q8—92no—
119C4⋊Q8—181no—
120C2×C4⋊C4—181no—
121C2×C4⋊C4—181no—
122C2×C42—91no—
123C4⋊C8—92no—
124C4⋊C8—92no—
125C4⋊C8—181no—
126C22⋊C8—181no—
127C4×C8—61no—
128C22×D3—61no—
129C22×D3—61no—
130C3×Q8—124no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—64no—
138C2×Dic3—24no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C4×D3—62no—
146C4×D3—62no—
147C4×D3—62no—
148C4×D3—62no—
149C4×D3—64no—
150C4×D3—64no—
151C4×D3—122no—
152C4×D3—122no—
153C4×D3—128no—
154Dic6—44no—
155Dic6—128no—
156C3×C8—122no—
157C3⋊C8—42no—
158C2×C32C2×#10011yescharacteristic
159C2×C32C2×#10311yescharacteristic
160C2×C32#41911yescharacteristic
161C3⋊D3—22no—
162C2×Q8—62no—
163C2×Q8—94no—
164C2×Q8—364no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—182no—
169M16—362no—
170C2×C8—62no—
171C2×C8—182no—
172C4⋊C4—62no—
173C4⋊C4—62no—
174C4⋊C4—182no—
175C4⋊C4—182no—
176C42—91no—
177C42—91no—
178C42—91no—
179C42GO+(4,𝔽2)11yescharacteristic
180C22×C3—21no—
181C22×C3—21no—
182C2×D3—62no—
183C2×D3—62no—
184C2×D3—62no—
185C2×D3—62no—
186C2×D3—121no—
187C2×D3—121no—
188C3×C4—22no—
189C3×C4—22no—
190C3×C4—22no—
191C3×C4—22no—
192C3×C4—22no—
193C3×C4—22no—
194C3×C4—124no—
195Dic3—44no—
196Dic3—61no—
197Dic3—61no—
198Dic3—61no—
199Dic3—61no—
200Dic3—62no—
201Dic3—62no—
202Dic3—121no—
203Dic3—121no—
204C32#154811yescharacteristic, complemented, Sylow
205C23—91no—
206Q8—124no—
207Q8—364no—
208C2×C4—64no—
209C2×C4—91no—
210C2×C4—92no—
211C2×C4—92no—
212C2×C4—91no—
213C2×C4—91no—
214C2×C4—182no—
215C2×C4—182no—
216C2×C4—364no—
217C2×C4D32⋊C411yescharacteristic
218C2×C4D32⋊C411yescharacteristic
219C2×C4C2×GO+(4,𝔽2)11yescharacteristic
220C8—122no—
221C8—362no—
222C2×C3—21no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—21no—
228D3—64no—
229D3—122no—
230C22—92no—
231C22—181no—
232C22—181no—
233C22C2×D32⋊C411yescharacteristic
234C4—91no—
235C4—91no—
236C4—124no—
237C4—181no—
238C4—181no—
239C4#6372712yes—
240C4#6373012yes—
241C4#6422612yes—
242C3—21no—
243C3—21no—
244C2—182no—
245C2C2×#6372711yescharacteristic
246C2C2×#6373011yescharacteristic
247C2#1059337411yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1548
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

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

Maximal subgroups

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

subgroupindex
#105939092
#105937282
#105902972
#105900402
#15489