Finite Group Databasebeta

← #11790049

Subgroups — #11790049

Order 1152.

314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C4×C4⋊#157C211yesmaximal, characteristic
2#10593726C211yesmaximal, characteristic
3C4×#3787C211yesmaximal, characteristic
4C2×#63744C212yesmaximal
5#10590090C212yesmaximal
6C2×C4⋊#157C411yescharacteristic
7C2×C4⋊#157C411yescharacteristic
8C2×C4×#157C2212yes—
9C2×#3787C2212yes—
10C2×#3787C2211yescharacteristic
11C2×#3787C2211yescharacteristic
12C42×C3⋊D3C2211yescharacteristic
13#63781C412yes—
14#63779—21no—
15C4⋊#622—21no—
16C4×#622—21no—
17C4×#622—21no—
18#63744—24no—
19C22×#157C2×C412yes—
20C22×#157C2×C412yes—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×#622—21no—
25C2×#622—21no—
26C2×#622—22no—
27C4⋊#157—22no—
28C4⋊#157C814yescomplemented
29C4×#157—22no—
30C4×#157—22no—
31#3787—21no—
32#3787—21no—
33#3787—22no—
34#3787—22no—
35#3787D412yes—
36#3787Q812yes—
37C32×C42Q811yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3Q811yescharacteristic
41#1939—91nomaximal, Sylow
42C42×D3—121no—
43C22×C3⋊D3C22×C411yescharacteristic
44C2×#157—22no—
45C2×#157—22no—
46C2×#157—22no—
47C2×#157—22no—
48C2×#157—22no—
49C2×#157C2×C814yes—
50C2×C32×C4C4⋊C411yescharacteristic
51C2×C32×C4C4⋊C411yescharacteristic
52C2×C32×C4C2×Q811yescharacteristic
53C2×C3⋊Dic3C4⋊C411yescharacteristic
54C2×C3⋊Dic3C4⋊C411yescharacteristic
55C2×C3⋊Dic3C2×D411yescharacteristic
56C4×C3⋊D3—21no—
57C4×C3⋊D3—21no—
58C4×C3⋊D3C2×C812yes—
59C4×C3⋊D3M1612yes—
60C4×C3⋊D3C2×D411yescharacteristic
61C4×C3⋊D3C2×Q811yescharacteristic
62C4×C3⋊D3#4111yescharacteristic
63C4×C3⋊D3#4111yescharacteristic
64#622—22no—
65#622—22no—
66#622—42no—
67C2×C4⋊C8—92no—
68C2×C4⋊C8—91no—
69C2×C4×C8—91no—
70C4×C4⋊C4—91no—
71#336—92no—
72C2×C4×D3—121no—
73C2×C4×D3—121no—
74C2×C4×D3—121no—
75C3×C42—41no—
76C4×Dic3—121no—
77C4×Dic3—121no—
78C4×Dic3—121no—
79C22×C32C2×C4⋊C411yescharacteristic
80C2×C3⋊D3C4×D411yescharacteristic
81C2×C3⋊D3C4×Q811yescharacteristic
82C2×C3⋊D3C22×C811yescharacteristic
83C2×C3⋊D3C2×M1611yescharacteristic
84C2×C3⋊D3#13111yescharacteristic
85C2×C3⋊D3#13111yescharacteristic
86#157—24no—
87#157—42no—
88C32×C4—21no—
89C32×C4C4⋊C812yescomplemented
90C32×C4#12511yescharacteristic
91C32×C4C4⋊Q811yescharacteristic
92C3⋊Dic3—21no—
93C3⋊Dic3C4⋊C812yescomplemented
94C3⋊Dic3#12111yescharacteristic
95C3⋊Dic3C22⋊Q811yescharacteristic
96C22×C8—91no—
97C22×C8—91no—
98C22×C8—92no—
99C2×C4⋊C4—91no—
100C2×C4⋊C4—91no—
101C2×C42—91no—
102C2×C42—92no—
103C4⋊C8—181no—
104C4⋊C8—181no—
105C4⋊C8—184no—
106C4×C8—181no—
107C4×C8—181no—
108#95—92no—
109C22×D3—121no—
110C2×C3×C4—41no—
111C2×C3×C4—41no—
112C2×C3×C4—41no—
113C2×Dic3—121no—
114C2×Dic3—121no—
115C2×Dic3—121no—
116C4×D3—122no—
117C4×D3—122no—
118C4×D3—121no—
119C4×D3—121no—
120C4×D3—121no—
121C4×D3—121no—
122C4×D3—122no—
123C4×D3—122no—
124C2×C32#38911yescharacteristic
125C2×C32C2×C4⋊C811yescharacteristic
126C2×C32#42411yescharacteristic
127C3⋊D3C8×D411yescharacteristic
128C3⋊D3#43611yescharacteristic
129C3⋊D3C8×Q811yescharacteristic
130C3⋊D3#44611yescharacteristic
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—92no—
134C22×C4—91no—
135C22×C4—92no—
136C2×C8—92no—
137C2×C8—92no—
138C2×C8—181no—
139C2×C8—181no—
140C2×C8—181no—
141C2×C8—181no—
142C2×C8—182no—
143C2×C8—182no—
144C2×C8—182no—
145C4⋊C4—94no—
146C4⋊C4—182no—
147C42—91no—
148C42—91no—
149C42—91no—
150C42—182no—
151C42—182no—
152C42PSU(3,𝔽2)11yescharacteristic
153C22×C3—41no—
154C2×D3—121no—
155C2×D3—121no—
156C2×D3—121no—
157C2×D3—121no—
158C2×D3—121no—
159C2×D3—121no—
160C3×C4—42no—
161C3×C4—42no—
162C3×C4—41no—
163C3×C4—41no—
164Dic3—122no—
165Dic3—121no—
166Dic3—121no—
167Dic3—122no—
168C32#193911yescharacteristic, complemented, Sylow
169C23—91no—
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—92no—
173C2×C4—92no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—94no—
179C2×C4—91no—
180C2×C4—181no—
181C2×C4—181no—
182C2×C4—182no—
183C2×C4—182no—
184C2×C4—182no—
185C2×C4—182no—
186C2×C4—182no—
187C2×C4#377711yescharacteristic
188C2×C4#377711yescharacteristic
189C2×C4C2×PSU(3,𝔽2)11yescharacteristic
190C8—182no—
191C8—182no—
192C8—362no—
193C2×C3—41no—
194C2×C3—41no—
195C2×C3—41no—
196D3—121no—
197D3—121no—
198D3—121no—
199D3—121no—
200C22—91no—
201C22—91no—
202C22—91no—
203C22—91no—
204C22—91no—
205C22—91no—
206C22C2×#377711yescharacteristic
207C4—21no—
208C4—92no—
209C4—91no—
210C4—91no—
211C4—184no—
212C4—181no—
213C4—362no—
214C4#6374412yescomplemented
215C4#6424311yescharacteristic
216C4C4⋊PSU(3,𝔽2)11yescharacteristic
217C3—41no—
218C2—91no—
219C2—91no—
220C2—91no—
221C2—91no—
222C2C2×#6374411yescharacteristic
223C2#1059354011yescharacteristic
224C2#1059355411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×PSU(3,𝔽2)
commutatorC2×C3⋊D3C22×C8
FittingC32×C42Q8
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42PSU(3,𝔽2)
hypocenterC32#1939
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
28. C4⋊#157C8semidirect
89. C32×C4C4⋊C8semidirect
93. C3⋊Dic3C4⋊C8semidirect
168. C32#1939semidirect
214. C4#63744semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#1572
#105937262
C4×#37872
C2×#637442
#105900902
#19399