Finite Group Databasebeta

← #11777092

Subgroups — #11777092

Order 1152.

284 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 59 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#10593727C211yesmaximal, characteristic
2#10590331C211yesmaximal, characteristic
3#10590299C211yesmaximal, characteristic
4#10590042C212yesmaximal, complemented
5#10590041C212yesmaximal, complemented
6C42×C3⋊D3C2211yescharacteristic
7C2×#3710—21no—
8#63778C412yes—
9C4⋊#622C412yes—
10C4×#622C2212yes—
11C3×C4⋊(C3⋊C8)—21no—
12C3×#803—21no—
13#63572C2211yescharacteristic
14#63572C2212yes—
15#63572C2211yescharacteristic
16#63557—21no—
17D3×C4⋊C8—61no—
18#4705—61no—
19C2×C4×C3⋊D3C2×C411yescharacteristic
20C2×C4×C3⋊D3D411yescharacteristic
21C2×C4×C3⋊D3Q811yescharacteristic
22C2×#622C2×C414yes—
23C32×C42D411yescharacteristic
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3Q811yescharacteristic
26C4×C3⋊Dic3C2311yescharacteristic
27C2×C3×C3⋊C8—21no—
28C2×C3×C3⋊C8—21no—
29C2×C3×C3⋊C8—22no—
30#3710—42no—
31#1573—91nomaximal, Sylow
32C2×D3×C8—62no—
33C42×D3—61no—
34C42×D3—61no—
35C3×C4⋊C8—61no—
36C3×#97—61no—
37(C2×D3)⋊C8—61no—
38(C2×D3)⋊C8—61no—
39Dic3⋊C8—61no—
40Dic3⋊C8—61no—
41Dic3⋊C8—62no—
42C4⋊(C3⋊C8)—21no—
43#803—21no—
44C22×C3⋊D3C4⋊C411yescharacteristic
45C2×C32×C4C4⋊C411yescharacteristic
46C2×C32×C4C4⋊C411yescharacteristic
47C2×C32×C4C2×D411yescharacteristic
48C2×C3⋊Dic3C4⋊C411yescharacteristic
49C2×C3⋊Dic3C22×C411yescharacteristic
50C2×C3⋊Dic3C2×Q811yescharacteristic
51C4×C3⋊D3—21no—
52C4×C3⋊D3—21no—
53C4×C3⋊D3—22no—
54C4×C3⋊D3—22no—
55#622—24no—
56C3×C3⋊C8—42no—
57C3×C3⋊C8—41no—
58C3×C3⋊C8—41no—
59#432—91no—
60#431—91no—
61C2×C4⋊C8—91no—
62#335—92no—
63#334—92no—
64C2×C4×D3—61no—
65C2×C4×D3—61no—
66C2×C4×D3—61no—
67C2×C4×D3—61no—
68C2×C4×D3—61no—
69C2×C4×D3—61no—
70C2×C3×C8—61no—
71C2×C3×C8—61no—
72C2×C3×C8—62no—
73C3×C42—21no—
74C3×C42—21no—
75C4×Dic3—61no—
76C4×Dic3—61no—
77C4×Dic3—61no—
78C4×Dic3—61no—
79C4×Dic3—61no—
80C4×Dic3—61no—
81C2×C3⋊C8—21no—
82C2×C3⋊C8—21no—
83C2×C3⋊C8—22no—
84D3×C8—124no—
85C22×C32C2×C4⋊C411yescharacteristic
86C2×C3⋊D3—21no—
87C2×C3⋊D3—21no—
88C2×C3⋊D3#10812yes—
89C32×C4—21no—
90C32×C4—21no—
91C32×C4AGL(1,ℤ/8)11yescharacteristic
92C32×C4#13711yescharacteristic
93C3⋊Dic3—21no—
94C3⋊Dic3—21no—
95C3⋊Dic3#13112yes—
96C22×C8—181no—
97C2×C42—91no—
98C4⋊C8—61no—
99C4⋊C8—91no—
100C4⋊C8—92no—
101C4⋊C8—91no—
102C4⋊C8—92no—
103C22⋊C8—92no—
104C22⋊C8—181no—
105#97—61no—
106C4×C8—92no—
107C22×D3—61no—
108C22×D3—61no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C4×D3—62no—
122C4×D3—64no—
123C4×D3—62no—
124C4×D3—122no—
125C4×D3—121no—
126C4×D3—121no—
127C4×D3—122no—
128C4×D3—122no—
129C3×C8—122no—
130C3×C8—121no—
131C3×C8—121no—
132C3⋊C8—42no—
133C3⋊C8—41no—
134C3⋊C8—41no—
135C2×C32#42411yescharacteristic
136C2×C32#42811yescharacteristic
137C2×C32C2×#10811yescharacteristic
138C3⋊D3—22no—
139C22×C4—91no—
140C22×C4—91no—
141C22×C4—91no—
142C2×C8—61no—
143C2×C8—61no—
144C2×C8—62no—
145C2×C8—94no—
146C2×C8—362no—
147C42—91no—
148C42—91no—
149C42—91no—
150C42GO+(4,𝔽2)11yescharacteristic
151C22×C3—21no—
152C22×C3—21no—
153C2×D3—62no—
154C2×D3—62no—
155C2×D3—62no—
156C2×D3—62no—
157C2×D3—121no—
158C2×D3—121no—
159C3×C4—22no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—41no—
165C3×C4—41no—
166C3×C4—41no—
167Dic3—62no—
168Dic3—62no—
169Dic3—62no—
170Dic3—121no—
171Dic3—121no—
172Dic3—121no—
173C32#157311yescharacteristic, complemented, Sylow
174C23—91no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—182no—
179C2×C4—182no—
180C2×C4—181no—
181C2×C4—181no—
182C2×C4#377311yescharacteristic
183C2×C4#377311yescharacteristic
184C2×C4C2×GO+(4,𝔽2)11yescharacteristic
185C8—122no—
186C8—121no—
187C8—121no—
188C8—184no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—21no—
194C2×C3—21no—
195D3—64no—
196D3—122no—
197C22—92no—
198C22—181no—
199C22—181no—
200C22C2×#377311yescharacteristic
201C4—21no—
202C4—21no—
203C4—92no—
204C4—181no—
205C4—181no—
206C4#6422411yescharacteristic
207C4#6422611yescharacteristic
208C3—21no—
209C3—21no—
210C2—182no—
211C2#1059332711yescharacteristic
212C2#1059333111yescharacteristic
213C2#1059339411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1573
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590042C2semidirect
5. #10590041C2semidirect
173. C32#1573semidirect

Maximal subgroups

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

subgroupindex
#105937272
#105903312
#105902992
#105900422
#105900412
#15739