Finite Group Databasebeta

← #11798956

Subgroups — #11798956

Order 1152.

270 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 43 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×#63736C212yesmaximal
2#10590905C211yesmaximal, characteristic
3#10590790C211yesmaximal, characteristic
4#10590177C211yesmaximal, characteristic
5#10590062C212yesmaximal
6C2×C3×Dic12—21no—
7#63873—21no—
8#63843—21no—
9C2×#3718C2212yes—
10C2×#3718C2211yescharacteristic
11C2×#3708C2212yes—
12#63736—24no—
13C8×C3⋊Dic3C2211yescharacteristic
14C3×#816—21no—
15#63576C2211yescharacteristic
16#5183—61no—
17#4790—61no—
18C2×C3×Dic6—21no—
19C2×C3×Dic6—22no—
20C2×C32×C8D411yescharacteristic
21C4×C3⋊Dic3D411yescharacteristic
22C2×C3⋊(C3⋊C8)C2311yescharacteristic
23C3×C4⋊Dic3—21no—
24C3×Dic12—42no—
25#3724—41no—
26#3724—41no—
27Dic3⋊Dic3—41no—
28Dic32—41no—
29#3718—22no—
30#3718—21no—
31#3718—22no—
32#3718D412yes—
33#3708—22no—
34#2209—91nomaximal, Sylow
35C2×C3×Q16—61no—
36Q8×Dic3—61no—
37#944—62no—
38C2×#216—61no—
39C2×#216—62no—
40C2×Dic12—21no—
41#887—61no—
42C3×#103—61no—
43#816—21no—
44C8×Dic3—61no—
45C8×Dic3—61no—
46#807—61no—
47C2×C32×C4C2×D411yescharacteristic
48C2×C3⋊Dic3D811yescharacteristic
49C2×C3⋊Dic3D811yescharacteristic
50C2×C3×Dic3—41no—
51C2×C3×Dic3—41no—
52C2×C3×Dic3—42no—
53C3×Dic6—22no—
54C3×Dic6—41no—
55C3×Dic6—42no—
56C3×Dic6—42no—
57C32×C8—21no—
58C3⋊(C3⋊C8)C2×D411yescharacteristic
59C3⋊(C3⋊C8)#4111yescharacteristic
60C2×Q32—92no—
61#494—91no—
62C4×Q16—91no—
63C4⋊C16—91no—
64#358—92no—
65C2×C3×Q8—61no—
66C2×C3×Q8—62no—
67C2×Dic6—21no—
68C2×Dic6—22no—
69C3×Q16—122no—
70C2×C3×C8—21no—
71C2×C3×C8—21no—
72C3×C4⋊C4—61no—
73#216—62no—
74#216—62no—
75#216—122no—
76#216—122no—
77C4⋊Dic3—21no—
78C4⋊Dic3—121no—
79Dic3⋊C4—121no—
80Dic3⋊C4—122no—
81Dic3⋊C4—122no—
82C4×Dic3—61no—
83C4×Dic3—61no—
84C4×Dic3—121no—
85C4×Dic3—121no—
86C2×C3⋊C8—61no—
87C2×C3⋊C8—61no—
88Dic12—42no—
89C22×C32C2×D811yescharacteristic
90C32×C4#12111yescharacteristic
91C32×C4AGL(1,ℤ/8)11yescharacteristic
92C3⋊Dic3—21no—
93C3⋊Dic3Q3212yescomplemented
94C3×Dic3—42no—
95C3×Dic3—82no—
96C3×Dic3—81no—
97C2×Q16—61no—
98C2×Q16—91no—
99C2×Q16—92no—
100C4⋊Q8—181no—
101C4×Q8—181no—
102Q32—184no—
103C2×C16—92no—
104#107—91no—
105#103—61no—
106C4×C8—91no—
107C3×Q8—62no—
108C3×Q8—121no—
109C3×Q8—122no—
110C3×Q8—122no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—121no—
114C2×C3×C4—121no—
115C2×C3×C4—122no—
116C2×Dic3—41no—
117C2×Dic3—41no—
118C2×Dic3—42no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C2×Dic3—61no—
122C2×Dic3—61no—
123Dic6—22no—
124Dic6—41no—
125Dic6—42no—
126Dic6—42no—
127C3×C8—22no—
128C3×C8—41no—
129C3⋊C8—61no—
130C3⋊C8—61no—
131C3⋊C8—61no—
132C3⋊C8—61no—
133C2×C32#45911yescharacteristic
134C2×C32C2×Q3211yescharacteristic
135C2×C32#51011yescharacteristic
136C2×Q8—61no—
137C2×Q8—62no—
138Q16—92no—
139Q16—122no—
140Q16—181no—
141Q16—182no—
142Q16—182no—
143C2×C8—91no—
144C2×C8GO+(4,𝔽2)11yescharacteristic
145C4⋊C4—61no—
146C4⋊C4—361no—
147C4⋊C4—361no—
148C4⋊C4—361no—
149C42—91no—
150C42—361no—
151C16—182no—
152C22×C3—21no—
153C22×C3—21no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—122no—
159C3×C4—242no—
160C3×C4—241no—
161Dic3—42no—
162Dic3—62no—
163Dic3—62no—
164Dic3—62no—
165Dic3—82no—
166Dic3—81no—
167Dic3—121no—
168C32#220911yescharacteristic, complemented, Sylow
169Q8—62no—
170Q8—121no—
171Q8—122no—
172Q8—122no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—121no—
176C2×C4—121no—
177C2×C4—122no—
178C2×C4C2×GO+(4,𝔽2)11yescharacteristic
179C8—21no—
180C8—91no—
181C8—91no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—21no—
188C22#6422511yescharacteristic
189C4—92no—
190C4—122no—
191C4—181no—
192C4—242no—
193C4—241no—
194C4#6423011yescharacteristic
195C4#6423611yescharacteristic
196C3—21no—
197C3—21no—
198C2#1059327911yescharacteristic
199C2#1059328011yescharacteristic
200C2#1059342611yescharacteristic
subgroupG/H
centerC22#64225
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32C2×D8
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2209
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
93. C3⋊Dic3Q32semidirect
168. C32#2209semidirect

Maximal subgroups

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

subgroupindex
C2×#637362
#105909052
#105907902
#105901772
#105900622
#22099