Finite Group Databasebeta

← #11799693

Subgroups — #11799693

Order 1152.

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

normal subgroups only

This group has 222 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
1C4×#3718C211yesmaximal, characteristic
2#10590314C211yesmaximal, characteristic
3C4⋊#3708C211yesmaximal, characteristic
4#10590069C211yesmaximal, characteristic
5#10590068C211yesmaximal, characteristic
6#10590062C211yesmaximal, characteristic
7#10590062C211yesmaximal, characteristic
8C3×#870—21no—
9C3×C4×Dic6—21no—
10C2×#3718C2211yescharacteristic
11C2×#3708C2211yescharacteristic
12C2×#3708C2211yescharacteristic
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14#63576C2211yescharacteristic
15#63576C2211yescharacteristic
16#63576C2211yescharacteristic
17#63574—21no—
18#63565—21no—
19#5065—61no—
20C4×#216—61no—
21C2×C3×Dic6—21no—
22C32×C42D411yescharacteristic
23C2×C3⋊(C3⋊C8)D411yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25C3×C4⋊Dic3—21no—
26C3×C4⋊Dic3—21no—
27C3×C4⋊Dic3—21no—
28C3×Dic3⋊C4—41no—
29C3×Dic3⋊C4—41no—
30C3×Dic3⋊C4—41no—
31C3×C4×Dic3—41no—
32#3718—21no—
33#3718Q812yes—
34#3708—21no—
35#3708—21no—
36#2229—91nomaximal, Sylow
37C3×#125—61no—
38C3×C4×Q8—61no—
39C2×#216—61no—
40#870—21no—
41C4×Dic6—21no—
42#835—61no—
43#810—61no—
44#808—61no—
45#808—61no—
46#807—61no—
47#807—61no—
48#807—61no—
49C4×C3⋊C8—61no—
50C4×C3⋊C8—61no—
51C2×C32×C4D811yescharacteristic
52C2×C32×C4D811yescharacteristic
53C2×C32×C4C2×D411yescharacteristic
54C2×C3×Dic3—41no—
55C2×C3×Dic3—41no—
56C2×C3×Dic3—41no—
57C2×C3×Dic3—41no—
58C3×Dic6—22no—
59C3×Dic6—41no—
60C3⋊(C3⋊C8)—21no—
61C3⋊(C3⋊C8)C2×Q811yescharacteristic
62C3⋊(C3⋊C8)#4111yescharacteristic
63#499—91no—
64C4×Q16—91no—
65#367—91no—
66#366—91no—
67C4⋊C16—91no—
68#358—91no—
69#358—91no—
70C2×C3×Q8—61no—
71C2×Dic6—21no—
72C3×C4⋊C4—61no—
73C3×C4⋊C4—61no—
74C3×C4⋊C4—61no—
75C3×C4⋊C4—121no—
76C3×C4⋊C4—121no—
77C3×C4⋊C4—121no—
78C3×C42—21no—
79C3×C42—21no—
80C3×C42—121no—
81#216—62no—
82#216—62no—
83C4⋊Dic3—21no—
84C4⋊Dic3—21no—
85C4⋊Dic3—21no—
86Dic3⋊C4—41no—
87Dic3⋊C4—41no—
88Dic3⋊C4—41no—
89C4×Dic3—41no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—61no—
92C2×C3⋊C8—61no—
93C2×C3⋊C8—61no—
94C22×C32C2×D811yescharacteristic
95C32×C4—21no—
96C32×C4—21no—
97C32×C4C22⋊Q811yescharacteristic
98C32×C4#13711yescharacteristic
99C3×Dic3—42no—
100C3×Dic3—81no—
101C3×Dic3—81no—
102C3×Dic3—81no—
103C2×Q16—91no—
104#125—61no—
105C4×Q8—61no—
106C2×C16—91no—
107C2×C16—91no—
108#107—91no—
109#107—91no—
110#107—91no—
111#106—181no—
112#103—181no—
113C4×C8—91no—
114C3×Q8—62no—
115C3×Q8—121no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—121no—
123C2×C3×C4—121no—
124C2×C3×C4—121no—
125C2×C3×C4—121no—
126C2×Dic3—41no—
127C2×Dic3—41no—
128C2×Dic3—41no—
129C2×Dic3—41no—
130Dic6—22no—
131Dic6—41no—
132C3⋊C8—61no—
133C3⋊C8—61no—
134C3⋊C8—61no—
135C3⋊C8—61no—
136C3⋊C8—62no—
137C3⋊C8—121no—
138C2×C32#47411yescharacteristic
139C2×C32#50811yescharacteristic
140C2×C32#51011yescharacteristic
141C2×Q8—61no—
142Q16—92no—
143Q16—181no—
144C2×C8—91no—
145C2×C8—91no—
146C4⋊C4—61no—
147C4⋊C4—61no—
148C4⋊C4—61no—
149C4⋊C4—121no—
150C4⋊C4—121no—
151C4⋊C4—121no—
152C42—121no—
153C42GO+(4,𝔽2)11yescharacteristic
154C16—181no—
155C16—181no—
156C22×C3—21no—
157C22×C3—21no—
158C3×C4—22no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—41no—
164C3×C4—41no—
165C3×C4—41no—
166C3×C4—122no—
167C3×C4—241no—
168C3×C4—241no—
169C3×C4—241no—
170Dic3—42no—
171Dic3—81no—
172Dic3—81no—
173Dic3—81no—
174C32#222911yescharacteristic, complemented, Sylow
175Q8—62no—
176Q8—121no—
177C2×C4—121no—
178C2×C4—121no—
179C2×C4—121no—
180C2×C4—121no—
181C2×C4#377411yescharacteristic
182C2×C4#377411yescharacteristic
183C2×C4C2×GO+(4,𝔽2)11yescharacteristic
184C8—91no—
185C8—91no—
186C8—181no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C22C2×#377411yescharacteristic
194C4—21no—
195C4—21no—
196C4—122no—
197C4—241no—
198C4—241no—
199C4—241no—
200C4D32⋊Q811yescharacteristic
201C4#6422611yescharacteristic
202C3—21no—
203C3—21no—
204C2#1059333311yescharacteristic
205C2#1059333611yescharacteristic
206C2#1059334711yescharacteristic
subgroupG/H
centerC22C2×#3774
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socle, prime radicalC22×C32C2×D8
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2229
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
174. C32#2229semidirect

Maximal subgroups

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

subgroupindex
C4×#37182
#105903142
C4⋊#37082
#105900692
#105900682
#105900622
#22299