Finite Group Databasebeta

← #11799511

Subgroups — #11799511

Order 1152.

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

normal subgroups only

This group has 258 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
1#10590902C211yesmaximal, characteristic, complemented
2#10590740C211yesmaximal, characteristic
3#10590177C211yesmaximal, characteristic, complemented
4#10590068C212yesmaximal, complemented
5#10590061C212yesmaximal
6#63919—21no—
7#63898—21no—
8C2×#3713C2211yescharacteristic
9C2×#3708C2212yes—
10C8×C3⋊Dic3C2211yescharacteristic
11C3×#821—21no—
12C3×#818—21no—
13#63576C2211yescharacteristic
14#63576C2212yes—
15#4874—61no—
16#4756—61no—
17C2×C3×D12—21no—
18C2×#627—41no—
19C2×D3×Dic3—41no—
20C2×C32×C8D411yescharacteristic
21C4×C3⋊Dic3D411yescharacteristic
22C2×C3⋊(C3⋊C8)C2311yescharacteristic
23C3×C4⋊Dic3—22no—
24C3×C4⋊Dic3—21no—
25#3724—41no—
26(C2×D3)⋊Dic3—41no—
27#3713—21no—
28#3713Q812yescomplemented
29#3708—22no—
30#2224—91nomaximal, Sylow
31D4×Dic3—61no—
32C2×#213—61no—
33#893—61no—
34#888—62no—
35C3×#107—61no—
36C3×#102—61no—
37#821—21no—
38#818—21no—
39C8×Dic3—61no—
40C8×Dic3—61no—
41#807—62no—
42#807—61no—
43C22×C3×D3—41no—
44C2×C32×C4C2×D411yescharacteristic
45C2×C3⋊Dic3D811yescharacteristic
46C2×C3⋊Dic3D811yescharacteristic
47C2×C3×Dic3—41no—
48C2×C3×Dic3—42no—
49C3×D12—22no—
50C3×D12—41no—
51#627—82no—
52D3×Dic3—82no—
53C32×C8—21no—
54C3⋊(C3⋊C8)C2×Q811yescharacteristic
55C3⋊(C3⋊C8)#4111yescharacteristic
56#500—91no—
57C4×D8—91no—
58#366—92no—
59C4⋊C16—91no—
60#357—92no—
61C2×C3×D4—61no—
62C22×Dic3—121no—
63C2×D12—21no—
64C2×C4×D3—121no—
65C2×Dic6—122no—
66C2×C3×C8—21no—
67C2×C3×C8—21no—
68C3×C4⋊C4—61no—
69C3×C4⋊C4—62no—
70#217—121no—
71#213—62no—
72#213—62no—
73(C2×D3)⋊C4—121no—
74C4⋊Dic3—22no—
75C4⋊Dic3—21no—
76Dic3⋊C4—122no—
77C4×Dic3—61no—
78C4×Dic3—61no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81C22×C32C2×D811yescharacteristic
82C2×C3×D3—42no—
83C2×C3×D3—81no—
84C2×C3×D3—81no—
85C32×C4C22⋊Q811yescharacteristic
86C32×C4#13711yescharacteristic
87C3⋊Dic3—21no—
88C3⋊Dic3D1612yes—
89C3×Dic3—81no—
90C3×Dic3—82no—
91C2×D8—91no—
92C4⋊Q8—181no—
93C4×D4—181no—
94C2×C16—92no—
95#107—61no—
96#107—92no—
97#107—91no—
98#102—61no—
99C4×C8—91no—
100C23×C3—121no—
101C22×D3—41no—
102C3×D4—62no—
103C3×D4—121no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—122no—
107C2×C3×C4—121no—
108C2×Dic3—42no—
109C2×Dic3—41no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—242no—
115D12—22no—
116D12—41no—
117C4×D3—242no—
118Dic6—244no—
119C3×C8—22no—
120C3×C8—41no—
121C3⋊C8—61no—
122C3⋊C8—61no—
123C3⋊C8—61no—
124C3⋊C8—61no—
125C2×C32#47411yescharacteristic
126C2×C32C2×D1611yescharacteristic
127C2×C32#51011yescharacteristic
128C3×D3—82no—
129C2×Q8—361no—
130C2×D4—61no—
131C22×C4—361no—
132D8—92no—
133D8—181no—
134C2×C8—91no—
135C2×C8GO+(4,𝔽2)11yescharacteristic
136C4⋊C4—61no—
137C4⋊C4—62no—
138C4⋊C4—361no—
139C22⋊C4—361no—
140C42—91no—
141C16—182no—
142C22×C3—21no—
143C22×C3—21no—
144C22×C3—122no—
145C22×C3—241no—
146C22×C3—241no—
147C2×D3—42no—
148C2×D3—81no—
149C2×D3—81no—
150C3×C4—21no—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—21no—
154C3×C4—242no—
155C3×C4—241no—
156Dic3—62no—
157Dic3—62no—
158Dic3—62no—
159Dic3—82no—
160Dic3—81no—
161Dic3—121no—
162C32#222411yescharacteristic, complemented, Sylow
163C23—121no—
164Q8—722no—
165D4—62no—
166D4—121no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—121no—
170C2×C4—122no—
171C2×C4—722no—
172C2×C4C2×GO+(4,𝔽2)11yescharacteristic
173C8—21no—
174C8—91no—
175C8—91no—
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—242no—
183D3—82no—
184C22—122no—
185C22—241no—
186C22—241no—
187C22#6422511yescharacteristic
188C4—92no—
189C4—181no—
190C4—241no—
191C4—242no—
192C4D32⋊Q811yescharacteristic
193C4#6423911yescharacteristic
194C3—21no—
195C3—21no—
196C2—242no—
197C2#1059327611yescharacteristic
198C2#1059327911yescharacteristic
199C2#1059336711yescharacteristic
subgroupG/H
centerC22#64225
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C2×D8
prime radicalC2×#3713C22
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2224
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
1. #10590902C2semidirect
3. #10590177C2semidirect
4. #10590068C2semidirect
28. #3713Q8semidirect
162. C32#2224semidirect

Maximal subgroups

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

subgroupindex
#105909022
#105907402
#105901772
#105900682
#105900612
#22249