Finite Group Databasebeta

← #11781191

Subgroups — #11781191

Order 1152.

276 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 47 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#10593359C212yesmaximal
2#10590902C211yesmaximal, characteristic, complemented
3C8×#625C211yesmaximal, characteristic
4#10590171C211yesmaximal, characteristic, complemented
5#10590040C212yesmaximal, complemented
6C2×C3×D3×C8—21no—
7#63919C2212yes—
8C4×#625C2211yescharacteristic
9C4⋊#622C2212yes—
10#63742—22no—
11#63739—22no—
12C8×C3⋊Dic3C2211yescharacteristic
13C3×#818—21no—
14#63576—21no—
15#63572C2211yescharacteristic
16(C2×D3)⋊(C3⋊C8)—21no—
17C8×#67—61no—
18#4874—61no—
19C2×C3×C4×D3—21no—
20C2×#627—22no—
21C2×#625D411yescharacteristic
22C2×#622—22no—
23C2×C32×C8D411yescharacteristic
24C4×C3⋊Dic3C2311yescharacteristic
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C3×C4⋊Dic3—22no—
27C2×C3×C3⋊C8—21no—
28C3×D3×C8—42no—
29#3724—22no—
30#3724D411yescharacteristic
31(C2×D3)⋊Dic3—21no—
32#1675—91nomaximal, Sylow
33C22×C3×C8—61no—
34C4×#67—61no—
35C2×D3×C8—21no—
36#888—62no—
37C3×#107—61no—
38#830—61no—
39(C2×D3)⋊C8—61no—
40#818—21no—
41Dic3⋊C8—61no—
42C8×Dic3—61no—
43C8×Dic3—61no—
44#807—62no—
45C22×C3×D3—21no—
46C2×C32×C4C2×D411yescharacteristic
47C2×C3⋊Dic3C2×D411yescharacteristic
48C2×C3⋊Dic3#4111yescharacteristic
49C2×C3×Dic3—21no—
50C2×C3×Dic3—42no—
51C3×C4×D3—41no—
52C3×C4×D3—41no—
53#627—82no—
54#625—21no—
55#625Q1612yes—
56#622—42no—
57C32×C8SD1612yes—
58C3⋊(C3⋊C8)—21no—
59C3×C3⋊C8—41no—
60#500—91no—
61#476—92no—
62C8×D4—91no—
63#335—91no—
64#333—92no—
65C22×C3×C4—61no—
66C2×#67—61no—
67C2×C4×D3—21no—
68C2×Dic6—122no—
69C2×C3×C8—21no—
70C2×C3×C8—21no—
71C2×C3×C8—61no—
72C2×C3×C8—122no—
73C3×C4⋊C4—62no—
74#217—61no—
75(C2×D3)⋊C4—61no—
76C4⋊Dic3—22no—
77Dic3⋊C4—61no—
78Dic3⋊C4—122no—
79C4×Dic3—61no—
80C4×Dic3—61no—
81C2×C3⋊C8—21no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8—61no—
84D3×C8—42no—
85C22×C32#12111yescharacteristic
86C2×C3×D3—22no—
87C2×C3×D3—41no—
88C2×C3×D3—41no—
89C32×C4C2×SD1611yescharacteristic
90C32×C4#13711yescharacteristic
91C3⋊Dic3—21no—
92C3⋊Dic3C2×Q1611yescharacteristic
93C3⋊Dic3#13511yescharacteristic
94C3×Dic3—41no—
95C3×Dic3—82no—
96C22×C8—61no—
97C4⋊Q8—92no—
98C4×D4—91no—
99#107—61no—
100#107—181no—
101#106—182no—
102C4⋊C8—91no—
103C4⋊C8—92no—
104#102—182no—
105C22⋊C8—181no—
106C4×C8—91no—
107C23×C3—61no—
108C22×D3—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—61no—
112C2×C3×C4—121no—
113C2×C3×C4—121no—
114C2×C3×C4—122no—
115#67—62no—
116#67—62no—
117C2×Dic3—21no—
118C2×Dic3—42no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C2×Dic3—61no—
122C2×Dic3—61no—
123C4×D3—41no—
124C4×D3—41no—
125Dic6—244no—
126C3×C8—22no—
127C3×C8—22no—
128C3×C8—121no—
129C3⋊C8—41no—
130C3⋊C8—62no—
131C3⋊C8—121no—
132C2×C32#46111yescharacteristic
133C2×C32#46711yescharacteristic
134C2×C32#47211yescharacteristic
135C3×D3—42no—
136C2×Q8—182no—
137C2×D4—91no—
138C22×C4—61no—
139C2×C8—61no—
140C2×C8—91no—
141C2×C8—122no—
142C2×C8—182no—
143C2×C8GO+(4,𝔽2)11yescharacteristic
144C4⋊C4—62no—
145C4⋊C4—91no—
146C4⋊C4—182no—
147C22⋊C4—181no—
148C42—91no—
149C22×C3—21no—
150C22×C3—21no—
151C22×C3—62no—
152C22×C3—121no—
153C22×C3—121no—
154C2×D3—22no—
155C2×D3—41no—
156C2×D3—41no—
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—121no—
162C3×C4—242no—
163Dic3—41no—
164Dic3—61no—
165Dic3—61no—
166Dic3—61no—
167Dic3—61no—
168Dic3—62no—
169Dic3—82no—
170Dic3—121no—
171C32#167511yescharacteristic, complemented, Sylow
172C23—61no—
173Q8—722no—
174D4—92no—
175D4—181no—
176C2×C4—61no—
177C2×C4—91no—
178C2×C4—91no—
179C2×C4—121no—
180C2×C4—121no—
181C2×C4—122no—
182C2×C4C2×GO+(4,𝔽2)11yescharacteristic
183C8—121no—
184C8—181no—
185C8—362no—
186C8#377512yes—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—122no—
194D3—42no—
195C22—62no—
196C22—121no—
197C22—121no—
198C22#6423011yescharacteristic
199C4—91no—
200C4—91no—
201C4—121no—
202C4—181no—
203C4—242no—
204C4#6422611yescharacteristic
205C4C2×#377511yescharacteristic
206C3—21no—
207C3—21no—
208C2—122no—
209C2#1059328811yescharacteristic
210C2#1059330111yescharacteristic
211C2#1059343711yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
prime radicalC2×#625D4
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1675
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10590902C2semidirect
4. #10590171C2semidirect
5. #10590040C2semidirect
171. C32#1675semidirect

Maximal subgroups

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

subgroupindex
#105933592
#105909022
C8×#6252
#105901712
#105900402
#16759