Finite Group Databasebeta

← #11781945

Subgroups — #11781945

Order 1152.

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

normal subgroups only

This group has 276 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#10593437C212yesmaximal
2#10590902C211yesmaximal, characteristic, complemented
3#10590734C211yesmaximal, characteristic
4#10590172C211yesmaximal, characteristic, complemented
5#10590039C212yesmaximal, complemented
6C2×#3775—22no—
7#63919C2212yes—
8C4×#625C2211yescharacteristic
9C2×#3711—21no—
10C4⋊#622C2212yes—
11#63740—22no—
12C8×C3⋊Dic3C2211yescharacteristic
13C3×(C2×D3)⋊C8—21no—
14C3×#818—21no—
15#63576—21no—
16#63572C2211yescharacteristic
17#4874—61no—
18#4729—61no—
19C2×C3×C4×D3—21no—
20C2×#627—22no—
21C2×#625D411yescharacteristic
22C2×#622—22no—
23#3775—44no—
24C2×C32×C8D411yescharacteristic
25C4×C3⋊Dic3C2311yescharacteristic
26C2×C3⋊(C3⋊C8)D411yescharacteristic
27C3×C4⋊Dic3—22no—
28C2×C3×C3⋊C8—21no—
29#3724—22no—
30#3724D411yescharacteristic
31(C2×D3)⋊Dic3—21no—
32#3711—42no—
33#1693—91nomaximal, Sylow
34C4×#67—61no—
35C2×#208—61no—
36C2×ΓL(1,𝔽25)—61no—
37#888—62no—
38C3×#107—61no—
39C3×C22⋊C8—61no—
40(C2×D3)⋊C8—21no—
41#818—21no—
42Dic3⋊C8—61no—
43C8×Dic3—61no—
44C8×Dic3—61no—
45#807—62no—
46C22×C3×D3—21no—
47C2×C32×C4C2×D411yescharacteristic
48C2×C3⋊Dic3C2×D411yescharacteristic
49C2×C3⋊Dic3#4111yescharacteristic
50C2×C3×Dic3—21no—
51C2×C3×Dic3—42no—
52C3×C4×D3—41no—
53C3×C4×D3—41no—
54#627—42no—
55#627—42no—
56#625—22no—
57#622—42no—
58C32×C8—21no—
59C3⋊(C3⋊C8)SD1612yescomplemented
60C3×C3⋊C8—41no—
61#500—91no—
62#461—92no—
63#436—91no—
64#334—91no—
65#332—92no—
66C22×C3×C4—61no—
67C2×#67—61no—
68C2×C4×D3—21no—
69C2×Dic6—122no—
70C2×C3×C8—21no—
71C2×C3×C8—21no—
72C2×C3×C8—61no—
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—
81#208—122no—
82C2×C3⋊C8—21no—
83C2×C3⋊C8—61no—
84C2×C3⋊C8—61no—
85ΓL(1,𝔽25)—122no—
86C22×C32#12111yescharacteristic
87C2×C3×D3—41no—
88C2×C3×D3—41no—
89C2×C3×D3—41no—
90C32×C4C2×SD1611yescharacteristic
91C32×C4#13711yescharacteristic
92C3⋊Dic3—21no—
93C3⋊Dic3AGL(1,ℤ/8)12yes—
94C3×Dic3—41no—
95C3×Dic3—82no—
96C2×SD16—182no—
97C2×M16—181no—
98C4⋊Q8—92no—
99C4×D4—91no—
100#107—61no—
101#107—181no—
102C4⋊C8—91no—
103C4⋊C8—92no—
104#103—182no—
105C22⋊C8—61no—
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—122no—
116C2×Dic3—21no—
117C2×Dic3—42no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C2×Dic3—61no—
122C4×D3—41no—
123C4×D3—41no—
124Dic6—242no—
125Dic6—242no—
126C3×C8—22no—
127C3×C8—41no—
128C3×C8—121no—
129C3⋊C8—41no—
130C3⋊C8—62no—
131C3⋊C8—62no—
132C2×C32#46111yescharacteristic
133C2×C32#46911yescharacteristic
134C2×C32#47311yescharacteristic
135C3×D3—81no—
136C2×Q8—182no—
137C2×D4—91no—
138C22×C4—61no—
139SD16—364no—
140M16—362no—
141C2×C8—61no—
142C2×C8—91no—
143C2×C8—182no—
144C2×C8GO+(4,𝔽2)11yescharacteristic
145C4⋊C4—62no—
146C4⋊C4—91no—
147C4⋊C4—182no—
148C22⋊C4—181no—
149C42—91no—
150C22×C3—21no—
151C22×C3—21no—
152C22×C3—121no—
153C22×C3—121no—
154C22×C3—121no—
155C2×D3—41no—
156C2×D3—41no—
157C2×D3—41no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—121no—
163C3×C4—242no—
164Dic3—41no—
165Dic3—62no—
166Dic3—62no—
167Dic3—62no—
168Dic3—82no—
169Dic3—121no—
170C32#169311yescharacteristic, complemented, Sylow
171C23—61no—
172Q8—362no—
173Q8—362no—
174D4—182no—
175C2×C4—61no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—121no—
179C2×C4—121no—
180C2×C4—122no—
181C2×C4C2×GO+(4,𝔽2)11yescharacteristic
182C8—21no—
183C8—92no—
184C8—121no—
185C8—362no—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—241no—
193D3—81no—
194C22—121no—
195C22—121no—
196C22—121no—
197C22#6423011yescharacteristic
198C4—92no—
199C4—121no—
200C4—181no—
201C4—242no—
202C4#6422711yescharacteristic
203C4#6423911yescharacteristic
204C3—21no—
205C3—21no—
206C2—241no—
207C2#1059328711yescharacteristic
208C2#1059330411yescharacteristic
209C2#1059343811yescharacteristic
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#1693
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. #10590172C2semidirect
5. #10590039C2semidirect
59. C3⋊(C3⋊C8)SD16semidirect
170. C32#1693semidirect

Maximal subgroups

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

subgroupindex
#105934372
#105909022
#105907342
#105901722
#105900392
#16939