Finite Group Databasebeta

← #11772821

Subgroups — #11772821

Order 1152.

258 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 40 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#10592759C211yesmaximal, characteristic
2C3×#4542C211yesmaximal, characteristic
3C3×#4541C211yesmaximal, characteristic
4#67549—31nomaximal
5#67545—31nomaximal
6C32×#124C2211yescharacteristic
7C2×#3756—21no—
8C2×#3754—21no—
9#64078C411yescharacteristic, complemented
10#63630C411yescharacteristic, complemented
11C3×#836—21no—
12C3×#834—21no—
13#5060—31no—
14#5060—31no—
15#5060—61no—
16C3×#355—31no—
17C3×#354—31no—
18#4542D311yescharacteristic
19#4541D311yescharacteristic
20C2×C32×Q8D411yescharacteristic
21C2×C32×D4D411yescharacteristic
22C2×#634—21no—
23C32×C22⋊C4—41no—
24C32×C42C2×C411yescharacteristic
25#3756—42no—
26#3754—42no—
27C4⋊(C3⋊Dic3)—41no—
28C2×C3⋊(C3⋊C8)—21no—
29C3×#217—41no—
30C3×#208—41no—
31#1407—91noSylow
32C3×#124—21no—
33C3×#124C2×D311yescharacteristic
34C3×#124C2×D311yescharacteristic
35C2×#216—62no—
36C2×#216—61no—
37C2×#216—61no—
38C2×#214—62no—
39C2×#214—61no—
40C2×#214—61no—
41#869—31no—
42#869—31no—
43#869—61no—
44C3×#101—61no—
45C3×#99—61no—
46#836—21no—
47#834—21no—
48#803—31no—
49#803—31no—
50#803—61no—
51C23×C32—21no—
52C32×Q8—41no—
53C32×D4—41no—
54C2×C32×C4—21no—
55C2×C32×C4—21no—
56C2×C32×C4C22⋊C411yescharacteristic
57C2×C3⋊Dic3—41no—
58#634—41no—
59#634—41no—
60C2×C3×Dic3—81no—
61C3⋊(C3⋊C8)—22no—
62C3×C3⋊C8—81no—
63#497—91no—
64#355—31no—
65#354—31no—
66C2×C3×Q8—21no—
67C2×C3×Q8D1211yescharacteristic
68C2×C3×Q8#6711yescharacteristic
69C2×C3×D4—21no—
70C2×C3×D4D1211yescharacteristic
71C2×C3×D4#6711yescharacteristic
72C2×Dic6—62no—
73C2×Dic6—61no—
74C2×Dic6—61no—
75C3×M16—121no—
76C3×C22⋊C4—41no—
77C3×C22⋊C4—41no—
78C3×C22⋊C4—42no—
79C3×C22⋊C4—121no—
80C3×C42—21no—
81C3×C42C4×D311yescharacteristic
82C3×C42C4×D311yescharacteristic
83#217—41no—
84#216—122no—
85#216—122no—
86#216—124no—
87#214—122no—
88#214—122no—
89#214—124no—
90C4⋊Dic3—122no—
91C4⋊Dic3—121no—
92C4⋊Dic3—121no—
93#208—41no—
94C2×C3⋊C8—62no—
95C2×C3⋊C8—61no—
96C2×C3⋊C8—61no—
97C22×C32—41no—
98C22×C32—81no—
99C22×C32#9911yescharacteristic
100C32×C4—21no—
101C32×C4—41no—
102C32×C4—41no—
103C3⋊Dic3—81no—
104C3×Dic3—161no—
105C2×Q16—181no—
106C2×SD16—181no—
107C4⋊Q8—91no—
108#124D3211yescharacteristic
109#101—61no—
110#99—61no—
111#97—91no—
112C23×C3—21no—
113C23×C3—21no—
114C23×C3—41no—
115C3×Q8—41no—
116C3×Q8—41no—
117C3×Q8—42no—
118C3×D4—41no—
119C3×D4—41no—
120C3×D4—42no—
121C2×C3×C4—22no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—41no—
128C2×C3×C4—241no—
129C2×C3×C4(C2×D3)⋊C411yescharacteristic
130C2×C3×C4(C2×D3)⋊C411yescharacteristic
131C2×Dic3—81no—
132C2×Dic3—122no—
133C2×Dic3—121no—
134C2×Dic3—121no—
135Dic6—122no—
136Dic6—121no—
137Dic6—121no—
138Dic6—122no—
139Dic6—121no—
140Dic6—121no—
141C3×C8—241no—
142C3⋊C8—64no—
143C3⋊C8—62no—
144C3⋊C8—62no—
145C3⋊C8—81no—
146C2×C32—21no—
147C2×C32—81no—
148C2×C32#35311yescharacteristic
149C2×Q8—181no—
150C2×Q8#62611yescharacteristic
151C2×D4#62611yescharacteristic
152Q16—362no—
153SD16—362no—
154M16—121no—
155C2×C8—181no—
156C4⋊C4—361no—
157C22⋊C4—41no—
158C22⋊C4—121no—
159C42#62411yescharacteristic
160C22×C3—21no—
161C22×C3—41no—
162C22×C3—41no—
163C22×C3—81no—
164C22×C3—81no—
165C22×C3—81no—
166C22×C3—82no—
167C22×C3#80611yescharacteristic
168C22×C3#80611yescharacteristic
169C3×C4—22no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—42no—
173C3×C4—41no—
174C3×C4—41no—
175C3×C4—41no—
176C3×C4—41no—
177C3×C4—81no—
178C3×C4—481no—
179Dic3—161no—
180Dic3—242no—
181Dic3—241no—
182Dic3—241no—
183C32#140711yescharacteristic, complemented, Sylow
184C23—21no—
185Q8—41no—
186Q8—361no—
187Q8—361no—
188D4—41no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—241no—
192C2×C4—361no—
193C2×C4#372211yescharacteristic
194C8—182no—
195C8—241no—
196C2×C3—22no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—81no—
201C2×C3—81no—
202C2×C3—161no—
203C2×C3#447411yescharacteristic
204C2×C3#447411yescharacteristic
205C22—41no—
206C22—81no—
207C22#6358111yescharacteristic
208C4—21no—
209C4—41no—
210C4—41no—
211C4—481no—
212C4—721no—
213C3—21no—
214C3#6754511yescharacteristic, complemented
215C3#6754911yescharacteristic, complemented
216C2—21no—
217C2—81no—
218C2#1058917911yescharacteristic
subgroupG/H
centerC2#10589179
commutatorC32×C42C2×C4
Frattini, hypercenter#124D32
Fitting, cosocleC32×#124C22
socleC2×C32#353
prime radicalC2×C32×D4D4
hypocenterC32#1407
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
9. #64078C4semidirect
10. #63630C4semidirect
183. C32#1407semidirect
214. C3#67545semidirect
215. C3#67549semidirect

Maximal subgroups

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

subgroupindex
#105927592
C3×#45422
C3×#45412
#675493
#675453