Finite Group Databasebeta

← #11786395

Subgroups — #11786395

Order 1152.

582 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C22×#3788C211yesmaximal, characteristic
2C2×#63779C212yesmaximal, complemented
3C2×#63778C211yesmaximal, characteristic
4#10592365C211yesmaximal, characteristic
5#10590207C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#622C2211yescharacteristic
8C22×#622C2211yescharacteristic
9C22×#622C2212yes—
10C2×#3788—22no—
11C2×#3788—24no—
12C2×#3752C412yes—
13C2×C4×C3⋊Dic3C2212yes—
14#63779—24no—
15#63778—22no—
16C32×#95C411yescharacteristic
17#63658C411yescharacteristic
18#4666—62no—
19C23×C3⋊D3C2×C411yescharacteristic
20C22×C32×C4C2×C412yes—
21C22×C32×C4C2×C411yescharacteristic
22C22×C3⋊Dic3C2×C412yes—
23C22×C3⋊Dic3C2311yescharacteristic
24C2×C4×C3⋊D3—22no—
25C2×C4×C3⋊D3—22no—
26C2×C4×C3⋊D3D412yes—
27C2×C4×C3⋊D3Q812yes—
28C2×#622—22no—
29C2×#622—22no—
30C2×#622—21no—
31C2×#622—21no—
32C2×#622—22no—
33C2×#622—22no—
34C2×#622D414yes—
35#3788—28no—
36#3752—24no—
37C4×C3⋊Dic3—22no—
38C4×C3⋊Dic3—22no—
39#1851—91nomaximal, Sylow
40C22×C4×D3—62no—
41C2×(C2×D3)⋊C4—64no—
42C2×C4×Dic3—64no—
43C3×#95—22no—
44C3⋊#95—62no—
45C23×C32C22×C411yescharacteristic
46C22×C3⋊D3—22no—
47C22×C3⋊D3—22no—
48C22×C3⋊D3—21no—
49C22×C3⋊D3—21no—
50C22×C3⋊D3C4⋊C412yes—
51C2×C32×C4—22no—
52C2×C32×C4—22no—
53C2×C32×C4—22no—
54C2×C32×C4—22no—
55C2×C32×C4C4⋊C412yes—
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3M1614yescomplemented
59C2×C3⋊Dic3C2×D412yes—
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3C2×Q811yescharacteristic
62C2×C3⋊Dic3#4112yes—
63C4×C3⋊D3—22no—
64C4×C3⋊D3—24no—
65C4×C3⋊D3—22no—
66#622—24no—
67#622—41no—
68#622—41no—
69C22×M16—91no—
70C2×C4⋊C8—92no—
71C2×C22⋊C8—91no—
72C4×C22⋊C4—91no—
73#336—92no—
74C23×D3—62no—
75C22×C3×C4—22no—
76C22×C3×C4—24no—
77C22×Dic3—62no—
78C22×Dic3—64no—
79C2×C4×D3—64no—
80C2×C4×D3—64no—
81C2×C4×D3—124no—
82C2×C4×D3—124no—
83(C2×D3)⋊C4—616no—
84C4×Dic3—124no—
85C4×Dic3—124no—
86C22×C32C2×C4⋊C411yescharacteristic
87C22×C32C4×D412yes—
88C22×C32C2×M1612yes—
89C22×C32#13111yescharacteristic
90C22×C32#13111yescharacteristic
91C2×C3⋊D3—22no—
92C2×C3⋊D3—22no—
93C2×C3⋊D3—22no—
94C2×C3⋊D3—42no—
95C2×C3⋊D3—42no—
96C32×C4—22no—
97C32×C4—42no—
98C3⋊Dic3—24no—
99C3⋊Dic3#12011yescharacteristic
100C3⋊Dic3C22⋊Q812yes—
101C3⋊Dic3#12311yescharacteristic
102C23×C4—91no—
103C2×M16—184no—
104C2×M16—182no—
105C22×C8—92no—
106C22×C8—91no—
107C22×C8—91no—
108C2×C22⋊C4—92no—
109C2×C42—92no—
110C4⋊C8—184no—
111C22⋊C8—182no—
112#95—91no—
113#95#15711yescharacteristic
114C23×C3—22no—
115C22×D3—64no—
116C22×D3—68no—
117C22×D3—124no—
118C22×D3—122no—
119C22×D3—122no—
120C2×C3×C4—28no—
121C2×C3×C4—24no—
122C2×C3×C4—44no—
123C2×C3×C4—44no—
124C2×C3×C4—44no—
125C2×Dic3—64no—
126C2×Dic3—62no—
127C2×Dic3—62no—
128C2×Dic3—64no—
129C2×Dic3—68no—
130C2×Dic3—124no—
131C2×Dic3—124no—
132C4×D3—124no—
133C4×D3—128no—
134C4×D3—124no—
135C2×C32#38511yescharacteristic
136C2×C32#42311yescharacteristic
137C2×C32#42411yescharacteristic
138C2×C32#43512yes—
139C2×C32#43612yes—
140C3⋊D3—42no—
141C24—91no—
142C22×C4—91no—
143C22×C4—92no—
144C22×C4—92no—
145C22×C4—92no—
146C22×C4—182no—
147C22×C4—182no—
148C22×C4C2×#15712yes—
149C22×C4C2×#15711yescharacteristic
150M16—188no—
151C2×C8—94no—
152C2×C8—182no—
153C2×C8—182no—
154C2×C8—181no—
155C2×C8—181no—
156C2×C8—182no—
157C2×C8—182no—
158C22⋊C4—184no—
159C42—182no—
160C42—182no—
161C22×C3—24no—
162C22×C3—22no—
163C22×C3—22no—
164C22×C3—24no—
165C22×C3—22no—
166C2×D3—68no—
167C2×D3—124no—
168C2×D3—124no—
169C2×D3—128no—
170C2×D3—128no—
171C3×C4—44no—
172C3×C4—48no—
173Dic3—62no—
174Dic3—64no—
175Dic3—62no—
176Dic3—128no—
177C32#185111yescharacteristic, complemented, Sylow
178C23—92no—
179C23—182no—
180C23—181no—
181C23—182no—
182C23—181no—
183C23C22×#15711yescharacteristic
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—91no—
189C2×C4—91no—
190C2×C4—92no—
191C2×C4—92no—
192C2×C4—94no—
193C2×C4—182no—
194C2×C4—182no—
195C2×C4—184no—
196C2×C4—182no—
197C2×C4—182no—
198C2×C4C4⋊#15712yes—
199C8—184no—
200C8—361no—
201C8—361no—
202C2×C3—22no—
203C2×C3—24no—
204C2×C3—22no—
205C2×C3—24no—
206C2×C3—22no—
207D3—128no—
208C22—182no—
209C22—182no—
210C22—182no—
211C22—362no—
212C22—362no—
213C22#6428312yes—
214C22C2×C4⋊#15711yescharacteristic
215C22#6428711yescharacteristic
216C22D4×#15712yes—
217C22#6428911yescharacteristic
218C4—22no—
219C4—42no—
220C4—91no—
221C4—91no—
222C4—92no—
223C4—184no—
224C3—22no—
225C2—362no—
226C2#1059372911yescharacteristic
227C2#1059374212yes—
228C2#1059374611yescharacteristic
229C2#1059375112yes—
230C2#1059375511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutator, socleC23×C32C22×C4
FittingC32×#95C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenter#95#157
hypocenterC32#1851
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63779C2semidirect
5. #10590207C2semidirect
58. C2×C3⋊Dic3M16semidirect
177. C32#1851semidirect

Maximal subgroups

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

subgroupindex
C22×#37882
C2×#637792
C2×#637782
#105923652
#105902072
#18519