Finite Group Databasebeta

← #11774367

Subgroups — #11774367

Order 1152.

570 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 70 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#10596187C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic, complemented
3#10593726C211yesmaximal, characteristic, complemented
4D4⋊#622C214yesmaximal, complemented
5C2×#3830—21no—
6C2×#3787—21no—
7C32×#127C411yescharacteristic
8#64147—21no—
9#64147C412yes—
10#64145—21no—
11D4×C3⋊Dic3—21no—
12D4×C3⋊Dic3C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14#64078C411yescharacteristic
15#63779—21no—
16#63778—21no—
17C4⋊#622—21no—
18C4⋊#622C2212yes—
19C4×#622C2212yes—
20#5716—62no—
21C2×C32×D4—21no—
22C2×C32×D4—21no—
23C2×C32×D4C2×C412yes—
24C2×#638—22no—
25C22×C3⋊Dic3—22no—
26#3830—42no—
27#3830—42no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×#634—21no—
32C2×#622—22no—
33C2×#622—22no—
34#3787—42no—
35C32×C42C2×C411yescharacteristic
36#3757—22no—
37#3757—22no—
38C4⋊(C3⋊Dic3)—21no—
39C4⋊(C3⋊Dic3)C2×C412yes—
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3C2311yescharacteristic
43#1480—91nomaximal, Sylow
44C2×#237—64no—
45C3×#127—22no—
46#938—64no—
47#938—64no—
48#936—64no—
49D4×Dic3—64no—
50D4×Dic3—64no—
51C42×D3—62no—
52#869—62no—
53C23×C32—22no—
54C22×C3⋊D3C22⋊C411yescharacteristic
55C32×D4—24no—
56C32×D4—42no—
57C32×D4—42no—
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C22⋊C411yescharacteristic
60C2×C32×C4C22×C411yescharacteristic
61#638—44no—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—42no—
64C2×C3⋊Dic3—42no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3C2×D411yescharacteristic
68C4×C3⋊D3—22no—
69C4×C3⋊D3—41no—
70C4×C3⋊D3D812yes—
71C4×C3⋊D3SD1612yes—
72#634—42no—
73#622—42no—
74#622—42no—
75#532—91no—
76#431—91no—
77C2×C4⋊C8—91no—
78D4⋊C8—94no—
79C2×C3×D4—24no—
80C2×C3×D4—24no—
81C2×C3×D4—24no—
82C2×#67—68no—
83C22×Dic3—68no—
84#237—128no—
85#237—128no—
86C2×C4×D3—62no—
87C2×C4×D3—62no—
88C2×C4×D3—62no—
89C2×Dic6—64no—
90C3×C42—22no—
91#217—68no—
92#217—68no—
93C4⋊Dic3—64no—
94C4⋊Dic3—64no—
95C4×Dic3—62no—
96C4×Dic3—62no—
97C4×Dic3—62no—
98C22×C32—42no—
99C22×C32—42no—
100C22×C32—42no—
101C22×C32C2×C22⋊C411yescharacteristic
102C2×C3⋊D3—21no—
103C2×C3⋊D3—21no—
104C2×C3⋊D3#10212yes—
105C32×C4—21no—
106C32×C4#10212yes—
107C32×C4#13112yes—
108C3⋊Dic3—21no—
109C3⋊Dic3—21no—
110C3⋊Dic3—42no—
111C3⋊Dic3C2×D811yescharacteristic
112C3⋊Dic3C2×SD1611yescharacteristic
113C2×#41—181no—
114C22×C8—181no—
115C4⋊Q8—91no—
116#127#15711yescharacteristic
117#124—181no—
118#121—92no—
119#121—181no—
120C4×D4—92no—
121C4×D4—181no—
122C2×C42—91no—
123C4⋊C8—92no—
124C4⋊C8—181no—
125C4⋊C8—181no—
126C22⋊C8—181no—
127C4×C8—92no—
128C23×C3—28no—
129C22×D3—62no—
130C3×D4—48no—
131C3×D4—48no—
132C3×D4—48no—
133C2×C3×C4—22no—
134C2×C3×C4—22no—
135C2×C3×C4—22no—
136#67—1216no—
137C2×Dic3—62no—
138C2×Dic3—62no—
139C2×Dic3—62no—
140C2×Dic3—68no—
141C2×Dic3—128no—
142C2×Dic3—128no—
143C4×D3—64no—
144C4×D3—64no—
145C4×D3—124no—
146C4×D3—124no—
147Dic6—128no—
148C2×C32—82no—
149C2×C32#40811yescharacteristic
150C2×C32C2×#10211yescharacteristic
151C2×C32#42111yescharacteristic
152C3⋊D3—22no—
153#41—362no—
154#41—362no—
155C2×Q8—181no—
156C2×D4—21no—
157C2×D4—21no—
158C2×D4—182no—
159C2×D4C2×#15712yes—
160C22×C4—91no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4—182no—
164C2×C8—182no—
165C2×C8—182no—
166C2×C8—362no—
167C4⋊C4—92no—
168C4⋊C4—181no—
169C22⋊C4—182no—
170C22⋊C4—182no—
171C42—91no—
172C42—91no—
173C42—91no—
174C42C2×#15711yescharacteristic
175C22×C3—22no—
176C22×C3—48no—
177C22×C3—48no—
178C22×C3—48no—
179C2×D3—64no—
180C2×D3—122no—
181C2×D3—122no—
182C3×C4—24no—
183C3×C4—24no—
184C3×C4—24no—
185Dic3—62no—
186Dic3—62no—
187Dic3—122no—
188Dic3—122no—
189Dic3—128no—
190C32#148011yescharacteristic, complemented, Sylow
191C23—22no—
192C23—91no—
193Q8—362no—
194D4—24no—
195D4—42no—
196D4—42no—
197D4—364no—
198C2×C4—91no—
199C2×C4—92no—
200C2×C4—92no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—182no—
204C2×C4—182no—
205C2×C4—361no—
206C2×C4—362no—
207C2×C4—362no—
208C2×C4C22⋊#15711yescharacteristic
209C2×C4C22⋊#15711yescharacteristic
210C2×C4C22×#15711yescharacteristic
211C8—362no—
212C8—362no—
213C2×C3—22no—
214C2×C3—22no—
215C2×C3—22no—
216C2×C3—88no—
217D3—124no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22—92no—
222C22—181no—
223C22—181no—
224C22C2×C22⋊#15711yescharacteristic
225C4—21no—
226C4—91no—
227C4—91no—
228C4—181no—
229C4—181no—
230C4—362no—
231C4#6378212yes—
232C4#6428712yes—
233C3—22no—
234C2—82no—
235C2—182no—
236C2C2×#6378211yescharacteristic
237C2#1059381611yescharacteristic
238C2#1059382311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#127C4
socleC22×C32C2×C22⋊C4
prime radical#10596187C2
cosocleC4×C3⋊Dic3C23
hypercenter#127#157
hypocenterC32#1480
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593727C2semidirect
3. #10593726C2semidirect
4. D4⋊#622C2semidirect
190. C32#1480semidirect

Maximal subgroups

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

subgroupindex
#105961872
#105937272
#105937262
D4⋊#6222
#14809