Finite Group Databasebeta

← #11774309

Subgroups — #11774309

Order 1152.

738 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C2×#64102C211yesmaximal, characteristic
2#10593795C211yesmaximal, characteristic, complemented
3#10593795C211yesmaximal, characteristic, complemented
4#10590160C214yesmaximal, complemented
5C22×C4⋊(C3⋊D3)C411yescharacteristic
6C22×C4×C3⋊D3—21no—
7C2×C32×C4⋊C4C411yescharacteristic
8C2×#3752—21no—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10#64102—21no—
11#64102—21no—
12#64102C412yes—
13#64102C2212yes—
14C22⋊#622—21no—
15C22⋊#622—21no—
16C4⋊#622—21no—
17C4⋊#622C2212yescomplemented
18C4×#622—21no—
19C4×#622C2212yescomplemented
20C2×#893—62no—
21C23×C3⋊D3—21no—
22C22×C32×C4—21no—
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×C4⋊(C3⋊D3)—21no—
27C2×C4⋊(C3⋊D3)—22no—
28C2×C4⋊(C3⋊D3)C814yescomplemented
29C2×C4⋊(C3⋊D3)C2×C412yes—
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—44no—
33C2×#622—22no—
34C2×#622—22no—
35C32×C4⋊C4—21no—
36C32×C4⋊C4C2×C412yes—
37#3752—22no—
38#3752—22no—
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3C2311yescharacteristic
43#1478—91nomaximal, Sylow
44C22×D12—62no—
45C22×C4×D3—64no—
46C2×C3×C4⋊C4—22no—
47C2×(C2×D3)⋊C4—64no—
48C2×C4×Dic3—62no—
49#893—64no—
50#893—64no—
51#893—64no—
52#893—64no—
53C23×C32C22⋊C411yescharacteristic
54C22×C3⋊D3—24no—
55C22×C3⋊D3—22no—
56C22×C3⋊D3—42no—
57C22×C3⋊D3—42no—
58C2×C32×C4—22no—
59C2×C32×C4—42no—
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C32×C4C2×C812yes—
62C2×C32×C4M1612yes—
63C2×C32×C4C22×C411yescharacteristic
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C4⋊(C3⋊D3)—24no—
71C4⋊(C3⋊D3)—22no—
72C4⋊(C3⋊D3)C2×C814yes—
73C4×C3⋊D3—44no—
74C4×C3⋊D3—44no—
75#622—42no—
76#622—42no—
77C2×C4×D4—91no—
78#431—91no—
79#431—91no—
80D4⋊C8—94no—
81C23×D3—64no—
82C22×C3×C4—24no—
83C22×C3×C4—22no—
84C22×Dic3—62no—
85C22×Dic3—62no—
86C2×D12—64no—
87C2×D12—68no—
88C2×D12—64no—
89C2×D12—68no—
90C2×C4×D3—68no—
91C2×C4×D3—68no—
92C2×C4×D3—1216no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—24no—
95(C2×D3)⋊C4—68no—
96(C2×D3)⋊C4—68no—
97C4×Dic3—62no—
98C4×Dic3—62no—
99C4×Dic3—62no—
100C4×Dic3—62no—
101C22×C32—21no—
102C22×C32—21no—
103C22×C32C22⋊C812yes—
104C22×C32C2×C22⋊C411yescharacteristic
105C2×C3⋊D3—24no—
106C2×C3⋊D3—48no—
107C2×C3⋊D3—42no—
108C2×C3⋊D3—42no—
109C32×C4—42no—
110C32×C4C22⋊C812yes—
111C32×C4C22×C811yescharacteristic
112C32×C4C2×M1611yescharacteristic
113C3⋊Dic3—21no—
114C3⋊Dic3—21no—
115C3⋊Dic3—21no—
116C3⋊Dic3AGL(1,ℤ/8)12yes—
117C22×D4—91no—
118C23×C4—181no—
119C4×D4—92no—
120C4×D4—92no—
121C4×D4—181no—
122C4×D4—181no—
123C2×C4⋊C4#15711yescharacteristic
124C2×C22⋊C4—181no—
125C2×C42—91no—
126C4⋊C8—92no—
127C4⋊C8—181no—
128C22⋊C8—181no—
129C22⋊C8—181no—
130C4×C8—92no—
131C4×C8—181no—
132C23×C3—22no—
133C22×D3—68no—
134C22×D3—616no—
135C22×D3—128no—
136C22×D3—128no—
137C2×C3×C4—28no—
138C2×C3×C4—22no—
139C2×C3×C4—24no—
140C2×C3×C4—24no—
141C2×C3×C4—22no—
142C2×C3×C4—48no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—68no—
148C2×Dic3—124no—
149D12—68no—
150D12—68no—
151D12—616no—
152C4×D3—1216no—
153C4×D3—1216no—
154C2×C32—22no—
155C2×C32C2×C22⋊C811yescharacteristic
156C2×C32#41811yescharacteristic
157C2×C32#42111yescharacteristic
158C3⋊D3—44no—
159C24—181no—
160C2×D4—92no—
161C2×D4—94no—
162C2×D4—182no—
163C2×D4—181no—
164C22×C4—21no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—182no—
168C22×C4—182no—
169C22×C4—364no—
170C22×C4C2×#15711yescharacteristic
171C2×C8—182no—
172C2×C8—182no—
173C4⋊C4—21no—
174C4⋊C4C2×#15712yes—
175C22⋊C4—182no—
176C22⋊C4—182no—
177C42—91no—
178C42—91no—
179C42—91no—
180C42—91no—
181C22×C3—24no—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—22no—
185C2×D3—616no—
186C2×D3—128no—
187C2×D3—1232no—
188C2×D3—128no—
189C3×C4—22no—
190C3×C4—22no—
191C3×C4—24no—
192C3×C4—48no—
193Dic3—64no—
194Dic3—64no—
195Dic3—122no—
196Dic3—122no—
197C32#147811yescharacteristic, complemented, Sylow
198C23—184no—
199C23—182no—
200C23—362no—
201C23—362no—
202C23C22⋊#15711yescharacteristic
203D4—94no—
204D4—182no—
205D4—184no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—91no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—182no—
213C2×C4—364no—
214C2×C4—364no—
215C2×C4—361no—
216C2×C4#378712yes—
217C2×C4#378812yes—
218C2×C4C22⋊#15711yescharacteristic
219C2×C4C22×#15711yescharacteristic
220C8—362no—
221C8—362no—
222C2×C3—28no—
223C2×C3—22no—
224C2×C3—22no—
225C2×C3—22no—
226D3—1216no—
227C22—21no—
228C22—21no—
229C22—184no—
230C22—368no—
231C22—362no—
232C22—362no—
233C22#6377812yes—
234C22C2×C22⋊#15711yescharacteristic
235C4—42no—
236C4—92no—
237C4—181no—
238C4—181no—
239C4—181no—
240C4#6377812yes—
241C4C2×#378711yescharacteristic
242C4C2×#378811yescharacteristic
243C3—22no—
244C2—22no—
245C2—364no—
246C2C2×#6377811yescharacteristic
247C2#1059381411yescharacteristic
248C2#1059383111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC4×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1478
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593795C2semidirect
3. #10593795C2semidirect
4. #10590160C2semidirect
17. C4⋊#622C22semidirect
19. C4×#622C22semidirect
28. C2×C4⋊(C3⋊D3)C8semidirect
197. C32#1478semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
#105937952
#105901602
#14789