Finite Group Databasebeta

← #100×#157 #11783783

Subgroups — #100×#157 #11783783

Order 1152.

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

normal subgroups only

This group has 546 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
1C2×D4×#157C211yesmaximal, characteristic
2#10593825C211yesmaximal, characteristic
3M16×#157C212yesmaximal, complemented
4C3⋊D3×#100C211yesmaximal, characteristic
5#10590188C212yesmaximal, complemented
6C23×#157C412yes—
7C2×D4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157C412yes—
9D4×#157—22no—
10D4×#157—22no—
11C2×C4⋊#157C2211yescharacteristic
12C2×C4×#157C2211yescharacteristic
13#64283C2212yes—
14M16×C3⋊D3C2212yes—
15#63788C414yescomplemented
16#63767—22no—
17C8×#157—22no—
18C32×#100C411yescharacteristic, complemented
19#63660C411yescharacteristic, complemented
20#63650C412yescomplemented
21D3×#100—62no—
22C23×C3⋊D3C2×C412yes—
23C22×#157—22no—
24C22×#157—22no—
25C22×#157—44no—
26C22×#157C2×C411yescharacteristic
27C22×#157C2×C412yes—
28C22×#157C2×C411yescharacteristic
29C2×C32×D4C2×C411yescharacteristic
30C2×#638C2×C412yes—
31D4×C3⋊D3—22no—
32D4×C3⋊D3—22no—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3C2311yescharacteristic
35C22⋊#157—24no—
36#3792C2×C414yescomplemented
37C4⋊#157—22no—
38C4×#157D412yes—
39C4×#157D412yes—
40#3788—22no—
41#3787—22no—
42C32×M16C2×C412yescomplemented
43#3748C2×C412yescomplemented
44#3743—22no—
45C8×C3⋊D3—22no—
46C4×#100—91nomaximal, Sylow
47C2×D3×D4—62no—
48D3×M16—64no—
49C3×#100—22no—
50#833—62no—
51#823—64no—
52C23×C32C4212yes—
53C22×C3⋊D3—22no—
54C22×C3⋊D3—22no—
55C22×C3⋊D3—42no—
56C22×C3⋊D3—42no—
57C22×C3⋊D3C4212yes—
58C22×C3⋊D3C22×C411yescharacteristic
59C2×#157—22no—
60C2×#157—22no—
61C2×#157—41no—
62C2×#157—44no—
63C2×#157—44no—
64C2×#157—42no—
65C2×#157C22⋊C411yescharacteristic
66C2×#157C22⋊C412yes—
67C2×#157C22⋊C411yescharacteristic
68C32×D4—22no—
69C2×C32×C4C22×C411yescharacteristic
70#638—24no—
71C2×C3⋊Dic3C22×C411yescharacteristic
72C4⋊(C3⋊D3)—22no—
73C4×C3⋊D3C2×D412yes—
74C4×C3⋊D3#4112yes—
75#622—24no—
76C32×C8—22no—
77C3⋊(C3⋊C8)—22no—
78C2×C4×D4—91no—
79C2×#100—91no—
80C2×#100—91no—
81C4×M16—92no—
82#343—92no—
83C23×D3—64no—
84C2×C3×D4—22no—
85C2×#67—64no—
86D3×D4—124no—
87D3×D4—124no—
88C2×D12—62no—
89C2×C4×D3—62no—
90C3×M16—24no—
91#208—64no—
92ΓL(1,𝔽25)—124no—
93D3×C8—124no—
94C22×C32—22no—
95C22×C32—42no—
96C22×C32C2×C4211yescharacteristic
97C2×C3⋊D3—21no—
98C2×C3⋊D3—21no—
99C2×C3⋊D3—22no—
100C2×C3⋊D3—44no—
101C2×C3⋊D3—42no—
102C2×C3⋊D3—42no—
103C2×C3⋊D3—42no—
104C2×C3⋊D3C2×C22⋊C411yescharacteristic
105C2×C3⋊D3#11711yescharacteristic
106#157—21no—
107#157—22no—
108#157—42no—
109#157#10012yesdirect product factor
110C32×C4C4×D412yes—
111C3⋊Dic3C4×D412yes—
112C22×D4—91no—
113C23×C4—92no—
114C2×M16—92no—
115C2×M16—92no—
116C4×D4—182no—
117C4×D4—182no—
118C2×C4⋊C4—91no—
119C2×C22⋊C4—92no—
120C2×C42—91no—
121#100—94no—
122#100—91no—
123#100—92no—
124#100#15711yescharacteristic, direct product factor
125#97—182no—
126C4×C8—182no—
127C23×C3—24no—
128C22×D3—62no—
129C22×D3—64no—
130C22×D3—124no—
131C22×D3—124no—
132C22×D3—244no—
133C22×D3—244no—
134C3×D4—44no—
135C2×C3×C4—22no—
136#67—128no—
137C2×Dic3—62no—
138D12—124no—
139C4×D3—64no—
140C4×D3—64no—
141C3×C8—44no—
142C3⋊C8—124no—
143C2×C32—21no—
144C2×C32—42no—
145C2×C32C4×C22⋊C411yescharacteristic
146C3⋊D3—21no—
147C3⋊D3—42no—
148C3⋊D3C2×#10011yescharacteristic
149C3⋊D3#41311yescharacteristic
150C24—92no—
151C2×D4—92no—
152C2×D4—91no—
153C2×D4—182no—
154C2×D4—182no—
155C2×D4C2×#15711yescharacteristic
156C22×C4—91no—
157C22×C4—91no—
158C22×C4—91no—
159C22×C4—92no—
160C22×C4—182no—
161C22×C4—182no—
162C22×C4—364no—
163M16—94no—
164M16—92no—
165M16—182no—
166M16—182no—
167M16C2×#15712yescomplemented
168C2×C8—182no—
169C2×C8—182no—
170C4⋊C4—182no—
171C22⋊C4—184no—
172C42—92no—
173C42—92no—
174C22×C3—22no—
175C22×C3—44no—
176C22×C3—84no—
177C2×D3—62no—
178C2×D3—62no—
179C2×D3—122no—
180C2×D3—122no—
181C2×D3—124no—
182C2×D3—244no—
183C2×D3—244no—
184C2×D3—248no—
185C2×D3—244no—
186C3×C4—24no—
187Dic3—64no—
188C32C4×#10011yescharacteristic, complemented, Sylow
189C23—91no—
190C23—92no—
191C23—182no—
192C23—182no—
193C23—362no—
194C23—362no—
195C23C4×#15712yes—
196D4—22no—
197D4—184no—
198D4—182no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—92no—
202C2×C4—92no—
203C2×C4—92no—
204C2×C4—91no—
205C2×C4—182no—
206C2×C4—182no—
207C2×C4—364no—
208C2×C4—361no—
209C2×C4—364no—
210C2×C4—362no—
211C2×C4C22×#15711yescharacteristic
212C8—22no—
213C8—184no—
214C8—182no—
215C2×C3—22no—
216C2×C3—42no—
217C2×C3—84no—
218D3—62no—
219D3—62no—
220D3—122no—
221D3—244no—
222C22—22no—
223C22—42no—
224C22—91no—
225C22—91no—
226C22—181no—
227C22—181no—
228C22—182no—
229C22—362no—
230C22—362no—
231C22—362no—
232C22—364no—
233C22C2×C4×#15711yescharacteristic
234C4—92no—
235C4—92no—
236C4—181no—
237C4—182no—
238C4—362no—
239C4D4×#15712yes—
240C3—22no—
241C2—21no—
242C2—42no—
243C2—91no—
244C2—91no—
245C2—181no—
246C2—362no—
247C2C22⋊C4×#15711yescharacteristic
subgroupG/H
centerC2C22⋊C4×#157
commutatorC22×C32C2×C42
FrattiniC2×C4C22×#157
FittingC32×#100C4
socleC2×C32C4×C22⋊C4
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenter#100#157
hypocenterC32C4×#100
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
3. M16×#157C2semidirect
5. #10590188C2semidirect
15. #63788C4semidirect
18. C32×#100C4semidirect
19. #63660C4semidirect
20. #63650C4semidirect
36. #3792C2×C4semidirect
42. C32×M16C2×C4semidirect
43. #3748C2×C4semidirect
109. #157#100direct (N × H)
124. #100#157direct (N × H)
167. M16C2×#157semidirect
188. C32C4×#100semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#1572
#105938252
M16×#1572
C3⋊D3×#1002
#105901882
C4×#1009