Finite Group Databasebeta

← #392×D269 #46814079

Subgroups — #392×D269 #46814079

Order 34432.

1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 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×D4×D269C213yesmaximal, complemented
2C2×C22⋊C4×D269C213yesmaximal, complemented
3#31770515C211yesmaximal, characteristic, complemented
4#31770514C213yesmaximal, complemented
5#31770513C213yesmaximal, complemented
6#95×D269C211yesmaximal, characteristic, complemented
7#392×C269C211yesmaximal, characteristic, complemented
8C24×D269C2213yes—
9C22×D1076C2213yescomplemented
10C22×C22⋊D269C2216yescomplemented
11C2×D4×D269—224no—
12C2×D4×D269—212no—
13C22×C4×D269C2211yescharacteristic
14C22×C4×D269C2213yes—
15C2×C22⋊Dic269C2213yescomplemented
16C2×#16864379C2213yescomplemented
17C2×#16864379C2213yescomplemented
18C22⋊C4×D269—212no—
19#22575360C2213yescomplemented
20C22×D4×C269C2213yescomplemented
21C2×C22⋊C4×C269C2213yescomplemented
22#95×C269C2211yescharacteristic, complemented
23C23×D269—26no—
24C23×D269—212no—
25C23×D269—212no—
26C23×D269—26no—
27C23×D269D4112yescomplemented
28C23×D269C2313yes—
29C23×D269C2311yescharacteristic
30C2×D1076—212no—
31C2×D1076—26no—
32C2×C22⋊D269—212no—
33C2×C22⋊D269—212no—
34C2×C22⋊D269—212no—
35D4×D269—296no—
36C22×Dic269C2311yescharacteristic
37C22×Dic269C2313yes—
38C2×C4×D269—212no—
39C2×C4×D269—26no—
40C2×C4×D269D4112yescomplemented
41C22⋊Dic269—26no—
42#16864379—26no—
43#16864379—26no—
44C24×C269C2313yes—
45C2×D4×C269—212no—
46C2×D4×C269—26no—
47C22×C4×C269C2311yescharacteristic
48C22×C4×C269C2313yes—
49C22⋊C4×C269—26no—
50C22×D269—23no—
51C22×D269—26no—
52C22×D269—26no—
53C22×D269—23no—
54C22×D269—248no—
55C22×D269—224no—
56C22×D269—412no—
57C22×D269—424no—
58C22×D269—412no—
59C22×D269C2×D416yes—
60C22×D269C2×D416yes—
61C22×D269C2×D416yescomplemented
62C22×D269#4112yes—
63D1076—224no—
64C22⋊D269—248no—
65C2×Dic269—26no—
66C2×Dic269—23no—
67C2×Dic269C2×D416yescomplemented
68C4×D269—224no—
69C4×D269—44no—
70C23×C269—23no—
71C23×C269—26no—
72C23×C269—26no—
73C23×C269—23no—
74C23×C269C2×D416yescomplemented
75C23×C269C2411yescharacteristic
76D4×C269—224no—
77C2×C4×C269—26no—
78C2×C4×C269—23no—
79C2×C4×C269C2×D416yescomplemented
80C22×C269—212no—
81C22×C269—26no—
82C22×C269—43no—
83C22×C269—46no—
84C22×C269—43no—
85C22×C269C22×D413yes—
86C22×C269C22×D413yes—
87C22×C269C2×#4111yescharacteristic
88C2×D269—212no—
89C2×D269—26no—
90C2×D269—43no—
91C2×D269—46no—
92C2×D269—43no—
93C2×D269—448no—
94C2×D269#120112yes—
95C2×D269#121112yes—
96C2×D269#12714yes—
97C4×C269—26no—
98C4×C269—41no—
99Dic269—26no—
100Dic269—41no—
101C2×C269—46no—
102C2×C269C2×#12013yes—
103C2×C269C2×#12113yes—
104C2×C269C2×#12711yescharacteristic
105D269—46no—
106D269#39218yesdirect product factor
107C269C2×#39211yescharacteristic, complemented, Sylow
108C2×#392—2691nomaximal, Sylow
109C23×D4—2693no—
110C22×C22⋊C4—2693no—
111#392—2693no—
112#392—2693no—
113#392—2691no—
114#392D26911yescharacteristic, direct product factor
115C2×#95—2691no—
116C25—2693no—
117C22×D4—2696no—
118C22×D4—2693no—
119C22×D4—53812no—
120C22×D4—53824no—
121C22×D4C2×D26913yescomplemented
122C23×C4—2693no—
123C23×C4—2691no—
124C2×C22⋊C4—2693no—
125C2×C22⋊C4—2693no—
126C2×C22⋊C4—2693no—
127C2×C22⋊C4—53812no—
128C2×C22⋊C4C2×D26913yescomplemented
129#95—2693no—
130#95C2×D26911yescharacteristic, complemented
131C24—2691no—
132C24—26912no—
133C24—2693no—
134C24—5386no—
135C24—53812no—
136C24—53812no—
137C24—5386no—
138C24C22×D26913yes—
139C2×D4—212no—
140C2×D4—26no—
141C2×D4—53812no—
142C2×D4—53812no—
143C2×D4—53896no—
144C2×D4—53812no—
145C2×D4—53812no—
146C2×D4—5386no—
147C22×C4—2693no—
148C22×C4—26912no—
149C22×C4—2691no—
150C22×C4—53812no—
151C22×C4—5386no—
152C22×C4C22×D26911yescharacteristic
153C22×C4C22×D26913yes—
154C22⋊C4—26no—
155C22⋊C4—5386no—
156C22⋊C4—5386no—
157C22⋊C4—5386no—
158C23—23no—
159C23—26no—
160C23—26no—
161C23—23no—
162C23—2696no—
163C23—2696no—
164C23—2692no—
165C23—2696no—
166C23—53848no—
167C23—53824no—
168C23—5383no—
169C23—5386no—
170C23—5386no—
171C23—5383no—
172C23—107612no—
173C23—107612no—
174C23—107624no—
175C23D4×D26916yescomplemented
176C23C23×D26911yescharacteristic
177D4—224no—
178D4—53824no—
179D4—53848no—
180C2×C4—26no—
181C2×C4—23no—
182C2×C4—2696no—
183C2×C4—53824no—
184C2×C4—5386no—
185C2×C4—5383no—
186C2×C4—10764no—
187C2×C4D4×D26916yescomplemented
188C22—212no—
189C22—26no—
190C22—43no—
191C22—43no—
192C22—46no—
193C22—2694no—
194C22—26912no—
195C22—26912no—
196C22—53812no—
197C22—5386no—
198C22—107648no—
199C22—10763no—
200C22—10763no—
201C22—10766no—
202C22C2×D4×D26913yes—
203C22C2×D4×D26913yes—
204C22#41×D26911yescharacteristic
205C4—26no—
206C4—41no—
207C4—5386no—
208C4—10761no—
209C2—46no—
210C2—2698no—
211C2—10766no—
212C2#120×D26913yes—
213C2#121×D26913yes—
214C2#127×D26911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutator, socle, cosocleC23×C269C24
Fitting#392×C269C2
hypercenter#392D269
hypocenterC269C2×#392
LCSG ▷ C23×C269 ▷ C269
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D269C2semidirect
2. C2×C22⋊C4×D269C2semidirect
3. #31770515C2semidirect
4. #31770514C2semidirect
5. #31770513C2semidirect
6. #95×D269C2semidirect
7. #392×C269C2semidirect
9. C22×D1076C22semidirect
10. C22×C22⋊D269C22semidirect
15. C2×C22⋊Dic269C22semidirect
16. C2×#16864379C22semidirect
17. C2×#16864379C22semidirect
19. #22575360C22semidirect
20. C22×D4×C269C22semidirect
21. C2×C22⋊C4×C269C22semidirect
22. #95×C269C22semidirect
27. C23×D269D4semidirect
40. C2×C4×D269D4semidirect
61. C22×D269C2×D4semidirect
67. C2×Dic269C2×D4semidirect
74. C23×C269C2×D4semidirect
79. C2×C4×C269C2×D4semidirect
106. D269#392direct (N × H)
107. C269C2×#392semidirect
114. #392D269direct (N × H)
121. C22×D4C2×D269semidirect
128. C2×C22⋊C4C2×D269semidirect
130. #95C2×D269semidirect
175. C23D4×D269semidirect
187. C2×C4D4×D269semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D2692
C2×C22⋊C4×D2692
#317705152
#317705142
#317705132
#95×D2692
#392×C2692
C2×#392269