Finite Group Databasebeta

← #392×D109 #28366226

Subgroups — #392×D109 #28366226

Order 13952.

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×D109C213yesmaximal, complemented
2C2×C22⋊C4×D109C213yesmaximal, complemented
3#20294936C211yesmaximal, characteristic, complemented
4#20294935C213yesmaximal, complemented
5#20294934C213yesmaximal, complemented
6#95×D109C211yesmaximal, characteristic, complemented
7#392×C109C211yesmaximal, characteristic, complemented
8C24×D109C2213yes—
9C22×D436C2213yescomplemented
10C22×C22⋊D109C2216yescomplemented
11C2×D4×D109—224no—
12C2×D4×D109—212no—
13C22×C4×D109C2211yescharacteristic
14C22×C4×D109C2213yes—
15C2×C22⋊Dic109C2213yescomplemented
16C2×#13182006C2213yescomplemented
17C2×#13182006C2213yescomplemented
18C22⋊C4×D109—212no—
19#16812606C2213yescomplemented
20C22×D4×C109C2213yescomplemented
21C2×C22⋊C4×C109C2213yescomplemented
22#95×C109C2211yescharacteristic, complemented
23C23×D109—26no—
24C23×D109—212no—
25C23×D109—212no—
26C23×D109—26no—
27C23×D109D4112yescomplemented
28C23×D109C2313yes—
29C23×D109C2311yescharacteristic
30C2×D436—212no—
31C2×D436—26no—
32C2×C22⋊D109—212no—
33C2×C22⋊D109—212no—
34C2×C22⋊D109—212no—
35D4×D109—296no—
36C22×Dic109C2311yescharacteristic
37C22×Dic109C2313yes—
38C2×C4×D109—212no—
39C2×C4×D109—26no—
40C2×C4×D109D4112yescomplemented
41C22⋊Dic109—26no—
42#13182006—26no—
43#13182006—26no—
44C24×C109C2313yes—
45C2×D4×C109—212no—
46C2×D4×C109—26no—
47C22×C4×C109C2311yescharacteristic
48C22×C4×C109C2313yes—
49C22⋊C4×C109—26no—
50C23×C109—23no—
51C23×C109—26no—
52C23×C109—26no—
53C23×C109—23no—
54C23×C109C2×D416yescomplemented
55C23×C109C2411yescharacteristic
56C22×D109—23no—
57C22×D109—26no—
58C22×D109—26no—
59C22×D109—23no—
60C22×D109—248no—
61C22×D109—224no—
62C22×D109—412no—
63C22×D109—424no—
64C22×D109—412no—
65C22×D109C2×D416yes—
66C22×D109C2×D416yes—
67C22×D109C2×D416yescomplemented
68C22×D109#4112yes—
69D4×C109—224no—
70C2×C4×C109—26no—
71C2×C4×C109—23no—
72C2×C4×C109C2×D416yescomplemented
73C22⋊D109—248no—
74C2×Dic109—26no—
75C2×Dic109—23no—
76C2×Dic109C2×D416yescomplemented
77D436—224no—
78C4×D109—224no—
79C4×D109—44no—
80C22×C109—212no—
81C22×C109—26no—
82C22×C109—43no—
83C22×C109—46no—
84C22×C109—43no—
85C22×C109C22×D413yes—
86C22×C109C22×D413yes—
87C22×C109C2×#4111yescharacteristic
88C2×D109—212no—
89C2×D109—26no—
90C2×D109—43no—
91C2×D109—46no—
92C2×D109—43no—
93C2×D109—448no—
94C2×D109#120112yes—
95C2×D109#121112yes—
96C2×D109#12714yes—
97C4×C109—26no—
98C4×C109—41no—
99Dic109—26no—
100Dic109—41no—
101C2×C109—46no—
102C2×C109C2×#12013yes—
103C2×C109C2×#12113yes—
104C2×C109C2×#12711yescharacteristic
105D109—46no—
106D109#39218yesdirect product factor
107C2×#392—1091nomaximal, Sylow
108C109C2×#39211yescharacteristic, complemented, Sylow
109C23×D4—1093no—
110C22×C22⋊C4—1093no—
111#392—1093no—
112#392—1093no—
113#392—1091no—
114#392D10911yescharacteristic, direct product factor
115C2×#95—1091no—
116C25—1093no—
117C22×D4—1096no—
118C22×D4—1093no—
119C22×D4—21812no—
120C22×D4—21824no—
121C22×D4C2×D10913yescomplemented
122C23×C4—1093no—
123C23×C4—1091no—
124C2×C22⋊C4—1093no—
125C2×C22⋊C4—1093no—
126C2×C22⋊C4—1093no—
127C2×C22⋊C4—21812no—
128C2×C22⋊C4C2×D10913yescomplemented
129#95—1093no—
130#95C2×D10911yescharacteristic, complemented
131C24—1091no—
132C24—10912no—
133C24—1093no—
134C24—2186no—
135C24—21812no—
136C24—21812no—
137C24—2186no—
138C24C22×D10913yes—
139C2×D4—212no—
140C2×D4—26no—
141C2×D4—21812no—
142C2×D4—21812no—
143C2×D4—21896no—
144C2×D4—21812no—
145C2×D4—21812no—
146C2×D4—2186no—
147C22×C4—1093no—
148C22×C4—10912no—
149C22×C4—1091no—
150C22×C4—2186no—
151C22×C4—21812no—
152C22×C4C22×D10911yescharacteristic
153C22×C4C22×D10913yes—
154C22⋊C4—26no—
155C22⋊C4—2186no—
156C22⋊C4—2186no—
157C22⋊C4—2186no—
158C23—23no—
159C23—26no—
160C23—26no—
161C23—23no—
162C23—1096no—
163C23—1096no—
164C23—1092no—
165C23—1096no—
166C23—43612no—
167C23—43624no—
168C23—43612no—
169C23—21848no—
170C23—21824no—
171C23—2183no—
172C23—2186no—
173C23—2186no—
174C23—2183no—
175C23D4×D10916yescomplemented
176C23C23×D10911yescharacteristic
177D4—224no—
178D4—21824no—
179D4—21848no—
180C2×C4—26no—
181C2×C4—23no—
182C2×C4—1096no—
183C2×C4—4364no—
184C2×C4—21824no—
185C2×C4—2183no—
186C2×C4—2186no—
187C2×C4D4×D10916yescomplemented
188C22—212no—
189C22—26no—
190C22—43no—
191C22—46no—
192C22—43no—
193C22—10912no—
194C22—10912no—
195C22—1094no—
196C22—43648no—
197C22—4363no—
198C22—4366no—
199C22—4363no—
200C22—21812no—
201C22—2186no—
202C22C2×D4×D10913yes—
203C22C2×D4×D10913yes—
204C22#41×D10911yescharacteristic
205C4—26no—
206C4—41no—
207C4—4361no—
208C4—2186no—
209C2—46no—
210C2—1098no—
211C2—4366no—
212C2#120×D10913yes—
213C2#121×D10913yes—
214C2#127×D10911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D109
commutator, socle, cosocleC23×C109C24
Fitting#392×C109C2
hypercenter#392D109
hypocenterC109C2×#392
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D109C2semidirect
2. C2×C22⋊C4×D109C2semidirect
3. #20294936C2semidirect
4. #20294935C2semidirect
5. #20294934C2semidirect
6. #95×D109C2semidirect
7. #392×C109C2semidirect
9. C22×D436C22semidirect
10. C22×C22⋊D109C22semidirect
15. C2×C22⋊Dic109C22semidirect
16. C2×#13182006C22semidirect
17. C2×#13182006C22semidirect
19. #16812606C22semidirect
20. C22×D4×C109C22semidirect
21. C2×C22⋊C4×C109C22semidirect
22. #95×C109C22semidirect
27. C23×D109D4semidirect
40. C2×C4×D109D4semidirect
54. C23×C109C2×D4semidirect
67. C22×D109C2×D4semidirect
72. C2×C4×C109C2×D4semidirect
76. C2×Dic109C2×D4semidirect
106. D109#392direct (N × H)
108. C109C2×#392semidirect
114. #392D109direct (N × H)
121. C22×D4C2×D109semidirect
128. C2×C22⋊C4C2×D109semidirect
130. #95C2×D109semidirect
175. C23D4×D109semidirect
187. C2×C4D4×D109semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1092
C2×C22⋊C4×D1092
#202949362
#202949352
#202949342
#95×D1092
#392×C1092
C2×#392109