Finite Group Databasebeta

← #28366200

Subgroups — #28366200

Order 13952.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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×#16812678C211yesmaximal, characteristic
2#20294930C212yesmaximal, complemented
3#20294923C212yesmaximal, complemented
4#20294920C212yesmaximal
5#20294914C212yesmaximal
6#20294913C212yesmaximal, complemented
7#20294911C212yesmaximal, complemented
8#20294886C211yesmaximal, characteristic
9#381×C109C211yesmaximal, characteristic
10C22×Dic218C2211yescharacteristic
11#16812678C418yescomplemented
12C2×C4⋊Dic109C2212yes—
13C2×C4⋊Dic109C2211yescharacteristic
14C2×#13182008C2212yes—
15C2×#13182008C2212yes—
16C2×#13182008C2212yes—
17C2×C22⋊Dic109C2211yescharacteristic
18C2×C22⋊Dic109C2211yescharacteristic
19C2×C22⋊Dic109C2212yes—
20C2×C4×Dic109C2212yes—
21C2×C4×Dic109C2212yes—
22#16812606C2212yes—
23#16812606C2212yes—
24#16812606C2212yes—
25#16812606C2212yes—
26#16812606C2212yes—
27C23×C4×C109C2211yescharacteristic
28C2×C22⋊C4×C109C2212yes—
29#95×C109C2211yescharacteristic
30#95×C109C2211yescharacteristic
31#95×C109C2212yes—
32C2×Dic218—42no—
33C2×Dic218C2×C414yes—
34C22×Dic109C2312yes—
35C22×Dic109C2312yes—
36C22×Dic109C2312yes—
37C22×Dic109C2312yes—
38C4⋊Dic109—42no—
39C4⋊Dic109C2×C414yes—
40#13182008—42no—
41#13182008—42no—
42#13182008C2×C418yes—
43C22⋊Dic109—41no—
44C22⋊Dic109—41no—
45C22⋊Dic109C2×C418yes—
46C4×Dic109—42no—
47C4×Dic109—42no—
48C24×C109C2311yescharacteristic
49C22×C4×C109—42no—
50C22×C4×C109C2×C414yes—
51C22×C4×C109C2312yes—
52C22×C4×C109C2312yes—
53C22×C4×C109C2311yescharacteristic
54C22×C4×C109C2311yescharacteristic
55C22⋊C4×C109—42no—
56C23×C109—22no—
57C23×C109—21no—
58C23×C109—22no—
59C23×C109—21no—
60C23×C109C22×C412yes—
61C23×C109C2411yescharacteristic
62C2×C4×C109—22no—
63C2×C4×C109—22no—
64C2×C4×C109—22no—
65C2×C4×C109—22no—
66C2×C4×C109—22no—
67C2×C4×C109—22no—
68C2×C4×C109—22no—
69C2×C4×C109—22no—
70C2×C4×C109—44no—
71C2×C4×C109C22×C412yes—
72C2×C4×C109C22×C412yes—
73C2×Dic109—22no—
74C2×Dic109—22no—
75C2×Dic109—22no—
76C2×Dic109—22no—
77C2×Dic109—22no—
78C2×Dic109—22no—
79C2×Dic109—22no—
80C2×Dic109—22no—
81C2×Dic109—22no—
82C2×Dic109—22no—
83C2×Dic109C22×C414yes—
84C2×Dic109C22×C414yes—
85Dic218—44no—
86C22×C109—22no—
87C22×C109—22no—
88C22×C109—22no—
89C22×C109—42no—
90C22×C109—42no—
91C22×C109C23×C411yescharacteristic
92C22×C109H(5,𝔽2)12yes—
93C22×C109H(5,𝔽2)11yescharacteristic
94C22×C1092−1+412yes—
95C22×C1092−1+411yescharacteristic
96C4×C109—22no—
97C4×C109—22no—
98C4×C109—42no—
99C4×C109—42no—
100Dic109—24no—
101Dic109—24no—
102Dic109—42no—
103Dic109—42no—
104C2×C109—42no—
105C2×C109#51811yescharacteristic
106C2×C109#51911yescharacteristic
107C2×C109#52011yescharacteristic
108C2×C109#56212yes—
109C2×C109#56312yes—
110#2378—1091nomaximal, Sylow
111C109#237811yescharacteristic, complemented, Sylow
112C2×C22⋊Q8—1091no—
113#391—1092no—
114#389—1092no—
115#388—1092no—
116#388—1092no—
117#387—1092no—
118#387—1092no—
119#381D10911yescharacteristic
120#380—1091no—
121C22×Q8—1091no—
122C23×C4C2×D10911yescharacteristic
123C22⋊Q8—1098no—
124C2×C4⋊C4—1092no—
125C2×C4⋊C4—1091no—
126C2×C4⋊C4—1092no—
127C2×C4⋊C4—1092no—
128C2×C4⋊C4—1092no—
129C2×C22⋊C4—1092no—
130C2×C22⋊C4—1091no—
131C2×C22⋊C4—1091no—
132C2×C22⋊C4C2×D10912yes—
133C2×C42—1092no—
134C2×C42—1092no—
135#95—1092no—
136#95—1092no—
137#95—1092no—
138#95—1092no—
139#95—1092no—
140#95C2×D10911yescharacteristic
141#95C2×D10912yes—
142#95C2×D10911yescharacteristic
143C24C22×D10911yescharacteristic
144C2×Q8—1094no—
145C2×Q8—4362no—
146C22×C4—42no—
147C22×C4—1092no—
148C22×C4—1092no—
149C22×C4—1092no—
150C22×C4—1092no—
151C22×C4C4×D10914yes—
152C22×C4C22×D10912yes—
153C22×C4C22×D10912yes—
154C22×C4C22×D10911yescharacteristic
155C22×C4C22×D10911yescharacteristic
156C4⋊C4—1098no—
157C4⋊C4—1094no—
158C4⋊C4—4362no—
159C4⋊C4—4362no—
160C4⋊C4—4362no—
161C22⋊C4—42no—
162C22⋊C4—1098no—
163C22⋊C4—4361no—
164C22⋊C4—4361no—
165C42—4362no—
166C42—4362no—
167C23—22no—
168C23—21no—
169C23—22no—
170C23—21no—
171C23C2×C4×D10912yes—
172C23C23×D10911yescharacteristic
173Q8—4364no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—1094no—
184C2×C4—1094no—
185C2×C4—2182no—
186C2×C4—2182no—
187C2×C4—2182no—
188C2×C4—2182no—
189C2×C4—2182no—
190C2×C4—2182no—
191C2×C4—2182no—
192C2×C4—2182no—
193C2×C4—2182no—
194C2×C4—2182no—
195C2×C4C2×C4×D10912yes—
196C2×C4C2×C4×D10912yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D10911yescharacteristic
203C22#1681274412yes—
204C22#1681274511yescharacteristic
205C22#1681274612yes—
206C22#1681274611yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—4362no—
212C4—4362no—
213C4—2184no—
214C4—2184no—
215C2—42no—
216C2#2029549911yescharacteristic
217C2#2029550311yescharacteristic
218C2#2029550611yescharacteristic
219C2#2029577312yes—
220C2#2029577912yes—
subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
Fitting#381×C109C2
socle, cosocleC23×C109C24
prime radicalC24×C109C23
hypercenter#381D109
hypocenterC109#2378
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #20294930C2semidirect
3. #20294923C2semidirect
6. #20294913C2semidirect
7. #20294911C2semidirect
11. #16812678C4semidirect
111. C109#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#168126782
#202949302
#202949232
#202949202
#202949142
#202949132
#202949112
#202948862
#381×C1092
#2378109