Finite Group Databasebeta

← #28366191

Subgroups — #28366191

Order 13952.

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

normal subgroups only

This group has 576 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×#16812673C211yesmaximal, characteristic
2#20294926C212yesmaximal, complemented
3#20294918C212yesmaximal, complemented
4#20294909C212yesmaximal, complemented
5#20294904C212yesmaximal, complemented
6#20294902C212yesmaximal, complemented
7#20294900C212yesmaximal, complemented
8#20294886C211yesmaximal, characteristic, complemented
9#381×C109C211yesmaximal, characteristic, complemented
10C22×D436C2211yescharacteristic
11C22×C22⋊D109C2212yes—
12C22×C4×D109C2212yes—
13#16812673C418yescomplemented
14C2×C4⋊Dic109C2212yes—
15C2×C4⋊Dic109C2211yescharacteristic
16C2×#13182008C2212yes—
17C2×C22⋊Dic109C2211yescharacteristic
18C2×C22⋊Dic109C2211yescharacteristic
19C2×#13182006C2212yes—
20C2×#13182006C2212yes—
21C2×#13182006C2212yes—
22C2×#13182006C2212yes—
23C2×C4×Dic109C2212yes—
24#16812606C2212yes—
25#16812606C2212yes—
26#16812606C2212yes—
27C23×C4×C109C2211yescharacteristic
28C2×C22⋊C4×C109C2212yes—
29#95×C109C2211yescharacteristic
30#95×C109C2211yescharacteristic
31#95×C109C2212yes—
32C23×D109C2312yes—
33C2×D436—42no—
34C2×D436C2×C414yes—
35C2×C22⋊D109—42no—
36C2×C22⋊D109—42no—
37C2×C22⋊D109C2×C418yescomplemented
38C22×Dic109C2312yes—
39C22×Dic109C2312yes—
40C22×Dic109C2312yes—
41C2×C4×D109—42no—
42C2×C4×D109—42no—
43C2×C4×D109—42no—
44C4⋊Dic109—42no—
45C4⋊Dic109C2×C414yescomplemented
46#13182008—42no—
47C22⋊Dic109—41no—
48C22⋊Dic109—41no—
49#13182006—42no—
50#13182006—42no—
51#13182006—42no—
52#13182006C2×C418yescomplemented
53C4×Dic109—42no—
54C24×C109C2311yescharacteristic
55C22×C4×C109—42no—
56C22×C4×C109C2×C414yescomplemented
57C22×C4×C109C2312yes—
58C22×C4×C109C2312yes—
59C22×C4×C109C2311yescharacteristic
60C22×C4×C109C2311yescharacteristic
61C22⋊C4×C109—42no—
62C23×C109—22no—
63C23×C109—21no—
64C23×C109—22no—
65C23×C109—21no—
66C23×C109C22×C412yes—
67C23×C109C2411yescharacteristic
68C22×D109—22no—
69C22×D109—22no—
70C22×D109—22no—
71C22×D109—22no—
72C22×D109—22no—
73C22×D109—22no—
74C22×D109C22×C414yes—
75C2×C4×C109—22no—
76C2×C4×C109—22no—
77C2×C4×C109—22no—
78C2×C4×C109—22no—
79C2×C4×C109—22no—
80C2×C4×C109—22no—
81C2×C4×C109—22no—
82C2×C4×C109—22no—
83C2×C4×C109—44no—
84C2×C4×C109C22×C412yes—
85C2×C4×C109C22×C412yes—
86C22⋊D109—48no—
87C2×Dic109—22no—
88C2×Dic109—22no—
89C2×Dic109—22no—
90C2×Dic109—22no—
91C2×Dic109—22no—
92C2×Dic109—22no—
93C2×Dic109—22no—
94C2×Dic109—22no—
95C2×Dic109C22×C414yes—
96D436—44no—
97C4×D109—48no—
98C22×C109—22no—
99C22×C109—22no—
100C22×C109—22no—
101C22×C109—42no—
102C22×C109—42no—
103C22×C109C23×C411yescharacteristic
104C22×C109H(5,𝔽2)12yes—
105C22×C109H(5,𝔽2)12yes—
106C22×C109H(5,𝔽2)11yescharacteristic
107C22×C1092−1+411yescharacteristic
108C2×D109—24no—
109C2×D109—24no—
110C2×D109—24no—
111C2×D109—42no—
112C2×D109—42no—
113C2×D109—42no—
114C2×D109—42no—
115C4×C109—22no—
116C4×C109—22no—
117C4×C109—42no—
118C4×C109—42no—
119Dic109—24no—
120Dic109—42no—
121Dic109—42no—
122C2×C109—42no—
123C2×C109#51811yescharacteristic
124C2×C109#51811yescharacteristic
125C2×C109#52011yescharacteristic
126C2×C109#56012yes—
127C2×C109#56212yes—
128D109—44no—
129#2377—1091nomaximal, Sylow
130C109#237711yescharacteristic, complemented, Sylow
131C2×#121—1091no—
132#390—1092no—
133#388—1092no—
134#387—1092no—
135#386—1092no—
136#386—1092no—
137#385—1092no—
138#381D10911yescharacteristic, complemented
139#380—1091no—
140C22×D4—1092no—
141C22×D4—1091no—
142C23×C4—1092no—
143C23×C4C2×D10911yescharacteristic
144#121—1098no—
145C2×C4⋊C4—1091no—
146C2×C4⋊C4—1092no—
147C2×C4⋊C4—1092no—
148C2×C22⋊C4—1092no—
149C2×C22⋊C4—1091no—
150C2×C22⋊C4—1091no—
151C2×C22⋊C4—1092no—
152C2×C22⋊C4—1092no—
153C2×C22⋊C4—1092no—
154C2×C22⋊C4C2×D10912yes—
155C2×C42—1092no—
156#95—1092no—
157#95—1092no—
158#95—1092no—
159#95C2×D10911yescharacteristic
160#95C2×D10912yes—
161#95C2×D10911yescharacteristic
162C24—1092no—
163C24C22×D10911yescharacteristic
164C2×D4—1098no—
165C2×D4—1094no—
166C2×D4—4362no—
167C2×D4—4362no—
168C2×D4—4362no—
169C22×C4—42no—
170C22×C4—1092no—
171C22×C4—1092no—
172C22×C4—1092no—
173C22×C4—4362no—
174C22×C4—4362no—
175C22×C4—4362no—
176C22×C4C4×D10914yescomplemented
177C22×C4C22×D10912yes—
178C22×C4C22×D10912yes—
179C22×C4C22×D10911yescharacteristic
180C22×C4C22×D10911yescharacteristic
181C4⋊C4—1094no—
182C4⋊C4—4362no—
183C4⋊C4—4362no—
184C22⋊C4—42no—
185C22⋊C4—1098no—
186C22⋊C4—4362no—
187C22⋊C4—4362no—
188C22⋊C4—4362no—
189C22⋊C4—4361no—
190C22⋊C4—4361no—
191C42—4362no—
192C23—22no—
193C23—21no—
194C23—22no—
195C23—21no—
196C23—1094no—
197C23—2182no—
198C23—2182no—
199C23—2182no—
200C23—2182no—
201C23—2182no—
202C23—2182no—
203C23C2×C4×D10912yes—
204C23C23×D10911yescharacteristic
205D4—4364no—
206D4—4368no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—44no—
216C2×C4—1094no—
217C2×C4—4368no—
218C2×C4—2182no—
219C2×C4—2182no—
220C2×C4—2182no—
221C2×C4—2182no—
222C2×C4—2182no—
223C2×C4—2182no—
224C2×C4—2182no—
225C2×C4—2182no—
226C2×C4C2×C4×D10912yes—
227C2×C4C2×C4×D10912yes—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—42no—
232C22—42no—
233C22—4362no—
234C22—4362no—
235C22—4362no—
236C22—4362no—
237C22—2184no—
238C22—2184no—
239C22—2184no—
240C22C22×C4×D10911yescharacteristic
241C22#1681274412yes—
242C22#1681274512yes—
243C22#1681274511yescharacteristic
244C22#1681274611yescharacteristic
245C4—22no—
246C4—22no—
247C4—42no—
248C4—42no—
249C4—4362no—
250C4—4362no—
251C4—2184no—
252C2—42no—
253C2—4364no—
254C2#2029549911yescharacteristic
255C2#2029550011yescharacteristic
256C2#2029550611yescharacteristic
257C2#2029576612yes—
258C2#2029577312yes—
subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
Fitting#381×C109C2
socle, cosocleC23×C109C24
prime radicalC2×#16812673C2
hypercenter#381D109
hypocenterC109#2377
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #20294926C2semidirect
3. #20294918C2semidirect
4. #20294909C2semidirect
5. #20294904C2semidirect
6. #20294902C2semidirect
7. #20294900C2semidirect
8. #20294886C2semidirect
9. #381×C109C2semidirect
13. #16812673C4semidirect
37. C2×C22⋊D109C2×C4semidirect
45. C4⋊Dic109C2×C4semidirect
52. #13182006C2×C4semidirect
56. C22×C4×C109C2×C4semidirect
130. C109#2377semidirect
138. #381D109semidirect
176. C22×C4C4×D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168126732
#202949262
#202949182
#202949092
#202949042
#202949022
#202949002
#202948862
#381×C1092
#2377109