Finite Group Databasebeta

← #28362941

Subgroups — #28362941

Order 13952.

852 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C23×C4×D109C211yesmaximal, characteristic
2C2×C22⋊#11724784C211yesmaximal, characteristic, complemented
3C2×#16812611C214yesmaximal, complemented
4C2×C22⋊C8×C109C211yesmaximal, characteristic, complemented
5C24×D109C411yescharacteristic
6C23×Dic109C411yescharacteristic
7C22×C4×D109—28no—
8C22×C4×D109—22no—
9C22×C4×D109—22no—
10C22×C4×D109C412yes—
11C22×C4×D109C2212yes—
12C22×#11724784C2212yescomplemented
13C22⋊#11724784—22no—
14#16812611—28no—
15C23×C4×C109C2211yescharacteristic
16C22×C8×C109C2212yescomplemented
17C22⋊C8×C109—22no—
18C23×D109—22no—
19C23×D109—22no—
20C23×D109—24no—
21C23×D109—24no—
22C23×D109C814yescomplemented
23C23×D109C2×C412yes—
24C22×Dic109—22no—
25C22×Dic109—24no—
26C22×Dic109C2×C412yes—
27C2×C4×D109—216no—
28C2×C4×D109—216no—
29C2×C4×D109—24no—
30C2×C4×D109—24no—
31C2×C4×D109—24no—
32C2×C4×D109—22no—
33C2×C4×D109—22no—
34C2×C4×D109—24no—
35C2×C4×D109D418yes—
36C2×#11724784—24no—
37C2×#11724784—22no—
38C24×C109C2×C411yescharacteristic
39C22×C4×C109—24no—
40C22×C4×C109C2×C411yescharacteristic
41C22×C4×C109D412yes—
42C22×C4×C109D412yes—
43C22×C4×C109C2311yescharacteristic
44C2×C8×C109—22no—
45C2×C8×C109—24no—
46C23×C109—22no—
47C23×C109—22no—
48C23×C109C22⋊C412yes—
49C23×C109C2×C812yes—
50C23×C109M1612yes—
51C23×C109C22×C411yescharacteristic
52C22×D109—28no—
53C22×D109—216no—
54C22×D109—28no—
55C22×D109—28no—
56C22×D109—22no—
57C22×D109—22no—
58C22×D109—22no—
59C22×D109—22no—
60C22×D109—216no—
61C22×D109C22⋊C414yes—
62C22×D109C2×C814yes—
63C22×D109M1614yes—
64C2×C4×C109—22no—
65C2×C4×C109—24no—
66C2×C4×C109—24no—
67C2×C4×C109C22⋊C412yes—
68C2×C4×C109C2×D414yes—
69C2×C4×C109C2×D411yescharacteristic
70C2×C4×C109C2×D411yescharacteristic
71C2×Dic109—28no—
72C2×Dic109—22no—
73C2×Dic109—22no—
74C2×Dic109C22⋊C414yes—
75C4×D109—216no—
76C4×D109—28no—
77C4×D109—28no—
78C8×C109—42no—
79#11724784—42no—
80C22×C109—22no—
81C22×C109—24no—
82C22×C109—22no—
83C22×C109—24no—
84C22×C109C22⋊C814yescomplemented
85C22×C109C2×C22⋊C412yes—
86C22×C109C2×C22⋊C411yescharacteristic
87C22×C109C22×C811yescharacteristic
88C22×C109C2×M1612yes—
89C22×C109C2×M1611yescharacteristic
90C2×D109—232no—
91C2×D109—24no—
92C2×D109—24no—
93C2×D109—24no—
94C2×D109—24no—
95C2×D109—24no—
96C2×D109—24no—
97C2×D109C22⋊C818yescomplemented
98C4×C109—22no—
99C4×C109#12012yes—
100C4×C109#12012yes—
101Dic109—24no—
102C2×C109—24no—
103C2×C109#37911yescharacteristic
104C2×C109C2×C22⋊C812yes—
105C2×C109C2×C22⋊C811yescharacteristic
106C2×C109#40712yes—
107C2×C109#40711yescharacteristic
108D109—28no—
109#1779—1091nomaximal, Sylow
110C109#177911yescharacteristic, complemented, Sylow
111C24×C4—1091no—
112C2×C22⋊C8—1091no—
113C2×C22⋊C8—1094no—
114C2×C22⋊C8D10911yescharacteristic, complemented
115C25—1091no—
116C23×C4—1092no—
117C23×C4—1091no—
118C23×C4—1092no—
119C23×C4—2188no—
120C23×C4—2182no—
121C23×C4—2182no—
122C23×C4C2×D10911yescharacteristic
123C22×C8—1092no—
124C22×C8C2×D10912yescomplemented
125C22⋊C8—22no—
126C22⋊C8—2188no—
127C22⋊C8—2182no—
128C24—1092no—
129C24—1094no—
130C24—2184no—
131C24—2184no—
132C24—2182no—
133C24—2182no—
134C24C4×D10911yescharacteristic
135C22×C4—24no—
136C22×C4—1092no—
137C22×C4—1098no—
138C22×C4—2184no—
139C22×C4—2184no—
140C22×C4—21816no—
141C22×C4—21816no—
142C22×C4—2184no—
143C22×C4—2182no—
144C22×C4—2184no—
145C22×C4—2184no—
146C22×C4—2182no—
147C22×C4—2182no—
148C22×C4C4×D10911yescharacteristic
149C22×C4D43612yes—
150C22×C4C22⋊D10912yes—
151C22×C4C22×D10911yescharacteristic
152C2×C8—24no—
153C2×C8—22no—
154C2×C8—2184no—
155C2×C8—2182no—
156C23—22no—
157C23—22no—
158C23—1094no—
159C23—1094no—
160C23—1094no—
161C23—21816no—
162C23—2188no—
163C23—21816no—
164C23—2188no—
165C23—2188no—
166C23—2182no—
167C23—2182no—
168C23—2182no—
169C23—2182no—
170C23#1318200612yes—
171C23C8×D10912yes—
172C23#1318201212yes—
173C23C2×C4×D10911yescharacteristic
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—1094no—
178C2×C4—21816no—
179C2×C4—2188no—
180C2×C4—2182no—
181C2×C4—2182no—
182C2×C4—2188no—
183C2×C4—2188no—
184C2×C4#1318200612yes—
185C2×C4D4×D10914yes—
186C2×C4C2×C22⋊D10911yescharacteristic
187C2×C4C2×D43611yescharacteristic
188C8—42no—
189C8—4362no—
190C22—24no—
191C22—24no—
192C22—22no—
193C22—22no—
194C22—1098no—
195C22—21832no—
196C22—2184no—
197C22—2184no—
198C22—2184no—
199C22—2184no—
200C22—2184no—
201C22—2184no—
202C22#1681261114yescomplemented
203C22C22⋊C4×D10912yes—
204C22C2×#1318200611yescharacteristic
205C22C2×C8×D10911yescharacteristic
206C22M16×D10912yes—
207C22C2×#1318201211yescharacteristic
208C4—22no—
209C4—2184no—
210C4#1681266712yes—
211C4#1681266912yes—
212C2—24no—
213C2—2188no—
214C2#2029488111yescharacteristic
215C2C22⋊C8×D10912yes—
216C2C2×#1681261111yescharacteristic
217C2#2029498812yes—
218C2#2029498911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D109
commutatorC22×C109C22×C8
FittingC2×C22⋊C8×C109C2
socleC23×C109C22×C4
prime radicalC24×D109C4
cosocleC22×C4×C109C23
hypercenterC2×C22⋊C8D109
hypocenterC109#1779
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#11724784C2semidirect
3. C2×#16812611C2semidirect
4. C2×C22⋊C8×C109C2semidirect
12. C22×#11724784C22semidirect
16. C22×C8×C109C22semidirect
22. C23×D109C8semidirect
84. C22×C109C22⋊C8semidirect
97. C2×D109C22⋊C8semidirect
110. C109#1779semidirect
114. C2×C22⋊C8D109semidirect
124. C22×C8C2×D109semidirect
202. C22#16812611semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1092
C2×C22⋊#117247842
C2×#168126112
C2×C22⋊C8×C1092
#1779109