Finite Group Databasebeta

← #28378369

Subgroups — #28378369

Order 13952.

266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 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
1#20296029C211yesmaximal, characteristic, complemented
2C4×#13182038C211yesmaximal, characteristic, complemented
3#20295876C212yesmaximal, complemented
4#20295874C212yesmaximal, complemented
5#20295494C211yesmaximal, characteristic
6C2×#13182038—21no—
7C2×#13182038—21no—
8#16812766—21no—
9C4⋊#11724786C2212yes—
10#16812754—21no—
11C4×#11724786C2212yes—
12C2×#13182029C411yescharacteristic
13#16812664C411yescharacteristic
14#16812664C2211yescharacteristic
15#16812661C411yescharacteristic
16#16812661C2211yescharacteristic
17#16812659—21no—
18#16812659—21no—
19#16812656—21no—
20C2×C4×Dic109C2211yescharacteristic
21C42×D109—21no—
22#117×C109C411yescharacteristic
23#13182038—24no—
24#13182038—42no—
25C2×#11724786—22no—
26C2×#11724786—22no—
27#13182029—22no—
28#13182029—22no—
29C2×Dic218C2×C411yescharacteristic
30C2×D436C2×C411yescharacteristic
31C2×C22⋊D109—21no—
32C22×Dic109D411yescharacteristic
33C22×Dic109D411yescharacteristic
34C2×C4×D109—21no—
35C2×C4×D109—21no—
36C2×C4×D109—21no—
37#13182008—21no—
38#13182008—21no—
39#13182006—21no—
40#13182006—21no—
41C4×Dic109—21no—
42C4×Dic109—21no—
43C4×Dic109C2×C411yescharacteristic
44C4×Dic109D411yescharacteristic
45C4×Dic109D411yescharacteristic
46C4×Dic109C2311yescharacteristic
47C22×C4×C109C2×C411yescharacteristic
48C4⋊C4×C109C2×C411yescharacteristic
49C4⋊C4×C109C2×C411yescharacteristic
50C22⋊C4×C109—21no—
51C42×C109—21no—
52C23×C109C22⋊C411yescharacteristic
53C22×D109—21no—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109—21no—
57C2×C4×C109—21no—
58C2×C4×C109C22⋊C411yescharacteristic
59C2×C4×C109C22×C411yescharacteristic
60C22⋊D109—24no—
61C2×Dic109—21no—
62C2×Dic109—22no—
63C2×Dic109—21no—
64C2×Dic109—21no—
65C2×Dic109C22⋊C411yescharacteristic
66C2×Dic109C22⋊C411yescharacteristic
67C2×Dic109C2×D411yescharacteristic
68C2×Dic109C2×D411yescharacteristic
69D436—21no—
70D436M1612yescomplemented
71C4×D109—24no—
72C4×D109—42no—
73C4×D109—41no—
74C4×D109—41no—
75Dic218—21no—
76Dic218M1612yescomplemented
77#11724786—24no—
78#11724786—42no—
79C22×C109—21no—
80C22×C109—21no—
81C22×C109—21no—
82C22×C109C2×C22⋊C411yescharacteristic
83C2×D109—22no—
84C2×D109—41no—
85C2×D109—41no—
86C4×C109—21no—
87C4×C109—41no—
88C4×C109—41no—
89C4×C109C2×M1611yescharacteristic
90C4×C109C2×M1611yescharacteristic
91Dic109—22no—
92Dic109—21no—
93Dic109—21no—
94Dic109#10412yes—
95Dic109AGL(1,ℤ/8)11yescharacteristic
96Dic109#13711yescharacteristic
97C2×C109—41no—
98C2×C109#40711yescharacteristic
99C2×C109#41711yescharacteristic
100C2×C109C2×#10411yescharacteristic
101D109—42no—
102#1489—1091nomaximal, Sylow
103C109#148911yescharacteristic, complemented, Sylow
104C4×#41—1091no—
105#423—1091no—
106C4×M16—1091no—
107Q8⋊C8—1092no—
108D4⋊C8—1092no—
109C2×#41—1091no—
110C2×M16—2181no—
111C2×M16—2181no—
112C4×Q8—1091no—
113C4×Q8—1091no—
114C4×D4—1091no—
115C4×D4—1091no—
116C4×D4—2181no—
117C4×D4—2181no—
118#117—2181no—
119#117#8913711yescharacteristic
120C2×C42—1091no—
121C2×C42—2181no—
122C4⋊C8—1092no—
123C4⋊C8—2181no—
124#97—2181no—
125C4×C8—1092no—
126#41—2182no—
127#41—2182no—
128C2×Q8—1091no—
129C2×D4—1091no—
130C2×D4—2181no—
131C22×C4—1091no—
132C22×C4—1091no—
133C22×C4—2181no—
134C22×C4—2181no—
135C22×C4—2181no—
136C22×C4C2×#8913711yescharacteristic
137M16—4362no—
138M16—2184no—
139C2×C8—2182no—
140C2×C8—2182no—
141C4⋊C4—2181no—
142C4⋊C4—2181no—
143C4⋊C4C2×#8913711yescharacteristic
144C4⋊C4C2×#8913711yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—2181no—
147C22⋊C4—2181no—
148C42—21no—
149C42—1091no—
150C42—1091no—
151C42—1091no—
152C42—1091no—
153C42—2181no—
154C42—2181no—
155C23—2181no—
156C23C22⋊#8913711yescharacteristic
157Q8—1092no—
158Q8—2181no—
159D4—1092no—
160D4—2184no—
161D4—2181no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—1091no—
167C2×C4—1091no—
168C2×C4—1091no—
169C2×C4—1091no—
170C2×C4—4361no—
171C2×C4—4361no—
172C2×C4—4362no—
173C2×C4—2184no—
174C2×C4—2181no—
175C2×C4—2182no—
176C2×C4—2181no—
177C2×C4—2181no—
178C2×C4C22⋊#8913711yescharacteristic
179C2×C4C22×#8913711yescharacteristic
180C8—4362no—
181C8—2184no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—4361no—
186C22—4361no—
187C22—2182no—
188C22C2×C22⋊#8913711yescharacteristic
189C4—21no—
190C4—41no—
191C4—41no—
192C4—1091no—
193C4—1091no—
194C4—1092no—
195C4—2182no—
196C4—2181no—
197C4—2181no—
198C4D109⋊M1611yescharacteristic
199C4D109⋊M1611yescharacteristic
200C2—41no—
201C2—4362no—
202C2#2029599811yescharacteristic
203C2#2029601711yescharacteristic
204C2D109⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#117×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×#13182029C4
cosocleC4×Dic109C23
hypercenter#117#89137
hypocenterC109#1489
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #20296029C2semidirect
2. C4×#13182038C2semidirect
3. #20295876C2semidirect
4. #20295874C2semidirect
70. D436M16semidirect
76. Dic218M16semidirect
103. C109#1489semidirect

Maximal subgroups

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

subgroupindex
#202960292
C4×#131820382
#202958762
#202958742
#202954942
#1489109