Finite Group Databasebeta

← #28372963

Subgroups — #28372963

Order 13952.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#20295537C211yesmaximal, characteristic
2#20295367C214yesmaximal, complemented
3#20295350C214yesmaximal, complemented
4#20295066C212yesmaximal, complemented
5#20295025C212yesmaximal, complemented
6#20294990C211yesmaximal, characteristic, complemented
7C2×#117×C109C211yesmaximal, characteristic, complemented
8C2×#13182029C2211yescharacteristic
9C2×#13182013C2212yes—
10#16812682—21no—
11#16812678C2212yes—
12#16812673C2212yes—
13#16812668—21no—
14C4×C22⋊D109—22no—
15#16812658C2211yescharacteristic
16#16812632C2214yescomplemented
17#16812630C2214yescomplemented
18#16812622C2214yescomplemented
19#16812619C2214yescomplemented
20C22⋊#11724784C2214yes—
21C23×C4×C109C2211yescharacteristic
22#117×C109—22no—
23#117×C109C2214yes—
24C2×C4⋊C4×C109C2212yes—
25C2×C22⋊C4×C109—21no—
26C2×C42×C109—21no—
27#13182029—24no—
28C2×Dic218C2311yescharacteristic
29C2×D436C2311yescharacteristic
30C2×C22⋊D109—22no—
31C2×C22⋊D109—21no—
32C2×C4×D109—21no—
33#13182013—24no—
34C2×#11724784C2314yes—
35C4⋊Dic109C2312yes—
36#13182008—22no—
37C22⋊Dic109—21no—
38C22⋊Dic109—22no—
39#13182006—22no—
40C4×Dic109—21no—
41C24×C109D411yescharacteristic
42C22×C4×C109—24no—
43C22×C4×C109—22no—
44C22×C4×C109D411yescharacteristic
45C22×C4×C109D412yes—
46C22×C4×C109C2312yes—
47C22×C4×C109C2311yescharacteristic
48C4⋊C4×C109—22no—
49C4⋊C4×C109C2314yes—
50C22⋊C4×C109—24no—
51C42×C109—24no—
52C23×C109—22no—
53C23×C109—42no—
54C23×C109C2×D412yes—
55C23×C109C2×D411yescharacteristic
56C22×D109—21no—
57C2×C4×C109—22no—
58C2×C4×C109—24no—
59C2×C4×C109—24no—
60C2×C4×C109—24no—
61C2×C4×C109—44no—
62C2×C4×C109C2×D412yes—
63C2×C4×C109C2×D411yescharacteristic
64C2×C4×C109#4114yes—
65C2×C4×C109C2411yescharacteristic
66C22⋊D109—44no—
67C22⋊D109—42no—
68C2×Dic109—22no—
69C2×Dic109—21no—
70D436—22no—
71C4×D109—42no—
72Dic218—22no—
73#11724784—24no—
74C22×C109—22no—
75C22×C109—22no—
76C22×C109—22no—
77C22×C109—22no—
78C22×C109—44no—
79C22×C109#12312yes—
80C22×C109C22×D411yescharacteristic
81C2×D109—41no—
82C2×D109—42no—
83C4×C109—22no—
84C4×C109—44no—
85C4×C109#12312yes—
86C4×C109C2×#4112yes—
87Dic109—41no—
88Dic109—42no—
89C2×C109—22no—
90C2×C109—42no—
91C2×C109C2×#12311yescharacteristic
92C2×C109#57512yes—
93D109—81no—
94#3093—1091nomaximal, Sylow
95C109#309311yescharacteristic, complemented, Sylow
96#525—1091no—
97C2×#117D10911yescharacteristic, complemented
98#485—1094no—
99#482—1094no—
100#428—1092no—
101#417—1092no—
102#407—1091no—
103C2×#41—1091no—
104C23×C4C2×D10911yescharacteristic
105C2×M16—1092no—
106#123—2181no—
107C22⋊Q8—1092no—
108#121—1092no—
109#120—2181no—
110C4×D4—2182no—
111#117—22no—
112#117—1091no—
113#117C2×D10914yes—
114C2×C4⋊C4C2×D10912yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—1094no—
118#106—1094no—
119#103—1094no—
120#102—1094no—
121C22⋊C8—1094no—
122C24C22⋊D10911yescharacteristic
123#41—2184no—
124C2×Q8—1091no—
125C2×D4—1091no—
126C2×D4—2182no—
127C2×D4—2181no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—2181no—
131C22×C4C22⋊D10911yescharacteristic
132C22×C4C22⋊D10912yes—
133C22×C4C22×D10912yes—
134C22×C4C22×D10911yescharacteristic
135M16—2184no—
136C2×C8—1094no—
137C4⋊C4—22no—
138C4⋊C4—1092no—
139C4⋊C4—2182no—
140C4⋊C4C22×D10914yes—
141C22⋊C4—24no—
142C22⋊C4—2181no—
143C22⋊C4—2182no—
144C22⋊C4—2182no—
145C42—24no—
146C42—2181no—
147C23—22no—
148C23—42no—
149C23—2181no—
150C23C2×C22⋊D10912yes—
151C23C2×C22⋊D10911yescharacteristic
152Q8—2182no—
153D4—4364no—
154D4—4362no—
155D4—2182no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—4362no—
162C2×C4—2182no—
163C2×C4—2181no—
164C2×C4C2×C22⋊D10912yes—
165C2×C4C2×C22⋊D10911yescharacteristic
166C2×C4#1318202914yes—
167C2×C4C23×D10911yescharacteristic
168C8—2184no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—4361no—
175C22—4362no—
176C22#1681268212yes—
177C22C22×C22⋊D10911yescharacteristic
178C4—22no—
179C4—44no—
180C4—4361no—
181C4—4362no—
182C4#1681268212yes—
183C4C2×#1318202912yes—
184C2—22no—
185C2—42no—
186C2—8721no—
187C2C2×#1681268211yescharacteristic
188C2#2029582412yes—
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×#117×C109C2
socleC22×C109C22×D4
prime radical#20295537C2
hypercenterC2×#117D109
hypocenterC109#3093
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #20295367C2semidirect
3. #20295350C2semidirect
4. #20295066C2semidirect
5. #20295025C2semidirect
6. #20294990C2semidirect
7. C2×#117×C109C2semidirect
16. #16812632C22semidirect
17. #16812630C22semidirect
18. #16812622C22semidirect
19. #16812619C22semidirect
95. C109#3093semidirect
97. C2×#117D109semidirect

Maximal subgroups

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

subgroupindex
#202955372
#202953672
#202953502
#202950662
#202950252
#202949902
C2×#117×C1092
#3093109