Finite Group Databasebeta

← #28364722

Subgroups — #28364722

Order 13952.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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#20295594C211yesmaximal, characteristic
2#20295009C212yesmaximal, complemented
3#20294823C211yesmaximal, characteristic, complemented
4#20294822C212yesmaximal, complemented
5#355×C109C211yesmaximal, characteristic, complemented
6C2×#13182030C2211yescharacteristic
7C2×D4×D109C411yescharacteristic
8M16×D109—22no—
9#16812696C411yescharacteristic
10#16812695C411yescharacteristic
11#16812688C2211yescharacteristic
12#16812672—22no—
13#16812669—22no—
14#16812656C411yescharacteristic
15#16812618C2212yescomplemented
16#16812615—22no—
17#124×C109C2211yescharacteristic
18#101×C109C2212yescomplemented
19C23×D109—21no—
20#13182030—42no—
21C2×D436—22no—
22C2×D436C2×C411yescharacteristic
23C2×D436C2×C411yescharacteristic
24C2×D436D412yes—
25C2×C22⋊D109—22no—
26C2×C22⋊D109—21no—
27D4×D109—42no—
28C2×C4×D109C2×C411yescharacteristic
29C2×C4×D109D412yes—
30#13182013—22no—
31#13182012—42no—
32C8×D109—42no—
33#13182008—21no—
34#13182006—21no—
35#13182006—22no—
36C4×Dic109C2×C411yescharacteristic
37C2×Q8×C109C2311yescharacteristic
38C2×D4×C109C2×C411yescharacteristic
39M16×C109—22no—
40C22⋊C4×C109—22no—
41C42×C109C2×C411yescharacteristic
42C23×C109—21no—
43C22×D109—21no—
44C22×D109—42no—
45C22×D109—82no—
46C22×D109C22⋊C411yescharacteristic
47C22×D109C22⋊C412yes—
48Q8×C109—41no—
49D4×C109—41no—
50C2×C4×C109—21no—
51C2×C4×C109C22×C411yescharacteristic
52C2×C4×C109C2×D412yes—
53C22⋊D109—42no—
54C22⋊D109—82no—
55C2×Dic109—21no—
56C2×Dic109C22⋊C411yescharacteristic
57D436—41no—
58D436—42no—
59D436—41no—
60D436—82no—
61C4×D109—22no—
62C4×D109—22no—
63C4×D109—22no—
64C8×C109—42no—
65#11724784—42no—
66C22×C109—42no—
67C22×C109—41no—
68C22×C109C2×C22⋊C411yescharacteristic
69C2×D109—21no—
70C2×D109—22no—
71C2×D109—42no—
72C2×D109—41no—
73C2×D109—42no—
74C2×D109—41no—
75C2×D109—84no—
76C4×C109—22no—
77C4×C109—21no—
78C4×C109—41no—
79Dic109—41no—
80Dic109#9912yes—
81C2×C109—21no—
82C2×C109—81no—
83C2×C109C2×#9911yescharacteristic
84D109—42no—
85D109—41no—
86D109—81no—
87#2134—1091nomaximal, Sylow
88C109#213411yescharacteristic, complemented, Sylow
89#535—1091no—
90#413—1092no—
91#355—1091no—
92#355—1092no—
93#355D10911yescharacteristic, complemented
94C2×#41—1091no—
95C22×D4—1091no—
96C2×M16—2182no—
97#127—1091no—
98#127—1091no—
99#124—1091no—
100#124C2×D10911yescharacteristic
101#121—2182no—
102#120—2182no—
103#117—1091no—
104#101—1092no—
105#101C2×D10912yescomplemented
106#100—2182no—
107C24—2181no—
108#41—4362no—
109C2×Q8C22×D10911yescharacteristic
110C2×D4—1091no—
111C2×D4—1091no—
112C2×D4—1092no—
113C2×D4—4362no—
114C2×D4—2182no—
115C2×D4—2181no—
116C2×D4—2182no—
117C2×D4C4×D10911yescharacteristic
118C22×C4—1091no—
119C22×C4—1092no—
120M16—22no—
121M16—4362no—
122M16—2182no—
123C2×C8—4362no—
124C4⋊C4—2181no—
125C22⋊C4—22no—
126C22⋊C4—2181no—
127C22⋊C4—2182no—
128C42—1091no—
129C42C4×D10911yescharacteristic
130C23—21no—
131C23—8722no—
132C23—1091no—
133C23—1092no—
134C23—4362no—
135C23—2181no—
136Q8—41no—
137D4—41no—
138D4—8722no—
139D4—8722no—
140D4—4361no—
141D4—4362no—
142D4—4361no—
143D4—4362no—
144C2×C4—21no—
145C2×C4—1091no—
146C2×C4—2182no—
147C2×C4—2182no—
148C2×C4—2182no—
149C2×C4—2181no—
150C2×C4C2×C4×D10911yescharacteristic
151C2×C4D4×D10912yes—
152C8—42no—
153C8—4362no—
154C22—42no—
155C22—41no—
156C22—8724no—
157C22—4362no—
158C22—4362no—
159C22—4361no—
160C22—4361no—
161C22—2181no—
162C22—2182no—
163C22C22⋊C4×D10911yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—1092no—
168C4—4361no—
169C2—21no—
170C2—81no—
171C2—8721no—
172C2—4361no—
173C2—4362no—
174C2#99×D10911yescharacteristic
subgroupG/H
centerC2#99×D109
commutatorC2×C4×C109C22×C4
FrattiniC2×Q8C22×D109
Fitting#355×C109C2
socleC2×C109C2×#99
prime radical#20295594C2
cosocleC2×Q8×C109C23
hypercenter#355D109
hypocenterC109#2134
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #20295009C2semidirect
3. #20294823C2semidirect
4. #20294822C2semidirect
5. #355×C109C2semidirect
15. #16812618C22semidirect
18. #101×C109C22semidirect
88. C109#2134semidirect
93. #355D109semidirect
105. #101C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202955942
#202950092
#202948232
#202948222
#355×C1092
#2134109