Finite Group Databasebeta

← #28364197

Subgroups — #28364197

Order 13952.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#20295652C211yesmaximal, characteristic, complemented
2#20294881C212yesmaximal
3#20294881C211yesmaximal, characteristic
4#20294792C212yesmaximal, complemented
5#342×C109C211yesmaximal, characteristic, complemented
6C24×D109C2211yescharacteristic
7#16812678—22no—
8#16812676—24no—
9C2×C22⋊Dic109C2211yescharacteristic
10C2×C22⋊Dic109C2212yes—
11C2×#13182006—24no—
12C2×#13182006—22no—
13C2×C22⋊C4×C109C2212yes—
14C2×C22⋊C4×C109C2211yescharacteristic
15C23×D109—22no—
16C23×D109—21no—
17C23×D109—21no—
18C23×D109—22no—
19C23×D109—44no—
20C23×D109Q812yescomplemented
21C2×Dic218—22no—
22C22×Dic109—21no—
23C22×Dic109D414yes—
24C4⋊Dic109—22no—
25#13182008—24no—
26C22⋊Dic109—22no—
27C22⋊Dic109—22no—
28C22⋊Dic109—22no—
29#13182006—48no—
30#13182006—44no—
31C24×C109C2311yescharacteristic
32C22×C4×C109—22no—
33C22×C4×C109D412yes—
34C22⋊C4×C109—22no—
35C22⋊C4×C109—22no—
36C22⋊C4×C109—22no—
37C23×C109—42no—
38C23×C109C2×D412yes—
39C23×C109C2×D411yescharacteristic
40C23×C109C2×Q811yescharacteristic
41C23×C109#4111yescharacteristic
42C23×C109#4112yes—
43C22×D109—28no—
44C22×D109—24no—
45C22×D109—24no—
46C22×D109—22no—
47C22×D109—44no—
48C22×D109—44no—
49C22×D109—48no—
50C22×D109—44no—
51C22×D109—42no—
52C22×D109—41no—
53C22×D109—42no—
54C22×D109—41no—
55C2×C4×C109—22no—
56C2×C4×C109—42no—
57C2×C4×C109—44no—
58C2×C4×C109—42no—
59C2×Dic109—24no—
60C2×Dic109—44no—
61C2×Dic109—42no—
62C2×Dic109—41no—
63Dic218—82no—
64C22×C109—24no—
65C22×C109—22no—
66C22×C109—41no—
67C22×C109—41no—
68C22×C109—42no—
69C22×C109#12011yescharacteristic
70C22×C109C22⋊Q812yes—
71C22×C109C22⋊Q811yescharacteristic
72C22×C109#12412yes—
73C22×C109#12411yescharacteristic
74C2×D109—28no—
75C2×D109—24no—
76C2×D109—44no—
77C2×D109—48no—
78C2×D109—44no—
79C2×D109—42no—
80C2×D109—42no—
81C2×D109—44no—
82C4×C109—42no—
83C4×C109—82no—
84Dic109—44no—
85Dic109—81no—
86C2×C109—21no—
87C2×C109—22no—
88C2×C109—22no—
89C2×C109—21no—
90C2×C109#39311yescharacteristic
91C2×C109B(4,𝔽2)12yes—
92D109—44no—
93#2029—1091nomaximal, Sylow
94C109#202911yescharacteristic, complemented, Sylow
95#543—1091no—
96#379—1092no—
97#379—1091no—
98#342—1092no—
99#342D10911yescharacteristic, complemented
100C25—1091no—
101C22⋊Q8—2184no—
102C22⋊Q8—2182no—
103C2×C22⋊C4—1092no—
104C2×C22⋊C4—1091no—
105C2×C22⋊C4—2184no—
106C2×C22⋊C4—2182no—
107C2×C22⋊C4C2×D10912yes—
108C2×C22⋊C4C2×D10911yescharacteristic
109C24—1092no—
110C24—4364no—
111C24—2181no—
112C24—2182no—
113C24—2182no—
114C24—2181no—
115C24C22×D10911yescharacteristic
116C2×Q8—2182no—
117C22×C4—22no—
118C22×C4—1094no—
119C22×C4—2181no—
120C22×C4D43612yes—
121C4⋊C4—2184no—
122C4⋊C4—2182no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—4364no—
127C22⋊C4—4368no—
128C22⋊C4—2182no—
129C22⋊C4—2182no—
130C22⋊C4—2182no—
131C23—42no—
132C23—4364no—
133C23—4362no—
134C23—4364no—
135C23—4368no—
136C23—4364no—
137C23—4361no—
138C23—4362no—
139C23—4361no—
140C23—2188no—
141C23—2184no—
142C23—2184no—
143C23—2182no—
144C23D4×D10912yes—
145C23C2×D43611yescharacteristic
146C23Q8×D10911yescharacteristic
147C23#1318202811yescharacteristic
148C23#1318202912yes—
149Q8—8722no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—4362no—
155C2×C4—4361no—
156C2×C4—4364no—
157C2×C4—2184no—
158C22—24no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22—42no—
163C22—4368no—
164C22—4364no—
165C22—4364no—
166C22—4362no—
167C22—4362no—
168C22—4364no—
169C22—2188no—
170C22—2184no—
171C22#1681266911yescharacteristic
172C22#1681267712yes—
173C22#1681267911yescharacteristic
174C22#1681268512yes—
175C22#1681268711yescharacteristic
176C4—42no—
177C4—82no—
178C4—8721no—
179C4—4364no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—4364no—
185C2#2029493911yescharacteristic
186C2#2029521412yes—
subgroupG/H
centerC22#16812669
commutator, cosocleC24×C109C23
FrattiniC24C22×D109
Fitting#342×C109C2
socleC22×C109#120
prime radicalC24×D109C22
hypercenter#342D109
hypocenterC109#2029
LCSG ▷ C24×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #20295652C2semidirect
4. #20294792C2semidirect
5. #342×C109C2semidirect
20. C23×D109Q8semidirect
94. C109#2029semidirect
99. #342D109semidirect

Maximal subgroups

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

subgroupindex
#202956522
#202948812
#202947922
#342×C1092
#2029109