Finite Group Databasebeta

← #28362059

Subgroups — #28362059

Order 13952.

236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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
2#20295362C212yesmaximal, complemented
3#20294962C211yesmaximal, characteristic
4#20294764C212yesmaximal, complemented
5#323×C109C211yesmaximal, characteristic
6#16812678—21no—
7#16812678C2212yes—
8#16812676—22no—
9#16812676—22no—
10C2×C4⋊Dic109C2211yescharacteristic
11C2×#13182008—21no—
12C2×C22⋊Dic109—21no—
13C2×C22⋊Dic109—21no—
14#16812633—22no—
15#16812624—22no—
16#16812606C2211yescharacteristic
17C2×C22⋊C4×C109C2211yescharacteristic
18C22⋊C8×C109C2212yes—
19C2×Dic218—21no—
20C2×Dic218D412yes—
21C22×Dic109—21no—
22C22×Dic109—21no—
23C22×Dic109—21no—
24C22×Dic109—21no—
25C4⋊Dic109—21no—
26C4⋊Dic109—22no—
27C4⋊Dic109D412yes—
28#13182008—22no—
29#13182008—22no—
30#13182008—42no—
31C22⋊Dic109—22no—
32C22⋊Dic109—22no—
33C22⋊Dic109—42no—
34C24×C109D411yescharacteristic
35C22×C4×C109D411yescharacteristic
36C22×C4×C109C2311yescharacteristic
37C2×C8×C109—22no—
38C22⋊C4×C109—22no—
39C23×C109—21no—
40C23×C109—21no—
41C23×C109—41no—
42C23×C109—41no—
43C23×C109Q1612yes—
44C23×C109C2×D411yescharacteristic
45C2×C4×C109—21no—
46C2×C4×C109—41no—
47C2×C4×C109—41no—
48C2×C4×C109C2×D412yes—
49C2×Dic109—22no—
50C2×Dic109—22no—
51C2×Dic109—22no—
52C2×Dic109—41no—
53C2×Dic109—41no—
54C2×Dic109—41no—
55C2×Dic109—41no—
56C2×Dic109—41no—
57C2×Dic109—81no—
58C2×Dic109—81no—
59Dic218—42no—
60Dic218—81no—
61C8×C109—42no—
62C22×C109—21no—
63C22×C109—21no—
64C22×C109—22no—
65C22×C109—42no—
66C22×C109—41no—
67C22×C109—41no—
68C22×C109—81no—
69C22×C109#12011yescharacteristic
70C22×C109C2×Q1611yescharacteristic
71C22×C109#13711yescharacteristic
72C4×C109—22no—
73C4×C109—41no—
74Dic109—42no—
75Dic109—42no—
76Dic109—42no—
77Dic109—81no—
78C2×C109—21no—
79C2×C109—21no—
80C2×C109—42no—
81C2×C109#45111yescharacteristic
82C2×C109#45311yescharacteristic
83C2×C109#45811yescharacteristic
84#1614—1091nomaximal, Sylow
85C109#161411yescharacteristic, complemented, Sylow
86#543—1091no—
87#484—1092no—
88#399—1091no—
89#328—1092no—
90#323D10911yescharacteristic
91C22⋊Q8—1092no—
92C22⋊Q8—2182no—
93C22⋊Q8—2182no—
94C22⋊Q8—2181no—
95C2×C4⋊C4—1091no—
96C2×C4⋊C4—2181no—
97C2×C22⋊C4—2181no—
98C2×C22⋊C4—2181no—
99C2×C22⋊C4C2×D10911yescharacteristic
100#107—2182no—
101#103—2182no—
102C22⋊C8C2×D10912yes—
103#95—1091no—
104C24D43611yescharacteristic
105C2×Q8—1092no—
106C2×Q8—2181no—
107C22×C4—2181no—
108C22×C4—2181no—
109C22×C4—2181no—
110C22×C4—2181no—
111C22×C4D43611yescharacteristic
112C22×C4C22×D10911yescharacteristic
113C2×C8—22no—
114C4⋊C4—1092no—
115C4⋊C4—4362no—
116C4⋊C4—2182no—
117C4⋊C4—2181no—
118C4⋊C4—2182no—
119C4⋊C4—2182no—
120C22⋊C4—22no—
121C22⋊C4—4362no—
122C22⋊C4—2182no—
123C22⋊C4—2182no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23Dic43612yes—
129C23C2×D43611yescharacteristic
130Q8—8721no—
131Q8—4362no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—8721no—
136C2×C4—8721no—
137C2×C4—4361no—
138C2×C4—4361no—
139C2×C4—4361no—
140C2×C4—4361no—
141C2×C4—4361no—
142C2×C4—2182no—
143C2×C4—2182no—
144C2×C4—2182no—
145C2×C4D4×D10912yes—
146C8—42no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1681266911yescharacteristic
155C22C2×Dic43611yescharacteristic
156C22#1681273211yescharacteristic
157C4—22no—
158C4—41no—
159C4—8721no—
160C4—4362no—
161C4—4362no—
162C4—4362no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#2029518411yescharacteristic
167C2#2029519611yescharacteristic
168C2#2029521711yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#323×C109C2
socleC22×C109#120
prime radicalC24×C109D4
hypercenter#323D109
hypocenterC109#1614
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #20295362C2semidirect
4. #20294764C2semidirect
85. C109#1614semidirect

Maximal subgroups

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

subgroupindex
#202956522
#202953622
#202949622
#202947642
#323×C1092
#1614109