Finite Group Databasebeta

← #28379304

Subgroups — #28379304

Order 13952.

258 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 52 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#20296007C212yesmaximal, complemented
2#20295933C212yesmaximal, complemented
3#20295930C212yesmaximal, complemented
4#20295575C211yesmaximal, characteristic
5#16812778—22no—
6#16812758—22no—
7#16812758C2214yes—
8C2×#13182030C2211yescharacteristic
9C2×#13182028C411yescharacteristic, complemented
10#16812697C411yescharacteristic, complemented
11#16812695C2211yescharacteristic
12#16812687C2211yescharacteristic
13#16812672—22no—
14#16812659—22no—
15C42×D109C411yescharacteristic, complemented
16#124×C109C411yescharacteristic, complemented
17C4⋊#89137—42no—
18C22⋊#89137—24no—
19C4×#89137—42no—
20#13182030—41no—
21#13182030—41no—
22#13182028—41no—
23#13182028—41no—
24C2×Dic218C2×C411yescharacteristic
25C2×D436D412yes—
26C2×D436C2311yescharacteristic
27C2×C22⋊D109—21no—
28C2×C22⋊D109—22no—
29C22×Dic109—21no—
30C2×C4×D109—21no—
31C2×C4×D109C2×C411yescharacteristic
32C2×C4×D109D412yes—
33#13182008—22no—
34#13182006—22no—
35C4×Dic109—21no—
36C4×Dic109C2×C411yescharacteristic
37C2×Q8×C109C2×C411yescharacteristic
38C2×D4×C109C2×C411yescharacteristic
39C22⋊C4×C109—22no—
40C42×C109C2×C411yescharacteristic
41C23×C109—21no—
42C22×D109C22⋊C411yescharacteristic
43C22×D109C2×D412yes—
44C2×#89137—44no—
45Q8×C109—41no—
46D4×C109—41no—
47C2×C4×C109—21no—
48C2×C4×C109C22⋊C412yes—
49C2×C4×C109C22×C411yescharacteristic
50C22⋊D109—44no—
51C22⋊D109—42no—
52C2×Dic109—21no—
53C2×Dic109—21no—
54C2×Dic109—41no—
55C2×Dic109—41no—
56C2×Dic109C22⋊C411yescharacteristic
57D436—42no—
58D436—41no—
59C4×D109—21no—
60C4×D109—21no—
61C4×D109—22no—
62C4×D109—22no—
63C4×D109—42no—
64Dic218—41no—
65C22×C109—42no—
66C22×C109—41no—
67C22×C109C2×C22⋊C411yescharacteristic
68C2×D109—21no—
69C2×D109—22no—
70C2×D109—41no—
71C2×D109—42no—
72#89137—84no—
73C4×C109—21no—
74C4×C109—22no—
75C4×C109—41no—
76Dic109—22no—
77Dic109—41no—
78Dic109#9911yescharacteristic
79Dic109#9911yescharacteristic
80C2×C109—21no—
81C2×C109—81no—
82C2×C109C2×#9911yescharacteristic
83D109—42no—
84D109—41no—
85#2126—1091nomaximal, Sylow
86C109#212611yescharacteristic, complemented, Sylow
87#532—1091no—
88#410—1092no—
89#354—1092no—
90#353—1092no—
91C2×#41—1091no—
92C2×#41—1091no—
93C4⋊Q8—1091no—
94#127—1091no—
95#124—1091no—
96#124#8913711yescharacteristic, complemented
97#121—2182no—
98C4×D4—2182no—
99#117—2182no—
100C2×C42—1091no—
101#99—1094no—
102#99—2182no—
103#41—4361no—
104#41—4361no—
105#41—4361no—
106#41—4361no—
107C2×Q8—1091no—
108C2×Q8C2×#8913711yescharacteristic
109C2×D4—1092no—
110C2×D4—1091no—
111C2×D4—2182no—
112C2×D4—2181no—
113C2×D4C2×#8913711yescharacteristic
114C22×C4—1092no—
115C22×C4—1091no—
116C22×C4—2181no—
117C22×C4—2181no—
118C4⋊C4—4362no—
119C4⋊C4—2182no—
120C22⋊C4—22no—
121C22⋊C4—2182no—
122C22⋊C4—2184no—
123C42—1091no—
124C42—4362no—
125C42—2181no—
126C42C2×#8913711yescharacteristic
127C23—21no—
128C23—1092no—
129C23—1091no—
130Q8—41no—
131Q8—4361no—
132D4—41no—
133D4—4362no—
134D4—4361no—
135D4—4362no—
136D4—4364no—
137C2×C4—21no—
138C2×C4—1091no—
139C2×C4—4362no—
140C2×C4—4364no—
141C2×C4—4361no—
142C2×C4—4361no—
143C2×C4—2182no—
144C2×C4—2182no—
145C2×C4—2181no—
146C2×C4—2181no—
147C2×C4—2181no—
148C2×C4—2181no—
149C2×C4C22⋊#8913712yes—
150C2×C4C22×#8913711yescharacteristic
151C22—42no—
152C22—41no—
153C22—4361no—
154C22—4362no—
155C22—2182no—
156C22—2181no—
157C22C2×C22⋊#8913711yescharacteristic
158C4—22no—
159C4—21no—
160C4—41no—
161C4—8724no—
162C4—1091no—
163C4—1091no—
164C4—4361no—
165C4—2182no—
166C2—21no—
167C2—81no—
168C2—4362no—
169C2—4361no—
170C2D109⋊#9911yescharacteristic
subgroupG/H
centerC2D109⋊#99
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#124×C109C4
socleC2×C109C2×#99
prime radical#20295575C2
cosocleC2×D436C23
hypercenter#124#89137
hypocenterC109#2126
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20296007C2semidirect
2. #20295933C2semidirect
3. #20295930C2semidirect
9. C2×#13182028C4semidirect
10. #16812697C4semidirect
15. C42×D109C4semidirect
16. #124×C109C4semidirect
86. C109#2126semidirect
96. #124#89137semidirect

Maximal subgroups

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

subgroupindex
#202960072
#202959332
#202959302
#202955752
#2126109