Finite Group Databasebeta

← #28379303

Subgroups — #28379303

Order 13952.

258 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 54 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#20296005C212yesmaximal, complemented
2#20295932C212yesmaximal, complemented
3#20295930C212yesmaximal, complemented
4#20295572C211yesmaximal, characteristic
5#16812778—22no—
6#16812758C2214yes—
7#16812757—22no—
8C2×#13182029C2211yescharacteristic
9#16812697C411yescharacteristic, complemented
10#16812695C2211yescharacteristic
11#16812688C2211yescharacteristic
12#16812686C411yescharacteristic, complemented
13#16812671—22no—
14C4×C22⋊D109—22no—
15C2×C4×Dic109C411yescharacteristic, complemented
16C2×#41×C109C411yescharacteristic, complemented
17C4⋊#89137—42no—
18C22⋊#89137—24no—
19C4×#89137—42no—
20#13182029—41no—
21#13182029—41no—
22C2×Dic218C2×C411yescharacteristic
23C2×D436C2311yescharacteristic
24C2×C22⋊D109—22no—
25C2×C22⋊D109D412yes—
26C22×Dic109—21no—
27C2×C4×D109D412yes—
28#13182008—22no—
29C22⋊Dic109—22no—
30#13182006—22no—
31C4×Dic109—21no—
32C4×Dic109C2×C411yescharacteristic
33C4×Dic109C2×C411yescharacteristic
34#41×C109—41no—
35#41×C109—41no—
36C2×Q8×C109C2×C411yescharacteristic
37C2×D4×C109—21no—
38C2×D4×C109C2×C411yescharacteristic
39C22×C4×C109—21no—
40C22×C4×C109C2×C411yescharacteristic
41C23×C109—21no—
42C23×C109C22⋊C411yescharacteristic
43C22×D109C2×D412yes—
44C2×#89137—44no—
45Q8×C109—41no—
46D4×C109—41no—
47D4×C109—42no—
48C2×C4×C109—21no—
49C2×C4×C109—21no—
50C2×C4×C109—21no—
51C2×C4×C109—41no—
52C2×C4×C109—41no—
53C2×C4×C109C22⋊C411yescharacteristic
54C2×C4×C109C22×C411yescharacteristic
55C22⋊D109—42no—
56C22⋊D109—44no—
57C2×Dic109—21no—
58C2×Dic109—21no—
59C2×Dic109—42no—
60C2×Dic109C22⋊C412yes—
61D436—41no—
62C4×D109—22no—
63C4×D109—22no—
64Dic218—41no—
65C22×C109—21no—
66C22×C109—41no—
67C22×C109—42no—
68C22×C109—41no—
69C22×C109C2×C22⋊C411yescharacteristic
70C2×D109—22no—
71C2×D109—42no—
72#89137—84no—
73C4×C109—21no—
74C4×C109—41no—
75C4×C109#9911yescharacteristic
76C4×C109#9911yescharacteristic
77Dic109—22no—
78Dic109—22no—
79Dic109—41no—
80C2×C109—21no—
81C2×C109—41no—
82C2×C109—81no—
83C2×C109C2×#9911yescharacteristic
84D109—42no—
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#8913711yescharacteristic, complemented
93C4⋊Q8—1091no—
94#127—1091no—
95#124—1091no—
96#124—1091no—
97#121—2182no—
98C4×D4—2182no—
99#117—2182no—
100C2×C42—1091no—
101#99—1094no—
102#99—2182no—
103#41—41no—
104#41—41no—
105#41—4361no—
106#41—4361no—
107C2×Q8—1091no—
108C2×Q8C2×#8913711yescharacteristic
109C2×D4—21no—
110C2×D4—1092no—
111C2×D4—1091no—
112C2×D4—2182no—
113C2×D4C2×#8913711yescharacteristic
114C22×C4—21no—
115C22×C4—1092no—
116C22×C4—2181no—
117C22×C4C2×#8913711yescharacteristic
118C4⋊C4—4362no—
119C4⋊C4—2182no—
120C22⋊C4—2182no—
121C22⋊C4—2182no—
122C22⋊C4—2184no—
123C42—1091no—
124C42—1091no—
125C42—4362no—
126C42—2181no—
127C23—21no—
128C23—1092no—
129C23C22⋊#8913711yescharacteristic
130Q8—41no—
131Q8—4361no—
132D4—41no—
133D4—42no—
134D4—4361no—
135D4—4362no—
136D4—4364no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—1092no—
143C2×C4—4364no—
144C2×C4—4362no—
145C2×C4—2181no—
146C2×C4—2181no—
147C2×C4—2182no—
148C2×C4—2182no—
149C2×C4C22⋊#8913711yescharacteristic
150C2×C4C22×#8913711yescharacteristic
151C22—21no—
152C22—41no—
153C22—42no—
154C22—41no—
155C22—4362no—
156C22—2182no—
157C22C2×C22⋊#8913711yescharacteristic
158C4—21no—
159C4—41no—
160C4—8724no—
161C4—4361no—
162C4—2182no—
163C4—2182no—
164C4#1681275711yescharacteristic
165C4#1681275711yescharacteristic
166C2—21no—
167C2—41no—
168C2—81no—
169C2—4362no—
170C2C2×#1681275711yescharacteristic
subgroupG/H
centerC4#16812757
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC2×#41×C109C4
socleC2×C109C2×#99
prime radical#20295572C2
cosocleC2×D436C23
hypercenterC2×#41#89137
hypocenterC109#2126
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20296005C2semidirect
2. #20295932C2semidirect
3. #20295930C2semidirect
9. #16812697C4semidirect
12. #16812686C4semidirect
15. C2×C4×Dic109C4semidirect
16. C2×#41×C109C4semidirect
86. C109#2126semidirect
92. C2×#41#89137semidirect

Maximal subgroups

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

subgroupindex
#202960052
#202959322
#202959302
#202955722
#2126109