Finite Group Databasebeta

← #28379306

Subgroups — #28379306

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#20295932C212yesmaximal, complemented
3#20295931C212yesmaximal, complemented
4#20295577C211yesmaximal, characteristic
5#16812778—22no—
6#16812758—22no—
7#16812758C2214yes—
8C2×#13182030C411yescharacteristic, complemented
9C2×#13182030C2211yescharacteristic
10#16812696C2211yescharacteristic
11#16812688C411yescharacteristic, complemented
12#16812688C2211yescharacteristic
13#16812674—22no—
14#16812661—22no—
15C42×D109C411yescharacteristic, complemented
16C4⋊Q8×C109C411yescharacteristic, complemented
17C4⋊#89137—42no—
18C22⋊#89137—24no—
19C4×#89137—42no—
20#13182030—41no—
21#13182030—41no—
22#13182030—41no—
23#13182030—41no—
24C2×D436—21no—
25C2×D436—22no—
26C2×D436C2×C411yescharacteristic
27C2×D436D412yes—
28C2×D436C2311yescharacteristic
29C2×C4×D109—21no—
30C2×C4×D109—21no—
31C2×C4×D109C2×C411yescharacteristic
32C2×C4×D109D412yes—
33#13182006—22no—
34#13182006—22no—
35C4×Dic109—21no—
36C4×Dic109C2×C411yescharacteristic
37C2×Q8×C109C2×C411yescharacteristic
38C2×Q8×C109C2×C411yescharacteristic
39C4⋊C4×C109—22no—
40C42×C109C2×C411yescharacteristic
41C22×D109—21no—
42C22×D109C22⋊C411yescharacteristic
43C22×D109C2×D412yes—
44C2×#89137—44no—
45Q8×C109—41no—
46Q8×C109—41no—
47C2×C4×C109—21no—
48C2×C4×C109—21no—
49C2×C4×C109C22⋊C412yes—
50C2×C4×C109C22×C411yescharacteristic
51C2×Dic109—21no—
52C2×Dic109C22⋊C411yescharacteristic
53D436—42no—
54D436—41no—
55D436—41no—
56D436—44no—
57D436—42no—
58C4×D109—21no—
59C4×D109—21no—
60C4×D109—22no—
61C4×D109—22no—
62C4×D109—42no—
63C4×D109—41no—
64C4×D109—41no—
65C22×C109C2×C22⋊C411yescharacteristic
66C2×D109—21no—
67C2×D109—22no—
68C2×D109—41no—
69C2×D109—42no—
70C2×D109—42no—
71C2×D109—41no—
72#89137—84no—
73C4×C109—22no—
74C4×C109—21no—
75C4×C109—22no—
76C4×C109—41no—
77Dic109—41no—
78Dic109#9911yescharacteristic
79Dic109#9911yescharacteristic
80C2×C109—21no—
81C2×C109C2×#9911yescharacteristic
82D109—42no—
83D109—41no—
84D109—81no—
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#8913711yescharacteristic, complemented
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—4361no—
104#41—4361no—
105#41—4361no—
106#41—4361no—
107C2×Q8C2×#8913711yescharacteristic
108C2×Q8C2×#8913711yescharacteristic
109C2×D4—1092no—
110C2×D4—1091no—
111C2×D4—1091no—
112C2×D4—2182no—
113C2×D4—2181no—
114C22×C4—1092no—
115C22×C4—1091no—
116C22×C4—2181no—
117C22×C4—2181no—
118C4⋊C4—22no—
119C4⋊C4—4362no—
120C22⋊C4—2182no—
121C22⋊C4—2184no—
122C22⋊C4—2182no—
123C42—1091no—
124C42—4362no—
125C42—2181no—
126C42C2×#8913711yescharacteristic
127C23—1092no—
128C23—1091no—
129C23—2181no—
130Q8—41no—
131Q8—41no—
132D4—4361no—
133D4—4364no—
134D4—4362no—
135D4—4361no—
136D4—4362no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—1091no—
140C2×C4—4362no—
141C2×C4—4361no—
142C2×C4—4361no—
143C2×C4—4364no—
144C2×C4—2182no—
145C2×C4—2182no—
146C2×C4—2181no—
147C2×C4—2181no—
148C2×C4—2181no—
149C2×C4C22⋊#8913712yes—
150C2×C4C22×#8913711yescharacteristic
151C22—4362no—
152C22—4361no—
153C22—4362no—
154C22—4361no—
155C22—2182no—
156C22—2181no—
157C22C2×C22⋊#8913711yescharacteristic
158C4—22no—
159C4—22no—
160C4—21no—
161C4—41no—
162C4—8724no—
163C4—1091no—
164C4—1091no—
165C4—4361no—
166C2—21no—
167C2—8721no—
168C2—4362no—
169C2—4361no—
170C2D109⋊#9911yescharacteristic
subgroupG/H
centerC2D109⋊#99
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4⋊Q8×C109C4
socleC2×C109C2×#99
prime radical#20295577C2
cosocleC2×D436C23
hypercenterC4⋊Q8#89137
hypocenterC109#2126
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #20296007C2semidirect
2. #20295932C2semidirect
3. #20295931C2semidirect
8. C2×#13182030C4semidirect
11. #16812688C4semidirect
15. C42×D109C4semidirect
16. C4⋊Q8×C109C4semidirect
86. C109#2126semidirect
93. C4⋊Q8#89137semidirect

Maximal subgroups

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

subgroupindex
#202960072
#202959322
#202959312
#202955772
#2126109