Finite Group Databasebeta

← #28378309

Subgroups — #28378309

Order 13952.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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#20295997C211yesmaximal, characteristic, complemented
2D109⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#20295870C214yesmaximal, complemented
4C2×#16812674C211yesmaximal, characteristic
5C2×#13182039—21no—
6C2×D109⋊C8—21no—
7#16812756—21no—
8#16812756—21no—
9C22⋊#11724786C2212yes—
10C22⋊#11724786C2212yes—
11C22×D436C412yes—
12C22×D436C411yescharacteristic
13C22×C4×D109C2211yescharacteristic
14#16812674—21no—
15#16812674—21no—
16#16812674—21no—
17#16812674—21no—
18C2×#13182006C2212yes—
19C2×C4⋊C4×C109C411yescharacteristic
20#13182039—42no—
21D109⋊C8—42no—
22C2×#11724786—22no—
23C2×#11724786—22no—
24C23×D109C2×C411yescharacteristic
25C23×D109C2×C412yes—
26C2×D436—22no—
27C2×D436—22no—
28C2×D436—21no—
29C2×D436—21no—
30C2×D436—42no—
31C2×D436—44no—
32C22×Dic109C2311yescharacteristic
33C2×C4×D109—42no—
34C2×C4×D109D411yescharacteristic
35C2×C4×D109D411yescharacteristic
36C2×C4×D109D411yescharacteristic
37C2×C4×D109D411yescharacteristic
38#13182006—22no—
39#13182006—22no—
40C22×C4×C109C2×C412yes—
41C22×C4×C109C2×C411yescharacteristic
42C4⋊C4×C109—21no—
43C4⋊C4×C109—21no—
44C23×C109C22×C411yescharacteristic
45C22×D109—22no—
46C22×D109—22no—
47C22×D109—22no—
48C22×D109—24no—
49C22×D109—41no—
50C22×D109—42no—
51C22×D109—42no—
52C22×D109C22⋊C411yescharacteristic
53C22×D109C22⋊C411yescharacteristic
54C2×C4×C109—22no—
55C2×C4×C109—22no—
56C2×C4×C109—42no—
57C2×C4×C109C22⋊C411yescharacteristic
58C2×C4×C109C22⋊C411yescharacteristic
59C2×Dic109—41no—
60C2×Dic109C2×D411yescharacteristic
61C2×Dic109C2×D411yescharacteristic
62D436—42no—
63D436—44no—
64D436—44no—
65D436—42no—
66C4×D109—22no—
67C4×D109—22no—
68C4×D109—41no—
69C4×D109—41no—
70#11724786—42no—
71#11724786—42no—
72C22×C109—21no—
73C22×C109—21no—
74C22×C109C2×C22⋊C411yescharacteristic
75C22×C109#13112yes—
76C2×D109—21no—
77C2×D109—21no—
78C2×D109—21no—
79C2×D109—21no—
80C2×D109—21no—
81C2×D109—44no—
82C2×D109—42no—
83C2×D109—42no—
84C2×D109—42no—
85C2×D109—84no—
86C2×D109#10012yes—
87C4×C109—21no—
88C4×C109—42no—
89C4×C109#9912yes—
90Dic109—21no—
91Dic109—21no—
92C2×C109—22no—
93C2×C109#40811yescharacteristic
94C2×C109C2×#9911yescharacteristic
95C2×C109C2×#10011yescharacteristic
96D109—22no—
97D109—41no—
98D109—82no—
99#1471—1091nomaximal, Sylow
100C109#147111yescharacteristic, complemented, Sylow
101C2×#121—1091no—
102#407—1091no—
103C2×C22⋊C8—1091no—
104#323—1094no—
105C22×D4—1092no—
106C22×D4—1091no—
107C23×C4—1091no—
108C2×M16—2181no—
109C22×C8—2181no—
110#121—2181no—
111#121—2181no—
112#121—2181no—
113#121—2181no—
114C2×C4⋊C4#8913711yescharacteristic
115C2×C22⋊C4—1092no—
116C22⋊C8—1092no—
117C22⋊C8—1092no—
118C22⋊C8—2181no—
119C22⋊C8—2181no—
120C24—1091no—
121C24—1092no—
122C2×D4—4362no—
123C2×D4—4364no—
124C2×D4—2182no—
125C2×D4—2182no—
126C2×D4—2181no—
127C2×D4—2181no—
128C22×C4—1091no—
129C22×C4—1091no—
130C22×C4—1091no—
131C22×C4—1091no—
132C22×C4—1091no—
133C22×C4—4362no—
134C22×C4C2×#8913712yes—
135C22×C4C2×#8913711yescharacteristic
136M16—4362no—
137C2×C8—4362no—
138C2×C8—2182no—
139C2×C8—2182no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C22⋊C4—2182no—
143C22⋊C4—2182no—
144C23—1091no—
145C23—1091no—
146C23—4362no—
147C23—4362no—
148C23—4361no—
149C23—2182no—
150C23—2184no—
151C23—2182no—
152C23—2182no—
153C23C22×#8913711yescharacteristic
154D4—4362no—
155D4—4364no—
156D4—4364no—
157D4—4362no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—1091no—
162C2×C4—1091no—
163C2×C4—4361no—
164C2×C4—4361no—
165C2×C4—4361no—
166C2×C4—2182no—
167C2×C4—2182no—
168C2×C4C22⋊#8913711yescharacteristic
169C2×C4C22⋊#8913711yescharacteristic
170C8—4362no—
171C8—4362no—
172C22—21no—
173C22—21no—
174C22—8724no—
175C22—1092no—
176C22—4364no—
177C22—4362no—
178C22—4362no—
179C22—4362no—
180C22—2181no—
181C22—2181no—
182C22—2181no—
183C22—2181no—
184C22—2181no—
185C22C2×C22⋊#8913711yescharacteristic
186C22#1681278712yes—
187C4—21no—
188C4—42no—
189C4—2181no—
190C4—2181no—
191C4#1681275812yes—
192C2—22no—
193C2—8722no—
194C2—4361no—
195C2—2182no—
196C2#2029600111yescharacteristic
197C2C2×#1681275811yescharacteristic
198C2D109⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
FittingC2×C4⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×#16812674C2
cosocleC22×Dic109C23
hypercenterC2×C4⋊C4#89137
hypocenterC109#1471
LCSG ▷ C23×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #20295997C2semidirect
2. D109⋊(C22⋊C8)C2semidirect
3. #20295870C2semidirect
100. C109#1471semidirect

Maximal subgroups

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

subgroupindex
#202959972
D109⋊(C22⋊C8)2
#202958702
C2×#168126742
#1471109