Finite Group Databasebeta

← D109⋊#324 #28378261

Subgroups — D109⋊#324 #28378261

Order 13952.

328 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D109⋊(C22⋊C8)C212yesmaximal
2#20295872C212yesmaximal, complemented
3#20295871C212yesmaximal, complemented
4C2×C4⋊C4×D109C211yesmaximal, characteristic
5C2×D109⋊C8—22no—
6#16812756—22no—
7C22⋊#11724786C2214yes—
8C22×C4×D109C411yescharacteristic
9C22×C4×D109C411yescharacteristic
10C22×C4×D109C2211yescharacteristic
11C2×C4⋊Dic109C2211yescharacteristic
12C2×#13182008C411yescharacteristic
13C2×#13182008C2211yescharacteristic
14C4⋊C4×D109—22no—
15C4⋊C4×D109—22no—
16C2×C4⋊C4×C109C411yescharacteristic
17D109⋊C8—44no—
18C2×#11724786—24no—
19C23×D109C2×C411yescharacteristic
20C22×Dic109C2×C411yescharacteristic
21C22×Dic109C2×C411yescharacteristic
22C22×Dic109C2311yescharacteristic
23C2×C4×D109—21no—
24C2×C4×D109—21no—
25C2×C4×D109—22no—
26C2×C4×D109—21no—
27C2×C4×D109—21no—
28C2×C4×D109—42no—
29C2×C4×D109—42no—
30C2×C4×D109C814yescomplemented
31C2×C4×D109D412yes—
32C2×C4×D109D412yes—
33C4⋊Dic109—22no—
34#13182008—22no—
35#13182008—22no—
36C22×C4×C109C2×C411yescharacteristic
37C22×C4×C109C2×C411yescharacteristic
38C22×C4×C109C2×C411yescharacteristic
39C4⋊C4×C109—22no—
40C23×C109C22×C411yescharacteristic
41C22×D109—22no—
42C22×D109—22no—
43C22×D109C22⋊C411yescharacteristic
44C22×D109C22⋊C411yescharacteristic
45C22×D109C2×C812yes—
46C22×D109M1612yes—
47C2×C4×C109—21no—
48C2×C4×C109—21no—
49C2×C4×C109—21no—
50C2×C4×C109—41no—
51C2×C4×C109—41no—
52C2×C4×C109C22⋊C412yes—
53C2×C4×C109C2×C812yescomplemented
54C2×Dic109—21no—
55C2×Dic109—21no—
56C2×Dic109—21no—
57C2×Dic109—41no—
58C2×Dic109—41no—
59C2×Dic109C2×C812yescomplemented
60C2×Dic109C2×D412yes—
61C4×D109—24no—
62C4×D109—24no—
63C4×D109—24no—
64C4×D109—42no—
65C4×D109—42no—
66C4×D109—42no—
67#11724786—44no—
68C22×C109—21no—
69C22×C109—21no—
70C22×C109C2×C22⋊C411yescharacteristic
71C22×C109C22×C811yescharacteristic
72C22×C109C2×M1611yescharacteristic
73C2×D109—21no—
74C2×D109—21no—
75C2×D109—24no—
76C2×D109—24no—
77C2×D109C22⋊C812yes—
78C2×D109C22⋊C812yes—
79C2×D109#9912yes—
80C2×D109#10112yes—
81C4×C109—22no—
82C4×C109—22no—
83C4×C109—41no—
84Dic109—22no—
85Dic109—22no—
86Dic109—41no—
87C2×C109—21no—
88C2×C109—21no—
89C2×C109C2×C22⋊C811yescharacteristic
90C2×C109C2×#9911yescharacteristic
91C2×C109C2×#10111yescharacteristic
92D109—22no—
93D109#32414yescomplemented
94C2×#324—1091nomaximal, Sylow
95C109C2×#32411yescharacteristic, complemented, Sylow
96C22×C4⋊C4—1091no—
97C2×C22⋊C8—1092no—
98#324—1092no—
99#324—1092no—
100C23×C4—1091no—
101C23×C4—1091no—
102C23×C4—1091no—
103C22×C8—2182no—
104C2×C4⋊C4—1091no—
105C2×C4⋊C4—1091no—
106C2×C4⋊C4—1091no—
107C2×C4⋊C4—2182no—
108C2×C4⋊C4—2182no—
109C2×C4⋊C4#8913711yescharacteristic
110C22⋊C8—1094no—
111C22⋊C8—2182no—
112C24—1091no—
113C22×C4—1091no—
114C22×C4—1091no—
115C22×C4—1092no—
116C22×C4—1092no—
117C22×C4—1094no—
118C22×C4—1091no—
119C22×C4—4362no—
120C22×C4—4362no—
121C22×C4—2181no—
122C22×C4—2181no—
123C22×C4—2181no—
124C22×C4—2181no—
125C22×C4—2182no—
126C22×C4C2×#8913711yescharacteristic
127C22×C4C2×#8913711yescharacteristic
128C22×C4C2×#8913711yescharacteristic
129C2×C8—4364no—
130C2×C8—2184no—
131C4⋊C4—22no—
132C4⋊C4—2182no—
133C4⋊C4—2182no—
134C4⋊C4—2182no—
135C23—1091no—
136C23—1091no—
137C23—1092no—
138C23—1092no—
139C23—2182no—
140C23—2182no—
141C23C22×#8913711yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—1092no—
148C2×C4—1092no—
149C2×C4—4362no—
150C2×C4—4362no—
151C2×C4—4362no—
152C2×C4—4361no—
153C2×C4—4361no—
154C2×C4—2184no—
155C2×C4—2184no—
156C2×C4—2184no—
157C2×C4—2181no—
158C2×C4—2181no—
159C2×C4—2181no—
160C2×C4C22⋊#8913712yes—
161C2×C4D109⋊C812yescomplemented
162C8—4364no—
163C22—21no—
164C22—21no—
165C22—1092no—
166C22—1092no—
167C22—1092no—
168C22—1092no—
169C22—2184no—
170C22—2184no—
171C22—2181no—
172C22—2181no—
173C22C2×C22⋊#8913711yescharacteristic
174C22C2×D109⋊C811yescharacteristic
175C22D109⋊M1611yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—4361no—
180C4—2182no—
181C4—2182no—
182C2—21no—
183C2—21no—
184C2—1094no—
185C2—2182no—
186C2D109⋊(C22⋊C8)11yescharacteristic
187C2D109⋊#9911yescharacteristic
188C2D109⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC22×C109C22×C8
FrattiniC23C22×#89137
FittingC2×C4⋊C4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC23×D109C2×C4
cosocleC22×Dic109C23
hypercenterC2×C4⋊C4#89137
hypocenterC109C2×#324
LCSG ▷ C22×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
2. #20295872C2semidirect
3. #20295871C2semidirect
30. C2×C4×D109C8semidirect
53. C2×C4×C109C2×C8semidirect
59. C2×Dic109C2×C8semidirect
93. D109#324semidirect
95. C109C2×#324semidirect
161. C2×C4D109⋊C8semidirect

Maximal subgroups

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

subgroupindex
D109⋊(C22⋊C8)2
#202958722
#202958712
C2×C4⋊C4×D1092
C2×#324109