Finite Group Databasebeta

← D109⋊#353 #28379298

Subgroups — D109⋊#353 #28379298

Order 13952.

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

normal subgroups only

This group has 368 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
1D109⋊#99C212yesmaximal, complemented
2#20295931C212yesmaximal, complemented
3#20295930C212yesmaximal, complemented
4#127×D109C211yesmaximal, characteristic
5C2×C22⋊#89137—22no—
6#16812758C2214yescomplemented
7#16812757—22no—
8C2×D4×D109—22no—
9C2×D4×D109C411yescharacteristic, complemented
10C2×D4×D109C2211yescharacteristic
11#16812696C2211yescharacteristic
12#16812695—22no—
13#16812695C411yescharacteristic, complemented
14#16812695C2211yescharacteristic
15C42×D109C411yescharacteristic, complemented
16#127×C109C411yescharacteristic, complemented
17C22×#89137—42no—
18C22⋊#89137—24no—
19C22⋊#89137—42no—
20C23×D109—21no—
21C23×D109D412yes—
22C2×D436—22no—
23C2×D436C2×C411yescharacteristic, complemented
24C2×D436C2311yescharacteristic
25C2×C22⋊D109—22no—
26C2×C22⋊D109—22no—
27C2×C22⋊D109—21no—
28C2×C22⋊D109D412yes—
29D4×D109—41no—
30D4×D109—41no—
31D4×D109—41no—
32D4×D109—41no—
33D4×D109—48no—
34C2×C4×D109—21no—
35C2×C4×D109C2×C411yescharacteristic
36C4×Dic109—21no—
37C4×Dic109C2×C411yescharacteristic, complemented
38C2×D4×C109—22no—
39C2×D4×C109C2×C411yescharacteristic
40C2×D4×C109C2×C411yescharacteristic, complemented
41C42×C109C2×C411yescharacteristic, complemented
42C23×C109—21no—
43C23×C109C22⋊C412yes—
44C22×D109—22no—
45C22×D109—22no—
46C22×D109—21no—
47C22×D109—44no—
48C22×D109—44no—
49C22×D109—41no—
50C22×D109—41no—
51C22×D109C22⋊C411yescharacteristic
52C22×D109C2×D412yes—
53C2×#89137—44no—
54C2×#89137—84no—
55D4×C109—41no—
56D4×C109—41no—
57D4×C109—44no—
58C2×C4×C109—21no—
59C2×C4×C109C22×C411yescharacteristic
60C22⋊D109—42no—
61C22⋊D109—44no—
62C22⋊D109—44no—
63C22⋊D109—42no—
64C2×Dic109—21no—
65C2×Dic109C22⋊C411yescharacteristic
66D436—41no—
67D436—41no—
68D436—44no—
69C4×D109—24no—
70C4×D109—21no—
71C4×D109—21no—
72C22×C109—22no—
73C22×C109—42no—
74C22×C109—42no—
75C22×C109—41no—
76C22×C109C2×C22⋊C411yescharacteristic
77C2×D109—22no—
78C2×D109—22no—
79C2×D109—44no—
80C2×D109—42no—
81C2×D109—42no—
82C2×D109—41no—
83C2×D109—82no—
84C2×D109—82no—
85C2×D109—82no—
86C2×D109#9911yescharacteristic
87C2×D109#9911yescharacteristic
88#89137—84no—
89C4×C109—22no—
90C4×C109—21no—
91Dic109—22no—
92Dic109—21no—
93C2×C109—21no—
94C2×C109—42no—
95C2×C109—81no—
96C2×C109C2×#9911yescharacteristic
97D109—21no—
98D109—42no—
99D109—81no—
100D109#35312yescomplemented
101C2×#353—1091nomaximal, Sylow
102C109C2×#35311yescharacteristic, complemented, Sylow
103C2×#127—1091no—
104C2×#99—1092no—
105#353—1092no—
106#353—1092no—
107C22×D4—1091no—
108C22×D4—1091no—
109C22×D4—2182no—
110#127—1091no—
111#127—1091no—
112#127—1091no—
113#127—2182no—
114#127#8913711yescharacteristic, complemented
115C2×C22⋊C4—2182no—
116C2×C42—1091no—
117#99—1094no—
118#99—2182no—
119C24—1092no—
120C24—2181no—
121C2×D4—22no—
122C2×D4—1092no—
123C2×D4—1091no—
124C2×D4—1091no—
125C2×D4—4361no—
126C2×D4—4361no—
127C2×D4—4368no—
128C2×D4—4361no—
129C2×D4—4361no—
130C2×D4—2182no—
131C2×D4—2181no—
132C2×D4—2182no—
133C2×D4—2182no—
134C2×D4C2×#8913711yescharacteristic
135C2×D4C2×#8913711yescharacteristic, complemented
136C22×C4—1091no—
137C22×C4—4362no—
138C22×C4—2181no—
139C22⋊C4—4362no—
140C22⋊C4—2184no—
141C42—1091no—
142C42—2181no—
143C42C2×#8913711yescharacteristic, complemented
144C23—21no—
145C23—1091no—
146C23—1092no—
147C23—4361no—
148C23—4361no—
149C23—4364no—
150C23—4364no—
151C23—2182no—
152C23—2182no—
153C23—2181no—
154C23C22⋊#8913712yes—
155D4—41no—
156D4—41no—
157D4—44no—
158D4—4361no—
159D4—4364no—
160D4—4361no—
161D4—4362no—
162D4—4364no—
163D4—4364no—
164D4—4362no—
165C2×C4—21no—
166C2×C4—8724no—
167C2×C4—1091no—
168C2×C4—4364no—
169C2×C4—2181no—
170C2×C4—2181no—
171C2×C4—2184no—
172C2×C4—2181no—
173C2×C4C22×#8913711yescharacteristic
174C22—22no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—8722no—
179C22—8722no—
180C22—8722no—
181C22—1091no—
182C22—1091no—
183C22—4362no—
184C22—4362no—
185C22—4364no—
186C22—4361no—
187C22—2182no—
188C22—2182no—
189C22C2×C22⋊#8913711yescharacteristic
190C4—22no—
191C4—21no—
192C4—8724no—
193C4—2182no—
194C4—2181no—
195C2—21no—
196C2—42no—
197C2—81no—
198C2—8721no—
199C2—1092no—
200C2—4362no—
201C2—2181no—
202C2D109⋊#9911yescharacteristic
subgroupG/H
centerC2D109⋊#99
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#127×C109C4
socleC2×C109C2×#99
prime radical#127×D109C2
cosocleC2×D436C23
hypercenter#127#89137
hypocenterC109C2×#353
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. D109⋊#99C2semidirect
2. #20295931C2semidirect
3. #20295930C2semidirect
6. #16812758C22semidirect
9. C2×D4×D109C4semidirect
13. #16812695C4semidirect
15. C42×D109C4semidirect
16. #127×C109C4semidirect
23. C2×D436C2×C4semidirect
37. C4×Dic109C2×C4semidirect
40. C2×D4×C109C2×C4semidirect
41. C42×C109C2×C4semidirect
100. D109#353semidirect
102. C109C2×#353semidirect
114. #127#89137semidirect
135. C2×D4C2×#89137semidirect
143. C42C2×#89137semidirect

Maximal subgroups

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

subgroupindex
D109⋊#992
#202959312
#202959302
#127×D1092
C2×#353109