Finite Group Databasebeta

← #28379037

Subgroups — #28379037

Order 13952.

360 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 68 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#20296093C211yesmaximal, characteristic
2#20296019C212yesmaximal, complemented
3D109⋊#100C211yesmaximal, characteristic
4#20295897C212yesmaximal, complemented
5#124×D109C211yesmaximal, characteristic
6D109⋊M16C2212yes—
7D4×#89137—24no—
8#16812778C2212yes—
9C2×C22⋊#89137—22no—
10#16812762—24no—
11#16812759—22no—
12C2×Q8×D109C2211yescharacteristic
13C2×D4×D109C2211yescharacteristic
14#16812688C411yescharacteristic, complemented
15#16812687C411yescharacteristic, complemented
16#16812686C411yescharacteristic, complemented
17#16812685—22no—
18C22⋊C4×D109—22no—
19C42×D109C2211yescharacteristic
20#124×C109C411yescharacteristic, complemented
21C22×#89137—24no—
22#13182039—22no—
23#13182038—22no—
24D109⋊C8—22no—
25C4⋊#89137D414yes—
26C22⋊#89137—24no—
27C22⋊#89137—22no—
28C4×#89137—22no—
29C23×D109D412yes—
30C2×Dic218—21no—
31C2×Dic218C2×C411yescharacteristic, complemented
32Q8×D109—22no—
33Q8×D109—22no—
34C2×D436C2×C411yescharacteristic
35C2×C22⋊D109D412yes—
36D4×D109—22no—
37D4×D109—22no—
38C2×C4×D109—21no—
39C2×C4×D109—21no—
40C2×C4×D109C2311yescharacteristic
41C22⋊Dic109—22no—
42#13182006—22no—
43#13182006—22no—
44C4×Dic109—21no—
45C4×Dic109C2×C411yescharacteristic, complemented
46C2×Q8×C109C2×C411yescharacteristic, complemented
47C2×D4×C109C2×C411yescharacteristic
48C22⋊C4×C109—22no—
49C42×C109C2×C411yescharacteristic, complemented
50C23×C109C22⋊C412yes—
51C22×D109—22no—
52C22×D109—22no—
53C22×D109—44no—
54C22×D109C22⋊C412yes—
55C22×D109C2×D411yescharacteristic
56C2×#89137—24no—
57C2×#89137—84no—
58Q8×C109—22no—
59D4×C109—22no—
60C2×C4×C109—21no—
61C2×C4×C109—21no—
62C2×C4×C109C22×C411yescharacteristic
63C22⋊D109—24no—
64C2×Dic109—21no—
65C2×Dic109—21no—
66C2×Dic109C2×D411yescharacteristic
67D436—22no—
68C4×D109—42no—
69C4×D109—41no—
70C4×D109—41no—
71C4×D109C2×D412yes—
72C4×D109#4112yes—
73Dic218—22no—
74Dic218—42no—
75#11724786—42no—
76C22×C109—22no—
77C22×C109—42no—
78C22×C109C2×C22⋊C411yescharacteristic
79C2×D109—22no—
80C2×D109—22no—
81C2×D109—44no—
82C2×D109—42no—
83C2×D109—82no—
84C2×D109#12011yescharacteristic
85C2×D109#12311yescharacteristic
86#89137—44no—
87C4×C109—41no—
88C4×C109—41no—
89C4×C109C4×D412yes—
90Dic109—41no—
91Dic109—41no—
92Dic109#12112yes—
93C2×C109—21no—
94C2×C109—42no—
95C2×C109#38611yescharacteristic
96D109—21no—
97D109—42no—
98D109#45512yes—
99#1885—1091nomaximal, Sylow
100C109#188511yescharacteristic, complemented, Sylow
101C2×#124—1091no—
102#518—1091no—
103#419—1092no—
104C2×#100—1091no—
105#339—1092no—
106C22×Q8—1091no—
107C22×D4—1091no—
108C2×M16—1092no—
109#124—1091no—
110#124—1091no—
111#124—1091no—
112#124—2182no—
113#124#8913711yescharacteristic, complemented
114C4×D4—2184no—
115#117—1092no—
116C2×C22⋊C4—2182no—
117C2×C22⋊C4—2182no—
118C2×C42—1091no—
119#103—2184no—
120#100—2182no—
121C24—1092no—
122C2×Q8—1091no—
123C2×Q8—2181no—
124C2×Q8—2182no—
125C2×Q8—2182no—
126C2×Q8C2×#8913711yescharacteristic, complemented
127C2×D4—1092no—
128C2×D4—1091no—
129C2×D4—2182no—
130C2×D4—2182no—
131C2×D4C2×#8913711yescharacteristic
132C22×C4—1091no—
133C22×C4—2181no—
134C22×C4—2181no—
135C22×C4—2184no—
136M16—2182no—
137M16—2182no—
138C2×C8—2182no—
139C4⋊C4—1094no—
140C22⋊C4—22no—
141C22⋊C4—2182no—
142C22⋊C4—2182no—
143C22⋊C4—2182no—
144C22⋊C4—2184no—
145C22⋊C4—2182no—
146C42—1091no—
147C42—2181no—
148C42—2182no—
149C42C2×#8913711yescharacteristic, complemented
150C23—1091no—
151C23—1092no—
152C23—4364no—
153C23—2182no—
154C23—2182no—
155C23C22⋊#8913712yes—
156Q8—22no—
157Q8—4362no—
158Q8—2182no—
159D4—22no—
160D4—2184no—
161D4—2182no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—8724no—
165C2×C4—1091no—
166C2×C4—1092no—
167C2×C4—1092no—
168C2×C4—4361no—
169C2×C4—4361no—
170C2×C4—4362no—
171C2×C4—2184no—
172C2×C4—2181no—
173C2×C4—2181no—
174C2×C4C22×#8913711yescharacteristic
175C8—4362no—
176C22—22no—
177C22—42no—
178C22—8722no—
179C22—1091no—
180C22—1091no—
181C22—4362no—
182C22—4364no—
183C22—2182no—
184C22—2182no—
185C22C2×C22⋊#8913711yescharacteristic
186C4—41no—
187C4—41no—
188C4—1092no—
189C4—4361no—
190C4—4364no—
191C4—4361no—
192C4D4×#8913712yes—
193C2—21no—
194C2—42no—
195C2—1092no—
196C2—4362no—
197C2—2181no—
198C2#2029597411yescharacteristic
subgroupG/H
centerC2#20295974
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#124×C109C4
socleC2×C109#386
prime radicalC2×D4×D109C22
cosocleC2×C4×D109C23
hypercenter#124#89137
hypocenterC109#1885
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #20296019C2semidirect
4. #20295897C2semidirect
14. #16812688C4semidirect
15. #16812687C4semidirect
16. #16812686C4semidirect
20. #124×C109C4semidirect
31. C2×Dic218C2×C4semidirect
45. C4×Dic109C2×C4semidirect
46. C2×Q8×C109C2×C4semidirect
49. C42×C109C2×C4semidirect
100. C109#1885semidirect
113. #124#89137semidirect
126. C2×Q8C2×#89137semidirect
149. C42C2×#89137semidirect

Maximal subgroups

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

subgroupindex
#202960932
#202960192
D109⋊#1002
#202958972
#124×D1092
#1885109