Finite Group Databasebeta

← #28378492

Subgroups — #28378492

Order 13952.

264 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 58 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#20296049C211yesmaximal, characteristic, complemented
2C4×#13182039C211yesmaximal, characteristic, complemented
3#20295882C212yesmaximal, complemented
4#20295881C212yesmaximal, complemented
5#124×D109C211yesmaximal, characteristic
6C2×#13182039—21no—
7#16812766—21no—
8#16812756—21no—
9#16812754C2212yescomplemented
10#16812754C2212yescomplemented
11C4×#11724786—21no—
12C2×Q8×D109C411yescharacteristic
13C2×D4×D109C411yescharacteristic
14#16812688C2211yescharacteristic
15#16812687C411yescharacteristic
16#16812686C2211yescharacteristic
17#16812685—21no—
18#16812685—21no—
19C22⋊C4×D109—21no—
20C22⋊C4×D109—21no—
21C42×D109C2211yescharacteristic
22#124×C109C411yescharacteristic
23#13182039—24no—
24C2×#11724786—22no—
25C2×#11724786—22no—
26C23×D109—21no—
27C2×Dic218—21no—
28C2×Dic218C2×C411yescharacteristic
29Q8×D109—42no—
30C2×D436C2×C411yescharacteristic
31C2×C22⋊D109—21no—
32D4×D109—42no—
33C2×C4×D109—21no—
34C2×C4×D109C2×C411yescharacteristic
35C2×C4×D109D411yescharacteristic
36C2×C4×D109D411yescharacteristic
37C22⋊Dic109—21no—
38C22⋊Dic109—21no—
39#13182006—21no—
40#13182006—21no—
41#13182006—21no—
42#13182006—21no—
43C4×Dic109D411yescharacteristic
44C4×Dic109D411yescharacteristic
45C4×Dic109C2311yescharacteristic
46C2×Q8×C109C2×C411yescharacteristic
47C2×D4×C109C2×C411yescharacteristic
48C22⋊C4×C109—21no—
49C22⋊C4×C109—21no—
50C42×C109C2×C411yescharacteristic
51C23×C109—21no—
52C22×D109—21no—
53C22×D109—42no—
54C22×D109—42no—
55C22×D109—42no—
56C22×D109C22⋊C411yescharacteristic
57Q8×C109—41no—
58D4×C109—41no—
59C2×C4×C109—21no—
60C2×C4×C109C22⋊C411yescharacteristic
61C2×C4×C109C22⋊C411yescharacteristic
62C2×C4×C109C22×C411yescharacteristic
63C22⋊D109—42no—
64C2×Dic109—21no—
65C2×Dic109C22⋊C411yescharacteristic
66C2×Dic109C2×D411yescharacteristic
67C2×Dic109C2×D411yescharacteristic
68D436—41no—
69C4×D109—22no—
70C4×D109—22no—
71C4×D109—41no—
72C4×D109—42no—
73Dic218—42no—
74Dic218—41no—
75#11724786—24no—
76#11724786—42no—
77C22×C109—41no—
78C22×C109—41no—
79C22×C109—41no—
80C22×C109C2×C22⋊C411yescharacteristic
81C2×D109—21no—
82C2×D109—21no—
83C2×D109—41no—
84C2×D109—41no—
85C2×D109—41no—
86C2×D109—84no—
87C2×D109#10412yes—
88C4×C109—21no—
89C4×C109—21no—
90C4×C109—21no—
91C4×C109—41no—
92Dic109—21no—
93Dic109—21no—
94Dic109—41no—
95Dic109#10012yes—
96C2×C109—81no—
97C2×C109C2×#10011yescharacteristic
98C2×C109C2×#10411yescharacteristic
99C2×C109#42111yescharacteristic
100D109—22no—
101D109—81no—
102#1527—1091nomaximal, Sylow
103C109#152711yescharacteristic, complemented, Sylow
104C2×#124—1091no—
105#432—1091no—
106C4×M16—1091no—
107#329—1092no—
108#329—1092no—
109C22×Q8—1091no—
110C22×D4—1091no—
111C2×M16—2181no—
112#124—1091no—
113#124—1091no—
114#124—1091no—
115#124—2181no—
116#124—2181no—
117#124#8913711yescharacteristic
118C2×C22⋊C4—2181no—
119C2×C22⋊C4—2181no—
120C2×C42—1091no—
121C4⋊C8—2181no—
122C22⋊C8—2181no—
123#97—1092no—
124#97—1092no—
125C4×C8—2181no—
126C24—2181no—
127C2×Q8—1091no—
128C2×Q8—4362no—
129C2×Q8—2181no—
130C2×Q8C2×#8913711yescharacteristic
131C2×D4—1091no—
132C2×D4—4362no—
133C2×D4—2181no—
134C2×D4C2×#8913711yescharacteristic
135C22×C4—1091no—
136C22×C4—1091no—
137C22×C4—1091no—
138C22×C4—2181no—
139M16—2184no—
140C2×C8—2182no—
141C2×C8—2182no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—2181no—
145C22⋊C4—2181no—
146C22⋊C4—2181no—
147C22⋊C4—2181no—
148C22⋊C4—2181no—
149C22⋊C4—2181no—
150C42—1091no—
151C42—1091no—
152C42—1091no—
153C42C2×#8913711yescharacteristic
154C23—21no—
155C23—1091no—
156C23—4362no—
157C23—4362no—
158C23—4362no—
159C23—2181no—
160Q8—41no—
161Q8—4361no—
162Q8—4362no—
163D4—41no—
164D4—4361no—
165D4—4362no—
166C2×C4—21no—
167C2×C4—1091no—
168C2×C4—1091no—
169C2×C4—1091no—
170C2×C4—4361no—
171C2×C4—4362no—
172C2×C4—2182no—
173C2×C4—2182no—
174C2×C4—2181no—
175C2×C4C22⋊#8913711yescharacteristic
176C2×C4C22⋊#8913711yescharacteristic
177C2×C4C22×#8913711yescharacteristic
178C8—4362no—
179C8—2184no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—8724no—
184C22—1092no—
185C22—4361no—
186C22—4361no—
187C22—4361no—
188C22—2181no—
189C22—2181no—
190C22C2×C22⋊#8913711yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—41no—
195C4—1092no—
196C4—4361no—
197C4—2181no—
198C4—2181no—
199C2—81no—
200C2—8721no—
201C2—2182no—
202C2D109⋊#10011yescharacteristic
203C2D109⋊#10411yescharacteristic
204C2#2029602311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#124×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×D4×D109C4
cosocleC4×Dic109C23
hypercenter#124#89137
hypocenterC109#1527
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20296049C2semidirect
2. C4×#13182039C2semidirect
3. #20295882C2semidirect
4. #20295881C2semidirect
9. #16812754C22semidirect
10. #16812754C22semidirect
103. C109#1527semidirect

Maximal subgroups

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

subgroupindex
#202960492
C4×#131820392
#202958822
#202958812
#124×D1092
#1527109