Finite Group Databasebeta

← #28378422

Subgroups — #28378422

Order 13952.

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

normal subgroups only

This group has 272 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
2#20295962C211yesmaximal, characteristic, complemented
3#20295878C212yesmaximal, complemented
4#20295877C212yesmaximal, complemented
5#20295573C211yesmaximal, characteristic
6C2×C4×#89137—21no—
7#16812766—21no—
8#16812756C2212yes—
9#16812754—21no—
10(C2×#89137)⋊C4—21no—
11(C2×#89137)⋊C4C2212yes—
12C2×#13182029—21no—
13#16812698C411yescharacteristic, complemented
14#16812695C411yescharacteristic, complemented
15#16812685—21no—
16#16812674C2211yescharacteristic
17#16812672—21no—
18#16812670C2211yescharacteristic
19C4×D436C411yescharacteristic, complemented
20C4×C22⋊D109—21no—
21C42×D109C2211yescharacteristic
22C4×D4×C109C411yescharacteristic, complemented
23C22×#89137—22no—
24C2×#11724786—22no—
25C4×#89137—24no—
26#13182029—44no—
27C2×Dic218—21no—
28C2×D436—21no—
29C2×D436C2×C411yescharacteristic
30C2×C22⋊D109—21no—
31C2×C22⋊D109—21no—
32C2×C22⋊D109—21no—
33C2×C4×D109—21no—
34C2×C4×D109D411yescharacteristic
35C2×C4×D109D411yescharacteristic
36C2×C4×D109C2311yescharacteristic
37C4⋊Dic109C2×C411yescharacteristic
38#13182008—21no—
39C22⋊Dic109—21no—
40#13182006—21no—
41#13182006—21no—
42C4×Dic109C2×C411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109D411yescharacteristic
45C2×D4×C109C2×C411yescharacteristic
46C22×C4×C109—21no—
47C4⋊C4×C109C2×C411yescharacteristic
48C22⋊C4×C109—21no—
49C42×C109C2×C411yescharacteristic
50C23×C109—21no—
51C22×D109—21no—
52C22×D109C2×D411yescharacteristic
53C2×#89137—24no—
54C2×#89137—42no—
55C2×#89137—42no—
56D4×C109—41no—
57C2×C4×C109—21no—
58C2×C4×C109—42no—
59C2×C4×C109C22⋊C411yescharacteristic
60C2×C4×C109C22⋊C411yescharacteristic
61C2×C4×C109C22×C411yescharacteristic
62C22⋊D109—42no—
63C22⋊D109—42no—
64C22⋊D109—42no—
65C2×Dic109—21no—
66C2×Dic109C22⋊C411yescharacteristic
67C2×Dic109C22⋊C411yescharacteristic
68C2×Dic109C2×D411yescharacteristic
69D436—41no—
70D436—42no—
71C4×D109—22no—
72C4×D109—22no—
73C4×D109—41no—
74C4×D109—42no—
75Dic218—42no—
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×D109AGL(1,ℤ/8)12yes—
87#89137—44no—
88C4×C109—21no—
89C4×C109—21no—
90C4×C109—21no—
91C4×C109—41no—
92Dic109—21no—
93Dic109—21no—
94Dic109—41no—
95Dic109#10412yes—
96C2×C109—81no—
97C2×C109#41011yescharacteristic
98C2×C109#41811yescharacteristic
99C2×C109C2×#10411yescharacteristic
100D109—22no—
101D109—81no—
102#1505—1091nomaximal, Sylow
103C109#150511yescharacteristic, complemented, Sylow
104#532—1091no—
105#432—1091no—
106#376—1091no—
107#327—1092no—
108#327—1092no—
109C2×#41—2181no—
110C4⋊Q8—1091no—
111#127—1091no—
112#124—2181no—
113#121—1091no—
114#121—1091no—
115#121—2181no—
116C4×D4—1091no—
117C4×D4—2181no—
118C4×D4#8913711yescharacteristic, complemented
119C2×C42—1091no—
120C2×C42—2181no—
121C4⋊C8—2181no—
122C22⋊C8—1092no—
123#97—2181no—
124#95—1092no—
125#95—2181no—
126#41—4364no—
127C2×Q8—2181no—
128C2×D4—1091no—
129C2×D4—2181no—
130C2×D4—2181no—
131C2×D4—2181no—
132C2×D4—2181no—
133C2×D4C2×#8913711yescharacteristic
134C22×C4—21no—
135C22×C4—1091no—
136C22×C4—1091no—
137C22×C4—1091no—
138C22×C4—2182no—
139C22×C4—2181no—
140C2×C8—2182no—
141C4⋊C4—1091no—
142C4⋊C4—2181no—
143C4⋊C4C2×#8913711yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—2181no—
146C22⋊C4—2181no—
147C22⋊C4—2181no—
148C42—1091no—
149C42—1091no—
150C42—1091no—
151C42—2184no—
152C42C2×#8913711yescharacteristic
153C23—21no—
154C23—1091no—
155C23—2181no—
156Q8—4362no—
157D4—41no—
158D4—4361no—
159D4—4362no—
160D4—4362no—
161D4—4362no—
162D4—4362no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—1091no—
166C2×C4—1091no—
167C2×C4—1091no—
168C2×C4—4362no—
169C2×C4—4361no—
170C2×C4—4362no—
171C2×C4—4362no—
172C2×C4—2182no—
173C2×C4—2182no—
174C2×C4—2184no—
175C2×C4—2181no—
176C2×C4C22⋊#8913711yescharacteristic
177C2×C4C22⋊#8913711yescharacteristic
178C2×C4C22×#8913711yescharacteristic
179C8—4362no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—1092no—
184C22—4361no—
185C22—4361no—
186C22—4361no—
187C22—2181no—
188C22—2181no—
189C22C2×C22⋊#8913711yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—1092no—
195C4—4364no—
196C4—4361no—
197C4—2181no—
198C4—2181no—
199C2—81no—
200C2—8721no—
201C2—2182no—
202C2#2029600511yescharacteristic
203C2#2029601811yescharacteristic
204C2D109⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radical#20295573C2
cosocleC2×C4×D109C23
hypercenterC4×D4#89137
hypocenterC109#1505
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20296049C2semidirect
2. #20295962C2semidirect
3. #20295878C2semidirect
4. #20295877C2semidirect
13. #16812698C4semidirect
14. #16812695C4semidirect
19. C4×D436C4semidirect
22. C4×D4×C109C4semidirect
103. C109#1505semidirect
118. C4×D4#89137semidirect

Maximal subgroups

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

subgroupindex
#202960492
#202959622
#202958782
#202958772
#202955732
#1505109