Finite Group Databasebeta

← #28362102

Subgroups — #28362102

Order 13952.

236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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#20295733C211yesmaximal, characteristic, complemented
2#20295398C211yesmaximal, characteristic, complemented
3#20295223C211yesmaximal, characteristic, complemented
4#20294774C211yesmaximal, characteristic, complemented
5#20294756C211yesmaximal, characteristic, complemented
6D4⋊#11724784C211yesmaximal, characteristic, complemented
7#459×C109C211yesmaximal, characteristic
8C2×#13182017—21no—
9C2×#13182017—22no—
10#16812699C2211yescharacteristic
11#16812690—21no—
12#16812678—21no—
13#16812676—22no—
14C4×Dic218C2211yescharacteristic
15D4×Dic109—21no—
16C2×C4⋊Dic109—21no—
17C4⋊#11724784C2211yescharacteristic
18#16812620—21no—
19C4×#11724784C2211yescharacteristic
20C2×D8×C109—21no—
21#127×C109C2211yescharacteristic
22C4×D4×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24#102×C109—21no—
25C2×Dic218D411yescharacteristic
26C2×Dic218D412yes—
27C22×Dic109—22no—
28#13182017—44no—
29#13182017—42no—
30C2×#11724784—21no—
31C2×#11724784—21no—
32C4⋊Dic109—22no—
33C4⋊Dic109—21no—
34C4⋊Dic109—21no—
35C4⋊Dic109D411yescharacteristic
36#13182008—22no—
37#13182008—21no—
38C22⋊Dic109—22no—
39C4×Dic109—21no—
40C2×D4×C109—21no—
41C2×D4×C109—21no—
42C2×D4×C109—21no—
43C2×D4×C109D411yescharacteristic
44C22×C4×C109—21no—
45D8×C109—42no—
46C2×C8×C109—21no—
47C4⋊C4×C109D411yescharacteristic
48C22⋊C4×C109—21no—
49C42×C109C2311yescharacteristic
50C23×C109—21no—
51C23×C109—41no—
52D4×C109—21no—
53D4×C109—42no—
54D4×C109—41no—
55D4×C109—41no—
56D4×C109—41no—
57D4×C109—41no—
58D4×C109SD1612yescomplemented
59C2×C4×C109—21no—
60C2×C4×C109—41no—
61C2×C4×C109—41no—
62C2×C4×C109C2×D411yescharacteristic
63C2×C4×C109C2×D411yescharacteristic
64C2×C4×C109C2×D411yescharacteristic
65C2×Dic109—21no—
66C2×Dic109—21no—
67C2×Dic109—22no—
68C2×Dic109—82no—
69Dic218—21no—
70Dic218—21no—
71Dic218—42no—
72C8×C109—41no—
73#11724784—22no—
74#11724784—41no—
75C22×C109—22no—
76C22×C109—41no—
77C22×C109—41no—
78C22×C109—81no—
79C22×C109—81no—
80C22×C109—81no—
81C22×C109#12011yescharacteristic
82C4×C109—21no—
83C4×C109—41no—
84C4×C109C2×SD1611yescharacteristic
85C4×C109#13511yescharacteristic
86C4×C109AGL(1,ℤ/8)11yescharacteristic
87C4×C109#13711yescharacteristic
88Dic109—41no—
89Dic109—42no—
90Dic109—41no—
91C2×C109—42no—
92C2×C109—161no—
93C2×C109#44811yescharacteristic
94C2×C109#44911yescharacteristic
95C2×C109#45311yescharacteristic
96#1622—1091nomaximal, Sylow
97C109#162211yescharacteristic, complemented, Sylow
98#554—1091no—
99#492—1091no—
100#460—1091no—
101#459D10911yescharacteristic
102#333—1091no—
103Q8⋊C8—1091no—
104D4⋊C8—1091no—
105C2×SD16—2181no—
106C2×SD16—2182no—
107C2×D8—21no—
108C4⋊Q8—1091no—
109#127C2×D10911yescharacteristic
110#125—2181no—
111C22⋊Q8—2182no—
112C22⋊Q8—2181no—
113C4×Q8—1091no—
114C4×D4—2181no—
115C4×D4C2×D10911yescharacteristic
116C2×C4⋊C4—2181no—
117C4⋊C8—1091no—
118C4⋊C8C2×D10911yescharacteristic
119#102—21no—
120#102—2181no—
121C4×C8—1091no—
122C2×Q8—1092no—
123C2×Q8—1091no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4C22⋊D10911yescharacteristic
128C22×C4—21no—
129C22×C4—2182no—
130SD16—4362no—
131SD16—4364no—
132D8—42no—
133C2×C8—21no—
134C2×C8—2181no—
135C2×C8—2181no—
136C4⋊C4—1091no—
137C4⋊C4—2182no—
138C4⋊C4—2182no—
139C4⋊C4—2181no—
140C4⋊C4—2181no—
141C4⋊C4—2181no—
142C4⋊C4C22⋊D10911yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—2182no—
145C42—2181no—
146C42C22×D10911yescharacteristic
147C23—21no—
148C23—41no—
149Q8—4362no—
150Q8—2181no—
151Q8—2181no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4#1318201712yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—8722no—
163C2×C4—2181no—
164C2×C4—2181no—
165C2×C4—2182no—
166C2×C4D4×D10911yescharacteristic
167C2×C4D4×D10911yescharacteristic
168C2×C4C2×C22⋊D10911yescharacteristic
169C8—41no—
170C8—4361no—
171C8—2182no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22#1681266711yescharacteristic
179C4—21no—
180C4—41no—
181C4—4361no—
182C4—4361no—
183C4—4362no—
184C4C2×#1318201711yescharacteristic
185C4#1681271811yescharacteristic
186C4#1681272311yescharacteristic
187C4#1681272911yescharacteristic
188C2—42no—
189C2—161no—
190C2#2029516411yescharacteristic
191C2#2029516811yescharacteristic
192C2#2029519211yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting, prime radical#459×C109C2
socleC22×C109#120
hypercenter#459D109
hypocenterC109#1622
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20295733C2semidirect
2. #20295398C2semidirect
3. #20295223C2semidirect
4. #20294774C2semidirect
5. #20294756C2semidirect
6. D4⋊#11724784C2semidirect
58. D4×C109SD16semidirect
97. C109#1622semidirect
158. D4#13182017semidirect

Maximal subgroups

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

subgroupindex
#202957332
#202953982
#202952232
#202947742
#202947562
D4⋊#117247842
#459×C1092
#1622109