Finite Group Databasebeta

← #28362101

Subgroups — #28362101

Order 13952.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#20295737C211yesmaximal, characteristic, complemented
2#20295223C211yesmaximal, characteristic, complemented
3#20295218C211yesmaximal, characteristic
4#20294775C211yesmaximal, characteristic, complemented
5#20294758C211yesmaximal, characteristic, complemented
6#20294755C211yesmaximal, characteristic, complemented
7#492×C109C211yesmaximal, characteristic, complemented
8C2×#13182017—21no—
9C2×#13182014—21no—
10#16812690—21no—
11#16812679—21no—
12#16812675—22no—
13C4×Dic218C2211yescharacteristic
14C4×D436C2211yescharacteristic
15#16812661—21no—
16C4⋊C4×D109—21no—
17C4⋊#11724784C2211yescharacteristic
18C4⋊#11724784C2211yescharacteristic
19#16812620—21no—
20#16812620—21no—
21C2×SD16×C109—22no—
22C4⋊Q8×C109C2211yescharacteristic
23#127×C109C2211yescharacteristic
24C4×C8×C109C2211yescharacteristic
25C2×Dic218D411yescharacteristic
26C2×D436D411yescharacteristic
27C2×C4×D109—21no—
28C2×C4×D109—22no—
29#13182017—42no—
30#13182014—42no—
31C2×#11724784—21no—
32C2×#11724784—21no—
33C4⋊Dic109—22no—
34C4⋊Dic109D411yescharacteristic
35C4⋊Dic109D411yescharacteristic
36#13182008—22no—
37#13182008—21no—
38#13182006—22no—
39#13182006—21no—
40C4×Dic109—21no—
41C2×Q8×C109D412yes—
42C2×D4×C109—21no—
43C2×D4×C109—21no—
44C2×D4×C109—21no—
45SD16×C109—44no—
46C2×C8×C109—21no—
47C4⋊C4×C109—21no—
48C4⋊C4×C109—21no—
49C42×C109C2311yescharacteristic
50C23×C109—41no—
51C22×D109—21no—
52Q8×C109—42no—
53D4×C109—42no—
54D4×C109—41no—
55D4×C109—41no—
56D4×C109—41no—
57D4×C109—41no—
58C2×C4×C109—22no—
59C2×C4×C109C2×D411yescharacteristic
60C2×C4×C109C2×D411yescharacteristic
61C2×C4×C109C2×D411yescharacteristic
62C2×Dic109—21no—
63C2×Dic109—21no—
64C2×Dic109—21no—
65D436—21no—
66D436SD1612yescomplemented
67C4×D109—41no—
68C4×D109—41no—
69C4×D109—82no—
70Dic218—21no—
71Dic218—21no—
72C8×C109—22no—
73#11724784—41no—
74#11724784—41no—
75C22×C109—81no—
76C22×C109—81no—
77C22×C109—81no—
78C22×C109#12011yescharacteristic
79C2×D109—22no—
80C2×D109—41no—
81C2×D109—41no—
82C4×C109—21no—
83C4×C109—42no—
84C4×C109C2×SD1611yescharacteristic
85C4×C109#13511yescharacteristic
86C4×C109AGL(1,ℤ/8)11yescharacteristic
87C4×C109#13711yescharacteristic
88Dic109—41no—
89Dic109—41no—
90Dic109—41no—
91C2×C109—161no—
92C2×C109#44811yescharacteristic
93C2×C109#44911yescharacteristic
94C2×C109#45311yescharacteristic
95D109—42no—
96#1622—1091nomaximal, Sylow
97C109#162211yescharacteristic, complemented, Sylow
98#554—1091no—
99#492D10911yescharacteristic, complemented
100#460—1091no—
101#459—1091no—
102#333—1091no—
103Q8⋊C8—1091no—
104D4⋊C8—1091no—
105C2×SD16—22no—
106C2×SD16—2181no—
107C2×D8—2181no—
108C4⋊Q8C2×D10911yescharacteristic
109#127C2×D10911yescharacteristic
110#125—2181no—
111C22⋊Q8—2181no—
112C22⋊Q8—2182no—
113C4×Q8—1091no—
114C4×D4—1091no—
115C4×D4—2181no—
116C2×C4⋊C4—2181no—
117C4⋊C8—1091no—
118C4⋊C8—1091no—
119#102—2181no—
120#102—2181no—
121C4×C8C2×D10911yescharacteristic
122C2×Q8—1091no—
123C2×Q8C22⋊D10912yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—1091no—
128C22×C4—2182no—
129C22×C4—2181no—
130SD16—44no—
131SD16—4362no—
132D8—4362no—
133C2×C8—21no—
134C2×C8—2181no—
135C2×C8—2181no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—1091no—
139C4⋊C4—1091no—
140C4⋊C4—2182no—
141C4⋊C4—2182no—
142C4⋊C4—2181no—
143C22⋊C4—2182no—
144C22⋊C4—2181no—
145C42—2181no—
146C42C22×D10911yescharacteristic
147C23—41no—
148C23—2181no—
149Q8—42no—
150Q8—2181no—
151Q8—2181no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—1092no—
158D4—2181no—
159C2×C4—22no—
160C2×C4—8722no—
161C2×C4—4361no—
162C2×C4—4361no—
163C2×C4—2181no—
164C2×C4—2181no—
165C2×C4—2181no—
166C2×C4D4×D10911yescharacteristic
167C2×C4D4×D10911yescharacteristic
168C2×C4C2×C22⋊D10911yescharacteristic
169C8—22no—
170C8—4361no—
171C8—4361no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—4361no—
176C22—4361no—
177C22—2182no—
178C22#1681266711yescharacteristic
179C4—21no—
180C4—42no—
181C4—4361no—
182C4—4361no—
183C4—4361no—
184C4SD16×D10911yescharacteristic
185C4#1681272011yescharacteristic
186C4#1681272611yescharacteristic
187C4#1681272811yescharacteristic
188C2—161no—
189C2—4362no—
190C2#2029516311yescharacteristic
191C2#2029517011yescharacteristic
192C2#2029519311yescharacteristic
subgroupG/H
centerC22#16812667
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#492×C109C2
socleC22×C109#120
prime radical#20295218C2
hypercenter#492D109
hypocenterC109#1622
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #20295737C2semidirect
2. #20295223C2semidirect
4. #20294775C2semidirect
5. #20294758C2semidirect
6. #20294755C2semidirect
7. #492×C109C2semidirect
66. D436SD16semidirect
97. C109#1622semidirect
99. #492D109semidirect

Maximal subgroups

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

subgroupindex
#202957372
#202952232
#202952182
#202947752
#202947582
#202947552
#492×C1092
#1622109