Finite Group Databasebeta

← #28362200

Subgroups — #28362200

Order 13952.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic218C211yesmaximal, characteristic
2#20295377C211yesmaximal, characteristic, complemented
3#20295322C211yesmaximal, characteristic, complemented
4#20295316C211yesmaximal, characteristic
5#20294773C211yesmaximal, characteristic, complemented
6#20294758C211yesmaximal, characteristic, complemented
7D4⋊C8×C109C211yesmaximal, characteristic
8C22×Dic218—21no—
9#16812699C2211yescharacteristic
10#16812699C2211yescharacteristic
11#16812698—21no—
12#16812678—21no—
13#16812676—22no—
14C4×Dic218C2211yescharacteristic
15D4×Dic109—21no—
16#16812633—21no—
17#16812630—21no—
18C4⋊#11724784C2211yescharacteristic
19#16812624—21no—
20#16812624—22no—
21#16812620—21no—
22C4×D4×C109C2211yescharacteristic
23C4⋊C8×C109C2211yescharacteristic
24C4×C8×C109C2211yescharacteristic
25C2×Dic218—22no—
26C2×Dic218—21no—
27C2×Dic218—21no—
28C2×Dic218—42no—
29C2×Dic218—42no—
30C2×Dic218D411yescharacteristic
31C22×Dic109—22no—
32C2×#11724784—21no—
33C4⋊Dic109—21no—
34C4⋊Dic109—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109D412yes—
37C4⋊Dic109D411yescharacteristic
38#13182008—22no—
39#13182008—21no—
40C22⋊Dic109—22no—
41C4×Dic109—21no—
42C2×D4×C109D411yescharacteristic
43C22×C4×C109—21no—
44C2×C8×C109—21no—
45C2×C8×C109—21no—
46C4⋊C4×C109D411yescharacteristic
47C22⋊C4×C109—21no—
48C42×C109C2311yescharacteristic
49C23×C109—21no—
50D4×C109—21no—
51D4×C109Q1612yes—
52C2×C4×C109—21no—
53C2×C4×C109—41no—
54C2×C4×C109—41no—
55C2×C4×C109C2×D411yescharacteristic
56C2×C4×C109C2×D411yescharacteristic
57C2×C4×C109C2×D411yescharacteristic
58C2×Dic109—21no—
59C2×Dic109—21no—
60C2×Dic109—22no—
61C2×Dic109—44no—
62C2×Dic109—41no—
63Dic218—21no—
64Dic218—44no—
65Dic218—41no—
66Dic218—41no—
67Dic218—42no—
68Dic218SD1612yes—
69C8×C109—41no—
70C8×C109—41no—
71#11724784—41no—
72C22×C109—22no—
73C22×C109—41no—
74C22×C109—41no—
75C22×C109#12011yescharacteristic
76C4×C109—21no—
77C4×C109—41no—
78C4×C109C2×SD1611yescharacteristic
79C4×C109C2×Q1611yescharacteristic
80C4×C109AGL(1,ℤ/8)11yescharacteristic
81C4×C109#13711yescharacteristic
82Dic109—22no—
83Dic109—42no—
84Dic109—41no—
85Dic109—81no—
86C2×C109—42no—
87C2×C109#45011yescharacteristic
88C2×C109#45111yescharacteristic
89C2×C109#45411yescharacteristic
90#1637—1091nomaximal, Sylow
91C109#163711yescharacteristic, complemented, Sylow
92D4×Q8—1091no—
93#487—1091no—
94#477—1091no—
95#476—1091no—
96#332—1091no—
97Q8⋊C8—1091no—
98D4⋊C8D10911yescharacteristic
99C22×Q8—2181no—
100C4⋊Q8—1091no—
101C4⋊Q8—1091no—
102C4⋊Q8—2181no—
103C22⋊Q8—2182no—
104C22⋊Q8—2181no—
105C4×Q8—1091no—
106C4×D4—2181no—
107C4×D4C2×D10911yescharacteristic
108#107—2181no—
109#106—2181no—
110C4⋊C8—1091no—
111C4⋊C8C2×D10911yescharacteristic
112#103—2182no—
113#103—2181no—
114#102—2181no—
115C4×C8C2×D10911yescharacteristic
116C2×Q8—1091no—
117C2×Q8—4362no—
118C2×Q8—4362no—
119C2×Q8—2182no—
120C2×Q8—2181no—
121C2×Q8—2181no—
122C2×D4D43611yescharacteristic
123C22×C4—21no—
124C22×C4—2182no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—2181no—
128C4⋊C4—1092no—
129C4⋊C4—1091no—
130C4⋊C4—2182no—
131C4⋊C4—2181no—
132C4⋊C4—2181no—
133C4⋊C4—2181no—
134C4⋊C4—2181no—
135C4⋊C4D43611yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—2182no—
138C42—2181no—
139C42C22×D10911yescharacteristic
140C23—21no—
141Q8—1092no—
142Q8—4362no—
143Q8—4364no—
144Q8—4361no—
145Q8—4361no—
146Q8—2181no—
147D4—21no—
148D4Dic43612yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—4361no—
153C2×C4—4364no—
154C2×C4—2181no—
155C2×C4—2182no—
156C2×C4—2181no—
157C2×C4D4×D10911yescharacteristic
158C2×C4D4×D10911yescharacteristic
159C2×C4C2×D43611yescharacteristic
160C8—41no—
161C8—41no—
162C8—4361no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1681266911yescharacteristic
167C4—21no—
168C4—41no—
169C4—8721no—
170C4—4362no—
171C4—4361no—
172C4—2182no—
173C4SD16×D10911yescharacteristic
174C4C2×Dic43611yescharacteristic
175C4#1681272311yescharacteristic
176C4#1681273211yescharacteristic
177C2—42no—
178C2#2029517811yescharacteristic
179C2#2029518411yescharacteristic
180C2#2029520011yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
FittingD4⋊C8×C109C2
socleC22×C109#120
prime radicalC2×D4×C109D4
hypercenterD4⋊C8D109
hypocenterC109#1637
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20295377C2semidirect
3. #20295322C2semidirect
5. #20294773C2semidirect
6. #20294758C2semidirect
91. C109#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2182
#202953772
#202953222
#202953162
#202947732
#202947582
D4⋊C8×C1092
#1637109