Finite Group Databasebeta

← #27194372

Subgroups — #27194372

Order 13184.

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

normal subgroups only

This group has 212 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#20268141C211yesmaximal, characteristic, complemented
2#20268071C211yesmaximal, characteristic, complemented
3#20267996C211yesmaximal, characteristic, complemented
4#20267540C211yesmaximal, characteristic, complemented
5D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
7#555×C103C211yesmaximal, characteristic
8C2×#13110093—21no—
9#15693021C2211yescharacteristic
10#15692954—21no—
11C4⋊(C103⋊C8)C2211yescharacteristic
12C4⋊(C103⋊C8)C2211yescharacteristic
13#15692945—22no—
14#15692944—21no—
15#15692942—21no—
16C4×C103⋊C8C2211yescharacteristic
17C4⋊Q8×C103C2211yescharacteristic
18#124×C103—22no—
19#121×C103—21no—
20#121×C103—21no—
21C4×D4×C103C2211yescharacteristic
22C4×D4×C103C2211yescharacteristic
23#117×C103—21no—
24#117×C103—21no—
25C2×Dic206—21no—
26#13110093—42no—
27C2×C103⋊C8—21no—
28C2×C103⋊C8—21no—
29C2×C103⋊C8—21no—
30C4⋊Dic103—21no—
31C4⋊Dic103—21no—
32C2×Q8×C103D412yes—
33C2×D4×C103—22no—
34C2×D4×C103D411yescharacteristic
35C2×D4×C103D411yescharacteristic
36C22×C4×C103—21no—
37C22×C4×C103—21no—
38C4⋊C4×C103—21no—
39C4⋊C4×C103—21no—
40C4⋊C4×C103D411yescharacteristic
41C4⋊C4×C103D411yescharacteristic
42C22⋊C4×C103—22no—
43C22⋊C4×C103—22no—
44C22⋊C4×C103—21no—
45C22⋊C4×C103—21no—
46C42×C103—22no—
47C42×C103C2311yescharacteristic
48C23×C103—21no—
49C23×C103—21no—
50Q8×C103—42no—
51D4×C103—21no—
52D4×C103—21no—
53D4×C103—21no—
54D4×C103—21no—
55D4×C103—82no—
56C2×C4×C103—21no—
57C2×C4×C103—21no—
58C2×C4×C103—22no—
59C2×C4×C103—41no—
60C2×C4×C103—41no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C2×Dic103—41no—
67Dic206—41no—
68Dic206—41no—
69C103⋊C8—41no—
70C103⋊C8—41no—
71C103⋊C8—41no—
72C22×C103—41no—
73C22×C103—41no—
74C22×C103—41no—
75C22×C103—41no—
76C22×C103—41no—
77C22×C103—41no—
78C22×C103#12011yescharacteristic
79C4×C103—21no—
80C4×C103—41no—
81C4×C103—41no—
82C4×C103—42no—
83C4×C103#13511yescharacteristic
84C4×C103#13511yescharacteristic
85C4×C103AGL(1,ℤ/8)11yescharacteristic
86C4×C103#13711yescharacteristic
87Dic103—81no—
88C2×C103—81no—
89C2×C103—81no—
90C2×C103#44911yescharacteristic
91C2×C103#45211yescharacteristic
92C2×C103#45511yescharacteristic
93#1646—1031nomaximal, Sylow
94C103#164611yescharacteristic, complemented, Sylow
95#555D10311yescharacteristic
96#487—1031no—
97#474—1031no—
98#461—1031no—
99#333—1031no—
100D4⋊C8—1031no—
101D4⋊C8—1031no—
102C2×SD16—2061no—
103C4⋊Q8—1031no—
104C4⋊Q8C2×D10311yescharacteristic
105#124—22no—
106#121—21no—
107#121—21no—
108C4×D4C2×D10311yescharacteristic
109C4×D4C2×D10311yescharacteristic
110#117—21no—
111#117—21no—
112#107—2061no—
113C4⋊C8—1031no—
114C4⋊C8—1031no—
115#103—2062no—
116#103—2061no—
117#102—2061no—
118C4×C8—1031no—
119C2×Q8—2061no—
120C2×Q8C22⋊D10312yes—
121C2×D4—22no—
122C2×D4C22⋊D10311yescharacteristic
123C2×D4C22⋊D10311yescharacteristic
124C22×C4—21no—
125C22×C4—21no—
126SD16—4122no—
127C2×C8—2061no—
128C2×C8—2061no—
129C2×C8—2061no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2061no—
133C4⋊C4—2061no—
134C4⋊C4C22⋊D10311yescharacteristic
135C4⋊C4C22⋊D10311yescharacteristic
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C42—22no—
141C42C22×D10311yescharacteristic
142C23—21no—
143C23—21no—
144Q8—42no—
145Q8—4121no—
146Q8—4121no—
147D4—21no—
148D4—21no—
149D4—21no—
150D4—21no—
151D4—82no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—4121no—
160C2×C4C2×C22⋊D10311yescharacteristic
161C2×C4C2×C22⋊D10311yescharacteristic
162C2×C4C2×C22⋊D10311yescharacteristic
163C8—4121no—
164C8—4121no—
165C8—4121no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#1569299011yescharacteristic
173C4—21no—
174C4—41no—
175C4—41no—
176C4—42no—
177C4—8241no—
178C4#1569304111yescharacteristic
179C4#1569304111yescharacteristic
180C4#1569304611yescharacteristic
181C4#1569305111yescharacteristic
182C2—81no—
183C2—81no—
184C2#2026793611yescharacteristic
185C2#2026795311yescharacteristic
186C2#2026796911yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting, prime radical#555×C103C2
socleC22×C103#120
hypercenter#555D103
hypocenterC103#1646
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #20268141C2semidirect
2. #20268071C2semidirect
3. #20267996C2semidirect
4. #20267540C2semidirect
5. D4⋊(C103⋊C8)C2semidirect
6. D4⋊(C103⋊C8)C2semidirect
94. C103#1646semidirect

Maximal subgroups

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

subgroupindex
#202681412
#202680712
#202679962
#202675402
D4⋊(C103⋊C8)2
#555×C1032
#1646103