Finite Group Databasebeta

← #27196492

Subgroups — #27196492

Order 13184.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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#20268419C211yesmaximal, characteristic
2#20267831C211yesmaximal, characteristic
3#20267656C211yesmaximal, characteristic
4#20267559C211yesmaximal, characteristic
5#20267552C211yesmaximal, characteristic
6#20267550C211yesmaximal, characteristic
7#428×C103C211yesmaximal, characteristic
8C2×#13110089C2211yescharacteristic
9#15693021—21no—
10#15693020—21no—
11#15693013—21no—
12#15693012—21no—
13#15692998—22no—
14#15692980C2211yescharacteristic
15C2×C4⋊Dic103C2211yescharacteristic
16C2×C4×Dic103C2211yescharacteristic
17#15692954—21no—
18#15692952—21no—
19C103⋊#95—22no—
20C2×M16×C103C2211yescharacteristic
21#117×C103C2211yescharacteristic
22C2×C4⋊C4×C103C2211yescharacteristic
23#107×C103—21no—
24#106×C103—21no—
25C2×Dic206—22no—
26C22×Dic103—21no—
27C22×Dic103D412yes—
28#13110089—21no—
29#13110089Q812yescomplemented
30C2×C103⋊C8—21no—
31C4⋊Dic103—22no—
32C4⋊Dic103—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103D411yescharacteristic
35C4⋊Dic103D411yescharacteristic
36Dic103⋊C4—22no—
37Dic103⋊C4—22no—
38C22⋊Dic103—21no—
39C4×Dic103—21no—
40C4×Dic103—21no—
41C4×Dic103Q812yescomplemented
42C22×C4×C103—21no—
43C22×C4×C103C2311yescharacteristic
44M16×C103—21no—
45M16×C103Q812yescomplemented
46C2×C8×C103—21no—
47C4⋊C4×C103—21no—
48C4⋊C4×C103—21no—
49C4⋊C4×C103D411yescharacteristic
50C4⋊C4×C103D411yescharacteristic
51C22⋊C4×C103—21no—
52C42×C103—21no—
53C23×C103C2×D411yescharacteristic
54C2×C4×C103—21no—
55C2×C4×C103—21no—
56C2×C4×C103—42no—
57C2×C4×C103—41no—
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×Q811yescharacteristic
61C2×C4×C103C2×Q811yescharacteristic
62C2×C4×C103C2×Q811yescharacteristic
63C2×C4×C103#4111yescharacteristic
64C2×Dic103—21no—
65C2×Dic103—21no—
66C2×Dic103—22no—
67C2×Dic103—22no—
68C2×Dic103—41no—
69C2×Dic103—41no—
70C2×Dic103—42no—
71Dic206—82no—
72C8×C103—22no—
73C103⋊C8—22no—
74C22×C103—21no—
75C22×C103—21no—
76C22×C103#12011yescharacteristic
77C22×C103C22⋊Q811yescharacteristic
78C22×C103C4⋊Q811yescharacteristic
79C4×C103—41no—
80C4×C103—41no—
81C4×C103—81no—
82C4×C103C22⋊Q811yescharacteristic
83C4×C103C22⋊Q811yescharacteristic
84C4×C103C4⋊Q811yescharacteristic
85C4×C103C4⋊Q811yescharacteristic
86Dic103—42no—
87Dic103—41no—
88Dic103—41no—
89Dic103—42no—
90C2×C103—21no—
91C2×C103—21no—
92C2×C103#39511yescharacteristic
93C2×C103#45411yescharacteristic
94C2×C103#45511yescharacteristic
95#2061—1031nomaximal, Sylow
96C103#206111yescharacteristic, complemented, Sylow
97#544—1031no—
98#428—1031no—
99#428D10311yescharacteristic
100#382—1031no—
101#343—1031no—
102#339—1031no—
103#339—1031no—
104C2×M16—1031no—
105C2×M16C2×D10311yescharacteristic
106C4⋊Q8—2061no—
107C4⋊Q8—2061no—
108#125—2061no—
109#125—2061no—
110C22⋊Q8—2062no—
111#117—1031no—
112#117C2×D10311yescharacteristic
113C2×C4⋊C4—1031no—
114C2×C4⋊C4C2×D10311yescharacteristic
115C2×C42—1031no—
116#107—21no—
117#107—2061no—
118#106—21no—
119#106—2061no—
120#95—2062no—
121C2×Q8—2062no—
122C22×C4—21no—
123C22×C4—1032no—
124C22×C4—2061no—
125C22×C4C22×D10311yescharacteristic
126M16—21no—
127M16—1032no—
128M16—2061no—
129M16Dic20612yescomplemented
130C2×C8—21no—
131C2×C8—2061no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—1031no—
135C4⋊C4—1031no—
136C4⋊C4—2062no—
137C4⋊C4—2062no—
138C4⋊C4—2062no—
139C4⋊C4—2061no—
140C4⋊C4—2061no—
141C4⋊C4C22⋊D10311yescharacteristic
142C4⋊C4C22⋊D10311yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—2061no—
145C42—21no—
146C42—1032no—
147C42—2061no—
148C42—2061no—
149C23D4×D10311yescharacteristic
150Q8—8242no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—4121no—
156C2×C4—4121no—
157C2×C4—4122no—
158C2×C4—2061no—
159C2×C4—2061no—
160C2×C4—2062no—
161C2×C4—2062no—
162C2×C4D4×D10311yescharacteristic
163C2×C4C2×C22⋊D10311yescharacteristic
164C2×C4Q8×D10311yescharacteristic
165C2×C4Q8×D10311yescharacteristic
166C2×C4C2×Dic20611yescharacteristic
167C2×C4#1311010511yescharacteristic
168C8—22no—
169C8—2062no—
170C22—21no—
171C22—21no—
172C22#1569298911yescharacteristic
173C22#1569299911yescharacteristic
174C22#1569302011yescharacteristic
175C4—41no—
176C4—41no—
177C4—81no—
178C4—4122no—
179C4—4121no—
180C4—4122no—
181C4—4121no—
182C4#1569299911yescharacteristic
183C4#1569300011yescharacteristic
184C4#1569301911yescharacteristic
185C4#1569302011yescharacteristic
186C2—21no—
187C2—21no—
188C2#2026771111yescharacteristic
189C2#2026796211yescharacteristic
190C2#2026796711yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#428×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
hypercenter#428D103
hypocenterC103#2061
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
29. #13110089Q8semidirect
41. C4×Dic103Q8semidirect
45. M16×C103Q8semidirect
96. C103#2061semidirect
129. M16Dic206semidirect

Maximal subgroups

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

subgroupindex
#202684192
#202678312
#202676562
#202675592
#202675522
#202675502
#428×C1032
#2061103