Finite Group Databasebeta

← #27196499

Subgroups — #27196499

Order 13184.

228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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#20267833C211yesmaximal, characteristic, complemented
2#20267817C211yesmaximal, characteristic, complemented
3#20267797C211yesmaximal, characteristic
4C2×#15692943C211yesmaximal, characteristic
5C2×#15692937C211yesmaximal, characteristic
6#20267559C211yesmaximal, characteristic, complemented
7C2×#108×C103C211yesmaximal, characteristic, complemented
8C22×D412C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10#15692980C2211yescharacteristic
11C2×C4⋊Dic103C2211yescharacteristic
12#15692955—21no—
13#15692953—21no—
14Dic103⋊C8—22no—
15#15692943—21no—
16#15692943—21no—
17#15692943—22no—
18#15692937—22no—
19C2×M16×C103C2211yescharacteristic
20C2×M16×C103C2211yescharacteristic
21C22×C8×C103C2211yescharacteristic
22#108×C103—22no—
23C23×D103—21no—
24C2×D412—21no—
25C2×D412—21no—
26C2×D412—21no—
27C2×D412—21no—
28C2×D412—21no—
29C2×D412Q812yes—
30C22×Dic103—21no—
31#13110089—21no—
32#13110089—21no—
33C2×C103⋊C8—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103D411yescharacteristic
37C4⋊Dic103D411yescharacteristic
38C22⋊Dic103—21no—
39C4×Dic103—21no—
40C22×C4×C103C2311yescharacteristic
41M16×C103—21no—
42M16×C103—21no—
43M16×C103—21no—
44M16×C103D412yes—
45C2×C8×C103—21no—
46C2×C8×C103—21no—
47C2×C8×C103—21no—
48C2×C8×C103—21no—
49C2×C8×C103D412yes—
50C23×C103#4111yescharacteristic
51C22×D103—22no—
52C22×D103—41no—
53C22×D103—41no—
54C22×D103—81no—
55C22×D103—81no—
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×Q811yescharacteristic
60C2×C4×C103#4111yescharacteristic
61C2×C4×C103#4111yescharacteristic
62C2×Dic103—21no—
63C2×Dic103—21no—
64C2×Dic103—41no—
65C2×Dic103—81no—
66D412—22no—
67D412—22no—
68D412—41no—
69D412—41no—
70C8×C103—22no—
71C8×C103—22no—
72C8×C103—41no—
73C103⋊C8—41no—
74C22×C103—21no—
75C22×C103—21no—
76C22×C103#12111yescharacteristic
77C22×C103C22⋊Q811yescharacteristic
78C22×C103#12611yescharacteristic
79C2×D103—42no—
80C2×D103—82no—
81C2×D103—81no—
82C2×D103—81no—
83C2×D103—82no—
84C4×C103#12111yescharacteristic
85C4×C103#12111yescharacteristic
86C4×C103C22⋊Q811yescharacteristic
87C4×C103C22⋊Q811yescharacteristic
88Dic103—41no—
89Dic103—41no—
90Dic103—81no—
91C2×C103—21no—
92C2×C103—21no—
93C2×C103#39611yescharacteristic
94C2×C103#47111yescharacteristic
95C2×C103#47211yescharacteristic
96D103—82no—
97#2063—1031nomaximal, Sylow
98C103#206311yescharacteristic, complemented, Sylow
99C2×#108D10311yescharacteristic, complemented
100#428—1031no—
101#424—1031no—
102#418—1031no—
103C2×#102—1031no—
104C2×#100—1031no—
105#343—1031no—
106C22×D4—1031no—
107C2×M16—1031no—
108C2×M16C2×D10311yescharacteristic
109C2×M16C2×D10311yescharacteristic
110C22×C8C2×D10311yescharacteristic
111#117—1031no—
112C2×C4⋊C4—1031no—
113#108—22no—
114#107—2061no—
115#106—2061no—
116C4⋊C8—2062no—
117#102—2061no—
118#102—2061no—
119#102—2062no—
120#100—2062no—
121C24—2061no—
122C2×D4—1032no—
123C2×D4—2061no—
124C2×D4—2061no—
125C2×D4—2061no—
126C2×D4—2061no—
127C2×D4—2061no—
128C22×C4—2061no—
129C22×C4C22×D10311yescharacteristic
130M16—21no—
131M16—21no—
132M16—21no—
133M16—2061no—
134M16—2061no—
135M16C22⋊D10312yes—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—2061no—
141C2×C8D41212yes—
142C4⋊C4—1031no—
143C4⋊C4—1031no—
144C4⋊C4—2061no—
145C4⋊C4—2061no—
146C22⋊C4—2061no—
147C42—2061no—
148C23—8241no—
149C23—8241no—
150C23—4121no—
151C23—4121no—
152C23—2062no—
153C23#1311010611yescharacteristic
154D4—4121no—
155D4—4121no—
156D4—2062no—
157D4—2062no—
158C2×C4—8241no—
159C2×C4—4121no—
160C2×C4—2061no—
161C2×C4—2061no—
162C2×C4D4×D10311yescharacteristic
163C2×C4C2×C22⋊D10311yescharacteristic
164C2×C4C2×D41211yescharacteristic
165C2×C4Q8×D10311yescharacteristic
166C2×C4#1311010411yescharacteristic
167C2×C4#1311010511yescharacteristic
168C8—22no—
169C8—22no—
170C8—41no—
171C8—4121no—
172C22—21no—
173C22—21no—
174C22—8242no—
175C22—8242no—
176C22—8241no—
177C22—8241no—
178C22—4122no—
179C22#1569299611yescharacteristic
180C22#1569299711yescharacteristic
181C22#1569301611yescharacteristic
182C4—8241no—
183C4—4121no—
184C4—4121no—
185C4#1569299311yescharacteristic
186C4#1569299511yescharacteristic
187C4#1569299911yescharacteristic
188C4#1569300111yescharacteristic
189C2—21no—
190C2—21no—
191C2—8242no—
192C2#2026771311yescharacteristic
193C2#2026805511yescharacteristic
194C2#2026806211yescharacteristic
subgroupG/H
centerC22#15692996
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
FittingC2×#108×C103C2
socleC22×C103#121
prime radicalC22×D412C22
hypercenterC2×#108D103
hypocenterC103#2063
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
1. #20267833C2semidirect
2. #20267817C2semidirect
6. #20267559C2semidirect
7. C2×#108×C103C2semidirect
98. C103#2063semidirect
99. C2×#108D103semidirect

Maximal subgroups

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

subgroupindex
#202678332
#202678172
#202677972
C2×#156929432
C2×#156929372
#202675592
C2×#108×C1032
#2063103