Finite Group Databasebeta

← #15764257

Subgroups — #15764257

Order 3328.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#11718363C212yesmaximal
2#13122904C211yesmaximal, characteristic
3#13115655C211yesmaximal, characteristic
4C2×#11718057C212yesmaximal
5C13×#1295C211yesmaximal, characteristic
6C2×#88124C2212yes—
7C2×#88123C2211yescharacteristic
8C2×C13×#97C2212yes—
9C13×#382C2211yescharacteristic
10C2×#88058—22no—
11C2×#88057—22no—
12#11718644—22no—
13C2×#88050—22no—
14C2×#88043C2211yescharacteristic
15#11718363—24no—
16#11718363—24no—
17#11718322—22no—
18#11718320—22no—
19#11718057—24no—
20C22×Dic26—21no—
21C22×C8×C13—22no—
22C2×C13×C4⋊C4D412yes—
23C2×C42×C13C2311yescharacteristic
24C2×C4⋊Dic13—22no—
25C2×C4⋊Dic13—22no—
26C2×C4⋊Dic13D412yes—
27C2×C4⋊Dic13D412yes—
28C2×#6101—22no—
29C2×#6101—22no—
30C22×#1055—21no—
31#88124—22no—
32#88124—22no—
33#88124—22no—
34#88124—22no—
35#88123—22no—
36#88123—21no—
37#88123D412yes—
38C13×#97—22no—
39C13×#97D414yes—
40C13×#95—22no—
41#88071—22no—
42#88071—24no—
43#88058—28no—
44#88057—28no—
45#88050—44no—
46#88043—22no—
47#10087—131nomaximal, Sylow
48C22×C4×C13—22no—
49C22×C4×C13C2×D411yescharacteristic
50C22×C4×C13C2×D412yes—
51C22×Dic13—22no—
52C22×Dic13—22no—
53C22×Dic13—41no—
54C2×Dic26—22no—
55C2×Dic26—42no—
56C2×Dic26—42no—
57C2×Dic26—41no—
58C2×C8×C13—28no—
59C2×C8×C13—24no—
60C13×C4⋊C4—42no—
61C42×C13C2×D412yes—
62C42×C13C2×D411yescharacteristic
63C42×C13#4111yescharacteristic
64C4⋊Dic13—24no—
65C4⋊Dic13—22no—
66C4⋊Dic13—22no—
67C4⋊Dic13—22no—
68C4⋊Dic13—22no—
69C4⋊Dic13—42no—
70C4⋊Dic13—82no—
71#6101—42no—
72#6101—42no—
73#6101—42no—
74#6101—42no—
75C2×#1055—22no—
76C2×#1055—41no—
77C2×#1055—41no—
78C2×#501—132no—
79#2822—131no—
80#1960—131no—
81C2×#330—132no—
82#1295D1311yescharacteristic
83C23×C13#12011yescharacteristic
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—24no—
87C2×C4×C13—42no—
88C2×C4×C13—44no—
89C2×C4×C13#12012yes—
90C2×C4×C13#12111yescharacteristic
91C2×C4×C13#12112yes—
92C2×C4×C13#12711yescharacteristic
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—44no—
99C2×Dic13—81no—
100C2×Dic13—81no—
101Dic26—44no—
102Dic26—82no—
103C8×C13—28no—
104#1055—42no—
105C2×C4⋊Q8—131no—
106C2×#125—132no—
107#501—264no—
108#501—264no—
109C2×#107—262no—
110C2×#106—262no—
111C2×#103—262no—
112C2×#97—131no—
113C2×#97C2×D1312yes—
114#400—262no—
115#398—262no—
116#398—262no—
117#382C2×D1311yescharacteristic
118#330—264no—
119C22×C13#39211yescharacteristic
120C22×C13#45311yescharacteristic
121C22×C13#45411yescharacteristic
122C22×C13#45614yes—
123C4×C13—22no—
124C4×C13—22no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—82no—
128Dic13—82no—
129Dic13—82no—
130Dic13—82no—
131C22×Q8—261no—
132C22×C8—22no—
133C22×C8—261no—
134C4⋊Q8—132no—
135C4⋊Q8—262no—
136C4⋊Q8—261no—
137#125—262no—
138#125—262no—
139#125—262no—
140#125—262no—
141C2×C4⋊C4—132no—
142C2×C4⋊C4—132no—
143C2×C4⋊C4—262no—
144C2×C4⋊C4—262no—
145C2×C4⋊C4—262no—
146C2×C4⋊C4—262no—
147C2×C4⋊C4D5212yes—
148C2×C42C22×D1311yescharacteristic
149#107—268no—
150#106—268no—
151#103—524no—
152#97—22no—
153#97—262no—
154#97D5214yes—
155#95—22no—
156#95—264no—
157#95—262no—
158C2×C13#166012yes—
159C2×C13#166312yes—
160C2×C13#200512yes—
161C2×C13#200611yescharacteristic
162C2×Q8—262no—
163C2×Q8—522no—
164C2×Q8—522no—
165C2×Q8—521no—
166C22×C4—22no—
167C22×C4—262no—
168C22×C4—262no—
169C22×C4—521no—
170C22×C4C2×D5211yescharacteristic
171C22×C4D4×D1312yes—
172C2×C8—28no—
173C2×C8—24no—
174C2×C8—262no—
175C2×C8—521no—
176C2×C8—521no—
177C4⋊C4—42no—
178C4⋊C4—262no—
179C4⋊C4—264no—
180C4⋊C4—262no—
181C4⋊C4—262no—
182C4⋊C4—262no—
183C4⋊C4—522no—
184C4⋊C4—522no—
185C4⋊C4—522no—
186C4⋊C4—522no—
187C4⋊C4—522no—
188C4⋊C4—1042no—
189C42C2×D5212yes—
190C42D4×D1311yescharacteristic
191C42#613111yescharacteristic
192C13#1008711yescharacteristic, complemented, Sylow
193C23#8813611yescharacteristic
194Q8—524no—
195Q8—1042no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—522no—
202C2×C4—522no—
203C2×C4—524no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4—1041no—
208C2×C4—1041no—
209C2×C4#8812811yescharacteristic
210C2×C4#8813612yes—
211C2×C4#8814912yes—
212C2×C4#8814911yescharacteristic
213C8—28no—
214C8—522no—
215C22#1171833211yescharacteristic
216C22#1171840811yescharacteristic
217C22#1171841411yescharacteristic
218C22#1171848714yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—1042no—
225C4—1042no—
226C4—1042no—
227C2#1311414812yes—
228C2#1311416512yes—
229C2#1311587512yes—
230C2#1311588011yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socle, prime radicalC23×C13#120
hypercenter#1295D13
hypocenterC13#10087
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
192. C13#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#117183632
#131229042
#131156552
C2×#117180572
C13×#12952
#1008713