Finite Group Databasebeta

← #15765991

Subgroups — #15765991

Order 3328.

400 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115808C212yesmaximal
2#13115655C211yesmaximal, characteristic
3#13112717C211yesmaximal, characteristic
4#13112717C212yesmaximal
5C13×#2844C211yesmaximal, characteristic
6C2×#88123C2211yescharacteristic
7C13×#400—21no—
8C13×#400—22no—
9C13×#395—21no—
10C13×#395—22no—
11C13×#382C2211yescharacteristic
12C13×#382C2212yes—
13C2×#88050—21no—
14C2×#88050—21no—
15C2×#88043C2211yescharacteristic
16C2×#88043C2212yes—
17#11718121—22no—
18#11718121—22no—
19C22×Q8×C13—21no—
20C22×Dic26—21no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4D411yescharacteristic
24C2×C13×C4⋊C4D412yes—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C4⋊C4D412yes—
27C2×C42×C13C2311yescharacteristic
28C2×C4⋊Dic13—22no—
29C22×#1055—21no—
30C22×#1055—22no—
31#88123—22no—
32#88123—21no—
33#88123Q812yescomplemented
34C13×#95—22no—
35C13×#95—21no—
36C13×#95—21no—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95—22no—
40#88050—42no—
41#88050—42no—
42#88043—22no—
43#88043—22no—
44#88043—22no—
45#10359—131nomaximal, Sylow
46C2×Q8×C13—81no—
47C2×Q8×C13—82no—
48C22×C4×C13—21no—
49C22×C4×C13—22no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13C2×D412yes—
53C22×C4×C13C2×D411yescharacteristic
54C22×Dic13—41no—
55C2×Dic26—22no—
56C2×Dic26—41no—
57C2×Dic26—41no—
58C2×Dic26—41no—
59C2×Dic26—41no—
60C2×Dic26—41no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—81no—
66C13×C4⋊C4—82no—
67C42×C13C2×Q811yescharacteristic
68C42×C13#4112yes—
69C42×C13#4111yescharacteristic
70C4⋊Dic13—24no—
71C4⋊Dic13—42no—
72C2×#1055—24no—
73C2×#1055—22no—
74C2×#1055—41no—
75C2×#1055—42no—
76C2×#1055—42no—
77C2×#1055—41no—
78#2844D1311yescharacteristic
79#1993—132no—
80#1960—131no—
81#1295—131no—
82#1295—132no—
83C23×C13#12011yescharacteristic
84Q8×C13—84no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13C22⋊Q812yes—
100C2×C4×C13C22⋊Q811yescharacteristic
101C2×C4×C13#12412yes—
102C2×C4×C13#12411yescharacteristic
103C2×Dic13—42no—
104C2×Dic13—81no—
105C2×Dic13—81no—
106Dic26—42no—
107Dic26—42no—
108Dic26—81no—
109Dic26—81no—
110#1055—42no—
111#1055—44no—
112C2×C4⋊Q8—131no—
113C2×#103—261no—
114C2×#103—261no—
115C2×#97—131no—
116C2×#97—132no—
117#400—22no—
118#400—21no—
119#395—22no—
120#395—21no—
121#382C2×D1311yescharacteristic
122#382C2×D1312yes—
123#340—262no—
124#340—262no—
125C22×C13#39311yescharacteristic
126C22×C13#45311yescharacteristic
127C22×C13#45411yescharacteristic
128C22×C13#45512yes—
129C22×C13#45612yes—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—81no—
135C4×C13—82no—
136C4×C13—81no—
137C4×C13—82no—
138Dic13—82no—
139C22×Q8—21no—
140C22×Q8—261no—
141C22×C8—262no—
142C22×C8—261no—
143C4⋊Q8—132no—
144C4⋊Q8—262no—
145C4⋊Q8—261no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—262no—
149C2×C4⋊C4C22⋊D1312yes—
150C2×C4⋊C4C22⋊D1312yes—
151C2×C4⋊C4C22⋊D1311yescharacteristic
152C2×C4⋊C4C22⋊D1311yescharacteristic
153C2×C42C22×D1311yescharacteristic
154#103—522no—
155#103—522no—
156#97—262no—
157#97—262no—
158#97—262no—
159#95—22no—
160#95—21no—
161#95—21no—
162#95—22no—
163#95—22no—
164#95—22no—
165C2×C13#165911yescharacteristic
166C2×C13#166011yescharacteristic
167C2×C13#166412yes—
168C2×C13#202711yescharacteristic
169C2×C13#202812yes—
170C2×Q8—81no—
171C2×Q8—82no—
172C2×Q8—262no—
173C2×Q8—521no—
174C2×Q8—521no—
175C2×Q8—521no—
176C2×Q8—521no—
177C2×Q8—521no—
178C22×C4—21no—
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—521no—
183C22×C4C2×C22⋊D1312yes—
184C22×C4C2×C22⋊D1311yescharacteristic
185C2×C8—262no—
186C2×C8—264no—
187C2×C8—522no—
188C2×C8—521no—
189C2×C8—522no—
190C2×C8—521no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—81no—
196C4⋊C4—82no—
197C4⋊C4—264no—
198C4⋊C4—522no—
199C42Q8×D1311yescharacteristic
200C42#613112yes—
201C42#613111yescharacteristic
202C13#1035911yescharacteristic, complemented, Sylow
203C23#8820711yescharacteristic
204Q8—84no—
205Q8—522no—
206Q8—522no—
207Q8—1041no—
208Q8—1041no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—522no—
224C2×C4—1041no—
225C2×C4—1041no—
226C2×C4#8820012yes—
227C2×C4#8820011yescharacteristic
228C2×C4#8820112yes—
229C2×C4#8820111yescharacteristic
230C8—522no—
231C8—524no—
232C22#1171889211yescharacteristic
233C22#1171890211yescharacteristic
234C22#1171890312yes—
235C22#1171890611yescharacteristic
236C22#1171890712yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—82no—
243C4—81no—
244C4—82no—
245C4—1042no—
246C2#1311414211yescharacteristic
247C2#1311414711yescharacteristic
248C2#1311417012yes—
249C2#1311598911yescharacteristic
250C2#1311599412yes—
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2844C2
socle, prime radicalC23×C13#120
hypercenter#2844D13
hypocenterC13#10359
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2844

Complements

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

NH ≅ G/Ntype
33. #88123Q8semidirect
202. C13#10359semidirect

Maximal subgroups

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

subgroupindex
#131158082
#131156552
#131127172
C13×#28442
#1035913