Finite Group Databasebeta

← #15767269

Subgroups — #15767269

Order 3328.

448 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 81 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#13115305C212yesmaximal
2#13115018C211yesmaximal, characteristic
3#13113356C212yesmaximal
4#13112713C211yesmaximal, characteristic
5C13×#3189C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2212yes—
7C22×#6099C2211yescharacteristic
8C13×#484—22no—
9C13×#467—21no—
10C13×#467—21no—
11C13×#451—22no—
12C2×C13×C22⋊C8C2211yescharacteristic
13C2×#88076—22no—
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2212yes—
16C2×#88054—21no—
17#11718142—21no—
18#11718130—22no—
19#11718130—22no—
20#11718122—22no—
21C22×Q8×C13D412yes—
22C23×C4×C13C2311yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C22×C8×C13D411yescharacteristic
26C22×C8×C13D411yescharacteristic
27C13×C22⋊Q8—22no—
28C13×C22⋊Q8—22no—
29C13×C22⋊Q8—22no—
30C13×C22⋊Q8—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4D412yes—
33C2×C13×C22⋊C4—22no—
34C2×C22⋊Dic13—21no—
35C2×C4×Dic13—21no—
36C2×#6099—22no—
37C2×#6099—22no—
38C2×#6099—42no—
39C22×#1055—21no—
40C13×#107—21no—
41C13×#107—21no—
42C13×#103—22no—
43C13×#103—22no—
44C13×C22⋊C8—22no—
45#88076—44no—
46#88071D411yescharacteristic
47#88071D411yescharacteristic
48C22⋊#1055—22no—
49C22⋊#1055—22no—
50#88054—42no—
51#10559—131nomaximal, Sylow
52C24×C13#4111yescharacteristic
53C2×Q8×C13—22no—
54C2×Q8×C13—22no—
55C2×Q8×C13—42no—
56C2×Q8×C13—42no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D412yes—
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13#4112yes—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C13×Q16—81no—
68C13×Q16—81no—
69C2×C8×C13—21no—
70C2×C8×C13—21no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C13×C22⋊C4—42no—
78C13×C22⋊C4—42no—
79C22⋊Dic13—42no—
80C4×Dic13—41no—
81C4×Dic13—41no—
82#6099—24no—
83#6099—42no—
84#6099—42no—
85#6099—42no—
86C2×#1055—22no—
87C2×#1055—41no—
88C2×#1055—41no—
89C2×#1055—42no—
90#3189D1311yescharacteristic
91#1901—132no—
92#1851—131no—
93#1508—132no—
94#1293—131no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13#12111yescharacteristic
100C23×C13#12312yes—
101Q8×C13—42no—
102Q8×C13—42no—
103Q8×C13—82no—
104C2×C4×C13—21no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—44no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—82no—
114C2×C4×C13#12011yescharacteristic
115C2×C4×C13#12112yes—
116C2×C4×C13#12411yescharacteristic
117C2×Dic13—22no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C8×C13—41no—
124C8×C13—41no—
125#1055—42no—
126#1055—82no—
127C22×M16—131no—
128C2×C22⋊Q8C2×D1312yes—
129#484—22no—
130#467—21no—
131#467—21no—
132#451—22no—
133C2×C4⋊C8—261no—
134C2×#101—262no—
135#407—132no—
136C2×C22⋊C8C2×D1311yescharacteristic
137C4×C22⋊C4—131no—
138#343—262no—
139#336—261no—
140#328—262no—
141#328—262no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—22no—
145C22×C13—22no—
146C22×C13—22no—
147C22×C13—81no—
148C22×C13—81no—
149C22×C13#39411yescharacteristic
150C22×C13#47311yescharacteristic
151C22×C13#47311yescharacteristic
152C4×C13—22no—
153C4×C13—21no—
154C4×C13—82no—
155C4×C13—82no—
156C4×C13B(4,𝔽2)11yescharacteristic
157C4×C13#45811yescharacteristic
158Dic13—42no—
159Dic13—81no—
160C22×Q8C22⋊D1312yes—
161C23×C4C22×D1311yescharacteristic
162C2×Q16—21no—
163C2×Q16—21no—
164C2×M16—262no—
165C2×M16—262no—
166C2×M16—522no—
167C22×C8—261no—
168C22×C8C22⋊D1311yescharacteristic
169C22×C8C22⋊D1311yescharacteristic
170C22⋊Q8—22no—
171C22⋊Q8—22no—
172C22⋊Q8—22no—
173C22⋊Q8—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4C22⋊D1312yes—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—261no—
178C2×C42—261no—
179#107—21no—
180#107—21no—
181C4⋊C8—522no—
182#103—22no—
183#103—22no—
184#101—524no—
185C22⋊C8—22no—
186C22⋊C8—262no—
187C22⋊C8—262no—
188#95—131no—
189#95—131no—
190C2×C13—21no—
191C2×C13—21no—
192C2×C13—42no—
193C2×C13#204411yescharacteristic
194C2×C13#204711yescharacteristic
195C2×C13#205011yescharacteristic
196C24#612911yescharacteristic
197C2×Q8—22no—
198C2×Q8—22no—
199C2×Q8—42no—
200C2×Q8—42no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—261no—
206C22×C4—261no—
207C22×C4D4×D1311yescharacteristic
208C22×C4#612912yes—
209C22×C4C2×C22⋊D1311yescharacteristic
210C22×C4C2×C22⋊D1312yes—
211Q16—81no—
212Q16—81no—
213M16—264no—
214M16—522no—
215M16—522no—
216M16—522no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—262no—
222C2×C8—521no—
223C2×C8—521no—
224C2×C8—522no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C22⋊C4—42no—
230C22⋊C4—42no—
231C22⋊C4—522no—
232C42—521no—
233C42—521no—
234C13#1055911yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23#8818912yes—
240C23#8819211yescharacteristic
241Q8—42no—
242Q8—42no—
243Q8—82no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—44no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—82no—
254C2×C4—262no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4#8819011yescharacteristic
261C2×C4#8819312yes—
262C2×C4#8820711yescharacteristic
263C8—41no—
264C8—41no—
265C8—522no—
266C8—1042no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—81no—
273C22—81no—
274C22#1171885311yescharacteristic
275C22#1171885311yescharacteristic
276C22#1171888311yescharacteristic
277C4—22no—
278C4—21no—
279C4—82no—
280C4—82no—
281C4—522no—
282C4—1041no—
283C4#1171890411yescharacteristic
284C4#1171890511yescharacteristic
285C2—21no—
286C2—21no—
287C2—42no—
288C2#1311608411yescharacteristic
289C2#1311610111yescharacteristic
290C2#1311612011yescharacteristic
subgroupG/H
centerC22#11718883
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#3189C2
socleC22×C13#394
prime radicalC24×C13#41
hypercenter#3189D13
hypocenterC13#10559
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
234. C13#10559semidirect

Maximal subgroups

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

subgroupindex
#131153052
#131150182
#131133562
#131127132
C13×#31892
#1055913