Finite Group Databasebeta

← #15750885

Subgroups — #15750885

Order 3328.

528 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 119 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#13117383C211yesmaximal, characteristic
2#13114580C212yesmaximal, complemented
3#13112661C212yesmaximal, complemented
4#13112657C211yesmaximal, characteristic
5C13×#1270C211yesmaximal, characteristic
6C2×#88190C411yescharacteristic
7C2×D4×Dic13C411yescharacteristic
8C2×#88141C411yescharacteristic
9C13×#390C2211yescharacteristic
10C2×C8×Dic13—22no—
11#11718638C411yescharacteristic
12#11718605—22no—
13C22⋊C4×Dic13—22no—
14C42×Dic13C2211yescharacteristic
15#11718590C2211yescharacteristic
16C13×#336C2212yes—
17#11718142—22no—
18#11718116C2212yes—
19C22×D4×C13C2×C411yescharacteristic
20C23×Dic13—21no—
21C22×Dic26C2×C411yescharacteristic
22C22×C8×C13—22no—
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C13×C22⋊C4—22no—
25C2×C42×C13C2311yescharacteristic
26C2×C22⋊Dic13—22no—
27C2×C22⋊Dic13—21no—
28#88190—22no—
29#88190C814yescomplemented
30D4×Dic13—42no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×C4×Dic13—21no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13D412yes—
37C2×C4×Dic13D412yes—
38C22×#1055—22no—
39#88141—42no—
40#88071—22no—
41#88071—22no—
42C8×Dic13—28no—
43#7567—131nomaximal, Sylow
44C24×C13—21no—
45C2×D4×C13—21no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13C2×C812yes—
49C22×C4×C13—21no—
50C22×C4×C13C22×C411yescharacteristic
51C22×C4×C13C2×D412yes—
52C22×Dic13—21no—
53C22×Dic13—21no—
54C22×Dic13—42no—
55C22×Dic13—44no—
56C22×Dic13C22⋊C411yescharacteristic
57C22×Dic13C22⋊C412yes—
58C22×Dic13C22⋊C411yescharacteristic
59C2×Dic26—21no—
60C2×Dic26—41no—
61C2×Dic26—41no—
62C2×Dic26C2×C812yes—
63C2×C8×C13—24no—
64C2×C8×C13—42no—
65C2×C8×C13—42no—
66C13×C4⋊C4—41no—
67C13×C22⋊C4—42no—
68C13×C22⋊C4—42no—
69C42×C13—41no—
70C22⋊Dic13—28no—
71C22⋊Dic13—42no—
72C4⋊Dic13—41no—
73#6101—42no—
74C4×Dic13—22no—
75C4×Dic13—22no—
76C4×Dic13—22no—
77C4×Dic13—24no—
78C4×Dic13—42no—
79C4×Dic13C2×C812yes—
80C4×Dic13M1612yes—
81C2×#1055—24no—
82C2×#1055—42no—
83C2×#1055—42no—
84C4×#124—131no—
85#1744—132no—
86#1272—132no—
87#1270—131no—
88#1270D1311yescharacteristic
89C23×C13—22no—
90C23×C13—41no—
91C23×C13—41no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13C2×C22⋊C411yescharacteristic
95D4×C13—42no—
96D4×C13—42no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—41no—
102C2×C4×C13—42no—
103C2×C4×C13C22×C811yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C2×C4×C13#13512yes—
106C2×C4×C13#13512yes—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—21no—
111C2×Dic13—22no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13—42no—
116C2×Dic13—84no—
117C2×Dic13C22⋊C814yes—
118C2×Dic13#10012yes—
119C2×Dic13#10414yes—
120Dic26—42no—
121Dic26—42no—
122C8×C13—44no—
123#1055—44no—
124C2×#124—131no—
125C2×C4×Q8—131no—
126C2×C4×D4—131no—
127C2×C4×C8—262no—
128#391—131no—
129#390C2×D1311yescharacteristic
130#388—262no—
131#382—131no—
132C4×C22⋊C4—262no—
133C43—131no—
134#336—132no—
135#336—262no—
136#336C2×D1312yes—
137C22×C13—42no—
138C22×C13—44no—
139C22×C13—81no—
140C22×C13—82no—
141C22×C13—81no—
142C22×C13C2×C22⋊C811yescharacteristic
143C22×C13#41011yescharacteristic
144C22×C13C2×#10011yescharacteristic
145C22×C13#41612yes—
146C22×C13C2×#10412yes—
147C4×C13—21no—
148C4×C13—21no—
149C4×C13—22no—
150C4×C13—22no—
151C4×C13—81no—
152Dic13—24no—
153Dic13—41no—
154Dic13—42no—
155Dic13—81no—
156Dic13#32914yes—
157C22×Q8—131no—
158C22×D4C4×D1311yescharacteristic
159C23×C4—261no—
160C22×C8—22no—
161C22×C8—262no—
162#124—134no—
163#124—262no—
164C4×Q8—522no—
165C4×D4—522no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4C4×D1311yescharacteristic
169C2×C22⋊C4—22no—
170C2×C22⋊C4—262no—
171C2×C22⋊C4—261no—
172C2×C42—131no—
173C2×C42—131no—
174C2×C42—132no—
175C2×C42—132no—
176C2×C42—261no—
177C2×C42C22×D1311yescharacteristic
178C4×C8—268no—
179#95—262no—
180#95—262no—
181C2×C13—82no—
182C2×C13#146011yescharacteristic
183C2×C13#147612yes—
184C2×C13#150012yes—
185C2×C13C2×#32911yescharacteristic
186C2×C13#154311yescharacteristic
187C24—21no—
188C2×Q8—132no—
189C2×Q8—261no—
190C2×Q8—521no—
191C2×Q8—521no—
192C2×D4—21no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4C8×D1312yes—
196C22×C4—21no—
197C22×C4—131no—
198C22×C4—132no—
199C22×C4—131no—
200C22×C4—261no—
201C22×C4—261no—
202C22×C4—522no—
203C22×C4—524no—
204C22×C4C2×C4×D1311yescharacteristic
205C22×C4D4×D1312yes—
206C2×C8—24no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—264no—
210C2×C8—522no—
211C2×C8—522no—
212C4⋊C4—41no—
213C4⋊C4—521no—
214C4⋊C4—522no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—268no—
218C22⋊C4—522no—
219C42—41no—
220C42—132no—
221C42—132no—
222C42—264no—
223C42—262no—
224C42—262no—
225C42—262no—
226C42—522no—
227C13#756711yescharacteristic, complemented, Sylow
228C23—22no—
229C23—41no—
230C23—41no—
231C23—42no—
232C23—42no—
233C23C22⋊C4×D1311yescharacteristic
234Q8—522no—
235Q8—522no—
236D4—42no—
237D4—42no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—132no—
245C2×C4—134no—
246C2×C4—134no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—261no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4—522no—
256C2×C4—1044no—
257C2×C4C2×C8×D1311yescharacteristic
258C2×C4M16×D1311yescharacteristic
259C2×C4#8816612yes—
260C2×C4#8817012yes—
261C8—44no—
262C8—524no—
263C22—42no—
264C22—44no—
265C22—81no—
266C22—81no—
267C22—82no—
268C22D13×C22⋊C811yescharacteristic
269C22#1171840111yescharacteristic
270C22D13×#10011yescharacteristic
271C22#1171843312yes—
272C22D13×#10412yes—
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—81no—
278C4—134no—
279C4—264no—
280C4—522no—
281C4—521no—
282C4—1041no—
283C2—82no—
284C2#1311315511yescharacteristic
285C2#1311321512yes—
286C2#1311331912yes—
287C2D13×#32911yescharacteristic
288C2#1311349511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1270C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#1270D13
hypocenterC13#7567
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13114580C2semidirect
3. #13112661C2semidirect
29. #88190C8semidirect
227. C13#7567semidirect

Maximal subgroups

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

subgroupindex
#131173832
#131145802
#131126612
#131126572
C13×#12702
#756713