Finite Group Databasebeta

← #15778072

Subgroups — #15778072

Order 3328.

470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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#13123533C211yesmaximal, characteristic
2#13116478C212yesmaximal
3#13114639C212yesmaximal, complemented
4#13112957C211yesmaximal, characteristic, complemented
5C13×#1392C211yesmaximal, characteristic, complemented
6#11719533C2211yescharacteristic
7C2×#88202C2211yescharacteristic
8C22×C8×D13C411yescharacteristic, complemented
9C13×#413C2212yes—
10C13×#408C2211yescharacteristic
11#11718901C2212yes—
12#11718787C411yescharacteristic, complemented
13#11718783—22no—
14#11718783C411yescharacteristic, complemented
15#11718763C411yescharacteristic, complemented
16#11718389—22no—
17#11718386—22no—
18#11718151—22no—
19#11718068C414yescomplemented
20#11718067C414yescomplemented
21C2×C13×#41C2311yescharacteristic
22C22×C4×D13C2×C411yescharacteristic
23C2×C13×M16—22no—
24C2×C13×M16C2×C411yescharacteristic
25C22×C8×C13C2×C411yescharacteristic
26#88202—41no—
27#88202—41no—
28#88200—21no—
29#88192—21no—
30#88191C2×C412yes—
31#88189C2×C412yes—
32C4×C22⋊D13—22no—
33#88180—22no—
34#88180C2×C411yescharacteristic
35C2×#6099C2×C411yescharacteristic
36C2×#6099D412yes—
37C22×#1055C2×C411yescharacteristic
38C22×#1055D412yes—
39C2×C8×D13—21no—
40C2×C8×D13—21no—
41C2×C8×D13—41no—
42C2×C8×D13—41no—
43C13×#101—22no—
44C13×#100C2×C414yes—
45C13×C22⋊C8—22no—
46#88074—22no—
47#88074C2×C414yes—
48#88060—22no—
49#88055—21no—
50#88055—42no—
51#88054—22no—
52C8×Dic13—21no—
53C8×Dic13—42no—
54#12623—131nomaximal, Sylow
55C23×D13C4211yescharacteristic
56C13×#41—41no—
57C13×#41—41no—
58C2×Q8×C13#4111yescharacteristic
59C2×D4×C13C22×C412yes—
60C2×D4×C13#4111yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D412yes—
63C2×C22⋊D13—22no—
64C22×Dic13C4211yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—41no—
68C2×C4×D13—41no—
69C13×M16—24no—
70C13×M16—42no—
71C13×M16—41no—
72C2×C8×C13—21no—
73C2×C8×C13—21no—
74C2×C8×C13—42no—
75C2×C8×C13—41no—
76C22⋊Dic13—22no—
77C22⋊Dic13—24no—
78C22⋊Dic13C4212yes—
79#6103—22no—
80C4⋊Dic13—21no—
81C4⋊Dic13—42no—
82#6101—22no—
83C4×Dic13—21no—
84C4×Dic13—42no—
85#6099—41no—
86#6099—42no—
87C2×#1055—21no—
88C2×#1055—21no—
89C2×#1055—22no—
90C2×#1055—22no—
91C2×#1055C22⋊C411yescharacteristic
92C2×#1055C22⋊C412yes—
93C2×#1055C22⋊C411yescharacteristic
94C8×D13—42no—
95C8×D13—41no—
96C8×D13—41no—
97#2929—131no—
98#2120—132no—
99#1757—132no—
100#1392D1311yescharacteristic, complemented
101#1391—131no—
102C23×C13C2×C4211yescharacteristic
103C23×C13C4×D412yes—
104C22×D13—21no—
105C22×D13—42no—
106C22×D13—41no—
107Q8×C13—41no—
108D4×C13—42no—
109D4×C13—41no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13#11711yescharacteristic
116C2×C4×C13C4×D412yes—
117C22⋊D13—44no—
118C2×Dic13—22no—
119C2×Dic13—21no—
120C2×Dic13—41no—
121C2×Dic13—44no—
122C4×D13—42no—
123C4×D13—41no—
124C4×D13—41no—
125C8×C13—44no—
126C8×C13—41no—
127C8×C13—41no—
128#1055—21no—
129#1055—22no—
130#1055#9911yescharacteristic
131#1055#9911yescharacteristic
132C2×#131—131no—
133C23×C8—131no—
134#525—131no—
135#435—262no—
136C8×D4—262no—
137#424—131no—
138#413C2×D1312yes—
139#410—132no—
140#408C2×D1311yescharacteristic
141#407—131no—
142#405—131no—
143#405—262no—
144#352—134no—
145AΣL(1,𝔽16)—134no—
146#344—262no—
147C22×C13—22no—
148C22×C13—21no—
149C22×C13—42no—
150C22×C13—41no—
151C22×C13C4×C22⋊C411yescharacteristic
152C2×D13—22no—
153C2×D13—41no—
154C2×D13—42no—
155C2×D13—41no—
156C2×D13—42no—
157C4×C13—22no—
158C4×C13—21no—
159C4×C13C2×#9911yescharacteristic
160C4×C13#41011yescharacteristic
161Dic13—42no—
162Dic13—41no—
163Dic13—84no—
164C2×#41C22×D1311yescharacteristic
165C23×C4—131no—
166#131—521no—
167#131—521no—
168C2×M16—22no—
169C2×M16—131no—
170C2×M16—132no—
171C2×M16C4×D1311yescharacteristic
172C22×C8—131no—
173C22×C8—132no—
174C22×C8—261no—
175C22×C8—261no—
176C22×C8—521no—
177C22×C8—521no—
178C22×C8C4×D1311yescharacteristic
179#123—132no—
180C22⋊Q8—261no—
181#121—261no—
182#120—132no—
183C4×D4—262no—
184#117—131no—
185#117—262no—
186C4⋊C8—262no—
187#101—22no—
188#100C4×D1314yes—
189#99—134no—
190#99—262no—
191C22⋊C8—22no—
192C22⋊C8—262no—
193#97—261no—
194#97—522no—
195C4×C8—261no—
196C4×C8—522no—
197C2×C13—21no—
198C2×C13—42no—
199C2×C13—41no—
200C2×C13C4×#9911yescharacteristic
201D13—42no—
202C24—131no—
203#41—41no—
204#41—41no—
205C2×Q8#612911yescharacteristic
206C2×D4—262no—
207C2×D4C2×C4×D1312yes—
208C2×D4#613111yescharacteristic
209C22×C4—131no—
210C22×C4—261no—
211C22×C4—261no—
212C22×C4—521no—
213C22×C4—521no—
214C22×C4C2×C4×D1311yescharacteristic
215C22×C4D4×D1312yes—
216M16—24no—
217M16—42no—
218M16—41no—
219M16—522no—
220M16—521no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—42no—
224C2×C8—41no—
225C2×C8—131no—
226C2×C8—131no—
227C2×C8—132no—
228C2×C8—262no—
229C2×C8—262no—
230C2×C8—261no—
231C2×C8—261no—
232C2×C8—521no—
233C2×C8—521no—
234C2×C8—522no—
235C4⋊C4—262no—
236C4⋊C4—261no—
237C4⋊C4—522no—
238C22⋊C4—132no—
239C22⋊C4—262no—
240C22⋊C4—262no—
241C22⋊C4—264no—
242C42—261no—
243C42—522no—
244C13#1262311yescharacteristic, complemented, Sylow
245C23—261no—
246C23—521no—
247C23—522no—
248C23C42×D1311yescharacteristic
249C23#8814712yes—
250Q8—41no—
251D4—42no—
252D4—41no—
253D4—524no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—262no—
259C2×C4—261no—
260C2×C4—522no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—524no—
265C2×C4C22⋊C4×D1311yescharacteristic
266C2×C4#8813512yes—
267C2×C4#8814611yescharacteristic
268C8—44no—
269C8—41no—
270C8—41no—
271C8—131no—
272C8—131no—
273C8—261no—
274C8—262no—
275C22—22no—
276C22—21no—
277C22—42no—
278C22—41no—
279C22—262no—
280C22—521no—
281C22—522no—
282C22—522no—
283C22—521no—
284C22#1171832711yescharacteristic
285C4—22no—
286C4—21no—
287C4—522no—
288C4—521no—
289C4—1044no—
290C4#1171840111yescharacteristic
291C4D13×#9911yescharacteristic
292C2—21no—
293C2—42no—
294C2—41no—
295C2—522no—
296C2#1311462311yescharacteristic
subgroupG/H
centerC4D13×#99
commutatorC23×C13C2×C42
FrattiniC2×#41C22×D13
FittingC13×#1392C2
socleC2×C13C4×#99
prime radical#11719533C22
cosocleC2×C13×#41C23
hypercenter#1392D13
hypocenterC13#12623
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1392

Complements

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

NH ≅ G/Ntype
3. #13114639C2semidirect
4. #13112957C2semidirect
5. C13×#1392C2semidirect
8. C22×C8×D13C4semidirect
12. #11718787C4semidirect
14. #11718783C4semidirect
15. #11718763C4semidirect
19. #11718068C4semidirect
20. #11718067C4semidirect
100. #1392D13semidirect
244. C13#12623semidirect

Maximal subgroups

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

subgroupindex
#131235332
#131164782
#131146392
#131129572
C13×#13922
#1262313