Finite Group Databasebeta

← #15772026

Subgroups — #15772026

Order 3328.

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

normal subgroups only

This group has 594 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#13117426C211yesmaximal, characteristic
2D13×#324C212yesmaximal, complemented
3#13112769C212yesmaximal, complemented
4#13112768C211yesmaximal, characteristic, complemented
5C13×#1318C211yesmaximal, characteristic, complemented
6C22×#6129C411yescharacteristic
7C2×C4⋊C4×D13C2211yescharacteristic
8C2×#88126C411yescharacteristic
9C13×#390C2211yescharacteristic
10#11718882C411yescharacteristic
11#11718635C2211yescharacteristic
12#11718617—22no—
13#11718603—22no—
14#11718590C411yescharacteristic
15D13×C22⋊C8—22no—
16C13×#324C2212yes—
17#11718120C2212yes—
18#11718061—22no—
19C22×D4×C13C2×C411yescharacteristic
20C22×C22⋊D13—21no—
21C23×Dic13—21no—
22C2×#6129—22no—
23C2×#6129—42no—
24C2×#6129—42no—
25C2×#6129C814yescomplemented
26C22×C4×D13C2×C411yescharacteristic
27C22×C4×D13D412yes—
28C22×Dic26C2×C411yescharacteristic
29C2×C13×C4⋊C4C2311yescharacteristic
30C2×C13×C22⋊C4—22no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C22⋊Dic13—22no—
33C2×#6103—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×#6101D412yes—
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C8×D13—42no—
39C4⋊C4×D13—42no—
40#88126—42no—
41C13×C22⋊C8—22no—
42#88071—22no—
43#88071—22no—
44C22⋊#1055—22no—
45#88060—42no—
46#11432—131nomaximal, Sylow
47C24×C13—21no—
48C23×D13C22⋊C411yescharacteristic
49C2×D4×C13—21no—
50C2×D4×C13—41no—
51C2×D4×C13—41no—
52C2×D4×C13C2×C812yescomplemented
53C22×C4×C13—21no—
54C22×C4×C13C22×C411yescharacteristic
55C22×C4×C13C2×D412yes—
56C2×C22⋊D13—24no—
57C2×C22⋊D13—42no—
58C2×C22⋊D13—42no—
59C22×Dic13—21no—
60C22×Dic13—24no—
61C22×Dic13—21no—
62C22×Dic13—42no—
63C22×Dic13—42no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C22⋊C412yes—
66#6129—48no—
67#6129—48no—
68C2×C4×D13—22no—
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—22no—
72C2×C4×D13—82no—
73C2×C4×D13C2×C812yes—
74C2×C4×D13M1612yes—
75C2×Dic26—21no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26C2×C812yescomplemented
79C2×C8×C13—42no—
80C13×C4⋊C4—41no—
81C13×C22⋊C4—82no—
82C42×C13—41no—
83C22⋊Dic13—82no—
84#6103—42no—
85C4⋊Dic13—41no—
86#6101—42no—
87#6101—42no—
88C4×Dic13—41no—
89C2×#1055—42no—
90C8×D13—84no—
91#2311—131no—
92C2×#324—132no—
93#1319—132no—
94#1318—131no—
95#1318D1311yescharacteristic, complemented
96C23×C13—22no—
97C23×C13—42no—
98C23×C13—42no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13C2×C22⋊C411yescharacteristic
102C22×D13—41no—
103C22×D13—41no—
104C22×D13C22⋊C812yes—
105C22×D13#9912yes—
106C22×D13#10012yes—
107D4×C13—42no—
108D4×C13—42no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13C22×C811yescharacteristic
117C2×C4×C13C2×M1611yescharacteristic
118C22⋊D13—48no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—22no—
122C2×Dic13—22no—
123C2×Dic13—48no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—42no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13C22⋊C812yes—
131C4×D13—24no—
132C4×D13—24no—
133C4×D13—44no—
134C4×D13—82no—
135Dic26—42no—
136Dic26—42no—
137C8×C13—82no—
138#1055—82no—
139C22×#41—131no—
140C2×#117—131no—
141C22×C4⋊C4—131no—
142C2×C22⋊C8—262no—
143#391—131no—
144#391—131no—
145#390—131no—
146#390C2×D1311yescharacteristic
147#386—262no—
148#380—262no—
149#324—132no—
150#324—262no—
151#324C2×D1312yes—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—44no—
155C22×C13—42no—
156C22×C13—82no—
157C22×C13—81no—
158C22×C13—81no—
159C22×C13C2×C22⋊C811yescharacteristic
160C22×C13C2×#9911yescharacteristic
161C22×C13C2×#10011yescharacteristic
162C2×D13—22no—
163C2×D13—22no—
164C2×D13—42no—
165C2×D13—42no—
166C2×D13#32314yes—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—42no—
170C4×C13—81no—
171Dic13—22no—
172Dic13—42no—
173Dic13—42no—
174Dic13—81no—
175C2×#41—134no—
176C2×#41—262no—
177C2×#41—522no—
178C2×#41—522no—
179C22×Q8—131no—
180C22×D4—261no—
181C22×D4C4×D1311yescharacteristic
182C23×C4—131no—
183C23×C4—132no—
184C23×C4—261no—
185C22×C8—522no—
186#117—522no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—132no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—522no—
191C2×C4⋊C4C22×D1311yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—261no—
194C2×C22⋊C4—262no—
195C2×C42—131no—
196C2×C42C4×D1311yescharacteristic
197C22⋊C8—22no—
198C22⋊C8—262no—
199C22⋊C8—522no—
200#95—262no—
201#95—262no—
202C2×C13—21no—
203C2×C13—21no—
204C2×C13—82no—
205C2×C13C2×#32311yescharacteristic
206C2×C13#212711yescharacteristic
207C2×C13#213311yescharacteristic
208D13—24no—
209C24—21no—
210C24—131no—
211#41—528no—
212#41—528no—
213C2×Q8—132no—
214C2×Q8—261no—
215C2×Q8—521no—
216C2×Q8—521no—
217C2×D4—21no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4—264no—
221C2×D4—522no—
222C2×D4—522no—
223C2×D4C8×D1312yescomplemented
224C22×C4—21no—
225C22×C4—131no—
226C22×C4—132no—
227C22×C4—132no—
228C22×C4—132no—
229C22×C4—262no—
230C22×C4—262no—
231C22×C4—262no—
232C22×C4—262no—
233C22×C4—264no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—522no—
237C22×C4—522no—
238C22×C4—1042no—
239C22×C4C2×C4×D1311yescharacteristic
240C22×C4D4×D1312yes—
241C2×C8—42no—
242C2×C8—522no—
243C2×C8—1044no—
244C4⋊C4—41no—
245C4⋊C4—522no—
246C4⋊C4—521no—
247C4⋊C4—522no—
248C22⋊C4—82no—
249C22⋊C4—522no—
250C22⋊C4—1042no—
251C42—41no—
252C42—521no—
253C13#1143211yescharacteristic, complemented, Sylow
254C23—22no—
255C23—42no—
256C23—42no—
257C23—41no—
258C23—41no—
259C23—132no—
260C23—132no—
261C23—132no—
262C23—521no—
263C23—521no—
264C23C22⋊C4×D1311yescharacteristic
265Q8—522no—
266Q8—522no—
267D4—42no—
268D4—42no—
269D4—528no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—132no—
278C2×C4—264no—
279C2×C4—264no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—262no—
283C2×C4—262no—
284C2×C4—524no—
285C2×C4—528no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—522no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—1042no—
293C2×C4C2×C8×D1311yescharacteristic
294C2×C4M16×D1311yescharacteristic
295C8—82no—
296C8—1042no—
297C22—21no—
298C22—21no—
299C22—44no—
300C22—42no—
301C22—82no—
302C22—81no—
303C22—81no—
304C22—134no—
305C22—262no—
306C22—262no—
307C22—522no—
308C22—522no—
309C22D13×C22⋊C811yescharacteristic
310C22D13×#9911yescharacteristic
311C22D13×#10011yescharacteristic
312C4—21no—
313C4—21no—
314C4—42no—
315C4—81no—
316C4—262no—
317C4—522no—
318C4—522no—
319C4—1041no—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—264no—
324C2D13×#32311yescharacteristic
325C2#1311650211yescharacteristic
326C2#1311652211yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1318C2
socleC22×C13C2×#99
prime radicalC22×#6129C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1318D13
hypocenterC13#11432
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. D13×#324C2semidirect
3. #13112769C2semidirect
4. #13112768C2semidirect
5. C13×#1318C2semidirect
25. C2×#6129C8semidirect
52. C2×D4×C13C2×C8semidirect
78. C2×Dic26C2×C8semidirect
95. #1318D13semidirect
223. C2×D4C8×D13semidirect
253. C13#11432semidirect

Maximal subgroups

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

subgroupindex
#131174262
D13×#3242
#131127692
#131127682
C13×#13182
#1143213