Finite Group Databasebeta

← #15773636

Subgroups — #15773636

Order 3328.

402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114913C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112860C212yesmaximal
4#13112857C212yesmaximal
5C13×#2396C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic, complemented
7C2×C13×#117C2211yescharacteristic
8C13×#400C411yescharacteristic, complemented
9C13×#399C2211yescharacteristic
10C13×#398—21no—
11C13×#396—21no—
12C13×#395C411yescharacteristic, complemented
13C13×#393C2211yescharacteristic
14C4×C13×C4⋊C4—21no—
15C4×C13×C4⋊C4C411yescharacteristic, complemented
16C4×C13×C22⋊C4—21no—
17#11718872—21no—
18#11718587—21no—
19#11718120—21no—
20#11718118—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C13×#117—41no—
28C13×#117—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C13×C22⋊C4C2311yescharacteristic
40C2×C42×C13—21no—
41C2×C42×C13—21no—
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C22⋊Dic13—22no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88071—41no—
52#88071—41no—
53C22⋊#1055—22no—
54C4⋊#1055—41no—
55#88043—41no—
56#11810—131nomaximal, Sylow
57C24×C13C2×D411yescharacteristic
58C2×Q8×C13—42no—
59C2×Q8×C13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—41no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—42no—
91C42×C13—41no—
92C42×C13—41no—
93C22⋊Dic13—42no—
94C22⋊Dic13—42no—
95C2×#1055—42no—
96#2396D1311yescharacteristic
97#1820—131no—
98#1464—131no—
99#1352—132no—
100#1351—132no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13C2×C22⋊C411yescharacteristic
106C23×C13#13712yes—
107Q8×C13—42no—
108Q8×C13—42no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13#9911yescharacteristic
137C2×C4×C13#9911yescharacteristic
138C2×Dic13—82no—
139C2×Dic13—82no—
140C2×Dic13—82no—
141#1055—82no—
142C2×C4×Q8Dic1311yescharacteristic, complemented
143C2×#117C2×D1311yescharacteristic
144#432—261no—
145#400Dic1311yescharacteristic, complemented
146#399C2×D1311yescharacteristic
147#398—21no—
148#396—21no—
149#395Dic1311yescharacteristic, complemented
150#393C2×D1311yescharacteristic
151#381—261no—
152C4×C4⋊C4—21no—
153C4×C4⋊C4Dic1311yescharacteristic, complemented
154C4×C22⋊C4—21no—
155#342—132no—
156#342—261no—
157#324—261no—
158#323—132no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—22no—
162C22×C13—42no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—81no—
166C22×C13C2×#9911yescharacteristic
167C22×C13#41911yescharacteristic
168C22×C13#42111yescharacteristic
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—42no—
172C4×C13—41no—
173C4×C13—42no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—81no—
179C4×C13—81no—
180Dic13—162no—
181C22×Q8C2×Dic1311yescharacteristic
182C23×C4C22⋊D1311yescharacteristic
183C4×Q8—41no—
184C4×Q8—41no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×Dic1311yescharacteristic
192C2×C4⋊C4C2×Dic1311yescharacteristic
193C2×C4⋊C4C22⋊D1311yescharacteristic
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—262no—
197C2×C22⋊C4C22⋊D1311yescharacteristic
198C2×C22⋊C4C22×D1311yescharacteristic
199C2×C42—21no—
200C2×C42—21no—
201C2×C42C2×Dic1311yescharacteristic
202C2×C42C22⋊D1311yescharacteristic
203C4⋊C8—521no—
204C22⋊C8—262no—
205#97—521no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—521no—
211#95—521no—
212#95C2×Dic1311yescharacteristic
213#95C2×Dic1311yescharacteristic
214C2×C13—21no—
215C2×C13—21no—
216C2×C13—42no—
217C2×C13#151111yescharacteristic
218C2×C13#212011yescharacteristic
219C2×C13#212611yescharacteristic
220C24C2×C22⋊D1311yescharacteristic
221C2×Q8—42no—
222C2×Q8—41no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—41no—
231C22×C4—522no—
232C22×C4C22⋊Dic1311yescharacteristic
233C22×C4C22⋊Dic1311yescharacteristic
234C22×C4C22⋊Dic1311yescharacteristic
235C22×C4C22⋊Dic1311yescharacteristic
236C22×C4C22×Dic1311yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238C2×C8—522no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—522no—
251C22⋊C4—522no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—42no—
257C42—41no—
258C42—41no—
259C13#1181011yescharacteristic, complemented, Sylow
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23#8819612yes—
265C23C2×C22⋊Dic1311yescharacteristic
266Q8—42no—
267Q8—42no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—1042no—
296C2×C4—1042no—
297C2×C4—1042no—
298C2×C4#8807411yescharacteristic
299C2×C4#8807411yescharacteristic
300C8—1042no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22C2×#8807411yescharacteristic
309C22#1171888611yescharacteristic
310C22#1171889711yescharacteristic
311C4—21no—
312C4—21no—
313C4—42no—
314C4—41no—
315C4—41no—
316C4—42no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—81no—
321C4—81no—
322C4—2082no—
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1311336911yescharacteristic
327C2#1311647711yescharacteristic
328C2#1311650111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2396C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2396D13
hypocenterC13#11810
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2396

Complements

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

NH ≅ G/Ntype
6. C2×C4×Q8×C13C4semidirect
8. C13×#400C4semidirect
12. C13×#395C4semidirect
15. C4×C13×C4⋊C4C4semidirect
142. C2×C4×Q8Dic13semidirect
145. #400Dic13semidirect
149. #395Dic13semidirect
153. C4×C4⋊C4Dic13semidirect
259. C13#11810semidirect

Maximal subgroups

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

subgroupindex
#131149132
#131131702
#131128602
#131128572
C13×#23962
#1181013