Finite Group Databasebeta

← #15773813

Subgroups — #15773813

Order 3328.

382 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 79 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#13120534C211yesmaximal, characteristic
2#13114913C211yesmaximal, characteristic
3#13112861C212yesmaximal
4#13112837C212yesmaximal
5C13×#1458C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×#88124C411yescharacteristic, complemented
8C13×#431—21no—
9#11718872—21no—
10#11718871—21no—
11#11718647C411yescharacteristic, complemented
12#11718644C411yescharacteristic, complemented
13#11718633—21no—
14#11718614C2211yescharacteristic
15#11718610C2211yescharacteristic
16#11718606—21no—
17#11718594—21no—
18#11718593C411yescharacteristic, complemented
19C13×#324—21no—
20C13×#323C2212yes—
21#11718118—21no—
22#11718118C2212yes—
23C23×C4×C13D411yescharacteristic
24C13×#117—41no—
25C13×#117—41no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C22⋊C4D411yescharacteristic
29C2×C13×C22⋊C4C2311yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—22no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42#88124—41no—
43#88124—41no—
44C13×C4⋊C8—41no—
45C13×C22⋊C8—22no—
46C4×C8×C13—41no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—41no—
53#88071—41no—
54#88071C2×C411yescharacteristic
55#88071C2×C411yescharacteristic
56#11846—131nomaximal, Sylow
57C24×C13C2×D411yescharacteristic
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—41no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—42no—
73C2×C8×C13—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—41no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C22⋊Dic13—42no—
83C22⋊Dic13—42no—
84C22⋊Dic13—42no—
85C22⋊Dic13—42no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88#6101—42no—
89#6101—42no—
90#6101—42no—
91#6101—41no—
92#6101—41no—
93C4×Dic13—42no—
94#2611—131no—
95#1820—131no—
96#1458D1311yescharacteristic
97#1352—132no—
98#1344—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13#13512yes—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#9911yescharacteristic
122C2×Dic13—22no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—82no—
135C2×Dic13—82no—
136C2×Dic13—82no—
137C8×C13—82no—
138C2×#125—131no—
139C2×#117C2×D1311yescharacteristic
140#431—21no—
141#400—131no—
142#399—131no—
143#398—131no—
144#397—131no—
145#389—261no—
146#388—261no—
147#387—261no—
148#385—261no—
149#381—261no—
150#376—131no—
151#342—132no—
152#342—261no—
153#324—21no—
154#323C2×D1312yes—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—22no—
158C22×C13—42no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—81no—
162C22×C13C2×#9911yescharacteristic
163C22×C13#41611yescharacteristic
164C22×C13#42111yescharacteristic
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172Dic13—42no—
173Dic13—81no—
174Dic13—81no—
175Dic13—81no—
176Dic13—162no—
177C23×C4D5211yescharacteristic
178#125—521no—
179#125—521no—
180#117—41no—
181#117—41no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4C4×D1311yescharacteristic
189C2×C4⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4—261no—
191C2×C22⋊C4—261no—
192C2×C22⋊C4—262no—
193C2×C22⋊C4D5211yescharacteristic
194C2×C22⋊C4C22×D1311yescharacteristic
195C2×C42—261no—
196C2×C42C4×D1311yescharacteristic
197C2×C42C22⋊D1311yescharacteristic
198C4⋊C8—41no—
199C22⋊C8—22no—
200C4×C8—41no—
201#95—131no—
202#95—131no—
203#95—261no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—521no—
209#95—521no—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13—42no—
213C2×C13#151611yescharacteristic
214C2×C13#212311yescharacteristic
215C2×C13#212611yescharacteristic
216C24C2×D5211yescharacteristic
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4—261no—
222C22×C4—261no—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4—522no—
226C22×C4#610311yescharacteristic
227C22×C4#610311yescharacteristic
228C22×C4#610311yescharacteristic
229C22×C4#610311yescharacteristic
230C22×C4C2×C4×D1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232C2×C8—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C4⋊C4—522no—
240C4⋊C4—521no—
241C4⋊C4—521no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—522no—
245C22⋊C4—522no—
246C22⋊C4—522no—
247C22⋊C4—522no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—522no—
253C13#1184611yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23#8815812yes—
259C23C2×#610311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—262no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—1042no—
288C2×C4—1042no—
289C2×C4—1042no—
290C2×C4#8804611yescharacteristic
291C2×C4#8804611yescharacteristic
292C8—82no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22C2×#8804611yescharacteristic
301C22#1171877411yescharacteristic
302C22#1171880011yescharacteristic
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—522no—
311C4—1041no—
312C4—1041no—
313C4—1041no—
314C4—2082no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1311339311yescharacteristic
319C2#1311649111yescharacteristic
320C2#1311649911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1458C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1458D13
hypocenterC13#11846
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
7. C2×#88124C4semidirect
11. #11718647C4semidirect
12. #11718644C4semidirect
18. #11718593C4semidirect
253. C13#11846semidirect

Maximal subgroups

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

subgroupindex
#131205342
#131149132
#131128612
#131128372
C13×#14582
#1184613