Finite Group Databasebeta

← #15772471

Subgroups — #15772471

Order 3328.

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

normal subgroups only

This group has 380 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#13119119C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic
3#13112783C212yesmaximal
4#13112765C212yesmaximal
5C13×#1464C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C22×#6101C411yescharacteristic
8C13×#432—21no—
9#11718872C411yescharacteristic
10#11718643—21no—
11#11718641—21no—
12#11718607C411yescharacteristic
13#11718607C2211yescharacteristic
14#11718604C411yescharacteristic
15#11718604C2211yescharacteristic
16#11718594—21no—
17#11718594—21no—
18#11718586—21no—
19C13×#324—21no—
20C13×#323C2212yes—
21#11718120—21no—
22#11718117C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13C2×C411yescharacteristic
25C23×Dic13C2×C411yescharacteristic
26C13×#117—41no—
27C13×#117—41no—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4C2311yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C22⋊Dic13C2×C411yescharacteristic
35C2×C22⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—41no—
41C2×#6101—41no—
42C13×C4⋊C8—41no—
43C13×C22⋊C8—22no—
44C13×#97—41no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53C22⋊#1055—22no—
54C4⋊#1055—41no—
55C4×#1055—41no—
56#11548—131nomaximal, Sylow
57C24×C13C22×C411yescharacteristic
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×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—22no—
73C22×Dic13—42no—
74C22×Dic13—41no—
75C22×Dic13—41no—
76C22×Dic13—41no—
77C2×C8×C13—42no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C22⋊Dic13—22no—
87C22⋊Dic13—41no—
88#6101—42no—
89#6101—42no—
90#6101—42no—
91#6101—41no—
92#6101—41no—
93C2×#1055—42no—
94#2484—131no—
95#1464D1311yescharacteristic
96#1458—131no—
97#1326—132no—
98#1317—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13#13112yes—
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—42no—
125C2×Dic13—41no—
126C2×Dic13—42no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—82no—
137C8×C13—82no—
138#1055—82no—
139C2×#117C2×D1311yescharacteristic
140C22×C4⋊C4—131no—
141#432—21no—
142#431—261no—
143#400—261no—
144#398—261no—
145#387—261no—
146#387—261no—
147#385—131no—
148#385—131no—
149#381—131no—
150#381—131no—
151#381—131no—
152#324—21no—
153#324—261no—
154#323—132no—
155#323C2×D1312yes—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—22no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13#40811yescharacteristic
164C22×C13C2×#9911yescharacteristic
165C22×C13#41311yescharacteristic
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173Dic13—42no—
174Dic13—81no—
175Dic13—81no—
176Dic13—81no—
177C23×C4—131no—
178C23×C4—131no—
179C23×C4C4×D1311yescharacteristic
180#117—41no—
181#117—41no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—521no—
187C2×C4⋊C4—521no—
188C2×C4⋊C4D5211yescharacteristic
189C2×C4⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4—131no—
191C2×C22⋊C4—131no—
192C2×C22⋊C4C4×D1311yescharacteristic
193C2×C22⋊C4C22×D1311yescharacteristic
194C2×C42D5211yescharacteristic
195C2×C42C22⋊D1311yescharacteristic
196C4⋊C8—41no—
197C4⋊C8—521no—
198C22⋊C8—22no—
199C22⋊C8—262no—
200#97—41no—
201C4×C8—521no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13—42no—
213C2×C13#146811yescharacteristic
214C2×C13#212011yescharacteristic
215C2×C13#212311yescharacteristic
216C24C2×C4×D1311yescharacteristic
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—262no—
226C22×C4—522no—
227C22×C4—521no—
228C22×C4—521no—
229C22×C4—521no—
230C22×C4#610311yescharacteristic
231C22×C4#610311yescharacteristic
232C22×C4#610311yescharacteristic
233C22×C4#610311yescharacteristic
234C22×C4C2×D5211yescharacteristic
235C22×C4C2×C22⋊D1311yescharacteristic
236C2×C8—42no—
237C2×C8—522no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—522no—
241C4⋊C4—522no—
242C4⋊C4—522no—
243C4⋊C4—521no—
244C4⋊C4—521no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—262no—
248C22⋊C4—521no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C13#1154811yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23#8816112yes—
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—522no—
278C2×C4—521no—
279C2×C4—522no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—1042no—
290C2×C4#8804611yescharacteristic
291C2×C4#8804611yescharacteristic
292C8—82no—
293C8—1042no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22C2×#8804611yescharacteristic
302C22#1171879011yescharacteristic
303C22#1171879311yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—522no—
312C4—1041no—
313C4—1041no—
314C4—1041no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1311318511yescharacteristic
319C2#1311647511yescharacteristic
320C2#1311649111yescharacteristic
subgroupG/H
centerC22C2×#88046
commutator, prime radicalC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1464C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#1464D13
hypocenterC13#11548
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
253. C13#11548semidirect

Maximal subgroups

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

subgroupindex
#131191192
#131131502
#131127832
#131127652
C13×#14642
#1154813