Finite Group Databasebeta

← #15772488

Subgroups — #15772488

Order 3328.

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

normal subgroups only

This group has 366 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#13119285C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112781C212yesmaximal, complemented
4#13112769C212yesmaximal, complemented
5C13×#1458C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×#88178C411yescharacteristic
8C13×#431—21no—
9C4×C22⋊Dic13C411yescharacteristic
10#11718638C411yescharacteristic
11#11718637C2211yescharacteristic
12#11718635C411yescharacteristic
13#11718635C2211yescharacteristic
14#11718613—21no—
15#11718613—21no—
16#11718594—21no—
17#11718594—21no—
18#11718587—21no—
19C13×#324C2212yes—
20C13×#323—21no—
21#11718120C2212yes—
22#11718117—21no—
23C23×C4×C13C2×C411yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C13×#117—41no—
26C13×#117—41no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36#88178—41no—
37#88178—41no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C13×C4⋊C8—41no—
44C13×C22⋊C8—22no—
45C4×C8×C13—41no—
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—
55#88043—41no—
56#11552—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
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—
72C2×Dic26—22no—
73C2×Dic26—41no—
74C2×Dic26—41no—
75C2×C8×C13—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—41no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C22⋊Dic13—42no—
85C22⋊Dic13—42no—
86C4⋊Dic13—41no—
87#6101—42no—
88#6101—42no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—22no—
92C4×Dic13—41no—
93C2×#1055—42no—
94#2499—131no—
95#1464—131no—
96#1458D1311yescharacteristic
97#1325—132no—
98#1319—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13C2×C22⋊C411yescharacteristic
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—42no—
114C2×C4×C13—42no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13#9911yescharacteristic
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#13112yes—
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—
134Dic26—82no—
135C8×C13—82no—
136#1055—82no—
137C2×C22⋊Q8—131no—
138C2×#117C2×D1311yescharacteristic
139#432—261no—
140#431—21no—
141#397—261no—
142#397—261no—
143#391—131no—
144#391—131no—
145#387—261no—
146#387—261no—
147#384—131no—
148#382—131no—
149C4×C22⋊C4—131no—
150#324—132no—
151#324C2×D1312yes—
152#323—21no—
153#323—261no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—81no—
160C22×C13—81no—
161C22×C13#40811yescharacteristic
162C22×C13C2×#9911yescharacteristic
163C22×C13#41311yescharacteristic
164C4×C13—22no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171Dic13—42no—
172Dic13—81no—
173Dic13—81no—
174Dic13—81no—
175C22×Q8—131no—
176C23×C4C4×D1311yescharacteristic
177C22⋊Q8—521no—
178C22⋊Q8—521no—
179#117—41no—
180#117—41no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4C4×D1311yescharacteristic
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C22⋊C4—261no—
188C2×C22⋊C4—261no—
189C2×C22⋊C4D5211yescharacteristic
190C2×C22⋊C4C22⋊D1311yescharacteristic
191C2×C42—131no—
192C2×C42—131no—
193C2×C42D5211yescharacteristic
194C2×C42C22⋊D1311yescharacteristic
195C4⋊C8—41no—
196C4⋊C8—521no—
197C22⋊C8—22no—
198C22⋊C8—262no—
199#97—521no—
200C4×C8—41no—
201#95—261no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—81no—
211C2×C13#146811yescharacteristic
212C2×C13#212611yescharacteristic
213C2×C13#213511yescharacteristic
214C24#610311yescharacteristic
215C2×Q8—262no—
216C2×Q8—521no—
217C2×Q8—521no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—261no—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4—261no—
226C22×C4#610311yescharacteristic
227C22×C4#610311yescharacteristic
228C22×C4#610311yescharacteristic
229C22×C4C2×C4×D1311yescharacteristic
230C22×C4C2×D5211yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232C2×C8—42no—
233C2×C8—522no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—521no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C4⋊C4—521no—
240C4⋊C4—521no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—522no—
244C22⋊C4—522no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—262no—
250C42—521no—
251C13#1155211yescharacteristic, complemented, Sylow
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23C2×#610311yescharacteristic
258Q8—1042no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—262no—
274C2×C4—521no—
275C2×C4—521no—
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#8804611yescharacteristic
286C2×C4#8804611yescharacteristic
287C2×C4#8815512yes—
288C8—82no—
289C8—1042no—
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22C2×#8804611yescharacteristic
298C22#1171877111yescharacteristic
299C22#1171879311yescharacteristic
300C4—22no—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—522no—
308C4—1041no—
309C4—1041no—
310C4—1041no—
311C2—21no—
312C2—21no—
313C2—81no—
314C2#1311318211yescharacteristic
315C2#1311649911yescharacteristic
316C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1458C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1458D13
hypocenterC13#11552
LCSG ▷ C22×C4×C13 ▷ C22×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
3. #13112781C2semidirect
4. #13112769C2semidirect
251. C13#11552semidirect

Maximal subgroups

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

subgroupindex
#131192852
#131131702
#131127812
#131127692
C13×#14582
#1155213