Finite Group Databasebeta

← #15756385

Subgroups — #15756385

Order 3328.

418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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#13117439C211yesmaximal, characteristic
2C2×#11718120C211yesmaximal, characteristic
3#13112683C212yesmaximal
4#13112682C212yesmaximal
5C2×C13×#324C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×C13×C22⋊C8C2212yes—
8#11718873C411yescharacteristic
9#11718873C411yescharacteristic
10#11718872C411yescharacteristic
11#11718872C411yescharacteristic
12C4×C22⋊Dic13C2211yescharacteristic
13C4×C22⋊Dic13C2211yescharacteristic
14C2×C22⋊#1055C2212yes—
15#11718642—21no—
16#11718642—21no—
17#11718642—21no—
18#11718642—21no—
19C13×#324—21no—
20C13×#324—21no—
21#11718120—21no—
22#11718120—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C22×C8×C13—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C22⋊Dic13C2×C411yescharacteristic
34C2×C22⋊Dic13C2×C411yescharacteristic
35C2×C22⋊Dic13C2×C411yescharacteristic
36C2×C22⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C22×#1055—22no—
42C13×C22⋊C8—22no—
43C13×C22⋊C8—22no—
44#88071—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54#8737—131nomaximal, Sylow
55C24×C13C22×C411yescharacteristic
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—81no—
63C22×C4×C13—81no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4112yes—
71C22×C4×C13#4112yes—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C2×C8×C13—42no—
77C2×C8×C13—82no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C22⋊Dic13—22no—
83C22⋊Dic13—22no—
84C22⋊Dic13—22no—
85C22⋊Dic13—22no—
86C4⋊Dic13—81no—
87C4⋊Dic13—81no—
88C4×Dic13—81no—
89C4×Dic13—81no—
90C2×#1055—42no—
91C2×#1055—82no—
92#2313—131no—
93C2×#324—131no—
94C2×#324D1311yescharacteristic
95#1282—132no—
96#1282—132no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13C2×C22⋊C411yescharacteristic
100C23×C13#11711yescharacteristic
101C23×C13#11711yescharacteristic
102C23×C13#13112yes—
103C23×C13#13112yes—
104C2×C4×C13—21no—
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—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—81no—
121C2×C4×C13—81no—
122C2×C4×C13#12312yes—
123C2×C4×C13#12312yes—
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—41no—
135C2×Dic13—41no—
136C8×C13—82no—
137#1055—82no—
138C22×C4⋊C4C2×D1311yescharacteristic
139C2×C22⋊C8—132no—
140C2×C22⋊C8C2×D1312yes—
141#387—261no—
142#387—261no—
143#387—261no—
144#387—261no—
145#381—131no—
146#381—131no—
147#380—131no—
148#380—131no—
149C4×C22⋊C4—131no—
150C4×C22⋊C4—131no—
151#324—21no—
152#324—21no—
153#324—261no—
154#324—261no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—42no—
162C22×C13—42no—
163C22×C13#38111yescharacteristic
164C22×C13#40811yescharacteristic
165C22×C13#40811yescharacteristic
166C22×C13#43312yes—
167C22×C13#43312yes—
168C4×C13—22no—
169C4×C13—22no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174Dic13—81no—
175Dic13—81no—
176Dic13—81no—
177Dic13—81no—
178C23×C4C4×D1311yescharacteristic
179C23×C4C4×D1311yescharacteristic
180C23×C4C22×D1311yescharacteristic
181C22×C8—22no—
182C22×C8—262no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4D5211yescharacteristic
188C2×C4⋊C4D5211yescharacteristic
189C2×C4⋊C4C22⋊D1311yescharacteristic
190C2×C4⋊C4C22⋊D1311yescharacteristic
191C2×C22⋊C4—131no—
192C2×C22⋊C4—131no—
193C2×C22⋊C4—131no—
194C2×C22⋊C4—131no—
195C2×C42—261no—
196C2×C42—261no—
197C22⋊C8—22no—
198C22⋊C8—22no—
199C22⋊C8—262no—
200C22⋊C8—262no—
201#95—261no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209C2×C13—21no—
210C2×C13—21no—
211C2×C13—22no—
212C2×C13—22no—
213C2×C13#181811yescharacteristic
214C2×C13#182811yescharacteristic
215C2×C13#183011yescharacteristic
216C24C2×C4×D1311yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—81no—
224C22×C4—81no—
225C22×C4—261no—
226C22×C4—261no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4#610311yescharacteristic
230C22×C4#610311yescharacteristic
231C22×C4#610311yescharacteristic
232C22×C4#610311yescharacteristic
233C22×C4C2×D5211yescharacteristic
234C22×C4#612912yes—
235C22×C4#612912yes—
236C22×C4C2×C22⋊D1311yescharacteristic
237C2×C8—42no—
238C2×C8—82no—
239C2×C8—522no—
240C2×C8—1042no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—1041no—
246C4⋊C4—1041no—
247C22⋊C4—262no—
248C22⋊C4—262no—
249C22⋊C4—262no—
250C22⋊C4—262no—
251C42—1041no—
252C42—1041no—
253C13#873711yescharacteristic, complemented, Sylow
254C23—41no—
255C23—41no—
256C23#8813111yescharacteristic
257C23#8813111yescharacteristic
258C23#8815512yes—
259C23#8816112yes—
260C23C2×#610311yescharacteristic
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—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
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—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4#8814012yes—
292C2×C4#8818912yes—
293C8—82no—
294C8—1042no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—42no—
302C22—42no—
303C22#1171838112yes—
304C22#1171838112yes—
305C22#1171860411yescharacteristic
306C22#1171877111yescharacteristic
307C22#1171879011yescharacteristic
308C4—22no—
309C4—22no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—1041no—
315C4—1041no—
316C4—1041no—
317C4—1041no—
318C2—21no—
319C2—21no—
320C2—22no—
321C2—22no—
322C2#1311490511yescharacteristic
323C2#1311494211yescharacteristic
324C2#1311494811yescharacteristic
subgroupG/H
centerC22#11718604
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#324C2
socleC22×C13#381
cosocleC23×C4×C13C23
hypercenterC2×#324D13
hypocenterC13#8737
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
253. C13#8737semidirect

Maximal subgroups

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

subgroupindex
#131174392
C2×#117181202
#131126832
#131126822
C2×C13×#3242
#873713