Finite Group Databasebeta

← #15756404

Subgroups — #15756404

Order 3328.

450 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 99 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#13117320C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112693C212yesmaximal, complemented
4#13112691C212yesmaximal, complemented
5C13×#1464C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×#88180C411yescharacteristic
8C22×C4×Dic13C411yescharacteristic
9C13×#432C2212yes—
10#11718646—21no—
11#11718646—21no—
12#11718611—21no—
13#11718611—21no—
14C4×C4⋊Dic13C411yescharacteristic
15C4×C4⋊Dic13C411yescharacteristic
16C4×C4⋊Dic13C2211yescharacteristic
17C4×C4⋊Dic13C2211yescharacteristic
18#11718587C2212yes—
19C13×#324—21no—
20C13×#323—21no—
21#11718120—21no—
22#11718117—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13—21no—
25C13×#117—22no—
26C13×#117—22no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C22⋊Dic13—21no—
34#88180—42no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13—42no—
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C13×C4⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×#97—22no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53C22⋊#1055—22no—
54C4⋊#1055—22no—
55#88043—22no—
56#8742—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
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—42no—
73C22×Dic13—42no—
74C22×Dic13—42no—
75C2×C8×C13—42no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C22⋊C4—22no—
79C13×C22⋊C4—22no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13#4112yes—
83C42×C13#4112yes—
84C22⋊Dic13—42no—
85C4⋊Dic13—42no—
86C4⋊Dic13—42no—
87C4⋊Dic13—42no—
88C4⋊Dic13—42no—
89C4⋊Dic13—42no—
90C4×Dic13—42no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93C4×Dic13—41no—
94C4×Dic13—41no—
95C2×#1055—42no—
96#2296—131no—
97#1464—131no—
98#1464D1311yescharacteristic
99#1285—132no—
100#1285—132no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13#10012yes—
106C23×C13C2×C22⋊C411yescharacteristic
107C2×C4×C13—24no—
108C2×C4×C13—24no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13#10112yes—
120C2×C4×C13#11711yescharacteristic
121C2×C4×C13#11711yescharacteristic
122C2×C4×C13#12312yes—
123C2×C4×C13#12312yes—
124C2×Dic13—22no—
125C2×Dic13—22no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—48no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C8×C13—82no—
138#1055—82no—
139C2×#117—131no—
140C2×#117C2×D1311yescharacteristic
141C22×C42—131no—
142#432—132no—
143#432C2×D1312yes—
144#389—261no—
145#389—261no—
146#385—261no—
147#385—261no—
148C4×C4⋊C4—131no—
149C4×C4⋊C4—131no—
150C4×C4⋊C4—131no—
151C4×C4⋊C4—131no—
152#324—21no—
153#324—261no—
154#323—21no—
155#323—261no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—22no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13#38111yescharacteristic
164C22×C13C2×#10011yescharacteristic
165C22×C13C2×#10111yescharacteristic
166C4×C13—22no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—41no—
172C4×C13—41no—
173Dic13—42no—
174Dic13—42no—
175Dic13—81no—
176Dic13—81no—
177C23×C4—261no—
178C23×C4C4×D1311yescharacteristic
179#117—22no—
180#117—22no—
181#117—522no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4D5211yescharacteristic
188C2×C4⋊C4C22⋊D1311yescharacteristic
189C2×C22⋊C4—261no—
190C2×C22⋊C4D5211yescharacteristic
191C2×C22⋊C4C22⋊D1311yescharacteristic
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—261no—
197C2×C42—522no—
198C2×C42C4×D1311yescharacteristic
199C2×C42C22×D1311yescharacteristic
200C4⋊C8—22no—
201C4⋊C8—262no—
202C22⋊C8—22no—
203C22⋊C8—262no—
204#97—22no—
205#97—262no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13—42no—
213C2×C13#182111yescharacteristic
214C2×C13#182711yescharacteristic
215C2×C13#182711yescharacteristic
216C24#610311yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—261no—
222C22×C4—261no—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4—522no—
226C22×C4—522no—
227C22×C4—522no—
228C22×C4#610311yescharacteristic
229C22×C4#610311yescharacteristic
230C22×C4#610311yescharacteristic
231C22×C4C2×C4×D1311yescharacteristic
232C22×C4C2×D5211yescharacteristic
233C22×C4C2×C22⋊D1311yescharacteristic
234C2×C8—42no—
235C2×C8—522no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—522no—
239C4⋊C4—522no—
240C4⋊C4—522no—
241C4⋊C4—522no—
242C4⋊C4—522no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—522no—
246C42—21no—
247C42—21no—
248C42—521no—
249C42—521no—
250C42—521no—
251C42—521no—
252C42—522no—
253C42#612912yes—
254C42#612912yes—
255C13#874211yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23#8806312yes—
261C23C2×#610311yescharacteristic
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—528no—
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#8806412yes—
288C2×C4#8813111yescharacteristic
289C2×C4#8813111yescharacteristic
290C2×C4#8814012yes—
291C2×C4#8818912yes—
292C8—82no—
293C8—1042no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#1171860411yescharacteristic
302C22C2×#8806311yescharacteristic
303C22C2×#8806411yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—22no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—522no—
312C4—522no—
313C4—1041no—
314C4—1041no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1311491411yescharacteristic
319C2#1311493711yescharacteristic
320C2#1311494111yescharacteristic
subgroupG/H
centerC22#11718604
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1464C2
socleC22×C13#381
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1464D13
hypocenterC13#8742
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13112693C2semidirect
4. #13112691C2semidirect
255. C13#8742semidirect

Maximal subgroups

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

subgroupindex
#131173202
#131131702
#131126932
#131126912
C13×#14642
#874213