Finite Group Databasebeta

← #15773828

Subgroups — #15773828

Order 3328.

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

normal subgroups only

This group has 376 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#13120413C211yesmaximal, characteristic
2#13114919C211yesmaximal, characteristic
3#13112867C212yesmaximal, complemented
4#13112843C212yesmaximal, complemented
5C13×#1458C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×C4×Dic26C411yescharacteristic
8C13×#431—21no—
9#11718871—21no—
10#11718868—21no—
11#11718644C2211yescharacteristic
12#11718640C2211yescharacteristic
13#11718639—21no—
14#11718614C411yescharacteristic
15#11718608C411yescharacteristic
16#11718605—21no—
17#11718598C411yescharacteristic
18#11718594—21no—
19C13×#324C2212yes—
20C13×#323—21no—
21#11718122—21no—
22#11718122C2212yes—
23C23×C4×C13D411yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C13×#117—41no—
26C13×#117—41no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C13×C22⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13—21no—
40C2×#6099—22no—
41C4×Dic26—41no—
42C4×Dic26—41no—
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#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—41no—
55C22⋊#1055—41no—
56#11849—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—41no—
73C2×Dic26—42no—
74C2×C8×C13—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—41no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C22⋊Dic13—42no—
84C22⋊Dic13—42no—
85C4⋊Dic13—41no—
86#6101—42no—
87#6101—41no—
88#6101—41no—
89#6101—42no—
90C4×Dic13—42no—
91#6099—42no—
92#6099—42no—
93C2×#1055—42no—
94#2599—131no—
95#1822—131no—
96#1458D1311yescharacteristic
97#1354—132no—
98#1346—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#13512yes—
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—42no—
135Dic26—42no—
136C8×C13—82no—
137#1055—82no—
138C2×C4×Q8—131no—
139C2×#117C2×D1311yescharacteristic
140#431—21no—
141#407—261no—
142#398—131no—
143#397—131no—
144#395—131no—
145#393—131no—
146#388—261no—
147#387—261no—
148#387—261no—
149#385—261no—
150#383—131no—
151#343—132no—
152#343—261no—
153#324C2×D1312yes—
154#323—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—42no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—81no—
162C22×C13C2×#9911yescharacteristic
163C22×C13#41611yescharacteristic
164C22×C13#42111yescharacteristic
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172Dic13—42no—
173Dic13—81no—
174Dic13—81no—
175Dic13—81no—
176C22×Q8—131no—
177C23×C4D5211yescharacteristic
178C2×M16—262no—
179C4×Q8—521no—
180C4×Q8—521no—
181#117—41no—
182#117—41no—
183C2×C4⋊C4—131no—
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⋊C4—261no—
191C2×C22⋊C4C4×D1311yescharacteristic
192C2×C22⋊C4C22⋊D1311yescharacteristic
193C2×C42—261no—
194C2×C42C4×D1311yescharacteristic
195C2×C42C22⋊D1311yescharacteristic
196C4⋊C8—41no—
197C22⋊C8—22no—
198C22⋊C8—521no—
199C22⋊C8—521no—
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—261no—
209C2×C13—21no—
210C2×C13—21no—
211C2×C13—81no—
212C2×C13#151611yescharacteristic
213C2×C13#212011yescharacteristic
214C2×C13#213511yescharacteristic
215C24#610311yescharacteristic
216C2×Q8—521no—
217C2×Q8—522no—
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
232M16—522no—
233M16—522no—
234C2×C8—42no—
235C2×C8—522no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—521no—
239C4⋊C4—522no—
240C4⋊C4—522no—
241C4⋊C4—521no—
242C4⋊C4—521no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—522no—
246C22⋊C4—522no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—522no—
252C13#1184911yescharacteristic, complemented, Sylow
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×#610311yescharacteristic
259Q8—522no—
260Q8—522no—
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#8804611yescharacteristic
288C2×C4#8804611yescharacteristic
289C2×C4#8815812yes—
290C8—82no—
291C8—1042no—
292C22—21no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22C2×#8804611yescharacteristic
300C22#1171877411yescharacteristic
301C22#1171880011yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—522no—
310C4—1041no—
311C4—1041no—
312C4—1041no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2#1311339311yescharacteristic
317C2#1311647511yescharacteristic
318C2#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#11849
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
3. #13112867C2semidirect
4. #13112843C2semidirect
252. C13#11849semidirect

Maximal subgroups

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

subgroupindex
#131204132
#131149192
#131128672
#131128432
C13×#14582
#1184913