Finite Group Databasebeta

← #15773972

Subgroups — #15773972

Order 3328.

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

normal subgroups only

This group has 476 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#13119835C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic, complemented
3#13112838C214yesmaximal, complemented
4C13×#1801C211yesmaximal, characteristic, complemented
5C2×C4×Q8×C13C2211yescharacteristic
6C2×#88201—21no—
7C2×#88128C411yescharacteristic
8C13×#423—21no—
9C2×C13×#101—21no—
10#11718652C412yes—
11#11718652C2212yes—
12#11718649—21no—
13#11718600—21no—
14#11718600—21no—
15C4×C4⋊Dic13C411yescharacteristic
16#11718586—21no—
17C13×#343C2212yes—
18#11718120—21no—
19#11718120C2212yes—
20C22×Q8×C13D411yescharacteristic
21C22×D52—21no—
22C22×D52—21no—
23C22×D52C2×C412yes—
24C2×C13×M16—22no—
25C4×Q8×C13—41no—
26C4×Q8×C13—41no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4C2311yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33#88201—42no—
34#88201—42no—
35C2×#6103—22no—
36C2×#6103—22no—
37C2×#6103—22no—
38C2×#6103—22no—
39C2×C4⋊Dic13—21no—
40C2×C4×Dic13—21no—
41#88128—41no—
42#88128—41no—
43C13×C4⋊C8—41no—
44C13×C4⋊C8—41no—
45C13×#101—42no—
46#88071C2×C412yes—
47C22⋊#1055—22no—
48C4⋊#1055—41no—
49C4×#1055—41no—
50#11882—131nomaximal, Sylow
51C23×D13—22no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13D812yes—
55C2×Q8×C13SD1612yes—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—22no—
64C2×D52—42no—
65C2×D52—42no—
66C2×D52—42no—
67C2×D52—42no—
68C2×D52—42no—
69C2×D52—41no—
70C2×D52—41no—
71C2×D52—42no—
72C2×D52—82no—
73C13×M16—42no—
74C13×M16—42no—
75C2×C8×C13—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85#6103—44no—
86#6103—42no—
87#6103—42no—
88#6103—82no—
89#6103—82no—
90C4⋊Dic13—42no—
91C4×Dic13—42no—
92C2×#1055—42no—
93#2548—131no—
94#1801D1311yescharacteristic, complemented
95#1461—131no—
96#1345—134no—
97C23×C13C2×C22⋊C411yescharacteristic
98C22×D13—42no—
99C22×D13—42no—
100C22×D13—42no—
101C22×D13—42no—
102C22×D13—42no—
103C22×D13—42no—
104C22×D13—42no—
105Q8×C13—42no—
106Q8×C13—42no—
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—22no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#10212yes—
123C2×C4×C13#10212yes—
124C2×C4×C13C2×D811yescharacteristic
125C2×C4×C13C2×SD1611yescharacteristic
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129D52—82no—
130D52—84no—
131D52—84no—
132D52—82no—
133C8×C13—82no—
134#1055—82no—
135C2×#127—131no—
136C2×#124—261no—
137C2×C4×Q8C2×D1311yescharacteristic
138#431—261no—
139#423—21no—
140C2×#101—21no—
141#394—132no—
142#394—132no—
143#390—261no—
144#390—261no—
145#390—261no—
146C4×C4⋊C4—131no—
147#343C2×D1312yes—
148#324—132no—
149#324—261no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13C2×#9911yescharacteristic
153C22×C13C2×#10211yescharacteristic
154C22×C13#42111yescharacteristic
155C2×D13—82no—
156C2×D13—82no—
157C2×D13—82no—
158C2×D13—82no—
159C2×D13—82no—
160C2×D13—82no—
161C2×D13—82no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—22no—
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13#35512yes—
171Dic13—82no—
172C22×Q8C22⋊D1311yescharacteristic
173C22×D4—132no—
174C22×D4—261no—
175C22×D4—261no—
176C2×M16—22no—
177#127—521no—
178#127—521no—
179#124—522no—
180#124—522no—
181C4×Q8—41no—
182C4×Q8—41no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4C4×D1311yescharacteristic
185C2×C4⋊C4D5211yescharacteristic
186C2×C4⋊C4C22×D1311yescharacteristic
187C2×C22⋊C4—262no—
188C2×C22⋊C4—262no—
189C2×C22⋊C4—262no—
190C2×C22⋊C4—262no—
191C2×C42—261no—
192C2×C42C4×D1311yescharacteristic
193C2×C42D5211yescharacteristic
194C2×C42C22⋊D1311yescharacteristic
195C4⋊C8—41no—
196C4⋊C8—41no—
197C4⋊C8—521no—
198#101—42no—
199C22⋊C8—262no—
200C4×C8—521no—
201#95—132no—
202C2×C13—21no—
203C2×C13—21no—
204C2×C13#151911yescharacteristic
205C2×C13#212211yescharacteristic
206C2×C13C2×#35511yescharacteristic
207D13—162no—
208C24—262no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8#610412yes—
212C2×Q8#610612yes—
213C2×D4—522no—
214C2×D4—522no—
215C2×D4—522no—
216C2×D4—522no—
217C2×D4—522no—
218C2×D4—521no—
219C2×D4—521no—
220C2×D4—522no—
221C2×D4—1042no—
222C22×C4—262no—
223C22×C4#610311yescharacteristic
224C22×C4#610311yescharacteristic
225C22×C4#610311yescharacteristic
226C22×C4#610311yescharacteristic
227C22×C4C2×C4×D1311yescharacteristic
228C22×C4C2×D5211yescharacteristic
229C22×C4C2×C22⋊D1311yescharacteristic
230M16—42no—
231M16—42no—
232C2×C8—42no—
233C2×C8—522no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—522no—
238C22⋊C4—522no—
239C22⋊C4—522no—
240C22⋊C4—524no—
241C22⋊C4—1042no—
242C22⋊C4—1042no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—522no—
250C13#1188211yescharacteristic, complemented, Sylow
251C23—522no—
252C23—522no—
253C23—522no—
254C23—522no—
255C23—522no—
256C23—522no—
257C23—522no—
258C23C2×#610311yescharacteristic
259Q8—42no—
260Q8—42no—
261D4—1044no—
262D4—1042no—
263D4—1044no—
264D4—1042no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4#8804611yescharacteristic
282C2×C4#8804611yescharacteristic
283C2×C4#8804912yes—
284C2×C4#8804912yes—
285C2×C4C2×#610411yescharacteristic
286C2×C4C2×#610611yescharacteristic
287C8—82no—
288C8—1042no—
289C22—21no—
290C22—21no—
291C22—1042no—
292C22—1042no—
293C22—1042no—
294C22—1042no—
295C22—1042no—
296C22—1042no—
297C22—1042no—
298C22C2×#8804611yescharacteristic
299C22C2×#8804911yescharacteristic
300C22#1171866611yescharacteristic
301C4—21no—
302C4—21no—
303C4—22no—
304C4—22no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—1042no—
310C4#1171806912yes—
311C2—21no—
312C2—21no—
313C2—2082no—
314C2#1311340311yescharacteristic
315C2#1311648711yescharacteristic
316C2C2×#1171806911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1801C2
socleC22×C13C2×#99
prime radicalC2×#88128C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1801D13
hypocenterC13#11882
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. #13113160C2semidirect
3. #13112838C2semidirect
4. C13×#1801C2semidirect
94. #1801D13semidirect
250. C13#11882semidirect

Maximal subgroups

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

subgroupindex
#131198352
#131131602
#131128382
C13×#18012
#1188213