Finite Group Databasebeta

← #15776853

Subgroups — #15776853

Order 3328.

302 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 67 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#13117072C211yesmaximal, characteristic, complemented
2#13116983C211yesmaximal, characteristic, complemented
3#13114354C211yesmaximal, characteristic, complemented
4#13112879C211yesmaximal, characteristic, complemented
5#13112818C211yesmaximal, characteristic, complemented
6#13112803C211yesmaximal, characteristic, complemented
7C13×#3403C211yesmaximal, characteristic
8C13×#559—21no—
9C13×#496—21no—
10C13×#495C2211yescharacteristic
11C13×#464—21no—
12C13×#463—21no—
13C13×#459—21no—
14C13×#446C2211yescharacteristic
15C13×#440—21no—
16C4×C13×D8C2211yescharacteristic
17#11718692—21no—
18#11718343C2211yescharacteristic
19#11718156—21no—
20#11718154—21no—
21#11718154—21no—
22#11718082—21no—
23#11718078—21no—
24C4⋊#6090C2211yescharacteristic
25#11718053C2211yescharacteristic
26#11718049C2211yescharacteristic
27C2×C13×Q16D411yescharacteristic
28C2×C13×SD16—21no—
29C2×C13×SD16—21no—
30C2×C13×D8—21no—
31C2×C13×D8D411yescharacteristic
32C2×C13×D8D411yescharacteristic
33C13×#127—21no—
34C13×#124—21no—
35C13×#124—21no—
36C13×#124—41no—
37C13×#123—41no—
38C13×#123—41no—
39C4×Q8×C13—21no—
40C4×Q8×C13D411yescharacteristic
41C4×D4×C13—21no—
42C4×D4×C13—21no—
43C4×D4×C13—41no—
44C2×#6107—41no—
45#88123—21no—
46C13×#107D411yescharacteristic
47C13×C4⋊C8—21no—
48C13×C4⋊C8D411yescharacteristic
49C13×#103—21no—
50C13×#102—21no—
51C13×#102—21no—
52C13×#97—21no—
53C4×C8×C13C2311yescharacteristic
54#88058—21no—
55#88058—21no—
56C2×#6090—21no—
57C2×#6090—21no—
58#88050—41no—
59C4⋊#1055—21no—
60#12390—131nomaximal, Sylow
61C2×Q8×C13—21no—
62C2×Q8×C13D811yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C2×Dic26—41no—
70C13×Q16—41no—
71C13×SD16—41no—
72C13×SD16—41no—
73C13×SD16—81no—
74C13×D8—21no—
75C13×D8—21no—
76C13×D8—41no—
77C13×D8—81no—
78C2×C8×C13—21no—
79C2×C8×C13C2×D411yescharacteristic
80C2×C8×C13C2×D411yescharacteristic
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4D811yescharacteristic
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C42×C13—21no—
92C42×C13—41no—
93C42×C13C2×D411yescharacteristic
94#6107—82no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97C2×#1055—41no—
98#6090—41no—
99#6090—41no—
100#3403D1311yescharacteristic
101#2243—131no—
102#2226—131no—
103#1694—131no—
104#1360—131no—
105#1338—131no—
106#1333—131no—
107C23×C13—41no—
108C23×C13—41no—
109Q8×C13—41no—
110Q8×C13—41no—
111Q8×C13—41no—
112D4×C13—41no—
113D4×C13—41no—
114D4×C13—41no—
115D4×C13—41no—
116D4×C13—82no—
117D4×C13—161no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—161no—
123C2×C4×C13—161no—
124C2×C4×C13#12011yescharacteristic
125C2×C4×C13C2×D811yescharacteristic
126C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
127C2×Dic13—81no—
128Dic26—81no—
129Dic26—81no—
130C8×C13—21no—
131C8×C13—41no—
132C8×C13#13511yescharacteristic
133C8×C13#13711yescharacteristic
134#1055—81no—
135#559—21no—
136#500—131no—
137#496—21no—
138#495C2×D1311yescharacteristic
139#464—21no—
140#463—21no—
141#462—261no—
142#459—21no—
143#446C2×D1311yescharacteristic
144#440—21no—
145C4×D8C2×D1311yescharacteristic
146#367—261no—
147C4⋊C16—131no—
148#358—261no—
149#357—261no—
150#357—261no—
151#346—131no—
152#334—131no—
153#332—261no—
154C22×C13—81no—
155C22×C13—81no—
156C22×C13—81no—
157C22×C13—81no—
158C22×C13—81no—
159C22×C13—81no—
160C22×C13#44711yescharacteristic
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—81no—
166C4×C13—81no—
167C4×C13#45211yescharacteristic
168C4×C13#45511yescharacteristic
169Dic13—161no—
170C2×Q16—521no—
171C2×Q16C22⋊D1311yescharacteristic
172C2×SD16—21no—
173C2×SD16—21no—
174C2×D8—21no—
175C2×D8C22⋊D1311yescharacteristic
176C2×D8C22⋊D1311yescharacteristic
177C4⋊Q8—261no—
178#127—21no—
179#124—21no—
180#124—21no—
181#124—41no—
182#123—41no—
183#123—41no—
184C4×Q8—21no—
185C4×Q8C22⋊D1311yescharacteristic
186C4×D4—21no—
187C4×D4—21no—
188C4×D4—41no—
189C2×C16—261no—
190C2×C16—261no—
191#107—261no—
192#107—261no—
193#107C22⋊D1311yescharacteristic
194C4⋊C8—21no—
195C4⋊C8—261no—
196C4⋊C8C22⋊D1311yescharacteristic
197#103—21no—
198#103—521no—
199#102—21no—
200#102—21no—
201#97—21no—
202C4×C8C22×D1311yescharacteristic
203C2×C13—161no—
204C2×C13—161no—
205C2×C13#164111yescharacteristic
206C2×C13#219011yescharacteristic
207C2×C13#219411yescharacteristic
208C2×Q8—21no—
209C2×Q8—521no—
210C2×Q8#610411yescharacteristic
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—41no—
214C2×D4—41no—
215C22×C4—41no—
216C22×C4—41no—
217Q16—41no—
218Q16—1042no—
219SD16—41no—
220SD16—41no—
221SD16—81no—
222D8—21no—
223D8—21no—
224D8—41no—
225D8—81no—
226C2×C8—21no—
227C2×C8—521no—
228C2×C8C2×C22⋊D1311yescharacteristic
229C2×C8C2×C22⋊D1311yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—521no—
234C4⋊C4—521no—
235C4⋊C4#610411yescharacteristic
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C42—21no—
243C42—41no—
244C42C2×C22⋊D1311yescharacteristic
245C16—521no—
246C16—521no—
247C13#1239011yescharacteristic, complemented, Sylow
248C23—41no—
249C23—41no—
250Q8—41no—
251Q8—41no—
252Q8—41no—
253Q8—1041no—
254Q8—1041no—
255D4—41no—
256D4—41no—
257D4—41no—
258D4—41no—
259D4—82no—
260D4—161no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—161no—
266C2×C4—161no—
267C2×C4—1041no—
268C2×C4C2×#610411yescharacteristic
269C2×C4#8818611yescharacteristic
270C2×C4#8820711yescharacteristic
271C8—21no—
272C8—41no—
273C8—1041no—
274C8#8820411yescharacteristic
275C8#8820511yescharacteristic
276C22—81no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22—81no—
282C22#1171887811yescharacteristic
283C4—21no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—81no—
288C4—81no—
289C4—2081no—
290C4#1171890011yescharacteristic
291C4#1171890311yescharacteristic
292C2—161no—
293C2—161no—
294C2#1311402911yescharacteristic
295C2#1311678211yescharacteristic
296C2#1311680711yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
Fitting, prime radicalC13×#3403C2
socleC22×C13#447
hypercenter#3403D13
hypocenterC13#12390
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #3403

Complements

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

NH ≅ G/Ntype
1. #13117072C2semidirect
2. #13116983C2semidirect
3. #13114354C2semidirect
4. #13112879C2semidirect
5. #13112818C2semidirect
6. #13112803C2semidirect
247. C13#12390semidirect

Maximal subgroups

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

subgroupindex
#131170722
#131169832
#131143542
#131128792
#131128182
#131128032
C13×#34032
#1239013