Finite Group Databasebeta

← #15776776

Subgroups — #15776776

Order 3328.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#13116988C211yesmaximal, characteristic, complemented
3#13114349C211yesmaximal, characteristic, complemented
4#13112879C211yesmaximal, characteristic, complemented
5#13112806C211yesmaximal, characteristic, complemented
6#13112794C211yesmaximal, characteristic, complemented
7C13×#3277C211yesmaximal, characteristic
8C2×C13×#137—21no—
9C13×#548—21no—
10C13×#495C2211yescharacteristic
11C13×#468—21no—
12C13×#464—21no—
13C13×#451—21no—
14C13×#449—21no—
15C4×C13×Q16C2211yescharacteristic
16C13×#436C2211yescharacteristic
17#11718680—21no—
18#11718343C2211yescharacteristic
19#11718156—21no—
20#11718156—21no—
21#11718154—21no—
22#11718081—21no—
23#11718078—21no—
24C4⋊#6090C2211yescharacteristic
25#11718053C2211yescharacteristic
26#11718049C2211yescharacteristic
27C2×C13×#41—21no—
28C22×Q8×C13—21no—
29C13×#137—42no—
30C13×#137—42no—
31C2×C13×Q16—21no—
32C2×C13×Q16D411yescharacteristic
33C2×C13×Q16D411yescharacteristic
34C2×C13×SD16—21no—
35C2×C13×SD16—21no—
36C2×C13×D8D411yescharacteristic
37C2×C13×M16—21no—
38C13×#124—21no—
39C13×#124—41no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—41no—
42C13×#121—21no—
43C13×#121—41no—
44C4×Q8×C13—21no—
45C4×D4×C13—41no—
46C4×D4×C13D411yescharacteristic
47C2×#6105—41no—
48#88123—21no—
49C13×#107D411yescharacteristic
50C13×C4⋊C8D411yescharacteristic
51C13×#103—21no—
52C13×#103—21no—
53C13×#102—21no—
54C13×C22⋊C8—21no—
55C4×C8×C13C2311yescharacteristic
56#88058—21no—
57#88058—21no—
58C2×#6090—21no—
59C2×#6090—21no—
60#88050—41no—
61C4⋊#1055—21no—
62#12379—131nomaximal, Sylow
63C13×#41—42no—
64C13×#41—81no—
65C2×Q8×C13—21no—
66C2×Q8×C13—21no—
67C2×Q8×C13—41no—
68C2×Q8×C13—42no—
69C2×Q8×C13—81no—
70C2×D4×C13—21no—
71C2×D4×C13—41no—
72C2×D4×C13—41no—
73C2×D4×C13D811yescharacteristic
74C22×C4×C13—21no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C2×Dic26—41no—
78C13×Q16—21no—
79C13×Q16—41no—
80C13×Q16—42no—
81C13×Q16SD1612yescomplemented
82C13×SD16—42no—
83C13×SD16—41no—
84C13×SD16—41no—
85C13×D8—41no—
86C13×M16—41no—
87C13×M16—41no—
88C2×C8×C13—21no—
89C2×C8×C13C2×D411yescharacteristic
90C2×C8×C13C2×D411yescharacteristic
91C13×C4⋊C4—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4D811yescharacteristic
95C13×C22⋊C4—21no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C42×C13—41no—
101C42×C13C2×D411yescharacteristic
102#6105—82no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105C2×#1055—41no—
106#6090—41no—
107#6090—41no—
108#3277D1311yescharacteristic
109#2243—131no—
110#2227—131no—
111#1693—131no—
112#1360—131no—
113#1334—131no—
114#1330—131no—
115C23×C13—21no—
116C23×C13—41no—
117Q8×C13—22no—
118Q8×C13—41no—
119Q8×C13—41no—
120Q8×C13—41no—
121Q8×C13—82no—
122D4×C13—41no—
123D4×C13—41no—
124D4×C13—41no—
125D4×C13—82no—
126D4×C13—82no—
127C2×C4×C13—21no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—82no—
134C2×C4×C13—82no—
135C2×C4×C13#12011yescharacteristic
136C2×C4×C13C2×D811yescharacteristic
137C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
138C2×Dic13—81no—
139Dic26—81no—
140Dic26—81no—
141C8×C13—21no—
142C8×C13—41no—
143C8×C13C2×SD1611yescharacteristic
144C8×C13AGL(1,ℤ/8)11yescharacteristic
145#1055—81no—
146C2×#137—21no—
147#548—21no—
148#500—131no—
149#495C2×D1311yescharacteristic
150#468—21no—
151#464—21no—
152#461—261no—
153#451—21no—
154#449—21no—
155C4×Q16C2×D1311yescharacteristic
156#436C2×D1311yescharacteristic
157#366—261no—
158C4⋊C16—131no—
159#358—261no—
160#358—261no—
161#357—261no—
162#346—131no—
163#334—131no—
164#332—261no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—81no—
169C22×C13—81no—
170C22×C13—81no—
171C22×C13#44711yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13—42no—
176C4×C13—81no—
177C4×C13—81no—
178C4×C13#45011yescharacteristic
179C4×C13#45511yescharacteristic
180Dic13—161no—
181C2×#41—21no—
182C22×Q8—21no—
183#137—42no—
184#137—42no—
185C2×Q16—21no—
186C2×Q16C22⋊D1311yescharacteristic
187C2×Q16C22⋊D1311yescharacteristic
188C2×SD16—21no—
189C2×SD16—21no—
190C2×SD16—521no—
191C2×D8C22⋊D1311yescharacteristic
192C2×M16—21no—
193C4⋊Q8—261no—
194#124—21no—
195#124—41no—
196C22⋊Q8—21no—
197C22⋊Q8—41no—
198#121—21no—
199#121—41no—
200C4×Q8—21no—
201C4×D4—41no—
202C4×D4C22⋊D1311yescharacteristic
203C2×C16—261no—
204C2×C16—261no—
205#107—261no—
206#107—261no—
207#107C22⋊D1311yescharacteristic
208C4⋊C8—261no—
209C4⋊C8C22⋊D1311yescharacteristic
210#103—21no—
211#103—21no—
212#103—521no—
213#102—21no—
214C22⋊C8—21no—
215C4×C8C22×D1311yescharacteristic
216C2×C13—81no—
217C2×C13—161no—
218C2×C13#163911yescharacteristic
219C2×C13#219011yescharacteristic
220C2×C13#219511yescharacteristic
221#41—42no—
222#41—81no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—41no—
226C2×Q8—42no—
227C2×Q8—81no—
228C2×Q8—521no—
229C2×D4—21no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4#610411yescharacteristic
233C22×C4—21no—
234C22×C4—41no—
235C22×C4—41no—
236Q16—21no—
237Q16—41no—
238Q16—42no—
239Q16#610512yescomplemented
240SD16—42no—
241SD16—41no—
242SD16—41no—
243SD16—1042no—
244D8—41no—
245M16—41no—
246M16—41no—
247C2×C8—21no—
248C2×C8—521no—
249C2×C8C2×C22⋊D1311yescharacteristic
250C2×C8C2×C22⋊D1311yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C4⋊C4#610411yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C42—41no—
263C42C2×C22⋊D1311yescharacteristic
264C16—521no—
265C16—521no—
266C13#1237911yescharacteristic, complemented, Sylow
267C23—21no—
268C23—41no—
269Q8—22no—
270Q8—41no—
271Q8—41no—
272Q8—41no—
273Q8—82no—
274Q8—1041no—
275Q8—1041no—
276D4—41no—
277D4—41no—
278D4—41no—
279D4—82no—
280D4—82no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—1041no—
290C2×C4C2×#610411yescharacteristic
291C2×C4#8818611yescharacteristic
292C2×C4#8820711yescharacteristic
293C8—21no—
294C8—41no—
295C8—1041no—
296C8#8818611yescharacteristic
297C8C2×#610511yescharacteristic
298C22—41no—
299C22—41no—
300C22—41no—
301C22—81no—
302C22—81no—
303C22—81no—
304C22#1171887811yescharacteristic
305C4—21no—
306C4—21no—
307C4—41no—
308C4—42no—
309C4—81no—
310C4—81no—
311C4—2081no—
312C4#1171887911yescharacteristic
313C4#1171890311yescharacteristic
314C2—81no—
315C2—161no—
316C2#1311401511yescharacteristic
317C2#1311678211yescharacteristic
318C2#1311681411yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
Fitting, prime radicalC13×#3277C2
socleC22×C13#447
hypercenter#3277D13
hypocenterC13#12379
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #3277

Complements

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

NH ≅ G/Ntype
1. #13117072C2semidirect
2. #13116988C2semidirect
3. #13114349C2semidirect
4. #13112879C2semidirect
5. #13112806C2semidirect
6. #13112794C2semidirect
81. C13×Q16SD16semidirect
239. Q16#6105semidirect
266. C13#12379semidirect

Maximal subgroups

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

subgroupindex
#131170722
#131169882
#131143492
#131128792
#131128062
#131127942
C13×#32772
#1237913