Finite Group Databasebeta

← #15760338

Subgroups — #15760338

Order 3328.

450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 109 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#13123919C211yesmaximal, characteristic
2#13120051C211yesmaximal, characteristic
3#13114829C211yesmaximal, characteristic
4#13113522C211yesmaximal, characteristic
5#13113520C211yesmaximal, characteristic
6#13112739C211yesmaximal, characteristic
7C13×#1303C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88064—21no—
14#11718635—22no—
15#11718597—21no—
16#11718590—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718492—22no—
20#11718380—22no—
21#11718340—22no—
22#11718320C414yes—
23#11718146—21no—
24#11718078—22no—
25#11718074—22no—
26C22×Dic26—21no—
27C22×Dic26D411yescharacteristic
28C2×C13×M16—21no—
29C2×C13×C4⋊C4—21no—
30C2×C42×C13—21no—
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13C2×C412yes—
34C2×C4⋊Dic13D411yescharacteristic
35C2×#6101C2×C412yes—
36C2×C4×Dic13D412yes—
37C2×#6099—21no—
38#88123—21no—
39#88123—21no—
40#88123—21no—
41#88123—21no—
42C4×Dic26—21no—
43C4×Dic26—21no—
44C4×Dic26—21no—
45C4×Dic26—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8D412yes—
49C13×C22⋊C8—21no—
50C4×C8×C13—21no—
51C13×#95C2×C412yes—
52#88071—24no—
53#88071—24no—
54C22⋊#1055—21no—
55#88064—42no—
56#88055—24no—
57#88054—24no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055D412yes—
61C4×#1055—21no—
62#9404—131nomaximal, Sylow
63C22×C4×C13—22no—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—22no—
68C22×Dic13C22⋊C412yes—
69C22×Dic13C22⋊C412yes—
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×Dic26—21no—
75C2×Dic26—21no—
76C2×Dic26—44no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C13×M16—41no—
80C13×M16—41no—
81C2×C8×C13—22no—
82C2×C8×C13—41no—
83C13×C4⋊C4—42no—
84C42×C13—41no—
85C42×C13—41no—
86C42×C13C2×D411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13#4111yescharacteristic
89C42×C13#4111yescharacteristic
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—22no—
93C4⋊Dic13—22no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96#6101—22no—
97#6101—22no—
98C4×Dic13—22no—
99C4×Dic13—22no—
100#6099—41no—
101#6099—41no—
102C2×#1055—22no—
103C2×#1055—41no—
104#2983—131no—
105#2568—131no—
106#1801—131no—
107#1549—131no—
108#1549—131no—
109#1303—131no—
110#1303D1311yescharacteristic
111C23×C13C2×C22⋊C411yescharacteristic
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13C4×D411yescharacteristic
118C2×C4×C13C4×D411yescharacteristic
119C2×C4×C13#12011yescharacteristic
120C2×C4×C13#12111yescharacteristic
121C2×C4×C13#12111yescharacteristic
122C2×C4×C13#12311yescharacteristic
123C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C13#13711yescharacteristic
125C2×C4×C13#13711yescharacteristic
126C2×C4×C13#13711yescharacteristic
127C2×Dic13—22no—
128C2×Dic13—22no—
129C2×Dic13—22no—
130C2×Dic13—22no—
131C2×Dic13—42no—
132C2×Dic13—44no—
133C2×Dic13—42no—
134Dic26—41no—
135Dic26—41no—
136Dic26—41no—
137Dic26—41no—
138Dic26—82no—
139Dic26—82no—
140C8×C13—42no—
141C8×C13—81no—
142#1055—42no—
143#1055—81no—
144C2×C4⋊Q8—131no—
145C2×C4×Q8—131no—
146#446—262no—
147#446—262no—
148#432—262no—
149#431—131no—
150#431C2×D1311yescharacteristic
151#423—131no—
152#423C2×D1311yescharacteristic
153C2×#101—261no—
154#400—134no—
155#391—261no—
156#391—262no—
157#382—261no—
158C4×C4⋊C4C2×D1311yescharacteristic
159#343—261no—
160#332—262no—
161#332—262no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13#38611yescharacteristic
165C22×C13#41711yescharacteristic
166C22×C13#41911yescharacteristic
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—82no—
171C4×C13#45412yes—
172C4×C13#46811yescharacteristic
173C4×C13#46811yescharacteristic
174C4×C13#47011yescharacteristic
175C4×C13#47011yescharacteristic
176Dic13—42no—
177Dic13—42no—
178Dic13—82no—
179C22×Q8—131no—
180C22×Q8—261no—
181C2×M16—21no—
182C2×M16—261no—
183C4⋊Q8—261no—
184C4⋊Q8—261no—
185C4⋊Q8—261no—
186C4⋊Q8—261no—
187C4×Q8—261no—
188C4×Q8—261no—
189C4×Q8—261no—
190C4×Q8—261no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—132no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—132no—
195C2×C4⋊C4—261no—
196C2×C42—21no—
197C2×C42—132no—
198C2×C42C22×D1311yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—132no—
202C4⋊C8—264no—
203C4⋊C8—261no—
204C4⋊C8—261no—
205C4⋊C8D5212yes—
206#101—522no—
207C22⋊C8—21no—
208C22⋊C8—261no—
209#97—264no—
210C4×C8—21no—
211C4×C8—261no—
212#95—264no—
213#95—264no—
214#95C4×D1312yes—
215C2×C13—21no—
216C2×C13—21no—
217C2×C13#188811yescharacteristic
218C2×C13#189411yescharacteristic
219C2×C13#191511yescharacteristic
220C2×Q8—261no—
221C2×Q8—261no—
222C2×Q8—261no—
223C2×Q8—261no—
224C2×Q8—261no—
225C2×Q8—261no—
226C2×Q8—524no—
227C2×Q8—521no—
228C2×Q8—521no—
229C22×C4—22no—
230C22×C4—132no—
231C22×C4—132no—
232C22×C4—262no—
233C22×C4C2×C4×D1311yescharacteristic
234C22×C4D4×D1311yescharacteristic
235C22×C4D4×D1311yescharacteristic
236M16—41no—
237M16—41no—
238M16—521no—
239M16—521no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—262no—
243C2×C8—521no—
244C4⋊C4—42no—
245C4⋊C4—262no—
246C4⋊C4—261no—
247C4⋊C4—262no—
248C4⋊C4—261no—
249C4⋊C4—262no—
250C4⋊C4—262no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C42—41no—
254C42—41no—
255C42—262no—
256C42—262no—
257C42C2×D5211yescharacteristic
258C42#612711yescharacteristic
259C42D4×D1311yescharacteristic
260C42#613111yescharacteristic
261C13#940411yescharacteristic, complemented, Sylow
262C23C22⋊C4×D1311yescharacteristic
263Q8—521no—
264Q8—521no—
265Q8—521no—
266Q8—521no—
267Q8—1042no—
268Q8—1042no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4—262no—
277C2×C4—262no—
278C2×C4—522no—
279C2×C4—524no—
280C2×C4—522no—
281C2×C4C4×D5211yescharacteristic
282C2×C4#8813611yescharacteristic
283C2×C4#8813811yescharacteristic
284C2×C4#8814711yescharacteristic
285C2×C4#8814811yescharacteristic
286C2×C4#8814911yescharacteristic
287C2×C4#8816511yescharacteristic
288C2×C4#8816911yescharacteristic
289C2×C4#8816911yescharacteristic
290C2×C4#8817211yescharacteristic
291C8—42no—
292C8—81no—
293C8—522no—
294C8—1041no—
295C22—21no—
296C22—21no—
297C22#1171832611yescharacteristic
298C22#1171843211yescharacteristic
299C22#1171846311yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—522no—
305C4—522no—
306C4—1042no—
307C4#1171844111yescharacteristic
308C4#1171847711yescharacteristic
309C4#1171848812yes—
310C4#1171852911yescharacteristic
311C4#1171854711yescharacteristic
312C2—21no—
313C2—21no—
314C2#1311523811yescharacteristic
315C2#1311526811yescharacteristic
316C2#1311538711yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1303C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1303D13
hypocenterC13#9404
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
261. C13#9404semidirect

Maximal subgroups

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

subgroupindex
#131239192
#131200512
#131148292
#131135222
#131135202
#131127392
C13×#13032
#940413