Finite Group Databasebeta

← #15773130

Subgroups — #15773130

Order 3328.

552 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 115 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#13114575C211yesmaximal, characteristic, complemented
2#13113150C211yesmaximal, characteristic, complemented
3#13112839C214yesmaximal, complemented
4C13×#2619C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×C13×#121—21no—
7C2×C13×#117C2211yescharacteristic
8C22×#6099—21no—
9C13×#394—21no—
10C13×#394C2212yes—
11C13×#392—21no—
12C13×#392C412yes—
13C13×#390—21no—
14C13×#382C411yescharacteristic
15#11718586—21no—
16#11718122—21no—
17#11718122C2212yes—
18#11718120C2212yes—
19#11718117—21no—
20C22×D4×C13—22no—
21C22×D4×C13—21no—
22C22×D4×C13—21no—
23C22×D4×C13C2×C412yes—
24C23×C4×C13D411yescharacteristic
25C13×#127—41no—
26C13×#127—41no—
27C13×#121—42no—
28C13×#121—42no—
29C13×#117—41no—
30C13×#117—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×#6099—24no—
42C2×#6099—22no—
43C2×#6099—41no—
44C2×#6099—42no—
45C22×#1055—41no—
46C13×#95—21no—
47C13×#95C2×C412yes—
48C22⋊#1055—22no—
49C4⋊#1055—41no—
50C4×#1055—41no—
51#11699—131nomaximal, Sylow
52C24×C13—22no—
53C24×C13C22⋊C411yescharacteristic
54C2×D4×C13—42no—
55C2×D4×C13—42no—
56C2×D4×C13—44no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C2×D4×C13—42no—
60C2×D4×C13—42no—
61C2×D4×C13—82no—
62C2×D4×C13—82no—
63C2×D4×C13—82no—
64C2×D4×C13—82no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13D812yes—
73C22×C4×C13SD1612yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—82no—
85C13×C22⋊C4—82no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—21no—
90#6099—24no—
91#6099—44no—
92#6099—42no—
93C2×#1055—42no—
94C2×#1055—44no—
95C2×#1055—42no—
96#2619D1311yescharacteristic
97#1742—131no—
98#1458—131no—
99#1345—134no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—42no—
111C23×C13#10212yes—
112C23×C13C2×C22⋊C411yescharacteristic
113D4×C13—84no—
114D4×C13—84no—
115D4×C13—88no—
116D4×C13—82no—
117D4×C13—82no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13#9911yescharacteristic
136C2×C4×C13#9911yescharacteristic
137C2×C4×C13#10212yes—
138C2×C4×C13#10412yes—
139C2×C4×C13C2×D811yescharacteristic
140C2×C4×C13C2×SD1611yescharacteristic
141#1055—44no—
142#1055—82no—
143C22×M16—261no—
144C2×#127Dic1311yescharacteristic
145C2×#121—21no—
146C2×#117C2×D1311yescharacteristic
147#431—261no—
148#394—21no—
149#394C2×D1312yes—
150#392—21no—
151#392Dic1312yes—
152#390—21no—
153#382Dic1311yescharacteristic
154#343—132no—
155#343—261no—
156#324—132no—
157#323—261no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—22no—
161C22×C13—42no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—81no—
165C22×C13—82no—
166C22×C13—82no—
167C22×C13—82no—
168C22×C13—82no—
169C22×C13—82no—
170C22×C13—82no—
171C22×C13—82no—
172C22×C13C2×#9911yescharacteristic
173C22×C13C2×#10211yescharacteristic
174C22×C13C2×#10411yescharacteristic
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—82no—
182C4×C13#32712yes—
183C4×C13#32712yes—
184C22×D4—22no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4C2×Dic1312yes—
188C23×C4C22⋊D1311yescharacteristic
189C2×M16—264no—
190C2×M16—262no—
191C2×M16—521no—
192C2×M16—522no—
193C22×C8—521no—
194#127—41no—
195#127—41no—
196#121—42no—
197#121—42no—
198#117—41no—
199#117—41no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C22⋊D1311yescharacteristic
202C2×C4⋊C4C22×D1311yescharacteristic
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4C2×Dic1311yescharacteristic
207C2×C22⋊C4C22⋊D1311yescharacteristic
208C2×C42C2×Dic1311yescharacteristic
209C2×C42C22⋊D1311yescharacteristic
210C4⋊C8—521no—
211C22⋊C8—262no—
212C4×C8—521no—
213#95—21no—
214#95C2×Dic1312yes—
215C2×C13—21no—
216C2×C13—21no—
217C2×C13—42no—
218C2×C13—162no—
219C2×C13C2×#32711yescharacteristic
220C2×C13#212211yescharacteristic
221C2×C13#213411yescharacteristic
222C24—22no—
223C24C22⋊Dic1311yescharacteristic
224C2×D4—42no—
225C2×D4—42no—
226C2×D4—44no—
227C2×D4—42no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—42no—
231C2×D4—82no—
232C2×D4—82no—
233C2×D4—82no—
234C2×D4—82no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4#610412yes—
240C22×C4#610512yes—
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22⋊Dic1311yescharacteristic
244C22×C4C22×Dic1311yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247M16—264no—
248M16—524no—
249M16—522no—
250C2×C8—522no—
251C2×C8—524no—
252C2×C8—522no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—82no—
261C22⋊C4—82no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—21no—
266C13#1169911yescharacteristic, complemented, Sylow
267C23—21no—
268C23—21no—
269C23—41no—
270C23—41no—
271C23—42no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23—42no—
276C23—42no—
277C23—42no—
278C23#8807212yes—
279C23C2×C22⋊Dic1311yescharacteristic
280D4—84no—
281D4—84no—
282D4—88no—
283D4—82no—
284D4—82no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4#8807212yes—
303C2×C4#8807411yescharacteristic
304C2×C4#8807411yescharacteristic
305C2×C4#8807712yes—
306C2×C4C2×#610411yescharacteristic
307C2×C4C2×#610511yescharacteristic
308C8—524no—
309C8—1042no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22—82no—
318C22—82no—
319C22—82no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—82no—
324C22C2×#8807211yescharacteristic
325C22C2×#8807411yescharacteristic
326C22C2×#8807711yescharacteristic
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—82no—
334C4#1171812912yes—
335C4#1171812912yes—
336C2—21no—
337C2—21no—
338C2—42no—
339C2—162no—
340C2C2×#1171812911yescharacteristic
341C2#1311648611yescharacteristic
342C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
Fitting, prime radicalC13×#2619C2
socleC22×C13C2×#99
cosocleC2×C13×C4⋊C4C23
hypercenter#2619D13
hypocenterC13#11699
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2619

Complements

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

NH ≅ G/Ntype
1. #13114575C2semidirect
2. #13113150C2semidirect
3. #13112839C2semidirect
266. C13#11699semidirect

Maximal subgroups

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

subgroupindex
#131145752
#131131502
#131128392
C13×#26192
#1169913