Finite Group Databasebeta

← #16786895

Subgroups — #16786895

Order 3328.

616 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130072C212yesmaximal, complemented
2#13129778C212yesmaximal, complemented
3#13129764C212yesmaximal, complemented
4#127×Dic13C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×D4×Dic13—22no—
7C2×D4×Dic13C411yescharacteristic
8C2×D4×Dic13C2211yescharacteristic
9C2×C22⋊#1057—22no—
10#11718882—22no—
11#11718882C411yescharacteristic
12#11718882C2211yescharacteristic
13#11718596C2211yescharacteristic
14C42×Dic13C411yescharacteristic
15#11718305—22no—
16#11718285C2214yes—
17C22×D4×C13—22no—
18C22×D4×C13C2×C411yescharacteristic
19C22×D4×C13C2×C411yescharacteristic
20C23×Dic13—21no—
21C23×Dic13D412yes—
22C22×#1057—42no—
23C13×#127—22no—
24C13×#127C814yescomplemented
25C2×C42×C13C2×C411yescharacteristic
26C2×C22⋊Dic13—22no—
27C2×C22⋊Dic13—21no—
28C2×C22⋊Dic13—22no—
29C2×C22⋊Dic13D412yes—
30D4×Dic13—41no—
31D4×Dic13—41no—
32D4×Dic13—48no—
33D4×Dic13—41no—
34D4×Dic13—41no—
35C2×C4⋊Dic13—22no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13C2311yescharacteristic
38C2×C4×Dic13—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C22⋊#1057—24no—
43C22⋊#1057—42no—
44#11475—131nomaximal, Sylow
45C24×C13—21no—
46C24×C13C22⋊C412yes—
47C2×D4×C13—28no—
48C2×D4×C13—21no—
49C2×D4×C13—41no—
50C2×D4×C13—41no—
51C2×D4×C13—41no—
52C2×D4×C13—41no—
53C2×D4×C13—44no—
54C2×D4×C13—44no—
55C2×D4×C13C2×C812yes—
56C2×D4×C13C2×C812yescomplemented
57C2×D4×C13M1612yes—
58C22×C4×C13—21no—
59C22×C4×C13C22×C411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—21no—
64C22×Dic13—44no—
65C22×Dic13—44no—
66C22×Dic13—41no—
67C22×Dic13—41no—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C2×D412yes—
71C2×#1057—44no—
72C2×#1057—84no—
73C42×C13—21no—
74C42×C13C2×C812yescomplemented
75C22⋊Dic13—42no—
76C22⋊Dic13—44no—
77C22⋊Dic13—44no—
78C22⋊Dic13—42no—
79C4⋊Dic13—41no—
80C4⋊Dic13—44no—
81C4⋊Dic13—41no—
82C4×Dic13—24no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85C4×Dic13—42no—
86C4×Dic13—41no—
87C4×#127—131no—
88#1459—132no—
89#1325—132no—
90#1318—132no—
91C23×C13—22no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13C22⋊C814yes—
101C23×C13C2×C22⋊C411yescharacteristic
102D4×C13—42no—
103D4×C13—42no—
104D4×C13—416no—
105D4×C13—42no—
106D4×C13—42no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13C22×C811yescharacteristic
113C2×C4×C13C2×M1611yescharacteristic
114C2×Dic13—22no—
115C2×Dic13—22no—
116C2×Dic13—21no—
117C2×Dic13—22no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—44no—
121C2×Dic13—41no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—41no—
125C2×Dic13—82no—
126C2×Dic13—82no—
127C2×Dic13—82no—
128C2×Dic13#9911yescharacteristic
129C2×Dic13#9911yescharacteristic
130#1057—84no—
131C2×#127#26111yescharacteristic
132C2×C4×D4—131no—
133C2×C4×D4—131no—
134C2×C4×D4—262no—
135C2×C22⋊C8—262no—
136#390—131no—
137#390—131no—
138#390—262no—
139#384—131no—
140C43—131no—
141#324—134no—
142#323—262no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—24no—
146C22×C13—44no—
147C22×C13—44no—
148C22×C13—42no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—82no—
152C22×C13—82no—
153C22×C13—81no—
154C22×C13—81no—
155C22×C13C2×C22⋊C811yescharacteristic
156C22×C13C2×#9911yescharacteristic
157C22×C13#41311yescharacteristic
158C4×C13—24no—
159C4×C13—21no—
160C4×C13—21no—
161Dic13—21no—
162Dic13—42no—
163Dic13—42no—
164Dic13—41no—
165Dic13—81no—
166Dic13#35312yes—
167C22×D4—22no—
168C22×D4C2×#26111yescharacteristic
169C22×D4C2×#26111yescharacteristic
170C23×C4—132no—
171C23×C4—261no—
172C22×C8—522no—
173#127—22no—
174#127#105714yescomplemented
175C4×D4—521no—
176C4×D4—521no—
177C4×D4—528no—
178C4×D4—521no—
179C4×D4—521no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—262no—
183C2×C22⋊C4—132no—
184C2×C22⋊C4—261no—
185C2×C22⋊C4—262no—
186C2×C22⋊C4—262no—
187C2×C42—131no—
188C2×C42—131no—
189C2×C42—261no—
190C2×C42—261no—
191C2×C42C2×#26111yescharacteristic
192C22⋊C8—264no—
193C22⋊C8—522no—
194C2×C13—21no—
195C2×C13—21no—
196C2×C13—44no—
197C2×C13—82no—
198C2×C13#145911yescharacteristic
199C2×C13C2×#35311yescharacteristic
200C2×C13#213211yescharacteristic
201C24—21no—
202C24C22⋊#26112yes—
203C2×D4—28no—
204C2×D4—21no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—44no—
210C2×D4—44no—
211C2×D4C2×#105712yes—
212C2×D4C2×#105712yescomplemented
213C2×D4#612212yes—
214C22×C4—21no—
215C22×C4—131no—
216C22×C4—132no—
217C22×C4—131no—
218C22×C4—262no—
219C22×C4—262no—
220C22×C4—261no—
221C22×C4—261no—
222C22×C4—521no—
223C22×C4—521no—
224C22×C4—524no—
225C22×C4—524no—
226C22×C4C22×#26111yescharacteristic
227C2×C8—524no—
228C2×C8—1044no—
229C4⋊C4—521no—
230C4⋊C4—521no—
231C4⋊C4—524no—
232C22⋊C4—522no—
233C22⋊C4—524no—
234C22⋊C4—524no—
235C22⋊C4—522no—
236C42—21no—
237C42—261no—
238C42—261no—
239C42—264no—
240C42—521no—
241C42—522no—
242C42C2×#105712yescomplemented
243C13#1147511yescharacteristic, complemented, Sylow
244C23—22no—
245C23—22no—
246C23—22no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—41no—
252C23—41no—
253C23C22⋊#105714yes—
254C23C2×C22⋊#26111yescharacteristic
255D4—42no—
256D4—42no—
257D4—42no—
258D4—416no—
259D4—42no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—131no—
266C2×C4—131no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—261no—
270C2×C4—262no—
271C2×C4—524no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—522no—
276C2×C4—522no—
277C2×C4—521no—
278C2×C4—1042no—
279C2×C4—1042no—
280C2×C4—1042no—
281C2×C4C22×#105711yescharacteristic
282C2×C4C2×#612211yescharacteristic
283C8—1044no—
284C22—21no—
285C22—21no—
286C22—24no—
287C22—44no—
288C22—44no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—82no—
293C22—82no—
294C22—81no—
295C22—81no—
296C22D13⋊#9911yescharacteristic
297C22#1171914811yescharacteristic
298C22C2×C22⋊#105711yescharacteristic
299C4—24no—
300C4—21no—
301C4—21no—
302C4—132no—
303C4—261no—
304C4—522no—
305C4—522no—
306C4—521no—
307C4—1041no—
308C2—21no—
309C2—21no—
310C2—44no—
311C2—82no—
312C2#1313007211yescharacteristic
313C2D13⋊#35311yescharacteristic
314C2#1313112811yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
Fitting, prime radicalC2×C13×#127C4
socleC22×C13C2×#99
cosocleC2×C4⋊Dic13C23
hypercenterC2×#127#261
hypocenterC13#11475
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #13130072C2semidirect
2. #13129778C2semidirect
3. #13129764C2semidirect
24. C13×#127C8semidirect
56. C2×D4×C13C2×C8semidirect
74. C42×C13C2×C8semidirect
174. #127#1057semidirect
212. C2×D4C2×#1057semidirect
242. C42C2×#1057semidirect
243. C13#11475semidirect

Maximal subgroups

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

subgroupindex
#131300722
#131297782
#131297642
#127×Dic132
#1147513