Finite Group Databasebeta

← #15778093

Subgroups — #15778093

Order 3328.

628 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C2×#11718137C212yesmaximal
2C4×#88074C212yesmaximal, complemented
3#13112961C212yesmaximal, complemented
4C13×#2328C211yesmaximal, characteristic
5C2×C13×#127C2211yescharacteristic
6C2×C4×D4×C13C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#390C411yescharacteristic, complemented
9C13×#390C2211yescharacteristic
10C13×#386—22no—
11C13×#386—22no—
12C13×#382C411yescharacteristic, complemented
13C13×#376C411yescharacteristic, complemented
14C2×#88074C2214yes—
15C4×C22⋊Dic13—22no—
16#11718137C418yescomplemented
17#11718118—22no—
18C22×D4×C13—22no—
19C22×D4×C13C2×C411yescharacteristic
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13D412yes—
23C13×#127—22no—
24C13×#127C2×C414yes—
25C4×D4×C13—42no—
26C4×D4×C13—42no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C22⋊C4—21no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4D412yes—
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C22⋊Dic13—24no—
37C2×C4×Dic13—42no—
38C13×#95—22no—
39C13×#95—21no—
40C13×#95—21no—
41#88074—24no—
42#88074C2×C418yescomplemented
43#88071—42no—
44#12628—131nomaximal, Sylow
45C24×C13—21no—
46C24×C13C2×D412yes—
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—82no—
54C2×D4×C13—82no—
55C2×D4×C13C4212yescomplemented
56C2×D4×C13C22×C412yes—
57C2×D4×C13#4112yes—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—42no—
64C22×C4×C13—82no—
65C22×C4×C13—82no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×Dic13—44no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C22⋊C4—42no—
74C13×C22⋊C4—42no—
75C13×C22⋊C4—82no—
76C13×C22⋊C4—82no—
77C42×C13—22no—
78C42×C13—21no—
79C42×C13—41no—
80C42×C13C4212yescomplemented
81C22⋊Dic13—28no—
82C22⋊Dic13—44no—
83C4×Dic13—84no—
84#2328D1311yescharacteristic
85C2×#353—132no—
86C4×#99—132no—
87#1393—132no—
88C23×C13—22no—
89C23×C13—22no—
90C23×C13—22no—
91C23×C13—42no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13C2×C22⋊C411yescharacteristic
98C23×C13C4×D414yes—
99D4×C13—42no—
100D4×C13—42no—
101D4×C13—42no—
102D4×C13—42no—
103D4×C13—88no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—41no—
110C2×C4×C13—44no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—82no—
121C2×C4×C13—84no—
122C2×C4×C13#9912yes—
123C2×C4×C13C2×C4211yescharacteristic
124C2×C4×C13#11711yescharacteristic
125C2×Dic13—48no—
126C2×Dic13—84no—
127C2×Dic13—84no—
128C2×#127C2×D1311yescharacteristic
129C2×C4×D4Dic1311yescharacteristic, complemented
130C2×C4×D4C2×D1311yescharacteristic
131C2×#99—134no—
132#390Dic1311yescharacteristic, complemented
133#390C2×D1311yescharacteristic
134#386—22no—
135#386—22no—
136#382Dic1311yescharacteristic, complemented
137C4×C22⋊C4—262no—
138#376Dic1311yescharacteristic, complemented
139#353—138no—
140#342—262no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—24no—
144C22×C13—44no—
145C22×C13—44no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—82no—
150C22×C13—82no—
151C22×C13—81no—
152C22×C13—81no—
153C22×C13C4×C22⋊C411yescharacteristic
154C22×C13C2×#9911yescharacteristic
155C22×C13#41011yescharacteristic
156C4×C13—22no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—42no—
160C4×C13—42no—
161C4×C13—41no—
162C4×C13—81no—
163C4×C13—81no—
164Dic13—88no—
165C22×D4—22no—
166C22×D4C2×Dic1311yescharacteristic
167C22×D4C22×D1311yescharacteristic
168C23×C4—21no—
169C23×C4C22⋊D1312yes—
170#127—22no—
171#127C4×D1314yes—
172C4×D4—42no—
173C4×D4—42no—
174C2×C4⋊C4C2×Dic1311yescharacteristic
175C2×C4⋊C4C2×Dic1311yescharacteristic
176C2×C22⋊C4—21no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—264no—
180C2×C22⋊C4C22⋊D1312yes—
181C2×C42—522no—
182C2×C42C2×Dic1311yescharacteristic
183C2×C42C2×Dic1311yescharacteristic
184C2×C42C2×Dic1311yescharacteristic
185#99—138no—
186#99—264no—
187#95—21no—
188#95—22no—
189#95—21no—
190#95—522no—
191C2×C13—21no—
192C2×C13—21no—
193C2×C13—44no—
194C2×C13—82no—
195C2×C13C4×#9911yescharacteristic
196C2×C13#212711yescharacteristic
197C2×C13#212811yescharacteristic
198C24—21no—
199C24C2×C22⋊D1312yes—
200C2×D4—28no—
201C2×D4—21no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—82no—
207C2×D4—82no—
208C2×D4C4×Dic1312yescomplemented
209C2×D4C2×C4×D1312yes—
210C2×D4#612712yes—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—42no—
217C22×C4—82no—
218C22×C4—82no—
219C22×C4—524no—
220C22×C4C22⋊Dic1311yescharacteristic
221C22×C4C22⋊Dic1312yes—
222C22×C4C22⋊Dic1311yescharacteristic
223C22×C4C22×Dic1311yescharacteristic
224C4⋊C4—41no—
225C4⋊C4—41no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—82no—
229C22⋊C4—82no—
230C22⋊C4—268no—
231C22⋊C4—524no—
232C42—22no—
233C42—21no—
234C42—41no—
235C42—1044no—
236C42C4×Dic1312yescomplemented
237C13#1262811yescharacteristic, complemented, Sylow
238C23—22no—
239C23—22no—
240C23—22no—
241C23—42no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—41no—
246C23—41no—
247C23C4×C22⋊D1314yes—
248C23C2×C22⋊Dic1311yescharacteristic
249D4—42no—
250D4—42no—
251D4—42no—
252D4—42no—
253D4—88no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—44no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—82no—
271C2×C4—84no—
272C2×C4—528no—
273C2×C4—1044no—
274C2×C4—1044no—
275C2×C4#8807412yes—
276C2×C4C2×C4×Dic1311yescharacteristic
277C2×C4#8818011yescharacteristic
278C22—21no—
279C22—21no—
280C22—24no—
281C22—44no—
282C22—44no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—82no—
287C22—82no—
288C22—81no—
289C22—81no—
290C22C4×C22⋊Dic1311yescharacteristic
291C22C2×#8807411yescharacteristic
292C22#1171890111yescharacteristic
293C4—21no—
294C4—21no—
295C4—22no—
296C4—42no—
297C4—42no—
298C4—41no—
299C4—81no—
300C4—81no—
301C4—1048no—
302C2—21no—
303C2—21no—
304C2—44no—
305C2—82no—
306C2C4×#8807411yescharacteristic
307C2#1311650511yescharacteristic
308C2#1311650811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC2×C4×C13C2×C42
FrattiniC22×D4C22×D13
FittingC13×#2328C2
socleC22×C13C2×#99
prime radicalC2×C13×#127C22
cosocleC22×D4×C13C23
hypercenter#2328D13
hypocenterC13#12628
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. C4×#88074C2semidirect
3. #13112961C2semidirect
6. C2×C4×D4×C13C4semidirect
8. C13×#390C4semidirect
12. C13×#382C4semidirect
13. C13×#376C4semidirect
16. #11718137C4semidirect
42. #88074C2×C4semidirect
55. C2×D4×C13C42semidirect
80. C42×C13C42semidirect
129. C2×C4×D4Dic13semidirect
132. #390Dic13semidirect
136. #382Dic13semidirect
138. #376Dic13semidirect
208. C2×D4C4×Dic13semidirect
236. C42C4×Dic13semidirect
237. C13#12628semidirect

Maximal subgroups

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

subgroupindex
C2×#117181372
C4×#880742
#131129612
C13×#23282
#1262813