Finite Group Databasebeta

← #15773606

Subgroups — #15773606

Order 3328.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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×#11718644C211yesmaximal, characteristic
2#13114916C211yesmaximal, characteristic
3#13112843C214yesmaximal, complemented
4C13×#1463C211yesmaximal, characteristic
5C22×C13×C4⋊C4C2211yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic
7C22×#6101—21no—
8C13×#407—21no—
9C2×#88071—21no—
10C2×#88071C411yescharacteristic
11#11718868—21no—
12#11718644—21no—
13#11718644—21no—
14#11718644C412yes—
15#11718644C2212yes—
16C13×#324—21no—
17C13×#324C2212yes—
18#11718122—21no—
19#11718122C2212yes—
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C2×C13×M16—41no—
26C2×C13×C4⋊C4—41no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4C2311yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—41no—
34C2×C4⋊Dic13—41no—
35C2×C4⋊Dic13C2×C412yes—
36C2×#6101—22no—
37C2×#6101—22no—
38C2×#6101—44no—
39C2×#6099—22no—
40C13×C22⋊C8—22no—
41C13×C22⋊C8—41no—
42#88071—22no—
43#88071—21no—
44#88071—22no—
45#88071C2×C412yes—
46C22⋊#1055—41no—
47C22⋊#1055—41no—
48#11803—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—41no—
58C22×C4×C13—42no—
59C22×C4×C13—42no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—24no—
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—42no—
70C22×Dic13—42no—
71C22×Dic13—42no—
72C22×Dic13—42no—
73C22×Dic13—41no—
74C22×Dic13—41no—
75C13×M16—82no—
76C2×C8×C13—42no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C4⋊Dic13—42no—
82C4⋊Dic13—42no—
83#6101—44no—
84#6101—44no—
85#6099—42no—
86#6099—42no—
87C2×#1055—42no—
88C2×#398—131no—
89#1821—131no—
90#1463D1311yescharacteristic
91#1346—134no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13#9911yescharacteristic
97C23×C13#9911yescharacteristic
98C23×C13C2×C22⋊C411yescharacteristic
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—81no—
118C2×C4×C13AGL(1,ℤ/8)12yes—
119C2×Dic13—24no—
120C2×Dic13—48no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—82no—
127C2×Dic13—82no—
128C8×C13—82no—
129#1055—82no—
130C22×C4⋊C4—131no—
131C22×C4⋊C4—261no—
132C22×C4⋊C4C2×D1311yescharacteristic
133#407—21no—
134#407—261no—
135#398—132no—
136#398—132no—
137#398—261no—
138#398—261no—
139C2×#95—131no—
140C2×#95—261no—
141#343—132no—
142#343—261no—
143#324—21no—
144#324C2×D1312yes—
145C22×C13—24no—
146C22×C13—24no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13#35212yes—
154C22×C13#35612yes—
155C22×C13C2×#9911yescharacteristic
156C22×C13#41811yescharacteristic
157C22×C13#42111yescharacteristic
158C4×C13—22no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164Dic13—44no—
165Dic13—82no—
166C23×C4—261no—
167C23×C4—261no—
168C23×C4C4×D1311yescharacteristic
169C23×C4D5211yescharacteristic
170C23×C4C22⋊D1311yescharacteristic
171C2×M16—41no—
172C2×M16—262no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—132no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4—262no—
178C2×C4⋊C4—262no—
179C2×C4⋊C4—521no—
180C2×C4⋊C4—521no—
181C2×C4⋊C4—524no—
182C2×C4⋊C4C4×D1311yescharacteristic
183C2×C4⋊C4D5211yescharacteristic
184C2×C4⋊C4C22⋊D1311yescharacteristic
185C2×C4⋊C4C22×D1311yescharacteristic
186C22⋊C8—22no—
187C22⋊C8—41no—
188C22⋊C8—521no—
189C22⋊C8—521no—
190#95—132no—
191#95—261no—
192#95—262no—
193#95—262no—
194C2×C13—21no—
195C2×C13—22no—
196C2×C13—22no—
197C2×C13—21no—
198C2×C13#151011yescharacteristic
199C2×C13C2×#35211yescharacteristic
200C2×C13C2×#35611yescharacteristic
201C24#610311yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—41no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—264no—
213C22×C4—262no—
214C22×C4—262no—
215C22×C4—522no—
216C22×C4—522no—
217C22×C4—522no—
218C22×C4—522no—
219C22×C4—521no—
220C22×C4—521no—
221C22×C4#610311yescharacteristic
222C22×C4#610311yescharacteristic
223C22×C4#610311yescharacteristic
224C22×C4C2×C4×D1311yescharacteristic
225C22×C4C2×D5211yescharacteristic
226C22×C4C2×C22⋊D1311yescharacteristic
227M16—82no—
228M16—522no—
229M16—522no—
230C2×C8—42no—
231C2×C8—522no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—522no—
237C4⋊C4—524no—
238C4⋊C4—522no—
239C4⋊C4—524no—
240C13#1180311yescharacteristic, complemented, Sylow
241C23—21no—
242C23—21no—
243C23—22no—
244C23—22no—
245C23#8804611yescharacteristic
246C23#8804611yescharacteristic
247C23C2×#610311yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—264no—
268C2×C4—528no—
269C2×C4—522no—
270C2×C4—522no—
271C2×C4—522no—
272C2×C4—522no—
273C2×C4—522no—
274C2×C4—1042no—
275C2×C4—1042no—
276C2×C4#8816212yes—
277C8—82no—
278C8—1042no—
279C22—24no—
280C22—24no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22#1171806412yes—
288C22#1171807012yes—
289C22C2×#8804611yescharacteristic
290C22#1171879211yescharacteristic
291C22#1171880011yescharacteristic
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—524no—
299C4—1042no—
300C2—21no—
301C2—21no—
302C2—22no—
303C2—22no—
304C2#1311336611yescharacteristic
305C2C2×#1171806411yescharacteristic
306C2C2×#1171807011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1463C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1463D13
hypocenterC13#11803
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #13112843C2semidirect
240. C13#11803semidirect

Maximal subgroups

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

subgroupindex
C2×#117186442
#131149162
#131128432
C13×#14632
#1180313