Finite Group Databasebeta

← #15774064

Subgroups — #15774064

Order 3328.

440 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114828C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112863C214yesmaximal, complemented
4C13×#2487C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C13×#400C2212yes—
8C13×#399C412yes—
9C13×#389—21no—
10C13×#386—21no—
11C13×#385—21no—
12C13×#380—21no—
13C13×#380C411yescharacteristic
14C2×#88073—21no—
15C2×C22⋊#1055—21no—
16#11718585—21no—
17#11718122C2212yes—
18#11718120C2212yes—
19#11718117—21no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×#6099—22no—
39C22×#1055—41no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95C2×C412yes—
43#88073—42no—
44C22⋊#1055—22no—
45C22⋊#1055—41no—
46C4⋊#1055—41no—
47C4⋊#1055—41no—
48#11903—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C24×C13C22⋊C411yescharacteristic
51C2×D4×C13—41no—
52C2×D4×C13—41no—
53C2×D4×C13SD1612yes—
54C2×D4×C13Q1612yes—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—82no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C13×C4⋊C4—41no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—82no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—82no—
80C42×C13—21no—
81C42×C13—21no—
82#6099—42no—
83#6099—42no—
84C2×#1055—42no—
85C2×#1055—42no—
86C2×#1055—82no—
87#2487D1311yescharacteristic
88#1800—131no—
89#1459—131no—
90#1353—134no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13#10312yes—
100C23×C13#10312yes—
101C23×C13C2×C22⋊C411yescharacteristic
102D4×C13—42no—
103D4×C13—42no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
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—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—81no—
123C2×C4×C13—84no—
124C2×C4×C13#9911yescharacteristic
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13C2×SD1611yescharacteristic
127C2×C4×C13C2×Q1611yescharacteristic
128#1055—82no—
129#1055—82no—
130C2×C4×D4C2×D1311yescharacteristic
131C22×C4⋊C4Dic1311yescharacteristic
132#423—261no—
133C2×#100—261no—
134C2×C22⋊C8—261no—
135#400C2×D1312yes—
136#399Dic1312yes—
137#389—21no—
138#386—21no—
139#385—21no—
140#380—21no—
141#380Dic1311yescharacteristic
142#343—132no—
143#324—132no—
144#323—261no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—22no—
148C22×C13—22no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—42no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—81no—
157C22×C13C2×#9911yescharacteristic
158C22×C13C2×#10311yescharacteristic
159C22×C13#42111yescharacteristic
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13—82no—
167C4×C13—82no—
168C4×C13#35212yes—
169C22×D4C22⋊D1311yescharacteristic
170C23×C4—21no—
171C23×C4C2×Dic1311yescharacteristic
172C23×C4C22⋊D1311yescharacteristic
173C2×M16—262no—
174C22×C8—521no—
175C4×D4—41no—
176C4×D4—41no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4C2×Dic1312yes—
183C2×C4⋊C4C22×D1311yescharacteristic
184C2×C22⋊C4—21no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4C2×Dic1311yescharacteristic
187C2×C22⋊C4C22⋊D1311yescharacteristic
188C2×C42C22⋊D1311yescharacteristic
189C4⋊C8—521no—
190C4⋊C8—521no—
191#100—522no—
192C22⋊C8—262no—
193C22⋊C8—521no—
194#95—22no—
195#95—22no—
196#95C2×Dic1312yes—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13—42no—
200C2×C13—42no—
201C2×C13#152011yescharacteristic
202C2×C13C2×#35211yescharacteristic
203C2×C13#213411yescharacteristic
204C24C22⋊Dic1311yescharacteristic
205C24C22⋊Dic1311yescharacteristic
206C2×D4—41no—
207C2×D4—41no—
208C2×D4#610612yes—
209C2×D4#610712yes—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—82no—
220C22×C4C22⋊Dic1311yescharacteristic
221C22×C4C22⋊Dic1311yescharacteristic
222C22×C4C22×Dic1311yescharacteristic
223C22×C4C2×C22⋊D1311yescharacteristic
224C22×C4C2×C22⋊D1311yescharacteristic
225M16—522no—
226M16—522no—
227C2×C8—522no—
228C2×C8—522no—
229C2×C8—1042no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—82no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—42no—
239C22⋊C4—82no—
240C42—21no—
241C42—21no—
242C13#1190311yescharacteristic, complemented, Sylow
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23#8807512yes—
252C23#8807512yes—
253C23C2×C22⋊Dic1311yescharacteristic
254D4—42no—
255D4—42no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—81no—
275C2×C4—84no—
276C2×C4#8807411yescharacteristic
277C2×C4#8807411yescharacteristic
278C2×C4C2×#610611yescharacteristic
279C2×C4C2×#610711yescharacteristic
280C8—1042no—
281C8—1042no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22C2×#8807411yescharacteristic
295C22C2×#8807511yescharacteristic
296C22#1171889711yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—82no—
304C4—82no—
305C4#1171813112yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—42no—
310C2#1311340811yescharacteristic
311C2C2×#1171813111yescharacteristic
312C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2487C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C4⋊C4C23
hypercenter#2487D13
hypocenterC13#11903
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
3. #13112863C2semidirect
242. C13#11903semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131131542
#131128632
C13×#24872
#1190313