Finite Group Databasebeta

← #15756560

Subgroups — #15756560

Order 3328.

466 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C4×#88074C211yesmaximal, characteristic
2#13113174C211yesmaximal, characteristic
3#13112722C212yesmaximal, complemented
4#13112688C212yesmaximal, complemented
5C13×#2357C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C13×#390—21no—
8C13×#388—21no—
9C13×#388—21no—
10C13×#382C411yescharacteristic, complemented
11C13×#381C411yescharacteristic, complemented
12C13×#381C2211yescharacteristic
13C4×C13×C4⋊C4—21no—
14C4×C13×C4⋊C4C411yescharacteristic, complemented
15C4×C13×C22⋊C4C411yescharacteristic, complemented
16C4×C13×C22⋊C4C2211yescharacteristic
17C2×#88074—21no—
18C4×C22⋊Dic13C2212yes—
19#11718868C2212yes—
20#11718120—21no—
21#11718118—21no—
22#11718117—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C4×D4×C13—22no—
27C4×D4×C13—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4—21no—
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C13×C22⋊C4D411yescharacteristic
37C2×C42×C13—21no—
38C2×C42×C13—21no—
39C2×C42×C13—21no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C22⋊Dic13—22no—
42C2×C4×Dic13—22no—
43C2×#6099—22no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95C2×C411yescharacteristic
48C13×#95C2×C411yescharacteristic
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88074—24no—
52#88071—22no—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55#8779—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C2×D411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—41no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—81no—
68C22×C4×C13—81no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4112yes—
75C22×C4×C13#4112yes—
76C22×Dic13—42no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C22⋊C4—22no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—81no—
85C13×C22⋊C4—81no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—42no—
89C42×C13—81no—
90C42×C13—81no—
91C22⋊Dic13—24no—
92C22⋊Dic13—42no—
93C4×Dic13—82no—
94#6099—82no—
95C2×#1055—42no—
96#2357D1311yescharacteristic
97C4×#99—131no—
98#1465—131no—
99#1297—132no—
100#1284—132no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13C2×C22⋊C411yescharacteristic
111C23×C13#12312yes—
112D4×C13—44no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13#10412yes—
138C2×C4×C13#11711yescharacteristic
139C2×C4×C13#11711yescharacteristic
140C2×C4×C13#12312yes—
141C2×Dic13—44no—
142C2×Dic13—82no—
143C2×Dic13—82no—
144#1055—82no—
145C2×C4×D4C2×D1311yescharacteristic
146C2×#99—261no—
147#407—132no—
148#390—21no—
149#388—21no—
150#388—21no—
151#382Dic1311yescharacteristic, complemented
152#381Dic1311yescharacteristic, complemented
153#381C2×D1311yescharacteristic
154C4×C4⋊C4—21no—
155C4×C4⋊C4Dic1311yescharacteristic, complemented
156C4×C22⋊C4—132no—
157C4×C22⋊C4Dic1311yescharacteristic, complemented
158C4×C22⋊C4C2×D1311yescharacteristic
159#342—261no—
160#324—261no—
161#323—261no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—22no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—81no—
171C22×C13—81no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13#38111yescharacteristic
175C22×C13C2×#10411yescharacteristic
176C22×C13#42111yescharacteristic
177C4×C13—22no—
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—42no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—81no—
185C4×C13—81no—
186C4×C13—81no—
187Dic13—84no—
188C22×D4C22⋊D1311yescharacteristic
189C23×C4C2×Dic1311yescharacteristic
190C23×C4C22×D1311yescharacteristic
191C2×M16—262no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4C22⋊D1311yescharacteristic
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—262no—
202C2×C22⋊C4C22⋊D1311yescharacteristic
203C2×C22⋊C4C22⋊D1311yescharacteristic
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42—262no—
208C2×C42C2×Dic1311yescharacteristic
209#99—264no—
210C22⋊C8—262no—
211C22⋊C8—262no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—262no—
216#95C2×Dic1311yescharacteristic
217#95C2×Dic1311yescharacteristic
218#95C2×Dic1311yescharacteristic
219#95C2×Dic1311yescharacteristic
220C2×C13—21no—
221C2×C13—21no—
222C2×C13—42no—
223C2×C13—81no—
224C2×C13#182611yescharacteristic
225C2×C13#182711yescharacteristic
226C2×C13#182811yescharacteristic
227C24C22⋊Dic1311yescharacteristic
228C24C2×C22⋊D1311yescharacteristic
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4—522no—
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22⋊Dic1311yescharacteristic
244C22×C4#612712yes—
245C22×C4#612712yes—
246C22×C4C22×Dic1311yescharacteristic
247C22×C4C2×C22⋊D1311yescharacteristic
248M16—1042no—
249C2×C8—522no—
250C4⋊C4—22no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—81no—
258C22⋊C4—81no—
259C22⋊C4—264no—
260C22⋊C4—522no—
261C42—21no—
262C42—21no—
263C42—42no—
264C42—81no—
265C42—81no—
266C42—1042no—
267C13#877911yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23#8818312yes—
278C23C2×C22⋊Dic1311yescharacteristic
279D4—44no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—524no—
305C2×C4—1042no—
306C2×C4—1042no—
307C2×C4#8807712yes—
308C2×C4#8818011yescharacteristic
309C2×C4#8818011yescharacteristic
310C2×C4#8818312yes—
311C8—1042no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22#1171887211yescharacteristic
325C22C2×#8807711yescharacteristic
326C22#1171889711yescharacteristic
327C4—22no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—1044no—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—81no—
342C2#1311493511yescharacteristic
343C2#1311494011yescharacteristic
344C2#1311494411yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2357C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2357D13
hypocenterC13#8779
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
3. #13112722C2semidirect
4. #13112688C2semidirect
10. C13×#382C4semidirect
11. C13×#381C4semidirect
14. C4×C13×C4⋊C4C4semidirect
15. C4×C13×C22⋊C4C4semidirect
151. #382Dic13semidirect
152. #381Dic13semidirect
155. C4×C4⋊C4Dic13semidirect
157. C4×C22⋊C4Dic13semidirect
267. C13#8779semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131742
#131127222
#131126882
C13×#23572
#877913