Finite Group Databasebeta

← #15756550

Subgroups — #15756550

Order 3328.

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

normal subgroups only

This group has 480 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×#2353C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C13×#388—21no—
8C13×#387—21no—
9C13×#386—21no—
10C13×#383C411yescharacteristic, complemented
11C13×#381C2211yescharacteristic
12C13×#380C411yescharacteristic, complemented
13C4×C13×C22⋊C4—21no—
14C4×C13×C22⋊C4C2211yescharacteristic
15C13×#376C411yescharacteristic, complemented
16C2×C13×#95C411yescharacteristic, complemented
17C2×#88074—21no—
18C4×C22⋊Dic13C2212yes—
19#11718868C2212yes—
20#11718120—21no—
21#11718118—21no—
22#11718117—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C4×D4×C13—22no—
28C4×D4×C13—22no—
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⋊C4D411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C42×C13—21no—
37C2×C42×C13—21no—
38C2×C42×C13C2×C411yescharacteristic
39C2×C22⋊Dic13—22no—
40C2×C4×Dic13—22no—
41C2×#6099—22no—
42C13×#95—21no—
43C13×#95—21no—
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#8777—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—42no—
68C22×C4×C13—42no—
69C22×C4×C13—81no—
70C22×C4×C13—81no—
71C22×C4×C13—81no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13#4112yes—
78C22×C4×C13#4112yes—
79C22×Dic13—42no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—81no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—81no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13—42no—
90C42×C13—81no—
91C22⋊Dic13—24no—
92C22⋊Dic13—42no—
93C4×Dic13—82no—
94#6099—82no—
95C2×#1055—42no—
96#2353D1311yescharacteristic
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—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13#10412yes—
110C23×C13C2×C22⋊C411yescharacteristic
111C23×C13#12312yes—
112D4×C13—44no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
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—41no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—84no—
139C2×C4×C13#11711yescharacteristic
140C2×C4×C13#11711yescharacteristic
141C2×C4×C13#12312yes—
142C2×Dic13—44no—
143C2×Dic13—82no—
144C2×Dic13—82no—
145#1055—82no—
146C2×C4×D4C2×D1311yescharacteristic
147C2×#99—261no—
148#407—132no—
149#388—21no—
150#387—21no—
151#386—21no—
152#383Dic1311yescharacteristic, complemented
153#381C2×D1311yescharacteristic
154#380Dic1311yescharacteristic, complemented
155C4×C22⋊C4—21no—
156C4×C22⋊C4—132no—
157C4×C22⋊C4C2×D1311yescharacteristic
158#376Dic1311yescharacteristic, complemented
159C2×#95Dic1311yescharacteristic, complemented
160#342—261no—
161#324—261no—
162#323—261no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—42no—
170C22×C13—42no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—81no—
174C22×C13—81no—
175C22×C13#38111yescharacteristic
176C22×C13C2×#10411yescharacteristic
177C22×C13#42111yescharacteristic
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—42no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—81no—
186C4×C13—81no—
187C4×C13—81no—
188Dic13—84no—
189C22×D4C22⋊D1311yescharacteristic
190C23×C4—21no—
191C23×C4C2×Dic1311yescharacteristic
192C23×C4C22×D1311yescharacteristic
193C2×M16—262no—
194C4×D4—22no—
195C4×D4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C22⋊D1311yescharacteristic
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—262no—
207C2×C42C2×Dic1311yescharacteristic
208#99—264no—
209C22⋊C8—262no—
210C22⋊C8—262no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—262no—
217#95C2×Dic1311yescharacteristic
218#95C2×Dic1311yescharacteristic
219#95C2×Dic1311yescharacteristic
220#95C2×Dic1311yescharacteristic
221C2×C13—21no—
222C2×C13—21no—
223C2×C13—42no—
224C2×C13—42no—
225C2×C13#182611yescharacteristic
226C2×C13#182711yescharacteristic
227C2×C13#182811yescharacteristic
228C24C22⋊Dic1311yescharacteristic
229C24C2×C22⋊D1311yescharacteristic
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—81no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4—522no—
245C22×C4C22⋊Dic1311yescharacteristic
246C22×C4C22⋊Dic1311yescharacteristic
247C22×C4C22⋊Dic1311yescharacteristic
248C22×C4#612712yes—
249C22×C4#612712yes—
250C22×C4C22×Dic1311yescharacteristic
251C22×C4C2×C22⋊D1311yescharacteristic
252M16—1042no—
253C2×C8—522no—
254C4⋊C4—22no—
255C4⋊C4—81no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—81no—
261C22⋊C4—264no—
262C22⋊C4—522no—
263C42—21no—
264C42—21no—
265C42—42no—
266C42—81no—
267C42—1042no—
268C13#877711yescharacteristic, complemented, Sylow
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23#8807712yes—
278C23#8818312yes—
279C23C2×C22⋊Dic1311yescharacteristic
280D4—44no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
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—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—84no—
307C2×C4—524no—
308C2×C4—1042no—
309C2×C4—1042no—
310C2×C4#8818011yescharacteristic
311C2×C4#8818011yescharacteristic
312C2×C4#8818312yes—
313C8—1042no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22#1171887211yescharacteristic
327C22C2×#8807711yescharacteristic
328C22#1171889711yescharacteristic
329C4—22no—
330C4—21no—
331C4—21no—
332C4—42no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—1044no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—42no—
344C2#1311493511yescharacteristic
345C2#1311494011yescharacteristic
346C2#1311494411yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2353C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2353D13
hypocenterC13#8777
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2353

Complements

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

NH ≅ G/Ntype
3. #13112722C2semidirect
4. #13112688C2semidirect
10. C13×#383C4semidirect
12. C13×#380C4semidirect
15. C13×#376C4semidirect
16. C2×C13×#95C4semidirect
152. #383Dic13semidirect
154. #380Dic13semidirect
158. #376Dic13semidirect
159. C2×#95Dic13semidirect
268. C13#8777semidirect

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×#23532
#877713