Finite Group Databasebeta

← #15756561

Subgroups — #15756561

Order 3328.

466 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 95 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#13117809C211yesmaximal, characteristic
2#13113174C211yesmaximal, characteristic
3#13112722C212yesmaximal, complemented
4#13112689C212yesmaximal, complemented
5C4×C13×#99C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×C13×#99—21no—
8C4×C13×C22⋊C4C2212yes—
9#11718882—21no—
10#11718872C411yescharacteristic, complemented
11#11718872C2211yescharacteristic
12C4×C22⋊Dic13C411yescharacteristic, complemented
13C4×C22⋊Dic13C2211yescharacteristic
14#11718868C2212yes—
15C4⋊C4×Dic13—21no—
16#11718612—21no—
17#11718612—21no—
18#11718597C411yescharacteristic, complemented
19C4×C4⋊Dic13C411yescharacteristic, complemented
20C13×#342—21no—
21#11718120—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⋊C4D411yescharacteristic
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C13×C22⋊C4D411yescharacteristic
32C2×C42×C13—22no—
33C2×C42×C13C2×C411yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13—21no—
43C2×#6099—22no—
44C13×#99—24no—
45C13×#95—22no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071C2×C411yescharacteristic
50#88071C2×C411yescharacteristic
51#88071C2×C411yescharacteristic
52#88071C2×C411yescharacteristic
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—42no—
64C22×C4×C13—81no—
65C22×C4×C13—81no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4112yes—
72C22×C4×C13#4112yes—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C13×C4⋊C4—22no—
78C13×C22⋊C4—22no—
79C13×C22⋊C4—22no—
80C13×C22⋊C4—24no—
81C13×C22⋊C4—42no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—82no—
85C22⋊Dic13—42no—
86C22⋊Dic13—42no—
87C22⋊Dic13—81no—
88C22⋊Dic13—81no—
89C4⋊Dic13—42no—
90C4⋊Dic13—42no—
91C4×Dic13—42no—
92C4×Dic13—81no—
93C4×Dic13—81no—
94#6099—82no—
95C2×#1055—42no—
96#2357—131no—
97C4×#99D1311yescharacteristic
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—21no—
116C2×C4×C13—21no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—44no—
124C2×C4×C13—81no—
125C2×C4×C13—81no—
126C2×C4×C13—82no—
127C2×C4×C13—82no—
128C2×C4×C13#10412yes—
129C2×C4×C13#11711yescharacteristic
130C2×C4×C13#11711yescharacteristic
131C2×C4×C13#12312yes—
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144#1055—82no—
145C2×C4×D4C2×D1311yescharacteristic
146C2×#99—21no—
147#407—132no—
148#390—261no—
149#388—261no—
150#388—261no—
151#382—131no—
152#381—131no—
153#381—131no—
154C4×C4⋊C4—131no—
155C4×C4⋊C4—261no—
156C4×C22⋊C4—131no—
157C4×C22⋊C4—131no—
158C4×C22⋊C4C2×D1312yes—
159#342—21no—
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—41no—
182C4×C13—41no—
183C4×C13—84no—
184Dic13—42no—
185Dic13—81no—
186Dic13—81no—
187Dic13—81no—
188C22×D4C22⋊D1311yescharacteristic
189C23×C4C4×D1311yescharacteristic
190C23×C4C22×D1311yescharacteristic
191C2×M16—262no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4D5211yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4—261no—
199C2×C22⋊C4—261no—
200C2×C22⋊C4—261no—
201C2×C22⋊C4—261no—
202C2×C22⋊C4D5211yescharacteristic
203C2×C22⋊C4C22⋊D1311yescharacteristic
204C2×C42—22no—
205C2×C42—261no—
206C2×C42—261no—
207C2×C42—261no—
208C2×C42C4×D1311yescharacteristic
209#99—24no—
210C22⋊C8—262no—
211C22⋊C8—262no—
212#95—22no—
213#95—131no—
214#95—131no—
215#95—131no—
216#95—131no—
217#95—261no—
218#95—261no—
219#95—261no—
220C2×C13—21no—
221C2×C13—21no—
222C2×C13—42no—
223C2×C13—81no—
224C2×C13#182611yescharacteristic
225C2×C13#182711yescharacteristic
226C2×C13#182811yescharacteristic
227C24#610311yescharacteristic
228C24C2×C22⋊D1311yescharacteristic
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—42no—
235C22×C4—81no—
236C22×C4—81no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4#610311yescharacteristic
242C22×C4#610311yescharacteristic
243C22×C4#610311yescharacteristic
244C22×C4C2×C4×D1311yescharacteristic
245C22×C4C2×D5211yescharacteristic
246C22×C4#612912yes—
247C22×C4#612912yes—
248M16—1042no—
249C2×C8—522no—
250C4⋊C4—22no—
251C4⋊C4—522no—
252C4⋊C4—522no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—24no—
256C22⋊C4—42no—
257C22⋊C4—522no—
258C22⋊C4—522no—
259C22⋊C4—1041no—
260C22⋊C4—1041no—
261C42—21no—
262C42—21no—
263C42—82no—
264C42—522no—
265C42—1041no—
266C42—1041no—
267C13#877911yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×#610311yescharacteristic
278C23#8818912yes—
279D4—44no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—44no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—262no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4#8804512yes—
308C2×C4#8813111yescharacteristic
309C2×C4#8813111yescharacteristic
310C2×C4#8814012yes—
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—
324C22C2×#8804511yescharacteristic
325C22#1171860411yescharacteristic
326C22#1171866611yescharacteristic
327C4—22no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—84no—
334C4—522no—
335C4—1041no—
336C4—1041no—
337C4—1041no—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—81no—
342C2#1311493611yescharacteristic
343C2#1311493711yescharacteristic
344C2#1311494211yescharacteristic
subgroupG/H
centerC22#11718604
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC4×C13×#99C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenterC4×#99D13
hypocenterC13#8779
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #13112722C2semidirect
4. #13112689C2semidirect
10. #11718872C4semidirect
12. C4×C22⋊Dic13C4semidirect
18. #11718597C4semidirect
19. C4×C4⋊Dic13C4semidirect
267. C13#8779semidirect

Maximal subgroups

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

subgroupindex
#131178092
#131131742
#131127222
#131126892
C4×C13×#992
#877913