Finite Group Databasebeta

← #30595847

Subgroups — #30595847

Order 15616.

426 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 86 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#21461735C211yesmaximal, characteristic, complemented
2#21461536C211yesmaximal, characteristic, complemented
3#21460637C212yesmaximal, complemented
4#21460635C212yesmaximal
5#21454183C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519832—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519770—21no—
13#16839665C411yescharacteristic
14#16839665C2211yescharacteristic
15#16839661C2211yescharacteristic
16#16839660C411yescharacteristic
17#16839658C411yescharacteristic
18#16839656—21no—
19#16839655—21no—
20#16839650—21no—
21C42×Dic61C2211yescharacteristic
22C61×#390C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26#14519832—24no—
27#14519770—44no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C4×Dic61C2×C411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C22×D4×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C42×C61C2×C411yescharacteristic
51C24×C61—21no—
52C2×D4×C61—22no—
53C2×D4×C61—41no—
54C2×D4×C61—41no—
55C22×C4×C61—21no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×#92420—24no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C4⋊C4×C61—22no—
72C22⋊C4×C61—42no—
73C22⋊C4×C61—42no—
74C42×C61—41no—
75C22⋊Dic61—42no—
76C22⋊Dic61—42no—
77C22⋊Dic61—41no—
78C22⋊Dic61—42no—
79C22⋊Dic61—41no—
80C4⋊Dic61—42no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83#11758196—42no—
84#11758196—42no—
85C4×Dic61—22no—
86C4×Dic61—22no—
87C4×Dic61—21no—
88C4×Dic61—22no—
89C4×Dic61—21no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92C23×C61—41no—
93C23×C61—41no—
94C23×C61—41no—
95C23×C61—41no—
96C23×C61—41no—
97C23×C61—41no—
98C23×C61—41no—
99C23×C61C2×C22⋊C411yescharacteristic
100D4×C61—82no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61#13112yes—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61#10412yes—
129C2×Dic61AGL(1,ℤ/8)11yescharacteristic
130C2×Dic61AGL(1,ℤ/8)12yes—
131C2×Dic61#13711yescharacteristic
132#92420—44no—
133#92420—82no—
134#7706—611nomaximal, Sylow
135C22×C61—81no—
136C22×C61—81no—
137C22×C61—81no—
138C22×C61—81no—
139C22×C61—81no—
140C22×C61—81no—
141C22×C61—81no—
142C22×C61#40811yescharacteristic
143C22×C61#41011yescharacteristic
144C22×C61#41311yescharacteristic
145C22×C61#41711yescharacteristic
146C22×C61#41811yescharacteristic
147C22×C61C2×#10411yescharacteristic
148C22×C61#42111yescharacteristic
149C4×C61—22no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—81no—
153Dic61—22no—
154Dic61—22no—
155Dic61—21no—
156Dic61—21no—
157Dic61—41no—
158Dic61—81no—
159Dic61—81no—
160#2860—611no—
161#1831—611no—
162#1745—611no—
163#1271—612no—
164#1270—612no—
165C2×C61—161no—
166C2×C61#147311yescharacteristic
167C2×C61#148311yescharacteristic
168C2×C61#149611yescharacteristic
169C2×C61#150511yescharacteristic
170C2×C61#151211yescharacteristic
171C2×C61#152911yescharacteristic
172C2×C61#155711yescharacteristic
173C2×#126—1221no—
174C2×C4⋊C8—1221no—
175C2×#97—1221no—
176#390—611no—
177#390—611no—
178#390#692311yescharacteristic
179#389—611no—
180#389—611no—
181#389—611no—
182#388—1221no—
183#388—1221no—
184#388—1221no—
185C43—611no—
186#336—612no—
187#336—612no—
188#336—1221no—
189#336—1221no—
190C61#770611yescharacteristic, complemented, Sylow
191C22×D4C2×#692311yescharacteristic
192C22×C8—1222no—
193C22×C8—1222no—
194#126—2444no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4C2×#692311yescharacteristic
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—1221no—
204C2×C22⋊C4—1221no—
205C2×C22⋊C4—1221no—
206C2×C22⋊C4—1221no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42C2×#692311yescharacteristic
214C4⋊C8—2442no—
215#97—1224no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219C24—21no—
220C2×D4—22no—
221C2×D4—41no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4C22⋊#692311yescharacteristic
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22×#692311yescharacteristic
233C2×C8—1224no—
234C2×C8—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C2×C8—2442no—
239C4⋊C4—22no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C4⋊C4—2442no—
243C4⋊C4—2442no—
244C4⋊C4—2442no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—2441no—
248C22⋊C4—2441no—
249C22⋊C4—2442no—
250C22⋊C4—2442no—
251C22⋊C4—2442no—
252C42—41no—
253C42—1222no—
254C42—1221no—
255C42—1221no—
256C42—1222no—
257C42—1222no—
258C42—2441no—
259C42—2441no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23C2×C22⋊#692311yescharacteristic
268D4—82no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—611no—
281C2×C4—611no—
282C2×C4—612no—
283C2×C4—612no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4#1451986412yes—
300C8—4882no—
301C8—2444no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#1684073611yescharacteristic
310C22#1684074111yescharacteristic
311C22#1684074911yescharacteristic
312C22#1684075311yescharacteristic
313C22#1684075411yescharacteristic
314C22D61⋊#10411yescharacteristic
315C22#1684076011yescharacteristic
316C4—22no—
317C4—41no—
318C4—41no—
319C4—81no—
320C4—1222no—
321C4—1222no—
322C4—1221no—
323C4—1221no—
324C4—4881no—
325C4—4881no—
326C4—2441no—
327C2—161no—
328C2#2146110011yescharacteristic
329C2#2146113511yescharacteristic
330C2#2146117911yescharacteristic
331C2#2146120911yescharacteristic
332C2#2146123011yescharacteristic
333C2#2146128511yescharacteristic
334C2#2146135111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#7706
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21461735C2semidirect
2. #21461536C2semidirect
3. #21460637C2semidirect
190. C61#7706semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214615362
#214606372
#214606352
#214541832
#770661