Finite Group Databasebeta

← #30595900

Subgroups — #30595900

Order 15616.

388 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 96 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#21461747C211yesmaximal, characteristic
2#21461734C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5#21454178C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519767—21no—
13#16839661C2211yescharacteristic
14#16839660C411yescharacteristic
15#16839659—21no—
16#16839658C2211yescharacteristic
17#16839657—21no—
18#16839631C411yescharacteristic
19#16839631C411yescharacteristic
20#16839626—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26#14519767—44no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C4×Dic61C2×C411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61C2311yescharacteristic
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C42×C61C2×C411yescharacteristic
49#95×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22×C411yescharacteristic
55C22×Dic61—21no—
56C22×Dic61—21no—
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C2×D411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C2×#92420—42no—
62C2×#92420—42no—
63C2×#92420—42no—
64C2×#92420—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C4⋊C4×C61—22no—
68C4⋊C4×C61—42no—
69C4⋊C4×C61—41no—
70C42×C61—22no—
71C4⋊Dic61—22no—
72C4⋊Dic61—42no—
73C4⋊Dic61—41no—
74#11758196—42no—
75#11758196—42no—
76#11758196—42no—
77#11758196—42no—
78#11758196—42no—
79#11758196—42no—
80C4×Dic61—22no—
81C4×Dic61—22no—
82C4×Dic61—41no—
83C4×Dic61—41no—
84C4×Dic61—41no—
85C4×Dic61SD1612yes—
86C4×Dic61Q1612yes—
87C23×C61C2×C22⋊C411yescharacteristic
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61#10312yes—
102C2×C4×C61#13112yes—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61#10112yes—
118C2×Dic61#10312yes—
119C2×Dic61C2×SD1611yescharacteristic
120C2×Dic61C2×Q1611yescharacteristic
121C2×Dic61AGL(1,ℤ/8)12yes—
122#92420—82no—
123#92420—82no—
124#7720—611nomaximal, Sylow
125C22×C61#40811yescharacteristic
126C22×C61#41011yescharacteristic
127C22×C61C2×#10111yescharacteristic
128C22×C61C2×#10311yescharacteristic
129C22×C61#41811yescharacteristic
130C22×C61#42111yescharacteristic
131C22×C61#42111yescharacteristic
132C4×C61—22no—
133C4×C61—22no—
134C4×C61—41no—
135C4×C61—81no—
136C4×C61—81no—
137Dic61—22no—
138Dic61—22no—
139Dic61—21no—
140Dic61—21no—
141Dic61—22no—
142Dic61—81no—
143Dic61—81no—
144#2859—611no—
145#1839—611no—
146#1831—611no—
147#1271—612no—
148#1271—612no—
149C2×C61#147011yescharacteristic
150C2×C61#148111yescharacteristic
151C2×C61#149611yescharacteristic
152C2×C61#151411yescharacteristic
153C2×C61#151811yescharacteristic
154C2×C61#153411yescharacteristic
155C2×C61#154911yescharacteristic
156C2×#125—1221no—
157C2×C4⋊C8—1221no—
158#389—611no—
159#389—611no—
160#389—611no—
161#389—1221no—
162#389—1221no—
163#389#692311yescharacteristic
164#384—611no—
165#384—611no—
166#382—1221no—
167C43—611no—
168#336—612no—
169#336—612no—
170#336—1221no—
171#336—1221no—
172#336—1221no—
173C61#772011yescharacteristic, complemented, Sylow
174C22×C8—1222no—
175C22×C8—1222no—
176#125—2444no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4—1221no—
184C2×C4⋊C4—1221no—
185C2×C4⋊C4—1221no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4C2×#692311yescharacteristic
188C2×C4⋊C4C2×#692311yescharacteristic
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—611no—
193C2×C42—611no—
194C2×C42—611no—
195C2×C42C2×#692311yescharacteristic
196C4⋊C8—2442no—
197#95—21no—
198#95—1221no—
199#95—1221no—
200#95—1221no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4C22⋊#692311yescharacteristic
210C22×C4C22⋊#692311yescharacteristic
211C22×C4C22×#692311yescharacteristic
212C2×C8—2442no—
213C2×C8—2442no—
214C2×C8—2442no—
215C2×C8—2442no—
216C2×C8—2442no—
217C2×C8—2442no—
218C4⋊C4—22no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—1222no—
222C4⋊C4—2441no—
223C4⋊C4—2442no—
224C4⋊C4—2442no—
225C4⋊C4—2442no—
226C4⋊C4—2442no—
227C4⋊C4—2442no—
228C4⋊C4—2442no—
229C4⋊C4—2442no—
230C42—22no—
231C42—612no—
232C42—612no—
233C42—1222no—
234C42—1222no—
235C42—2441no—
236C42—2441no—
237C42—2441no—
238C23C2×C22⋊#692311yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—612no—
253C2×C4—612no—
254C2×C4—611no—
255C2×C4—611no—
256C2×C4—612no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4#1451984012yes—
272C2×C4#1451986412yes—
273C8—4882no—
274C8—4882no—
275C22#1684073511yescharacteristic
276C22#1684074111yescharacteristic
277C22D61⋊#10111yescharacteristic
278C22C2×#1451984011yescharacteristic
279C22#1684075411yescharacteristic
280C22#1684075911yescharacteristic
281C22#1684075911yescharacteristic
282C4—22no—
283C4—22no—
284C4—41no—
285C4—81no—
286C4—81no—
287C4—1221no—
288C4—1221no—
289C4—1222no—
290C4—1222no—
291C4—1222no—
292C4—4881no—
293C4—4881no—
294C2#2146109111yescharacteristic
295C2#2146112711yescharacteristic
296C2#2146117811yescharacteristic
297C2#2146123811yescharacteristic
298C2#2146125211yescharacteristic
299C2#2146130211yescharacteristic
300C2#2146133511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7720
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
173. C61#7720semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214617342
#214606382
#214606372
#214541782
#772061