Finite Group Databasebeta

← #30595859

Subgroups — #30595859

Order 15616.

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

normal subgroups only

This group has 372 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
2#21461536C211yesmaximal, characteristic
3#21460640C212yesmaximal
4#21460638C212yesmaximal
5#21454202C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519832—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12#16839668C411yescharacteristic
13#16839667C411yescharacteristic
14#16839667C2211yescharacteristic
15#16839661C411yescharacteristic
16#16839658C2211yescharacteristic
17#16839648—21no—
18#16839645—21no—
19#16839643—21no—
20#16839629—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26#14519832—24no—
27C22×Dic122C2×C411yescharacteristic
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61C2311yescharacteristic
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
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×Dic122—22no—
62C2×Dic122—41no—
63C2×Dic122—41no—
64C2×#92420—24no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C42×C61—41no—
74C4⋊Dic61—22no—
75C4⋊Dic61—42no—
76#11758196—41no—
77#11758196—41no—
78C4×Dic61—22no—
79C4×Dic61—22no—
80C4×Dic61—21no—
81C4×Dic61—21no—
82C4×Dic61—22no—
83C4×Dic61—41no—
84C4×Dic61—41no—
85C23×C61C2×C22⋊C411yescharacteristic
86C2×C4×C61—21no—
87C2×C4×C61—21no—
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—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61#13112yes—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61#10412yes—
117C2×Dic61AGL(1,ℤ/8)11yescharacteristic
118C2×Dic61#13711yescharacteristic
119C2×Dic61#13712yes—
120Dic122—82no—
121#92420—44no—
122#92420—82no—
123#7709—611nomaximal, Sylow
124C22×C61#40811yescharacteristic
125C22×C61#41011yescharacteristic
126C22×C61#41311yescharacteristic
127C22×C61#41711yescharacteristic
128C22×C61#41911yescharacteristic
129C22×C61C2×#10411yescharacteristic
130C22×C61#42111yescharacteristic
131C4×C61—22no—
132C4×C61—41no—
133C4×C61—41no—
134C4×C61—81no—
135C4×C61—81no—
136Dic61—22no—
137Dic61—22no—
138Dic61—21no—
139Dic61—21no—
140Dic61—41no—
141Dic61—81no—
142Dic61—81no—
143#2863—611no—
144#1831—611no—
145#1745—611no—
146#1272—612no—
147#1271—612no—
148C2×C61#147311yescharacteristic
149C2×C61#148311yescharacteristic
150C2×C61#149711yescharacteristic
151C2×C61#150611yescharacteristic
152C2×C61#151211yescharacteristic
153C2×C61#152911yescharacteristic
154C2×C61#155911yescharacteristic
155C2×C4⋊C8—1221no—
156C2×#97—1221no—
157#391—611no—
158#391—611no—
159#391—611no—
160#389—611no—
161#389—611no—
162#389#692311yescharacteristic
163#387—1221no—
164#387—1221no—
165#387—1221no—
166#383—1221no—
167C43—611no—
168#336—612no—
169#336—612no—
170#336—1221no—
171#336—1221no—
172C61#770911yescharacteristic, complemented, Sylow
173C22×Q8—611no—
174C22×C8—1222no—
175C22×C8—1222no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4C2×#692311yescharacteristic
181C2×C4⋊C4C2×#692311yescharacteristic
182C2×C42—611no—
183C2×C42—611no—
184C2×C42—611no—
185C2×C42—611no—
186C2×C42—611no—
187C2×C42—611no—
188C2×C42C2×#692311yescharacteristic
189C4⋊C8—2442no—
190#97—1224no—
191#95—21no—
192#95—1221no—
193#95—1221no—
194#95—1221no—
195#95—1221no—
196#95—1221no—
197#95—1221no—
198#95—1221no—
199#95—1221no—
200C2×Q8—1222no—
201C2×Q8—2441no—
202C2×Q8—2441no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4C22⋊#692311yescharacteristic
212C22×C4C22⋊#692311yescharacteristic
213C22×C4C22×#692311yescharacteristic
214C2×C8—1224no—
215C2×C8—2442no—
216C2×C8—2442no—
217C2×C8—2442no—
218C2×C8—2442no—
219C2×C8—2442no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—1222no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2442no—
227C42—41no—
228C42—1222no—
229C42—1221no—
230C42—1221no—
231C42—1222no—
232C42—1222no—
233C42—2441no—
234C42—2441no—
235C23C2×C22⋊#692311yescharacteristic
236Q8—4882no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—611no—
252C2×C4—611no—
253C2×C4—612no—
254C2×C4—612no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4#1451986512yes—
271C8—4882no—
272C8—2444no—
273C22#1684073711yescharacteristic
274C22#1684074111yescharacteristic
275C22#1684074911yescharacteristic
276C22#1684075311yescharacteristic
277C22#1684075511yescharacteristic
278C22D61⋊#10411yescharacteristic
279C22#1684076011yescharacteristic
280C4—22no—
281C4—41no—
282C4—41no—
283C4—81no—
284C4—81no—
285C4—1222no—
286C4—1222no—
287C4—1221no—
288C4—1221no—
289C4—4881no—
290C4—4881no—
291C4—2441no—
292C2#2146110211yescharacteristic
293C2#2146113711yescharacteristic
294C2#2146118311yescharacteristic
295C2#2146121211yescharacteristic
296C2#2146123011yescharacteristic
297C2#2146128511yescharacteristic
298C2#2146135511yescharacteristic
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#7709
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
172. C61#7709semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214615362
#214606402
#214606382
#214542022
#770961