Finite Group Databasebeta

← #30595788

Subgroups — #30595788

Order 15616.

410 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461604C211yesmaximal, characteristic
2C4×C4⋊#92420C211yesmaximal, characteristic
3#21460640C212yesmaximal
4#21460637C212yesmaximal
5#21454202C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420—21no—
8C2×#14519832—21no—
9C2×C4×#92420—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12#16839668C411yescharacteristic
13#16839667C411yescharacteristic
14#16839667C2211yescharacteristic
15#16839661C2211yescharacteristic
16#16839658C411yescharacteristic
17#16839648—21no—
18#16839645—21no—
19#16839643—21no—
20#16839629—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—24no—
26C4⋊#92420—24no—
27#14519832—42no—
28C4×#92420—42no—
29C22×Dic122C2×C411yescharacteristic
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61C2311yescharacteristic
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51#95×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×Dic61—21no—
58C22×Dic61—21no—
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C22×Dic61C2×D411yescharacteristic
63C2×Dic122—22no—
64C2×Dic122—41no—
65C2×Dic122—41no—
66C2×#92420—24no—
67C2×#92420—24no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C4⋊C4×C61—22no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—42no—
75C42×C61—22no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—42no—
80C4×Dic61—22no—
81C4×Dic61—22no—
82C4×Dic61—21no—
83C4×Dic61—21no—
84C4×Dic61—41no—
85C4×Dic61—41no—
86C4×Dic61SD1612yes—
87C4×Dic61Q1612yes—
88C23×C61C2×C22⋊C411yescharacteristic
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#10412yes—
103C2×C4×C61#13112yes—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61#10312yes—
119C2×Dic61#10412yes—
120C2×Dic61C2×SD1611yescharacteristic
121C2×Dic61C2×Q1611yescharacteristic
122C2×Dic61AGL(1,ℤ/8)11yescharacteristic
123C2×Dic61#13711yescharacteristic
124Dic122—82no—
125#92420—44no—
126#92420—44no—
127#7689—611nomaximal, Sylow
128C22×C61#40811yescharacteristic
129C22×C61#41011yescharacteristic
130C22×C61#41311yescharacteristic
131C22×C61C2×#10311yescharacteristic
132C22×C61#41711yescharacteristic
133C22×C61C2×#10411yescharacteristic
134C22×C61C2×#10411yescharacteristic
135C4×C61—22no—
136C4×C61—22no—
137C4×C61—22no—
138C4×C61—81no—
139C4×C61—81no—
140Dic61—22no—
141Dic61—21no—
142Dic61—21no—
143Dic61—21no—
144Dic61—21no—
145Dic61—22no—
146Dic61—81no—
147Dic61—81no—
148#2863—611no—
149#1767—611no—
150C4×C4⋊C8—611no—
151#1272—612no—
152#1271—612no—
153C2×C61#147311yescharacteristic
154C2×C61#148311yescharacteristic
155C2×C61#149311yescharacteristic
156C2×C61#150311yescharacteristic
157C2×C61#150911yescharacteristic
158C2×C61#152411yescharacteristic
159C2×C61#155011yescharacteristic
160C2×C4⋊C8—1221no—
161C2×C4⋊C8—1221no—
162C2×#97—1221no—
163C2×C4×C8—1221no—
164#391—611no—
165#391—611no—
166#391—611no—
167#389—611no—
168#389—611no—
169#389#692311yescharacteristic
170#387—1221no—
171#387—1221no—
172#387—1221no—
173#383—1221no—
174C43—611no—
175#336—612no—
176#336—612no—
177C61#768911yescharacteristic, complemented, Sylow
178C22×Q8—611no—
179C22×C8—1222no—
180C22×C8—1222no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—611no—
183C2×C4⋊C4—1221no—
184C2×C4⋊C4—1221no—
185C2×C4⋊C4C2×#692311yescharacteristic
186C2×C4⋊C4C2×#692311yescharacteristic
187C2×C42—611no—
188C2×C42—611no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—611no—
193C2×C42C2×#692311yescharacteristic
194C4⋊C8—1224no—
195C4⋊C8—1224no—
196#97—2442no—
197C4×C8—2442no—
198#95—21no—
199#95—1221no—
200#95—1221no—
201#95—1221no—
202#95—1221no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206#95—1221no—
207C2×Q8—1222no—
208C2×Q8—2441no—
209C2×Q8—2441no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4C22⋊#692311yescharacteristic
219C22×C4C22⋊#692311yescharacteristic
220C22×C4C22×#692311yescharacteristic
221C2×C8—1224no—
222C2×C8—1224no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C2×C8—2442no—
227C4⋊C4—22no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—2441no—
231C4⋊C4—2442no—
232C4⋊C4—2441no—
233C4⋊C4—2441no—
234C42—22no—
235C42—612no—
236C42—612no—
237C42—1221no—
238C42—1222no—
239C42—1221no—
240C42—1222no—
241C42—2441no—
242C42—2441no—
243C23C2×C22⋊#692311yescharacteristic
244Q8—4882no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—612no—
258C2×C4—611no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—611no—
262C2×C4—612no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4#1451984012yes—
278C2×C4#1451984112yes—
279C2×C4#1451986412yes—
280C8—2444no—
281C8—2444no—
282C22#1684073511yescharacteristic
283C22#1684074311yescharacteristic
284C22#1684074811yescharacteristic
285C22C2×#1451984011yescharacteristic
286C22#1684075311yescharacteristic
287C22C2×#1451984111yescharacteristic
288C22D61⋊#10411yescharacteristic
289C4—22no—
290C4—22no—
291C4—22no—
292C4—81no—
293C4—81no—
294C4—1222no—
295C4—1222no—
296C4—1221no—
297C4—1221no—
298C4—1221no—
299C4—1221no—
300C4—4881no—
301C4—4881no—
302C2#2146110311yescharacteristic
303C2#2146113411yescharacteristic
304C2#2146116711yescharacteristic
305C2#2146120211yescharacteristic
306C2#2146122211yescharacteristic
307C2#2146126911yescharacteristic
308C2#2146133611yescharacteristic
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#7689
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
177. C61#7689semidirect

Maximal subgroups

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

subgroupindex
#214616042
C4×C4⋊#924202
#214606402
#214606372
#214542022
#768961