Finite Group Databasebeta

← #29568636

Subgroups — #29568636

Order 15616.

352 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21445962C211yesmaximal, characteristic
2#21445936C211yesmaximal, characteristic
3#21443642C212yesmaximal
4#21443642C212yesmaximal
5C61×#2864C211yesmaximal, characteristic
6C2×C4⋊#92418—21no—
7#16839517—21no—
8#16839517—21no—
9#16839517—21no—
10#16839517C2212yes—
11#16839517C2212yes—
12C61×#389C411yescharacteristic
13C61×#389C411yescharacteristic
14C61×#389C2211yescharacteristic
15C61×#389C2211yescharacteristic
16C61×#387—21no—
17C61×#387—21no—
18C61×#387—21no—
19C61×#387—21no—
20C61×#382C411yescharacteristic
21C61×#382C411yescharacteristic
22C43×C61C2211yescharacteristic
23C22×#92418—22no—
24C22×#92418—22no—
25C4⋊#92418—42no—
26C2×C4⋊C4×C61—21no—
27C2×C4⋊C4×C61—21no—
28C2×C4⋊C4×C61—21no—
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61C2×C411yescharacteristic
31C2×C4⋊C4×C61C2×C411yescharacteristic
32C2×C4⋊C4×C61C2×C411yescharacteristic
33C2×C4⋊C4×C61C2×C411yescharacteristic
34C2×C42×C61C2×C411yescharacteristic
35C2×C42×C61C2×C411yescharacteristic
36C2×C42×C61D411yescharacteristic
37C2×C42×C61D411yescharacteristic
38C2×C42×C61D411yescharacteristic
39C2×C42×C61D411yescharacteristic
40C2×C42×C61C2311yescharacteristic
41#95×C61—21no—
42#95×C61—21no—
43#95×C61—21no—
44#95×C61—21no—
45#95×C61—21no—
46#95×C61—21no—
47#95×C61—21no—
48#95×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62C4⋊C4×C61—42no—
63C4⋊C4×C61—42no—
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C42×C61—22no—
70C42×C61—22no—
71C42×C61—22no—
72C42×C61—21no—
73C42×C61—21no—
74C42×C61—41no—
75C42×C61—41no—
76C42×C61—41no—
77C2×#92418—42no—
78C2×#92418—42no—
79C2×#92418—42no—
80C2×#92418—42no—
81C2×#92418—42no—
82C2×#92418—42no—
83C23×C61C2×C22⋊C411yescharacteristic
84C2×C4×C61—21no—
85C2×C4×C61—21no—
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—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#10112yes—
114C2×C4×C61#13112yes—
115C2×C4×C61#13512yes—
116C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C61#13711yescharacteristic
118#92418—82no—
119#92418—82no—
120#7717—611nomaximal, Sylow
121C22×C61#40811yescharacteristic
122C22×C61#41011yescharacteristic
123C22×C61C2×#10111yescharacteristic
124C22×C61#41611yescharacteristic
125C22×C61#41711yescharacteristic
126C22×C61#42111yescharacteristic
127C22×C61#42111yescharacteristic
128C4×C61—22no—
129C4×C61—22no—
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—22no—
133C4×C61—41no—
134C4×C61—41no—
135C4×C61—41no—
136C4×C61—81no—
137C4×C61—81no—
138C4×C61—81no—
139C4×C61—81no—
140#2864D6111yescharacteristic
141#1839—611no—
142#1831—611no—
143#1271—612no—
144#1271—612no—
145C2×C61#147011yescharacteristic
146C2×C61#148211yescharacteristic
147C2×C61#149511yescharacteristic
148C2×C61#151211yescharacteristic
149C2×C61#152111yescharacteristic
150C2×C61#153711yescharacteristic
151C2×C61#155211yescharacteristic
152C2×C4⋊C8—1221no—
153#389Dic6111yescharacteristic
154#389Dic6111yescharacteristic
155#389C2×D6111yescharacteristic
156#389C2×D6111yescharacteristic
157#387—21no—
158#387—21no—
159#387—21no—
160#387—21no—
161#382Dic6111yescharacteristic
162#382Dic6111yescharacteristic
163C43C2×D6111yescharacteristic
164#336—612no—
165#336—612no—
166#336—1221no—
167#336—1221no—
168#336—1221no—
169C61#771711yescharacteristic, complemented, Sylow
170C22×C8—1222no—
171C22×C8—1222no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4C2×Dic6111yescharacteristic
177C2×C4⋊C4C2×Dic6111yescharacteristic
178C2×C4⋊C4C2×Dic6111yescharacteristic
179C2×C4⋊C4C2×Dic6111yescharacteristic
180C2×C42C2×Dic6111yescharacteristic
181C2×C42C2×Dic6111yescharacteristic
182C2×C42C22⋊D6111yescharacteristic
183C2×C42C22⋊D6111yescharacteristic
184C2×C42C22⋊D6111yescharacteristic
185C2×C42C22⋊D6111yescharacteristic
186C2×C42C22×D6111yescharacteristic
187C4⋊C8—2442no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4C22⋊Dic6111yescharacteristic
201C22×C4C22⋊Dic6111yescharacteristic
202C22×C4C22⋊Dic6111yescharacteristic
203C22×C4C22⋊Dic6111yescharacteristic
204C22×C4C22×Dic6111yescharacteristic
205C22×C4C2×C22⋊D6111yescharacteristic
206C22×C4C2×C22⋊D6111yescharacteristic
207C2×C8—2442no—
208C2×C8—2442no—
209C2×C8—2442no—
210C2×C8—2442no—
211C2×C8—2442no—
212C2×C8—2442no—
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C42—22no—
223C42—22no—
224C42—22no—
225C42—21no—
226C42—21no—
227C42—41no—
228C42—41no—
229C42—41no—
230C23C2×C22⋊Dic6111yescharacteristic
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
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—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4#1451969612yes—
261C2×C4#1451978412yes—
262C2×C4#1451979712yes—
263C2×C4#1451980211yescharacteristic
264C2×C4#1451980711yescharacteristic
265C8—4882no—
266C8—4882no—
267C22#1683972911yescharacteristic
268C22#1683973611yescharacteristic
269C22C2×#1451969611yescharacteristic
270C22#1683975811yescharacteristic
271C22#1683976311yescharacteristic
272C22#1683977911yescharacteristic
273C22#1683977911yescharacteristic
274C4—21no—
275C4—21no—
276C4—22no—
277C4—22no—
278C4—22no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—81no—
283C4—81no—
284C4—81no—
285C4—81no—
286C2#2144417511yescharacteristic
287C2#2144422711yescharacteristic
288C2#2144428411yescharacteristic
289C2#2144435711yescharacteristic
290C2#2144439611yescharacteristic
291C2#2144445711yescharacteristic
292C2#2144451911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2864C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2864D61
hypocenterC61#7717
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #2864

Complements

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

NH ≅ G/Ntype
169. C61#7717semidirect

Maximal subgroups

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

subgroupindex
#214459622
#214459362
#214436422
C61×#28642
#771761