Finite Group Databasebeta

← #29584778

Subgroups — #29584778

Order 15616.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446756C211yesmaximal, characteristic
2#21445946C211yesmaximal, characteristic
3#21445824C211yesmaximal, characteristic
4#21443703C211yesmaximal, characteristic
5#21443702C211yesmaximal, characteristic
6#21443653C211yesmaximal, characteristic
7C61×#1803C211yesmaximal, characteristic
8C2×C4⋊#92418C2211yescharacteristic
9C2×C4⋊#92418C2211yescharacteristic
10C2×#14519701—21no—
11C2×C4×#92418C2211yescharacteristic
12#16839632C2211yescharacteristic
13#16839524—21no—
14#16839524—21no—
15#16839524—21no—
16#16839517—21no—
17#16839517—21no—
18C2×C4×Q8×C61C2211yescharacteristic
19C2×C4⋊C8×C61C2211yescharacteristic
20C2×#103×C61—21no—
21C61×#384C2211yescharacteristic
22C61×#340—21no—
23C22×#92418—21no—
24C22×#92418—21no—
25C22×#92418D411yescharacteristic
26C22×#92418D411yescharacteristic
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C4⋊#92418—21no—
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34#14519701—42no—
35C4×#92418—21no—
36C4×#92418—21no—
37C22×Q8×C61D411yescharacteristic
38C22×C8×C61—21no—
39C4×Q8×C61—21no—
40C4×Q8×C61—21no—
41C4×Q8×C61—21no—
42C4×Q8×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C42×C61—21no—
49C2×C42×C61C2311yescharacteristic
50C4⋊C8×C61—21no—
51C4⋊C8×C61—21no—
52#103×C61—42no—
53C2×Q8×C61—21no—
54C2×Q8×C61—21no—
55C2×Q8×C61—21no—
56C2×Q8×C61—21no—
57C2×Q8×C61—21no—
58C2×Q8×C61SD1612yes—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61#4111yescharacteristic
65C22×Dic61—41no—
66C2×C8×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61—41no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—81no—
78C42×C61—41no—
79C42×C61—41no—
80C42×C61#4111yescharacteristic
81C42×C61#4111yescharacteristic
82C42×C61#4111yescharacteristic
83C42×C61#4111yescharacteristic
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—81no—
89C2×#92418—21no—
90C2×#92418—21no—
91C2×#92418—21no—
92C2×#92418—21no—
93C2×#92418—21no—
94C2×#92418—21no—
95C2×#92418—41no—
96C2×#92418—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101C23×C61#12111yescharacteristic
102Q8×C61—22no—
103Q8×C61—22no—
104Q8×C61—41no—
105Q8×C61—41no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—81no—
115C2×C4×C61—81no—
116C2×C4×C61—81no—
117C2×C4×C61#12311yescharacteristic
118C2×C4×C61#12311yescharacteristic
119C2×C4×C61#12311yescharacteristic
120C2×C4×C61#12411yescharacteristic
121C2×C4×C61#12611yescharacteristic
122C2×C4×C61#12611yescharacteristic
123C2×C4×C61C2×SD1611yescharacteristic
124C2×C4×C61#13511yescharacteristic
125C2×C4×C61#13511yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C61#13711yescharacteristic
129C2×C4×C61#13711yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C2×Dic61—81no—
132C2×Dic61—81no—
133C2×Dic61—81no—
134C8×C61—81no—
135#92418—41no—
136#92418—41no—
137#92418—81no—
138#92418—81no—
139#10626—611nomaximal, Sylow
140C22×C61#39711yescharacteristic
141C22×C61#46411yescharacteristic
142C22×C61#46411yescharacteristic
143C22×C61#46511yescharacteristic
144C22×C61#46811yescharacteristic
145C22×C61#47211yescharacteristic
146C22×C61#47311yescharacteristic
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—42no—
150C4×C61—81no—
151C4×C61—161no—
152C4×C61#48111yescharacteristic
153C4×C61#48211yescharacteristic
154C4×C61#48311yescharacteristic
155C4×C61#48511yescharacteristic
156C4×C61#48511yescharacteristic
157C4×C61#48511yescharacteristic
158C4×C61#48811yescharacteristic
159C4×C61#49111yescharacteristic
160Dic61—161no—
161#1984—611no—
162#1834—611no—
163#1803—611no—
164#1803D6111yescharacteristic
165#1296—611no—
166#1296—611no—
167#1277—611no—
168C2×C61#167811yescharacteristic
169C2×C61#168011yescharacteristic
170C2×C61#169811yescharacteristic
171C2×C61#170011yescharacteristic
172C2×C61#207411yescharacteristic
173C2×C61#207711yescharacteristic
174C2×C61#207811yescharacteristic
175C2×C4×Q8C2×D6111yescharacteristic
176C2×C4⋊C8—611no—
177C2×C4⋊C8—611no—
178C2×C4⋊C8C2×D6111yescharacteristic
179C2×#103—21no—
180C2×#103—1221no—
181C2×C4×C8—611no—
182#384—611no—
183#384C2×D6111yescharacteristic
184#340—21no—
185#340—1221no—
186#340—1221no—
187#340—1221no—
188#336—1221no—
189#336—1221no—
190C61#1062611yescharacteristic, complemented, Sylow
191C22×Q8C22⋊D6111yescharacteristic
192C22×C8—21no—
193C22×C8—611no—
194C22×C8—611no—
195C22×C8—1221no—
196C22×C8—1221no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4C22⋊D6111yescharacteristic
209C2×C42—21no—
210C2×C42C22×D6111yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—1221no—
214C4⋊C8—1221no—
215C4⋊C8—1221no—
216C4⋊C8—1221no—
217#103—42no—
218#103—2442no—
219C4×C8—1221no—
220C4×C8—1221no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8#1175820112yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—41no—
230C22×C4—2441no—
231C22×C4D4×D6111yescharacteristic
232C22×C4#1175822411yescharacteristic
233C22×C4C2×C22⋊D6111yescharacteristic
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—1221no—
238C2×C8—1221no—
239C2×C8—1221no—
240C2×C8—1221no—
241C2×C8—1221no—
242C2×C8—1221no—
243C2×C8—2441no—
244C2×C8—2441no—
245C2×C8—2441no—
246C2×C8—2441no—
247C2×C8—2441no—
248C2×C8—2441no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—4881no—
259C4⋊C4—2441no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C42—41no—
264C42—41no—
265C42#1175822211yescharacteristic
266C42#1175822211yescharacteristic
267C42#1175822411yescharacteristic
268C42#1175822411yescharacteristic
269C23#1451974911yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—4881no—
286C2×C4—4881no—
287C2×C4—4881no—
288C2×C4#1451975811yescharacteristic
289C2×C4#1451975911yescharacteristic
290C2×C4#1451976011yescharacteristic
291C2×C4#1451976311yescharacteristic
292C2×C4#1451977011yescharacteristic
293C2×C4#1451977011yescharacteristic
294C2×C4C2×#1175820111yescharacteristic
295C2×C4#1451979711yescharacteristic
296C2×C4#1451979811yescharacteristic
297C2×C4#1451980011yescharacteristic
298C2×C4#1451980311yescharacteristic
299C2×C4#1451980611yescharacteristic
300C2×C4#1451980711yescharacteristic
301C2×C4#1451980911yescharacteristic
302C8—81no—
303C8—4881no—
304C8—4881no—
305C8—2441no—
306C8—2441no—
307C22#1683969011yescharacteristic
308C22#1683998211yescharacteristic
309C22#1683998611yescharacteristic
310C22#1683999311yescharacteristic
311C22#1684000611yescharacteristic
312C22#1684003011yescharacteristic
313C22#1684003511yescharacteristic
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—161no—
319C4—9761no—
320C4#1684008011yescharacteristic
321C4#1684008311yescharacteristic
322C4#1684009011yescharacteristic
323C4#1684010111yescharacteristic
324C4#1684010211yescharacteristic
325C4#1684010311yescharacteristic
326C4#1684011811yescharacteristic
327C4#1684012911yescharacteristic
328C2#2144523711yescharacteristic
329C2#2144524711yescharacteristic
330C2#2144535711yescharacteristic
331C2#2144537511yescharacteristic
332C2#2144724011yescharacteristic
333C2#2144725611yescharacteristic
334C2#2144726211yescharacteristic
subgroupG/H
centerC23#14519749
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1803C2
socle, prime radicalC23×C61#121
hypercenter#1803D61
hypocenterC61#10626
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
190. C61#10626semidirect

Maximal subgroups

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

subgroupindex
#214467562
#214459462
#214458242
#214437032
#214437022
#214436532
C61×#18032
#1062661