Finite Group Databasebeta

← #29584744

Subgroups — #29584744

Order 15616.

366 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446756C211yesmaximal, characteristic
2#21445975C211yesmaximal, characteristic
3#21445824C211yesmaximal, characteristic
4#21443703C211yesmaximal, characteristic
5#21443702C211yesmaximal, characteristic
6#21443653C211yesmaximal, characteristic
7C61×#1803C211yesmaximal, characteristic
8C2×#14519708—21no—
9C2×#14519708—21no—
10C2×C4⋊#92418C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519701—21no—
13C2×C4×#92418C2211yescharacteristic
14#16839632C2211yescharacteristic
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—
30#14519708—42no—
31#14519708—42no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34C4⋊#92418—21no—
35C4⋊#92418—21no—
36#14519701—42no—
37C4×#92418—21no—
38C4×#92418—21no—
39C22×Q8×C61D411yescharacteristic
40C22×C8×C61—21no—
41C4×Q8×C61—21no—
42C4×Q8×C61—21no—
43C4×Q8×C61—21no—
44C4×Q8×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C42×C61—21no—
51C2×C42×C61C2311yescharacteristic
52C4⋊C8×C61—21no—
53C4⋊C8×C61—21no—
54#103×C61—42no—
55C2×Q8×C61—21no—
56C2×Q8×C61—21no—
57C2×Q8×C61—21no—
58C2×Q8×C61—21no—
59C2×Q8×C61—21no—
60C2×Q8×C61SD1612yes—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—41no—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61#4111yescharacteristic
67C22×Dic61—41no—
68C2×C8×C61—41no—
69C2×C8×C61—41no—
70C2×C8×C61—41no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—81no—
80C42×C61—41no—
81C42×C61—41no—
82C42×C61#4111yescharacteristic
83C42×C61#4111yescharacteristic
84C42×C61#4111yescharacteristic
85C42×C61#4111yescharacteristic
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—81no—
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—
101C2×#92418SD1612yes—
102C2×#92418Q1612yes—
103C23×C61#12111yescharacteristic
104Q8×C61—22no—
105Q8×C61—22no—
106Q8×C61—41no—
107Q8×C61—41no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—22no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—81no—
117C2×C4×C61—81no—
118C2×C4×C61—81no—
119C2×C4×C61#12311yescharacteristic
120C2×C4×C61#12311yescharacteristic
121C2×C4×C61#12311yescharacteristic
122C2×C4×C61#12411yescharacteristic
123C2×C4×C61#12611yescharacteristic
124C2×C4×C61#12611yescharacteristic
125C2×C4×C61C2×SD1611yescharacteristic
126C2×C4×C61C2×SD1611yescharacteristic
127C2×C4×C61C2×Q1611yescharacteristic
128C2×C4×C61#13511yescharacteristic
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C2×C4×C61#13711yescharacteristic
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C8×C61—81no—
137#92418—22no—
138#92418—22no—
139#92418—81no—
140#92418—81no—
141#10620—611nomaximal, Sylow
142C22×C61#39711yescharacteristic
143C22×C61#46011yescharacteristic
144C22×C61#46211yescharacteristic
145C22×C61#46511yescharacteristic
146C22×C61#46811yescharacteristic
147C22×C61#47111yescharacteristic
148C22×C61#47111yescharacteristic
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—42no—
152C4×C61—81no—
153C4×C61—161no—
154C4×C61#48111yescharacteristic
155C4×C61#48211yescharacteristic
156C4×C61#48311yescharacteristic
157C4×C61#48311yescharacteristic
158C4×C61#48411yescharacteristic
159C4×C61#48511yescharacteristic
160C4×C61#48711yescharacteristic
161C4×C61#48911yescharacteristic
162Dic61—161no—
163#1984—611no—
164#1844—611no—
165#1803—611no—
166#1803D6111yescharacteristic
167#1296—611no—
168#1296—611no—
169#1277—611no—
170C2×C61#166611yescharacteristic
171C2×C61#167211yescharacteristic
172C2×C61#168611yescharacteristic
173C2×C61#169211yescharacteristic
174C2×C61#207211yescharacteristic
175C2×C61#207711yescharacteristic
176C2×C61#207911yescharacteristic
177C2×C4×Q8C2×D6111yescharacteristic
178C2×#106—1221no—
179C2×#106—1221no—
180C2×C4⋊C8—611no—
181C2×C4⋊C8—611no—
182C2×C4⋊C8C2×D6111yescharacteristic
183C2×#103—21no—
184C2×#103—1221no—
185C2×C4×C8—611no—
186#384—611no—
187#384C2×D6111yescharacteristic
188#340—21no—
189#340—1221no—
190#336—1221no—
191#336—1221no—
192C61#1062011yescharacteristic, complemented, Sylow
193C22×Q8C22⋊D6111yescharacteristic
194C22×C8—21no—
195C22×C8—611no—
196C22×C8—611no—
197C22×C8—1221no—
198C22×C8—1221no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4C22⋊D6111yescharacteristic
211C2×C42—21no—
212C2×C42C22×D6111yescharacteristic
213#106—2442no—
214#106—2442no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—1221no—
218C4⋊C8—1221no—
219C4⋊C8—1221no—
220C4⋊C8—1221no—
221#103—42no—
222#103—2442no—
223C4×C8—1221no—
224C4×C8—1221no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8#1175820112yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—2441no—
235C22×C4D4×D6111yescharacteristic
236C22×C4#1175822411yescharacteristic
237C22×C4C2×C22⋊D6111yescharacteristic
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—612no—
242C2×C8—612no—
243C2×C8—1221no—
244C2×C8—1221no—
245C2×C8—1221no—
246C2×C8—1221no—
247C2×C8—2441no—
248C2×C8—2441no—
249C2×C8—2441no—
250C2×C8—2441no—
251C2×C8—2441no—
252C2×C8—2441no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—4881no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C42—41no—
268C42—41no—
269C42#1175822211yescharacteristic
270C42#1175822211yescharacteristic
271C42#1175822411yescharacteristic
272C42#1175822411yescharacteristic
273C23#1451974911yescharacteristic
274Q8—22no—
275Q8—22no—
276Q8—41no—
277Q8—41no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—4881no—
290C2×C4—4881no—
291C2×C4—4881no—
292C2×C4#1451975811yescharacteristic
293C2×C4#1451975911yescharacteristic
294C2×C4#1451976011yescharacteristic
295C2×C4#1451976311yescharacteristic
296C2×C4#1451977011yescharacteristic
297C2×C4#1451977011yescharacteristic
298C2×C4SD16×D6111yescharacteristic
299C2×C4C2×#1175820111yescharacteristic
300C2×C4Q16×D6111yescharacteristic
301C2×C4#1451979711yescharacteristic
302C2×C4#1451980311yescharacteristic
303C2×C4#1451980411yescharacteristic
304C2×C4#1451980711yescharacteristic
305C2×C4#1451980911yescharacteristic
306C8—81no—
307C8—1222no—
308C8—1222no—
309C8—4881no—
310C8—4881no—
311C22#1683969011yescharacteristic
312C22#1683996011yescharacteristic
313C22#1683997011yescharacteristic
314C22#1683999311yescharacteristic
315C22#1684000611yescharacteristic
316C22#1684002311yescharacteristic
317C22#1684002711yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—81no—
322C4—161no—
323C4—9761no—
324C4#1684008011yescharacteristic
325C4#1684008311yescharacteristic
326C4#1684009011yescharacteristic
327C4#1684009111yescharacteristic
328C4#1684009611yescharacteristic
329C4#1684010311yescharacteristic
330C4#1684011111yescharacteristic
331C4#1684012311yescharacteristic
332C2#2144516911yescharacteristic
333C2#2144520311yescharacteristic
334C2#2144528911yescharacteristic
335C2#2144532311yescharacteristic
336C2#2144723011yescharacteristic
337C2#2144725611yescharacteristic
338C2#2144726711yescharacteristic
subgroupG/H
centerC23#14519749
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1803C2
socle, prime radicalC23×C61#121
hypercenter#1803D61
hypocenterC61#10620
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
192. C61#10620semidirect

Maximal subgroups

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

subgroupindex
#214467562
#214459752
#214458242
#214437032
#214437022
#214436532
C61×#18032
#1062061