Finite Group Databasebeta

← #29584486

Subgroups — #29584486

Order 15616.

442 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450854C211yesmaximal, characteristic
2#21446580C211yesmaximal, characteristic
3#21445978C211yesmaximal, characteristic
4#21443703C211yesmaximal, characteristic
5#21443660C211yesmaximal, characteristic
6#21443658C211yesmaximal, characteristic
7C61×#1947C211yesmaximal, characteristic
8C2×#14519769—21no—
9C2×#14519710—22no—
10C2×#14519708—21no—
11C2×C4⋊#92418C2211yescharacteristic
12C2×C4×#92418C2211yescharacteristic
13#16839696—22no—
14#16839660—21no—
15#16839658—21no—
16#16839632C2211yescharacteristic
17#16839631—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19#16839524—21no—
20C2×#107×C61—21no—
21C2×C4⋊C8×C61C2211yescharacteristic
22C61×#384C2211yescharacteristic
23C4×C4⋊C4×C61C2211yescharacteristic
24C61×#340—21no—
25C22×#92418—21no—
26C22×#92418—21no—
27#14519769—42no—
28#14519769—42no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D412yes—
34C2×#11758196—22no—
35C2×#11758196—22no—
36C2×#11758196—22no—
37C2×C4×Dic61—21no—
38#14519710—44no—
39#14519708—42no—
40C4⋊#92418—21no—
41C4⋊#92418Q812yes—
42C4×#92418—21no—
43C4×#92418Q812yes—
44#14519684—22no—
45#14519684—21no—
46C22×C8×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C42×C61—21no—
53C2×C42×C61C2311yescharacteristic
54#107×C61—42no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61Q812yes—
57#95×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—41no—
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—22no—
67C2×C8×C61—22no—
68C2×C8×C61—41no—
69C2×C8×C61—41no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61—42no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C42×C61—41no—
80C42×C61—41no—
81C42×C61C2×Q811yescharacteristic
82C42×C61C2×Q811yescharacteristic
83C42×C61C2×Q811yescharacteristic
84C42×C61#4111yescharacteristic
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—42no—
92C4⋊Dic61D812yes—
93C4⋊Dic61Q1612yes—
94#11758196—44no—
95#11758196—44no—
96#11758196—82no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C2×#92418—22no—
100C2×#92418—22no—
101C2×#92418—22no—
102C2×#92418—22no—
103C2×#92418—41no—
104C2×#92418—41no—
105C23×C61#12011yescharacteristic
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
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×C61C22⋊Q811yescharacteristic
118C2×C4×C61C22⋊Q811yescharacteristic
119C2×C4×C61C22⋊Q811yescharacteristic
120C2×C4×C61C4⋊Q811yescharacteristic
121C2×C4×C61C4⋊Q811yescharacteristic
122C2×C4×C61C4⋊Q811yescharacteristic
123C2×C4×C61C2×D811yescharacteristic
124C2×C4×C61C2×Q1611yescharacteristic
125C2×C4×C61#13511yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61#13711yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C2×Dic61—22no—
132C2×Dic61—22no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C8×C61—42no—
141#92418—24no—
142#92418—42no—
143#10579—611nomaximal, Sylow
144C22×C61#39511yescharacteristic
145C22×C61#44711yescharacteristic
146C22×C61#44911yescharacteristic
147C22×C61#45111yescharacteristic
148C22×C61#45211yescharacteristic
149C22×C61#45311yescharacteristic
150C22×C61#45611yescharacteristic
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—81no—
154C4×C61—81no—
155C4×C61—161no—
156C4×C61#47411yescharacteristic
157C4×C61#47711yescharacteristic
158C4×C61#47811yescharacteristic
159C4×C61#47911yescharacteristic
160C4×C61#49911yescharacteristic
161C4×C61#50011yescharacteristic
162C4×C61#50111yescharacteristic
163C4×C61#50111yescharacteristic
164Dic61—42no—
165Dic61—42no—
166Dic61—82no—
167#2552—611no—
168#1948—611no—
169#1947D6111yescharacteristic
170#1845—611no—
171#1296—611no—
172#1279—611no—
173#1279—611no—
174C2×C61#162111yescharacteristic
175C2×C61#163211yescharacteristic
176C2×C61#164711yescharacteristic
177C2×C61#164811yescharacteristic
178C2×C61#205711yescharacteristic
179C2×C61#205911yescharacteristic
180C2×C61#206011yescharacteristic
181C2×#125—1221no—
182C2×#107—21no—
183C2×#107—1222no—
184C2×#106—1221no—
185C2×C4⋊C8—611no—
186C2×C4⋊C8C2×D6111yescharacteristic
187C2×C4×C8—611no—
188#398—1222no—
189#389—1221no—
190#389—1221no—
191#384—611no—
192#384—1221no—
193#384C2×D6111yescharacteristic
194C4×C4⋊C4—611no—
195C4×C4⋊C4C2×D6111yescharacteristic
196#340—21no—
197#340—1221no—
198C61#1057911yescharacteristic, complemented, Sylow
199C22×C8—21no—
200C22×C8—1221no—
201C22×C8—1221no—
202#125—2442no—
203#125—2442no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—612no—
210C2×C4⋊C4—1222no—
211C2×C4⋊C4—1222no—
212C2×C4⋊C4—1222no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4C22⋊D6111yescharacteristic
216C2×C4⋊C4C22⋊D6111yescharacteristic
217C2×C42—21no—
218C2×C42—1221no—
219C2×C42C22×D6111yescharacteristic
220#107—42no—
221#107—2444no—
222#106—2442no—
223C4⋊C8—21no—
224C4⋊C8—612no—
225C4⋊C8—1221no—
226C4⋊C8Dic12212yes—
227C4×C8—612no—
228C4×C8—1221no—
229#95—21no—
230#95—1222no—
231#95—1221no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—41no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—1222no—
238C22×C4D4×D6111yescharacteristic
239C22×C4D4×D6111yescharacteristic
240C22×C4C2×C22⋊D6111yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—1222no—
245C2×C8—1222no—
246C2×C8—1222no—
247C2×C8—1222no—
248C2×C8—2441no—
249C2×C8—2441no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—612no—
260C4⋊C4—612no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—4882no—
264C4⋊C4—2442no—
265C4⋊C4—2444no—
266C4⋊C4—2444no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C42—41no—
272C42—41no—
273C42—2441no—
274C42—2441no—
275C42C2×Dic12211yescharacteristic
276C42#1175822211yescharacteristic
277C42Q8×D6111yescharacteristic
278C42Q8×D6111yescharacteristic
279C23#1451974511yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—1222no—
292C2×C4—1222no—
293C2×C4—2442no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4#1451975511yescharacteristic
301C2×C4#1451975511yescharacteristic
302C2×C4#1451975611yescharacteristic
303C2×C4#1451977511yescharacteristic
304C2×C4#1451977611yescharacteristic
305C2×C4#1451977611yescharacteristic
306C2×C4D8×D6111yescharacteristic
307C2×C4Q16×D6111yescharacteristic
308C2×C4#1451979711yescharacteristic
309C2×C4#1451979711yescharacteristic
310C2×C4#1451980111yescharacteristic
311C2×C4#1451980311yescharacteristic
312C2×C4#1451980811yescharacteristic
313C2×C4#1451980911yescharacteristic
314C8—42no—
315C8—1224no—
316C8—2442no—
317C22#1683968211yescharacteristic
318C22#1683989411yescharacteristic
319C22#1683990511yescharacteristic
320C22#1683991611yescharacteristic
321C22#1683992211yescharacteristic
322C22#1683992811yescharacteristic
323C22#1683994311yescharacteristic
324C4—21no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—161no—
329C4—4882no—
330C4—2442no—
331C4—2442no—
332C4#1684004111yescharacteristic
333C4#1684005611yescharacteristic
334C4#1684006211yescharacteristic
335C4#1684006911yescharacteristic
336C4#1684016111yescharacteristic
337C4#1684016611yescharacteristic
338C4#1684016811yescharacteristic
339C4#1684017011yescharacteristic
340C2#2144488311yescharacteristic
341C2#2144495211yescharacteristic
342C2#2144505311yescharacteristic
343C2#2144505911yescharacteristic
344C2#2144714511yescharacteristic
345C2#2144715711yescharacteristic
346C2#2144716211yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1947C2
socle, prime radicalC23×C61#120
hypercenter#1947D61
hypocenterC61#10579
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
198. C61#10579semidirect

Maximal subgroups

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

subgroupindex
#214508542
#214465802
#214459782
#214437032
#214436602
#214436582
C61×#19472
#1057961