Finite Group Databasebeta

← #29584483

Subgroups — #29584483

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#21450855C211yesmaximal, characteristic
2#21446583C211yesmaximal, characteristic
3#21446578C211yesmaximal, characteristic
4#21445978C211yesmaximal, characteristic
5#21443658C211yesmaximal, characteristic
6#21443658C211yesmaximal, characteristic
7C61×#1296C211yesmaximal, characteristic
8C2×#14519768—21no—
9C2×#14519711—21no—
10C2×#14519710—22no—
11C2×#14519709—21no—
12C2×C4×#92418C2211yescharacteristic
13#16839695—22no—
14#16839661—21no—
15#16839658—21no—
16#16839632C2211yescharacteristic
17#16839631—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19C4×C4⋊Dic61C2211yescharacteristic
20#16839525—21no—
21#16839525—21no—
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C61×#384C2211yescharacteristic
25C22×#92418—21no—
26#14519768—42no—
27#14519768—42no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—22no—
37C2×#11758196—22no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61—21no—
40#14519711—42no—
41#14519710—44no—
42#14519709—42no—
43C4×#92418—21no—
44C4×#92418Q812yes—
45#14519684—22no—
46#14519684—21no—
47#14519684—21no—
48C22×C8×C61—21no—
49C22×C8×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61D412yes—
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61Q812yes—
57C4⋊C8×C61Q812yes—
58C22×C4×C61—22no—
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—41no—
67C2×C8×C61—22no—
68C2×C8×C61—22no—
69C2×C8×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C4⋊C4×C61—42no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C42×C61C2×Q811yescharacteristic
79C42×C61C2×Q811yescharacteristic
80C42×C61C2×Q811yescharacteristic
81C42×C61#4111yescharacteristic
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87C4⋊Dic61—21no—
88C4⋊Dic61—44no—
89C4⋊Dic61—42no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61D812yes—
95C4⋊Dic61Q1612yes—
96#11758196—44no—
97#11758196—82no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C4×Dic61—41no—
101C4×Dic61—41no—
102C2×#92418—22no—
103C2×#92418—22no—
104C2×#92418—22no—
105C23×C61#12011yescharacteristic
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—42no—
109C2×C4×C61—42no—
110C2×C4×C61—42no—
111C2×C4×C61C22⋊Q811yescharacteristic
112C2×C4×C61C22⋊Q811yescharacteristic
113C2×C4×C61C22⋊Q811yescharacteristic
114C2×C4×C61C4⋊Q811yescharacteristic
115C2×C4×C61C4⋊Q811yescharacteristic
116C2×C4×C61C4⋊Q811yescharacteristic
117C2×C4×C61C2×D811yescharacteristic
118C2×C4×C61C2×Q1611yescharacteristic
119C2×C4×C61#13511yescharacteristic
120C2×C4×C61#13511yescharacteristic
121C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C61#13711yescharacteristic
124C2×C4×C61#13711yescharacteristic
125C2×Dic61—22no—
126C2×Dic61—22no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—81no—
138C2×Dic61—81no—
139C2×Dic61—81no—
140C8×C61—42no—
141C8×C61—42no—
142#92418—24no—
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—82no—
154C4×C61#47411yescharacteristic
155C4×C61#47711yescharacteristic
156C4×C61#47811yescharacteristic
157C4×C61#47911yescharacteristic
158C4×C61#49911yescharacteristic
159C4×C61#50011yescharacteristic
160C4×C61#50111yescharacteristic
161C4×C61#50111yescharacteristic
162Dic61—42no—
163Dic61—42no—
164Dic61—81no—
165Dic61—81no—
166Dic61—161no—
167#2552—611no—
168#1948—611no—
169#1947—611no—
170#1845—611no—
171#1296D6111yescharacteristic
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—1221no—
183C2×#107—1222no—
184C2×#106—1221no—
185C2×C4⋊C8C2×D6111yescharacteristic
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⋊C4—611no—
196#340—1221no—
197#340—1221no—
198C61#1057911yescharacteristic, complemented, Sylow
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—1221no—
202#125—2442no—
203#125—2442no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—1222no—
211C2×C4⋊C4—1222no—
212C2×C4⋊C4—1222no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4D24412yes—
217C2×C42—1221no—
218C2×C42—1221no—
219C2×C42C22×D6111yescharacteristic
220#107—2444no—
221#107—2442no—
222#106—2442no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8Dic12212yes—
226C4⋊C8Dic12212yes—
227C4×C8—612no—
228C4×C8—1221no—
229#95—1222no—
230#95—1221no—
231#95—1221no—
232C22×C4—22no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4—2441no—
238C22×C4C2×D24411yescharacteristic
239C22×C4D4×D6111yescharacteristic
240C22×C4D4×D6111yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—1222no—
248C2×C8—1222no—
249C2×C8—1222no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—612no—
256C4⋊C4—612no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
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—2441no—
272C42—2441no—
273C42—2441no—
274C42—2441no—
275C42C2×Dic12211yescharacteristic
276C42C2×Dic12211yescharacteristic
277C42#1175822411yescharacteristic
278C42Q8×D6111yescharacteristic
279C23#1451974711yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—1222no—
286C2×C4—1222no—
287C2×C4—4881no—
288C2×C4—4881no—
289C2×C4—4881no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4#1451975411yescharacteristic
301C2×C4#1451975411yescharacteristic
302C2×C4#1451975711yescharacteristic
303C2×C4#1451977611yescharacteristic
304C2×C4#1451977611yescharacteristic
305C2×C4#1451977711yescharacteristic
306C2×C4D8×D6111yescharacteristic
307C2×C4Q16×D6111yescharacteristic
308C2×C4#1451979811yescharacteristic
309C2×C4#1451979811yescharacteristic
310C2×C4#1451980111yescharacteristic
311C2×C4#1451980411yescharacteristic
312C2×C4#1451980611yescharacteristic
313C2×C4#1451980911yescharacteristic
314C8—42no—
315C8—42no—
316C8—1224no—
317C22#1683968311yescharacteristic
318C22#1683989711yescharacteristic
319C22#1683990811yescharacteristic
320C22#1683991911yescharacteristic
321C22#1683992711yescharacteristic
322C22#1683993211yescharacteristic
323C22#1683994711yescharacteristic
324C4—21no—
325C4—21no—
326C4—82no—
327C4—9761no—
328C4—4881no—
329C4—4881no—
330C4—2442no—
331C4—2442no—
332C4#1684004011yescharacteristic
333C4#1684005511yescharacteristic
334C4#1684006411yescharacteristic
335C4#1684006711yescharacteristic
336C4#1684016211yescharacteristic
337C4#1684016611yescharacteristic
338C4#1684016911yescharacteristic
339C4#1684017011yescharacteristic
340C2#2144488511yescharacteristic
341C2#2144495411yescharacteristic
342C2#2144505511yescharacteristic
343C2#2144506211yescharacteristic
344C2#2144714611yescharacteristic
345C2#2144715611yescharacteristic
346C2#2144716511yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socle, prime radicalC23×C61#120
hypercenter#1296D61
hypocenterC61#10579
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

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
#214508552
#214465832
#214465782
#214459782
#214436582
C61×#12962
#1057961