Finite Group Databasebeta

← #29593596

Subgroups — #29593596

Order 15616.

308 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458900C211yesmaximal, characteristic
2#21448088C211yesmaximal, characteristic
3#21447866C211yesmaximal, characteristic, complemented
4#21443861C211yesmaximal, characteristic
5#21443801C211yesmaximal, characteristic, complemented
6#21443788C211yesmaximal, characteristic, complemented
7C61×#1690C211yesmaximal, characteristic, complemented
8#16840485—21no—
9C2×#14519723—21no—
10C2×#14519723—21no—
11C2×#14519720—21no—
12#16840156—21no—
13#16840146C2211yescharacteristic
14#16839985—21no—
15#16839978—21no—
16#16839973—21no—
17#16839864—21no—
18C4×Dic244C2211yescharacteristic
19C4⋊#11758185C2211yescharacteristic
20#16839566—21no—
21#16839538C2211yescharacteristic
22C61×#494C2211yescharacteristic
23C61×#475—21no—
24C61×#446C2211yescharacteristic
25C61×#334C2211yescharacteristic
26C61×#332—21no—
27C2×Dic244—21no—
28C2×Dic244D411yescharacteristic
29C2×Dic244D411yescharacteristic
30C2×#11758190—21no—
31C2×#11758190—21no—
32C2×D488D411yescharacteristic
33#14519777—21no—
34#14519772—41no—
35#14519772—41no—
36#14519765—21no—
37#14519765—21no—
38#14519753—41no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C4×D244—21no—
42#14519735—41no—
43#14519723—42no—
44#14519723—42no—
45#14519720—42no—
46C2×#11758185—21no—
47C2×#11758185—21no—
48#14519711D411yescharacteristic
49#14519702—21no—
50#14519702—21no—
51#14519699—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C4⋊Q8×C61—21no—
55C4×Q8×C61D411yescharacteristic
56#106×C61—41no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61D411yescharacteristic
60#103×C61—41no—
61#97×C61—21no—
62C4×C8×C61C2311yescharacteristic
63C2×Q8×C61—41no—
64C2×Q8×C61D811yescharacteristic
65C2×D244—21no—
66C2×C4×D61—41no—
67C2×Dic122—21no—
68C2×Dic122—21no—
69Q16×C61—41no—
70Q16×C61—41no—
71Q16×C61—41no—
72Q16×C61—41no—
73C2×C8×C61—21no—
74C2×C8×C61—41no—
75C2×C8×C61C2×D411yescharacteristic
76C2×C8×C61C2×D411yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61D811yescharacteristic
81C42×C61—21no—
82C42×C61C2×D411yescharacteristic
83#11758198—41no—
84#11758198—41no—
85#11758198—41no—
86#11758198—41no—
87#11758198—41no—
88C4⋊Dic61—21no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—41no—
92#11758196—41no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95Dic244—21no—
96Dic244—21no—
97Dic244—41no—
98Dic244—81no—
99D488—41no—
100#11758190—41no—
101#11758190—41no—
102#11758190—81no—
103#11758185—22no—
104#11758185—41no—
105C22×D61—41no—
106Q8×C61—41no—
107Q8×C61—81no—
108Q8×C61—81no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—81no—
112C2×C4×C61#12011yescharacteristic
113C2×C4×C61C2×D811yescharacteristic
114C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118D244—41no—
119D244—41no—
120C4×D61—82no—
121Dic122—41no—
122Dic122—41no—
123Dic122—41no—
124Dic122—41no—
125C8×C61—21no—
126C8×C61—41no—
127C8×C61—81no—
128C8×C61#13511yescharacteristic
129C8×C61AGL(1,ℤ/8)11yescharacteristic
130#12339—611nomaximal, Sylow
131C22×C61#44711yescharacteristic
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—81no—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—41no—
138C4×C61—41no—
139C4×C61—161no—
140C4×C61#44911yescharacteristic
141C4×C61#45311yescharacteristic
142Dic61—81no—
143Dic61—81no—
144Dic61—81no—
145#3402—611no—
146#2251—611no—
147#2209—611no—
148#1690D6111yescharacteristic, complemented
149#1360—611no—
150#1338—611no—
151#1334—611no—
152C2×C61#162111yescharacteristic
153C2×C61#219111yescharacteristic
154C2×C61#219511yescharacteristic
155D61—161no—
156#556—1221no—
157C2×Q32—1221no—
158C2×Q32—1221no—
159C2×SD32—1221no—
160#497—1221no—
161#495—611no—
162#494C2×D6111yescharacteristic
163#475—21no—
164#464—1221no—
165#463—1221no—
166#462—1221no—
167#446C2×D6111yescharacteristic
168#440—1221no—
169C4×Q16—611no—
170C4⋊C16—611no—
171#358—1221no—
172#346—611no—
173#334C2×D6111yescharacteristic
174#332—21no—
175C61#1233911yescharacteristic, complemented, Sylow
176C2×Q16—21no—
177C2×Q16—21no—
178C2×Q16—611no—
179C2×Q16—611no—
180C2×Q16—1221no—
181C2×SD16—1221no—
182C2×SD16—1221no—
183C2×D8—611no—
184C4⋊Q8—21no—
185C4⋊Q8—1221no—
186#126—2441no—
187#126—2441no—
188#124—1221no—
189#124—1221no—
190C22⋊Q8—2441no—
191C4×Q8—1221no—
192C4×Q8—1221no—
193C4×Q8C22⋊D6111yescharacteristic
194C4×D4—1221no—
195#117—2441no—
196Q32—2442no—
197Q32—2442no—
198SD32—2442no—
199C2×C16—1221no—
200C2×C16—1221no—
201#107—611no—
202#106—41no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8C22⋊D6111yescharacteristic
206#103—41no—
207#103—1221no—
208#103—1221no—
209#102—1221no—
210#97—21no—
211C4×C8C22×D6111yescharacteristic
212C2×Q8—41no—
213C2×Q8—1221no—
214C2×Q8—1221no—
215C2×Q8#1175819911yescharacteristic
216C2×D4—1221no—
217C22×C4—2441no—
218Q16—41no—
219Q16—41no—
220Q16—41no—
221Q16—41no—
222Q16—1221no—
223Q16—1221no—
224Q16—4881no—
225Q16—2441no—
226SD16—4881no—
227SD16—2441no—
228SD16—2441no—
229D8—2441no—
230C2×C8—21no—
231C2×C8—41no—
232C2×C8D4×D6111yescharacteristic
233C2×C8D4×D6111yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—1221no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C4⋊C4#1175819911yescharacteristic
243C22⋊C4—2441no—
244C22⋊C4—2441no—
245C22⋊C4—2441no—
246C22⋊C4—2441no—
247C22⋊C4—2441no—
248C42—21no—
249C42—2441no—
250C42—2441no—
251C42C2×C22⋊D6111yescharacteristic
252C16—1222no—
253C16—2441no—
254C23—2441no—
255Q8—41no—
256Q8—81no—
257Q8—81no—
258Q8—2441no—
259Q8—2441no—
260Q8—2441no—
261Q8—2441no—
262D4—2441no—
263D4—2441no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—81no—
267C2×C4—4882no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4#1451974511yescharacteristic
272C2×C4C2×#1175819911yescharacteristic
273C2×C4#1451980211yescharacteristic
274C8—21no—
275C8—41no—
276C8—81no—
277C8#1451979811yescharacteristic
278C8#1451980411yescharacteristic
279C22—4881no—
280C22—4881no—
281C22—4881no—
282C22#1683989511yescharacteristic
283C4—21no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—161no—
288C4—4881no—
289C4—4881no—
290C4—4881no—
291C4#1683990611yescharacteristic
292C4#1683992811yescharacteristic
293C2—9761no—
294C2#2144488211yescharacteristic
295C2#2144776911yescharacteristic
296C2#2144779511yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1690C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#1690D61
hypocenterC61#12339
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #1690

Complements

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

NH ≅ G/Ntype
3. #21447866C2semidirect
5. #21443801C2semidirect
6. #21443788C2semidirect
7. C61×#1690C2semidirect
148. #1690D61semidirect
175. C61#12339semidirect

Maximal subgroups

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

subgroupindex
#214589002
#214480882
#214478662
#214438612
#214438012
#214437882
C61×#16902
#1233961