Finite Group Databasebeta

← #29591352

Subgroups — #29591352

Order 15616.

300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 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#21456406C211yesmaximal, characteristic
2#21447617C211yesmaximal, characteristic
3#21444566C211yesmaximal, characteristic
4#21443874C211yesmaximal, characteristic, complemented
5#21443869C211yesmaximal, characteristic, complemented
6#21443867C211yesmaximal, characteristic, complemented
7C61×#1364C211yesmaximal, characteristic, complemented
8#16840317—21no—
9#16840142C2211yescharacteristic
10#16840114—21no—
11#16840004—21no—
12#16840004C412yes—
13#16839856—21no—
14#16839856C412yes—
15#16839814—21no—
16C4×C8×D61C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839541—21no—
19C16×Dic61—21no—
20#16839515C2211yescharacteristic
21#16839512—21no—
22C61×#500C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244C2×C412yes—
27C2×C8×D61C2×C411yescharacteristic
28C2×C8×D61D411yescharacteristic
29#14519777—21no—
30#14519768—41no—
31#14519757—22no—
32#14519753—41no—
33Q8×Dic61—41no—
34#14519742—22no—
35#14519735—41no—
36C42×D61D411yescharacteristic
37C2×#11758185—21no—
38C4⋊#92418—21no—
39#14519700—22no—
40#14519700—22no—
41#14519689—41no—
42C4×#92418D411yescharacteristic
43C8×Dic61—41no—
44C8×Dic61C2×C411yescharacteristic
45C8×Dic61D411yescharacteristic
46C4⋊Q8×C61—21no—
47C2×C16×C61—21no—
48#107×C61—21no—
49#107×C61C2×C412yes—
50C4⋊C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—41no—
53C2×C4×D61C22⋊C411yescharacteristic
54C2×C4×D61D811yescharacteristic
55C2×C4×D61SD1611yescharacteristic
56C2×Dic122—22no—
57C2×C8×C61—41no—
58C2×C8×C61C22×C411yescharacteristic
59C2×C8×C61C2×D411yescharacteristic
60C4⋊C4×C61—22no—
61C4⋊C4×C61—41no—
62C42×C61C2×D411yescharacteristic
63#11758198—42no—
64C4⋊Dic61—41no—
65C4⋊Dic61—41no—
66C4⋊Dic61—42no—
67#11758196—42no—
68C4×Dic61—42no—
69C4×Dic61C22⋊C411yescharacteristic
70C4×Dic61D811yescharacteristic
71C4×Dic61SD1611yescharacteristic
72C2×#92418—41no—
73C2×#92418C22⋊C411yescharacteristic
74C2×#92418C22⋊C411yescharacteristic
75Dic244—42no—
76Dic244—41no—
77Dic244—41no—
78C8×D61—21no—
79C8×D61—21no—
80C8×D61—41no—
81C16×C61—41no—
82#11758185—41no—
83C22×D61#10211yescharacteristic
84Q8×C61—81no—
85Q8×C61—81no—
86C2×C4×C61—42no—
87C2×C4×C61C2×C22⋊C411yescharacteristic
88C2×C4×C61C2×D811yescharacteristic
89C2×C4×C61C2×SD1611yescharacteristic
90C2×Dic61—42no—
91C2×Dic61#10211yescharacteristic
92C2×Dic61#10211yescharacteristic
93C2×Dic61#10211yescharacteristic
94C4×D61—21no—
95C4×D61—21no—
96C4×D61—21no—
97C4×D61—21no—
98C4×D61—22no—
99Dic122—42no—
100Dic122—42no—
101C8×C61—21no—
102C8×C61—81no—
103C8×C61#13511yescharacteristic
104C8×C61#13511yescharacteristic
105#92418—21no—
106#92418—21no—
107#92418—81no—
108#11950—611nomaximal, Sylow
109C22×C61C2×#10211yescharacteristic
110C2×D61—21no—
111C2×D61—21no—
112C2×D61—21no—
113C4×C61—21no—
114C4×C61—82no—
115C4×C61#41311yescharacteristic
116C4×C61#41611yescharacteristic
117C4×C61#50811yescharacteristic
118C4×C61#50811yescharacteristic
119Dic61—21no—
120Dic61—21no—
121Dic61—82no—
122Dic61#36212yes—
123#3170—611no—
124#2162—611no—
125#1564—611no—
126#1364—611no—
127#1364D6111yescharacteristic, complemented
128#1362—611no—
129#1362—611no—
130C2×C61#154011yescharacteristic
131C2×C61#213811yescharacteristic
132C2×C61C2×#36211yescharacteristic
133D61—41no—
134#533—1221no—
135#500C2×D6111yescharacteristic
136#494—611no—
137#487—1221no—
138#467—612no—
139#467—1221no—
140C4×Q16—612no—
141C4×Q16—1221no—
142#431—1221no—
143C2×C4×C8—611no—
144C4⋊C16—611no—
145C4⋊C16C2×D6111yescharacteristic
146C22⋊C16—1221no—
147C4×C16—1221no—
148#335—611no—
149#335C2×D6111yescharacteristic
150#334—1221no—
151C61#1195011yescharacteristic, complemented, Sylow
152C2×Q16—612no—
153C2×Q16—1221no—
154C22×C8—611no—
155C22×C8—611no—
156C4⋊Q8—21no—
157C4⋊Q8—1221no—
158#125—2441no—
159C22⋊Q8—1222no—
160C22⋊Q8—2441no—
161C4×Q8—1222no—
162C4×Q8—2441no—
163#117—2441no—
164C2×C42—611no—
165C2×C16—21no—
166C2×C16—1221no—
167#107—21no—
168#107C4×D6112yes—
169C4⋊C8—21no—
170C4⋊C8—1221no—
171#103—1222no—
172#103—1222no—
173C22⋊C8—2441no—
174C4×C8—611no—
175C4×C8—611no—
176C4×C8—611no—
177C4×C8—2441no—
178C4×C8C22×D6111yescharacteristic
179C2×Q8—41no—
180C2×Q8—1222no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—611no—
184Q16—2442no—
185Q16—2441no—
186Q16—2441no—
187C2×C8—41no—
188C2×C8—611no—
189C2×C8—611no—
190C2×C8—1221no—
191C2×C8—1221no—
192C2×C8—2441no—
193C2×C8—2441no—
194C2×C8C2×C4×D6111yescharacteristic
195C2×C8D4×D6111yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—41no—
198C4⋊C4—2442no—
199C4⋊C4—2442no—
200C4⋊C4—2441no—
201C4⋊C4—2441no—
202C22⋊C4—2442no—
203C42—611no—
204C42—611no—
205C42—611no—
206C42—2442no—
207C42D4×D6111yescharacteristic
208C16—41no—
209C16—2441no—
210C23—611no—
211Q8—81no—
212Q8—81no—
213Q8—2442no—
214Q8—2442no—
215C2×C4—42no—
216C2×C4—611no—
217C2×C4—611no—
218C2×C4—611no—
219C2×C4—1222no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—2442no—
225C2×C4C22⋊C4×D6111yescharacteristic
226C2×C4D8×D6111yescharacteristic
227C2×C4SD16×D6111yescharacteristic
228C8—21no—
229C8—81no—
230C8—1221no—
231C8—1221no—
232C8—4881no—
233C8#1451979811yescharacteristic
234C8#1451980011yescharacteristic
235C22—1221no—
236C22—1221no—
237C22—1221no—
238C22#102×D6111yescharacteristic
239C4—21no—
240C4—82no—
241C4—612no—
242C4—1221no—
243C4—1221no—
244C4—4882no—
245C4#1683974511yescharacteristic
246C4#1683975711yescharacteristic
247C4#1684019111yescharacteristic
248C4#1684019311yescharacteristic
249C2—2441no—
250C2#2144446711yescharacteristic
251C2#2144752311yescharacteristic
252C2#362×D6111yescharacteristic
subgroupG/H
centerC22#102×D61
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1364C2
socleC22×C61C2×#102
prime radicalC22×D61#102
cosocleC4×C8×C61C23
hypercenter#1364D61
hypocenterC61#11950
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
4. #21443874C2semidirect
5. #21443869C2semidirect
6. #21443867C2semidirect
7. C61×#1364C2semidirect
127. #1364D61semidirect
151. C61#11950semidirect

Maximal subgroups

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

subgroupindex
#214564062
#214476172
#214445662
#214438742
#214438692
#214438672
C61×#13642
#1195061