Finite Group Databasebeta

← #30608389

Subgroups — #30608389

Order 15616.

326 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 56 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#21462093C212yesmaximal
2#21460960C212yesmaximal, complemented
3#21460959C211yesmaximal, characteristic, complemented
4#21460958C211yesmaximal, characteristic, complemented
5#21456166C211yesmaximal, characteristic
6#16840743—22no—
7#16840668—22no—
8#16840667C2212yes—
9#16840667C2212yes—
10#16840318C411yescharacteristic, complemented
11#16840313C2211yescharacteristic
12#16840130C411yescharacteristic, complemented
13#16840128C2211yescharacteristic
14#16840127C2211yescharacteristic
15#16840123—22no—
16#16839757—22no—
17#97×D61C411yescharacteristic, complemented
18C61×#491C411yescharacteristic, complemented
19#14519856—42no—
20#14519836—22no—
21#14519836—22no—
22#14519836—42no—
23C2×#11758226D412yes—
24C2×C8×D61—21no—
25#14519776—21no—
26#14519774C2311yescharacteristic
27#14519769C2×C411yescharacteristic
28#14519766D412yes—
29#14519755—41no—
30#14519752—41no—
31#14519742—41no—
32#14519739—41no—
33#14519735—21no—
34C42×D61C2×C411yescharacteristic
35#14519701—22no—
36#14519699—22no—
37#14519697—22no—
38#14519688C2×C411yescharacteristic
39#14519687—21no—
40C4⋊Q8×C61C2×C411yescharacteristic
41#125×C61C2×C411yescharacteristic
42#103×C61—22no—
43#97×C61C2×C411yescharacteristic
44C2×Q8×C61C22⋊C412yes—
45#11758226—42no—
46#11758226—42no—
47C2×D244—22no—
48C2×D244—41no—
49C2×D244C2×D412yes—
50C2×C4×D61—22no—
51C2×C4×D61—21no—
52C2×C4×D61C22⋊C411yescharacteristic
53C2×Dic122—41no—
54C22⋊#6923—42no—
55C22⋊#6923—42no—
56C4⋊#6923—82no—
57C4×#6923—82no—
58C2×C8×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61—41no—
61C4⋊C4×C61—41no—
62C42×C61C22×C411yescharacteristic
63#11758198—42no—
64#11758198—41no—
65C4⋊Dic61—21no—
66#11758196—41no—
67#11758196—41no—
68C4×Dic61—21no—
69C4×Dic61—41no—
70C4×Dic61C22⋊C411yescharacteristic
71C2×#92418—21no—
72C8×D61—41no—
73C8×D61—41no—
74C22×D61—22no—
75C22×D61#9911yescharacteristic
76C2×#6923—82no—
77C2×#6923—82no—
78Q8×C61—42no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—41no—
82C2×C4×C61C2×C22⋊C411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—41no—
85C2×Dic61#9911yescharacteristic
86D244—42no—
87D244—82no—
88D244—82no—
89C4×D61—21no—
90C4×D61—21no—
91C4×D61—42no—
92C4×D61—42no—
93C4×D61—81no—
94Dic122—82no—
95C8×C61—41no—
96#92418—41no—
97#13594—611nomaximal, Sylow
98C22×C61C2×#9911yescharacteristic
99C2×D61—21no—
100C2×D61—41no—
101C2×D61—42no—
102C2×D61—82no—
103#6923—162no—
104#6923—162no—
105C4×C61—21no—
106C4×C61—41no—
107C4×C61—42no—
108C4×C61—81no—
109Dic61—41no—
110Dic61—81no—
111Dic61#35411yescharacteristic
112Dic61#35411yescharacteristic
113#3135—611no—
114#2126—612no—
115#1412—611no—
116#1412—611no—
117#1412—612no—
118C2×C61—21no—
119C2×C61C2×#35411yescharacteristic
120D61—41no—
121D61—82no—
122#533—611no—
123#532—611no—
124#491—611no—
125#491#692311yescharacteristic, complemented
126#490—611no—
127#490—611no—
128#489—1222no—
129#416—1222no—
130#410—1222no—
131C2×#97—611no—
132#354—1222no—
133#353—612no—
134#353—612no—
135C61#1359411yescharacteristic, complemented, Sylow
136C2×#41—612no—
137C22×C8—1221no—
138C4⋊Q8—1221no—
139C4⋊Q8C2×#692311yescharacteristic
140#127—611no—
141#125—611no—
142#125C2×#692311yescharacteristic
143#124—612no—
144C22⋊Q8—2441no—
145#121—2441no—
146C4×Q8—2441no—
147C4×D4—2441no—
148#117—1221no—
149#117—2442no—
150C2×C42—611no—
151#103—22no—
152#103—1222no—
153#102—1222no—
154#102—1222no—
155#99—1222no—
156#99—1222no—
157#99—2442no—
158#97—611no—
159#97—1221no—
160#97C2×#692311yescharacteristic
161#41—2442no—
162#41—2442no—
163C2×Q8—2441no—
164C2×Q8C22⋊#692312yes—
165C2×D4—612no—
166C2×D4—1222no—
167C2×D4—2441no—
168C22×C4—611no—
169C22×C4—1222no—
170C22×C4—1221no—
171C2×C8—21no—
172C2×C8—1221no—
173C2×C8—2441no—
174C2×C8—2441no—
175C4⋊C4—21no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—1221no—
179C4⋊C4—4882no—
180C4⋊C4—2441no—
181C4⋊C4—2441no—
182C22⋊C4—2442no—
183C22⋊C4—2441no—
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C42—611no—
187C42—1221no—
188C42—4882no—
189C42—2441no—
190C42C22×#692311yescharacteristic
191C23—611no—
192C23—1222no—
193Q8—42no—
194Q8—4882no—
195D4—4882no—
196D4—4882no—
197D4—2442no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—611no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—4881no—
206C2×C4—4882no—
207C2×C4—4882no—
208C2×C4—2442no—
209C2×C4—2442no—
210C2×C4—2441no—
211C2×C4C2×C22⋊#692311yescharacteristic
212C8—41no—
213C8—2441no—
214C22—1221no—
215C22—4882no—
216C22—2441no—
217C22—2442no—
218C22D61⋊#9911yescharacteristic
219C4—21no—
220C4—41no—
221C4—42no—
222C4—81no—
223C4—611no—
224C4—611no—
225C4—9762no—
226C4—9762no—
227C4—4881no—
228C4—2441no—
229C2—21no—
230C2—4882no—
231C2—2441no—
232C2D61⋊#35411yescharacteristic
subgroupG/H
centerC2D61⋊#354
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#491C4
socleC2×C61C2×#354
prime radical#16840313C22
cosocle#14519774C23
hypercenter#491#6923
hypocenterC61#13594
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #21460960C2semidirect
3. #21460959C2semidirect
4. #21460958C2semidirect
10. #16840318C4semidirect
12. #16840130C4semidirect
17. #97×D61C4semidirect
18. C61×#491C4semidirect
125. #491#6923semidirect
135. C61#13594semidirect

Maximal subgroups

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

subgroupindex
#214620932
#214609602
#214609592
#214609582
#214561662
#1359461