Finite Group Databasebeta

← #30608388

Subgroups — #30608388

Order 15616.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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#21462092C212yesmaximal
2#21460959C212yesmaximal, complemented
3#21460958C212yesmaximal, complemented
4#21456167C211yesmaximal, characteristic
5#16840741—22no—
6#16840669—22no—
7#16840667C2214yes—
8#16840312C2211yescharacteristic
9#16840132C411yescharacteristic, complemented
10#16840132C411yescharacteristic, complemented
11#16840128C2211yescharacteristic
12#16840128C2211yescharacteristic
13#16840124—22no—
14#16839756—22no—
15C2×#14519688C411yescharacteristic, complemented
16C61×#533C411yescharacteristic, complemented
17#14519856—42no—
18#14519836—24no—
19#14519835—42no—
20C2×#11758222D412yes—
21C22×#92418—21no—
22#14519777C2×C411yescharacteristic
23#14519774C2311yescharacteristic
24#14519765D412yes—
25#14519751—41no—
26C4×D244—41no—
27#14519700—22no—
28#14519700—22no—
29#14519697—22no—
30#14519697—22no—
31#14519688—21no—
32#14519688C2×C411yescharacteristic
33#14519688C2×C411yescharacteristic
34C4⋊Q8×C61—21no—
35#125×C61C2×C411yescharacteristic
36#125×C61C2×C411yescharacteristic
37C22⋊Q8×C61—41no—
38C4×Q8×C61—41no—
39#117×C61—21no—
40C2×C42×C61C2×C411yescharacteristic
41C2×Q8×C61—41no—
42C22×C4×C61—21no—
43C22×C4×C61C22⋊C411yescharacteristic
44C2×C22⋊D61—22no—
45#11758222—42no—
46#11758222—42no—
47C2×D244—41no—
48C2×D244C2×D412yes—
49C2×C4×D61—22no—
50C2×Dic122C22⋊C412yes—
51C22⋊#6923—44no—
52C4⋊#6923—82no—
53C4×#6923—82no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61—41no—
57C4⋊C4×C61—41no—
58C4⋊C4×C61—41no—
59C22⋊C4×C61—41no—
60C42×C61—21no—
61C42×C61—41no—
62C42×C61C22⋊C411yescharacteristic
63C42×C61C22×C411yescharacteristic
64#11758198—42no—
65C4⋊Dic61—41no—
66C2×#92418—21no—
67C2×#92418—21no—
68C2×#92418—41no—
69C2×#92418—41no—
70C23×C61#9911yescharacteristic
71C22×D61—22no—
72C2×#6923—84no—
73Q8×C61—82no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—81no—
81C2×C4×C61#9911yescharacteristic
82C2×C4×C61C2×C22⋊C411yescharacteristic
83C22⋊D61—82no—
84C2×Dic61—22no—
85D244—42no—
86D244—82no—
87C4×D61—42no—
88C4×D61—42no—
89Dic122—42no—
90#92418—41no—
91#92418—41no—
92#13594—611nomaximal, Sylow
93C22×C61—21no—
94C22×C61—41no—
95C22×C61C2×#9911yescharacteristic
96C2×D61—42no—
97C2×D61—82no—
98#6923—164no—
99C4×C61—21no—
100C4×C61—41no—
101C4×C61—41no—
102C4×C61—81no—
103C4×C61—81no—
104C4×C61#35411yescharacteristic
105C4×C61#35411yescharacteristic
106Dic61—42no—
107#3135—611no—
108#2126—612no—
109#1412—612no—
110#1412—612no—
111C2×C61—21no—
112C2×C61—41no—
113C2×C61C2×#35411yescharacteristic
114D61—82no—
115#533#692311yescharacteristic, complemented
116#532—611no—
117#491—611no—
118#491—611no—
119#490—611no—
120#490—611no—
121#489—1222no—
122#416—1222no—
123#410—1222no—
124C2×#97—611no—
125#354—1222no—
126#353—614no—
127C61#1359411yescharacteristic, complemented, Sylow
128C2×#41—612no—
129C22×C8—1221no—
130C4⋊Q8—21no—
131C4⋊Q8—611no—
132#127—611no—
133#125C2×#692311yescharacteristic
134#125C2×#692311yescharacteristic
135#124—612no—
136C22⋊Q8—41no—
137#121—2441no—
138C4×Q8—41no—
139C4×D4—2441no—
140#117—21no—
141#117—2442no—
142C2×C42C2×#692311yescharacteristic
143#103—1222no—
144#103—1222no—
145#102—1222no—
146#102—1222no—
147#99—1224no—
148#99—2442no—
149#97—611no—
150#97—611no—
151#97—1221no—
152#41—2442no—
153#41—2442no—
154C2×Q8—41no—
155C2×Q8—612no—
156C2×D4—612no—
157C2×D4—1222no—
158C2×D4—2441no—
159C22×C4—21no—
160C22×C4—1222no—
161C22×C4C22⋊#692311yescharacteristic
162C2×C8—1221no—
163C2×C8—1221no—
164C2×C8—2441no—
165C2×C8—2441no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—4882no—
172C4⋊C4—2441no—
173C22⋊C4—41no—
174C22⋊C4—2442no—
175C22⋊C4—2444no—
176C42—21no—
177C42—41no—
178C42—4882no—
179C42C22⋊#692311yescharacteristic
180C42C22×#692311yescharacteristic
181C23—1222no—
182C23#1451983511yescharacteristic
183Q8—82no—
184Q8—2442no—
185D4—4882no—
186D4—4882no—
187D4—2442no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—1222no—
196C2×C4—4884no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4#1451983511yescharacteristic
200C2×C4C2×C22⋊#692311yescharacteristic
201C8—2441no—
202C8—2441no—
203C22—21no—
204C22—41no—
205C22—4882no—
206C22—2442no—
207C22C2×#1451983511yescharacteristic
208C4—21no—
209C4—41no—
210C4—41no—
211C4—81no—
212C4—81no—
213C4—9764no—
214C4—2442no—
215C4#1684066811yescharacteristic
216C4#1684066811yescharacteristic
217C2—21no—
218C2—41no—
219C2—4882no—
220C2C2×#1684066811yescharacteristic
subgroupG/H
centerC4#16840668
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#533C4
socleC2×C61C2×#354
prime radical#16840312C22
cosocle#14519774C23
hypercenter#533#6923
hypocenterC61#13594
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #21460959C2semidirect
3. #21460958C2semidirect
9. #16840132C4semidirect
10. #16840132C4semidirect
15. C2×#14519688C4semidirect
16. C61×#533C4semidirect
115. #533#6923semidirect
127. C61#13594semidirect

Maximal subgroups

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

subgroupindex
#214620922
#214609592
#214609582
#214561672
#1359461