Finite Group Databasebeta

← #29570938

Subgroups — #29570938

Order 15616.

444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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#21448374C211yesmaximal, characteristic
2#21445567C212yesmaximal
3C2×#16839503C212yesmaximal
4#21443700C211yesmaximal, characteristic
5C61×#1295C211yesmaximal, characteristic
6C2×#14519769C2211yescharacteristic
7C2×#14519688C2212yes—
8#16839658C412yes—
9#16839644—22no—
10C4⋊C4×Dic61C412yes—
11#16839613—22no—
12C42×Dic61C2211yescharacteristic
13#16839516—22no—
14#16839516—22no—
15#16839503C418yescomplemented
16C2×#97×C61C2212yes—
17C61×#382C2211yescharacteristic
18C22×#92418—22no—
19#14519769—21no—
20#14519769—21no—
21#14519769C2×C414yes—
22C2×C4⋊Dic61C2×C412yes—
23C2×#11758196—22no—
24C2×#11758196—22no—
25C2×C4×Dic61—22no—
26C2×C4×Dic61C2×C411yescharacteristic
27C2×C4×Dic61C2×C411yescharacteristic
28C2×C4×Dic61D412yes—
29C2×C4×Dic61D412yes—
30#14519688—22no—
31#14519688C2×C414yes—
32#14519684—22no—
33#14519684—22no—
34C22×C8×C61—22no—
35C2×C4⋊C4×C61C2×C412yes—
36C2×C42×C61C2311yescharacteristic
37#97×C61—22no—
38#97×C61C2×C414yes—
39#95×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61C22×C411yescharacteristic
42C22×C4×C61C2×D412yes—
43C22×Dic61—22no—
44C22×Dic61C22⋊C411yescharacteristic
45C22×Dic61C22⋊C412yes—
46C22×Dic61C22⋊C411yescharacteristic
47C2×C8×C61—24no—
48C2×C8×C61—42no—
49C2×C8×C61—42no—
50C4⋊C4×C61—42no—
51C42×C61C22×C412yes—
52C42×C61#4111yescharacteristic
53C42×C61#4111yescharacteristic
54C4⋊Dic61—22no—
55C4⋊Dic61C4214yes—
56#11758196—24no—
57#11758196—24no—
58#11758196—44no—
59C4×Dic61—22no—
60C4×Dic61—41no—
61C4×Dic61—42no—
62C4×Dic61—42no—
63C4×Dic61—44no—
64C2×#92418—24no—
65C2×#92418—42no—
66C2×#92418—42no—
67C23×C61C2×C22⋊C411yescharacteristic
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61C2×C4211yescharacteristic
76C2×C4×C61#11711yescharacteristic
77C2×C4×C61C4×D412yes—
78C2×C4×C61C4×D412yes—
79C2×Dic61—22no—
80C2×Dic61—24no—
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61#10112yes—
89C8×C61—44no—
90#92418—44no—
91#8225—611nomaximal, Sylow
92C22×C61C4×C22⋊C411yescharacteristic
93C22×C61C2×#10111yescharacteristic
94C22×C61#41311yescharacteristic
95C22×C61#42112yes—
96C22×C61#42112yes—
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—22no—
100C4×C61—22no—
101C4×C61—82no—
102Dic61—22no—
103Dic61—41no—
104Dic61—44no—
105Dic61—42no—
106C4×#125—611no—
107#1745—612no—
108C2×#330—612no—
109#1295—611no—
110#1295D6111yescharacteristic
111C2×C61#153411yescharacteristic
112C2×C61#153512yes—
113C2×C61#153711yescharacteristic
114C2×C61C4×#10111yescharacteristic
115C2×C61#175912yes—
116C2×#125—611no—
117C2×#97—612no—
118C2×#97C2×D6112yes—
119#389—612no—
120#387—1222no—
121#382C2×D6111yescharacteristic
122C4×C4⋊C4—612no—
123C4×C4⋊C4—1222no—
124C43—611no—
125#336—1222no—
126#336—1222no—
127#330—618no—
128C61#822511yescharacteristic, complemented, Sylow
129C22×C8—22no—
130C22×C8—1222no—
131#125—614no—
132#125—1221no—
133#125—1221no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—1222no—
136C2×C4⋊C4—1222no—
137C2×C4⋊C4C4×D6112yes—
138C2×C42—611no—
139C2×C42—611no—
140C2×C42—612no—
141C2×C42—612no—
142C2×C42—1222no—
143C2×C42C22×D6111yescharacteristic
144#97—22no—
145#97—614no—
146#97—1222no—
147#97C4×D6114yes—
148#95—22no—
149#95—1222no—
150#95—1222no—
151C22×C4—22no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—612no—
155C22×C4—1222no—
156C22×C4C2×C4×D6111yescharacteristic
157C22×C4D4×D6112yes—
158C2×C8—24no—
159C2×C8—42no—
160C2×C8—42no—
161C2×C8—1224no—
162C2×C8—2442no—
163C2×C8—2442no—
164C4⋊C4—42no—
165C4⋊C4—614no—
166C4⋊C4—1222no—
167C4⋊C4—1224no—
168C4⋊C4—1224no—
169C4⋊C4—2444no—
170C42—1222no—
171C42—2441no—
172C42—2442no—
173C42—2442no—
174C42—2444no—
175C42C2×C4×D6112yes—
176C42#1175822411yescharacteristic
177C42#1175822611yescharacteristic
178C23C22⋊C4×D6111yescharacteristic
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—612no—
187C2×C4—1222no—
188C2×C4—1221no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1224no—
194C2×C4—2442no—
195C2×C4—2442no—
196C2×C4C42×D6111yescharacteristic
197C2×C4#1451973511yescharacteristic
198C2×C4#1451973712yes—
199C2×C4#1451973912yes—
200C8—44no—
201C8—2444no—
202C22#1683960911yescharacteristic
203C22#101×D6111yescharacteristic
204C22#1683974311yescharacteristic
205C22#1683977712yes—
206C22#1683977712yes—
207C4—21no—
208C4—21no—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—1222no—
213C4—2442no—
214C4—2441no—
215C4—2444no—
216C2#2144444411yescharacteristic
217C2#2144444712yes—
218C2#2144445511yescharacteristic
219C2#2144561411yescharacteristic
220C2#2144562812yes—
subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1295D61
hypocenterC61#8225
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
15. #16839503C4semidirect
128. C61#8225semidirect

Maximal subgroups

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

subgroupindex
#214483742
#214455672
C2×#168395032
#214437002
C61×#12952
#822561