Finite Group Databasebeta

← #29572779

Subgroups — #29572779

Order 15616.

456 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 117 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#21445673C212yesmaximal
3C2×#16839503C212yesmaximal
4#21443700C211yesmaximal, characteristic
5C61×#1295C211yesmaximal, characteristic
6C2×#14519769C2211yescharacteristic
7C2×#14519706—22no—
8C2×#14519688C2212yes—
9#16839658C412yes—
10#16839644—22no—
11C4⋊C4×Dic61C412yes—
12#16839613—22no—
13C42×Dic61C2211yescharacteristic
14#16839516—22no—
15#16839503—24no—
16C2×#97×C61C2212yes—
17C61×#382C2211yescharacteristic
18C22×#92418—22no—
19#14519769—22no—
20#14519769D412yes—
21#14519769Q812yes—
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#14519706—28no—
31#14519688—22no—
32#14519688—22no—
33#14519684—22no—
34#14519684—22no—
35C22×C8×C61—22no—
36C2×C4⋊C4×C61C2×C412yes—
37C2×C42×C61C2311yescharacteristic
38#97×C61—22no—
39#97×C61—22no—
40#95×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61C22×C411yescharacteristic
43C22×C4×C61C2×D412yes—
44C22×Dic61—22no—
45C22×Dic61C22⋊C411yescharacteristic
46C22×Dic61C22⋊C412yes—
47C22×Dic61C22⋊C411yescharacteristic
48C2×C8×C61—24no—
49C2×C8×C61—42no—
50C2×C8×C61—42no—
51C4⋊C4×C61—42no—
52C42×C61C2×D411yescharacteristic
53C42×C61C2×Q811yescharacteristic
54C42×C61#4112yes—
55C4⋊Dic61—22no—
56C4⋊Dic61C4⋊C414yes—
57#11758196—24no—
58#11758196—24no—
59#11758196—44no—
60C4×Dic61—22no—
61C4×Dic61—24no—
62C4×Dic61—41no—
63C4×Dic61—42no—
64C4×Dic61—44no—
65C2×#92418—24no—
66C2×#92418—42no—
67C2×#92418—42no—
68C23×C61C2×C22⋊C411yescharacteristic
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61C2×C4⋊C411yescharacteristic
77C2×C4×C61#11711yescharacteristic
78C2×C4×C61#12112yes—
79C2×C4×C61C22⋊Q812yes—
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—
89C2×Dic61#10414yes—
90C8×C61—44no—
91#92418—44no—
92#8580—611nomaximal, Sylow
93C22×C61#38011yescharacteristic
94C22×C61C2×#10111yescharacteristic
95C22×C61#41311yescharacteristic
96C22×C61C2×#10412yes—
97C22×C61#42112yes—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—22no—
101C4×C61—22no—
102C4×C61—82no—
103Dic61—41no—
104Dic61—44no—
105Dic61—42no—
106Dic61#33014yescomplemented
107C4×#125—611no—
108#1767—612no—
109C2×#330—612no—
110#1295—611no—
111#1295D6111yescharacteristic
112C2×C61C2×#33011yescharacteristic
113C2×C61#152912yes—
114C2×C61#153711yescharacteristic
115C2×C61#180111yescharacteristic
116C2×C61#180612yes—
117C2×#125—611no—
118C2×C4⋊C8—1222no—
119C2×#97—612no—
120C2×#97C2×D6112yes—
121#389—612no—
122#387—1222no—
123#382C2×D6111yescharacteristic
124C4×C4⋊C4—612no—
125C4×C4⋊C4—1222no—
126C43—611no—
127#336—1222no—
128#330—1224no—
129C61#858011yescharacteristic, complemented, Sylow
130C22×C8—22no—
131C22×C8—1222no—
132#125—612no—
133#125—612no—
134#125—1222no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—1222no—
137C2×C4⋊C4—1222no—
138C2×C4⋊C4C4×D6112yes—
139C2×C42—611no—
140C2×C42—612no—
141C2×C42—611no—
142C2×C42—612no—
143C2×C42—1222no—
144C2×C42C22×D6111yescharacteristic
145C4⋊C8—1228no—
146#97—22no—
147#97—22no—
148#97—1222no—
149#97—1222no—
150#95—22no—
151#95—1222no—
152#95—1222no—
153C22×C4—22no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—612no—
157C22×C4—1222no—
158C22×C4C2×C4×D6111yescharacteristic
159C22×C4D4×D6112yes—
160C2×C8—24no—
161C2×C8—42no—
162C2×C8—42no—
163C2×C8—1224no—
164C2×C8—2442no—
165C2×C8—2442no—
166C4⋊C4—42no—
167C4⋊C4—614no—
168C4⋊C4—1222no—
169C4⋊C4—1224no—
170C4⋊C4—1224no—
171C4⋊C4—2444no—
172C42—1224no—
173C42—1222no—
174C42—2441no—
175C42—2442no—
176C42—2444no—
177C42#1175822212yes—
178C42D4×D6111yescharacteristic
179C42Q8×D6111yescharacteristic
180C23C22⋊C4×D6111yescharacteristic
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—612no—
189C2×C4—614no—
190C2×C4—1221no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1224no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4C4⋊C4×D6111yescharacteristic
199C2×C4#1451973411yescharacteristic
200C2×C4#1451975012yes—
201C2×C4#1451975512yes—
202C8—44no—
203C8—2444no—
204C22#1683962111yescharacteristic
205C22#101×D6111yescharacteristic
206C22#1683974311yescharacteristic
207C22#104×D6112yes—
208C22#1683977712yes—
209C4—21no—
210C4—21no—
211C4—22no—
212C4—22no—
213C4—82no—
214C4—614no—
215C4—2442no—
216C4—2441no—
217C4—2444no—
218C2#330×D6111yescharacteristic
219C2#2144442312yes—
220C2#2144445511yescharacteristic
221C2#2144581411yescharacteristic
222C2#2144583812yes—
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1295D61
hypocenterC61#8580
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
106. Dic61#330semidirect
129. C61#8580semidirect

Maximal subgroups

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

subgroupindex
#214483742
#214456732
C2×#168395032
#214437002
C61×#12952
#858061