Finite Group Databasebeta

← #29572778

Subgroups — #29572778

Order 15616.

456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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#125×Dic61C211yesmaximal, characteristic
2#21445673C212yesmaximal
3C2×#16839504C211yesmaximal, characteristic
4#21443701C212yesmaximal
5C2×C61×#330C211yesmaximal, characteristic
6C2×#14519706—22no—
7C2×#14519688C2212yes—
8#16839661C412yes—
9#16839648—22no—
10#16839628C2211yescharacteristic
11C4⋊C4×Dic61—22no—
12C4⋊C4×Dic61C412yes—
13C42×Dic61C2211yescharacteristic
14#16839516—22no—
15#16839504—22no—
16C2×#125×C61C2211yescharacteristic
17C2×#97×C61C2212yes—
18C61×#330—22no—
19C22×#92418—22no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61C2×C412yes—
22C2×C4×Dic61—22no—
23C2×C4×Dic61C2×C411yescharacteristic
24C2×C4×Dic61C2×C411yescharacteristic
25C2×C4×Dic61D412yes—
26C2×C4×Dic61D412yes—
27#14519706—28no—
28#14519688—22no—
29#14519688—22no—
30#14519684—22no—
31#14519684—22no—
32#14519684—22no—
33C22×C8×C61—22no—
34#125×C61—22no—
35#125×C61D412yes—
36#125×C61Q812yes—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61C2×C412yes—
39C2×C42×C61C2311yescharacteristic
40#97×C61—22no—
41#97×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61C22×C411yescharacteristic
44C22×C4×C61C2×D412yes—
45C22×Dic61—22no—
46C22×Dic61C22⋊C411yescharacteristic
47C22×Dic61C22⋊C412yes—
48C22×Dic61C22⋊C411yescharacteristic
49C2×C8×C61—24no—
50C2×C8×C61—42no—
51C2×C8×C61—42no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61—24no—
54C4⋊C4×C61—24no—
55C4⋊C4×C61C4⋊C414yes—
56C42×C61C2×D411yescharacteristic
57C42×C61C2×Q811yescharacteristic
58C42×C61#4112yes—
59C4⋊Dic61—44no—
60C4⋊Dic61—42no—
61C4×Dic61—22no—
62C4×Dic61—24no—
63C4×Dic61—41no—
64C4×Dic61—42no—
65C4×Dic61—44no—
66C2×#92418—24no—
67C2×#92418—42no—
68C2×#92418—42no—
69C23×C61C2×C22⋊C411yescharacteristic
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—24no—
75C2×C4×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61C2×C4⋊C411yescharacteristic
78C2×C4×C61#11711yescharacteristic
79C2×C4×C61#12112yes—
80C2×C4×C61C22⋊Q812yes—
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61#10112yes—
90C2×Dic61#10414yes—
91C8×C61—44no—
92#92418—44no—
93#8580—611nomaximal, Sylow
94C22×C61#38011yescharacteristic
95C22×C61C2×#10111yescharacteristic
96C22×C61#41311yescharacteristic
97C22×C61C2×#10412yes—
98C22×C61#42112yes—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—22no—
102C4×C61—22no—
103C4×C61—44no—
104Dic61—41no—
105Dic61—42no—
106Dic61—82no—
107Dic61#33014yescomplemented
108C4×#125—611no—
109#1767—612no—
110C2×#330—611no—
111C2×#330D6111yescharacteristic
112#1295—612no—
113C2×C61C2×#33011yescharacteristic
114C2×C61#152912yes—
115C2×C61#153711yescharacteristic
116C2×C61#180111yescharacteristic
117C2×C61#180612yes—
118C2×#125C2×D6111yescharacteristic
119C2×C4⋊C8—1222no—
120C2×#97—612no—
121C2×#97C2×D6112yes—
122#389—612no—
123#387—1222no—
124#382—611no—
125C4×C4⋊C4—612no—
126C4×C4⋊C4—1222no—
127C43—611no—
128#336—1222no—
129#330—22no—
130#330—1222no—
131C61#858011yescharacteristic, complemented, Sylow
132C22×C8—22no—
133C22×C8—1222no—
134#125—22no—
135#125Dic12212yes—
136#125C22⋊D6112yes—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—1222no—
140C2×C4⋊C4C4×D6112yes—
141C2×C42—611no—
142C2×C42—612no—
143C2×C42—611no—
144C2×C42—612no—
145C2×C42—1222no—
146C2×C42C22×D6111yescharacteristic
147C4⋊C8—1228no—
148#97—22no—
149#97—22no—
150#97—1222no—
151#97—1222no—
152#95—1222no—
153#95—1222no—
154#95—1222no—
155C22×C4—22no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—612no—
159C22×C4—1222no—
160C22×C4C2×C4×D6111yescharacteristic
161C22×C4D4×D6112yes—
162C2×C8—24no—
163C2×C8—42no—
164C2×C8—42no—
165C2×C8—1224no—
166C2×C8—2442no—
167C2×C8—2442no—
168C4⋊C4—22no—
169C4⋊C4—24no—
170C4⋊C4—24no—
171C4⋊C4—2442no—
172C4⋊C4—2444no—
173C4⋊C4#1175819614yes—
174C42—1224no—
175C42—1222no—
176C42—2441no—
177C42—2442no—
178C42—2444no—
179C42C2×Dic12211yescharacteristic
180C42#1175822412yes—
181C42C2×C22⋊D6111yescharacteristic
182C23C22⋊C4×D6111yescharacteristic
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—612no—
191C2×C4—614no—
192C2×C4—1221no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4C2×#1175819611yescharacteristic
201C2×C4#1451973311yescharacteristic
202C2×C4#1451974912yes—
203C2×C4#1451975412yes—
204C8—44no—
205C8—2444no—
206C22#1683962011yescharacteristic
207C22#101×D6111yescharacteristic
208C22#1683974511yescharacteristic
209C22#104×D6112yes—
210C22#1683977712yes—
211C4—21no—
212C4—21no—
213C4—22no—
214C4—22no—
215C4—44no—
216C4—614no—
217C4—4882no—
218C4—2442no—
219C4—2441no—
220C2#330×D6111yescharacteristic
221C2#2144442512yes—
222C2#2144445511yescharacteristic
223C2#2144581311yescharacteristic
224C2#2144583712yes—
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#330C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenterC2×#330D61
hypocenterC61#8580
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
107. Dic61#330semidirect
131. C61#8580semidirect

Maximal subgroups

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

subgroupindex
#125×Dic612
#214456732
C2×#168395042
#214437012
C2×C61×#3302
#858061