Finite Group Databasebeta

← #30607248

Subgroups — #30607248

Order 15616.

670 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461648C212yesmaximal
2#21460913C214yesmaximal, complemented
3#21448309C211yesmaximal, characteristic
4C2×#14519836C2214yes—
5C2×#14519835—22no—
6#16840705—22no—
7C22×#11758222C2211yescharacteristic
8C2×#14519736C411yescharacteristic, complemented
9#16839668C412yescomplemented
10#16839664C2212yes—
11#16839641—22no—
12C4×#11758198—22no—
13C22×C42×C61C411yescharacteristic, complemented
14C2×C22⋊#6923—24no—
15#14519836—28no—
16#14519835—44no—
17(C2×#6923)⋊C4—44no—
18C2×#11758222—24no—
19C2×#11758222—42no—
20C2×#11758222—42no—
21C22×Dic122C2×C411yescharacteristic
22C22×D244C2311yescharacteristic
23C22×C22⋊D61D412yes—
24C22×C4×D61D412yes—
25#14519736—42no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C22⋊Dic61—21no—
28C2×#11758198—24no—
29C2×C4×Dic61—21no—
30#14519684—24no—
31C23×C4×C61—21no—
32C23×C4×C61C2×C411yescharacteristic
33C2×C42×C61—21no—
34C2×C42×C61—42no—
35C2×C42×C61C2×C412yes—
36C24×C61C22⋊C411yescharacteristic
37C23×D61C2×D412yes—
38C22×#6923—44no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—44no—
44C22×C4×C61—42no—
45C22×C4×C61C22⋊C411yescharacteristic
46C22×C4×C61C22×C411yescharacteristic
47C2×C22⋊D61—24no—
48C2×C22⋊D61—24no—
49C2×C22⋊D61—42no—
50C22×Dic61—22no—
51C22×Dic61C22⋊C412yes—
52#11758222—416no—
53C2×D244—41no—
54C2×D244—41no—
55C2×D244#4114yes—
56C2×C4×D61—24no—
57C2×C4×D61—24no—
58C2×C4×D61—42no—
59C2×Dic122—22no—
60C2×Dic122—41no—
61C2×Dic122—41no—
62C22⋊#6923—44no—
63C22⋊#6923—44no—
64C42×C61—42no—
65C42×C61—42no—
66C22⋊Dic61—42no—
67#11758198—48no—
68C4⋊Dic61—42no—
69C4×Dic61—42no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—42no—
73C23×C61#9912yes—
74C23×C61C2×C22⋊C411yescharacteristic
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—44no—
78C22×D61#12314yes—
79C2×#6923—84no—
80C2×#6923—88no—
81C2×C4×C61—28no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—24no—
87C2×C4×C61—42no—
88C2×C4×C61—48no—
89C2×C4×C61—42no—
90C2×C4×C61#9912yes—
91C2×C4×C61#11712yes—
92C22⋊D61—48no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—44no—
97C2×Dic61—42no—
98D244—44no—
99C4×D61—48no—
100Dic122—44no—
101#12857—611nomaximal, Sylow
102C22×C61—22no—
103C22×C61—22no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61#38111yescharacteristic
108C22×C61C2×#9911yescharacteristic
109C22×C61C2×#9911yescharacteristic
110C2×D61—24no—
111C2×D61—44no—
112C2×D61—44no—
113C2×D61—82no—
114#6923—164no—
115C4×C61—22no—
116C4×C61—22no—
117C4×C61—44no—
118Dic61—42no—
119Dic61—82no—
120#2297—611no—
121#1782—612no—
122#1393—614no—
123C2×C61—21no—
124C2×C61—21no—
125C2×C61—42no—
126C2×C61#181911yescharacteristic
127C2×C61#212612yes—
128D61—44no—
129C22×#41—611no—
130C2×#117—611no—
131C22×C42#692311yescharacteristic, complemented
132C2×#99—614no—
133C2×#99—1222no—
134#391—612no—
135#390—612no—
136#386—1222no—
137#381—1222no—
138C4×C22⋊C4—1222no—
139C61#1285711yescharacteristic, complemented, Sylow
140C2×#41—1224no—
141C2×#41—2442no—
142C2×#41—2442no—
143C22×Q8—611no—
144C22×D4—612no—
145C22×D4—611no—
146C23×C4—21no—
147C23×C4—612no—
148C23×C4C2×#692311yescharacteristic
149#117—2442no—
150C2×C4⋊C4—612no—
151C2×C22⋊C4—1224no—
152C2×C22⋊C4—1221no—
153C2×C22⋊C4—1224no—
154C2×C42—21no—
155C2×C42—42no—
156C2×C42—1221no—
157C2×C42C2×#692312yes—
158#99—1228no—
159#99—2444no—
160#95—1224no—
161#95—2444no—
162C24—612no—
163C24C22⋊#692311yescharacteristic
164#41—24416no—
165C2×Q8—1222no—
166C2×Q8—2441no—
167C2×Q8—2441no—
168C2×D4—614no—
169C2×D4—1224no—
170C2×D4—1224no—
171C2×D4—2441no—
172C2×D4—2441no—
173C2×D4—2442no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—44no—
179C22×C4—42no—
180C22×C4—612no—
181C22×C4—1224no—
182C22×C4—1224no—
183C22×C4—1222no—
184C22×C4—2442no—
185C22×C4—2444no—
186C22×C4C22⋊#692311yescharacteristic
187C22×C4C22×#692311yescharacteristic
188C4⋊C4—2442no—
189C22⋊C4—2448no—
190C22⋊C4—2444no—
191C22⋊C4—2444no—
192C22⋊C4—2442no—
193C42—42no—
194C42—42no—
195C42—2442no—
196C23—21no—
197C23—21no—
198C23—42no—
199C23—614no—
200C23—1222no—
201C23—1222no—
202C23—2444no—
203C23#1451983512yes—
204C23C2×C22⋊#692311yescharacteristic
205Q8—2444no—
206D4—2444no—
207D4—2448no—
208C2×C4—28no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—24no—
214C2×C4—42no—
215C2×C4—48no—
216C2×C4—42no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—4884no—
221C2×C4—4888no—
222C2×C4—2448no—
223C2×C4—2444no—
224C2×C4—2442no—
225C2×C4#1451983612yes—
226C2×C4#1451985612yes—
227C22—22no—
228C22—22no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—1224no—
233C22—4882no—
234C22—2444no—
235C22—2444no—
236C22#1684070511yescharacteristic
237C22C2×#1451983511yescharacteristic
238C22C2×#1451983611yescharacteristic
239C4—22no—
240C4—22no—
241C4—44no—
242C4—9764no—
243C4—4882no—
244C4—2442no—
245C2—21no—
246C2—21no—
247C2—42no—
248C2—2444no—
249C2#2146171411yescharacteristic
250C2#2146209212yes—
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C42×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758222C22
cosocleC22×D244C23
hypercenterC22×C42#6923
hypocenterC61#12857
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #21460913C2semidirect
8. C2×#14519736C4semidirect
9. #16839668C4semidirect
13. C22×C42×C61C4semidirect
131. C22×C42#6923semidirect
139. C61#12857semidirect

Maximal subgroups

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

subgroupindex
#214616482
#214609132
#214483092
#1285761