Finite Group Databasebeta

← #29575045

Subgroups — #29575045

Order 15616.

572 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#16839701C211yesmaximal, characteristic
2#21448422C211yesmaximal, characteristic
3#21445910C212yesmaximal
4#21443699C212yesmaximal
5C2×C61×#324C211yesmaximal, characteristic
6C22×C4⋊Dic61C2211yescharacteristic
7#16839701—22no—
8#16839701C414yescomplemented
9#16839648—24no—
10#16839625—21no—
11#16839622C2212yes—
12C4×C22⋊Dic61—21no—
13C2×#14519684—21no—
14C2×#14519684—21no—
15C2×#14519684C2211yescharacteristic
16#16839525—24no—
17C22×C4⋊C4×C61C2211yescharacteristic
18C2×C22⋊C8×C61C2212yes—
19C61×#324—22no—
20C23×Dic61—21no—
21C23×Dic61—21no—
22C2×C4⋊Dic61—22no—
23C2×C4⋊Dic61—22no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61C2×C412yes—
26C2×C4⋊Dic61D414yes—
27C2×C22⋊Dic61—22no—
28C2×C4×Dic61—22no—
29#14519684—22no—
30#14519684—24no—
31#14519684—24no—
32#14519684—24no—
33#14519684—21no—
34#14519684—22no—
35#14519684C2×C412yes—
36C23×C4×C61D411yescharacteristic
37C23×C4×C61D411yescharacteristic
38C23×C4×C61C2311yescharacteristic
39C22×C8×C61—22no—
40C2×C4⋊C4×C61—22no—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61C2×C412yes—
43C2×C4⋊C4×C61D412yes—
44C22⋊C8×C61—22no—
45C22⋊C8×C61—22no—
46C24×C61C2×D411yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—21no—
53C22×C4×C61—42no—
54C22×C4×C61—42no—
55C22×C4×C61C22⋊C412yes—
56C22×C4×C61C22⋊C412yes—
57C22×C4×C61C22×C411yescharacteristic
58C22×C4×C61C2×D412yes—
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61#4112yes—
61C22×Dic61—22no—
62C22×Dic61—22no—
63C22×Dic61—24no—
64C22×Dic61—42no—
65C22×Dic61—42no—
66C22×Dic61—44no—
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61—42no—
70C2×C8×C61—44no—
71C2×C8×C61—42no—
72C4⋊C4×C61—24no—
73C4⋊C4×C61—24no—
74C22⋊Dic61—42no—
75C22⋊Dic61—42no—
76C4⋊Dic61—24no—
77C4⋊Dic61—42no—
78C4⋊Dic61—44no—
79C4×Dic61—82no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61C2×C22⋊C411yescharacteristic
83C23×C61#12011yescharacteristic
84C23×C61#12311yescharacteristic
85C23×C61#13512yes—
86C23×C61#13712yes—
87C2×C4×C61—24no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—81no—
100C2×C4×C61C4×D412yes—
101C2×C4×C61#12112yes—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—44no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—44no—
108C2×Dic61—44no—
109C2×Dic61—44no—
110C2×Dic61—84no—
111C2×Dic61—82no—
112C2×Dic61—82no—
113C8×C61—82no—
114#9022—611nomaximal, Sylow
115C22×C61—24no—
116C22×C61—24no—
117C22×C61—21no—
118C22×C61—21no—
119C22×C61—21no—
120C22×C61—21no—
121C22×C61#38611yescharacteristic
122C22×C61#41611yescharacteristic
123C22×C61#41911yescharacteristic
124C22×C61#45212yes—
125C22×C61#45412yes—
126C22×C61#45812yes—
127C22×C61#48512yes—
128C4×C61—22no—
129C4×C61—22no—
130C4×C61—42no—
131C4×C61—42no—
132Dic61—82no—
133Dic61—84no—
134Dic61—82no—
135C2×#400—611no—
136#2313—611no—
137#1824—612no—
138C2×#324D6111yescharacteristic
139#1294—612no—
140C2×C61—21no—
141C2×C61—21no—
142C2×C61—22no—
143C2×C61#161514yes—
144C2×C61#187311yescharacteristic
145C2×C61#188811yescharacteristic
146C2×C61#189011yescharacteristic
147C22×C4⋊C4—611no—
148C22×C4⋊C4C2×D6111yescharacteristic
149C2×C22⋊C8C2×D6112yes—
150#400—614no—
151#400—1222no—
152#387—1224no—
153#381—1221no—
154#380—612no—
155C4×C22⋊C4—1221no—
156C2×#95—611no—
157C2×#95—1221no—
158C2×#95—1221no—
159#340—1224no—
160#324—22no—
161C61#902211yescharacteristic, complemented, Sylow
162C23×C4—1221no—
163C23×C4—1221no—
164C23×C4D24411yescharacteristic
165C23×C4D24411yescharacteristic
166C23×C4C22×D6111yescharacteristic
167C22×C8—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4—614no—
172C2×C4⋊C4—1222no—
173C2×C4⋊C4—1222no—
174C2×C4⋊C4—1221no—
175C2×C4⋊C4C4×D6112yes—
176C2×C4⋊C4C22⋊D6112yes—
177C2×C22⋊C4—1222no—
178C2×C42—1222no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181#95—612no—
182#95—1222no—
183#95—1224no—
184#95—1224no—
185#95—1224no—
186#95—1222no—
187#95—1221no—
188C24C2×D24411yescharacteristic
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—1222no—
198C22×C4—1222no—
199C22×C4—1224no—
200C22×C4—2442no—
201C22×C4—2442no—
202C22×C4—2444no—
203C22×C4—2441no—
204C22×C4—2441no—
205C22×C4—2442no—
206C22×C4#1175819812yes—
207C22×C4#1175819812yes—
208C22×C4C2×C4×D6111yescharacteristic
209C22×C4D4×D6112yes—
210C22×C4#1175822412yes—
211C22×C4C2×C22⋊D6111yescharacteristic
212C2×C8—44no—
213C2×C8—42no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—1224no—
217C4⋊C4—2444no—
218C4⋊C4—2442no—
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C42—4882no—
222C23—22no—
223C23—22no—
224C23C2×#1175819811yescharacteristic
225C23#1451974711yescharacteristic
226C23#1451976111yescharacteristic
227C23#1451979912yes—
228C23#1451981012yes—
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—81no—
242C2×C4—4884no—
243C2×C4—4882no—
244C2×C4—4882no—
245C2×C4—2442no—
246C2×C4—2442no—
247C2×C4—2444no—
248C2×C4—2444no—
249C2×C4—2444no—
250C2×C4—2442no—
251C2×C4—2442no—
252C2×C4—2444no—
253C2×C4#1451973712yes—
254C2×C4#1451974912yes—
255C8—82no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—24no—
261C22—24no—
262C22#1683963911yescharacteristic
263C22#1683975911yescharacteristic
264C22#1683977211yescharacteristic
265C22#1683992612yes—
266C22#1683993712yes—
267C22#1683995312yes—
268C22#1684010412yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—4882no—
274C4—4882no—
275C4—4884no—
276C2—21no—
277C2—21no—
278C2—22no—
279C2#2144485214yes—
280C2#2144612911yescharacteristic
281C2#2144622011yescharacteristic
282C2#2144623011yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenterC2×#324D61
hypocenterC61#9022
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
8. #16839701C4semidirect
161. C61#9022semidirect

Maximal subgroups

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

subgroupindex
C2×#168397012
#214484222
#214459102
#214436992
C2×C61×#3242
#902261