Finite Group Databasebeta

← #29583014

Subgroups — #29583014

Order 15616.

500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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#21451789C211yesmaximal, characteristic
2#21445906C212yesmaximal
3#21444086C211yesmaximal, characteristic
4#21443699C212yesmaximal
5C61×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic61C2211yescharacteristic
7#16839704—22no—
8#16839696—22no—
9#16839635—22no—
10#16839622C2212yes—
11C2×#14519684—22no—
12C2×#14519684C2211yescharacteristic
13#16839525—22no—
14#16839525—22no—
15C2×C22⋊C8×C61C2212yes—
16C2×#95×C61C2211yescharacteristic
17C23×Dic61—21no—
18C23×Dic61—21no—
19C2×C4⋊Dic61—22no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61—21no—
22C2×C4⋊Dic61D412yes—
23C2×C4⋊Dic61D412yes—
24C2×C4⋊Dic61Q812yes—
25C2×#11758196—22no—
26C2×#11758196—22no—
27C2×C22⋊Dic61—22no—
28#14519684—22no—
29#14519684—22no—
30#14519684—22no—
31#14519684—22no—
32#14519684—44no—
33C23×C4×C61D412yes—
34C23×C4×C61C2311yescharacteristic
35C22×C8×C61—22no—
36C22⋊C8×C61—22no—
37C22⋊C8×C61—22no—
38#95×C61—22no—
39C24×C61C2×D411yescharacteristic
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—42no—
44C22×C4×C61—42no—
45C22×C4×C61—42no—
46C22×C4×C61C2×D412yes—
47C22×C4×C61C2×Q811yescharacteristic
48C22×C4×C61#4112yes—
49C22×C4×C61#4111yescharacteristic
50C22×Dic61—22no—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61—22no—
54C22×Dic61—41no—
55C22×Dic61—42no—
56C22×Dic61—41no—
57C22×Dic61—41no—
58C22×Dic61—41no—
59C22×Dic61—42no—
60C22×Dic61—42no—
61C22×Dic61—42no—
62C2×C8×C61—42no—
63C2×C8×C61—42no—
64C2×C8×C61—42no—
65C22⋊Dic61—42no—
66C22⋊Dic61—42no—
67C4⋊Dic61—24no—
68C4⋊Dic61—42no—
69C4⋊Dic61—42no—
70C4⋊Dic61—42no—
71#11758196—82no—
72#11758196—82no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—22no—
76C23×C61#12011yescharacteristic
77C23×C61C22⋊Q811yescharacteristic
78C23×C61#12411yescharacteristic
79C23×C61#13512yes—
80C23×C61AGL(1,ℤ/8)12yes—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61—42no—
86C2×C4×C61—44no—
87C2×C4×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61—82no—
91C2×C4×C61C22⋊Q812yes—
92C2×C4×C61#12412yes—
93C2×Dic61—44no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—44no—
103C2×Dic61—82no—
104C2×Dic61—81no—
105C2×Dic61—82no—
106C2×Dic61—81no—
107C2×Dic61—81no—
108C2×Dic61—81no—
109C8×C61—82no—
110#10346—611nomaximal, Sylow
111C22×C61—22no—
112C22×C61—22no—
113C22×C61—22no—
114C22×C61—22no—
115C22×C61—21no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—21no—
119C22×C61#39311yescharacteristic
120C22×C61#44912yes—
121C22×C61#45511yescharacteristic
122C22×C61#45611yescharacteristic
123C22×C61#45812yes—
124C22×C61#47812yes—
125C22×C61#48811yescharacteristic
126C22×C61#49011yescharacteristic
127C4×C61—22no—
128C4×C61—22no—
129C4×C61—82no—
130Dic61—82no—
131Dic61—82no—
132Dic61—82no—
133Dic61—82no—
134#2646—611no—
135#1823—612no—
136#1445—611no—
137#1294—612no—
138#1280D6111yescharacteristic
139C2×C61—21no—
140C2×C61—22no—
141C2×C61—21no—
142C2×C61#160912yes—
143C2×C61#161212yes—
144C2×C61#202511yescharacteristic
145C2×C61#202811yescharacteristic
146C2×C61#203011yescharacteristic
147C22×C4⋊C4—611no—
148C2×C22⋊C8C2×D6112yes—
149#400—1222no—
150#398—1222no—
151#385—1222no—
152#380—612no—
153C2×#95—611no—
154C2×#95—1222no—
155C2×#95C2×D6111yescharacteristic
156#340—1222no—
157#340—1222no—
158C61#1034611yescharacteristic, complemented, Sylow
159C23×C4—1221no—
160C23×C4—1221no—
161C23×C4D24412yes—
162C23×C4C22×D6111yescharacteristic
163C22×C8—22no—
164C2×C4⋊C4—612no—
165C2×C4⋊C4—612no—
166C2×C4⋊C4—612no—
167C2×C4⋊C4—1222no—
168C2×C4⋊C4—1222no—
169C2×C4⋊C4—1222no—
170C2×C4⋊C4—1222no—
171C2×C4⋊C4—1221no—
172C2×C22⋊C4—1222no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175#95—22no—
176#95—1222no—
177#95—1222no—
178#95—1222no—
179#95—1222no—
180#95—2444no—
181C24C2×D24411yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—1222no—
189C22×C4—1222no—
190C22×C4—1222no—
191C22×C4—1222no—
192C22×C4—2441no—
193C22×C4—2442no—
194C22×C4—2441no—
195C22×C4—2441no—
196C22×C4—2441no—
197C22×C4—2442no—
198C22×C4—2442no—
199C22×C4—2442no—
200C22×C4#1175822212yes—
201C22×C4D4×D6112yes—
202C22×C4#1175822411yescharacteristic
203C22×C4Q8×D6111yescharacteristic
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C4⋊C4—1224no—
208C4⋊C4—4882no—
209C4⋊C4—4882no—
210C4⋊C4—2442no—
211C4⋊C4—2442no—
212C4⋊C4—2442no—
213C22⋊C4—2442no—
214C22⋊C4—2442no—
215C23—21no—
216C23—21no—
217C23—22no—
218C23#1451974711yescharacteristic
219C23#1451975711yescharacteristic
220C23#1451976511yescharacteristic
221C23#1451979912yes—
222C23#1451980512yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—4881no—
234C2×C4—4882no—
235C2×C4—4881no—
236C2×C4—4881no—
237C2×C4—4881no—
238C2×C4—4882no—
239C2×C4—2442no—
240C2×C4—2444no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4—2442no—
244C2×C4—2442no—
245C2×C4—2444no—
246C2×C4—2442no—
247C2×C4—2442no—
248C2×C4—2442no—
249C2×C4#1451975512yes—
250C2×C4#1451976312yes—
251C8—82no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—22no—
260C22#1683967511yescharacteristic
261C22#1683990912yes—
262C22#1683994211yescharacteristic
263C22#1683994711yescharacteristic
264C22#1683995312yes—
265C22#1684006312yes—
266C22#1684011711yescharacteristic
267C22#1684012711yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—4882no—
272C4—4882no—
273C4—4882no—
274C4—4882no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#2144481812yes—
279C2#2144483512yes—
280C2#2144696611yescharacteristic
281C2#2144698111yescharacteristic
282C2#2144698711yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#1280D61
hypocenterC61#10346
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
158. C61#10346semidirect

Maximal subgroups

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

subgroupindex
#214517892
#214459062
#214440862
#214436992
C61×#12802
#1034661