Finite Group Databasebeta

← #29583005

Subgroups — #29583005

Order 15616.

640 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 109 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#21445753C212yesmaximal
2#21444089C211yesmaximal, characteristic
3#21443697C212yesmaximal
4#21443662C211yesmaximal, characteristic
5C61×#2646C211yesmaximal, characteristic
6C23×Dic122C2211yescharacteristic
7C2×#14519700—22no—
8C2×#14519700—22no—
9C2×C22⋊#92418C2212yes—
10C2×#14519684—22no—
11C2×#14519684C2211yescharacteristic
12C61×#400—22no—
13C61×#398—22no—
14C61×#385—22no—
15C61×#380C2212yes—
16C2×#95×C61C2211yescharacteristic
17C22×Dic122—22no—
18C22×Dic122—22no—
19C22×Dic122—21no—
20C22×Dic122—44no—
21C22×Dic122Q812yes—
22C23×Dic61—21no—
23C23×Dic61—21no—
24C22×#92418—22no—
25#14519700—44no—
26#14519700—44no—
27C22⋊#92418—22no—
28C22⋊#92418—22no—
29#14519684—22no—
30#14519684—44no—
31C23×C4×C61D412yes—
32C23×C4×C61C2311yescharacteristic
33C2×C4⋊C4×C61—22no—
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61D412yes—
36C2×C4⋊C4×C61D412yes—
37C2×C22⋊C4×C61—22no—
38#95×C61—22no—
39#95×C61—22no—
40#95×C61—22no—
41#95×C61—22no—
42C24×C61C2×D411yescharacteristic
43C22×C4×C61—22no—
44C22×C4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61—22no—
47C22×C4×C61—22no—
48C22×C4×C61—42no—
49C22×C4×C61—42no—
50C22×C4×C61—42no—
51C22×C4×C61C2×D412yes—
52C22×C4×C61C2×Q811yescharacteristic
53C22×C4×C61#4112yes—
54C22×C4×C61#4111yescharacteristic
55C22×Dic61—24no—
56C22×Dic61—22no—
57C22×Dic61—22no—
58C22×Dic61—42no—
59C22×Dic61—41no—
60C22×Dic61—41no—
61C22×Dic61—41no—
62C22×Dic61—42no—
63C22×Dic61—41no—
64C22×Dic61—42no—
65C2×Dic122—24no—
66C2×Dic122—24no—
67C2×Dic122—24no—
68C2×Dic122—44no—
69C2×Dic122—48no—
70C2×Dic122—44no—
71C2×Dic122—42no—
72C2×Dic122—42no—
73C2×Dic122—42no—
74C4⋊C4×C61—42no—
75C4⋊C4×C61—42no—
76C4⋊C4×C61—82no—
77C4⋊C4×C61—82no—
78C22⋊C4×C61—42no—
79C22⋊C4×C61—42no—
80C2×#92418—42no—
81C2×#92418—42no—
82C2×#92418—42no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—22no—
86C23×C61#12011yescharacteristic
87C23×C61C22⋊Q811yescharacteristic
88C23×C61#12411yescharacteristic
89C23×C61#13512yes—
90C23×C61#13712yes—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—42no—
96C2×C4×C61—44no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61—42no—
106C2×C4×C61—82no—
107C2×C4×C61C22⋊Q812yes—
108C2×C4×C61#12412yes—
109C2×Dic61—24no—
110C2×Dic61—42no—
111C2×Dic61—44no—
112C2×Dic61—42no—
113C2×Dic61—44no—
114C2×Dic61—44no—
115C2×Dic61—42no—
116C2×Dic61—82no—
117C2×Dic61—81no—
118C2×Dic61—81no—
119Dic122—28no—
120Dic122—44no—
121Dic122—44no—
122Dic122—44no—
123#92418—82no—
124#10345—611nomaximal, Sylow
125C22×C61—22no—
126C22×C61—22no—
127C22×C61—22no—
128C22×C61—22no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—21no—
133C22×C61#39311yescharacteristic
134C22×C61#45212yes—
135C22×C61#45511yescharacteristic
136C22×C61#45611yescharacteristic
137C22×C61B(4,𝔽2)12yes—
138C22×C61#47912yes—
139C22×C61#48811yescharacteristic
140C22×C61#49111yescharacteristic
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—82no—
144C4×C61—82no—
145C4×C61—82no—
146Dic61—44no—
147Dic61—82no—
148#2646D6111yescharacteristic
149#1787—612no—
150#1446—611no—
151#1294—612no—
152#1280—611no—
153C2×C61—21no—
154C2×C61—22no—
155C2×C61—21no—
156C2×C61#160312yes—
157C2×C61#160612yes—
158C2×C61#202611yescharacteristic
159C2×C61#202811yescharacteristic
160C2×C61#202911yescharacteristic
161C23×Q8—611no—
162C2×#103—1222no—
163C2×#103—1222no—
164C2×C22⋊C8—612no—
165#400—22no—
166#398—22no—
167#385—22no—
168#380C2×D6112yes—
169C2×#95—611no—
170C2×#95—1222no—
171C2×#95C2×D6111yescharacteristic
172C61#1034511yescharacteristic, complemented, Sylow
173C22×Q8—612no—
174C22×Q8—1221no—
175C22×Q8—1222no—
176C22×Q8—1222no—
177C22×Q8—2444no—
178C23×C4—1221no—
179C23×C4—1221no—
180C23×C4C22⋊D6112yes—
181C23×C4C22×D6111yescharacteristic
182C22×C8—1222no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4C22⋊D6112yes—
186C2×C4⋊C4C22⋊D6112yes—
187C2×C22⋊C4—22no—
188#103—2444no—
189#103—2444no—
190C22⋊C8—1222no—
191C22⋊C8—1222no—
192#95—22no—
193#95—22no—
194#95—22no—
195#95—22no—
196#95—1222no—
197#95—2444no—
198C24C2×C22⋊D6111yescharacteristic
199C2×Q8—1224no—
200C2×Q8—1224no—
201C2×Q8—1224no—
202C2×Q8—2442no—
203C2×Q8—2442no—
204C2×Q8—2444no—
205C2×Q8—2444no—
206C2×Q8—2448no—
207C2×Q8—2442no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—1224no—
217C22×C4—1222no—
218C22×C4—1222no—
219C22×C4—2442no—
220C22×C4—2441no—
221C22×C4—2441no—
222C22×C4—2442no—
223C22×C4—2442no—
224C22×C4—2441no—
225C22×C4—2441no—
226C22×C4Q8×D6111yescharacteristic
227C22×C4#1175822612yes—
228C22×C4#1175822611yescharacteristic
229C22×C4C2×C22⋊D6112yes—
230C2×C8—2442no—
231C2×C8—2442no—
232C2×C8—2442no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—82no—
236C4⋊C4—82no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1451974611yescharacteristic
243C23#1451975311yescharacteristic
244C23#1451976611yescharacteristic
245C23#1451979712yes—
246C23#1451980712yes—
247Q8—1228no—
248Q8—2444no—
249Q8—2444no—
250Q8—2444no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—82no—
267C2×C4—1224no—
268C2×C4—4881no—
269C2×C4—4882no—
270C2×C4—4881no—
271C2×C4—2442no—
272C2×C4—2444no—
273C2×C4—2442no—
274C2×C4—2444no—
275C2×C4—2444no—
276C2×C4—2442no—
277C2×C4#1451975312yes—
278C2×C4#1451976612yes—
279C8—4882no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22#1683967311yescharacteristic
289C22#1683992412yes—
290C22#1683994011yescharacteristic
291C22#1683994511yescharacteristic
292C22#1683994912yes—
293C22#1684006612yes—
294C22#1684011911yescharacteristic
295C22#1684013211yescharacteristic
296C4—22no—
297C4—22no—
298C4—82no—
299C4—82no—
300C4—82no—
301C4—4882no—
302C4—2444no—
303C2—21no—
304C2—22no—
305C2—21no—
306C2#2144478212yes—
307C2#2144479912yes—
308C2#2144696711yescharacteristic
309C2#2144697711yescharacteristic
310C2#2144698211yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2646C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#2646D61
hypocenterC61#10345
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2646

Complements

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

NH ≅ G/Ntype
172. C61#10345semidirect

Maximal subgroups

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

subgroupindex
#214457532
#214440892
#214436972
#214436622
C61×#26462
#1034561