Finite Group Databasebeta

← #29568830

Subgroups — #29568830

Order 15616.

480 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 83 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#21453765C211yesmaximal, characteristic
2#21446961C212yesmaximal, complemented
3#21446901C211yesmaximal, characteristic
4#21443644C212yesmaximal, complemented
5C61×#1270C211yesmaximal, characteristic
6C22×#11758200—21no—
7C2×#14519777C2211yescharacteristic
8C2×#14519702—22no—
9C2×#14519700—21no—
10#16839701—21no—
11#16839674—22no—
12#16839668C2212yes—
13#16839642—21no—
14#16839637—22no—
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#390C2211yescharacteristic
18C61×#336C2212yes—
19C22×Dic122—21no—
20C22×Dic122D412yes—
21C23×Dic61—21no—
22C2×#11758200—42no—
23C2×#11758200—42no—
24C2×#11758200—42no—
25C22×#92418—21no—
26#14519777—42no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61D412yes—
30C2×C22⋊Dic61—22no—
31C2×C22⋊Dic61—21no—
32#14519702—44no—
33#14519700—42no—
34#14519684—22no—
35#14519684—21no—
36#14519684—22no—
37#14519684—22no—
38C22×D4×C61D411yescharacteristic
39C22×C8×C61—22no—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C22⋊C4×C61—22no—
42C2×C42×C61C2311yescharacteristic
43C24×C61—21no—
44C2×D4×C61—21no—
45C2×D4×C61—41no—
46C2×D4×C61—41no—
47C2×D4×C61SD1612yes—
48C22×C4×C61—21no—
49C22×C4×C61C2×D411yescharacteristic
50C22×C4×C61C2×D412yes—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61—41no—
54C22×Dic61—81no—
55C22×Dic61—82no—
56C2×Dic122—22no—
57C2×Dic122—22no—
58C2×Dic122—22no—
59C2×Dic122—42no—
60C2×Dic122—42no—
61C2×Dic122—41no—
62C2×Dic122—41no—
63C2×Dic122—41no—
64C2×Dic122—41no—
65C2×Dic122—41no—
66C2×C8×C61—42no—
67C2×C8×C61—42no—
68C2×C8×C61—42no—
69C4⋊C4×C61—41no—
70C22⋊C4×C61—42no—
71C22⋊C4×C61—42no—
72C42×C61—41no—
73C22⋊Dic61—82no—
74C22⋊Dic61—81no—
75#11758200—48no—
76C4⋊Dic61—24no—
77C4⋊Dic61—42no—
78C4⋊Dic61—42no—
79C4⋊Dic61—81no—
80C2×#92418—22no—
81C2×#92418—41no—
82C2×#92418—41no—
83C23×C61—22no—
84C23×C61—42no—
85C23×C61—41no—
86C23×C61—42no—
87C23×C61—41no—
88C23×C61#12011yescharacteristic
89D4×C61—42no—
90D4×C61—81no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—42no—
96C2×C4×C61—41no—
97C2×C4×C61C2×SD1611yescharacteristic
98C2×C4×C61#13512yes—
99C2×C4×C61#13711yescharacteristic
100C2×C4×C61#13712yes—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—84no—
109C2×Dic61—81no—
110C2×Dic61—81no—
111Dic122—42no—
112Dic122—42no—
113Dic122—44no—
114Dic122—81no—
115Dic122—81no—
116Dic122—82no—
117C8×C61—82no—
118#92418—42no—
119#7755—611nomaximal, Sylow
120C22×C61—42no—
121C22×C61—44no—
122C22×C61—82no—
123C22×C61—81no—
124C22×C61—81no—
125C22×C61#44811yescharacteristic
126C22×C61#45212yes—
127C22×C61#45311yescharacteristic
128C22×C61#45512yes—
129C22×C61B(4,𝔽2)11yescharacteristic
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—22no—
133C4×C61—22no—
134C4×C61—81no—
135Dic61—82no—
136Dic61—82no—
137Dic61—82no—
138#2804—611no—
139#2024—612no—
140#2013—611no—
141#1272—612no—
142#1270D6111yescharacteristic
143C2×C61—82no—
144C2×C61#159611yescharacteristic
145C2×C61#160612yes—
146C2×C61#163011yescharacteristic
147C2×C61#164312yes—
148C2×C61#165911yescharacteristic
149C22×SD16—1221no—
150C2×C4⋊Q8—611no—
151C2×#103—1222no—
152C2×#103—1221no—
153#400—1221no—
154#393—1222no—
155#391—612no—
156#390C2×D6111yescharacteristic
157#386—1221no—
158#385—1222no—
159#340—1222no—
160#336—611no—
161#336C2×D6112yes—
162C61#775511yescharacteristic, complemented, Sylow
163C22×Q8—612no—
164C22×Q8—1221no—
165C22×D4D24411yescharacteristic
166C23×C4—1221no—
167C2×SD16—2442no—
168C2×SD16—2442no—
169C2×SD16—2442no—
170C22×C8—22no—
171C22×C8—1221no—
172C4⋊Q8—2442no—
173C2×C4⋊C4—612no—
174C2×C4⋊C4—1222no—
175C2×C4⋊C4—1221no—
176C2×C4⋊C4D24411yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—1222no—
179C2×C22⋊C4—1221no—
180C2×C42C22×D6111yescharacteristic
181#103—2442no—
182#103—2444no—
183#95—1222no—
184#95—1221no—
185#95—1222no—
186#95—1222no—
187C24—21no—
188C2×Q8—1222no—
189C2×Q8—1222no—
190C2×Q8—1222no—
191C2×Q8—2441no—
192C2×Q8—2441no—
193C2×Q8—2441no—
194C2×Q8—2442no—
195C2×Q8—2442no—
196C2×Q8—2441no—
197C2×Q8—2441no—
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4#1175819012yes—
202C22×C4—21no—
203C22×C4—1222no—
204C22×C4—1222no—
205C22×C4—4882no—
206C22×C4—4881no—
207C22×C4—2441no—
208C22×C4C2×D24411yescharacteristic
209C22×C4D4×D6112yes—
210SD16—2448no—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—1222no—
215C2×C8—2441no—
216C2×C8—2441no—
217C4⋊C4—41no—
218C4⋊C4—1224no—
219C4⋊C4—4881no—
220C4⋊C4—2442no—
221C4⋊C4—2442no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—4882no—
225C22⋊C4—4881no—
226C42—41no—
227C23—22no—
228C23—42no—
229C23—41no—
230C23—42no—
231C23—41no—
232C23#1451974711yescharacteristic
233Q8—4882no—
234Q8—4881no—
235Q8—4881no—
236Q8—2442no—
237Q8—2442no—
238Q8—2444no—
239D4—42no—
240D4—81no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—4884no—
248C2×C4—4881no—
249C2×C4—4881no—
250C2×C4—2442no—
251C2×C4—2442no—
252C2×C4—2442no—
253C2×C4—2442no—
254C2×C4—2442no—
255C2×C4—2442no—
256C2×C4—2442no—
257C2×C4C2×#1175819011yescharacteristic
258C2×C4#1451979612yes—
259C2×C4#1451980612yes—
260C2×C4#1451981011yescharacteristic
261C8—82no—
262C8—2442no—
263C22—42no—
264C22—44no—
265C22—81no—
266C22—81no—
267C22—82no—
268C22#1683990311yescharacteristic
269C22#1683992512yes—
270C22#1683993211yescharacteristic
271C22#1683994112yes—
272C22#1683995011yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—81no—
278C4—4882no—
279C4—4882no—
280C4—4882no—
281C2—82no—
282C2#2144474411yescharacteristic
283C2#2144480012yes—
284C2#2144494111yescharacteristic
285C2#2144502812yes—
286C2#2144512611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#1270D61
hypocenterC61#7755
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21446961C2semidirect
4. #21443644C2semidirect
162. C61#7755semidirect

Maximal subgroups

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

subgroupindex
#214537652
#214469612
#214469012
#214436442
C61×#12702
#775561