Finite Group Databasebeta

← #29581003

Subgroups — #29581003

Order 15616.

528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 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#21456343C211yesmaximal, characteristic, complemented
2#21455827C212yesmaximal
3#21444221C212yesmaximal, complemented
4#21443650C211yesmaximal, characteristic, complemented
5C61×#1955C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840171—22no—
8#16840171—22no—
9#16840092—22no—
10#16840052—22no—
11#16839967—22no—
12#16839913—22no—
13C4×#11758200—24no—
14#16839815C2212yes—
15#16839800—22no—
16#16839492—24no—
17C2×C4×D4×C61C2211yescharacteristic
18C2×C4⋊C8×C61C2211yescharacteristic
19C2×C22⋊C8×C61—22no—
20C2×#97×C61C2211yescharacteristic
21C2×#11758200—24no—
22#14519777D412yes—
23#14519777D412yes—
24#14519769—22no—
25#14519756—22no—
26#14519756—22no—
27C4×Dic122—22no—
28C4×Dic122—22no—
29#14519736—22no—
30#14519711—22no—
31#14519711—22no—
32#14519709—24no—
33#14519708—24no—
34C4⋊#92418—22no—
35#14519700—24no—
36#14519698—24no—
37C22⋊#92418—22no—
38C4×#92418D414yes—
39C22×D4×C61D411yescharacteristic
40C23×C4×C61—21no—
41C22×C8×C61—21no—
42C22×C8×C61D412yes—
43C4×D4×C61—22no—
44C4×D4×C61—22no—
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C22⋊C4×C61—21no—
47C2×C42×C61C2311yescharacteristic
48C4⋊C8×C61—22no—
49C22⋊C8×C61—44no—
50#97×C61—22no—
51C24×C61—21no—
52C2×D4×C61—22no—
53C2×D4×C61—42no—
54C22×C4×C61—21no—
55C22×C4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61—42no—
58C22×C4×C61—42no—
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61#4111yescharacteristic
62C2×Dic122—22no—
63C2×Dic122—22no—
64C2×C8×C61—22no—
65C2×C8×C61—22no—
66C2×C8×C61—41no—
67C2×C8×C61—42no—
68C2×C8×C61SD1614yescomplemented
69C4⋊C4×C61—22no—
70C22⋊C4×C61—42no—
71C42×C61C2×D412yes—
72C42×C61C2×D412yes—
73C22⋊Dic61—42no—
74#11758200—48no—
75C4⋊Dic61—22no—
76C4⋊Dic61—22no—
77C4⋊Dic61—22no—
78C4⋊Dic61—22no—
79#11758196—42no—
80#11758196—42no—
81C4×Dic61—42no—
82C2×#92418—24no—
83C23×C61—22no—
84C23×C61—41no—
85C23×C61—42no—
86C23×C61—41no—
87C23×C61—42no—
88C23×C61#12111yescharacteristic
89D4×C61—24no—
90D4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—42no—
95C2×C4×C61—82no—
96C2×C4×C61—81no—
97C2×C4×C61—81no—
98C2×C4×C61#12012yes—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61#12112yes—
101C2×C4×C61#12711yescharacteristic
102C2×C4×C61C2×SD1612yes—
103C2×C4×C61#13712yes—
104C2×Dic61—42no—
105C2×Dic61—42no—
106Dic122—44no—
107Dic122—44no—
108C8×C61—24no—
109C8×C61—81no—
110#92418—44no—
111#10036—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—21no—
114C22×C61—44no—
115C22×C61—42no—
116C22×C61—82no—
117C22×C61—81no—
118C22×C61—81no—
119C22×C61#39211yescharacteristic
120C22×C61#46112yes—
121C4×C61—22no—
122C4×C61—22no—
123C4×C61—81no—
124C4×C61#44812yes—
125C4×C61#49211yescharacteristic
126C4×C61#49711yescharacteristic
127Dic61—82no—
128Dic61—82no—
129#3162—611no—
130#3101—612no—
131#1955D6111yescharacteristic
132#1481—612no—
133#1275—611no—
134C2×C61—22no—
135C2×C61—82no—
136C2×C61#201011yescharacteristic
137C2×C61#201311yescharacteristic
138C2×C61#201711yescharacteristic
139#533—612no—
140C2×C4×D4C2×D6111yescharacteristic
141#501—1222no—
142#501—1222no—
143#483—1222no—
144#476—1222no—
145#461—1222no—
146#450—1222no—
147C4×SD16—1224no—
148#431—612no—
149#427—1222no—
150C2×C4⋊C8C2×D6111yescharacteristic
151C2×C22⋊C8—22no—
152C2×#97C2×D6111yescharacteristic
153Q8⋊C8—1224no—
154C61#1003611yescharacteristic, complemented, Sylow
155C22×D4D24411yescharacteristic
156C23×C4—21no—
157C2×SD16—1224no—
158C22×C8—21no—
159C22×C8C22⋊D6112yes—
160C4⋊Q8—612no—
161C4⋊Q8—612no—
162#125—1222no—
163C22⋊Q8—1222no—
164C22⋊Q8—1222no—
165C4×Q8—1222no—
166C4×Q8—1222no—
167C4×D4—22no—
168C4×D4—22no—
169#117—1222no—
170C2×C4⋊C4D24411yescharacteristic
171C2×C22⋊C4—21no—
172C2×C42C22×D6111yescharacteristic
173#107—1222no—
174#107—1222no—
175#106—1224no—
176#106—1224no—
177C4⋊C8—22no—
178C4⋊C8—1222no—
179#103—1224no—
180#102—1224no—
181C22⋊C8—44no—
182C22⋊C8—1222no—
183#97—22no—
184C4×C8—614no—
185C24—21no—
186C2×Q8—1222no—
187C2×Q8—1222no—
188C2×D4—22no—
189C2×D4—42no—
190C22×C4—21no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4C2×D24411yescharacteristic
196C22×C4#1175822211yescharacteristic
197C22×C4C2×C22⋊D6111yescharacteristic
198SD16—2448no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—42no—
203C2×C8—1224no—
204C2×C8#1175820014yescomplemented
205C4⋊C4—22no—
206C4⋊C4—1222no—
207C4⋊C4—1222no—
208C4⋊C4—1222no—
209C4⋊C4—1222no—
210C4⋊C4—2442no—
211C4⋊C4—2442no—
212C22⋊C4—42no—
213C22⋊C4—2442no—
214C42—2442no—
215C42D4×D6112yes—
216C42D4×D6112yes—
217C23—22no—
218C23—41no—
219C23—42no—
220C23—42no—
221C23—41no—
222C23#1451975111yescharacteristic
223Q8—2444no—
224Q8—2444no—
225D4—24no—
226D4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—81no—
232C2×C4—82no—
233C2×C4—81no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4#1451974511yescharacteristic
237C2×C4#1451974712yes—
238C2×C4#1451975012yes—
239C2×C4#1451977311yescharacteristic
240C2×C4C2×#1175820012yes—
241C2×C4#1451980712yes—
242C8—24no—
243C8—81no—
244C8—2444no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—81no—
252C22#1683967111yescharacteristic
253C22#1683996712yes—
254C4—22no—
255C4—22no—
256C4—81no—
257C4—4882no—
258C4—4882no—
259C4#1683990012yes—
260C4#1684013411yescharacteristic
261C4#1684015711yescharacteristic
262C2—22no—
263C2—82no—
264C2#2144688611yescharacteristic
265C2#2144690111yescharacteristic
266C2#2144692311yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1955C2
socleC22×C61#392
prime radicalC22×D4×C61D4
hypercenter#1955D61
hypocenterC61#10036
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #21456343C2semidirect
3. #21444221C2semidirect
4. #21443650C2semidirect
68. C2×C8×C61SD16semidirect
154. C61#10036semidirect
204. C2×C8#11758200semidirect

Maximal subgroups

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

subgroupindex
#214563432
#214558272
#214442212
#214436502
C61×#19552
#1003661