Finite Group Databasebeta

← #29572580

Subgroups — #29572580

Order 15616.

656 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 115 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#21460314C211yesmaximal, characteristic
2#21446796C212yesmaximal
3#21444557C211yesmaximal, characteristic
4#21444556C212yesmaximal
5C61×#1994C211yesmaximal, characteristic
6C61⋊#564C414yescomplemented
7#16840491—22no—
8#16840490—22no—
9#16840487—22no—
10#16840374—22no—
11#16840372—24no—
12#16840319C2212yes—
13#16839786C2212yes—
14#16839522—24no—
15#16839509—22no—
16#16839508—22no—
17#16839507—22no—
18C61×#533C2211yescharacteristic
19C61×#423C2211yescharacteristic
20C43×C61C2211yescharacteristic
21C61×#339—22no—
22C2×#11758194—22no—
23#14519777—22no—
24#14519777D412yes—
25#14519777D412yes—
26#14519775—24no—
27#14519770—28no—
28#14519769—22no—
29#14519769C2×C414yes—
30#14519768—24no—
31#14519768—28no—
32#14519767—28no—
33#14519767—28no—
34#14519756—22no—
35#14519756—22no—
36Q8×Dic61—24no—
37C4×Dic122—24no—
38C4×Dic122—22no—
39C4×Dic122—22no—
40#14519742—24no—
41#14519736D414yes—
42C4⋊#92418—22no—
43C4⋊#92418—22no—
44C2×M16×C61—21no—
45C4⋊Q8×C61D412yes—
46#125×C61C2×C412yes—
47C22⋊Q8×C61—22no—
48C4×Q8×C61—22no—
49#117×C61D412yes—
50C2×C42×C61—21no—
51C2×C42×C61—22no—
52C2×C42×C61C2311yescharacteristic
53C4⋊C8×C61—22no—
54C2×Q8×C61—22no—
55C22×C4×C61—41no—
56C22×C4×C61C2×D412yes—
57C22×C4×C61C2×D411yescharacteristic
58C2×Dic122—22no—
59C2×Dic122—22no—
60M16×C61—42no—
61C2×C8×C61—41no—
62C4⋊C4×C61—24no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61C22⋊C414yes—
65C22⋊C4×C61—22no—
66C42×C61—22no—
67C42×C61—22no—
68C42×C61—24no—
69C42×C61—42no—
70C42×C61—41no—
71C42×C61C22×C411yescharacteristic
72C42×C61C2×D411yescharacteristic
73C42×C61C2×D412yes—
74C22⋊Dic61—24no—
75C4⋊Dic61—28no—
76C4⋊Dic61—22no—
77C4⋊Dic61—22no—
78C4⋊Dic61C22⋊C414yes—
79C4⋊Dic61C22⋊C414yes—
80#11758196—28no—
81#11758196—28no—
82#11758196—24no—
83#11758196—24no—
84C4×Dic61—28no—
85C4×Dic61—24no—
86#11758194—44no—
87C2×#92418—42no—
88C23×C61#12011yescharacteristic
89Q8×C61—42no—
90Q8×C61—42no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—24no—
96C2×C4×C61—42no—
97C2×C4×C61—44no—
98C2×C4×C61C2×C22⋊C412yes—
99C2×C4×C61C2×C22⋊C411yescharacteristic
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61#12012yes—
102C2×Dic61—24no—
103C2×Dic61—24no—
104Dic122—42no—
105Dic122—42no—
106Dic122—42no—
107Dic122—42no—
108C8×C61—81no—
109#92418—82no—
110#8533—611nomaximal, Sylow
111C22×C61—21no—
112C22×C61—22no—
113C22×C61#37911yescharacteristic
114C4×C61—21no—
115C4×C61—22no—
116C4×C61—44no—
117C4×C61—44no—
118C4×C61#45412yes—
119C4×C61#45411yescharacteristic
120C4×C61#45611yescharacteristic
121C4×C61#45612yes—
122Dic61—44no—
123Dic61—44no—
124#3556—611no—
125#1994—612no—
126#1994D6111yescharacteristic
127#1561—612no—
128#1561—611no—
129C2×C61—41no—
130C2×C61#179311yescharacteristic
131C2×C61#179312yes—
132#564—614no—
133#557—1222no—
134#557—1222no—
135#557—1222no—
136#541—1224no—
137#541—1222no—
138#533—612no—
139#533C2×D6111yescharacteristic
140#423—612no—
141#423C2×D6111yescharacteristic
142C43C2×D6111yescharacteristic
143#339—22no—
144#339—1224no—
145#332—1222no—
146#332—1222no—
147#332—1222no—
148C61#853311yescharacteristic, complemented, Sylow
149C2×M16—21no—
150C2×M16—1222no—
151C4⋊Q8—612no—
152C4⋊Q8—612no—
153C4⋊Q8—1222no—
154C4⋊Q8—1224no—
155C4⋊Q8D24412yes—
156#126—1228no—
157#125—614no—
158#125—1222no—
159#125—1228no—
160#125—1228no—
161#125—1224no—
162#125—1228no—
163#125C4×D6112yes—
164C22⋊Q8—22no—
165C22⋊Q8—1222no—
166C22⋊Q8—1222no—
167C4×Q8—22no—
168C4×Q8—1224no—
169C4×Q8—1224no—
170C4×Q8—1224no—
171C4×Q8—1222no—
172C4×Q8—1222no—
173#117—614no—
174#117C22⋊D6112yes—
175C2×C42—22no—
176C2×C42—21no—
177C2×C42C22×D6111yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—1222no—
180C4⋊C8—1222no—
181C2×Q8—22no—
182C2×Q8—1222no—
183C2×Q8—1222no—
184C22×C4—41no—
185C22×C4D4×D6112yes—
186C22×C4C2×C22⋊D6111yescharacteristic
187M16—42no—
188M16—2444no—
189C2×C8—41no—
190C2×C8—2442no—
191C4⋊C4—24no—
192C4⋊C4—22no—
193C4⋊C4—614no—
194C4⋊C4—614no—
195C4⋊C4—1228no—
196C4⋊C4—1228no—
197C4⋊C4—1228no—
198C4⋊C4—1224no—
199C4⋊C4—1224no—
200C4⋊C4—1222no—
201C4⋊C4—1222no—
202C4⋊C4#1175819814yes—
203C22⋊C4—22no—
204C22⋊C4—1224no—
205C42—22no—
206C42—22no—
207C42—24no—
208C42—42no—
209C42—41no—
210C42—1228no—
211C42—1224no—
212C42C2×C4×D6111yescharacteristic
213C42C2×D24411yescharacteristic
214C42D4×D6112yes—
215C23#1451974511yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—2442no—
219Q8—2442no—
220Q8—2442no—
221Q8—2442no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—1224no—
230C2×C4—1224no—
231C2×C4C22⋊C4×D6112yes—
232C2×C4C2×#1175819811yescharacteristic
233C2×C4#1451974511yescharacteristic
234C2×C4#1451974712yes—
235C8—81no—
236C8—4882no—
237C22—21no—
238C22—22no—
239C22#1683961711yescharacteristic
240C4—21no—
241C4—22no—
242C4—44no—
243C4—44no—
244C4—2444no—
245C4—2444no—
246C4#1683993411yescharacteristic
247C4#1683993612yes—
248C4#1683994411yescharacteristic
249C4#1683994612yes—
250C2—41no—
251C2#2144577711yescharacteristic
252C2#2144577912yes—
subgroupG/H
centerC22#16839617
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1994C2
socleC22×C61#379
prime radicalC23×C61#120
cosocleC2×C42×C61C23
hypercenter#1994D61
hypocenterC61#8533
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
6. C61⋊#564C4semidirect
148. C61#8533semidirect

Maximal subgroups

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

subgroupindex
#214603142
#214467962
#214445572
#214445562
C61×#19942
#853361