Finite Group Databasebeta

← #29581008

Subgroups — #29581008

Order 15616.

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

normal subgroups only

This group has 476 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
2#21455858C212yesmaximal
3#21444221C212yesmaximal
4#21443650C211yesmaximal, characteristic
5C61×#1985C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840171—22no—
8#16840171—22no—
9#16840097—22no—
10#16840057—22no—
11#16839972—22no—
12#16839918—22no—
13C4×#11758202—24no—
14#16839815C2212yes—
15#16839800—22no—
16#16839492—24no—
17C2×C4×Q8×C61C2211yescharacteristic
18C2×C4⋊C8×C61C2211yescharacteristic
19C2×#97×C61C2211yescharacteristic
20C61×#336—22no—
21C2×#11758202—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#14519710—24no—
33#14519709—24no—
34C4⋊#92418—22no—
35#14519701—24no—
36#14519700—24no—
37C22⋊#92418—22no—
38C4×#92418D414yes—
39C22×Q8×C61D411yescharacteristic
40C22×C8×C61—21no—
41C22×C8×C61D412yes—
42C4×Q8×C61—22no—
43C4×Q8×C61—22no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C42×C61—21no—
47C2×C42×C61C2311yescharacteristic
48C4⋊C8×C61—22no—
49#97×C61—22no—
50C2×Q8×C61—22no—
51C2×Q8×C61—42no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61#4111yescharacteristic
57C2×Dic122—22no—
58C2×Dic122—22no—
59C2×C8×C61—22no—
60C2×C8×C61—22no—
61C2×C8×C61—41no—
62C2×C8×C61—42no—
63C2×C8×C61Q1614yescomplemented
64C4⋊C4×C61—22no—
65C4⋊C4×C61—42no—
66C42×C61—41no—
67C42×C61—41no—
68C42×C61C2×D412yes—
69C42×C61C2×D412yes—
70C22⋊Dic61—42no—
71#11758202—48no—
72C4⋊Dic61—22no—
73C4⋊Dic61—22no—
74C4⋊Dic61—22no—
75C4⋊Dic61—22no—
76#11758196—42no—
77#11758196—42no—
78C4×Dic61—42no—
79C2×#92418—24no—
80C23×C61#12111yescharacteristic
81Q8×C61—24no—
82Q8×C61—42no—
83C2×C4×C61—22no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—42no—
89C2×C4×C61—41no—
90C2×C4×C61#12012yes—
91C2×C4×C61#12011yescharacteristic
92C2×C4×C61#12112yes—
93C2×C4×C61#12711yescharacteristic
94C2×C4×C61C2×Q1612yes—
95C2×C4×C61#13712yes—
96C2×Dic61—42no—
97C2×Dic61—42no—
98Dic122—44no—
99Dic122—44no—
100C8×C61—24no—
101C8×C61—81no—
102#92418—44no—
103#10037—611nomaximal, Sylow
104C22×C61—21no—
105C22×C61—21no—
106C22×C61#39211yescharacteristic
107C22×C61#46212yes—
108C4×C61—22no—
109C4×C61—22no—
110C4×C61—42no—
111C4×C61—81no—
112C4×C61#45112yes—
113C4×C61#49411yescharacteristic
114C4×C61#49711yescharacteristic
115Dic61—82no—
116Dic61—82no—
117#3162—611no—
118#3104—612no—
119#1985D6111yescharacteristic
120#1481—612no—
121#1275—611no—
122C2×C61—22no—
123C2×C61#201011yescharacteristic
124C2×C61#201611yescharacteristic
125C2×C61#201711yescharacteristic
126#533—612no—
127C2×C4×Q8C2×D6111yescharacteristic
128#501—1222no—
129#501—1222no—
130#484—1222no—
131#477—1222no—
132#462—1222no—
133#451—1222no—
134C4×Q16—1224no—
135#431—612no—
136#427—1222no—
137C2×C4⋊C8C2×D6111yescharacteristic
138C2×#97C2×D6111yescharacteristic
139#336—22no—
140Q8⋊C8—1224no—
141C61#1003711yescharacteristic, complemented, Sylow
142C22×Q8D24411yescharacteristic
143C2×Q16—1224no—
144C22×C8—21no—
145C22×C8C22⋊D6112yes—
146C4⋊Q8—612no—
147C4⋊Q8—612no—
148#125—1222no—
149C22⋊Q8—1222no—
150C22⋊Q8—1222no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—1222no—
154C4×Q8—1222no—
155#117—1222no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4D24411yescharacteristic
158C2×C42—21no—
159C2×C42C22×D6111yescharacteristic
160#107—1224no—
161#107—1222no—
162#107—1222no—
163#106—1224no—
164C4⋊C8—22no—
165C4⋊C8—1222no—
166#103—1224no—
167#103—1224no—
168C22⋊C8—1222no—
169#97—22no—
170C4×C8—614no—
171C2×Q8—22no—
172C2×Q8—42no—
173C2×Q8—1222no—
174C2×Q8—1222no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4C2×D24411yescharacteristic
178C22×C4#1175822211yescharacteristic
179C22×C4C2×C22⋊D6111yescharacteristic
180Q16—2448no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8—1224no—
186C2×C8#1175820214yescomplemented
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C22⋊C4—2442no—
196C42—41no—
197C42—41no—
198C42—2442no—
199C42D4×D6112yes—
200C42D4×D6112yes—
201C23#1451975111yescharacteristic
202Q8—24no—
203Q8—42no—
204Q8—2444no—
205Q8—2444no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4#1451974511yescharacteristic
216C2×C4#1451974712yes—
217C2×C4#1451975012yes—
218C2×C4#1451977311yescharacteristic
219C2×C4C2×#1175820212yes—
220C2×C4#1451980712yes—
221C8—24no—
222C8—81no—
223C8—2444no—
224C22—21no—
225C22—21no—
226C22#1683967111yescharacteristic
227C22#1683997212yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—81no—
232C4—4882no—
233C4—4882no—
234C4#1683991712yes—
235C4#1684014111yescharacteristic
236C4#1684015711yescharacteristic
237C2—22no—
238C2#2144688611yescharacteristic
239C2#2144691811yescharacteristic
240C2#2144692311yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1985C2
socleC22×C61#392
prime radicalC23×C61#121
hypercenter#1985D61
hypocenterC61#10037
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
63. C2×C8×C61Q16semidirect
141. C61#10037semidirect
186. C2×C8#11758202semidirect

Maximal subgroups

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

subgroupindex
#214563432
#214558582
#214442212
#214436502
C61×#19852
#1003761