Finite Group Databasebeta

← #29584141

Subgroups — #29584141

Order 15616.

402 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 99 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#21457164C211yesmaximal, characteristic
2#21446796C212yesmaximal
3#21444507C212yesmaximal
4#21443694C211yesmaximal, characteristic
5C61×#1842C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840058—22no—
8#16840003—22no—
9#16839973—22no—
10#16839786C2212yes—
11#16839522—22no—
12#16839522—22no—
13#16839510—22no—
14#16839509—22no—
15C2×C4⋊C8×C61—22no—
16C2×C4⋊C8×C61C2211yescharacteristic
17C2×C4⋊C8×C61C2211yescharacteristic
18C43×C61C2211yescharacteristic
19C2×Dic244—22no—
20C2×#11758194—22no—
21#14519777D412yes—
22#14519777D412yes—
23#14519769—22no—
24#14519756—22no—
25#14519756—22no—
26C4×Dic122—22no—
27C4×Dic122—22no—
28#14519736—22no—
29#14519711—22no—
30C4⋊#92418—22no—
31C4⋊#92418—22no—
32#14519702—24no—
33C22×C8×C61—21no—
34C22×C8×C61D412yes—
35C2×C42×C61—21no—
36C2×C42×C61—21no—
37C2×C42×C61D411yescharacteristic
38C2×C42×C61D411yescharacteristic
39C2×C42×C61C2311yescharacteristic
40C4⋊C8×C61—22no—
41C4⋊C8×C61—22no—
42C4⋊C8×C61—44no—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C2×D411yescharacteristic
46C22×C4×C61C2×D411yescharacteristic
47C22×C4×C61#4111yescharacteristic
48C2×Dic122—22no—
49C2×Dic122—22no—
50C2×C8×C61—22no—
51C2×C8×C61—42no—
52C2×C8×C61—42no—
53C2×C8×C61—41no—
54C42×C61—22no—
55C42×C61—22no—
56C42×C61—21no—
57C42×C61—22no—
58C42×C61—42no—
59C42×C61Q1612yescomplemented
60C42×C61C2×D412yes—
61C42×C61#4112yes—
62C22⋊Dic61—42no—
63C4⋊Dic61—22no—
64C4⋊Dic61—22no—
65C4⋊Dic61—22no—
66C4⋊Dic61—22no—
67#11758196—42no—
68#11758196—42no—
69C4×Dic61—42no—
70#11758194—42no—
71#11758194—42no—
72C2×#92418—42no—
73Dic244—82no—
74C23×C61#12111yescharacteristic
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61#12011yescharacteristic
85C2×C4×C61#12112yes—
86C2×C4×C61#12312yes—
87C2×C4×C61#12411yescharacteristic
88C2×C4×C61C2×Q1611yescharacteristic
89C2×C4×C61#13511yescharacteristic
90C2×C4×C61#13712yes—
91C2×Dic61—42no—
92C2×Dic61—42no—
93Dic122—42no—
94Dic122—42no—
95Dic122—82no—
96C8×C61—42no—
97C8×C61—81no—
98#92418—82no—
99#10522—611nomaximal, Sylow
100C22×C61—21no—
101C22×C61—21no—
102C22×C61#39411yescharacteristic
103C22×C61#46711yescharacteristic
104C22×C61#47011yescharacteristic
105C4×C61—24no—
106C4×C61—22no—
107C4×C61—21no—
108C4×C61—42no—
109C4×C61#45311yescharacteristic
110C4×C61#45611yescharacteristic
111C4×C61#46212yes—
112C4×C61#46412yes—
113Dic61—82no—
114Dic61—82no—
115#3249—611no—
116#1994—612no—
117#1842D6111yescharacteristic
118#1550—612no—
119#1292—611no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61#203911yescharacteristic
123C2×C61#205011yescharacteristic
124C2×C61#205611yescharacteristic
125#533—612no—
126#477—1222no—
127#467—1222no—
128#462—1222no—
129#423—612no—
130C2×C4⋊C8—22no—
131C2×C4⋊C8C2×D6111yescharacteristic
132C2×C4⋊C8C2×D6111yescharacteristic
133C43C2×D6111yescharacteristic
134#339—1222no—
135#339—1222no—
136#333—1222no—
137#332—1222no—
138C61#1052211yescharacteristic, complemented, Sylow
139C2×Q16—1222no—
140C2×M16—1222no—
141C22×C8—21no—
142C22×C8C22⋊D6112yes—
143C4⋊Q8—612no—
144C4⋊Q8—612no—
145#125—1222no—
146C22⋊Q8—1222no—
147C22⋊Q8—1222no—
148C4×Q8—1222no—
149C4×Q8—1222no—
150#117—1222no—
151C2×C42—21no—
152C2×C42—21no—
153C2×C42D24411yescharacteristic
154C2×C42D24411yescharacteristic
155C2×C42C22×D6111yescharacteristic
156#107—1222no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8—44no—
160C4⋊C8—1222no—
161C4⋊C8—1222no—
162#103—1224no—
163C2×Q8—1222no—
164C2×Q8—1222no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C2×D24411yescharacteristic
168C22×C4#1175822211yescharacteristic
169C22×C4C2×C22⋊D6111yescharacteristic
170Q16—4882no—
171M16—2442no—
172M16—2442no—
173C2×C8—22no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—41no—
177C2×C8—2442no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—1222no—
182C4⋊C4—2442no—
183C4⋊C4—2442no—
184C22⋊C4—2442no—
185C42—22no—
186C42—22no—
187C42—21no—
188C42—22no—
189C42—42no—
190C42—2442no—
191C42Dic24412yescomplemented
192C42D4×D6112yes—
193C42#1175822612yes—
194C23#1451975111yescharacteristic
195Q8—4882no—
196Q8—2442no—
197Q8—2442no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—2442no—
208C2×C4—2442no—
209C2×C4#1451974511yescharacteristic
210C2×C4#1451975212yes—
211C2×C4#1451976212yes—
212C2×C4#1451976611yescharacteristic
213C2×C4C2×Dic24411yescharacteristic
214C2×C4#1451979911yescharacteristic
215C2×C4#1451981012yes—
216C8—42no—
217C8—81no—
218C8—4882no—
219C22—21no—
220C22—21no—
221C22#1683967911yescharacteristic
222C22#1684000311yescharacteristic
223C22#1684002011yescharacteristic
224C4—24no—
225C4—21no—
226C4—22no—
227C4—42no—
228C4—4882no—
229C4—4882no—
230C4#1683992911yescharacteristic
231C4#1683994411yescharacteristic
232C4#1683997312yes—
233C4#1683998512yes—
234C2—21no—
235C2—21no—
236C2#2144704311yescharacteristic
237C2#2144710611yescharacteristic
238C2#2144714211yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1842C2
socleC22×C61#394
prime radicalC23×C61#121
hypercenter#1842D61
hypocenterC61#10522
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1842

Complements

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

NH ≅ G/Ntype
59. C42×C61Q16semidirect
138. C61#10522semidirect
191. C42Dic244semidirect

Maximal subgroups

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

subgroupindex
#214571642
#214467962
#214445072
#214436942
C61×#18422
#1052261