Finite Group Databasebeta

← #29584998

Subgroups — #29584998

Order 15616.

320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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#21446758C211yesmaximal, characteristic
2#21445993C211yesmaximal, characteristic
3#21444593C211yesmaximal, characteristic
4#21444249C211yesmaximal, characteristic
5#21444247C211yesmaximal, characteristic
6#21443649C211yesmaximal, characteristic
7C61×#1571C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16839815C2211yescharacteristic
10C2×#14519712—22no—
11#16839786C2211yescharacteristic
12C2×#14519688C2211yescharacteristic
13#16839516—22no—
14#16839514—22no—
15#16839494—22no—
16#16839492—22no—
17C61×#431C2211yescharacteristic
18C61×#423C2211yescharacteristic
19C2×C4⋊C8×C61C2211yescharacteristic
20C61×#335—22no—
21C22×Dic122Q811yescharacteristic
22C2×#11758194—21no—
23C22×#92418D412yes—
24C4×Dic122—21no—
25C4×Dic122—21no—
26C4×Dic122—21no—
27C4×Dic122—21no—
28C2×C4⋊Dic61Q811yescharacteristic
29C2×#11758196—21no—
30C2×C4×Dic61—21no—
31#14519712—44no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34C4⋊#92418—21no—
35C22⋊#92418—21no—
36#14519688—21no—
37#14519688—21no—
38C4×#92418D412yes—
39C2×M16×C61—21no—
40C22×C8×C61—21no—
41C2×C42×C61C2311yescharacteristic
42C4⋊C8×C61—21no—
43C4⋊C8×C61—21no—
44C4⋊C8×C61—21no—
45C4⋊C8×C61—21no—
46C4⋊C8×C61—21no—
47C22⋊C8×C61—21no—
48C4×C8×C61D412yes—
49C22×C4×C61C2×D411yescharacteristic
50C22×C4×C61C2×Q811yescharacteristic
51C22×C4×C61#4111yescharacteristic
52C22×Dic61—21no—
53C22×Dic61—21no—
54C2×Dic122—21no—
55C2×Dic122—21no—
56C2×Dic122—42no—
57M16×C61—42no—
58C2×C8×C61—22no—
59C2×C8×C61—41no—
60C2×C8×C61—41no—
61C2×C8×C61—42no—
62C42×C61C2×D411yescharacteristic
63C42×C61C2×D411yescharacteristic
64C42×C61#4111yescharacteristic
65C42×C61#4111yescharacteristic
66C4⋊Dic61—21no—
67C4⋊Dic61—21no—
68#11758196—41no—
69#11758196—41no—
70C4×Dic61—41no—
71C4×Dic61—41no—
72#11758194—42no—
73C2×#92418—22no—
74C2×#92418—22no—
75C2×#92418—22no—
76C2×#92418—41no—
77C2×#92418Q1614yes—
78C23×C61C22⋊Q811yescharacteristic
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61C22⋊Q811yescharacteristic
82C2×C4×C61C22⋊Q811yescharacteristic
83C2×C4×C61#12311yescharacteristic
84C2×C4×C61#12311yescharacteristic
85C2×C4×C61#12311yescharacteristic
86C2×C4×C61#12711yescharacteristic
87C2×C4×C61C2×Q1612yes—
88C2×C4×C61AGL(1,ℤ/8)12yes—
89C2×Dic61—22no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92C2×Dic61—42no—
93C2×Dic61—41no—
94Dic122—22no—
95Dic122—22no—
96Dic122—41no—
97Dic122—41no—
98C8×C61—42no—
99C8×C61—81no—
100C8×C61—81no—
101#92418—24no—
102#92418—42no—
103#92418—81no—
104#10662—611nomaximal, Sylow
105C22×C61—21no—
106C22×C61—21no—
107C22×C61#39911yescharacteristic
108C22×C61#47712yes—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—21no—
112C4×C61—21no—
113C4×C61#48412yes—
114C4×C61#49411yescharacteristic
115C4×C61#49611yescharacteristic
116Dic61—42no—
117Dic61—81no—
118#1985—611no—
119#1849—611no—
120#1571—611no—
121#1571D6111yescharacteristic
122#1487—611no—
123#1487—611no—
124#1275—611no—
125C2×C61—22no—
126C2×C61#209111yescharacteristic
127C2×C61#209511yescharacteristic
128C2×C61#209811yescharacteristic
129C2×C4×Q8—611no—
130#431—611no—
131#431C2×D6111yescharacteristic
132C2×#108—1222no—
133#423—611no—
134#423C2×D6111yescharacteristic
135C2×C4⋊C8C2×D6111yescharacteristic
136C2×#97—611no—
137#336—1222no—
138#335—22no—
139#335—1222no—
140Q8⋊C8—1222no—
141Q8⋊C8—1222no—
142C61#1066211yescharacteristic, complemented, Sylow
143C22×Q8—611no—
144C2×M16—21no—
145C2×M16—1221no—
146C22×C8—21no—
147C22×C8—612no—
148C4×Q8—1221no—
149C4×Q8—1221no—
150C4×Q8—1221no—
151C4×Q8—1221no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—1221no—
154C2×C42—1221no—
155C2×C42C22×D6111yescharacteristic
156#108—2444no—
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8—21no—
160C4⋊C8—21no—
161C4⋊C8—21no—
162C4⋊C8—1221no—
163C4⋊C8—1221no—
164C4⋊C8—1221no—
165C22⋊C8—21no—
166C22⋊C8—1221no—
167#97—1221no—
168#97—1221no—
169C4×C8—612no—
170C4×C8C22⋊D6112yes—
171C2×Q8—1221no—
172C2×Q8—1221no—
173C2×Q8—2442no—
174C22×C4—1221no—
175C22×C4—1221no—
176C22×C4#1175822211yescharacteristic
177C22×C4D4×D6111yescharacteristic
178C22×C4Q8×D6111yescharacteristic
179M16—42no—
180M16—2442no—
181C2×C8—22no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8—614no—
186C2×C8—1222no—
187C2×C8—1222no—
188C2×C8—1222no—
189C2×C8—2441no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4—2441no—
193C4⋊C4—2441no—
194C42—2441no—
195C42—2441no—
196C42#1175822211yescharacteristic
197C42D4×D6111yescharacteristic
198C42#1175822611yescharacteristic
199C42C2×C22⋊D6111yescharacteristic
200C23#1451975511yescharacteristic
201Q8—1222no—
202Q8—1222no—
203Q8—2441no—
204Q8—2441no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—1222no—
208C2×C4—2442no—
209C2×C4—2441no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4#1451975311yescharacteristic
213C2×C4#1451975511yescharacteristic
214C2×C4#1451976011yescharacteristic
215C2×C4#1451976211yescharacteristic
216C2×C4#1451976211yescharacteristic
217C2×C4#1451977311yescharacteristic
218C2×C4Q16×D6112yes—
219C2×C4#1451980112yes—
220C8—42no—
221C8—81no—
222C8—81no—
223C8—1224no—
224C8—4881no—
225C8—2442no—
226C22—21no—
227C22—21no—
228C22#1683969711yescharacteristic
229C22#1684005612yes—
230C4—21no—
231C4—21no—
232C4—21no—
233C4—21no—
234C4—4881no—
235C4—2442no—
236C4#1684009912yes—
237C4#1684014011yescharacteristic
238C4#1684015011yescharacteristic
239C2—22no—
240C2#2144733411yescharacteristic
241C2#2144735411yescharacteristic
242C2#2144737511yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1571C2
socleC22×C61#399
prime radicalC23×C61C22⋊Q8
hypercenter#1571D61
hypocenterC61#10662
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
142. C61#10662semidirect

Maximal subgroups

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

subgroupindex
#214467582
#214459932
#214445932
#214442492
#214442472
#214436492
C61×#15712
#1066261