Finite Group Databasebeta

← #29584748

Subgroups — #29584748

Order 15616.

402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 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#21446613C211yesmaximal, characteristic
2#21445816C212yesmaximal
3#21443702C212yesmaximal, complemented
4#21443654C211yesmaximal, characteristic, complemented
5C61×#1834C211yesmaximal, characteristic, complemented
6C2×C4×D244C2211yescharacteristic
7C2×C4⋊#92418C2212yes—
8C2×C4⋊#92418C2211yescharacteristic
9C2×#14519697—22no—
10C2×#14519689—22no—
11#16839524—22no—
12C2×C4×C8×C61C2211yescharacteristic
13C61×#384C2212yes—
14C61×#340—22no—
15C22×D244D411yescharacteristic
16C22×C4×D61—21no—
17C22×#92418—21no—
18C22×#92418—22no—
19C4×D244—22no—
20C4×D244—22no—
21C2×C4⋊Dic61D411yescharacteristic
22C2×#11758198—21no—
23C4⋊#92418—22no—
24C4⋊#92418—22no—
25C4⋊#92418—22no—
26#14519697—44no—
27#14519689—44no—
28C22×C8×C61D412yes—
29C2×C4⋊C4×C61—22no—
30C2×C4⋊C4×C61—22no—
31C2×C4⋊C4×C61—22no—
32C2×C42×C61C2311yescharacteristic
33C4×C8×C61—22no—
34C23×D61—21no—
35C22×C4×C61—42no—
36C22×C4×C61C2×D411yescharacteristic
37C22×C4×C61C2×D411yescharacteristic
38C22×C4×C61#4111yescharacteristic
39C22×Dic61—21no—
40C2×D244—22no—
41C2×D244—22no—
42C2×D244—21no—
43C2×D244D812yes—
44C2×C4×D61—41no—
45C2×C4×D61—41no—
46C2×C4×D61—42no—
47C2×C4×D61—42no—
48C2×C8×C61—22no—
49C2×C8×C61—22no—
50C2×C8×C61—22no—
51C4⋊C4×C61—42no—
52C4⋊C4×C61—42no—
53C4⋊C4×C61—42no—
54C4⋊C4×C61—42no—
55C4⋊C4×C61—82no—
56C42×C61#4112yes—
57C42×C61#4112yes—
58#11758198—42no—
59C4⋊Dic61—22no—
60C2×#92418—42no—
61C2×#92418—41no—
62C2×#92418—42no—
63C2×#92418—42no—
64C2×#92418—42no—
65C23×C61#12111yescharacteristic
66C22×D61—22no—
67C22×D61—41no—
68C22×D61—42no—
69C22×D61—41no—
70C22×D61—42no—
71C2×C4×C61—22no—
72C2×C4×C61—82no—
73C2×C4×C61—82no—
74C2×C4×C61—82no—
75C2×C4×C61#12312yes—
76C2×C4×C61#12311yescharacteristic
77C2×C4×C61#12411yescharacteristic
78C2×C4×C61#12612yes—
79C2×C4×C61C2×D811yescharacteristic
80C2×C4×C61#13512yes—
81C2×C4×C61#13511yescharacteristic
82C2×C4×C61AGL(1,ℤ/8)12yes—
83C2×C4×C61#13712yes—
84C2×Dic61—41no—
85C2×Dic61—42no—
86D244—24no—
87D244—42no—
88C4×D61—82no—
89C4×D61—81no—
90C4×D61—81no—
91C8×C61—42no—
92#92418—82no—
93#92418—81no—
94#10621—611nomaximal, Sylow
95C22×C61#39711yescharacteristic
96C22×C61#46312yes—
97C22×C61#46611yescharacteristic
98C22×C61#47011yescharacteristic
99C22×C61#47112yes—
100C2×D61—42no—
101C2×D61—44no—
102C2×D61—81no—
103C2×D61—81no—
104C2×D61—82no—
105C4×C61—22no—
106C4×C61—162no—
107C4×C61#48012yes—
108C4×C61#48212yes—
109C4×C61#48512yes—
110C4×C61#48811yescharacteristic
111C4×C61#49011yescharacteristic
112Dic61—81no—
113#1954—611no—
114#1834D6111yescharacteristic, complemented
115#1802—612no—
116#1296—612no—
117#1277—611no—
118C2×C61#168112yes—
119C2×C61#170312yes—
120C2×C61#207311yescharacteristic
121C2×C61#207511yescharacteristic
122C2×C61#207911yescharacteristic
123D61—82no—
124C2×C4×D4—611no—
125C2×C4⋊C8—612no—
126C2×C4⋊C8—611no—
127C2×#102—1222no—
128C2×C22⋊C8—1222no—
129C2×C4×C8C2×D6111yescharacteristic
130#384C2×D6112yes—
131#340—22no—
132#340—1222no—
133C61#1062111yescharacteristic, complemented, Sylow
134C22×D4—611no—
135C23×C4—1221no—
136C22×C8—1222no—
137C22×C8—1221no—
138C22×C8C22⋊D6112yes—
139C4×D4—1222no—
140C4×D4—1222no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—611no—
145C2×C22⋊C4—1221no—
146C2×C42C22×D6111yescharacteristic
147C4⋊C8—1222no—
148C4⋊C8—1222no—
149C4⋊C8—1222no—
150#102—2444no—
151C22⋊C8—2444no—
152C4×C8—22no—
153C24—1221no—
154C2×D4—612no—
155C2×D4—1222no—
156C2×D4—1222no—
157C2×D4—1221no—
158C22×C4—42no—
159C22×C4—1221no—
160C22×C4—2441no—
161C22×C4—2441no—
162C22×C4—2442no—
163C22×C4—2442no—
164C22×C4D4×D6111yescharacteristic
165C22×C4#1175822411yescharacteristic
166C22×C4C2×C22⋊D6111yescharacteristic
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—2442no—
171C2×C8—2442no—
172C2×C8—2441no—
173C2×C8—2442no—
174C2×C8—2442no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—82no—
180C4⋊C4—1222no—
181C22⋊C4—2442no—
182C42#1175822212yes—
183C42#1175822612yes—
184C23—1222no—
185C23—2441no—
186C23—2442no—
187C23—2441no—
188C23—2442no—
189C23#1451974811yescharacteristic
190D4—1224no—
191D4—2442no—
192C2×C4—22no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—4882no—
197C2×C4—4881no—
198C2×C4—4881no—
199C2×C4—2441no—
200C2×C4—2442no—
201C2×C4#1451976011yescharacteristic
202C2×C4#1451976212yes—
203C2×C4#1451976611yescharacteristic
204C2×C4#1451977212yes—
205C2×C4D8×D6111yescharacteristic
206C2×C4#1451979611yescharacteristic
207C2×C4#1451979712yes—
208C2×C4#1451980212yes—
209C2×C4#1451980912yes—
210C8—42no—
211C8—4882no—
212C8—4881no—
213C22—4882no—
214C22—4881no—
215C22—4881no—
216C22—2442no—
217C22—2444no—
218C22#1683968811yescharacteristic
219C22#1683997412yes—
220C22#1683999511yescharacteristic
221C22#1684001711yescharacteristic
222C22#1684002212yes—
223C4—22no—
224C4—162no—
225C4—4881no—
226C4#1684007712yes—
227C4#1684008612yes—
228C4#1684010512yes—
229C4#1684011911yescharacteristic
230C4#1684012811yescharacteristic
231C2—4882no—
232C2#2144525312yes—
233C2#2144539112yes—
234C2#2144723311yescharacteristic
235C2#2144724311yescharacteristic
236C2#2144726511yescharacteristic
subgroupG/H
centerC23#14519748
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1834C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenter#1834D61
hypocenterC61#10621
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
3. #21443702C2semidirect
4. #21443654C2semidirect
5. C61×#1834C2semidirect
114. #1834D61semidirect
133. C61#10621semidirect

Maximal subgroups

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

subgroupindex
#214466132
#214458162
#214437022
#214436542
C61×#18342
#1062161