Finite Group Databasebeta

← #29584749

Subgroups — #29584749

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#21445947C211yesmaximal, characteristic, complemented
3#21445820C212yesmaximal
4#21443703C212yesmaximal, complemented
5C61×#1277C211yesmaximal, characteristic, complemented
6C2×C4×D244C2211yescharacteristic
7C2×C4⋊#92418C2211yescharacteristic
8C2×#14519699—22no—
9C2×#14519689—22no—
10#16839632C2212yes—
11#16839525—22no—
12#16839525—22no—
13C2×C4⋊C8×C61C2212yes—
14C2×C4×C8×C61C2211yescharacteristic
15C22×D244D411yescharacteristic
16C22×C4×D61—21no—
17C22×#92418—21no—
18C4×D244—22no—
19C4×D244—22no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61—22no—
22C2×C4⋊Dic61—22no—
23C2×C4⋊Dic61D411yescharacteristic
24C2×#11758198—21no—
25C4⋊#92418—22no—
26#14519699—44no—
27#14519689—44no—
28C22×C8×C61—22no—
29C22×C8×C61D412yes—
30C2×C42×C61C2311yescharacteristic
31C4⋊C8×C61—22no—
32C4⋊C8×C61—22no—
33C4×C8×C61—22no—
34C23×D61—21no—
35C22×C4×C61C2×D411yescharacteristic
36C22×C4×C61C2×D411yescharacteristic
37C22×C4×C61#4111yescharacteristic
38C22×Dic61—21no—
39C22×Dic61—42no—
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—
51C2×C8×C61—42no—
52C2×C8×C61—42no—
53C2×C8×C61—42no—
54C42×C61#4112yes—
55C42×C61#4112yes—
56#11758198—42no—
57C4⋊Dic61—22no—
58C4⋊Dic61—42no—
59C4⋊Dic61—42no—
60C4⋊Dic61—42no—
61C4⋊Dic61—42no—
62C4⋊Dic61—82no—
63C2×#92418—41no—
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#12312yes—
73C2×C4×C61#12311yescharacteristic
74C2×C4×C61#12411yescharacteristic
75C2×C4×C61#12612yes—
76C2×C4×C61C2×D811yescharacteristic
77C2×C4×C61#13512yes—
78C2×C4×C61#13511yescharacteristic
79C2×C4×C61AGL(1,ℤ/8)12yes—
80C2×C4×C61#13712yes—
81C2×Dic61—41no—
82C2×Dic61—42no—
83C2×Dic61—82no—
84C2×Dic61—82no—
85C2×Dic61—82no—
86D244—24no—
87D244—42no—
88C4×D61—82no—
89C4×D61—81no—
90C4×D61—81no—
91C8×C61—42no—
92C8×C61—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#48012yes—
107C4×C61#48212yes—
108C4×C61#48512yes—
109C4×C61#48811yescharacteristic
110C4×C61#49011yescharacteristic
111Dic61—81no—
112Dic61—162no—
113#1954—611no—
114#1834—611no—
115#1802—612no—
116#1296—612no—
117#1277D6111yescharacteristic, complemented
118C2×C61#168112yes—
119C2×C61#170312yes—
120C2×C61#207311yescharacteristic
121C2×C61#207511yescharacteristic
122C2×C61#207911yescharacteristic
123D61—82no—
124C2×C4×D4—611no—
125C2×C4⋊C8—611no—
126C2×C4⋊C8C2×D6112yes—
127C2×#102—1222no—
128C2×C22⋊C8—1222no—
129C2×C4×C8C2×D6111yescharacteristic
130#384—612no—
131#340—1222no—
132#340—1222no—
133C61#1062111yescharacteristic, complemented, Sylow
134C22×D4—611no—
135C23×C4—1221no—
136C22×C8—22no—
137C22×C8—1221no—
138C22×C8D24412yes—
139C4×D4—1222no—
140C4×D4—1222no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—1222no—
143C2×C4⋊C4—1222no—
144C2×C4⋊C4—1222no—
145C2×C22⋊C4—1221no—
146C2×C42C22×D6111yescharacteristic
147C4⋊C8—22no—
148C4⋊C8—22no—
149C4⋊C8—1222no—
150#102—2444no—
151C22⋊C8—2444no—
152C4×C8—22no—
153C24—1221no—
154C2×D4—612no—
155C2×D4—1222no—
156C2×D4—1221no—
157C2×D4—1222no—
158C22×C4—1221no—
159C22×C4—2442no—
160C22×C4—2441no—
161C22×C4—2441no—
162C22×C4—2442no—
163C22×C4—2442no—
164C22×C4C2×D24411yescharacteristic
165C22×C4D4×D6111yescharacteristic
166C22×C4#1175822611yescharacteristic
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—2441no—
174C2×C8—2442no—
175C4⋊C4—1222no—
176C4⋊C4—4882no—
177C4⋊C4—2442no—
178C4⋊C4—2442no—
179C4⋊C4—2442no—
180C4⋊C4—2442no—
181C22⋊C4—2442no—
182C42#1175822212yes—
183C42#1175822412yes—
184C23—1222no—
185C23—2441no—
186C23—2442no—
187C23—2441no—
188C23—2442no—
189C23#1451975211yescharacteristic
190D4—1224no—
191D4—2442no—
192C2×C4—22no—
193C2×C4—4882no—
194C2×C4—4882no—
195C2×C4—4882no—
196C2×C4—4882no—
197C2×C4—4881no—
198C2×C4—4881no—
199C2×C4—2441no—
200C2×C4—2442no—
201C2×C4#1451975912yes—
202C2×C4#1451976111yescharacteristic
203C2×C4#1451976511yescharacteristic
204C2×C4#1451977212yes—
205C2×C4D8×D6111yescharacteristic
206C2×C4#1451979912yes—
207C2×C4#1451980011yescharacteristic
208C2×C4#1451980512yes—
209C2×C4#1451980612yes—
210C8—42no—
211C8—82no—
212C8—4881no—
213C22—4882no—
214C22—4881no—
215C22—4881no—
216C22—2442no—
217C22—2444no—
218C22#1683968911yescharacteristic
219C22#1683997812yes—
220C22#1683999911yescharacteristic
221C22#1684002111yescharacteristic
222C22#1684002612yes—
223C4—22no—
224C4—9762no—
225C4—4881no—
226C4#1684007412yes—
227C4#1684008712yes—
228C4#1684010212yes—
229C4#1684011711yescharacteristic
230C4#1684012711yescharacteristic
231C2—4882no—
232C2#2144525712yes—
233C2#2144539512yes—
234C2#2144723411yescharacteristic
235C2#2144724411yescharacteristic
236C2#2144726611yescharacteristic
subgroupG/H
centerC23#14519752
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenter#1277D61
hypocenterC61#10621
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #21445947C2semidirect
4. #21443703C2semidirect
5. C61×#1277C2semidirect
117. #1277D61semidirect
133. C61#10621semidirect

Maximal subgroups

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

subgroupindex
#214466132
#214459472
#214458202
#214437032
C61×#12772
#1062161