Finite Group Databasebeta

← #29584990

Subgroups — #29584990

Order 15616.

372 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 101 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#21446617C211yesmaximal, characteristic
2#21445994C211yesmaximal, characteristic, complemented
3#21444594C212yesmaximal, complemented
4#21444245C212yesmaximal
5C61×#1275C211yesmaximal, characteristic, complemented
6C2×C4×D244C2211yescharacteristic
7C2×#14519713—22no—
8#16839786C2212yes—
9C2×C4⋊#92418C2211yescharacteristic
10C2×#14519689—22no—
11#16839515—24no—
12#16839491—24no—
13C61×#431C2212yes—
14C2×#97×C61C2211yescharacteristic
15C22×D244Q811yescharacteristic
16C22×C4×D61—21no—
17C2×#11758194—22no—
18C22×#92418—21no—
19C4×D244—22no—
20C4×D244—22no—
21C2×C4⋊Dic61Q811yescharacteristic
22C2×#11758198—21no—
23#14519713—44no—
24C4⋊#92418—22no—
25C4⋊#92418—22no—
26C4⋊#92418—22no—
27#14519689—44no—
28C22×C8×C61D412yes—
29C2×C42×C61C2311yescharacteristic
30C4⋊C8×C61—22no—
31C22⋊C8×C61—22no—
32#97×C61—22no—
33C4×C8×C61D414yes—
34C23×D61—21no—
35C22×C4×C61C2×D411yescharacteristic
36C22×C4×C61C2×Q811yescharacteristic
37C22×C4×C61#4111yescharacteristic
38C22×Dic61—21no—
39C2×D244—22no—
40C2×D244—42no—
41C2×C4×D61—41no—
42C2×C4×D61—41no—
43C2×C4×D61—42no—
44C2×C4×D61—42no—
45C2×C8×C61—22no—
46C2×C8×C61—22no—
47C2×C8×C61—24no—
48C2×C8×C61D814yes—
49C42×C61C2×D412yes—
50C42×C61#4112yes—
51#11758198—42no—
52C4⋊Dic61—22no—
53#11758194—44no—
54C2×#92418—41no—
55C2×#92418—42no—
56C2×#92418—42no—
57C23×C61C22⋊Q811yescharacteristic
58C22×D61—22no—
59C22×D61—41no—
60C22×D61—42no—
61C22×D61—41no—
62C22×D61—42no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61C22⋊Q812yes—
66C2×C4×C61#12312yes—
67C2×C4×C61#12311yescharacteristic
68C2×C4×C61#12711yescharacteristic
69C2×C4×C61C2×D812yes—
70C2×C4×C61#13712yes—
71C2×Dic61—41no—
72C2×Dic61—42no—
73D244—24no—
74D244—42no—
75C4×D61—82no—
76C4×D61—81no—
77C4×D61—81no—
78C8×C61—24no—
79C8×C61—44no—
80#92418—81no—
81#92418—82no—
82#10660—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—21no—
85C22×C61#39911yescharacteristic
86C22×C61#47412yes—
87C2×D61—44no—
88C2×D61—42no—
89C2×D61—82no—
90C2×D61—81no—
91C2×D61—81no—
92C4×C61—22no—
93C4×C61—22no—
94C4×C61#48012yes—
95C4×C61#49311yescharacteristic
96C4×C61#49711yescharacteristic
97Dic61—81no—
98#1955—611no—
99#1849—611no—
100#1571—612no—
101#1486—612no—
102#1275D6111yescharacteristic, complemented
103C2×C61—22no—
104C2×C61#209111yescharacteristic
105C2×C61#209311yescharacteristic
106C2×C61#209811yescharacteristic
107D61—82no—
108C2×C4×D4—611no—
109#431C2×D6112yes—
110C2×#108—1222no—
111#423—612no—
112C2×C4⋊C8—611no—
113C2×C22⋊C8—1222no—
114C2×#97C2×D6111yescharacteristic
115#335—1224no—
116D4⋊C8—1224no—
117C61#1066011yescharacteristic, complemented, Sylow
118C22×D4—611no—
119C23×C4—1221no—
120C2×M16—1222no—
121C22×C8—1221no—
122C22×C8D24412yes—
123C4×D4—1222no—
124C4×D4—1222no—
125C2×C4⋊C4—611no—
126C2×C22⋊C4—1221no—
127C2×C42C22×D6111yescharacteristic
128#108—2444no—
129C4⋊C8—22no—
130C4⋊C8—1222no—
131C4⋊C8—1222no—
132C4⋊C8—1222no—
133C22⋊C8—22no—
134C22⋊C8—2444no—
135#97—22no—
136C4×C8D24414yes—
137C24—1221no—
138C2×D4—1222no—
139C2×D4—2442no—
140C22×C4—1221no—
141C22×C4—2442no—
142C22×C4—2441no—
143C22×C4—2441no—
144C22×C4—2442no—
145C22×C4C2×D24411yescharacteristic
146C22×C4#1175822411yescharacteristic
147C22×C4Q8×D6111yescharacteristic
148M16—2444no—
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—24no—
152C2×C8—2441no—
153C2×C8—2442no—
154C2×C8—2442no—
155C2×C8D48814yes—
156C4⋊C4—1222no—
157C22⋊C4—2442no—
158C42C2×D24412yes—
159C42#1175822412yes—
160C23—1222no—
161C23—2441no—
162C23—2442no—
163C23—2441no—
164C23—2442no—
165C23#1451975711yescharacteristic
166D4—1224no—
167D4—2442no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—4882no—
171C2×C4—4881no—
172C2×C4—4881no—
173C2×C4—2441no—
174C2×C4—2442no—
175C2×C4#1451975712yes—
176C2×C4#1451976112yes—
177C2×C4#1451976111yescharacteristic
178C2×C4#1451977411yescharacteristic
179C2×C4C2×D48812yes—
180C2×C4#1451981012yes—
181C8—24no—
182C8—44no—
183C8—4881no—
184C8—4882no—
185C22—21no—
186C22—21no—
187C22—4882no—
188C22—4881no—
189C22—4881no—
190C22—2444no—
191C22—2442no—
192C22#1683969911yescharacteristic
193C22#1684004312yes—
194C4—22no—
195C4—22no—
196C4—4881no—
197C4#1684007612yes—
198C4#1684013911yescharacteristic
199C4#1684015611yescharacteristic
200C2—22no—
201C2—4882no—
202C2#2144733611yescharacteristic
203C2#2144734611yescharacteristic
204C2#2144737311yescharacteristic
subgroupG/H
centerC2×C4#14519774
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1275C2
socleC22×C61#399
prime radicalC22×D244Q8
hypercenter#1275D61
hypocenterC61#10660
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
2. #21445994C2semidirect
3. #21444594C2semidirect
5. C61×#1275C2semidirect
102. #1275D61semidirect
117. C61#10660semidirect

Maximal subgroups

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

subgroupindex
#214466172
#214459942
#214445942
#214442452
C61×#12752
#1066061