Finite Group Databasebeta

← #29567563

Subgroups — #29567563

Order 15616.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#21447048C211yesmaximal, characteristic
2#21443700C211yesmaximal, characteristic, complemented
3C61×#1324C211yesmaximal, characteristic, complemented
4#16840343C411yescharacteristic
5C2×#14519705—21no—
6#16839761—21no—
7C2×#14519688—21no—
8#16839531C411yescharacteristic
9C61×#382C2211yescharacteristic
10C61×#324—21no—
11C2×#11758222—21no—
12C2×#11758194—21no—
13C22×#92418—41no—
14#14519757—41no—
15#14519752—41no—
16#14519751—41no—
17#14519705—41no—
18#14519705—41no—
19#14519700—41no—
20#14519697—41no—
21#14519688—22no—
22#14519688—41no—
23C2×C4⋊C4×C61C2×C411yescharacteristic
24C2×C4⋊C4×C61D411yescharacteristic
25C2×C42×C61D411yescharacteristic
26C22⋊C8×C61—41no—
27#95×C61—41no—
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61—21no—
31C22×C4×C61C22⋊C411yescharacteristic
32C2×C22⋊D61—41no—
33#11758222—41no—
34#11758222—41no—
35#11758222—41no—
36#11758222—41no—
37C2×D244—21no—
38C2×D244—41no—
39C2×C4×D61—41no—
40C2×Dic122—21no—
41C2×C8×C61—81no—
42C4⋊C4×C61—41no—
43C4⋊C4×C61—41no—
44C42×C61—21no—
45C42×C61D811yescharacteristic
46C42×C61SD1611yescharacteristic
47#11758198—42no—
48C4⋊Dic61—41no—
49#11758194—41no—
50#11758194—41no—
51C2×#92418—42no—
52C2×#92418—42no—
53C2×#92418—42no—
54C2×#92418—41no—
55C23×C61#9911yescharacteristic
56C22×D61—41no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—81no—
66C2×C4×C61—81no—
67C2×C4×C61#10211yescharacteristic
68C2×C4×C61#10411yescharacteristic
69C22⋊D61—81no—
70C22⋊D61—81no—
71C2×Dic61—41no—
72D244—41no—
73D244—41no—
74D244—161no—
75C4×D61—81no—
76C4×D61—81no—
77Dic122—41no—
78Dic122—41no—
79C8×C61—161no—
80#92418—44no—
81#92418—81no—
82#7416—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—21no—
85C22×C61#32711yescharacteristic
86C22×C61AΣL(1,𝔽16)11yescharacteristic
87C22×C61#35511yescharacteristic
88C2×D61—81no—
89C2×D61—81no—
90C2×D61—81no—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61—41no—
94C4×C61—41no—
95C4×C61—81no—
96C4×C61—81no—
97Dic61—81no—
98#2040—611no—
99#1324D6111yescharacteristic, complemented
100#1295—611no—
101C2×C61—21no—
102C2×C61—21no—
103C2×C61#134511yescharacteristic
104C2×C61#140311yescharacteristic
105C2×C61#140411yescharacteristic
106D61—161no—
107#537—611no—
108C2×#104—1221no—
109#417—1221no—
110C2×#97—1221no—
111#382C2×D6111yescharacteristic
112#343—611no—
113#324—21no—
114C61#741611yescharacteristic, complemented, Sylow
115C2×#41—1221no—
116C2×M16—1221no—
117C22×C8—2441no—
118C22⋊Q8—2441no—
119#121—2441no—
120#121—2441no—
121C2×C4⋊C4C4×D6111yescharacteristic
122C2×C4⋊C4C22⋊D6111yescharacteristic
123C2×C42D24411yescharacteristic
124#104—2441no—
125#104—2441no—
126#103—2441no—
127#102—2441no—
128C22⋊C8—41no—
129#97—1222no—
130#97—2441no—
131#95—41no—
132#41—2441no—
133#41—2441no—
134#41—2441no—
135#41—2441no—
136C2×Q8—1221no—
137C2×D4—1221no—
138C2×D4—2441no—
139C2×D4—2441no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—2441no—
144C22×C4#1175819811yescharacteristic
145M16—2441no—
146M16—2441no—
147C2×C8—81no—
148C2×C8—2441no—
149C2×C8—2442no—
150C2×C8—2442no—
151C2×C8—2442no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—2441no—
155C22⋊C4—2442no—
156C42—21no—
157C42#1175819011yescharacteristic
158C42D48811yescharacteristic
159C23—2441no—
160C23#1451969111yescharacteristic
161Q8—2441no—
162Q8—2441no—
163D4—9761no—
164D4—4881no—
165D4—4881no—
166D4—2441no—
167D4—2441no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—4881no—
179C2×C4—4881no—
180C2×C4—2441no—
181C2×C4#1451969911yescharacteristic
182C2×C4#1451970311yescharacteristic
183C8—161no—
184C8—4881no—
185C8—2444no—
186C22—21no—
187C22—21no—
188C22—4881no—
189C22—4881no—
190C22—4881no—
191C22#1683949711yescharacteristic
192C22#1683954811yescharacteristic
193C22#1683955811yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—81no—
199C4—81no—
200C4—4881no—
201C2—21no—
202C2—21no—
203C2—9761no—
204C2#2144382311yescharacteristic
205C2#2144396611yescharacteristic
206C2#2144396911yescharacteristic
subgroupG/H
centerC22#16839548
commutatorC2×C4⋊C4×C61C2×C4
Frattini#382C2×D61
FittingC61×#1324C2
socleC22×C61AΣL(1,𝔽16)
prime radical#16840343C4
cosocleC61×#382C22
hypercenter#1324D61
hypocenterC61#7416
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1324

Complements

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

NH ≅ G/Ntype
2. #21443700C2semidirect
3. C61×#1324C2semidirect
99. #1324D61semidirect
114. C61#7416semidirect

Maximal subgroups

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

subgroupindex
#214470482
#214437002
C61×#13242
#741661