Finite Group Databasebeta

← #29594297

Subgroups — #29594297

Order 15616.

228 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 71 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#21448075C211yesmaximal, characteristic
2#21445189C211yesmaximal, characteristic, complemented
3#21445179C211yesmaximal, characteristic
4#21443891C211yesmaximal, characteristic, complemented
5#21443869C211yesmaximal, characteristic, complemented
6#21443866C211yesmaximal, characteristic
7C61×#2183C211yesmaximal, characteristic, complemented
8C2×#14519722—21no—
9C2×#14519722—21no—
10#16840142C2211yescharacteristic
11#16840139C2211yescharacteristic
12#16840047—21no—
13#16839962—21no—
14#16839515C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839509—21no—
17#16839505—21no—
18C8×Q8×C61C2211yescharacteristic
19C61×C4⋊C16—21no—
20C61×C4⋊C16C2211yescharacteristic
21C61×#346—21no—
22C4×C16×C61C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×#11758201—41no—
26C2×D488—21no—
27C2×D488—21no—
28#14519777—21no—
29#14519774—21no—
30#14519722—42no—
31#14519722—42no—
32#14519708—41no—
33C4⋊#92418—21no—
34C4⋊#92418—21no—
35#14519701—41no—
36#14519697—41no—
37C4×Q8×C61D411yescharacteristic
38C2×C16×C61—21no—
39C2×C16×C61D411yescharacteristic
40C2×C16×C61D411yescharacteristic
41C4⋊C8×C61—21no—
42C4⋊C8×C61D411yescharacteristic
43C4×C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61D811yescharacteristic
46C2×D244—41no—
47C2×D244—41no—
48C2×D244—41no—
49C2×Dic122—41no—
50C2×C8×C61—21no—
51C2×C8×C61C2×D411yescharacteristic
52C2×C8×C61#4111yescharacteristic
53C4⋊C4×C61—21no—
54C4⋊C4×C61D811yescharacteristic
55C42×C61—21no—
56C42×C61C2×D411yescharacteristic
57#11758201—82no—
58C4⋊Dic61—41no—
59C4⋊Dic61—41no—
60C2×#92418—41no—
61C2×#92418—41no—
62Dic244—41no—
63Dic244—41no—
64Dic244—81no—
65D488—41no—
66D488—41no—
67D488—81no—
68C16×C61—21no—
69C16×C61—41no—
70C16×C61SD1612yescomplemented
71C22×D61—81no—
72Q8×C61—21no—
73Q8×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61#12111yescharacteristic
77C2×C4×C61C2×D811yescharacteristic
78C2×C4×C61#13511yescharacteristic
79C2×Dic61—81no—
80D244—81no—
81D244—81no—
82D244—81no—
83D244—81no—
84D244—161no—
85Dic122—81no—
86Dic122—81no—
87C8×C61—21no—
88C8×C61—41no—
89C8×C61C2×SD1611yescharacteristic
90C8×C61AGL(1,ℤ/8)11yescharacteristic
91#92418—81no—
92#92418—81no—
93#12444—611nomaximal, Sylow
94C22×C61#46611yescharacteristic
95C2×D61—161no—
96C2×D61—161no—
97C2×D61—161no—
98C4×C61—21no—
99C4×C61—41no—
100C4×C61—41no—
101C4×C61#46011yescharacteristic
102C4×C61#47211yescharacteristic
103C4×C61#50911yescharacteristic
104C4×C61#51011yescharacteristic
105Dic61—161no—
106#2248—611no—
107#2183D6111yescharacteristic, complemented
108#1670—611no—
109#1668—611no—
110#1371—611no—
111#1362—611no—
112#1361—611no—
113C2×C61#166811yescharacteristic
114C2×C61#222011yescharacteristic
115C2×C61#222311yescharacteristic
116D61—321no—
117C2×SD32—1221no—
118C2×SD32—1221no—
119#494—611no—
120#493—611no—
121#475—1221no—
122#460—1221no—
123C8×Q8C2×D6111yescharacteristic
124C4⋊C16—21no—
125C4⋊C16C2×D6111yescharacteristic
126#346—21no—
127C4×C16C2×D6111yescharacteristic
128#335—611no—
129#335—611no—
130#332—1221no—
131#331—1221no—
132C61#1244411yescharacteristic, complemented, Sylow
133C2×Q16—1221no—
134C2×Q16—1221no—
135C2×SD16—2441no—
136C2×D8—1221no—
137C2×D8—1221no—
138C4⋊Q8—1221no—
139#127—1221no—
140C4×Q8D24411yescharacteristic
141SD32—2442no—
142SD32—2442no—
143C2×C16—21no—
144C2×C16C22⋊D6111yescharacteristic
145C2×C16C22⋊D6111yescharacteristic
146#106—2441no—
147C4⋊C8—21no—
148C4⋊C8—1221no—
149C4⋊C8—1221no—
150C4⋊C8D24411yescharacteristic
151#103—2441no—
152#102—2441no—
153C4×C8—21no—
154C4×C8C22×D6111yescharacteristic
155C2×Q8—2441no—
156C2×Q8D48811yescharacteristic
157C2×D4—2441no—
158C2×D4—2441no—
159C2×D4—2441no—
160Q16—4881no—
161Q16—2441no—
162Q16—2441no—
163SD16—4882no—
164D8—4881no—
165D8—2441no—
166D8—2441no—
167C2×C8—21no—
168C2×C8—2441no—
169C2×C8—2441no—
170C2×C8#1175822211yescharacteristic
171C2×C8C2×C22⋊D6111yescharacteristic
172C4⋊C4—21no—
173C4⋊C4—2441no—
174C4⋊C4—2441no—
175C4⋊C4D48811yescharacteristic
176C42—21no—
177C42C2×D24411yescharacteristic
178C16—21no—
179C16—41no—
180C16#1175820112yescomplemented
181C23—4881no—
182Q8—21no—
183Q8—21no—
184Q8—4881no—
185Q8—4881no—
186D4—9761no—
187D4—4881no—
188D4—4881no—
189D4—4881no—
190D4—4881no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—4881no—
194C2×C4#1451975111yescharacteristic
195C2×C4C2×D48811yescharacteristic
196C2×C4#1451979911yescharacteristic
197C8—21no—
198C8—41no—
199C8—4881no—
200C8—4881no—
201C8C2×#1175820111yescharacteristic
202C8#1451980211yescharacteristic
203C22—9761no—
204C22—9761no—
205C22—9761no—
206C22#1683999811yescharacteristic
207C4—21no—
208C4—41no—
209C4—41no—
210C4—9761no—
211C4#1683996211yescharacteristic
212C4#1684003211yescharacteristic
213C4#1684020011yescharacteristic
214C4#1684020511yescharacteristic
215C2—19521no—
216C2#2144517911yescharacteristic
217C2#2144793211yescharacteristic
218C2#2144794911yescharacteristic
subgroupG/H
centerC22#16839998
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2183C2
socleC22×C61#466
prime radical#16840139C22
hypercenter#2183D61
hypocenterC61#12444
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #2183

Complements

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

NH ≅ G/Ntype
2. #21445189C2semidirect
4. #21443891C2semidirect
5. #21443869C2semidirect
7. C61×#2183C2semidirect
70. C16×C61SD16semidirect
107. #2183D61semidirect
132. C61#12444semidirect
180. C16#11758201semidirect

Maximal subgroups

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

subgroupindex
#214480752
#214451892
#214451792
#214438912
#214438692
#214438662
C61×#21832
#1244461