Finite Group Databasebeta

← #29594294

Subgroups — #29594294

Order 15616.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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#21447727C211yesmaximal, characteristic, complemented
2#21445186C211yesmaximal, characteristic, complemented
3#21445176C211yesmaximal, characteristic
4#21443891C211yesmaximal, characteristic, complemented
5#21443868C211yesmaximal, characteristic, complemented
6#21443865C211yesmaximal, characteristic
7C61×#2248C211yesmaximal, characteristic
8#16840044—21no—
9#16839959—21no—
10C8×Dic122C2211yescharacteristic
11C4⋊#11758185C2211yescharacteristic
12#16839580—21no—
13#16839537—21no—
14#16839515C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839508—21no—
17#16839506—21no—
18C2×SD32×C61—21no—
19C2×SD32×C61—21no—
20C61×#494C2211yescharacteristic
21C61×#493C2211yescharacteristic
22C4×C16×C61C2211yescharacteristic
23C2×#11758200—41no—
24C4×Dic122D411yescharacteristic
25C2×#11758185—21no—
26#14519708—41no—
27C4⋊#92418—21no—
28C4⋊#92418—21no—
29C4⋊#92418D411yescharacteristic
30#14519706—21no—
31#14519700—41no—
32#14519698—41no—
33C8×Dic61—21no—
34C2×Q16×C61—21no—
35C2×Q16×C61—21no—
36C2×D8×C61—21no—
37C2×D8×C61—21no—
38C4⋊Q8×C61—21no—
39#127×C61—21no—
40SD32×C61—42no—
41SD32×C61—42no—
42C2×C16×C61D411yescharacteristic
43C2×C16×C61D411yescharacteristic
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×D4×C61—41no—
47C2×D4×C61—41no—
48C2×D4×C61—41no—
49C2×Dic122D811yescharacteristic
50Q16×C61—41no—
51Q16×C61—41no—
52Q16×C61—81no—
53D8×C61—41no—
54D8×C61—41no—
55D8×C61—81no—
56C2×C8×C61C2×D411yescharacteristic
57C2×C8×C61#4111yescharacteristic
58C4⋊C4×C61—41no—
59C4⋊C4×C61—41no—
60C42×C61C2×D411yescharacteristic
61#11758200—82no—
62C4⋊Dic61D811yescharacteristic
63#11758196—21no—
64C4×Dic61—21no—
65C2×#92418—21no—
66C2×#92418—41no—
67C2×#92418—41no—
68C16×C61—21no—
69C16×C61SD1612yescomplemented
70#11758185—41no—
71C23×C61—81no—
72Q8×C61—81no—
73Q8×C61—81no—
74D4×C61—81no—
75D4×C61—81no—
76D4×C61—81no—
77D4×C61—81no—
78D4×C61—161no—
79C2×C4×C61—81no—
80C2×C4×C61#12111yescharacteristic
81C2×C4×C61C2×D811yescharacteristic
82C2×C4×C61#13511yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85Dic122—21no—
86Dic122—21no—
87C8×C61—21no—
88C8×C61C2×SD1611yescharacteristic
89C8×C61AGL(1,ℤ/8)11yescharacteristic
90#92418—41no—
91#92418—81no—
92#92418—81no—
93#12444—611nomaximal, Sylow
94C22×C61—161no—
95C22×C61—161no—
96C22×C61—161no—
97C22×C61#46611yescharacteristic
98C4×C61—21no—
99C4×C61—161no—
100C4×C61#46011yescharacteristic
101C4×C61#47211yescharacteristic
102C4×C61#50911yescharacteristic
103C4×C61#51011yescharacteristic
104Dic61—41no—
105Dic61—41no—
106#2248D6111yescharacteristic
107#2183—611no—
108#1670—611no—
109#1668—611no—
110#1371—611no—
111#1362—611no—
112#1361—611no—
113C2×C61—321no—
114C2×C61#166811yescharacteristic
115C2×C61#222011yescharacteristic
116C2×C61#222311yescharacteristic
117C2×SD32—21no—
118C2×SD32—21no—
119#494C2×D6111yescharacteristic
120#493C2×D6111yescharacteristic
121#475—1221no—
122#460—1221no—
123C8×Q8—611no—
124C4⋊C16—611no—
125C4⋊C16—1221no—
126#346—1221no—
127C4×C16C2×D6111yescharacteristic
128#335—611no—
129#335—611no—
130#332—1221no—
131#331—1221no—
132C61#1244411yescharacteristic, complemented, Sylow
133C2×Q16—21no—
134C2×Q16—21no—
135C2×SD16—2441no—
136C2×D8—21no—
137C2×D8—21no—
138C4⋊Q8—21no—
139#127—21no—
140C4×Q8—611no—
141SD32—42no—
142SD32—42no—
143C2×C16—1221no—
144C2×C16C22⋊D6111yescharacteristic
145C2×C16C22⋊D6111yescharacteristic
146#106—2441no—
147C4⋊C8—611no—
148C4⋊C8—1221no—
149C4⋊C8—1221no—
150C4⋊C8—1221no—
151#103—2441no—
152#102—2441no—
153C4×C8—1221no—
154C4×C8C22×D6111yescharacteristic
155C2×Q8—41no—
156C2×Q8—611no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160Q16—41no—
161Q16—41no—
162Q16—81no—
163SD16—4882no—
164D8—41no—
165D8—41no—
166D8—81no—
167C2×C8—1221no—
168C2×C8—2441no—
169C2×C8—2441no—
170C2×C8#1175822411yescharacteristic
171C2×C8C2×C22⋊D6111yescharacteristic
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—611no—
175C4⋊C4—1221no—
176C42—1221no—
177C42D4×D6111yescharacteristic
178C16—21no—
179C16—2441no—
180C16#1175820012yescomplemented
181C23—81no—
182Q8—81no—
183Q8—81no—
184Q8—1221no—
185Q8—1221no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—81no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4#1451974811yescharacteristic
195C2×C4D8×D6111yescharacteristic
196C2×C4#1451979611yescharacteristic
197C8—21no—
198C8—4881no—
199C8—4881no—
200C8—2441no—
201C8C2×#1175820011yescharacteristic
202C8#1451980311yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1683999511yescharacteristic
207C4—21no—
208C4—161no—
209C4—2441no—
210C4—2441no—
211C4#1683995911yescharacteristic
212C4#1684002911yescharacteristic
213C4#1684019911yescharacteristic
214C4#1684020111yescharacteristic
215C2—321no—
216C2#2144517611yescharacteristic
217C2#2144792911yescharacteristic
218C2#2144794611yescharacteristic
subgroupG/H
centerC22#16839995
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2248C2
socleC22×C61#466
prime radicalC61×#493C22
hypercenter#2248D61
hypocenterC61#12444
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #21447727C2semidirect
2. #21445186C2semidirect
4. #21443891C2semidirect
5. #21443868C2semidirect
69. C16×C61SD16semidirect
132. C61#12444semidirect
180. C16#11758200semidirect

Maximal subgroups

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

subgroupindex
#214477272
#214451862
#214451762
#214438912
#214438682
#214438652
C61×#22482
#1244461