Finite Group Databasebeta

← #29594298

Subgroups — #29594298

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#21448075C211yesmaximal, characteristic
2#21447727C211yesmaximal, characteristic, complemented
3#21445190C211yesmaximal, characteristic, complemented
4#21445180C211yesmaximal, characteristic
5#21443867C211yesmaximal, characteristic, complemented
6#21443864C211yesmaximal, characteristic
7C61×#1371C211yesmaximal, characteristic, complemented
8C2×#14519722—21no—
9C2×#14519722—21no—
10#16840142C2211yescharacteristic
11#16840139C2211yescharacteristic
12#16840048—21no—
13#16839963—21no—
14C8×Dic122C2211yescharacteristic
15C4⋊#11758185C2211yescharacteristic
16#16839580—21no—
17#16839537—21no—
18#16839507—21no—
19#16839505—21no—
20C4×C16×C61C2211yescharacteristic
21C61×#335C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×#11758190—41no—
26C2×D488—21no—
27C2×D488—21no—
28#14519777—21no—
29#14519774—21no—
30C4×Dic122D411yescharacteristic
31#14519722—42no—
32#14519722—42no—
33C2×#11758185—21no—
34#14519709—41no—
35C4⋊#92418D411yescharacteristic
36#14519706—21no—
37#14519702—41no—
38#14519699—41no—
39C8×Dic61—21no—
40C2×C16×C61D411yescharacteristic
41C2×C16×C61D411yescharacteristic
42C4⋊C8×C61—21no—
43C4⋊C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×D244—41no—
46C2×D244—41no—
47C2×D244—41no—
48C2×Dic122—41no—
49C2×Dic122D811yescharacteristic
50C2×C8×C61—41no—
51C2×C8×C61—41no—
52C2×C8×C61C2×D411yescharacteristic
53C2×C8×C61#4111yescharacteristic
54C42×C61C2×D411yescharacteristic
55C4⋊Dic61—41no—
56C4⋊Dic61—41no—
57C4⋊Dic61D811yescharacteristic
58#11758196—21no—
59C4×Dic61—21no—
60C2×#92418—21no—
61Dic244—41no—
62Dic244—41no—
63Dic244—81no—
64D488—41no—
65D488—41no—
66D488—81no—
67#11758190—82no—
68C16×C61—21no—
69C16×C61SD1612yescomplemented
70#11758185—41no—
71C22×D61—81no—
72C2×C4×C61#12111yescharacteristic
73C2×C4×C61C2×D811yescharacteristic
74C2×C4×C61#13511yescharacteristic
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—81no—
78D244—81no—
79D244—81no—
80D244—81no—
81D244—81no—
82D244—161no—
83Dic122—21no—
84Dic122—21no—
85Dic122—81no—
86Dic122—81no—
87C8×C61—21no—
88C8×C61—81no—
89C8×C61—81no—
90C8×C61C2×SD1611yescharacteristic
91C8×C61AGL(1,ℤ/8)11yescharacteristic
92#92418—41no—
93#12444—611nomaximal, Sylow
94C22×C61#46611yescharacteristic
95C2×D61—161no—
96C2×D61—161no—
97C2×D61—161no—
98C4×C61—21no—
99C4×C61#46011yescharacteristic
100C4×C61#47211yescharacteristic
101C4×C61#50911yescharacteristic
102C4×C61#51011yescharacteristic
103Dic61—41no—
104Dic61—41no—
105Dic61—161no—
106#2248—611no—
107#2183—611no—
108#1670—611no—
109#1668—611no—
110#1371D6111yescharacteristic, complemented
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×Q8—611no—
124C4⋊C16—611no—
125C4⋊C16—1221no—
126#346—1221no—
127C4×C16C2×D6111yescharacteristic
128#335C2×D6111yescharacteristic
129#335C2×D6111yescharacteristic
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×Q8—611no—
141SD32—2442no—
142SD32—2442no—
143C2×C16—1221no—
144C2×C16D24411yescharacteristic
145C2×C16D24411yescharacteristic
146#106—2441no—
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—611no—
150C4⋊C8—1221no—
151#103—2441no—
152#102—2441no—
153C4×C8—1221no—
154C4×C8C22×D6111yescharacteristic
155C2×Q8—611no—
156C2×Q8—2441no—
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—41no—
168C2×C8—41no—
169C2×C8—1221no—
170C2×C8C2×D24411yescharacteristic
171C2×C8#1175822611yescharacteristic
172C4⋊C4—611no—
173C4⋊C4—1221no—
174C4⋊C4—2441no—
175C4⋊C4—2441no—
176C42—1221no—
177C42D4×D6111yescharacteristic
178C16—21no—
179C16—2441no—
180C16#1175819012yescomplemented
181C23—4881no—
182Q8—1221no—
183Q8—1221no—
184Q8—4881no—
185Q8—4881no—
186D4—9761no—
187D4—4881no—
188D4—4881no—
189D4—4881no—
190D4—4881no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—4881no—
194C2×C4#1451975211yescharacteristic
195C2×C4D8×D6111yescharacteristic
196C2×C4#1451980011yescharacteristic
197C8—21no—
198C8—81no—
199C8—81no—
200C8—2441no—
201C8C2×#1175819011yescharacteristic
202C8#1451980511yescharacteristic
203C22—9761no—
204C22—9761no—
205C22—9761no—
206C22#1683999911yescharacteristic
207C4—21no—
208C4—9761no—
209C4—2441no—
210C4—2441no—
211C4#1683996311yescharacteristic
212C4#1684003311yescharacteristic
213C4#1684019611yescharacteristic
214C4#1684020411yescharacteristic
215C2—19521no—
216C2#2144518011yescharacteristic
217C2#2144793311yescharacteristic
218C2#2144795011yescharacteristic
subgroupG/H
centerC22#16839999
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1371C2
socleC22×C61#466
prime radical#16840139C22
hypercenter#1371D61
hypocenterC61#12444
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1371

Complements

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

NH ≅ G/Ntype
2. #21447727C2semidirect
3. #21445190C2semidirect
5. #21443867C2semidirect
7. C61×#1371C2semidirect
69. C16×C61SD16semidirect
110. #1371D61semidirect
132. C61#12444semidirect
180. C16#11758190semidirect

Maximal subgroups

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

subgroupindex
#214480752
#214477272
#214451902
#214451802
#214438672
#214438642
C61×#13712
#1244461