Finite Group Databasebeta

← #29594299

Subgroups — #29594299

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#21448076C211yesmaximal, characteristic
2#21447728C211yesmaximal, characteristic, complemented
3#21445179C211yesmaximal, characteristic
4#21443890C211yesmaximal, characteristic, complemented
5#21443868C211yesmaximal, characteristic, complemented
6#21443864C211yesmaximal, characteristic
7C61×#1670C211yesmaximal, characteristic, complemented
8C2×#14519720—21no—
9C2×#14519720—21no—
10#16840139C2211yescharacteristic
11#16839962—21no—
12C4⋊#11758185—21no—
13C4⋊#11758185C2211yescharacteristic
14#16839538—21no—
15C4×#11758185C2211yescharacteristic
16#16839515C2211yescharacteristic
17#16839505—21no—
18C61×#494C2211yescharacteristic
19C61×#475—21no—
20C8×Q8×C61C2211yescharacteristic
21C61×#335C2211yescharacteristic
22C61×#332—21no—
23C2×#11758201—41no—
24C2×D488—21no—
25C2×D488—21no—
26#14519774—21no—
27#14519720—42no—
28#14519720—42no—
29C2×#11758185—21no—
30C2×#11758185D411yescharacteristic
31C2×#11758185D411yescharacteristic
32C4⋊#92418—21no—
33#14519697—41no—
34C2×Q16×C61—21no—
35C2×Q16×C61—21no—
36C4⋊Q8×C61—21no—
37C4×Q8×C61D411yescharacteristic
38#106×C61—41no—
39C4⋊C8×C61—21no—
40C4⋊C8×C61—21no—
41C4⋊C8×C61D411yescharacteristic
42#103×C61—41no—
43C4×C8×C61—21no—
44C4×C8×C61C2311yescharacteristic
45C2×Q8×C61—41no—
46C2×Q8×C61D811yescharacteristic
47C2×D244—41no—
48C2×D244—41no—
49C2×D244—41no—
50Q16×C61—41no—
51Q16×C61—41no—
52Q16×C61—81no—
53C2×C8×C61—21no—
54C2×C8×C61—41no—
55C2×C8×C61C2×D411yescharacteristic
56C2×C8×C61#4111yescharacteristic
57C4⋊C4×C61—21no—
58C4⋊C4×C61—41no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61D811yescharacteristic
61C42×C61—21no—
62C42×C61C2×D411yescharacteristic
63#11758201—82no—
64C2×#92418—41no—
65D488—41no—
66D488—41no—
67D488—81no—
68#11758185—21no—
69#11758185—41no—
70#11758185SD1612yescomplemented
71C22×D61—81no—
72Q8×C61—21no—
73Q8×C61—21no—
74Q8×C61—81no—
75Q8×C61—81no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—81no—
79C2×C4×C61#12111yescharacteristic
80C2×C4×C61C2×D811yescharacteristic
81C2×C4×C61#13511yescharacteristic
82D244—81no—
83D244—81no—
84D244—81no—
85D244—81no—
86D244—161no—
87C8×C61—21no—
88C8×C61—41no—
89C8×C61—81no—
90C8×C61C2×SD1611yescharacteristic
91C8×C61AGL(1,ℤ/8)11yescharacteristic
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—161no—
102C4×C61#46011yescharacteristic
103C4×C61#47211yescharacteristic
104C4×C61#50911yescharacteristic
105C4×C61#51011yescharacteristic
106#2248—611no—
107#2183—611no—
108#1670D6111yescharacteristic, complemented
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#494C2×D6111yescharacteristic
120#493—611no—
121#475—21no—
122#460—1221no—
123C8×Q8C2×D6111yescharacteristic
124C4⋊C16—611no—
125C4⋊C16—1221no—
126#346—1221no—
127C4×C16—611no—
128#335—611no—
129#335C2×D6111yescharacteristic
130#332—21no—
131#331—1221no—
132C61#1244411yescharacteristic, complemented, Sylow
133C2×Q16—21no—
134C2×Q16—21no—
135C2×SD16—2441no—
136C2×D8—1221no—
137C2×D8—1221no—
138C4⋊Q8—21no—
139#127—1221no—
140C4×Q8C22⋊D6111yescharacteristic
141SD32—2442no—
142SD32—2442no—
143C2×C16—611no—
144C2×C16—611no—
145C2×C16—1221no—
146#106—41no—
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—1221no—
150C4⋊C8C22⋊D6111yescharacteristic
151#103—41no—
152#102—2441no—
153C4×C8—21no—
154C4×C8C22×D6111yescharacteristic
155C2×Q8—41no—
156C2×Q8#1175819911yescharacteristic
157C2×D4—2441no—
158C2×D4—2441no—
159C2×D4—2441no—
160Q16—41no—
161Q16—41no—
162Q16—81no—
163SD16—4882no—
164D8—4881no—
165D8—2441no—
166D8—2441no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—2441no—
170C2×C8D4×D6111yescharacteristic
171C2×C8#1175822411yescharacteristic
172C4⋊C4—21no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4#1175819911yescharacteristic
176C42—21no—
177C42C2×C22⋊D6111yescharacteristic
178C16—612no—
179C16—1221no—
180C16—2441no—
181C23—4881no—
182Q8—21no—
183Q8—21no—
184Q8—81no—
185Q8—81no—
186D4—9761no—
187D4—4881no—
188D4—4881no—
189D4—4881no—
190D4—4881no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—81no—
194C2×C4#1451974911yescharacteristic
195C2×C4C2×#1175819911yescharacteristic
196C2×C4#1451979711yescharacteristic
197C8—21no—
198C8—41no—
199C8—81no—
200C8—4881no—
201C8SD16×D6111yescharacteristic
202C8#1451980411yescharacteristic
203C22—9761no—
204C22—9761no—
205C22—9761no—
206C22#1683999611yescharacteristic
207C4—21no—
208C4—41no—
209C4—41no—
210C4—161no—
211C4#1683996011yescharacteristic
212C4#1684003011yescharacteristic
213C4#1684019711yescharacteristic
214C4#1684020311yescharacteristic
215C2—19521no—
216C2#2144517711yescharacteristic
217C2#2144793411yescharacteristic
218C2#2144795111yescharacteristic
subgroupG/H
centerC22#16839996
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1670C2
socleC22×C61#466
prime radical#16840139C22
hypercenter#1670D61
hypocenterC61#12444
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

Complements

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

NH ≅ G/Ntype
2. #21447728C2semidirect
4. #21443890C2semidirect
5. #21443868C2semidirect
7. C61×#1670C2semidirect
70. #11758185SD16semidirect
108. #1670D61semidirect
132. C61#12444semidirect

Maximal subgroups

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

subgroupindex
#214480762
#214477282
#214451792
#214438902
#214438682
#214438642
C61×#16702
#1244461