Finite Group Databasebeta

← #29594433

Subgroups — #29594433

Order 15616.

240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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#21448044C211yesmaximal, characteristic, complemented
2#21447638C211yesmaximal, characteristic, complemented
3#21445205C211yesmaximal, characteristic, complemented
4#21445175C211yesmaximal, characteristic
5#21443890C211yesmaximal, characteristic, complemented
6#21443866C211yesmaximal, characteristic, complemented
7C61×#1364C211yesmaximal, characteristic, complemented
8C2×C16×D61—21no—
9#16840139C2211yescharacteristic
10#16839964—21no—
11#16839958—21no—
12C8×D244C2211yescharacteristic
13#16839562—21no—
14#16839562—21no—
15#16839541—21no—
16C4×#11758185C2211yescharacteristic
17#16839515C2211yescharacteristic
18#16839508—21no—
19#16839505—21no—
20C61×#500C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×#11758201—41no—
24C2×D488—21no—
25C2×D488—21no—
26C2×D488—41no—
27C2×C8×D61—21no—
28#14519774—21no—
29C4×D244D411yescharacteristic
30C2×#11758185D411yescharacteristic
31C2×#11758185D411yescharacteristic
32C16×D61—42no—
33C4⋊#92418—21no—
34C4⋊#92418D411yescharacteristic
35#14519701—41no—
36#14519699—41no—
37#14519689—21no—
38C4⋊Q8×C61—21no—
39C2×C16×C61—21no—
40#107×C61—21no—
41#107×C61—21no—
42C4⋊C8×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×Q8×C61—41no—
45C2×D244—41no—
46C2×D244—41no—
47C2×D244—41no—
48C2×D244D811yescharacteristic
49C2×C4×D61—21no—
50C2×C8×C61—41no—
51C2×C8×C61C2×D411yescharacteristic
52C2×C8×C61#4111yescharacteristic
53C4⋊C4×C61—41no—
54C4⋊C4×C61—41no—
55C42×C61C2×D411yescharacteristic
56#11758201—82no—
57#11758198—21no—
58C4⋊Dic61D811yescharacteristic
59C2×#92418—21no—
60C2×#92418—41no—
61D488—41no—
62D488—41no—
63D488—81no—
64D488—82no—
65C8×D61—41no—
66C8×D61—41no—
67C16×C61—41no—
68#11758185—21no—
69#11758185—21no—
70C22×D61—21no—
71C22×D61—81no—
72Q8×C61—81no—
73Q8×C61—81no—
74C2×C4×C61—81no—
75C2×C4×C61#12111yescharacteristic
76C2×C4×C61C2×D811yescharacteristic
77C2×C4×C61#13511yescharacteristic
78C2×Dic61—21no—
79D244—21no—
80D244—81no—
81D244—81no—
82D244—81no—
83D244—81no—
84D244—161no—
85D244D1612yes—
86C4×D61—41no—
87C4×D61—41no—
88C8×C61—21no—
89C8×C61—81no—
90C8×C61#13511yescharacteristic
91C8×C61AGL(1,ℤ/8)11yescharacteristic
92#92418—41no—
93#92418—81no—
94#12467—611nomaximal, Sylow
95C22×C61#46611yescharacteristic
96C2×D61—22no—
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—161no—
100C2×D61—161no—
101C2×D61—161no—
102C4×C61—21no—
103C4×C61—161no—
104C4×C61#46311yescharacteristic
105C4×C61#47111yescharacteristic
106C4×C61C2×D1611yescharacteristic
107C4×C61#50811yescharacteristic
108Dic61—41no—
109#2240—611no—
110D4×C16—611no—
111#1673—611no—
112#1667—611no—
113#1371—611no—
114#1364D6111yescharacteristic, complemented
115#1361—611no—
116C2×C61#168111yescharacteristic
117C2×C61#221511yescharacteristic
118C2×C61#222311yescharacteristic
119D61—42no—
120D61—321no—
121C22×C16—1221no—
122#500C2×D6111yescharacteristic
123#493—611no—
124#461—1221no—
125#459—1221no—
126C8×D4—611no—
127C4⋊C16C2×D6111yescharacteristic
128#357—1221no—
129#357—1221no—
130C22⋊C16—1221no—
131C4×C16—611no—
132#335—611no—
133#335C2×D6111yescharacteristic
134#332—1221no—
135#331—1221no—
136C61#1246711yescharacteristic, complemented, Sylow
137C2×SD16—2441no—
138C2×D8—1221no—
139C2×D8—1221no—
140C2×D8—2441no—
141C22×C8—1221no—
142C4⋊Q8—21no—
143#127—1221no—
144C4×D4—611no—
145C2×C16—21no—
146C2×C16—611no—
147C2×C16—611no—
148C2×C16—2442no—
149#107—21no—
150#107—21no—
151C4⋊C8—21no—
152C4⋊C8—611no—
153C4⋊C8—1221no—
154#103—2441no—
155#102—2441no—
156C22⋊C8—1221no—
157C4×C8C22×D6111yescharacteristic
158C2×Q8—41no—
159C2×D4—611no—
160C2×D4—2441no—
161C2×D4—2441no—
162C2×D4—2441no—
163C22×C4—1221no—
164SD16—4882no—
165D8—4881no—
166D8—4882no—
167D8—2441no—
168D8—2441no—
169C2×C8—41no—
170C2×C8—1221no—
171C2×C8—2441no—
172C2×C8—2441no—
173C2×C8—2441no—
174C2×C8#1175822211yescharacteristic
175C2×C8D4×D6111yescharacteristic
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—611no—
179C22⋊C4—1221no—
180C42D4×D6111yescharacteristic
181C16—41no—
182C16—1221no—
183C16—1221no—
184C23—1221no—
185C23—4881no—
186Q8—81no—
187Q8—81no—
188D4—612no—
189D4—1221no—
190D4—9761no—
191D4—4881no—
192D4—4881no—
193D4—4881no—
194D4—4881no—
195C2×C4—81no—
196C2×C4—1221no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4#1451975011yescharacteristic
200C2×C4D8×D6111yescharacteristic
201C2×C4#1451979811yescharacteristic
202C8—21no—
203C8—81no—
204C8—4881no—
205C8—2441no—
206C8#1451980011yescharacteristic
207C8#1451980411yescharacteristic
208C22—1222no—
209C22—9761no—
210C22—9761no—
211C22—9761no—
212C22—2441no—
213C22—2441no—
214C22#1683999711yescharacteristic
215C4—21no—
216C4—161no—
217C4—2441no—
218C4#1683998011yescharacteristic
219C4#1684002811yescharacteristic
220C4D16×D6111yescharacteristic
221C4#1684019311yescharacteristic
222C2—19521no—
223C2—2442no—
224C2#2144525911yescharacteristic
225C2#2144790411yescharacteristic
226C2#2144795211yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1364C2
socleC22×C61#466
prime radical#21445175C2
hypercenter#1364D61
hypocenterC61#12467
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
1. #21448044C2semidirect
2. #21447638C2semidirect
3. #21445205C2semidirect
5. #21443890C2semidirect
6. #21443866C2semidirect
7. C61×#1364C2semidirect
114. #1364D61semidirect
136. C61#12467semidirect

Maximal subgroups

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

subgroupindex
#214480442
#214476382
#214452052
#214451752
#214438902
#214438662
C61×#13642
#1246761