Finite Group Databasebeta

← #29594438

Subgroups — #29594438

Order 15616.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#21448043C211yesmaximal, characteristic, complemented
2C16×D244C211yesmaximal, characteristic, complemented
3#21445219C211yesmaximal, characteristic, complemented
4#21445175C211yesmaximal, characteristic
5#21443878C211yesmaximal, characteristic, complemented
6#21443864C211yesmaximal, characteristic, complemented
7C61×#1372C211yesmaximal, characteristic, complemented
8C2×C16×D61—21no—
9#16840167C2211yescharacteristic
10#16840139C2211yescharacteristic
11#16840053—21no—
12#16839958—21no—
13C8×D244C2211yescharacteristic
14C4⋊#11758185C2211yescharacteristic
15#16839564—21no—
16#16839564—21no—
17#16839541—21no—
18#16839510—21no—
19#16839505—21no—
20C4×C16×C61C2211yescharacteristic
21C61×#335C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×D488—21no—
24C2×D488—21no—
25C2×D488—41no—
26C2×C8×D61—21no—
27#14519777—21no—
28#14519774—21no—
29C4×D244D411yescharacteristic
30C2×#11758185—21no—
31C16×D61—42no—
32#14519711—21no—
33#14519711—21no—
34#14519709—41no—
35C4⋊#92418D411yescharacteristic
36#14519699—41no—
37#14519699—41no—
38#14519689—21no—
39C2×C16×C61D411yescharacteristic
40C2×C16×C61D411yescharacteristic
41C4⋊C8×C61—21no—
42C4⋊C8×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×D244—41no—
45C2×D244—41no—
46C2×D244—41no—
47C2×D244D811yescharacteristic
48C2×C4×D61—21no—
49C2×Dic122—41no—
50C2×C8×C61—41no—
51C2×C8×C61—41no—
52C2×C8×C61C2×D411yescharacteristic
53C2×C8×C61#4111yescharacteristic
54C42×C61C2×D411yescharacteristic
55#11758198—21no—
56C4⋊Dic61—41no—
57C4⋊Dic61—41no—
58C4⋊Dic61D811yescharacteristic
59C2×#92418—21no—
60D488—41no—
61D488—41no—
62D488—81no—
63D488—82no—
64C8×D61—41no—
65C8×D61—41no—
66C16×C61—21no—
67C16×C61—21no—
68#11758185—41no—
69C22×D61—21no—
70C22×D61—81no—
71C2×C4×C61#12111yescharacteristic
72C2×C4×C61C2×D811yescharacteristic
73C2×C4×C61#13511yescharacteristic
74C2×Dic61—21no—
75C2×Dic61—81no—
76D244—21no—
77D244—81no—
78D244—81no—
79D244—81no—
80D244—81no—
81D244—161no—
82D244SD3212yes—
83C4×D61—41no—
84C4×D61—41no—
85Dic122—161no—
86C8×C61—21no—
87C8×C61—81no—
88C8×C61—81no—
89C8×C61#13511yescharacteristic
90C8×C61AGL(1,ℤ/8)11yescharacteristic
91#92418—41no—
92#12468—611nomaximal, Sylow
93C22×C61#46611yescharacteristic
94C2×D61—22no—
95C2×D61—41no—
96C2×D61—41no—
97C2×D61—161no—
98C2×D61—161no—
99C2×D61—161no—
100C4×C61—21no—
101C4×C61#46311yescharacteristic
102C4×C61#47111yescharacteristic
103C4×C61C2×SD3211yescharacteristic
104C4×C61#50811yescharacteristic
105Dic61—41no—
106Dic61—161no—
107#2240—611no—
108D4×C16—611no—
109#1675—611no—
110#1667—611no—
111#1372D6111yescharacteristic, complemented
112#1365—611no—
113#1361—611no—
114C2×C61#168111yescharacteristic
115C2×C61#221711yescharacteristic
116C2×C61#222111yescharacteristic
117D61—42no—
118D61—321no—
119C22×C16—1221no—
120#500—611no—
121#493—611no—
122#476—1221no—
123#459—1221no—
124C8×D4—611no—
125C4⋊C16—611no—
126#357—1221no—
127#357—1221no—
128C22⋊C16—1221no—
129C4×C16C2×D6111yescharacteristic
130#335C2×D6111yescharacteristic
131#335C2×D6111yescharacteristic
132#333—1221no—
133#331—1221no—
134C61#1246811yescharacteristic, complemented, Sylow
135C2×D8—1221no—
136C2×D8—1221no—
137C2×D8—2441no—
138C22×C8—1221no—
139C4⋊Q8—1221no—
140#127—1221no—
141C4×D4—611no—
142C2×C16—1221no—
143C2×C16—2442no—
144C2×C16D24411yescharacteristic
145C2×C16D24411yescharacteristic
146#107—1221no—
147#107—1221no—
148#106—2441no—
149C4⋊C8—21no—
150C4⋊C8—21no—
151C4⋊C8—611no—
152#102—2441no—
153#102—2441no—
154C22⋊C8—1221no—
155C4×C8C22×D6111yescharacteristic
156C2×Q8—2441no—
157C2×D4—611no—
158C2×D4—2441no—
159C2×D4—2441no—
160C2×D4—2441no—
161C22×C4—1221no—
162D8—4881no—
163D8—4882no—
164D8—2441no—
165D8—2441no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—1221no—
169C2×C8—2441no—
170C2×C8—2441no—
171C2×C8C2×D24411yescharacteristic
172C2×C8#1175822611yescharacteristic
173C4⋊C4—611no—
174C4⋊C4—2441no—
175C4⋊C4—2441no—
176C22⋊C4—1221no—
177C42D4×D6111yescharacteristic
178C16—21no—
179C16—21no—
180C16—2441no—
181C23—1221no—
182C23—4881no—
183Q8—9761no—
184D4—612no—
185D4—1221no—
186D4—9761no—
187D4—4881no—
188D4—4881no—
189D4—4881no—
190D4—4881no—
191C2×C4—1221no—
192C2×C4—4881no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4#1451975211yescharacteristic
196C2×C4D8×D6111yescharacteristic
197C2×C4#1451980011yescharacteristic
198C8—21no—
199C8—81no—
200C8—81no—
201C8—2441no—
202C8#1451979911yescharacteristic
203C8#1451980511yescharacteristic
204C22—1222no—
205C22—9761no—
206C22—9761no—
207C22—9761no—
208C22—2441no—
209C22—2441no—
210C22#1683999911yescharacteristic
211C4—21no—
212C4—9761no—
213C4—2441no—
214C4#1683997811yescharacteristic
215C4#1684002611yescharacteristic
216C4SD32×D6111yescharacteristic
217C4#1684019311yescharacteristic
218C2—19521no—
219C2—2442no—
220C2#2144525711yescharacteristic
221C2#2144791611yescharacteristic
222C2#2144794011yescharacteristic
subgroupG/H
centerC22#16839999
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1372C2
socleC22×C61#466
prime radical#21445175C2
hypercenter#1372D61
hypocenterC61#12468
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1372

Complements

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

NH ≅ G/Ntype
1. #21448043C2semidirect
2. C16×D244C2semidirect
3. #21445219C2semidirect
5. #21443878C2semidirect
6. #21443864C2semidirect
7. C61×#1372C2semidirect
111. #1372D61semidirect
134. C61#12468semidirect

Maximal subgroups

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

subgroupindex
#214480432
C16×D2442
#214452192
#214451752
#214438782
#214438642
C61×#13722
#1246861