Finite Group Databasebeta

← #29594440

Subgroups — #29594440

Order 15616.

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

normal subgroups only

This group has 234 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#21445215C211yesmaximal, characteristic, complemented
4#21445175C211yesmaximal, characteristic
5#21443892C211yesmaximal, characteristic, complemented
6#21443866C211yesmaximal, characteristic, complemented
7C61×#1365C211yesmaximal, characteristic, complemented
8C2×C16×D61—21no—
9#16840139C2211yescharacteristic
10#16840049—21no—
11#16839958—21no—
12C8×D244C2211yescharacteristic
13#16839562—21no—
14#16839562—21no—
15#16839541—21no—
16C4×#11758185C2211yescharacteristic
17#16839515C2211yescharacteristic
18#16839511—21no—
19#16839505—21no—
20C61×#500C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×D488—21no—
24C2×D488—21no—
25C2×D488—41no—
26C2×C8×D61—21no—
27#14519774—21no—
28C4×D244D411yescharacteristic
29C2×#11758185D411yescharacteristic
30C2×#11758185D411yescharacteristic
31C16×D61—42no—
32#14519708—41no—
33C4⋊#92418—21no—
34C4⋊#92418D411yescharacteristic
35#14519699—41no—
36#14519697—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#11758198—21no—
57C4⋊Dic61D811yescharacteristic
58C2×#92418—21no—
59C2×#92418—41no—
60D488—41no—
61D488—41no—
62D488—81no—
63D488—82no—
64C8×D61—41no—
65C8×D61—41no—
66C16×C61—41no—
67#11758185—21no—
68#11758185—21no—
69C22×D61—21no—
70C22×D61—81no—
71Q8×C61—161no—
72C2×C4×C61—81no—
73C2×C4×C61#12111yescharacteristic
74C2×C4×C61C2×D811yescharacteristic
75C2×C4×C61#13511yescharacteristic
76C2×Dic61—21no—
77D244—21no—
78D244—81no—
79D244—81no—
80D244—81no—
81D244—81no—
82D244—161no—
83D244SD3212yes—
84C4×D61—41no—
85C4×D61—41no—
86C8×C61—21no—
87C8×C61—81no—
88C8×C61#13511yescharacteristic
89C8×C61AGL(1,ℤ/8)11yescharacteristic
90#92418—41no—
91#92418—81no—
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—161no—
102C4×C61#46311yescharacteristic
103C4×C61#47111yescharacteristic
104C4×C61C2×SD3211yescharacteristic
105C4×C61#50811yescharacteristic
106Dic61—41no—
107#2240—611no—
108D4×C16—611no—
109#1675—611no—
110#1667—611no—
111#1372—611no—
112#1365D6111yescharacteristic, complemented
113#1361—611no—
114C2×C61#168111yescharacteristic
115C2×C61#221711yescharacteristic
116C2×C61#222111yescharacteristic
117D61—42no—
118D61—321no—
119C22×C16—1221no—
120#500C2×D6111yescharacteristic
121#493—611no—
122#476—1221no—
123#459—1221no—
124C8×D4—611no—
125C4⋊C16C2×D6111yescharacteristic
126#357—1221no—
127#357—1221no—
128C22⋊C16—1221no—
129C4×C16—611no—
130#335—611no—
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—21no—
140#127—1221no—
141C4×D4—611no—
142C2×C16—21no—
143C2×C16—611no—
144C2×C16—611no—
145C2×C16—2442no—
146#107—21no—
147#107—21no—
148#106—2441no—
149C4⋊C8—21no—
150C4⋊C8—611no—
151C4⋊C8—1221no—
152#102—2441no—
153#102—2441no—
154C22⋊C8—1221no—
155C4×C8C22×D6111yescharacteristic
156C2×Q8—41no—
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—1221no—
168C2×C8—2441no—
169C2×C8—2441no—
170C2×C8—2441no—
171C2×C8#1175822211yescharacteristic
172C2×C8D4×D6111yescharacteristic
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—611no—
176C22⋊C4—1221no—
177C42D4×D6111yescharacteristic
178C16—41no—
179C16—1221no—
180C16—1221no—
181C23—1221no—
182C23—4881no—
183Q8—161no—
184D4—612no—
185D4—1221no—
186D4—9761no—
187D4—4881no—
188D4—4881no—
189D4—4881no—
190D4—4881no—
191C2×C4—81no—
192C2×C4—1221no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4#1451975011yescharacteristic
196C2×C4D8×D6111yescharacteristic
197C2×C4#1451979811yescharacteristic
198C8—21no—
199C8—81no—
200C8—4881no—
201C8—2441no—
202C8#1451980011yescharacteristic
203C8#1451980411yescharacteristic
204C22—1222no—
205C22—9761no—
206C22—9761no—
207C22—9761no—
208C22—2441no—
209C22—2441no—
210C22#1683999711yescharacteristic
211C4—21no—
212C4—161no—
213C4—2441no—
214C4#1683998011yescharacteristic
215C4#1684002811yescharacteristic
216C4SD32×D6111yescharacteristic
217C4#1684019511yescharacteristic
218C2—19521no—
219C2—2442no—
220C2#2144525911yescharacteristic
221C2#2144791811yescharacteristic
222C2#2144793811yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1365C2
socleC22×C61#466
prime radical#21445175C2
hypercenter#1365D61
hypocenterC61#12468
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
1. #21448044C2semidirect
2. #21447638C2semidirect
3. #21445215C2semidirect
5. #21443892C2semidirect
6. #21443866C2semidirect
7. C61×#1365C2semidirect
112. #1365D61semidirect
134. C61#12468semidirect

Maximal subgroups

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

subgroupindex
#214480442
#214476382
#214452152
#214451752
#214438922
#214438662
C61×#13652
#1246861