Finite Group Databasebeta

← #29594437

Subgroups — #29594437

Order 15616.

234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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
2#21445218C211yesmaximal, characteristic, complemented
3#21445174C211yesmaximal, characteristic
4#21443893C211yesmaximal, characteristic, complemented
5#21443876C211yesmaximal, characteristic, complemented
6#21443866C211yesmaximal, characteristic, complemented
7D4×C16×C61C211yesmaximal, characteristic, complemented
8#16840167C2211yescharacteristic
9#16840139C2211yescharacteristic
10#16840052—21no—
11#16839957—21no—
12#16839564—21no—
13#16839564—21no—
14#16839515C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839510—21no—
17#16839505—21no—
18C22×C16×C61—21no—
19C8×D4×C61C2211yescharacteristic
20C61×C4⋊C16C2211yescharacteristic
21C61×C22⋊C16—21no—
22C4×C16×C61C2211yescharacteristic
23C2×D488—21no—
24C2×D488—21no—
25C2×#11758199—41no—
26#14519777—21no—
27#14519774—21no—
28#14519711—21no—
29#14519711—21no—
30#14519708—41no—
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33#14519698—41no—
34#14519697—41no—
35C22×C8×C61—21no—
36C4×D4×C61D411yescharacteristic
37C2×C16×C61—21no—
38C2×C16×C61—42no—
39C2×C16×C61D411yescharacteristic
40C2×C16×C61D411yescharacteristic
41C4⋊C8×C61D411yescharacteristic
42C22⋊C8×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×D4×C61D811yescharacteristic
45C22×C4×C61—21no—
46C2×D244—41no—
47C2×D244—41no—
48C2×D244—41no—
49C2×Dic122—41no—
50C2×C8×C61—21no—
51C2×C8×C61—41no—
52C2×C8×C61—41no—
53C2×C8×C61C2×D411yescharacteristic
54C2×C8×C61#4111yescharacteristic
55C4⋊C4×C61D811yescharacteristic
56C22⋊C4×C61—21no—
57C42×C61C2×D411yescharacteristic
58#11758199—82no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61C2×#92418—41no—
62C2×#92418—41no—
63D488—41no—
64D488—41no—
65D488—81no—
66C16×C61—21no—
67C16×C61—21no—
68C16×C61—41no—
69C23×C61—21no—
70C22×D61—81no—
71D4×C61—21no—
72D4×C61SD3212yes—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61#12111yescharacteristic
77C2×C4×C61C2×D811yescharacteristic
78C2×C4×C61#13511yescharacteristic
79C2×Dic61—81no—
80D244—81no—
81D244—81no—
82D244—81no—
83D244—81no—
84D244—161no—
85Dic122—161no—
86C8×C61—21no—
87C8×C61—41no—
88C8×C61#13511yescharacteristic
89C8×C61AGL(1,ℤ/8)11yescharacteristic
90#92418—81no—
91#92418—81no—
92#12468—611nomaximal, Sylow
93C22×C61—22no—
94C22×C61—41no—
95C22×C61—41no—
96C22×C61#46611yescharacteristic
97C2×D61—161no—
98C2×D61—161no—
99C2×D61—161no—
100C4×C61—21no—
101C4×C61—41no—
102C4×C61#46311yescharacteristic
103C4×C61#47111yescharacteristic
104C4×C61C2×SD3211yescharacteristic
105C4×C61#50811yescharacteristic
106Dic61—161no—
107#2240—611no—
108D4×C16D6111yescharacteristic, complemented
109#1675—611no—
110#1667—611no—
111#1372—611no—
112#1365—611no—
113#1361—611no—
114C2×C61—42no—
115C2×C61#168111yescharacteristic
116C2×C61#221711yescharacteristic
117C2×C61#222111yescharacteristic
118D61—321no—
119C22×C16—21no—
120#500—611no—
121#493—611no—
122#476—1221no—
123#459—1221no—
124C8×D4C2×D6111yescharacteristic
125C4⋊C16C2×D6111yescharacteristic
126#357—1221no—
127#357—1221no—
128C22⋊C16—21no—
129C4×C16C2×D6111yescharacteristic
130#335—611no—
131#335—611no—
132#333—1221no—
133#331—1221no—
134C61#1246811yescharacteristic, complemented, Sylow
135C2×D8—1221no—
136C2×D8—1221no—
137C2×D8—2441no—
138C22×C8—21no—
139C4⋊Q8—1221no—
140#127—1221no—
141C4×D4D24411yescharacteristic
142C2×C16—21no—
143C2×C16—42no—
144C2×C16C22⋊D6111yescharacteristic
145C2×C16C22⋊D6111yescharacteristic
146#107—1221no—
147#107—1221no—
148#106—2441no—
149C4⋊C8—1221no—
150C4⋊C8—1221no—
151C4⋊C8D24411yescharacteristic
152#102—2441no—
153#102—2441no—
154C22⋊C8—21no—
155C4×C8C22×D6111yescharacteristic
156C2×Q8—2441no—
157C2×D4—2441no—
158C2×D4—2441no—
159C2×D4—2441no—
160C2×D4D48811yescharacteristic
161C22×C4—21no—
162D8—4881no—
163D8—4882no—
164D8—2441no—
165D8—2441no—
166C2×C8—21no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—2441no—
170C2×C8—2441no—
171C2×C8#1175822211yescharacteristic
172C2×C8C2×C22⋊D6111yescharacteristic
173C4⋊C4—2441no—
174C4⋊C4—2441no—
175C4⋊C4D48811yescharacteristic
176C22⋊C4—21no—
177C42C2×D24411yescharacteristic
178C16—21no—
179C16—21no—
180C16—41no—
181C23—21no—
182C23—4881no—
183Q8—9761no—
184D4—21no—
185D4—9761no—
186D4—4881no—
187D4—4881no—
188D4—4881no—
189D4—4881no—
190D4#1451972212yes—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—4881no—
195C2×C4#1451975111yescharacteristic
196C2×C4C2×D48811yescharacteristic
197C2×C4#1451979911yescharacteristic
198C8—21no—
199C8—41no—
200C8—4881no—
201C8—4881no—
202C8#1451979711yescharacteristic
203C8#1451980311yescharacteristic
204C22—22no—
205C22—41no—
206C22—41no—
207C22—9761no—
208C22—9761no—
209C22—9761no—
210C22#1683999811yescharacteristic
211C4—21no—
212C4—41no—
213C4—9761no—
214C4#1683997711yescharacteristic
215C4#1684002511yescharacteristic
216C4C2×#1451972211yescharacteristic
217C4#1684019411yescharacteristic
218C2—42no—
219C2—19521no—
220C2#2144525611yescharacteristic
221C2#2144791511yescharacteristic
222C2#2144793911yescharacteristic
subgroupG/H
centerC22#16839998
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingD4×C16×C61C2
socleC22×C61#466
prime radical#21445174C2
hypercenterD4×C16D61
hypocenterC61#12468
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #21448043C2semidirect
2. #21445218C2semidirect
4. #21443893C2semidirect
5. #21443876C2semidirect
6. #21443866C2semidirect
7. D4×C16×C61C2semidirect
108. D4×C16D61semidirect
134. C61#12468semidirect

Maximal subgroups

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

subgroupindex
#214480432
#214452182
#214451742
#214438932
#214438762
#214438662
D4×C16×C612
#1246861