Finite Group Databasebeta

← #29594430

Subgroups — #29594430

Order 15616.

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

normal subgroups only

This group has 240 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#21445208C211yesmaximal, characteristic, complemented
3#21445174C211yesmaximal, characteristic
4#21443891C211yesmaximal, characteristic, complemented
5#21443873C211yesmaximal, characteristic, complemented
6#21443866C211yesmaximal, characteristic, complemented
7D4×C16×C61C211yesmaximal, characteristic, complemented
8#16840167C2211yescharacteristic
9#16840139C2211yescharacteristic
10#16839967—21no—
11#16839957—21no—
12#16839564—21no—
13#16839564—21no—
14#16839515C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839507—21no—
17#16839505—21no—
18C22×C16×C61—21no—
19C8×D4×C61C2211yescharacteristic
20C61×C4⋊C16C2211yescharacteristic
21C61×C22⋊C16—21no—
22C4×C16×C61C2211yescharacteristic
23C2×#11758200—41no—
24C2×D488—21no—
25C2×D488—21no—
26C2×#11758199—41no—
27#14519777—21no—
28#14519774—21no—
29#14519711—21no—
30#14519711—21no—
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33#14519700—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#11758200—82no—
59#11758199—82no—
60C4⋊Dic61—41no—
61C4⋊Dic61—41no—
62C2×#92418—41no—
63C2×#92418—41no—
64D488—41no—
65D488—41no—
66D488—81no—
67C16×C61—21no—
68C16×C61—21no—
69C16×C61—41no—
70C23×C61—21no—
71C22×D61—81no—
72D4×C61—21no—
73D4×C61D1612yes—
74C2×C4×C61—21no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61#12111yescharacteristic
78C2×C4×C61C2×D811yescharacteristic
79C2×C4×C61#13511yescharacteristic
80C2×Dic61—81no—
81D244—81no—
82D244—81no—
83D244—81no—
84D244—81no—
85D244—161no—
86Dic122—81no—
87Dic122—81no—
88C8×C61—21no—
89C8×C61—41no—
90C8×C61#13511yescharacteristic
91C8×C61AGL(1,ℤ/8)11yescharacteristic
92#92418—81no—
93#92418—81no—
94#12467—611nomaximal, Sylow
95C22×C61—22no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61#46611yescharacteristic
99C2×D61—161no—
100C2×D61—161no—
101C2×D61—161no—
102C4×C61—21no—
103C4×C61—41no—
104C4×C61#46311yescharacteristic
105C4×C61#47111yescharacteristic
106C4×C61C2×D1611yescharacteristic
107C4×C61#50811yescharacteristic
108Dic61—161no—
109#2240—611no—
110D4×C16D6111yescharacteristic, complemented
111#1673—611no—
112#1667—611no—
113#1371—611no—
114#1364—611no—
115#1361—611no—
116C2×C61—42no—
117C2×C61#168111yescharacteristic
118C2×C61#221511yescharacteristic
119C2×C61#222311yescharacteristic
120D61—321no—
121C22×C16—21no—
122#500—611no—
123#493—611no—
124#461—1221no—
125#459—1221no—
126C8×D4C2×D6111yescharacteristic
127C4⋊C16C2×D6111yescharacteristic
128#357—1221no—
129#357—1221no—
130C22⋊C16—21no—
131C4×C16C2×D6111yescharacteristic
132#335—611no—
133#335—611no—
134#332—1221no—
135#331—1221no—
136C61#1246711yescharacteristic, complemented, Sylow
137C2×SD16—2441no—
138C2×D8—1221no—
139C2×D8—1221no—
140C2×D8—2441no—
141C22×C8—21no—
142C4⋊Q8—1221no—
143#127—1221no—
144C4×D4D24411yescharacteristic
145C2×C16—21no—
146C2×C16—42no—
147C2×C16C22⋊D6111yescharacteristic
148C2×C16C22⋊D6111yescharacteristic
149#107—1221no—
150#107—1221no—
151C4⋊C8—1221no—
152C4⋊C8—1221no—
153C4⋊C8D24411yescharacteristic
154#103—2441no—
155#102—2441no—
156C22⋊C8—21no—
157C4×C8C22×D6111yescharacteristic
158C2×Q8—2441no—
159C2×D4—2441no—
160C2×D4—2441no—
161C2×D4—2441no—
162C2×D4D48811yescharacteristic
163C22×C4—21no—
164SD16—4882no—
165D8—4881no—
166D8—4882no—
167D8—2441no—
168D8—2441no—
169C2×C8—21no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—2441no—
173C2×C8—2441no—
174C2×C8#1175822211yescharacteristic
175C2×C8C2×C22⋊D6111yescharacteristic
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C4⋊C4D48811yescharacteristic
179C22⋊C4—21no—
180C42C2×D24411yescharacteristic
181C16—21no—
182C16—21no—
183C16—41no—
184C23—21no—
185C23—4881no—
186Q8—4881no—
187Q8—4881no—
188D4—21no—
189D4—9761no—
190D4—4881no—
191D4—4881no—
192D4—4881no—
193D4—4881no—
194D4D97612yes—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—4881no—
199C2×C4#1451975111yescharacteristic
200C2×C4C2×D48811yescharacteristic
201C2×C4#1451979911yescharacteristic
202C8—21no—
203C8—41no—
204C8—4881no—
205C8—4881no—
206C8#1451979711yescharacteristic
207C8#1451980311yescharacteristic
208C22—22no—
209C22—41no—
210C22—41no—
211C22—9761no—
212C22—9761no—
213C22—9761no—
214C22#1683999811yescharacteristic
215C4—21no—
216C4—41no—
217C4—9761no—
218C4#1683997711yescharacteristic
219C4#1684002511yescharacteristic
220C4C2×D97611yescharacteristic
221C4#1684019411yescharacteristic
222C2—42no—
223C2—19521no—
224C2#2144525611yescharacteristic
225C2#2144790511yescharacteristic
226C2#2144794911yescharacteristic
subgroupG/H
centerC22#16839998
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingD4×C16×C61C2
socleC22×C61#466
prime radical#21445174C2
hypercenterD4×C16D61
hypocenterC61#12467
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. #21445208C2semidirect
4. #21443891C2semidirect
5. #21443873C2semidirect
6. #21443866C2semidirect
7. D4×C16×C61C2semidirect
110. D4×C16D61semidirect
136. C61#12467semidirect

Maximal subgroups

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

subgroupindex
#214480432
#214452082
#214451742
#214438912
#214438732
#214438662
D4×C16×C612
#1246761