Finite Group Databasebeta

← #29594451

Subgroups — #29594451

Order 15616.

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

normal subgroups only

This group has 224 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#21448047C211yesmaximal, characteristic, complemented
2#21445208C211yesmaximal, characteristic
3#21445184C211yesmaximal, characteristic
4#21443893C211yesmaximal, characteristic, complemented
5#21443873C211yesmaximal, characteristic, complemented
6#21443869C211yesmaximal, characteristic, complemented
7D4×C16×C61C211yesmaximal, characteristic
8#16840167C2211yescharacteristic
9#16840142C2211yescharacteristic
10#16840042—21no—
11#16839967—21no—
12#16839567—21no—
13#16839567—21no—
14#16839515C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839509—21no—
17#16839507—21no—
18C22×C16×C61—21no—
19C8×D4×C61C2211yescharacteristic
20C61×C4⋊C16C2211yescharacteristic
21C61×C22⋊C16—21no—
22C4×C16×C61C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×#11758200—41no—
26#14519777—21no—
27#14519777—21no—
28#14519711—21no—
29#14519711—21no—
30#14519710—41no—
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33#14519700—41no—
34#14519698—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×Dic122—41no—
47C2×Dic122—41no—
48C2×C8×C61—21no—
49C2×C8×C61—41no—
50C2×C8×C61—41no—
51C2×C8×C61C2×D411yescharacteristic
52C2×C8×C61#4111yescharacteristic
53C4⋊C4×C61D811yescharacteristic
54C22⋊C4×C61—21no—
55C42×C61C2×D411yescharacteristic
56#11758200—82no—
57C4⋊Dic61—41no—
58C4⋊Dic61—41no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61C2×#92418—41no—
62C2×#92418—41no—
63Dic244—41no—
64Dic244—41no—
65Dic244—81no—
66C16×C61—21no—
67C16×C61—21no—
68C16×C61—41no—
69C23×C61—21no—
70D4×C61—21no—
71D4×C61SD3212yes—
72C2×C4×C61—21no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61#12111yescharacteristic
76C2×C4×C61C2×D811yescharacteristic
77C2×C4×C61#13511yescharacteristic
78C2×Dic61—81no—
79C2×Dic61—81no—
80Dic122—81no—
81Dic122—81no—
82Dic122—81no—
83Dic122—81no—
84C8×C61—21no—
85C8×C61—41no—
86C8×C61#13511yescharacteristic
87C8×C61AGL(1,ℤ/8)11yescharacteristic
88#92418—81no—
89#92418—81no—
90#12470—611nomaximal, Sylow
91C22×C61—22no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61#46611yescharacteristic
95C4×C61—21no—
96C4×C61—41no—
97C4×C61#46311yescharacteristic
98C4×C61#47111yescharacteristic
99C4×C61C2×SD3211yescharacteristic
100C4×C61#50811yescharacteristic
101Dic61—161no—
102Dic61—161no—
103#2241—611no—
104D4×C16D6111yescharacteristic
105#1673—611no—
106#1669—611no—
107#1372—611no—
108#1364—611no—
109#1362—611no—
110C2×C61—42no—
111C2×C61#168111yescharacteristic
112C2×C61#221711yescharacteristic
113C2×C61#222211yescharacteristic
114C22×C16—21no—
115#500—611no—
116#494—611no—
117#474—1221no—
118#461—1221no—
119C8×D4C2×D6111yescharacteristic
120C4⋊C16C2×D6111yescharacteristic
121#358—1221no—
122#358—1221no—
123C22⋊C16—21no—
124C4×C16C2×D6111yescharacteristic
125#335—611no—
126#335—611no—
127#332—1221no—
128#332—1221no—
129C61#1247011yescharacteristic, complemented, Sylow
130C2×Q16—1221no—
131C2×Q16—1221no—
132C2×SD16—2441no—
133C22×C8—21no—
134C4⋊Q8—1221no—
135C4⋊Q8—1221no—
136C4×D4D24411yescharacteristic
137C2×C16—21no—
138C2×C16—42no—
139C2×C16C22⋊D6111yescharacteristic
140C2×C16C22⋊D6111yescharacteristic
141#107—1221no—
142#107—1221no—
143#107—2441no—
144C4⋊C8—1221no—
145C4⋊C8—1221no—
146C4⋊C8D24411yescharacteristic
147#103—2441no—
148#102—2441no—
149C22⋊C8—21no—
150C4×C8C22×D6111yescharacteristic
151C2×Q8—2441no—
152C2×Q8—2441no—
153C2×D4D48811yescharacteristic
154C22×C4—21no—
155Q16—4881no—
156Q16—2441no—
157Q16—2441no—
158SD16—4882no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—2441no—
163C2×C8—2441no—
164C2×C8#1175822211yescharacteristic
165C2×C8C2×C22⋊D6111yescharacteristic
166C4⋊C4—2441no—
167C4⋊C4—2441no—
168C4⋊C4—2441no—
169C4⋊C4—2441no—
170C4⋊C4D48811yescharacteristic
171C22⋊C4—21no—
172C42C2×D24411yescharacteristic
173C16—21no—
174C16—21no—
175C16—41no—
176C23—21no—
177Q8—4881no—
178Q8—4881no—
179Q8—4881no—
180Q8—4881no—
181D4—21no—
182D4#1451972212yes—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—4881no—
187C2×C4—4881no—
188C2×C4#1451975111yescharacteristic
189C2×C4C2×D48811yescharacteristic
190C2×C4#1451979911yescharacteristic
191C8—21no—
192C8—41no—
193C8—4881no—
194C8—4881no—
195C8#1451979711yescharacteristic
196C8#1451980311yescharacteristic
197C22—22no—
198C22—41no—
199C22—41no—
200C22#1683999811yescharacteristic
201C4—21no—
202C4—41no—
203C4—9761no—
204C4—9761no—
205C4#1683997711yescharacteristic
206C4#1684002511yescharacteristic
207C4C2×#1451972211yescharacteristic
208C4#1684019411yescharacteristic
209C2—42no—
210C2#2144525611yescharacteristic
211C2#2144791511yescharacteristic
212C2#2144794411yescharacteristic
subgroupG/H
centerC22#16839998
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingD4×C16×C61C2
socleC22×C61#466
prime radicalC2×D4×C61D8
hypercenterD4×C16D61
hypocenterC61#12470
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. #21448047C2semidirect
4. #21443893C2semidirect
5. #21443873C2semidirect
6. #21443869C2semidirect
129. C61#12470semidirect

Maximal subgroups

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

subgroupindex
#214480472
#214452082
#214451842
#214438932
#214438732
#214438692
D4×C16×C612
#1247061