Finite Group Databasebeta

← #29593733

Subgroups — #29593733

Order 15616.

288 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 73 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
1Q8×Dic244C211yesmaximal, characteristic
2#21448047C211yesmaximal, characteristic
3#21447870C211yesmaximal, characteristic
4#21445189C211yesmaximal, characteristic
5#21443876C211yesmaximal, characteristic
6#21443784C211yesmaximal, characteristic
7C61×Q8⋊C16C211yesmaximal, characteristic
8Q8×Dic122—21no—
9C2×Dic488—21no—
10#16840167—21no—
11#16840167C2211yescharacteristic
12#16840142C2211yescharacteristic
13#16840058—22no—
14#16840058—21no—
15#16840047—21no—
16C4×Dic244—21no—
17C4×Dic244C2211yescharacteristic
18#16839567—22no—
19#16839567—21no—
20#16839515C2211yescharacteristic
21#16839509—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—21no—
27C2×Dic244D411yescharacteristic
28#14519777—22no—
29#14519777—21no—
30#14519777—21no—
31#14519776—42no—
32#14519776—41no—
33Q8×Dic61—41no—
34C4×Dic122—22no—
35C4×Dic122—21no—
36Dic488—42no—
37#14519711—22no—
38#14519711—21no—
39#14519711D412yes—
40#14519711D411yescharacteristic
41#14519708—41no—
42C4⋊#92418—21no—
43#14519702—22no—
44#14519702—21no—
45#14519701—41no—
46C4×Q8×C61D411yescharacteristic
47C2×C16×C61—21no—
48C2×C16×C61—21no—
49C4⋊C8×C61—21no—
50C4⋊C8×C61D411yescharacteristic
51C4×C8×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×Q8×C61D811yescharacteristic
54C2×Dic122—21no—
55C2×Dic122—41no—
56C2×Dic122—42no—
57C2×Dic122—41no—
58C2×C8×C61—21no—
59C2×C8×C61C2×D411yescharacteristic
60C2×C8×C61C2×D411yescharacteristic
61C4⋊C4×C61—21no—
62C4⋊C4×C61D811yescharacteristic
63C42×C61—21no—
64C42×C61C2×D411yescharacteristic
65C4⋊Dic61—22no—
66C4⋊Dic61—21no—
67C4⋊Dic61—42no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70C4⋊Dic61—41no—
71#11758196—42no—
72#11758196—41no—
73C4×Dic61—42no—
74C4×Dic61—41no—
75C2×#92418—41no—
76Dic244—21no—
77Dic244—42no—
78Dic244—41no—
79Dic244—41no—
80Dic244SD1612yes—
81C16×C61—41no—
82C16×C61—41no—
83Q8×C61—21no—
84Q8×C61Q3212yescomplemented
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61#12011yescharacteristic
88C2×C4×C61C2×D811yescharacteristic
89C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
90C2×Dic61—41no—
91C2×Dic61—42no—
92C2×Dic61—41no—
93C2×Dic61—81no—
94Dic122—22no—
95Dic122—41no—
96Dic122—81no—
97Dic122—81no—
98Dic122—161no—
99Dic122—162no—
100C8×C61—21no—
101C8×C61—41no—
102C8×C61C2×SD1611yescharacteristic
103C8×C61#13711yescharacteristic
104#92418—81no—
105#12358—611nomaximal, Sylow
106C22×C61#44711yescharacteristic
107C4×C61—22no—
108C4×C61—21no—
109C4×C61—41no—
110C4×C61#44811yescharacteristic
111C4×C61#45411yescharacteristic
112C4×C61C2×Q3211yescharacteristic
113C4×C61#51011yescharacteristic
114Dic61—42no—
115Dic61—82no—
116Dic61—81no—
117Dic61—161no—
118Q8×Q16—611no—
119#2241—611no—
120#2209—611no—
121#1670—611no—
122#1365—611no—
123Q8⋊C16D6111yescharacteristic
124#1332—611no—
125C2×C61#162711yescharacteristic
126C2×C61#218811yescharacteristic
127C2×C61#219411yescharacteristic
128Q82—1221no—
129C2×Q32—1221no—
130#500—611no—
131#500—1221no—
132#494—611no—
133#477—1222no—
134#477—1221no—
135#475—1221no—
136C8×Q8C2×D6111yescharacteristic
137C4×Q16—611no—
138C4×Q16—1221no—
139C4⋊C16C2×D6111yescharacteristic
140#358—1221no—
141#358—1222no—
142C4×C16C2×D6111yescharacteristic
143#335—611no—
144#332—1221no—
145C61#1235811yescharacteristic, complemented, Sylow
146C2×Q16—611no—
147C2×Q16—1221no—
148C2×Q16—1221no—
149C4⋊Q8—1222no—
150C4⋊Q8—1221no—
151C4⋊Q8—1221no—
152C4⋊Q8—2442no—
153C4⋊Q8—2441no—
154C4×Q8—1222no—
155C4×Q8—1221no—
156C4×Q8—2441no—
157C4×Q8D24411yescharacteristic
158Q32—2442no—
159C2×C16—21no—
160C2×C16—21no—
161#107—611no—
162#107—612no—
163#107—1222no—
164#107—1221no—
165#106—2441no—
166C4⋊C8—21no—
167C4⋊C8—1221no—
168C4⋊C8D24411yescharacteristic
169#103—1222no—
170#103—1221no—
171#103—2441no—
172C4×C8—21no—
173C4×C8C22×D6111yescharacteristic
174C2×Q8—1221no—
175C2×Q8—2442no—
176C2×Q8—2441no—
177C2×Q8—2441no—
178C2×Q8D48811yescharacteristic
179Q16—612no—
180Q16—1221no—
181Q16—2442no—
182Q16—2441no—
183Q16—2441no—
184C2×C8—21no—
185C2×C8—2441no—
186C2×C8D4×D6111yescharacteristic
187C2×C8D4×D6111yescharacteristic
188C4⋊C4—21no—
189C4⋊C4—1222no—
190C4⋊C4—1221no—
191C4⋊C4—2442no—
192C4⋊C4—2442no—
193C4⋊C4—2441no—
194C4⋊C4—2441no—
195C4⋊C4—2441no—
196C4⋊C4—2441no—
197C4⋊C4D48811yescharacteristic
198C42—21no—
199C42—2442no—
200C42—2441no—
201C42C2×D24411yescharacteristic
202C16—41no—
203C16—41no—
204Q8—21no—
205Q8—1222no—
206Q8—9761no—
207Q8—9762no—
208Q8—4881no—
209Q8—4881no—
210Q8—2441no—
211Q8Dic48812yescomplemented
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—4881no—
215C2×C4—2442no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4#1451974711yescharacteristic
219C2×C4C2×D48811yescharacteristic
220C2×C4#1451980511yescharacteristic
221C8—21no—
222C8—41no—
223C8—4881no—
224C8SD16×D6111yescharacteristic
225C8#1451980911yescharacteristic
226C22#1683989811yescharacteristic
227C4—22no—
228C4—21no—
229C4—41no—
230C4—9761no—
231C4—4882no—
232C4—4881no—
233C4—2442no—
234C4#1683990211yescharacteristic
235C4#1683993611yescharacteristic
236C4C2×Dic48811yescharacteristic
237C4#1684020511yescharacteristic
238C2#2144492411yescharacteristic
239C2#2144775511yescharacteristic
240C2#2144779211yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socle, prime radicalC22×C61#447
hypercenterQ8⋊C16D61
hypocenterC61#12358
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
84. Q8×C61Q32semidirect
145. C61#12358semidirect
211. Q8Dic488semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic2442
#214480472
#214478702
#214451892
#214438762
#214437842
C61×Q8⋊C162
#1235861