Finite Group Databasebeta

← #29593921

Subgroups — #29593921

Order 15616.

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

normal subgroups only

This group has 282 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#21458825C211yesmaximal, characteristic
2#21448047C211yesmaximal, characteristic
3#21447972C211yesmaximal, characteristic
4#21445223C211yesmaximal, characteristic
5#21443869C211yesmaximal, characteristic
6#21443784C211yesmaximal, characteristic
7C61×Q8⋊C16C211yesmaximal, characteristic
8#16840491—21no—
9#16840167C2211yescharacteristic
10#16840142—21no—
11#16840142C2211yescharacteristic
12#16840057—21no—
13#16839973—22no—
14#16839973—21no—
15C4×Dic244—21no—
16C4×Dic244C2211yescharacteristic
17#16839588—21no—
18#16839567—21no—
19#16839567—22no—
20#16839515C2211yescharacteristic
21#16839510—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—22no—
27C2×Dic244D411yescharacteristic
28C2×Dic244D412yes—
29#14519777—22no—
30#14519777—21no—
31#14519777—21no—
32#14519768—42no—
33#14519768—41no—
34Q8×Dic61—41no—
35C4×Dic122—22no—
36C4×Dic122—21no—
37#14519711—21no—
38#14519711—21no—
39#14519711D411yescharacteristic
40#14519710—41no—
41C4⋊#92418—21no—
42#14519702—22no—
43#14519702—21no—
44#14519701—41no—
45C4×Q8×C61D411yescharacteristic
46C2×C16×C61—21no—
47C2×C16×C61—21no—
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50C4×C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61D811yescharacteristic
53C2×Dic122—21no—
54C2×Dic122—22no—
55C2×Dic122—41no—
56C2×C8×C61—21no—
57C2×C8×C61C2×D411yescharacteristic
58C2×C8×C61C2×D411yescharacteristic
59C4⋊C4×C61—21no—
60C4⋊C4×C61D811yescharacteristic
61C42×C61—21no—
62C42×C61C2×D411yescharacteristic
63C4⋊Dic61—21no—
64C4⋊Dic61—42no—
65C4⋊Dic61—42no—
66C4⋊Dic61—41no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70#11758196—42no—
71#11758196—41no—
72C4×Dic61—42no—
73C4×Dic61—41no—
74C2×#92418—41no—
75Dic244—21no—
76Dic244—21no—
77Dic244—42no—
78Dic244—41no—
79Dic244—41no—
80Dic244—82no—
81C16×C61—41no—
82C16×C61—41no—
83Q8×C61—21no—
84Q8×C61Q3212yes—
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—41no—
95Dic122—42no—
96Dic122—42no—
97Dic122—41no—
98Dic122—161no—
99C8×C61—21no—
100C8×C61—41no—
101C8×C61#13511yescharacteristic
102C8×C61#13711yescharacteristic
103#92418—81no—
104#12386—611nomaximal, Sylow
105C22×C61#44711yescharacteristic
106C4×C61—22no—
107C4×C61—21no—
108C4×C61—41no—
109C4×C61#45211yescharacteristic
110C4×C61#45511yescharacteristic
111C4×C61C2×Q3211yescharacteristic
112C4×C61#51011yescharacteristic
113Dic61—81no—
114Dic61—82no—
115Dic61—81no—
116Dic61—161no—
117#3395—611no—
118#2241—611no—
119#2227—611no—
120#1676—611no—
121#1362—611no—
122Q8⋊C16D6111yescharacteristic
123#1332—611no—
124C2×C61#164111yescharacteristic
125C2×C61#218811yescharacteristic
126C2×C61#219311yescharacteristic
127#557—1221no—
128#500—611no—
129#494—611no—
130#494—1221no—
131#477—1221no—
132#462—1222no—
133#462—1221no—
134C8×Q8C2×D6111yescharacteristic
135C4×Q16—611no—
136C4×Q16—1221no—
137#366—1221no—
138C4⋊C16C2×D6111yescharacteristic
139#358—1221no—
140#358—1222no—
141C4×C16C2×D6111yescharacteristic
142#335—611no—
143#333—1221no—
144C61#1238611yescharacteristic, complemented, Sylow
145C2×Q16—611no—
146C2×Q16—612no—
147C2×Q16—1222no—
148C2×Q16—1221no—
149C4⋊Q8—1222no—
150C4⋊Q8—1221no—
151C4⋊Q8—1221no—
152#125—2442no—
153#125—2441no—
154C4×Q8—1222no—
155C4×Q8—1221no—
156C4×Q8—2441no—
157C4×Q8D24411yescharacteristic
158C2×C16—21no—
159C2×C16—21no—
160#107—611no—
161#107—1221no—
162#107—1221no—
163#107—2441no—
164C4⋊C8—21no—
165C4⋊C8—1221no—
166C4⋊C8D24411yescharacteristic
167#103—1222no—
168#103—1221no—
169#103—2441no—
170C4×C8—21no—
171C4×C8C22×D6111yescharacteristic
172C2×Q8—1221no—
173C2×Q8—1222no—
174C2×Q8—2441no—
175C2×Q8D48811yescharacteristic
176Q16—1221no—
177Q16—1221no—
178Q16—4882no—
179Q16—2442no—
180Q16—2441no—
181Q16—2441no—
182C2×C8—21no—
183C2×C8—2441no—
184C2×C8D4×D6111yescharacteristic
185C2×C8D4×D6111yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—1221no—
188C4⋊C4—2442no—
189C4⋊C4—2442no—
190C4⋊C4—2442no—
191C4⋊C4—2441no—
192C4⋊C4—2441no—
193C4⋊C4—2441no—
194C4⋊C4—2441no—
195C4⋊C4—2441no—
196C4⋊C4D48811yescharacteristic
197C42—21no—
198C42—2442no—
199C42—2441no—
200C42C2×D24411yescharacteristic
201C16—41no—
202C16—41no—
203Q8—21no—
204Q8—9761no—
205Q8—2441no—
206Q8—2442no—
207Q8—2441no—
208Q8—2442no—
209Q8Dic48812yes—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—4881no—
213C2×C4—2441no—
214C2×C4—2442no—
215C2×C4—2441no—
216C2×C4#1451974711yescharacteristic
217C2×C4C2×D48811yescharacteristic
218C2×C4#1451980511yescharacteristic
219C8—21no—
220C8—41no—
221C8—4881no—
222C8#1451979811yescharacteristic
223C8#1451980911yescharacteristic
224C22#1683989811yescharacteristic
225C4—22no—
226C4—21no—
227C4—41no—
228C4—9761no—
229C4—4881no—
230C4—4881no—
231C4—4882no—
232C4#1683992711yescharacteristic
233C4#1683994111yescharacteristic
234C4C2×Dic48811yescharacteristic
235C4#1684020511yescharacteristic
236C2#2144501411yescharacteristic
237C2#2144775511yescharacteristic
238C2#2144778511yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socle, prime radicalC22×C61#447
hypercenterQ8⋊C16D61
hypocenterC61#12386
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
144. C61#12386semidirect

Maximal subgroups

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

subgroupindex
#214588252
#214480472
#214479722
#214452232
#214438692
#214437842
C61×Q8⋊C162
#1238661