Finite Group Databasebeta

← #30605721

Subgroups — #30605721

Order 15616.

268 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 64 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#21462192C211yesmaximal, characteristic
2#21462162C211yesmaximal, characteristic
3#21460839C212yesmaximal, complemented
4#21460828C212yesmaximal, complemented
5#21456472C211yesmaximal, characteristic
6C2×#14519851—21no—
7#16840685—21no—
8#16840685C2212yes—
9#16840685C2212yes—
10#16840658—21no—
11#16840654—21no—
12#16840374C411yescharacteristic
13#16840161C2211yescharacteristic
14#16840141C2211yescharacteristic
15#16840132C411yescharacteristic
16#16840130C411yescharacteristic
17#16840018—21no—
18#16840001—21no—
19#16839867—21no—
20C4×#11758202—21no—
21#16839718C2211yescharacteristic
22C61×#541C411yescharacteristic
23#14519851—22no—
24#14519851—22no—
25#14519851—41no—
26C2×#11758187—41no—
27C2×#11758202—21no—
28C2×#11758202—21no—
29C2×#11758194D411yescharacteristic
30C22×#92418D411yescharacteristic
31#14519777C2×C411yescharacteristic
32#14519770—41no—
33#14519769C2×C411yescharacteristic
34#14519767—41no—
35#14519756—21no—
36C4×Dic122—21no—
37#14519710—21no—
38#14519708—21no—
39#14519701—21no—
40#14519701—21no—
41#14519700—21no—
42#14519700—21no—
43#14519688C2×C411yescharacteristic
44#14519688D411yescharacteristic
45C4×#92418D411yescharacteristic
46C4×#92418C2311yescharacteristic
47C4⋊Q8×C61C2×C411yescharacteristic
48#126×C61—41no—
49#125×C61—41no—
50#125×C61C2×C411yescharacteristic
51C22⋊Q8×C61—21no—
52C4×Q8×C61—21no—
53#117×C61C2×C411yescharacteristic
54C2×Q8×C61—21no—
55C22×C4×C61C22⋊C411yescharacteristic
56C2×Dic122—21no—
57C4⋊C4×C61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C4⋊C4×C61—41no—
62C4⋊C4×C61—41no—
63C22⋊C4×C61—21no—
64C22⋊C4×C61—41no—
65C42×C61—41no—
66C42×C61C22⋊C411yescharacteristic
67C42×C61C22×C411yescharacteristic
68C22⋊Dic61—41no—
69#11758202—42no—
70#11758202—41no—
71#11758202—41no—
72C4⋊Dic61—21no—
73C4⋊Dic61—41no—
74#11758196—41no—
75#11758196—41no—
76#11758196—41no—
77C4×Dic61—41no—
78#11758194—22no—
79C2×#92418—21no—
80C2×#92418—21no—
81C2×#92418C22⋊C411yescharacteristic
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84C2×#92418C2×D411yescharacteristic
85#11758187—42no—
86#11758187—42no—
87C23×C61#10011yescharacteristic
88Q8×C61—41no—
89Q8×C61—41no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61#10011yescharacteristic
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C2×Dic61—41no—
99C2×Dic61—41no—
100Dic122—41no—
101Dic122—41no—
102#92418—21no—
103#92418—21no—
104#92418#13512yes—
105#92418AGL(1,ℤ/8)11yescharacteristic
106#92418#13711yescharacteristic
107#11990—611nomaximal, Sylow
108C22×C61—21no—
109C22×C61—41no—
110C22×C61C2×#10011yescharacteristic
111C4×C61—21no—
112C4×C61—41no—
113C4×C61—41no—
114C4×C61—81no—
115C4×C61—81no—
116C4×C61#41611yescharacteristic
117C4×C61#41711yescharacteristic
118Dic61—81no—
119Dic61—81no—
120#3177—611no—
121#2166—611no—
122#2153—611no—
123#1366—612no—
124#1358—612no—
125C2×C61—21no—
126C2×C61—41no—
127C2×C61#155111yescharacteristic
128#541—611no—
129#541#692311yescharacteristic
130C2×M32—1221no—
131#499—611no—
132#494—611no—
133#491—611no—
134#491—611no—
135#470—1221no—
136#467—1221no—
137#441—1221no—
138C4×Q16—1221no—
139#405—611no—
140#364—612no—
141#364—612no—
142#364—1221no—
143#349—1221no—
144#347—1221no—
145C61#1199011yescharacteristic, complemented, Sylow
146C2×Q16—1221no—
147C2×Q16—1221no—
148C2×M16—611no—
149C22×C8—611no—
150C4⋊Q8—611no—
151C4⋊Q8C2×#692311yescharacteristic
152#126—41no—
153#126—2441no—
154#125—41no—
155#125—611no—
156#125—2441no—
157#125C2×#692311yescharacteristic
158C22⋊Q8—21no—
159C22⋊Q8—1221no—
160C4×Q8—21no—
161C4×Q8—1221no—
162#117C2×#692311yescharacteristic
163M32—1222no—
164M32—1222no—
165M32—2441no—
166C2×C16—2441no—
167#107—1221no—
168#106—1221no—
169#103—1221no—
170#103—1221no—
171#103—1221no—
172#103—1221no—
173#97—611no—
174#97—611no—
175C4×C8—611no—
176C4×C8—611no—
177C2×Q8—21no—
178C2×Q8—1221no—
179C22×C4C22⋊#692311yescharacteristic
180Q16—2442no—
181Q16—2441no—
182Q16—2441no—
183M16—1222no—
184C2×C8—611no—
185C2×C8—611no—
186C2×C8—611no—
187C2×C8—611no—
188C2×C8—1221no—
189C2×C8—1221no—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—1221no—
197C4⋊C4—2441no—
198C4⋊C4—2441no—
199C4⋊C4—2441no—
200C4⋊C4—2441no—
201C22⋊C4—21no—
202C22⋊C4—41no—
203C22⋊C4—2441no—
204C42—41no—
205C42—2441no—
206C42C22⋊#692311yescharacteristic
207C42C22×#692311yescharacteristic
208C16—2442no—
209C16—2442no—
210C23#1451983711yescharacteristic
211Q8—41no—
212Q8—41no—
213Q8—2441no—
214Q8—2441no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4#1451983711yescharacteristic
224C2×C4C2×C22⋊#692311yescharacteristic
225C8—612no—
226C8—611no—
227C8—611no—
228C8—1221no—
229C8—1221no—
230C22—21no—
231C22—41no—
232C22C2×#1451983711yescharacteristic
233C4—21no—
234C4—41no—
235C4—41no—
236C4—81no—
237C4—81no—
238C4—4881no—
239C4—4881no—
240C4#1684075211yescharacteristic
241C4#1684075311yescharacteristic
242C2—21no—
243C2—41no—
244C2#2146133811yescharacteristic
subgroupG/H
centerC2#21461338
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#541C4
socleC2×C61#1551
prime radicalC23×C61#100
cosocleC4×#92418C23
hypercenter#541#6923
hypocenterC61#11990
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
3. #21460839C2semidirect
4. #21460828C2semidirect
145. C61#11990semidirect

Maximal subgroups

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

subgroupindex
#214621922
#214621622
#214608392
#214608282
#214564722
#1199061