Finite Group Databasebeta

← #29583575

Subgroups — #29583575

Order 15616.

478 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 125 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#21451192C211yesmaximal, characteristic
2#21445978C211yesmaximal, characteristic
3#21445825C212yesmaximal
4C2×#16839492C212yesmaximal
5C61×#1296C211yesmaximal, characteristic
6C2×C4×Dic122C2212yes—
7C2×#14519710—22no—
8C2×#14519702—22no—
9C2×C4×#92418C2211yescharacteristic
10#16839692—22no—
11#16839667—22no—
12#16839661—22no—
13#16839632C2211yescharacteristic
14#16839525—22no—
15#16839492—24no—
16C2×C4⋊C8×C61C2212yes—
17C61×#384C2211yescharacteristic
18C22×Dic122D412yes—
19C22×#92418—21no—
20C4×Dic122—22no—
21C4×Dic122—22no—
22C4×Dic122—22no—
23C4×Dic122—22no—
24C2×C4⋊Dic61—22no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—22no—
27C2×C4⋊Dic61D412yes—
28C2×#11758196—22no—
29C2×C4×Dic61—22no—
30#14519710—44no—
31#14519702—44no—
32C4×#92418—21no—
33C4×#92418D412yes—
34#14519684—24no—
35#14519684—22no—
36C22×C8×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61D412yes—
39C2×C42×C61C2311yescharacteristic
40C4⋊C8×C61—22no—
41C4⋊C8×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61C2×D411yescharacteristic
44C22×C4×C61C2×D412yes—
45C22×Dic61—22no—
46C22×Dic61—22no—
47C22×Dic61—41no—
48C2×Dic122—22no—
49C2×Dic122—22no—
50C2×Dic122—22no—
51C2×Dic122—22no—
52C2×Dic122—22no—
53C2×Dic122Q1614yes—
54C2×C8×C61—42no—
55C2×C8×C61—42no—
56C2×C8×C61—42no—
57C4⋊C4×C61—42no—
58C4⋊C4×C61—42no—
59C4⋊C4×C61—42no—
60C42×C61C2×D411yescharacteristic
61C42×C61#4111yescharacteristic
62C42×C61#4112yes—
63C4⋊Dic61—22no—
64C4⋊Dic61—22no—
65C4⋊Dic61—42no—
66C4⋊Dic61—42no—
67C4⋊Dic61—42no—
68C4⋊Dic61—82no—
69#11758196—42no—
70#11758196—42no—
71C4×Dic61—42no—
72C4×Dic61—42no—
73C2×#92418—22no—
74C2×#92418—22no—
75C2×#92418—22no—
76C23×C61#12011yescharacteristic
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—44no—
80C2×C4×C61—42no—
81C2×C4×C61#12111yescharacteristic
82C2×C4×C61#12112yes—
83C2×C4×C61#12312yes—
84C2×C4×C61#12411yescharacteristic
85C2×C4×C61C2×Q1612yes—
86C2×C4×C61#13512yes—
87C2×C4×C61AGL(1,ℤ/8)12yes—
88C2×C4×C61#13712yes—
89C2×Dic61—24no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—82no—
96C2×Dic61—81no—
97Dic122—24no—
98Dic122—24no—
99Dic122—42no—
100Dic122—42no—
101C8×C61—82no—
102#92418—24no—
103#10439—611nomaximal, Sylow
104C22×C61#39411yescharacteristic
105C22×C61#44912yes—
106C22×C61#45112yes—
107C22×C61#45311yescharacteristic
108C22×C61#45611yescharacteristic
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—82no—
112C4×C61#46712yes—
113C4×C61#46812yes—
114C4×C61#48412yes—
115C4×C61#48512yes—
116Dic61—44no—
117Dic61—82no—
118Dic61—161no—
119#2582—611no—
120#1845—611no—
121#1803—612no—
122C2×Q8⋊C8—612no—
123#1296D6111yescharacteristic
124C2×C61#162011yescharacteristic
125C2×C61#163311yescharacteristic
126C2×C61#164812yes—
127C2×C61#203612yes—
128C2×C61#203911yescharacteristic
129C2×C4×Q8—612no—
130C2×#107—1222no—
131C2×C4⋊C8C2×D6112yes—
132C2×#103—1222no—
133C2×C4×C8—611no—
134#398—1222no—
135#391—1222no—
136#389—1222no—
137#384—611no—
138#384C2×D6111yescharacteristic
139#340—1222no—
140Q8⋊C8—1224no—
141C61#1043911yescharacteristic, complemented, Sylow
142C22×Q8—612no—
143C22×C8—22no—
144C22×C8—1221no—
145C4×Q8—1222no—
146C4×Q8—1222no—
147C4×Q8—1222no—
148C4×Q8—1222no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—1222no—
152C2×C4⋊C4—1222no—
153C2×C4⋊C4—1221no—
154C2×C4⋊C4—1222no—
155C2×C4⋊C4D24412yes—
156C2×C42—1222no—
157C2×C42C22×D6111yescharacteristic
158#107—2444no—
159C4⋊C8—22no—
160C4⋊C8—22no—
161#103—2444no—
162C4×C8—612no—
163C4×C8—1221no—
164#95—1224no—
165#95—1222no—
166C2×Q8—614no—
167C2×Q8—1222no—
168C2×Q8—1222no—
169C2×Q8—1222no—
170C2×Q8—1222no—
171C2×Q8—1222no—
172C22×C4—22no—
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4—2441no—
176C22×C4C2×D24411yescharacteristic
177C22×C4D4×D6112yes—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—1222no—
182C2×C8—1222no—
183C2×C8—1222no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—1222no—
188C4⋊C4—1222no—
189C4⋊C4—4882no—
190C4⋊C4—2442no—
191C4⋊C4—2442no—
192C4⋊C4—2442no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C42—2442no—
196C42—2442no—
197C42#1175822212yes—
198C42D4×D6111yescharacteristic
199C42#1175822611yescharacteristic
200C23#1451974711yescharacteristic
201Q8—1224no—
202Q8—1224no—
203Q8—2442no—
204Q8—2442no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4—1224no—
210C2×C4—4882no—
211C2×C4—4881no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4—2442no—
217C2×C4#1451975012yes—
218C2×C4#1451975211yescharacteristic
219C2×C4#1451976212yes—
220C2×C4#1451976511yescharacteristic
221C2×C4Q16×D6112yes—
222C2×C4#1451979812yes—
223C2×C4#1451980112yes—
224C2×C4#1451980612yes—
225C8—82no—
226C8—1224no—
227C22#1683968011yescharacteristic
228C22#1683990812yes—
229C22#1683991912yes—
230C22#1683993211yescharacteristic
231C22#1683994711yescharacteristic
232C4—21no—
233C4—21no—
234C4—82no—
235C4—9761no—
236C4—4882no—
237C4—2444no—
238C4#1684000212yes—
239C4#1684000712yes—
240C4#1684009912yes—
241C4#1684010612yes—
242C2#2144487911yescharacteristic
243C2#2144496011yescharacteristic
244C2#2144506212yes—
245C2#2144702512yes—
246C2#2144704411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socle, prime radicalC23×C61#120
hypercenter#1296D61
hypocenterC61#10439
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
141. C61#10439semidirect

Maximal subgroups

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

subgroupindex
#214511922
#214459782
#214458252
C2×#168394922
C61×#12962
#1043961