Finite Group Databasebeta

← #29583571

Subgroups — #29583571

Order 15616.

478 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 133 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#21445978C211yesmaximal, characteristic
2#21445824C212yesmaximal
3C2×Q8⋊#92418C212yesmaximal
4#21443702C211yesmaximal, characteristic
5C61×#2582C211yesmaximal, characteristic
6C2×#14519710—22no—
7C2×C4⋊#92418C2212yes—
8C2×#14519701—22no—
9C2×C4×#92418C2211yescharacteristic
10#16839632C2211yescharacteristic
11#16839524—22no—
12Q8⋊#92418—24no—
13C2×C4×Q8×C61C2212yes—
14C61×#398—22no—
15C61×#391—22no—
16C61×#389—22no—
17C61×#384C2211yescharacteristic
18C22×#92418—21no—
19C22×#92418—22no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61—21no—
22#14519710—44no—
23C4⋊#92418—22no—
24C4⋊#92418—22no—
25#14519701—44no—
26C4×#92418—21no—
27C4×#92418D412yes—
28C22×Q8×C61D412yes—
29C4×Q8×C61—22no—
30C4×Q8×C61—22no—
31C4×Q8×C61—22no—
32C4×Q8×C61—22no—
33C2×C4⋊C4×C61—22no—
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61—22no—
36C2×C4⋊C4×C61D412yes—
37C2×C4⋊C4×C61D412yes—
38C2×C42×C61—22no—
39C2×C42×C61C2311yescharacteristic
40#95×C61—24no—
41#95×C61—22no—
42C2×Q8×C61—22no—
43C2×Q8×C61—22no—
44C2×Q8×C61—22no—
45C2×Q8×C61—22no—
46C2×Q8×C61—22no—
47C2×Q8×C61Q1614yes—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61C2×D411yescharacteristic
52C22×C4×C61C2×D412yes—
53C22×Dic61—41no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—42no—
57C4⋊C4×C61—42no—
58C4⋊C4×C61—42no—
59C4⋊C4×C61—42no—
60C4⋊C4×C61—42no—
61C4⋊C4×C61—82no—
62C42×C61—42no—
63C42×C61—42no—
64C42×C61C2×D411yescharacteristic
65C42×C61#4111yescharacteristic
66C42×C61#4112yes—
67C4⋊Dic61—42no—
68C4⋊Dic61—42no—
69C4⋊Dic61—42no—
70C2×#92418—22no—
71C2×#92418—22no—
72C2×#92418—22no—
73C2×#92418—42no—
74C2×#92418—42no—
75C2×#92418—42no—
76C23×C61#12011yescharacteristic
77Q8×C61—24no—
78Q8×C61—24no—
79Q8×C61—42no—
80Q8×C61—42no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—24no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61—44no—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61#12111yescharacteristic
92C2×C4×C61#12112yes—
93C2×C4×C61#12312yes—
94C2×C4×C61#12411yescharacteristic
95C2×C4×C61C2×Q1612yes—
96C2×C4×C61#13512yes—
97C2×C4×C61AGL(1,ℤ/8)12yes—
98C2×C4×C61#13712yes—
99C2×Dic61—82no—
100C2×Dic61—81no—
101#92418—24no—
102#92418—82no—
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—44no—
112C4×C61—82no—
113C4×C61—82no—
114C4×C61#46712yes—
115C4×C61#46812yes—
116C4×C61#48412yes—
117C4×C61#48512yes—
118Dic61—161no—
119#2582D6111yescharacteristic
120#1845—611no—
121#1803—612no—
122C2×Q8⋊C8—612no—
123#1296—611no—
124C2×C61#162011yescharacteristic
125C2×C61#163311yescharacteristic
126C2×C61#164812yes—
127C2×C61#203612yes—
128C2×C61#203911yescharacteristic
129C2×C4×Q8C2×D6112yes—
130C2×#107—1222no—
131C2×C4⋊C8—612no—
132C2×#103—1222no—
133C2×C4×C8—611no—
134#398—22no—
135#391—22no—
136#389—22no—
137#384—611no—
138#384C2×D6111yescharacteristic
139#340—1222no—
140Q8⋊C8—1224no—
141C61#1043911yescharacteristic, complemented, Sylow
142C22×Q8C22⋊D6112yes—
143C22×C8—1221no—
144C22×C8—1222no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—1222no—
153C2×C4⋊C4—1221no—
154C2×C4⋊C4C22⋊D6112yes—
155C2×C4⋊C4C22⋊D6112yes—
156C2×C42—22no—
157C2×C42C22×D6111yescharacteristic
158#107—2444no—
159C4⋊C8—1222no—
160C4⋊C8—1222no—
161#103—2444no—
162C4×C8—612no—
163C4×C8—1221no—
164#95—24no—
165#95—22no—
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8—22no—
171C2×Q8#1175820214yes—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—2441no—
176C22×C4C2×C22⋊D6111yescharacteristic
177C22×C4C2×C22⋊D6112yes—
178C2×C8—1222no—
179C2×C8—1222no—
180C2×C8—1222no—
181C2×C8—2442no—
182C2×C8—2442no—
183C2×C8—2442no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—82no—
192C4⋊C4—2442no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C42—42no—
196C42—42no—
197C42D4×D6111yescharacteristic
198C42#1175822411yescharacteristic
199C42#1175822412yes—
200C23#1451974611yescharacteristic
201Q8—24no—
202Q8—24no—
203Q8—42no—
204Q8—42no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—24no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—44no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—4882no—
216C2×C4—4881no—
217C2×C4#1451974811yescharacteristic
218C2×C4#1451974912yes—
219C2×C4#1451975812yes—
220C2×C4#1451976411yescharacteristic
221C2×C4C2×#1175820212yes—
222C2×C4#1451979712yes—
223C2×C4#1451980212yes—
224C2×C4#1451980812yes—
225C8—1224no—
226C8—4882no—
227C22#1683967611yescharacteristic
228C22#1683990712yes—
229C22#1683991812yes—
230C22#1683993011yescharacteristic
231C22#1683994511yescharacteristic
232C4—21no—
233C4—21no—
234C4—44no—
235C4—82no—
236C4—82no—
237C4—9761no—
238C4#1684000112yes—
239C4#1684001012yes—
240C4#1684009512yes—
241C4#1684010012yes—
242C2#2144487811yescharacteristic
243C2#2144495911yescharacteristic
244C2#2144506112yes—
245C2#2144701912yes—
246C2#2144704011yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2582C2
socle, prime radicalC23×C61#120
hypercenter#2582D61
hypocenterC61#10439
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2582

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
#214459782
#214458242
C2×Q8⋊#924182
#214437022
C61×#25822
#1043961