Finite Group Databasebeta

← #29582367

Subgroups — #29582367

Order 15616.

560 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#16840057C212yesmaximal
2#21446620C211yesmaximal, characteristic
3C2×Q8⋊#92418C212yesmaximal
4#21443702C211yesmaximal, characteristic
5C61×#2582C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7#16840057—24no—
8#16840057—24no—
9C2×#14519710—22no—
10C2×C4⋊#92418C2212yes—
11C2×#14519701—22no—
12C2×#14519700—22no—
13C2×C4×#92418C2211yescharacteristic
14Q8⋊#92418—24no—
15C2×C4×Q8×C61C2212yes—
16C61×#398—22no—
17C61×#391—22no—
18C61×#389—22no—
19C61×#384C2211yescharacteristic
20C22×Dic122—21no—
21C22×#92418—21no—
22C22×#92418—22no—
23#14519777—22no—
24#14519777—21no—
25#14519777D412yes—
26C2×C4⋊Dic61—22no—
27#14519710—28no—
28C4⋊#92418—22no—
29C4⋊#92418D414yes—
30#14519701—28no—
31#14519700—44no—
32C4×#92418—22no—
33C22×Q8×C61D412yes—
34C4×Q8×C61—22no—
35C4×Q8×C61—22no—
36C4×Q8×C61—22no—
37C4×Q8×C61—22no—
38C2×C4⋊C4×C61—22no—
39C2×C4⋊C4×C61—22no—
40C2×C4⋊C4×C61—22no—
41C2×C4⋊C4×C61D412yes—
42C2×C4⋊C4×C61D412yes—
43C2×C42×C61—22no—
44C2×C42×C61C2311yescharacteristic
45#95×C61—24no—
46#95×C61—22no—
47C2×Q8×C61—22no—
48C2×Q8×C61—22no—
49C2×Q8×C61—22no—
50C2×Q8×C61—22no—
51C2×Q8×C61—22no—
52C2×Q8×C61Q1614yes—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D412yes—
58C22×Dic61—41no—
59C2×Dic122—22no—
60C2×Dic122—42no—
61C2×Dic122—42no—
62C2×Dic122—41no—
63C4⋊C4×C61—22no—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—42no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—42no—
68C4⋊C4×C61—42no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—82no—
71C42×C61—42no—
72C42×C61—42no—
73C42×C61C2×D411yescharacteristic
74C42×C61C2×D412yes—
75C42×C61#4111yescharacteristic
76C4⋊Dic61—24no—
77C4⋊Dic61—42no—
78C2×#92418—22no—
79C2×#92418—24no—
80C2×#92418—41no—
81C2×#92418—41no—
82C2×#92418—42no—
83C2×#92418—42no—
84C23×C61#12011yescharacteristic
85Q8×C61—24no—
86Q8×C61—24no—
87Q8×C61—42no—
88Q8×C61—42no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—24no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—44no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61#12012yes—
100C2×C4×C61#12111yescharacteristic
101C2×C4×C61#12112yes—
102C2×C4×C61#12711yescharacteristic
103C2×C4×C61C2×Q1612yes—
104C2×C4×C61#13512yes—
105C2×C4×C61#13712yes—
106C2×C4×C61#13712yes—
107C2×Dic61—42no—
108C2×Dic61—81no—
109C2×Dic61—81no—
110Dic122—44no—
111Dic122—82no—
112#92418—42no—
113#92418—44no—
114#10237—611nomaximal, Sylow
115C22×C61#39211yescharacteristic
116C22×C61#45112yes—
117C22×C61#45212yes—
118C22×C61#45311yescharacteristic
119C22×C61#45411yescharacteristic
120C4×C61—21no—
121C4×C61—21no—
122C4×C61—44no—
123C4×C61—82no—
124C4×C61—82no—
125C4×C61#45112yes—
126C4×C61#45212yes—
127C4×C61#46712yes—
128C4×C61#47012yes—
129Dic61—82no—
130C2×#477—612no—
131#2582D6111yescharacteristic
132#1956—611no—
133C2×Q8⋊C8—612no—
134#1296—611no—
135C2×C61#163011yescharacteristic
136C2×C61#163311yescharacteristic
137C2×C61#163612yes—
138C2×C61#200112yes—
139C2×C61#200611yescharacteristic
140C2×C4⋊Q8—611no—
141C2×C4×Q8C2×D6112yes—
142#477—1224no—
143#477—1224no—
144C2×#107—1222no—
145C2×C4⋊C8—612no—
146C2×#103—1222no—
147C2×#103—1222no—
148C2×C4×C8—611no—
149#398—22no—
150#391—22no—
151#389—22no—
152#384C2×D6111yescharacteristic
153Q8⋊C8—1224no—
154C61#1023711yescharacteristic, complemented, Sylow
155C22×Q8—1221no—
156C22×Q8C22⋊D6112yes—
157C22×C8—1221no—
158C22×C8—1222no—
159C4⋊Q8—612no—
160C4⋊Q8—1222no—
161C4⋊Q8—1221no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×Q8—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—1222no—
170C2×C4⋊C4C22⋊D6112yes—
171C2×C4⋊C4C22⋊D6112yes—
172C2×C42—22no—
173C2×C42C22×D6111yescharacteristic
174#107—1228no—
175C4⋊C8—614no—
176C4⋊C8—1222no—
177#103—1228no—
178#103—2444no—
179C4×C8—1222no—
180#95—24no—
181#95—22no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—22no—
187C2×Q8—1222no—
188C2×Q8—2442no—
189C2×Q8—2442no—
190C2×Q8—2441no—
191C2×Q8#1175820214yes—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—2441no—
196C22×C4C2×C22⋊D6111yescharacteristic
197C22×C4C2×C22⋊D6112yes—
198C2×C8—1222no—
199C2×C8—1224no—
200C2×C8—2441no—
201C2×C8—2442no—
202C2×C8—2441no—
203C2×C8—2442no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—82no—
212C4⋊C4—1224no—
213C4⋊C4—2442no—
214C42—42no—
215C42—42no—
216C42D4×D6111yescharacteristic
217C42D4×D6112yes—
218C42#1175822411yescharacteristic
219C23#1451974611yescharacteristic
220Q8—24no—
221Q8—24no—
222Q8—42no—
223Q8—42no—
224Q8—4882no—
225Q8—2444no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—24no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—4881no—
237C2×C4—4881no—
238C2×C4—2442no—
239C2×C4#1451974512yes—
240C2×C4#1451974811yescharacteristic
241C2×C4#1451974912yes—
242C2×C4#1451977311yescharacteristic
243C2×C4C2×#1175820212yes—
244C2×C4#1451979712yes—
245C2×C4#1451980712yes—
246C2×C4#1451980812yes—
247C8—2442no—
248C8—2444no—
249C22#1683967011yescharacteristic
250C22#1683991812yes—
251C22#1683992412yes—
252C22#1683993011yescharacteristic
253C22#1683993511yescharacteristic
254C4—21no—
255C4—21no—
256C4—44no—
257C4—82no—
258C4—82no—
259C4—4882no—
260C4#1683991712yes—
261C4#1683992212yes—
262C4#1684000112yes—
263C4#1684001812yes—
264C2#2144494011yescharacteristic
265C2#2144495911yescharacteristic
266C2#2144497712yes—
267C2#2144682712yes—
268C2#2144686111yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2582C2
socle, prime radicalC23×C61#120
hypercenter#2582D61
hypocenterC61#10237
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
154. C61#10237semidirect

Maximal subgroups

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

subgroupindex
C2×#168400572
#214466202
C2×Q8⋊#924182
#214437022
C61×#25822
#1023761