Finite Group Databasebeta

← #29582366

Subgroups — #29582366

Order 15616.

560 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16840054C212yesmaximal
2#21451192C211yesmaximal, characteristic
3C2×#16839494C212yesmaximal
4#21443702C211yesmaximal, characteristic
5C61×#1956C211yesmaximal, characteristic
6C2×C4×Dic122C2212yes—
7#16840054—24no—
8#16840054—24no—
9C2×#14519710—22no—
10C2×C4⋊#92418C2212yes—
11C2×#14519700—22no—
12#16839692—22no—
13#16839667—22no—
14#16839661—22no—
15#16839494—24no—
16C2×C4⋊Q8×C61C2211yescharacteristic
17C2×#103×C61—22no—
18C2×C4×C8×C61C2211yescharacteristic
19C61×#384C2211yescharacteristic
20C22×Dic122D412yes—
21C22×#92418—22no—
22C4×Dic122—22no—
23C4×Dic122—22no—
24C4×Dic122—22no—
25C4×Dic122—22no—
26C2×C4⋊Dic61—22no—
27C2×C4⋊Dic61D412yes—
28C2×#11758196—22no—
29C2×C4×Dic61—22no—
30#14519710—28no—
31C4⋊#92418—22no—
32C4⋊#92418D414yes—
33#14519700—28no—
34#14519684—24no—
35#14519684—22no—
36C22×Q8×C61—21no—
37C22×C8×C61—21no—
38C4⋊Q8×C61—22no—
39C4⋊Q8×C61—21no—
40C4⋊Q8×C61D412yes—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61—22no—
43C2×C4⋊C4×C61D412yes—
44C2×C42×C61C2311yescharacteristic
45#103×C61—44no—
46C4×C8×C61—22no—
47C2×Q8×C61—22no—
48C2×Q8×C61—42no—
49C2×Q8×C61—42no—
50C2×Q8×C61—41no—
51C22×C4×C61—22no—
52C22×C4×C61—41no—
53C22×C4×C61C2×D411yescharacteristic
54C22×C4×C61C2×D412yes—
55C22×Dic61—22no—
56C22×Dic61—22no—
57C2×Dic122—22no—
58C2×Dic122—22no—
59C2×Dic122—22no—
60C2×Dic122—22no—
61C2×Dic122—22no—
62C2×Dic122Q1614yes—
63C2×C8×C61—22no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C4⋊C4×C61—24no—
67C4⋊C4×C61—42no—
68C4⋊C4×C61—42no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—42no—
71C42×C61C2×D411yescharacteristic
72C42×C61C2×D412yes—
73C42×C61#4111yescharacteristic
74C4⋊Dic61—22no—
75C4⋊Dic61—22no—
76C4⋊Dic61—82no—
77#11758196—42no—
78#11758196—42no—
79C4×Dic61—42no—
80C4×Dic61—42no—
81C2×#92418—24no—
82C2×#92418—42no—
83C2×#92418—42no—
84C23×C61#12011yescharacteristic
85Q8×C61—44no—
86Q8×C61—82no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—42no—
90C2×C4×C61—44no—
91C2×C4×C61—42no—
92C2×C4×C61—81no—
93C2×C4×C61—81no—
94C2×C4×C61#12012yes—
95C2×C4×C61#12111yescharacteristic
96C2×C4×C61#12112yes—
97C2×C4×C61#12711yescharacteristic
98C2×C4×C61C2×Q1612yes—
99C2×C4×C61#13512yes—
100C2×C4×C61#13712yes—
101C2×C4×C61#13712yes—
102C2×Dic61—24no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108Dic122—24no—
109Dic122—24no—
110Dic122—42no—
111Dic122—42no—
112C8×C61—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—82no—
123C4×C61—82no—
124C4×C61#45112yes—
125C4×C61#45212yes—
126C4×C61#46712yes—
127C4×C61#47012yes—
128Dic61—44no—
129Dic61—82no—
130C2×#477—612no—
131#2582—611no—
132#1956D6111yescharacteristic
133C2×Q8⋊C8—612no—
134#1296—611no—
135C2×C61#163011yescharacteristic
136C2×C61#163311yescharacteristic
137C2×C61#163612yes—
138C2×C61#200112yes—
139C2×C61#200611yescharacteristic
140C2×C4⋊Q8C2×D6111yescharacteristic
141C2×C4×Q8—612no—
142#477—1224no—
143#477—1224no—
144C2×#107—1222no—
145C2×C4⋊C8—612no—
146C2×#103—22no—
147C2×#103—1222no—
148C2×C4×C8C2×D6111yescharacteristic
149#398—1222no—
150#391—1222no—
151#389—1222no—
152#384C2×D6111yescharacteristic
153Q8⋊C8—1224no—
154C61#1023711yescharacteristic, complemented, Sylow
155C22×Q8—21no—
156C22×Q8—612no—
157C22×C8—21no—
158C22×C8—1222no—
159C4⋊Q8—21no—
160C4⋊Q8—22no—
161C4⋊Q8D24412yes—
162C4×Q8—1222no—
163C4×Q8—1222no—
164C4×Q8—1222no—
165C4×Q8—1222no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—612no—
169C2×C4⋊C4—1222no—
170C2×C4⋊C4—1222no—
171C2×C4⋊C4C22⋊D6112yes—
172C2×C42—1222no—
173C2×C42C22×D6111yescharacteristic
174#107—1228no—
175C4⋊C8—614no—
176C4⋊C8—1222no—
177#103—44no—
178#103—1228no—
179C4×C8—22no—
180#95—1224no—
181#95—1222no—
182C2×Q8—22no—
183C2×Q8—42no—
184C2×Q8—42no—
185C2×Q8—41no—
186C2×Q8—614no—
187C2×Q8—1222no—
188C2×Q8—1222no—
189C2×Q8—1222no—
190C2×Q8—1222no—
191C2×Q8—1222no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4—1222no—
195C22×C4—1222no—
196C22×C4D4×D6112yes—
197C22×C4C2×C22⋊D6111yescharacteristic
198C2×C8—22no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—1224no—
202C2×C8—2442no—
203C2×C8—2442no—
204C4⋊C4—24no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—1222no—
210C4⋊C4—1222no—
211C4⋊C4—4882no—
212C4⋊C4—2442no—
213C4⋊C4—2442no—
214C42—2442no—
215C42—2442no—
216C42C2×D24411yescharacteristic
217C42#1175822211yescharacteristic
218C42D4×D6112yes—
219C23#1451974511yescharacteristic
220Q8—44no—
221Q8—82no—
222Q8—1224no—
223Q8—1224no—
224Q8—2442no—
225Q8—2442no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—1224no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4—2442no—
238C2×C4—2442no—
239C2×C4#1451974712yes—
240C2×C4#1451975012yes—
241C2×C4#1451975111yescharacteristic
242C2×C4#1451977311yescharacteristic
243C2×C4Q16×D6112yes—
244C2×C4#1451979812yes—
245C2×C4#1451980612yes—
246C2×C4#1451980912yes—
247C8—42no—
248C8—2444no—
249C22#1683967111yescharacteristic
250C22#1683991612yes—
251C22#1683992112yes—
252C22#1683992911yescharacteristic
253C22#1683993411yescharacteristic
254C4—21no—
255C4—21no—
256C4—82no—
257C4—82no—
258C4—4882no—
259C4—2444no—
260C4#1683991912yes—
261C4#1683992712yes—
262C4#1684000212yes—
263C4#1684001912yes—
264C2#2144493811yescharacteristic
265C2#2144495711yescharacteristic
266C2#2144497412yes—
267C2#2144682812yes—
268C2#2144686011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1956C2
socle, prime radicalC23×C61#120
hypercenter#1956D61
hypocenterC61#10237
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

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×#168400542
#214511922
C2×#168394942
#214437022
C61×#19562
#1023761