Finite Group Databasebeta

← #29580871

Subgroups — #29580871

Order 15616.

696 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 105 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#21455827C212yesmaximal, complemented
2#21446800C211yesmaximal, characteristic, complemented
3#21444244C212yesmaximal, complemented
4#21443648C211yesmaximal, characteristic, complemented
5C61×#2397C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16840092—22no—
8#16840052—22no—
9#16839967—22no—
10#16839913—22no—
11C4×#11758200—24no—
12#16839815C2212yes—
13#16839786C2211yescharacteristic
14#16839522—22no—
15D4⋊#92418—24no—
16C2×C4×D4×C61—22no—
17C2×C4×D4×C61C2212yes—
18C61×#399—22no—
19C61×#392—22no—
20C61×#376C2211yescharacteristic
21C2×#11758200—24no—
22C2×#11758194—21no—
23#14519777D412yescomplemented
24#14519769—21no—
25#14519756—22no—
26C4×Dic122—22no—
27#14519736—21no—
28#14519708—24no—
29C4⋊#92418—22no—
30C4⋊#92418—22no—
31#14519700—24no—
32#14519698—24no—
33C22⋊#92418—22no—
34C4×#92418D414yescomplemented
35C22×D4×C61—22no—
36C22×D4×C61D412yes—
37C23×C4×C61—22no—
38C4×D4×C61—22no—
39C4×D4×C61—22no—
40C4×D4×C61—22no—
41C4×D4×C61—22no—
42C4×D4×C61—44no—
43C4×D4×C61—44no—
44C2×C4⋊C4×C61—22no—
45C2×C4⋊C4×C61D412yes—
46C2×C22⋊C4×C61—24no—
47C2×C22⋊C4×C61—22no—
48C2×C42×C61D412yes—
49C2×C42×C61C2311yescharacteristic
50#95×C61—22no—
51C24×C61—22no—
52C2×D4×C61—22no—
53C2×D4×C61—22no—
54C2×D4×C61—44no—
55C2×D4×C61—44no—
56C2×D4×C61—48no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—42no—
60C22×C4×C61—42no—
61C22×C4×C61—44no—
62C22×C4×C61—44no—
63C22×C4×C61C2×D412yes—
64C22×C4×C61C2×D411yescharacteristic
65C2×Dic122—22no—
66C4⋊C4×C61—22no—
67C4⋊C4×C61—22no—
68C4⋊C4×C61—44no—
69C22⋊C4×C61—48no—
70C22⋊C4×C61—42no—
71C22⋊C4×C61—42no—
72C42×C61—22no—
73C42×C61SD1614yescomplemented
74C42×C61C2×D411yescharacteristic
75C42×C61C2×D412yes—
76C42×C61#4111yescharacteristic
77C22⋊Dic61—41no—
78#11758200—48no—
79C4⋊Dic61—22no—
80C4⋊Dic61—22no—
81#11758196—42no—
82C4×Dic61—41no—
83#11758194—42no—
84C2×#92418—24no—
85C2×#92418—41no—
86C23×C61—24no—
87C23×C61—44no—
88C23×C61—42no—
89C23×C61—42no—
90C23×C61—44no—
91C23×C61#12011yescharacteristic
92D4×C61—24no—
93D4×C61—24no—
94D4×C61—42no—
95D4×C61—42no—
96D4×C61—416no—
97C2×C4×C61—24no—
98C2×C4×C61—42no—
99C2×C4×C61—44no—
100C2×C4×C61—42no—
101C2×C4×C61—44no—
102C2×C4×C61—84no—
103C2×C4×C61—82no—
104C2×C4×C61—82no—
105C2×C4×C61#12012yes—
106C2×C4×C61#12112yes—
107C2×C4×C61#12111yescharacteristic
108C2×C4×C61#12711yescharacteristic
109C2×C4×C61C2×SD1612yes—
110C2×C4×C61AGL(1,ℤ/8)12yes—
111C2×Dic61—42no—
112Dic122—44no—
113#92418—44no—
114#92418—81no—
115#10015—611nomaximal, Sylow
116C22×C61—22no—
117C22×C61—48no—
118C22×C61—44no—
119C22×C61—84no—
120C22×C61—82no—
121C22×C61—82no—
122C22×C61#39211yescharacteristic
123C22×C61#45012yes—
124C4×C61—22no—
125C4×C61—22no—
126C4×C61—44no—
127C4×C61—82no—
128C4×C61#46012yes—
129C4×C61#49211yescharacteristic
130C4×C61#49611yescharacteristic
131Dic61—82no—
132#3101—612no—
133#2397D6111yescharacteristic
134#1995—611no—
135#1486—612no—
136#1274—611no—
137C2×C61—22no—
138C2×C61—84no—
139C2×C61#201012yes—
140C2×C61#201411yescharacteristic
141#533—611no—
142C2×C4×D4—22no—
143C2×C4×D4C2×D6112yes—
144#483—1222no—
145#476—1222no—
146#461—1222no—
147#450—1222no—
148C4×SD16—1224no—
149#431—612no—
150#423—611no—
151#399—22no—
152#392—22no—
153#376C2×D6111yescharacteristic
154#339—1222no—
155D4⋊C8—1224no—
156C61#1001511yescharacteristic, complemented, Sylow
157C22×D4—22no—
158C22×D4C22⋊D6112yes—
159C23×C4—22no—
160C2×SD16—1224no—
161C2×M16—1221no—
162C4⋊Q8—612no—
163#125—1221no—
164C22⋊Q8—1222no—
165C4×Q8—1222no—
166C4×D4—22no—
167C4×D4—22no—
168C4×D4—22no—
169C4×D4—22no—
170C4×D4—44no—
171C4×D4—44no—
172#117—1221no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4C22⋊D6112yes—
175C2×C22⋊C4—24no—
176C2×C22⋊C4—22no—
177C2×C42C22⋊D6112yes—
178C2×C42C22×D6111yescharacteristic
179#106—1224no—
180C4⋊C8—1222no—
181C4⋊C8—1222no—
182#103—1224no—
183#102—1224no—
184C22⋊C8—1222no—
185C4×C8—614no—
186#95—22no—
187C24—22no—
188C2×Q8—1222no—
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—44no—
192C2×D4—44no—
193C2×D4—48no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—44no—
199C22×C4—44no—
200C22×C4C2×C22⋊D6112yes—
201C22×C4C2×C22⋊D6111yescharacteristic
202SD16—2448no—
203M16—2442no—
204C2×C8—1224no—
205C2×C8—2441no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—44no—
209C4⋊C4—1222no—
210C4⋊C4—1222no—
211C4⋊C4—2442no—
212C22⋊C4—48no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—2441no—
216C42—22no—
217C42—2441no—
218C42#1175820014yescomplemented
219C42D4×D6111yescharacteristic
220C42D4×D6112yes—
221C42#1175822411yescharacteristic
222C23—24no—
223C23—44no—
224C23—42no—
225C23—44no—
226C23—42no—
227C23#1451974611yescharacteristic
228Q8—2444no—
229D4—24no—
230D4—24no—
231D4—42no—
232D4—42no—
233D4—416no—
234C2×C4—24no—
235C2×C4—42no—
236C2×C4—44no—
237C2×C4—44no—
238C2×C4—42no—
239C2×C4—84no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4—2442no—
243C2×C4#1451974512yes—
244C2×C4#1451974811yescharacteristic
245C2×C4#1451974912yes—
246C2×C4#1451977311yescharacteristic
247C2×C4C2×#1175820012yes—
248C2×C4#1451980312yes—
249C8—4881no—
250C8—2444no—
251C22—22no—
252C22—48no—
253C22—44no—
254C22—84no—
255C22—82no—
256C22—82no—
257C22#1683967011yescharacteristic
258C22#1683991312yes—
259C4—22no—
260C4—22no—
261C4—44no—
262C4—82no—
263C4—4882no—
264C4#1683995912yes—
265C4#1684013411yescharacteristic
266C4#1684014911yescharacteristic
267C2—22no—
268C2—84no—
269C2#2144688412yes—
270C2#2144690711yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
Fitting, prime radicalC61×#2397C2
socleC22×C61#392
hypercenter#2397D61
hypocenterC61#10015
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #21455827C2semidirect
2. #21446800C2semidirect
3. #21444244C2semidirect
4. #21443648C2semidirect
23. #14519777D4semidirect
34. C4×#92418D4semidirect
73. C42×C61SD16semidirect
156. C61#10015semidirect
218. C42#11758200semidirect

Maximal subgroups

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

subgroupindex
#214558272
#214468002
#214442442
#214436482
C61×#23972
#1001561