Finite Group Databasebeta

← #29577388

Subgroups — #29577388

Order 15616.

594 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 135 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#21450772C211yesmaximal, characteristic
2#21445811C211yesmaximal, characteristic
3#21444503C212yesmaximal, complemented
4#21443721C212yesmaximal, complemented
5C61×#2972C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7C2×#14519756—22no—
8#16839786C2212yes—
9C2×#14519694—21no—
10#16839698C414yes—
11#16839665—21no—
12#16839631—21no—
13C4×C4⋊Dic61C2211yescharacteristic
14#16839531—21no—
15#16839509—24no—
16C2×C4×D4×C61C2211yescharacteristic
17C8×D4×C61—24no—
18C61×#431C2212yes—
19C2×C22⋊C8×C61—22no—
20C22×Dic122—21no—
21C2×#11758194—22no—
22#14519777—22no—
23#14519777—22no—
24#14519756—48no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2×C412yes—
28C2×#11758196—24no—
29C2×C22⋊Dic61—24no—
30C2×C4×Dic61—21no—
31C4⋊#92418—22no—
32C4⋊#92418—22no—
33#14519694—42no—
34#14519684C2×C412yes—
35C22×D4×C61D411yescharacteristic
36C23×C4×C61D412yes—
37C22×C8×C61—24no—
38C4×D4×C61—22no—
39C4×D4×C61—22no—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C22⋊C4×C61C2×C412yes—
42C2×C42×C61C2311yescharacteristic
43C4⋊C8×C61D414yes—
44C22⋊C8×C61—24no—
45C22⋊C8×C61—22no—
46C4×C8×C61—22no—
47C24×C61C22⋊C412yes—
48C2×D4×C61—22no—
49C2×D4×C61—22no—
50C2×D4×C61SD1612yes—
51C2×D4×C61Q1612yes—
52C22×C4×C61—22no—
53C22×C4×C61—22no—
54C22×C4×C61—44no—
55C22×C4×C61C22⋊C412yes—
56C22×C4×C61C22×C411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×Dic61—22no—
60C22×Dic61—22no—
61C2×Dic122—44no—
62C2×Dic122—41no—
63C2×Dic122—41no—
64C2×C8×C61—24no—
65C2×C8×C61—84no—
66C4⋊C4×C61—22no—
67C22⋊C4×C61—24no—
68C42×C61C2×D412yes—
69C42×C61#4112yes—
70C22⋊Dic61—48no—
71C4⋊Dic61—24no—
72C4⋊Dic61—24no—
73C4⋊Dic61—42no—
74#11758196—48no—
75C4×Dic61—42no—
76#11758194—42no—
77#11758194—42no—
78C2×#92418—42no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—42no—
82C23×C61—42no—
83C23×C61#10314yes—
84C23×C61C2×C22⋊C411yescharacteristic
85D4×C61—24no—
86D4×C61—24no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—41no—
90C2×C4×C61—44no—
91C2×C4×C61—42no—
92C2×C4×C61—82no—
93C2×C4×C61C4×D412yes—
94C2×C4×C61#12011yescharacteristic
95C2×C4×C61#12112yes—
96C2×C4×C61#12311yescharacteristic
97C2×C4×C61C2×SD1611yescharacteristic
98C2×C4×C61C2×Q1611yescharacteristic
99C2×C4×C61#13512yes—
100C2×Dic61—24no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—44no—
104C2×Dic61—42no—
105Dic122—82no—
106Dic122—82no—
107C8×C61—44no—
108#92418—82no—
109#9395—611nomaximal, Sylow
110C22×C61—21no—
111C22×C61—21no—
112C22×C61—24no—
113C22×C61—44no—
114C22×C61—42no—
115C22×C61—42no—
116C22×C61—82no—
117C22×C61#38611yescharacteristic
118C22×C61C2×#10311yescharacteristic
119C22×C61#41611yescharacteristic
120C4×C61—21no—
121C4×C61—22no—
122C4×C61—42no—
123C4×C61#45312yes—
124C4×C61#46512yes—
125C4×C61#46712yes—
126Dic61—44no—
127Dic61—82no—
128#2972D6111yescharacteristic
129#2542—611no—
130#1800—611no—
131#1549—612no—
132#1303—612no—
133C2×C61—21no—
134C2×C61—21no—
135C2×C61—44no—
136C2×C61#188711yescharacteristic
137C2×C61#189211yescharacteristic
138C2×C61#191511yescharacteristic
139C2×C4⋊Q8—611no—
140C2×C22⋊Q8—1222no—
141C2×C4×D4C2×D6111yescharacteristic
142C8×D4—24no—
143#431C2×D6112yes—
144#423—612no—
145C2×#100—1221no—
146C2×C22⋊C8—22no—
147#399—614no—
148#390—1221no—
149#384—1221no—
150C4×C4⋊C4—611no—
151#343—1221no—
152#332—1224no—
153C61#939511yescharacteristic, complemented, Sylow
154C22×Q8—1221no—
155C22×D4D24411yescharacteristic
156C23×C4C22⋊D6112yes—
157C2×M16—1222no—
158C22×C8—24no—
159C4⋊Q8—1222no—
160C4⋊Q8—1222no—
161C22⋊Q8—2448no—
162C4×D4—22no—
163C4×D4—22no—
164C2×C4⋊C4—612no—
165C2×C4⋊C4—1221no—
166C2×C4⋊C4—1224no—
167C2×C4⋊C4—1221no—
168C2×C4⋊C4D24411yescharacteristic
169C2×C22⋊C4—1224no—
170C2×C22⋊C4C4×D6112yes—
171C2×C42—1221no—
172C2×C42C22×D6111yescharacteristic
173C4⋊C8—1222no—
174C4⋊C8—1222no—
175C4⋊C8C22⋊D6114yes—
176#100—2442no—
177C22⋊C8—24no—
178C22⋊C8—22no—
179C4×C8—22no—
180#95—612no—
181C24#1175819812yes—
182C2×Q8—2444no—
183C2×Q8—2441no—
184C2×Q8—2441no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4#1175819012yes—
188C2×D4Dic24412yes—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—44no—
192C22×C4—1222no—
193C22×C4—1222no—
194C22×C4#1175819812yes—
195C22×C4C2×C4×D6111yescharacteristic
196C22×C4C2×D24411yescharacteristic
197C22×C4C2×C22⋊D6111yescharacteristic
198M16—2442no—
199M16—2442no—
200C2×C8—24no—
201C2×C8—84no—
202C2×C8—2442no—
203C4⋊C4—22no—
204C4⋊C4—1224no—
205C4⋊C4—1224no—
206C4⋊C4—2448no—
207C4⋊C4—2442no—
208C22⋊C4—24no—
209C22⋊C4—2448no—
210C42—2442no—
211C42#1175822212yes—
212C42C2×C22⋊D6112yes—
213C23—22no—
214C23—22no—
215C23—42no—
216C23—42no—
217C23#1451970214yes—
218C23C2×#1175819811yescharacteristic
219Q8—4882no—
220Q8—4882no—
221D4—24no—
222D4—24no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—44no—
227C2×C4—42no—
228C2×C4—82no—
229C2×C4—1224no—
230C2×C4—2444no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4—2442no—
234C2×C4C4×C22⋊D6112yes—
235C2×C4#1451974611yescharacteristic
236C2×C4#1451975112yes—
237C2×C4#1451976011yescharacteristic
238C2×C4C2×#1175819011yescharacteristic
239C2×C4C2×Dic24411yescharacteristic
240C2×C4#1451979912yes—
241C8—44no—
242C8—4882no—
243C22—21no—
244C22—21no—
245C22—24no—
246C22—44no—
247C22—42no—
248C22—42no—
249C22—82no—
250C22#1683964111yescharacteristic
251C22C2×#1451970211yescharacteristic
252C22#1683975911yescharacteristic
253C4—21no—
254C4—22no—
255C4—42no—
256C4—4882no—
257C4—2444no—
258C4#1683993012yes—
259C4#1683999112yes—
260C4#1684000312yes—
261C2—21no—
262C2—21no—
263C2—44no—
264C2#2144621711yescharacteristic
265C2#2144624211yescharacteristic
266C2#2144637111yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2972C2
socleC22×C61#386
prime radicalC22×D4×C61D4
cosocleC2×C42×C61C23
hypercenter#2972D61
hypocenterC61#9395
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
3. #21444503C2semidirect
4. #21443721C2semidirect
153. C61#9395semidirect

Maximal subgroups

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

subgroupindex
#214507722
#214458112
#214445032
#214437212
C61×#29722
#939561