Finite Group Databasebeta

← #29573421

Subgroups — #29573421

Order 15616.

526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 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#21448226C211yesmaximal, characteristic
2#21445581C211yesmaximal, characteristic
3#21443701C214yesmaximal, complemented
4C61×#1749C211yesmaximal, characteristic
5C2×#14519736C412yes—
6C2×C22⋊#92418—21no—
7C2×#14519688C2212yes—
8#16839632C411yescharacteristic
9#16839632C411yescharacteristic
10#16839628C2212yes—
11#16839622—21no—
12#16839622—21no—
13C4×C4⋊Dic61—21no—
14C4×C4⋊Dic61—21no—
15#16839517—21no—
16C22×C42×C61C2211yescharacteristic
17C2×C22⋊C8×C61—21no—
18C2×#97×C61C2212yes—
19C61×#336—21no—
20C22×#92418—22no—
21#14519736—44no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C4⋊Dic61C2×C412yes—
28C2×C22⋊Dic61—22no—
29C2×C4×Dic61—22no—
30C22⋊#92418—24no—
31#14519688—24no—
32#14519684—22no—
33#14519684—22no—
34C23×C4×C61C2×C411yescharacteristic
35C23×C4×C61D411yescharacteristic
36C23×C4×C61D411yescharacteristic
37C22×C8×C61—22no—
38C2×C42×C61—24no—
39C2×C42×C61C2×C411yescharacteristic
40C2×C42×C61D411yescharacteristic
41C2×C42×C61D411yescharacteristic
42C2×C42×C61C2311yescharacteristic
43C22⋊C8×C61—24no—
44#97×C61—24no—
45C24×C61C22⋊C411yescharacteristic
46C22×C4×C61—22no—
47C22×C4×C61—22no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—41no—
54C22×C4×C61—41no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×Dic61—22no—
62C22×Dic61—22no—
63C2×C8×C61—24no—
64C2×C8×C61—42no—
65C2×C8×C61—42no—
66C42×C61—22no—
67C42×C61—22no—
68C42×C61—22no—
69C42×C61#4114yes—
70C22⋊Dic61—44no—
71C4⋊Dic61—42no—
72C4⋊Dic61—42no—
73C4⋊Dic61—42no—
74C4⋊Dic61—42no—
75C4⋊Dic61—42no—
76C4⋊Dic61—42no—
77C4×Dic61—44no—
78C2×#92418—24no—
79C2×#92418—42no—
80C2×#92418—42no—
81C23×C61—21no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61#10112yes—
88C23×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61—28no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—44no—
103C2×C4×C61—44no—
104C2×C4×C61#10012yes—
105C2×C4×C61#10412yes—
106C2×C4×C61#10412yes—
107C2×C4×C61#11712yes—
108C2×C4×C61#12312yes—
109C2×C4×C61#12312yes—
110C2×Dic61—42no—
111C2×Dic61—42no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116C8×C61—44no—
117#92418—44no—
118#8721—611nomaximal, Sylow
119C22×C61—22no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61#38111yescharacteristic
127C22×C61C2×#10011yescharacteristic
128C22×C61C2×#10111yescharacteristic
129C22×C61C2×#10411yescharacteristic
130C22×C61C2×#10411yescharacteristic
131C22×C61#42111yescharacteristic
132C22×C61#42111yescharacteristic
133C4×C61—22no—
134C4×C61—22no—
135C4×C61—22no—
136C4×C61—22no—
137C4×C61—22no—
138C4×C61—22no—
139Dic61—82no—
140Dic61—82no—
141#2285—611no—
142#1749—611no—
143#1749D6111yescharacteristic
144#1295—614no—
145C2×C61—42no—
146C2×C61#152511yescharacteristic
147C2×C61#153111yescharacteristic
148C2×C61#153111yescharacteristic
149C2×C61#153611yescharacteristic
150C2×C61#182111yescharacteristic
151C2×C61#182611yescharacteristic
152C2×C61#182611yescharacteristic
153C2×#117—612no—
154C22×C42C2×D6111yescharacteristic
155C2×C22⋊C8—21no—
156C2×C22⋊C8—1221no—
157C2×#97—612no—
158C2×#97C2×D6112yes—
159#384—611no—
160#384—611no—
161#382—612no—
162#380—1221no—
163#380—1221no—
164C4×C4⋊C4—1221no—
165C4×C4⋊C4—1221no—
166#336—21no—
167#336—1221no—
168C61#872111yescharacteristic, complemented, Sylow
169C23×C4C4×D6111yescharacteristic
170C23×C4D24411yescharacteristic
171C23×C4C22⋊D6111yescharacteristic
172C22×C8—22no—
173C22×C8—1222no—
174#117—2444no—
175C2×C4⋊C4—612no—
176C2×C4⋊C4—612no—
177C2×C4⋊C4—1221no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—1221no—
181C2×C22⋊C4—1222no—
182C2×C42—24no—
183C2×C42—1222no—
184C2×C42C4×D6111yescharacteristic
185C2×C42D24411yescharacteristic
186C2×C42C22⋊D6111yescharacteristic
187C2×C42C22×D6111yescharacteristic
188C22⋊C8—24no—
189C22⋊C8—1224no—
190#97—24no—
191#97—1224no—
192#95—1222no—
193#95—1222no—
194C24#1175819811yescharacteristic
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—1222no—
205C22×C4—1222no—
206C22×C4#1175819811yescharacteristic
207C22×C4#1175819811yescharacteristic
208C22×C4#1175819811yescharacteristic
209C22×C4C2×C4×D6111yescharacteristic
210C22×C4C2×D24411yescharacteristic
211C22×C4C2×C22⋊D6111yescharacteristic
212C2×C8—24no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—1224no—
216C2×C8—2442no—
217C2×C8—2442no—
218C4⋊C4—2442no—
219C4⋊C4—2442no—
220C4⋊C4—2442no—
221C4⋊C4—2442no—
222C4⋊C4—2442no—
223C4⋊C4—2442no—
224C22⋊C4—2444no—
225C42—22no—
226C42—22no—
227C42—22no—
228C42—2444no—
229C42#1175822414yes—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23#1451969512yes—
237C23C2×#1175819811yescharacteristic
238C2×C4—28no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—44no—
252C2×C4—44no—
253C2×C4—2442no—
254C2×C4—2442no—
255C2×C4—2442no—
256C2×C4—2442no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4#1451969312yes—
260C2×C4#1451970312yes—
261C2×C4#1451970512yes—
262C2×C4#1451973312yes—
263C2×C4#1451975812yes—
264C2×C4#1451976112yes—
265C8—44no—
266C8—2444no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22#1683962311yescharacteristic
275C22C2×#1451969311yescharacteristic
276C22C2×#1451969511yescharacteristic
277C22C2×#1451970311yescharacteristic
278C22C2×#1451970511yescharacteristic
279C22#1683977811yescharacteristic
280C22#1683978011yescharacteristic
281C4—22no—
282C4—22no—
283C4—22no—
284C4—22no—
285C4—22no—
286C4—22no—
287C4—4882no—
288C4—4882no—
289C2—42no—
290C2#2144441011yescharacteristic
291C2#2144443311yescharacteristic
292C2#2144443511yescharacteristic
293C2#2144445311yescharacteristic
294C2#2144589711yescharacteristic
295C2#2144591611yescharacteristic
296C2#2144591911yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1749C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1749D61
hypocenterC61#8721
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. #21443701C2semidirect
168. C61#8721semidirect

Maximal subgroups

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

subgroupindex
#214482262
#214455812
#214437012
C61×#17492
#872161