Finite Group Databasebeta

← #29568294

Subgroups — #29568294

Order 15616.

582 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839660C211yesmaximal, characteristic
2#21445799C211yesmaximal, characteristic
3#21443643C214yesmaximal, complemented
4C61×#1797C211yesmaximal, characteristic
5C22×C4⋊Dic61C411yescharacteristic
6C22×C4⋊Dic61C411yescharacteristic
7C22×#11758196—21no—
8C2×C4⋊#92418—21no—
9C2×C22⋊#92418—21no—
10#16839660—21no—
11#16839660—21no—
12#16839660C412yes—
13#16839660C2212yes—
14C2×#14519684—21no—
15#16839517C2212yes—
16C22×C42×C61C2211yescharacteristic
17C2×C4⋊C8×C61—21no—
18C2×C22⋊C8×C61—21no—
19C61×#336C2212yes—
20C23×Dic61—21no—
21C23×Dic61—21no—
22C22×#92418—22no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—24no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—42no—
27C2×C4⋊Dic61C2×C412yes—
28C2×C4⋊Dic61C2×C412yes—
29C2×#11758196—22no—
30C2×#11758196—22no—
31C2×#11758196—42no—
32C2×#11758196—42no—
33C4⋊#92418—42no—
34C22⋊#92418—42no—
35#14519684—22no—
36#14519684—22no—
37C23×C4×C61C2×C411yescharacteristic
38C23×C4×C61D411yescharacteristic
39C23×C4×C61D411yescharacteristic
40C22×C8×C61—22no—
41C2×C42×C61—42no—
42C2×C42×C61C2×C411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C2×C42×C61C2311yescharacteristic
46C4⋊C8×C61—42no—
47C22⋊C8×C61—42no—
48C24×C61C22⋊C411yescharacteristic
49C22×C4×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—41no—
53C22×C4×C61—41no—
54C22×C4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61D812yes—
60C22×C4×C61SD1612yes—
61C22×C4×C61SD1612yes—
62C22×C4×C61Q1612yes—
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×Dic61—24no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—42no—
70C22×Dic61—42no—
71C22×Dic61—42no—
72C22×Dic61—42no—
73C22×Dic61—42no—
74C2×C8×C61—42no—
75C2×C8×C61—42no—
76C2×C8×C61—42no—
77C42×C61—22no—
78C42×C61—22no—
79C42×C61—41no—
80C42×C61—41no—
81C4⋊Dic61—24no—
82C4⋊Dic61—22no—
83C4⋊Dic61—42no—
84C4⋊Dic61—42no—
85C4⋊Dic61M1614yes—
86#11758196—44no—
87#11758196—42no—
88#11758196—42no—
89C2×#92418—42no—
90C2×#92418—42no—
91C2×#92418—42no—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61#10112yes—
97C23×C61#10212yes—
98C23×C61#10312yes—
99C23×C61C2×C22⋊C411yescharacteristic
100C2×C4×C61—28no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61#9912yes—
118C2×C4×C61#10212yes—
119C2×C4×C61#10312yes—
120C2×C4×C61C2×M1612yes—
121C2×C4×C61C2×D811yescharacteristic
122C2×C4×C61C2×SD1611yescharacteristic
123C2×C4×C61C2×SD1611yescharacteristic
124C2×C4×C61C2×Q1611yescharacteristic
125C2×Dic61—24no—
126C2×Dic61—48no—
127C2×Dic61—42no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61—84no—
133C8×C61—82no—
134#92418—82no—
135#7641—611nomaximal, Sylow
136C22×C61—22no—
137C22×C61—22no—
138C22×C61—22no—
139C22×C61—22no—
140C22×C61—22no—
141C22×C61—22no—
142C22×C61#33214yes—
143C22×C61#40711yescharacteristic
144C22×C61C2×#9911yescharacteristic
145C22×C61C2×#10111yescharacteristic
146C22×C61C2×#10211yescharacteristic
147C22×C61C2×#10311yescharacteristic
148C22×C61#42111yescharacteristic
149C22×C61#42111yescharacteristic
150C4×C61—22no—
151C4×C61—22no—
152C4×C61—21no—
153C4×C61—22no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—22no—
157C4×C61—21no—
158Dic61—44no—
159Dic61—82no—
160C2×#389—611no—
161#1797—611no—
162#1797D6111yescharacteristic
163#1271—614no—
164C2×C61—24no—
165C2×C61#146311yescharacteristic
166C2×C61#148611yescharacteristic
167C2×C61#148711yescharacteristic
168C2×C61#151911yescharacteristic
169C2×C61#152011yescharacteristic
170C2×C61#153411yescharacteristic
171C2×C61C2×#33211yescharacteristic
172C22×C4⋊C4—611no—
173C22×C4⋊C4—611no—
174C22×C4⋊C4—1221no—
175C22×C42C2×D6111yescharacteristic
176C2×C4⋊C8—21no—
177C2×C4⋊C8—1221no—
178C2×C22⋊C8—21no—
179C2×C22⋊C8—1221no—
180#389—612no—
181#389—612no—
182#389—1221no—
183#389—1221no—
184C2×#95—1221no—
185#336—612no—
186#336C2×D6112yes—
187C61#764111yescharacteristic, complemented, Sylow
188C23×C4—1221no—
189C23×C4—1221no—
190C23×C4C4×D6111yescharacteristic
191C23×C4D24411yescharacteristic
192C23×C4C22⋊D6111yescharacteristic
193C22×C8—22no—
194C22×C8—1222no—
195C2×C4⋊C4—612no—
196C2×C4⋊C4—612no—
197C2×C4⋊C4—1224no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1222no—
201C2×C4⋊C4—1222no—
202C2×C4⋊C4—2442no—
203C2×C4⋊C4—2442no—
204C2×C4⋊C4—2442no—
205C2×C42—42no—
206C2×C42C4×D6111yescharacteristic
207C2×C42D24411yescharacteristic
208C2×C42C22⋊D6111yescharacteristic
209C2×C42C22×D6111yescharacteristic
210C4⋊C8—42no—
211C4⋊C8—2442no—
212C22⋊C8—42no—
213C22⋊C8—2442no—
214#95—1222no—
215#95—1222no—
216C24#1175819811yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—1224no—
225C22×C4—1222no—
226C22×C4—1222no—
227C22×C4—2442no—
228C22×C4—2442no—
229C22×C4—2442no—
230C22×C4—2442no—
231C22×C4—2442no—
232C22×C4#1175819012yes—
233C22×C4Dic24412yes—
234C22×C4#1175819811yescharacteristic
235C22×C4#1175819811yescharacteristic
236C22×C4#1175819811yescharacteristic
237C22×C4#1175819912yes—
238C22×C4#1175820112yes—
239C22×C4C2×C4×D6111yescharacteristic
240C22×C4C2×D24411yescharacteristic
241C22×C4C2×C22⋊D6111yescharacteristic
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—2442no—
246C2×C8—2442no—
247C2×C8—2442no—
248C4⋊C4—614no—
249C4⋊C4—1224no—
250C4⋊C4—1222no—
251C4⋊C4—2442no—
252C4⋊C4—2442no—
253C4⋊C4—2444no—
254C4⋊C4—2442no—
255C4⋊C4—2442no—
256C42—22no—
257C42—22no—
258C42—41no—
259C42—41no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23#1451969512yes—
265C23#1451969712yes—
266C23#1451970212yes—
267C23C2×#1175819811yescharacteristic
268C2×C4—28no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—1224no—
286C2×C4—4884no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2448no—
291C2×C4—2442no—
292C2×C4—2442no—
293C2×C4#1451969112yes—
294C2×C4#1451969712yes—
295C2×C4#1451970212yes—
296C2×C4M16×D6112yes—
297C2×C4C2×#1175819911yescharacteristic
298C2×C4C2×#1175820111yescharacteristic
299C2×C4C2×#1175819011yescharacteristic
300C2×C4C2×Dic24411yescharacteristic
301C8—82no—
302C8—4882no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22#1683950914yes—
310C22#1683972511yescharacteristic
311C22C2×#1451969111yescharacteristic
312C22C2×#1451969511yescharacteristic
313C22C2×#1451969711yescharacteristic
314C22C2×#1451970211yescharacteristic
315C22#1683977811yescharacteristic
316C22#1683978011yescharacteristic
317C4—21no—
318C4—22no—
319C4—21no—
320C4—21no—
321C4—22no—
322C4—21no—
323C4—22no—
324C4—22no—
325C4—4882no—
326C4—2444no—
327C2—24no—
328C2#2144414811yescharacteristic
329C2#2144424311yescharacteristic
330C2#2144424911yescharacteristic
331C2#2144438611yescharacteristic
332C2#2144439211yescharacteristic
333C2#2144444511yescharacteristic
334C2C2×#1683950911yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1797C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1797D61
hypocenterC61#7641
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #21443643C2semidirect
187. C61#7641semidirect

Maximal subgroups

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

subgroupindex
C2×#168396602
#214457992
#214436432
C61×#17972
#764161