Finite Group Databasebeta

← #29568512

Subgroups — #29568512

Order 15616.

530 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454129C211yesmaximal, characteristic
2#21445581C211yesmaximal, characteristic
3#21443643C212yesmaximal, complemented
4#21443641C212yesmaximal, complemented
5C2×C61×#336C211yesmaximal, characteristic
6C2×#14519769C411yescharacteristic
7C2×C22⋊#92418—21no—
8C2×#14519688—21no—
9#16839660C2211yescharacteristic
10#16839660C2211yescharacteristic
11#16839646—21no—
12#16839646—21no—
13#16839635—21no—
14#16839635—21no—
15#16839628C411yescharacteristic
16#16839622C411yescharacteristic
17#16839622C411yescharacteristic
18#16839517C2212yes—
19C23×C8×C61—21no—
20C22×C42×C61C2211yescharacteristic
21C61×#336—21no—
22C61×#336C2212yes—
23C22×#92418—22no—
24#14519769—42no—
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C22⋊#92418—24no—
36#14519688—42no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43C23×C4×C61C2×C411yescharacteristic
44C23×C4×C61D411yescharacteristic
45C23×C4×C61D411yescharacteristic
46C22×C8×C61—24no—
47C22×C8×C61—22no—
48C22×C8×C61—42no—
49C22×C8×C61—42no—
50C2×C42×C61—42no—
51C2×C42×C61C2×C411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61C2311yescharacteristic
55C24×C61C22⋊C411yescharacteristic
56C22×C4×C61—22no—
57C22×C4×C61—22no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C2×C8×C61—24no—
77C2×C8×C61—48no—
78C2×C8×C61—42no—
79C2×C8×C61—42no—
80C42×C61—22no—
81C42×C61—22no—
82C42×C61—41no—
83C42×C61—41no—
84C22⋊Dic61—42no—
85C22⋊Dic61—42no—
86C4⋊Dic61—22no—
87C4⋊Dic61—22no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—42no—
91#11758196—42no—
92#11758196—42no—
93#11758196—41no—
94#11758196—41no—
95C2×#92418—24no—
96C2×#92418—42no—
97C2×#92418—42no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61#10112yes—
103C23×C61#10412yes—
104C23×C61#10412yes—
105C23×C61C2×C22⋊C411yescharacteristic
106C2×C4×C61—24no—
107C2×C4×C61—24no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—44no—
123C2×C4×C61—44no—
124C2×C4×C61#9912yes—
125C2×C4×C61#13112yes—
126C2×C4×C61#13512yes—
127C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C61#13711yescharacteristic
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C8×C61—44no—
142#92418—44no—
143#7691—611nomaximal, Sylow
144C22×C61—22no—
145C22×C61—22no—
146C22×C61—22no—
147C22×C61—22no—
148C22×C61—22no—
149C22×C61—22no—
150C22×C61#33014yes—
151C22×C61#40811yescharacteristic
152C22×C61C2×#9911yescharacteristic
153C22×C61C2×#10111yescharacteristic
154C22×C61#41611yescharacteristic
155C22×C61#41711yescharacteristic
156C22×C61C2×#10411yescharacteristic
157C22×C61C2×#10411yescharacteristic
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—21no—
161C4×C61—22no—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165Dic61—81no—
166Dic61—81no—
167Dic61—81no—
168Dic61—81no—
169#2851—611no—
170#1749—611no—
171C2×#336D6111yescharacteristic
172#1271—612no—
173#1271—612no—
174C2×C61—24no—
175C2×C61#147211yescharacteristic
176C2×C61#148311yescharacteristic
177C2×C61#149411yescharacteristic
178C2×C61#150111yescharacteristic
179C2×C61#150411yescharacteristic
180C2×C61C2×#33011yescharacteristic
181C2×C61#155211yescharacteristic
182C23×C8—21no—
183C2×#125—611no—
184C22×C42C2×D6111yescharacteristic
185C2×C22⋊C8—1221no—
186C2×#97—1221no—
187#389—611no—
188#389—611no—
189#387—1221no—
190#387—1221no—
191#385—1221no—
192#385—1221no—
193#382—611no—
194#380—611no—
195#380—611no—
196#336—21no—
197#336—612no—
198#336C2×D6112yes—
199C61#769111yescharacteristic, complemented, Sylow
200C23×C4C4×D6111yescharacteristic
201C23×C4D24411yescharacteristic
202C23×C4C22⋊D6111yescharacteristic
203C22×C8—24no—
204C22×C8—22no—
205C22×C8—42no—
206C22×C8—42no—
207C22×C8—1222no—
208#125—2442no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C42—42no—
220C2×C42C4×D6111yescharacteristic
221C2×C42D24411yescharacteristic
222C2×C42C22⋊D6111yescharacteristic
223C2×C42C22×D6111yescharacteristic
224C22⋊C8—1224no—
225#97—2442no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232C24#1175819811yescharacteristic
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4#1175819811yescharacteristic
248C22×C4#1175819811yescharacteristic
249C22×C4#1175819811yescharacteristic
250C22×C4C2×C4×D6111yescharacteristic
251C22×C4C2×D24411yescharacteristic
252C22×C4C2×C22⋊D6111yescharacteristic
253C2×C8—24no—
254C2×C8—48no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—1224no—
258C2×C8—2442no—
259C2×C8—2442no—
260C4⋊C4—1222no—
261C4⋊C4—1222no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2442no—
265C4⋊C4—2441no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C4⋊C4—2441no—
269C22⋊C4—2442no—
270C22⋊C4—2442no—
271C42—22no—
272C42—22no—
273C42—41no—
274C42—41no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23#1451969512yes—
280C23#1451970312yes—
281C23#1451970512yes—
282C23C2×#1175819811yescharacteristic
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4#1451969112yes—
314C2×C4#1451978312yes—
315C2×C4#1451979912yes—
316C2×C4#1451980311yescharacteristic
317C2×C4#1451980811yescharacteristic
318C8—44no—
319C8—2444no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22#1683950314yes—
327C22#1683972811yescharacteristic
328C22C2×#1451969111yescharacteristic
329C22C2×#1451969511yescharacteristic
330C22#1683975911yescharacteristic
331C22#1683976111yescharacteristic
332C22C2×#1451970311yescharacteristic
333C22C2×#1451970511yescharacteristic
334C4—22no—
335C4—22no—
336C4—21no—
337C4—21no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—4881no—
342C4—4881no—
343C4—4881no—
344C4—4881no—
345C2—24no—
346C2#2144418211yescharacteristic
347C2#2144423011yescharacteristic
348C2#2144428011yescharacteristic
349C2#2144431111yescharacteristic
350C2#2144432111yescharacteristic
351C2C2×#1683950311yescharacteristic
352C2#2144451711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#336C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC2×#336D61
hypocenterC61#7691
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #21443643C2semidirect
4. #21443641C2semidirect
199. C61#7691semidirect

Maximal subgroups

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

subgroupindex
#214541292
#214455812
#214436432
#214436412
C2×C61×#3362
#769161