Finite Group Databasebeta

← #29568184

Subgroups — #29568184

Order 15616.

428 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448296C211yesmaximal, characteristic
2#21445936C211yesmaximal, characteristic
3#21443644C212yesmaximal
4#21443641C212yesmaximal
5C61×#1767C211yesmaximal, characteristic
6C2×C4×Dic122C411yescharacteristic
7C2×C4⋊#92418—21no—
8#16839668C411yescharacteristic
9#16839668C2211yescharacteristic
10#16839660C411yescharacteristic
11#16839660C2211yescharacteristic
12#16839646—21no—
13#16839646—21no—
14C4×#11758196—21no—
15C4×C4⋊Dic61C411yescharacteristic
16#16839608—21no—
17#16839517—21no—
18#16839517C2212yes—
19C2×C4⋊C8×C61—21no—
20C2×#97×C61—21no—
21C43×C61C2211yescharacteristic
22C61×#336C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—22no—
25C4×Dic122—22no—
26C4×Dic122—22no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35C4⋊#92418—42no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43C22×C8×C61—22no—
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61C2×C411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50C2×C42×C61C2311yescharacteristic
51C4⋊C8×C61—24no—
52#97×C61—42no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61C22×C411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C2×Dic122—21no—
65C2×Dic122—41no—
66C2×Dic122—41no—
67C2×Dic122M1612yes—
68C2×C8×C61—24no—
69C2×C8×C61—42no—
70C2×C8×C61—42no—
71C42×C61—22no—
72C42×C61—21no—
73C42×C61—21no—
74C42×C61—21no—
75C42×C61—21no—
76C42×C61—41no—
77C42×C61—41no—
78C42×C61—41no—
79C42×C61SD1612yes—
80C42×C61Q1612yes—
81C4⋊Dic61—21no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61M1612yes—
85#11758196—24no—
86#11758196—42no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—24no—
90C4×Dic61—42no—
91C2×#92418—42no—
92C2×#92418—42no—
93C2×#92418—42no—
94C23×C61C2×C22⋊C411yescharacteristic
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—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#10312yes—
111C2×C4×C61#10312yes—
112C2×C4×C61#10412yes—
113C2×C4×C61C2×M1611yescharacteristic
114C2×C4×C61C2×M1611yescharacteristic
115C2×C4×C61C2×SD1611yescharacteristic
116C2×C4×C61C2×Q1611yescharacteristic
117C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C61#13711yescharacteristic
119C2×Dic61—22no—
120C2×Dic61—22no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131Dic122—42no—
132Dic122—42no—
133C8×C61—44no—
134#92418—82no—
135#7615—611nomaximal, Sylow
136C22×C61#40711yescharacteristic
137C22×C61#41011yescharacteristic
138C22×C61#41311yescharacteristic
139C22×C61C2×#10311yescharacteristic
140C22×C61#41711yescharacteristic
141C22×C61C2×#10411yescharacteristic
142C22×C61#42111yescharacteristic
143C4×C61—22no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—22no—
147C4×C61—21no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—22no—
152C4×C61—41no—
153Dic61—42no—
154Dic61—42no—
155Dic61—81no—
156Dic61—81no—
157#2295—611no—
158#1831—611no—
159#1767D6111yescharacteristic
160#1272—612no—
161#1271—612no—
162C2×C61#146411yescharacteristic
163C2×C61#148711yescharacteristic
164C2×C61#148911yescharacteristic
165C2×C61#150311yescharacteristic
166C2×C61#151211yescharacteristic
167C2×C61#153211yescharacteristic
168C2×C61#155011yescharacteristic
169C2×C4×Q8—611no—
170C2×C4⋊C8—21no—
171C2×C4⋊C8—1221no—
172C2×#97—21no—
173#391—611no—
174#391—611no—
175#389—611no—
176#389—611no—
177#387—1221no—
178#387—1221no—
179C4×C4⋊C4—611no—
180C4×C4⋊C4—1221no—
181#376—1221no—
182C43C2×D6111yescharacteristic
183#336—612no—
184#336—1221no—
185#336C2×D6112yes—
186C61#761511yescharacteristic, complemented, Sylow
187C22×Q8—611no—
188C22×C8—22no—
189C22×C8—1222no—
190C4×Q8—1222no—
191C4×Q8—1222no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C42—1221no—
199C2×C42—1221no—
200C2×C42C4×D6111yescharacteristic
201C2×C42C4×D6111yescharacteristic
202C2×C42D24411yescharacteristic
203C2×C42D24411yescharacteristic
204C2×C42C22⋊D6111yescharacteristic
205C2×C42C22⋊D6111yescharacteristic
206C2×C42C22×D6111yescharacteristic
207C4⋊C8—24no—
208C4⋊C8—2442no—
209#97—42no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217C2×Q8—612no—
218C2×Q8—1221no—
219C2×Q8—2441no—
220C2×Q8—2441no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4#1175819811yescharacteristic
226C22×C4#1175819811yescharacteristic
227C22×C4#1175819811yescharacteristic
228C22×C4#1175819811yescharacteristic
229C22×C4C2×C4×D6111yescharacteristic
230C22×C4C2×D24411yescharacteristic
231C22×C4C2×C22⋊D6111yescharacteristic
232C2×C8—24no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—2442no—
236C2×C8—2442no—
237C2×C8—2442no—
238C4⋊C4—612no—
239C4⋊C4—1224no—
240C4⋊C4—1221no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2442no—
245C4⋊C4—2441no—
246C42—21no—
247C42—22no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—1224no—
255C42—2442no—
256C42#1175820012yes—
257C42#1175820212yes—
258C23C2×#1175819811yescharacteristic
259Q8—2442no—
260Q8—2442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—1222no—
277C2×C4—1222no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4#1451970012yes—
289C2×C4#1451970012yes—
290C2×C4#1451970512yes—
291C2×C4M16×D6111yescharacteristic
292C2×C4M16×D6111yescharacteristic
293C2×C4C2×#1175820011yescharacteristic
294C2×C4C2×#1175820211yescharacteristic
295C2×C4#1451980511yescharacteristic
296C2×C4#1451981011yescharacteristic
297C8—44no—
298C8—4882no—
299C22#1683972511yescharacteristic
300C22#1683973511yescharacteristic
301C22#1683974411yescharacteristic
302C22C2×#1451970011yescharacteristic
303C22#1683976411yescharacteristic
304C22C2×#1451970511yescharacteristic
305C22#1683977811yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—4881no—
317C4—4881no—
318C4—2442no—
319C4—2442no—
320C2#2144415111yescharacteristic
321C2#2144424711yescharacteristic
322C2#2144425911yescharacteristic
323C2#2144431711yescharacteristic
324C2#2144435811yescharacteristic
325C2#2144443711yescharacteristic
326C2#2144451011yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1767C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1767D61
hypocenterC61#7615
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
186. C61#7615semidirect

Maximal subgroups

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

subgroupindex
#214482962
#214459362
#214436442
#214436412
C61×#17672
#761561