Finite Group Databasebeta

← #29570008

Subgroups — #29570008

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839815C211yesmaximal, characteristic
2C2×C4×C4⋊Dic61C211yesmaximal, characteristic
3#21443697C214yesmaximal
4C61×#2285C211yesmaximal, characteristic
5C22×C4⋊Dic61—21no—
6C22×C4×Dic61—21no—
7#16839815—22no—
8#16839815C414yescomplemented
9C2×C4⋊#92418—21no—
10C2×C22⋊#92418C2212yes—
11C2×C4×#92418—21no—
12C4×C4⋊Dic61—22no—
13C4×C4⋊Dic61C414yescomplemented
14C2×#14519684C2212yes—
15C2×#117×C61—21no—
16C22×C42×C61C2211yescharacteristic
17C61×#384C412yescomplemented
18C61×#382—21no—
19C61×#380—21no—
20C61×#380C2212yes—
21C4×C4⋊C4×C61—21no—
22C4×C4⋊C4×C61C412yescomplemented
23C23×Dic61—22no—
24C22×#92418—22no—
25C2×C4⋊Dic61—28no—
26C2×C4⋊Dic61—24no—
27C2×C4×Dic61—24no—
28C2×C4×Dic61—42no—
29C2×C4×Dic61—42no—
30C4⋊#92418—24no—
31C22⋊#92418—22no—
32C22⋊#92418C2×C414yes—
33C4×#92418—24no—
34#14519684—22no—
35#14519684C2×C414yes—
36C23×C4×C61D411yescharacteristic
37C23×C4×C61D411yescharacteristic
38C23×C4×C61C2311yescharacteristic
39#117×C61—42no—
40#117×C61—42no—
41C2×C4⋊C4×C61—22no—
42C2×C4⋊C4×C61—22no—
43C2×C4⋊C4×C61C2×C414yes—
44C2×C22⋊C4×C61—22no—
45C2×C42×C61—22no—
46C2×C42×C61C2×C412yes—
47C2×C42×C61C2×C412yes—
48C2×C42×C61C2×C411yescharacteristic
49C2×C42×C61C2×C411yescharacteristic
50C2×C42×C61D412yes—
51C2×C42×C61D411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C2×C42×C61Q812yes—
54#95×C61—22no—
55#95×C61—22no—
56C24×C61C2×D411yescharacteristic
57C22×C4×C61—24no—
58C22×C4×C61—24no—
59C22×C4×C61—42no—
60C22×C4×C61C22⋊C412yes—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C412yes—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C4⋊C412yes—
67C22×C4×C61C4⋊C412yes—
68C22×C4×C61D812yes—
69C22×C4×C61SD1612yes—
70C22×C4×C61SD1612yes—
71C22×C4×C61Q1612yes—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×Q811yescharacteristic
78C22×Dic61—28no—
79C22×Dic61—24no—
80C22×Dic61—44no—
81C22×Dic61—42no—
82C22×Dic61—42no—
83C4⋊C4×C61—44no—
84C4⋊C4×C61—44no—
85C4⋊C4×C61—44no—
86C22⋊C4×C61—42no—
87C22⋊C4×C61—42no—
88C42×C61—44no—
89C42×C61C4212yes—
90C42×C61C4212yes—
91C42×C61C22⋊C412yes—
92C42×C61C22⋊C412yes—
93C42×C61C4⋊C412yes—
94C42×C61C4⋊C412yes—
95C42×C61C4⋊C412yes—
96C42×C61C4⋊C412yes—
97C4⋊Dic61—216no—
98C4×Dic61—48no—
99C2×#92418—24no—
100C2×#92418—44no—
101C23×C61—22no—
102C23×C61—22no—
103C23×C61C2×C22⋊C411yescharacteristic
104C23×C61C2×C22⋊C411yescharacteristic
105C23×C61C2×C4⋊C411yescharacteristic
106C23×C61C2×D811yescharacteristic
107C23×C61C2×SD1611yescharacteristic
108C23×C61C2×SD1611yescharacteristic
109C23×C61C2×Q1611yescharacteristic
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—24no—
114C2×C4×C61—24no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—44no—
120C2×C4×C61—44no—
121C2×C4×C61—44no—
122C2×C4×C61#9512yes—
123C2×C4×C61#9512yes—
124C2×C4×C61#9512yes—
125C2×C4×C61#9512yes—
126C2×C4×C61#10214yes—
127C2×C4×C61#10212yes—
128C2×C4×C61#10212yes—
129C2×C4×C61#10314yes—
130C2×C4×C61#10312yes—
131C2×C4×C61#10312yes—
132C2×C4×C61#10414yes—
133C2×C4×C61#10614yes—
134C2×C4×C61#10714yes—
135C2×C4×C61C2×C4211yescharacteristic
136C2×C4×C61C2×C22⋊C411yescharacteristic
137C2×C4×C61C2×C4⋊C411yescharacteristic
138C2×C4×C61C2×C4⋊C411yescharacteristic
139C2×Dic61—28no—
140C2×Dic61—44no—
141C2×Dic61—48no—
142C2×Dic61—48no—
143C2×Dic61—44no—
144#92418—44no—
145#8014—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—22no—
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—22no—
154C22×C61C2×#9511yescharacteristic
155C22×C61#41012yes—
156C22×C61C2×#10211yescharacteristic
157C22×C61C2×#10211yescharacteristic
158C22×C61C2×#10311yescharacteristic
159C22×C61C2×#10311yescharacteristic
160C22×C61C2×#10412yes—
161C22×C61C2×#10611yescharacteristic
162C22×C61C2×#10711yescharacteristic
163C4×C61—22no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—84no—
169C4×C61#33914yes—
170C4×C61#34014yes—
171C4×C61#34014yes—
172Dic61—48no—
173C2×#431—611no—
174#2285D6111yescharacteristic
175C2×C4×C4⋊C4—611no—
176#1294—614no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61#150212yes—
182C2×C61#150312yes—
183C2×C61C2×#33911yescharacteristic
184C2×C61C2×#34011yescharacteristic
185C2×C61#174011yescharacteristic
186C2×#117—21no—
187C22×C4⋊C4—1221no—
188C22×C42—1221no—
189C22×C42C2×D6111yescharacteristic
190#431—614no—
191#431—1222no—
192C2×C4⋊C8—1221no—
193C2×C22⋊C8—612no—
194C2×C4×C8—1221no—
195#384Dic6112yescomplemented
196#382—21no—
197#380—21no—
198#380C2×D6112yes—
199C4×C4⋊C4—21no—
200C4×C4⋊C4—614no—
201C4×C4⋊C4—1222no—
202C4×C4⋊C4Dic6112yescomplemented
203C2×#95—612no—
204C61#801411yescharacteristic, complemented, Sylow
205C23×C4—1222no—
206C23×C4C22⋊D6111yescharacteristic
207C23×C4C22⋊D6111yescharacteristic
208C23×C4C22×D6111yescharacteristic
209C22×C8—1222no—
210#117—42no—
211#117—42no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—1228no—
215C2×C4⋊C4—1224no—
216C2×C4⋊C4C2×Dic6114yes—
217C2×C22⋊C4—22no—
218C2×C42—22no—
219C2×C42—1224no—
220C2×C42—2442no—
221C2×C42—2442no—
222C2×C42Dic12212yes—
223C2×C42C4×D6112yes—
224C2×C42C4×D6112yes—
225C2×C42D24412yes—
226C2×C42C2×Dic6111yescharacteristic
227C2×C42C2×Dic6111yescharacteristic
228C2×C42C22⋊D6111yescharacteristic
229C2×C42C22⋊D6111yescharacteristic
230C4⋊C8—1224no—
231C22⋊C8—614no—
232C22⋊C8—1222no—
233C4×C8—1224no—
234#95—22no—
235#95—22no—
236#95—614no—
237#95—1222no—
238C24C2×C22⋊D6111yescharacteristic
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—42no—
242C22×C4—1228no—
243C22×C4—1224no—
244C22×C4—2444no—
245C22×C4—2442no—
246C22×C4—2442no—
247C22×C4#1175819612yes—
248C22×C4#1175819612yes—
249C22×C4#1175819812yes—
250C22×C4#1175819812yes—
251C22×C4#1175819912yes—
252C22×C4#1175820012yes—
253C22×C4#1175820112yes—
254C22×C4#1175820212yes—
255C22×C4C22⋊Dic6111yescharacteristic
256C22×C4C22⋊Dic6111yescharacteristic
257C22×C4C22⋊Dic6111yescharacteristic
258C22×C4C22⋊Dic6111yescharacteristic
259C22×C4C2×Dic12211yescharacteristic
260C22×C4C2×C4×D6111yescharacteristic
261C22×C4C2×C4×D6111yescharacteristic
262C22×C4C2×D24411yescharacteristic
263C22×C4C22×Dic6111yescharacteristic
264C22×C4C2×C22⋊D6111yescharacteristic
265C2×C8—1224no—
266C2×C8—2444no—
267C4⋊C4—44no—
268C4⋊C4—44no—
269C4⋊C4—44no—
270C4⋊C4—12216no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C42—44no—
274C42—2448no—
275C42C4×Dic6112yes—
276C42C4×Dic6112yes—
277C42#1175819612yes—
278C42#1175819612yes—
279C42C4⋊Dic6112yes—
280C42C4⋊Dic6112yes—
281C42#1175819812yes—
282C42#1175819812yes—
283C23—22no—
284C23—22no—
285C23C2×#1175819811yescharacteristic
286C23C2×C22⋊Dic6111yescharacteristic
287C23C2×#1175819611yescharacteristic
288C23C2×#1175819911yescharacteristic
289C23C2×#1175820111yescharacteristic
290C23C2×#1175820011yescharacteristic
291C23C2×#1175820211yescharacteristic
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—1228no—
305C2×C4—2444no—
306C2×C4—2448no—
307C2×C4—2448no—
308C2×C4—2444no—
309C2×C4#1451968412yes—
310C2×C4#1451968412yes—
311C2×C4#1451968412yes—
312C2×C4#1451968412yes—
313C2×C4#1451969714yes—
314C2×C4#1451969812yes—
315C2×C4#1451969812yes—
316C2×C4#1451970014yes—
317C2×C4#1451970112yes—
318C2×C4#1451970112yes—
319C2×C4#1451970414yes—
320C2×C4#1451970814yes—
321C2×C4#1451971014yes—
322C2×C4C2×C4×Dic6111yescharacteristic
323C2×C4C2×#1175819811yescharacteristic
324C2×C4C2×#1175819611yescharacteristic
325C2×C4C2×C4⋊Dic6111yescharacteristic
326C8—2444no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—22no—
334C22—22no—
335C22C2×#1451968411yescharacteristic
336C22#1683973612yes—
337C22C2×#1451969711yescharacteristic
338C22C2×#1451969811yescharacteristic
339C22C2×#1451970011yescharacteristic
340C22C2×#1451970111yescharacteristic
341C22C2×#1451970412yes—
342C22C2×#1451970811yescharacteristic
343C22C2×#1451971011yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—84no—
350C4—2448no—
351C4#1683952114yes—
352C4#1683952414yes—
353C4#1683952414yes—
354C2—21no—
355C2—21no—
356C2—21no—
357C2—21no—
358C2#2144431412yes—
359C2#2144431812yes—
360C2C2×#1683952111yescharacteristic
361C2C2×#1683952411yescharacteristic
362C2#2144555211yescharacteristic
subgroupG/H
centerC22×C4C22⋊Dic61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#2285C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#2285D61
hypocenterC61#8014
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
8. #16839815C4semidirect
13. C4×C4⋊Dic61C4semidirect
17. C61×#384C4semidirect
22. C4×C4⋊C4×C61C4semidirect
195. #384Dic61semidirect
202. C4×C4⋊C4Dic61semidirect
204. C61#8014semidirect

Maximal subgroups

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

subgroupindex
C2×#168398152
C2×C4×C4⋊Dic612
#214436972
C61×#22852
#801461