Finite Group Databasebeta

← #29570232

Subgroups — #29570232

Order 15616.

648 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758194C211yesmaximal, characteristic
2#21448217C211yesmaximal, characteristic
3#21443711C214yesmaximal, complemented
4C61×#2920C211yesmaximal, characteristic
5C22×#11758194—21no—
6C4×#11758194—21no—
7C4×#11758194—21no—
8C4×#11758194C412yescomplemented
9C4×#11758194C2212yes—
10C2×#14519688C412yescomplemented
11C2×C4×#92418—21no—
12#16839630—21no—
13#16839628C412yes—
14#16839625C412yes—
15#16839622—21no—
16C4×C4⋊Dic61—21no—
17C4×C22⋊Dic61—21no—
18#16839608C2212yes—
19C22×C42×C61C2211yescharacteristic
20C61×#432—21no—
21C61×#432C2212yes—
22C61×#431—21no—
23C61×#431C412yescomplemented
24C61×#423C412yescomplemented
25C61×#407—21no—
26C4×M16×C61—21no—
27C2×#11758194—28no—
28C2×#11758194—22no—
29C2×#11758194—22no—
30C22×#92418—22no—
31C2×C4⋊Dic61—22no—
32C2×C22⋊Dic61—22no—
33C2×C4×Dic61—22no—
34#14519688—22no—
35#14519688C2×C414yes—
36C4×#92418—22no—
37C4×#92418—22no—
38#14519684—22no—
39#14519684—22no—
40#14519684—22no—
41#14519684C2×C414yes—
42C23×C4×C61C2×C411yescharacteristic
43C23×C4×C61D411yescharacteristic
44C23×C4×C61D411yescharacteristic
45C2×M16×C61—22no—
46C2×C42×C61C2×C411yescharacteristic
47C2×C42×C61C2×C411yescharacteristic
48C2×C42×C61C2×C411yescharacteristic
49C2×C42×C61C2×C411yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C2×C42×C61Q811yescharacteristic
56C2×C42×C61Q811yescharacteristic
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—22no—
59C4⋊C8×C61C2×C414yes—
60C22⋊C8×C61—22no—
61C22⋊C8×C61—22no—
62#97×C61—22no—
63C4×C8×C61—22no—
64C24×C61C22⋊C411yescharacteristic
65C22×C4×C61—24no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61C4211yescharacteristic
69C22×C4×C61C4211yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C4⋊C411yescharacteristic
78C22×C4×C61C4⋊C411yescharacteristic
79C22×C4×C61C4⋊C411yescharacteristic
80C22×C4×C61C4⋊C411yescharacteristic
81C22×C4×C61C4⋊C411yescharacteristic
82C22×C4×C61C4⋊C411yescharacteristic
83C22×C4×C61C22×C411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×Dic61—24no—
87M16×C61—44no—
88C2×C8×C61—24no—
89C42×C61C4211yescharacteristic
90C42×C61C4211yescharacteristic
91C42×C61C22⋊C411yescharacteristic
92C42×C61C22⋊C411yescharacteristic
93C42×C61C22⋊C411yescharacteristic
94C42×C61C22⋊C411yescharacteristic
95C42×C61C4⋊C411yescharacteristic
96C42×C61C4⋊C411yescharacteristic
97C42×C61C4⋊C411yescharacteristic
98C42×C61C4⋊C411yescharacteristic
99C42×C61C4⋊C411yescharacteristic
100C42×C61C4⋊C411yescharacteristic
101C42×C61C22×C411yescharacteristic
102C42×C61C22×C411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61C2×Q811yescharacteristic
105C22⋊Dic61—44no—
106C4⋊Dic61—44no—
107C4×Dic61—44no—
108#11758194—28no—
109#11758194—28no—
110C2×#92418—28no—
111C2×#92418—24no—
112C23×C61—22no—
113C23×C61—22no—
114C23×C61—41no—
115C23×C61#9511yescharacteristic
116C23×C61#9511yescharacteristic
117C23×C61C2×C22⋊C411yescharacteristic
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
123C2×C4×C61—22no—
124C2×C4×C61—22no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61#9511yescharacteristic
136C2×C4×C61#9511yescharacteristic
137C2×C4×C61#9511yescharacteristic
138C2×C4×C61#9511yescharacteristic
139C2×C4×C61#9511yescharacteristic
140C2×C4×C61#9511yescharacteristic
141C2×C4×C61#10414yes—
142C2×C4×C61C2×C4211yescharacteristic
143C2×C4×C61C2×C22⋊C411yescharacteristic
144C2×C4×C61C2×C22⋊C411yescharacteristic
145C2×C4×C61C2×C4⋊C411yescharacteristic
146C2×C4×C61C2×C4⋊C411yescharacteristic
147C2×C4×C61C2×C4⋊C411yescharacteristic
148C2×Dic61—44no—
149C2×Dic61—44no—
150C2×Dic61—44no—
151C8×C61—44no—
152#92418—28no—
153#8074—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—44no—
162C22×C61#34412yes—
163C22×C61C2×#9511yescharacteristic
164C22×C61C2×#10412yes—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61#33912yes—
175C4×C61#33912yes—
176C4×C61#42112yes—
177Dic61—84no—
178#2920D6111yescharacteristic
179C2×C4×M16—611no—
180#2283—611no—
181#1300—614no—
182C2×C61—22no—
183C2×C61—22no—
184C2×C61—41no—
185C2×C61C2×#33911yescharacteristic
186C2×C61#173311yescharacteristic
187C2×C61C2×#34411yescharacteristic
188C22×M16—1221no—
189C22×C42C2×D6111yescharacteristic
190#432—21no—
191#432C2×D6112yes—
192#431—21no—
193#431Dic6112yescomplemented
194#423Dic6112yescomplemented
195#407—21no—
196C4×M16—21no—
197C4×M16—612no—
198C4×M16—612no—
199C4×M16—1221no—
200C4×M16—1221no—
201C2×#97—612no—
202C2×C4×C8—1221no—
203#383—1221no—
204#382—612no—
205#381—612no—
206#380—1221no—
207C4×C4⋊C4—1221no—
208C4×C22⋊C4—1221no—
209#376—612no—
210C61#807411yescharacteristic, complemented, Sylow
211C23×C4C4×D6111yescharacteristic
212C23×C4D24411yescharacteristic
213C23×C4C22⋊D6111yescharacteristic
214C2×M16—22no—
215C2×M16—1228no—
216C2×M16—1222no—
217C2×M16—1222no—
218C22×C8—1222no—
219C2×C4⋊C4—1222no—
220C2×C22⋊C4—1222no—
221C2×C42—1222no—
222C2×C42Dic12211yescharacteristic
223C2×C42Dic12211yescharacteristic
224C2×C42C4×D6111yescharacteristic
225C2×C42C4×D6111yescharacteristic
226C2×C42C4×D6111yescharacteristic
227C2×C42D24411yescharacteristic
228C2×C42C2×Dic6111yescharacteristic
229C2×C42C2×Dic6111yescharacteristic
230C2×C42C22⋊D6111yescharacteristic
231C2×C42C22⋊D6111yescharacteristic
232C2×C42C22⋊D6111yescharacteristic
233C2×C42C22×D6111yescharacteristic
234C4⋊C8—22no—
235C4⋊C8C2×Dic6114yes—
236C22⋊C8—22no—
237C22⋊C8—22no—
238#97—22no—
239#97—614no—
240#97—1222no—
241C4×C8—22no—
242C4×C8—1222no—
243C4×C8—1222no—
244#95—614no—
245#95—1222no—
246#95—1222no—
247#95—1222no—
248C24#1175819811yescharacteristic
249C22×C4—24no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—1224no—
253C22×C4C4×Dic6111yescharacteristic
254C22×C4C4×Dic6111yescharacteristic
255C22×C4#1175819611yescharacteristic
256C22×C4#1175819611yescharacteristic
257C22×C4#1175819611yescharacteristic
258C22×C4#1175819611yescharacteristic
259C22×C4C4⋊Dic6111yescharacteristic
260C22×C4C4⋊Dic6111yescharacteristic
261C22×C4#1175819811yescharacteristic
262C22×C4#1175819811yescharacteristic
263C22×C4#1175819811yescharacteristic
264C22×C4#1175819811yescharacteristic
265C22×C4#1175819811yescharacteristic
266C22×C4C22⋊Dic6111yescharacteristic
267C22×C4C22⋊Dic6111yescharacteristic
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4C2×D24411yescharacteristic
270C22×C4C2×C22⋊D6111yescharacteristic
271M16—44no—
272M16—1228no—
273M16—1228no—
274C2×C8—24no—
275C2×C8—1228no—
276C2×C8—1224no—
277C4⋊C4—2444no—
278C22⋊C4—2444no—
279C42—2444no—
280C42C4×Dic6111yescharacteristic
281C42C4×Dic6111yescharacteristic
282C42#1175819611yescharacteristic
283C42#1175819611yescharacteristic
284C42#1175819611yescharacteristic
285C42#1175819611yescharacteristic
286C42C4⋊Dic6111yescharacteristic
287C42C4⋊Dic6111yescharacteristic
288C42#1175819811yescharacteristic
289C42#1175819811yescharacteristic
290C42C22⋊Dic6111yescharacteristic
291C42C22⋊Dic6111yescharacteristic
292C42C2×Dic12211yescharacteristic
293C42C2×C4×D6111yescharacteristic
294C42C22×Dic6111yescharacteristic
295C42C2×C22⋊D6111yescharacteristic
296C23—22no—
297C23—22no—
298C23—41no—
299C23#1451968411yescharacteristic
300C23#1451968411yescharacteristic
301C23C2×#1175819811yescharacteristic
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—2444no—
320C2×C4—2444no—
321C2×C4—2444no—
322C2×C4#1451968411yescharacteristic
323C2×C4#1451968411yescharacteristic
324C2×C4#1451968411yescharacteristic
325C2×C4#1451968411yescharacteristic
326C2×C4#1451968411yescharacteristic
327C2×C4#1451968411yescharacteristic
328C2×C4#1451970314yes—
329C2×C4C2×C4×Dic6111yescharacteristic
330C2×C4C2×#1175819811yescharacteristic
331C2×C4C2×C22⋊Dic6111yescharacteristic
332C2×C4C2×#1175819611yescharacteristic
333C2×C4C2×#1175819611yescharacteristic
334C2×C4C2×C4⋊Dic6111yescharacteristic
335C8—44no—
336C8—1228no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—44no—
345C22#1683953312yes—
346C22C2×#1451968411yescharacteristic
347C22C2×#1451970312yes—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—4884no—
358C4#1683952312yes—
359C4#1683952312yes—
360C4#1683977912yes—
361C2—22no—
362C2—22no—
363C2—41no—
364C2C2×#1683952311yescharacteristic
365C2#2144552811yescharacteristic
366C2C2×#1683953311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic61
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC61×#2920C2
socleC22×C61C2×#95
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2920D61
hypocenterC61#8074
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
3. #21443711C2semidirect
8. C4×#11758194C4semidirect
10. C2×#14519688C4semidirect
23. C61×#431C4semidirect
24. C61×#423C4semidirect
193. #431Dic61semidirect
194. #423Dic61semidirect
210. C61#8074semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581942
#214482172
#214437112
C61×#29202
#807461