Finite Group Databasebeta

← #29569690

Subgroups — #29569690

Order 15616.

666 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839819C211yesmaximal, characteristic
2C2×#16839819C211yesmaximal, characteristic
3#21443667C214yesmaximal
4C4×#117×C61C211yesmaximal, characteristic
5#16839819—21no—
6#16839819—21no—
7#16839819—21no—
8#16839819—21no—
9#16839819—21no—
10#16839819—21no—
11#16839819C412yescomplemented
12#16839819C412yescomplemented
13C2×C4⋊#92418—21no—
14C2×C4⋊#92418C412yescomplemented
15C2×C22⋊#92418C2212yes—
16C2×C22⋊#92418C2212yes—
17C2×#14519688—21no—
18C2×#14519688C412yescomplemented
19C2×#117×C61C412yes—
20C22×C42×C61C2211yescharacteristic
21C4×C4⋊C4×C61—21no—
22C4×C4⋊C4×C61—21no—
23C4×C22⋊C4×C61C412yes—
24C4×C22⋊C4×C61C2212yes—
25C61×#376—21no—
26C43×C61—21no—
27C22×#92418—22no—
28C22×#92418C2×C414yes—
29C4⋊#92418—22no—
30C4⋊#92418—22no—
31C4⋊#92418—22no—
32C4⋊#92418—22no—
33C22⋊#92418—22no—
34C22⋊#92418—22no—
35C22⋊#92418—22no—
36C22⋊#92418C2×C414yes—
37#14519688—22no—
38#14519688—22no—
39#14519688—22no—
40#14519688—22no—
41C23×C4×C61C2×C411yescharacteristic
42C23×C4×C61C2×C411yescharacteristic
43C23×C4×C61C2311yescharacteristic
44#117×C61—28no—
45C2×C4⋊C4×C61—22no—
46C2×C22⋊C4×C61C2×C414yes—
47C2×C42×C61—22no—
48C2×C42×C61—22no—
49C2×C42×C61—22no—
50C2×C42×C61C2×C411yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C2×C42×C61D411yescharacteristic
56C2×C42×C61D411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C2×C42×C61Q811yescharacteristic
61C2×C42×C61Q811yescharacteristic
62#95×C61—22no—
63#95×C61—22no—
64C24×C61C22×C411yescharacteristic
65C22×C4×C61—24no—
66C22×C4×C61—24no—
67C22×C4×C61—42no—
68C22×C4×C61—42no—
69C22×C4×C61C4211yescharacteristic
70C22×C4×C61C4211yescharacteristic
71C22×C4×C61C4211yescharacteristic
72C22×C4×C61C4211yescharacteristic
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×C61C22×C411yescharacteristic
82C22×C4×C61C22×C411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×Q811yescharacteristic
87C4⋊C4×C61—28no—
88C22⋊C4×C61—24no—
89C22⋊C4×C61M1618yes—
90C42×C61—28no—
91C42×C61—44no—
92C42×C61—44no—
93C42×C61C22⋊C411yescharacteristic
94C42×C61C22⋊C411yescharacteristic
95C42×C61C22⋊C411yescharacteristic
96C42×C61C22⋊C411yescharacteristic
97C42×C61C22⋊C411yescharacteristic
98C42×C61C22⋊C411yescharacteristic
99C42×C61C22⋊C411yescharacteristic
100C42×C61C22⋊C411yescharacteristic
101C42×C61C4⋊C411yescharacteristic
102C42×C61C4⋊C411yescharacteristic
103C42×C61C4⋊C411yescharacteristic
104C42×C61C4⋊C411yescharacteristic
105C42×C61C4⋊C411yescharacteristic
106C42×C61C4⋊C411yescharacteristic
107C42×C61C4⋊C411yescharacteristic
108C42×C61C4⋊C411yescharacteristic
109C2×#92418—24no—
110C2×#92418—24no—
111C2×#92418—44no—
112C2×#92418—44no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61C2×C4211yescharacteristic
116C23×C61C2×C22⋊C411yescharacteristic
117C23×C61C2×C4⋊C411yescharacteristic
118C23×C61C2×M1614yes—
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—22no—
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—28no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—44no—
139C2×C4×C61—44no—
140C2×C4×C61#9511yescharacteristic
141C2×C4×C61#9511yescharacteristic
142C2×C4×C61#9511yescharacteristic
143C2×C4×C61#9511yescharacteristic
144C2×C4×C61#9511yescharacteristic
145C2×C4×C61#9511yescharacteristic
146C2×C4×C61#9511yescharacteristic
147C2×C4×C61#9511yescharacteristic
148C2×C4×C61C2×C22⋊C411yescharacteristic
149C2×C4×C61C2×C22⋊C411yescharacteristic
150C2×C4×C61C2×C4⋊C411yescharacteristic
151C2×C4×C61C2×C4⋊C411yescharacteristic
152#92418—44no—
153#92418—44no—
154#7930—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—44no—
162C22×C61C2×#9511yescharacteristic
163C22×C61C4×M1612yes—
164C22×C61#40712yes—
165C22×C61#42312yes—
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—21no—
175C4×C61—21no—
176C4×C61—48no—
177C4×C61#34412yes—
178C4×C61#41012yes—
179C2×#432—611no—
180C2×#432—611no—
181C4×#117D6111yescharacteristic
182#1282—614no—
183C2×C61—22no—
184C2×C61—22no—
185C2×C61—22no—
186C2×C61#172811yescharacteristic
187C2×C61#174011yescharacteristic
188C2×C61C2×#34411yescharacteristic
189C2×#117Dic6112yes—
190C22×C42C2×D6111yescharacteristic
191#432—612no—
192#432—612no—
193#432—1221no—
194#432—1221no—
195#432—1221no—
196#432—1221no—
197#432—1221no—
198#432—1221no—
199C2×C4⋊C8—612no—
200C2×C4⋊C8—1221no—
201C2×C22⋊C8—612no—
202C2×C22⋊C8—612no—
203C2×#97—612no—
204C2×#97—1221no—
205C4×C4⋊C4—21no—
206C4×C4⋊C4—21no—
207C4×C22⋊C4Dic6112yes—
208C4×C22⋊C4C2×D6112yes—
209#376—21no—
210C43—21no—
211C61#793011yescharacteristic, complemented, Sylow
212C23×C4C2×Dic6111yescharacteristic
213C23×C4C2×Dic6111yescharacteristic
214C23×C4C22×D6111yescharacteristic
215C22×C8—614no—
216C22×C8—1222no—
217#117—28no—
218C2×C4⋊C4—22no—
219C2×C22⋊C4C2×Dic6114yes—
220C2×C42—22no—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42Dic12211yescharacteristic
224C2×C42Dic12211yescharacteristic
225C2×C42C4×D6111yescharacteristic
226C2×C42C4×D6111yescharacteristic
227C2×C42C4×D6111yescharacteristic
228C2×C42C4×D6111yescharacteristic
229C2×C42D24411yescharacteristic
230C2×C42D24411yescharacteristic
231C2×C42C22⋊D6111yescharacteristic
232C2×C42C22⋊D6111yescharacteristic
233C2×C42C22⋊D6111yescharacteristic
234C2×C42C22⋊D6111yescharacteristic
235C4⋊C8—1222no—
236C4⋊C8—1222no—
237C4⋊C8—1222no—
238C4⋊C8—1222no—
239C22⋊C8—614no—
240C22⋊C8—1222no—
241C22⋊C8—1222no—
242C22⋊C8—1222no—
243#97—1222no—
244#97—1222no—
245#97—1222no—
246#97—1222no—
247#95—22no—
248#95—22no—
249C24C22×Dic6111yescharacteristic
250C22×C4—24no—
251C22×C4—24no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4C4×Dic6111yescharacteristic
255C22×C4C4×Dic6111yescharacteristic
256C22×C4C4×Dic6111yescharacteristic
257C22×C4C4×Dic6111yescharacteristic
258C22×C4C4⋊Dic6111yescharacteristic
259C22×C4C4⋊Dic6111yescharacteristic
260C22×C4C4⋊Dic6111yescharacteristic
261C22×C4C4⋊Dic6111yescharacteristic
262C22×C4C22⋊Dic6111yescharacteristic
263C22×C4C22⋊Dic6111yescharacteristic
264C22×C4C22⋊Dic6111yescharacteristic
265C22×C4C22⋊Dic6111yescharacteristic
266C22×C4C2×Dic12211yescharacteristic
267C22×C4C2×C4×D6111yescharacteristic
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4C2×D24411yescharacteristic
270C22×C4C2×C22⋊D6111yescharacteristic
271C22×C4C2×C22⋊D6111yescharacteristic
272C2×C8—1224no—
273C2×C8—1224no—
274C2×C8—2444no—
275C2×C8—2444no—
276C4⋊C4—28no—
277C22⋊C4—24no—
278C22⋊C4#1175819418yes—
279C42—28no—
280C42—44no—
281C42—44no—
282C42#1175819611yescharacteristic
283C42#1175819611yescharacteristic
284C42#1175819611yescharacteristic
285C42#1175819611yescharacteristic
286C42#1175819611yescharacteristic
287C42#1175819611yescharacteristic
288C42#1175819611yescharacteristic
289C42#1175819611yescharacteristic
290C42#1175819811yescharacteristic
291C42#1175819811yescharacteristic
292C42#1175819811yescharacteristic
293C42#1175819811yescharacteristic
294C42#1175819811yescharacteristic
295C42#1175819811yescharacteristic
296C42#1175819811yescharacteristic
297C42#1175819811yescharacteristic
298C23—41no—
299C23—41no—
300C23C2×C4×Dic6111yescharacteristic
301C23C2×C22⋊Dic6111yescharacteristic
302C23C2×C4⋊Dic6111yescharacteristic
303C23C2×#1175819414yes—
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—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—28no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—44no—
324C2×C4—44no—
325C2×C4#1451968411yescharacteristic
326C2×C4#1451968411yescharacteristic
327C2×C4#1451968411yescharacteristic
328C2×C4#1451968411yescharacteristic
329C2×C4#1451968411yescharacteristic
330C2×C4#1451968411yescharacteristic
331C2×C4#1451968411yescharacteristic
332C2×C4#1451968411yescharacteristic
333C2×C4C2×#1175819811yescharacteristic
334C2×C4C2×#1175819811yescharacteristic
335C2×C4C2×#1175819611yescharacteristic
336C2×C4C2×#1175819611yescharacteristic
337C8—2444no—
338C8—2444no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—44no—
346C22C2×#1451968411yescharacteristic
347C22C4×#1175819412yes—
348C22#1683972612yes—
349C22#1683978612yes—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—48no—
361C4#1683953212yes—
362C4#1683973512yes—
363C2—22no—
364C2—22no—
365C2—22no—
366C2#2144551311yescharacteristic
367C2#2144555111yescharacteristic
368C2C2×#1683953211yescharacteristic
subgroupG/H
centerC2×C4C2×#11758198
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC4×#117×C61C2
socleC22×C61C2×#95
prime radicalC24×C61C22×C4
cosocleC23×C4×C61C23
hypercenterC4×#117D61
hypocenterC61#7930
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
11. #16839819C4semidirect
12. #16839819C4semidirect
14. C2×C4⋊#92418C4semidirect
18. C2×#14519688C4semidirect
211. C61#7930semidirect

Maximal subgroups

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

subgroupindex
C2×#168398192
#214436672
C4×#117×C612
#793061