Finite Group Databasebeta

← #29574008

Subgroups — #29574008

Order 15616.

612 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448437C211yesmaximal, characteristic
2#21446009C212yesmaximal
3#21444072C211yesmaximal, characteristic
4#21443699C212yesmaximal
5C2×C61×#324C211yesmaximal, characteristic
6C2×#14519736—21no—
7C22×C4⋊Dic61C2211yescharacteristic
8C2×#14519711—22no—
9#16839661—22no—
10#16839661—22no—
11#16839622—21no—
12#16839622C2212yes—
13C2×#14519684—21no—
14C2×#14519684—21no—
15C2×#14519684C2211yescharacteristic
16#16839525—22no—
17C22×C4⋊C4×C61C2211yescharacteristic
18C2×C22⋊C8×C61C2212yes—
19C61×#324C414yescomplemented
20C23×Dic61—21no—
21C23×Dic61—21no—
22#14519736—42no—
23#14519736—42no—
24C2×C4⋊Dic61—22no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—42no—
30C2×C4⋊Dic61D412yes—
31C2×C4⋊Dic61D412yes—
32C2×C22⋊Dic61—22no—
33C2×C4×Dic61—22no—
34#14519711—44no—
35#14519684—22no—
36#14519684—22no—
37#14519684—22no—
38#14519684—42no—
39#14519684—42no—
40C23×C4×C61D411yescharacteristic
41C23×C4×C61D411yescharacteristic
42C23×C4×C61C2311yescharacteristic
43C22×C8×C61—22no—
44C2×C4⋊C4×C61—22no—
45C2×C4⋊C4×C61—22no—
46C2×C4⋊C4×C61C2×C412yes—
47C2×C4⋊C4×C61Q812yes—
48C22⋊C8×C61—22no—
49C22⋊C8×C61C2×C414yes—
50C24×C61C2×D411yescharacteristic
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61—41no—
61C22×C4×C61C4⋊C412yes—
62C22×C4×C61C4⋊C412yes—
63C22×C4×C61D812yes—
64C22×C4×C61Q1612yes—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D412yes—
67C22×C4×C61C2×Q811yescharacteristic
68C22×C4×C61#4112yes—
69C22×Dic61—22no—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61—41no—
81C22×Dic61—41no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C2×C8×C61—24no—
86C2×C8×C61—42no—
87C2×C8×C61—42no—
88C4⋊C4×C61—24no—
89C4⋊C4×C61—24no—
90C22⋊Dic61—42no—
91C22⋊Dic61—42no—
92C4⋊Dic61—24no—
93C4⋊Dic61—42no—
94C4⋊Dic61—42no—
95C4⋊Dic61—42no—
96C4⋊Dic61—42no—
97C4⋊Dic61—42no—
98C4⋊Dic61—81no—
99C4⋊Dic61—81no—
100C4×Dic61—44no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61C2×C4⋊C411yescharacteristic
106C23×C61#12011yescharacteristic
107C23×C61#12311yescharacteristic
108C23×C61C2×D811yescharacteristic
109C23×C61C2×Q1611yescharacteristic
110C23×C61AGL(1,ℤ/8)11yescharacteristic
111C23×C61#13711yescharacteristic
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—22no—
115C2×C4×C61—22no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—81no—
128C2×C4×C61#10714yescomplemented
129C2×C4×C61C4×D412yes—
130C2×C4×C61C22⋊Q812yes—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148C2×Dic61—81no—
149C2×Dic61—81no—
150C2×Dic61—81no—
151C8×C61—44no—
152#8856—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61#38511yescharacteristic
166C22×C61C2×#10711yescharacteristic
167C22×C61#42811yescharacteristic
168C22×C61#44711yescharacteristic
169C22×C61#45111yescharacteristic
170C22×C61#45411yescharacteristic
171C22×C61#45611yescharacteristic
172C22×C61B(4,𝔽2)11yescharacteristic
173C22×C61#45811yescharacteristic
174C22×C61#48011yescharacteristic
175C22×C61#48411yescharacteristic
176C4×C61—24no—
177C4×C61—22no—
178C4×C61—22no—
179C4×C61—42no—
180Dic61—82no—
181Dic61—82no—
182Dic61—82no—
183Dic61—82no—
184#2316—611no—
185#1852—612no—
186C2×#324D6111yescharacteristic
187#1441—611no—
188#1294—612no—
189C2×C61—21no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—21no—
193C2×C61#159811yescharacteristic
194C2×C61#160511yescharacteristic
195C2×C61#161011yescharacteristic
196C2×C61#161711yescharacteristic
197C2×C61#185211yescharacteristic
198C2×C61#185711yescharacteristic
199C2×C61#186711yescharacteristic
200C2×#117—1221no—
201C22×C4⋊C4—611no—
202C22×C4⋊C4C2×D6111yescharacteristic
203C2×#107—1222no—
204C2×C22⋊C8C2×D6112yes—
205#389—1222no—
206#389—1222no—
207#380—612no—
208#380—1221no—
209C2×#95—611no—
210C2×#95—1221no—
211C2×#95—1221no—
212#340—1222no—
213#324Dic6114yescomplemented
214C61#885611yescharacteristic, complemented, Sylow
215C23×C4—1221no—
216C23×C4—1221no—
217C23×C4D24411yescharacteristic
218C23×C4D24411yescharacteristic
219C23×C4C22×D6111yescharacteristic
220C22×C8—22no—
221#117—2442no—
222#117—2442no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—612no—
226C2×C4⋊C4—612no—
227C2×C4⋊C4—1222no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—2442no—
233C2×C4⋊C4Dic12212yes—
234C2×C4⋊C4C2×Dic6112yes—
235C2×C22⋊C4—1222no—
236C2×C42—1222no—
237#107—2444no—
238C22⋊C8—22no—
239C22⋊C8C2×Dic6114yes—
240#95—1222no—
241#95—1222no—
242#95—1222no—
243#95—2442no—
244#95—2442no—
245C24C2×D24411yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—1222no—
257C22×C4—1222no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4D48812yes—
273C22×C4Dic24412yes—
274C22×C4C4⋊Dic6112yes—
275C22×C4C4⋊Dic6112yes—
276C22×C4C2×Dic12211yescharacteristic
277C22×C4D4×D6112yes—
278C22×C4#1175822412yes—
279C22×C4C22×Dic6111yescharacteristic
280C2×C8—24no—
281C2×C8—42no—
282C2×C8—42no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—1224no—
286C4⋊C4—4881no—
287C4⋊C4—4881no—
288C4⋊C4—2442no—
289C4⋊C4—2442no—
290C4⋊C4—2442no—
291C4⋊C4—2442no—
292C4⋊C4—2442no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C42—2444no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23C2×C4⋊Dic6111yescharacteristic
301C23#1451974711yescharacteristic
302C23#1451976111yescharacteristic
303C23C2×D48811yescharacteristic
304C23C2×Dic24411yescharacteristic
305C23#1451980511yescharacteristic
306C23#1451981011yescharacteristic
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—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—4881no—
324C2×C4—4881no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4#1451971114yescomplemented
344C2×C4D4×Dic6112yes—
345C2×C4#1451975412yes—
346C8—44no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#1683963711yescharacteristic
360C22C2×#1451971111yescharacteristic
361C22#1683980411yescharacteristic
362C22#1683989811yescharacteristic
363C22#1683992011yescharacteristic
364C22#1683993711yescharacteristic
365C22#1683994711yescharacteristic
366C22#1683995011yescharacteristic
367C22#1683995311yescharacteristic
368C22#1684007611yescharacteristic
369C22#1684009811yescharacteristic
370C4—24no—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—4882no—
375C4—4882no—
376C4—4882no—
377C4—4882no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#2144475611yescharacteristic
383C2#2144479511yescharacteristic
384C2#2144482411yescharacteristic
385C2#2144486311yescharacteristic
386C2#2144600911yescharacteristic
387C2#2144603611yescharacteristic
388C2#2144610211yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenterC2×#324D61
hypocenterC61#8856
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
19. C61×#324C4semidirect
128. C2×C4×C61#107semidirect
213. #324Dic61semidirect
214. C61#8856semidirect
343. C2×C4#14519711semidirect

Maximal subgroups

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

subgroupindex
#214484372
#214460092
#214440722
#214436992
C2×C61×#3242
#885661