Finite Group Databasebeta

← #29573338

Subgroups — #29573338

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839607C211yesmaximal, characteristic
2#21445885C212yesmaximal
3#21443662C211yesmaximal, characteristic
4#21443661C212yesmaximal
5C61×#1280C211yesmaximal, characteristic
6C22×C4×Dic61C411yescharacteristic
7C22×C4×Dic61C411yescharacteristic
8C22×C4×Dic61C2211yescharacteristic
9C2×C22⋊#92418C2212yes—
10#16839607—24no—
11C2×#14519684C411yescharacteristic
12C2×#14519684C411yescharacteristic
13C2×#14519684C2211yescharacteristic
14#16839516—24no—
15C2×C22⋊C8×C61C2212yes—
16C2×#95×C61C2211yescharacteristic
17C23×Dic61C2×C411yescharacteristic
18C23×Dic61C2×C411yescharacteristic
19C23×Dic61C2×C411yescharacteristic
20C23×Dic61C2×C411yescharacteristic
21C22×#92418—22no—
22C2×C4×Dic61—22no—
23C2×C4×Dic61—22no—
24C2×C4×Dic61—21no—
25C2×C4×Dic61—21no—
26C2×C4×Dic61—22no—
27C2×C4×Dic61—22no—
28C2×C4×Dic61—22no—
29C2×C4×Dic61—22no—
30C2×C4×Dic61C814yescomplemented
31C2×C4×Dic61D414yes—
32C22⋊#92418—22no—
33C22⋊#92418—22no—
34#14519684—22no—
35#14519684—22no—
36#14519684—22no—
37C23×C4×C61C2×C411yescharacteristic
38C23×C4×C61C2×C411yescharacteristic
39C23×C4×C61C2311yescharacteristic
40C22×C8×C61—22no—
41C22⋊C8×C61—22no—
42C22⋊C8×C61—22no—
43#95×C61—22no—
44C24×C61C22×C411yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—41no—
50C22×C4×C61—41no—
51C22×C4×C61—41no—
52C22×C4×C61—41no—
53C22×C4×C61—41no—
54C22×C4×C61—41no—
55C22×C4×C61C2×C812yes—
56C22×C4×C61M1612yes—
57C22×C4×C61C2×D412yes—
58C22×C4×C61#4112yes—
59C22×C4×C61#4111yescharacteristic
60C22×C4×C61#4111yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—41no—
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61C22⋊C412yes—
78C22×Dic61C22⋊C412yes—
79C22×Dic61C2×C812yes—
80C22×Dic61C2×C812yes—
81C22×Dic61M1612yes—
82C22×Dic61M1612yes—
83C2×C8×C61—42no—
84C2×C8×C61—42no—
85C2×C8×C61—42no—
86C4×Dic61—28no—
87C4×Dic61—24no—
88C4×Dic61—24no—
89C4×Dic61—28no—
90C2×#92418—42no—
91C2×#92418—42no—
92C2×#92418—42no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61C2×C22⋊C411yescharacteristic
98C23×C61#11711yescharacteristic
99C23×C61#11711yescharacteristic
100C23×C61C22×C811yescharacteristic
101C23×C61C2×M1611yescharacteristic
102C23×C61C2×M1611yescharacteristic
103C23×C61C2×M1611yescharacteristic
104C2×C4×C61—22no—
105C2×C4×C61—22no—
106C2×C4×C61—22no—
107C2×C4×C61—22no—
108C2×C4×C61—41no—
109C2×C4×C61—42no—
110C2×C4×C61—41no—
111C2×C4×C61—42no—
112C2×C4×C61—42no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61#12312yes—
120C2×C4×C61#12312yes—
121C2×Dic61—22no—
122C2×Dic61—22no—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—22no—
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61C22⋊C814yes—
143C8×C61—82no—
144#92418—82no—
145#8699—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61#38111yescharacteristic
159C22×C61C2×C22⋊C811yescharacteristic
160C22×C61#40711yescharacteristic
161C22×C61#41011yescharacteristic
162C22×C61#41011yescharacteristic
163C22×C61#41311yescharacteristic
164C22×C61#41311yescharacteristic
165C22×C61#43111yescharacteristic
166C22×C61#43111yescharacteristic
167C22×C61#43211yescharacteristic
168C22×C61#43211yescharacteristic
169C4×C61—22no—
170C4×C61—22no—
171C4×C61—42no—
172C4×C61—42no—
173Dic61—24no—
174Dic61—42no—
175Dic61—42no—
176Dic61—42no—
177C2×#376—611no—
178#1817—612no—
179#1280—612no—
180#1280—611no—
181#1280D6111yescharacteristic
182C2×C61—21no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61#145811yescharacteristic
187C2×C61#145811yescharacteristic
188C2×C61#146411yescharacteristic
189C2×C61#146411yescharacteristic
190C2×C61#181711yescharacteristic
191C2×C61#182011yescharacteristic
192C2×C61#182211yescharacteristic
193C22×C42—611no—
194C22×C42—611no—
195C22×C42—611no—
196C2×C22⋊C8—612no—
197C2×C22⋊C8C2×D6112yes—
198#376—1224no—
199C2×#95—611no—
200C2×#95—611no—
201C2×#95—611no—
202C2×#95C2×D6111yescharacteristic
203#336—1224no—
204C61#869911yescharacteristic, complemented, Sylow
205C23×C4—611no—
206C23×C4—611no—
207C23×C4—611no—
208C23×C4—611no—
209C23×C4C4×D6111yescharacteristic
210C23×C4C4×D6111yescharacteristic
211C23×C4C22×D6111yescharacteristic
212C22×C8—22no—
213C22×C8—1222no—
214C2×C42—614no—
215C2×C42—614no—
216C2×C42—1222no—
217C2×C42—1222no—
218C2×C42—1222no—
219C2×C42—1222no—
220C2×C42—1222no—
221C2×C42—1222no—
222C2×C42—1221no—
223C2×C42—1221no—
224C22⋊C8—22no—
225C22⋊C8—22no—
226C22⋊C8—1222no—
227C22⋊C8—1222no—
228#95—22no—
229#95—1222no—
230#95—1222no—
231#95—1222no—
232C24C2×C4×D6111yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—612no—
244C22×C4—612no—
245C22×C4—612no—
246C22×C4—612no—
247C22×C4—612no—
248C22×C4—612no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—2441no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4C8×D6112yes—
266C22×C4#1175818912yes—
267C22×C4#1175822212yes—
268C22×C4D4×D6112yes—
269C22×C4#1175822411yescharacteristic
270C22×C4#1175822611yescharacteristic
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—2442no—
275C2×C8—2442no—
276C2×C8—2442no—
277C42—1228no—
278C42—1228no—
279C42—1224no—
280C42—1224no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23C22⋊C4×D6111yescharacteristic
286C23#1451973411yescharacteristic
287C23#1451973511yescharacteristic
288C23C2×C8×D6111yescharacteristic
289C23M16×D6111yescharacteristic
290C23M16×D6111yescharacteristic
291C23C2×#1175818911yescharacteristic
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—614no—
308C2×C4—1222no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4—1222no—
312C2×C4—1222no—
313C2×C4—1222no—
314C2×C4—1222no—
315C2×C4—1222no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—2442no—
320C2×C4—2442no—
321C2×C4—2442no—
322C2×C4—2442no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4#1451975912yes—
330C2×C4#1451976212yes—
331C8—82no—
332C8—4882no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22#1683962411yescharacteristic
346C22C22⋊C8×D6111yescharacteristic
347C22#1683972411yescharacteristic
348C22#1683973411yescharacteristic
349C22#1683973411yescharacteristic
350C22#1683974311yescharacteristic
351C22#1683974511yescharacteristic
352C22#1683981311yescharacteristic
353C22#1683981411yescharacteristic
354C22#1683981711yescharacteristic
355C22#1683981811yescharacteristic
356C4—22no—
357C4—22no—
358C4—42no—
359C4—42no—
360C4—1224no—
361C4—2442no—
362C4—2442no—
363C4—2442no—
364C2—21no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2#2144413011yescharacteristic
369C2#2144413211yescharacteristic
370C2#2144415011yescharacteristic
371C2#2144415211yescharacteristic
372C2#2144588611yescharacteristic
373C2#2144589511yescharacteristic
374C2#2144590111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC23×C4×C61C23
hypercenter#1280D61
hypocenterC61#8699
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
30. C2×C4×Dic61C8semidirect
204. C61#8699semidirect

Maximal subgroups

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

subgroupindex
C2×#168396072
#214458852
#214436622
#214436612
C61×#12802
#869961