Finite Group Databasebeta

← #28478604

Subgroups — #28478604

Order 15104.

606 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432729C211yesmaximal, characteristic
2C2×C4×#11745664C211yesmaximal, characteristic
3#21421967C214yesmaximal, complemented
4C59×#2920C211yesmaximal, characteristic
5C22×#11745664—21no—
6#16837459—21no—
7#16837459C2212yes—
8#16837455—21no—
9#16837455C412yes—
10#16837426—21no—
11#16837366C412yes—
12C4×#11745664—21no—
13C4×#11745664—21no—
14C4×#11745664—21no—
15C4×#11745664C412yes—
16C4×#11745664C2212yes—
17C2×#14273638—21no—
18C2×C4×C59⋊C8C412yes—
19C22×C42×C59C2211yescharacteristic
20C59×#432—21no—
21C59×#432C2212yes—
22C59×#431—21no—
23C59×#431C412yes—
24C59×#423C412yes—
25C59×#407—21no—
26C4×M16×C59—21no—
27C2×#11745664—28no—
28C2×#11745664—22no—
29C2×#11745664—22no—
30C2×#11745664—22no—
31C22×C59⋊C8—22no—
32C4⋊(C59⋊C8)—22no—
33C4⋊(C59⋊C8)—22no—
34C22⋊(C59⋊C8)—22no—
35C22⋊(C59⋊C8)C2×C414yes—
36#14273638—22no—
37#14273638—22no—
38#14273638—22no—
39C4×C59⋊C8—22no—
40C4×C59⋊C8—22no—
41C4×C59⋊C8C2×C414yes—
42C23×C4×C59C2×C411yescharacteristic
43C23×C4×C59D411yescharacteristic
44C23×C4×C59Q811yescharacteristic
45C2×M16×C59—22no—
46C2×C42×C59C2×C411yescharacteristic
47C2×C42×C59C2×C411yescharacteristic
48C2×C42×C59C2×C411yescharacteristic
49C2×C42×C59C2×C411yescharacteristic
50C2×C42×C59C2×C411yescharacteristic
51C2×C42×C59D411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C2×C42×C59D411yescharacteristic
54C2×C42×C59D411yescharacteristic
55C2×C42×C59D411yescharacteristic
56C2×C42×C59Q811yescharacteristic
57C2×C42×C59C2311yescharacteristic
58C4⋊C8×C59—22no—
59C4⋊C8×C59C2×C414yes—
60C22⋊C8×C59—22no—
61C22⋊C8×C59—22no—
62#97×C59—22no—
63C4×C8×C59—22no—
64C24×C59C4⋊C411yescharacteristic
65C22×C4×C59—24no—
66C22×C4×C59—42no—
67C22×C4×C59—42no—
68C22×C4×C59C4211yescharacteristic
69C22×C4×C59C4211yescharacteristic
70C22×C4×C59C22⋊C411yescharacteristic
71C22×C4×C59C22⋊C411yescharacteristic
72C22×C4×C59C22⋊C411yescharacteristic
73C22×C4×C59C22⋊C411yescharacteristic
74C22×C4×C59C22⋊C411yescharacteristic
75C22×C4×C59C22⋊C411yescharacteristic
76C22×C4×C59C4⋊C411yescharacteristic
77C22×C4×C59C4⋊C411yescharacteristic
78C22×C4×C59C4⋊C411yescharacteristic
79C22×C4×C59C4⋊C411yescharacteristic
80C22×C4×C59C4⋊C411yescharacteristic
81C22×C4×C59C4⋊C411yescharacteristic
82C22×C4×C59C4⋊C411yescharacteristic
83C22×C4×C59C22×C411yescharacteristic
84C22×C4×C59C2×D411yescharacteristic
85C22×C4×C59C2×Q811yescharacteristic
86M16×C59—44no—
87C2×C8×C59—24no—
88C42×C59C4211yescharacteristic
89C42×C59C4211yescharacteristic
90C42×C59C22⋊C411yescharacteristic
91C42×C59C22⋊C411yescharacteristic
92C42×C59C22⋊C411yescharacteristic
93C42×C59C22⋊C411yescharacteristic
94C42×C59C22⋊C411yescharacteristic
95C42×C59C22⋊C411yescharacteristic
96C42×C59C4⋊C411yescharacteristic
97C42×C59C4⋊C411yescharacteristic
98C42×C59C4⋊C411yescharacteristic
99C42×C59C4⋊C411yescharacteristic
100C42×C59C22×C411yescharacteristic
101C42×C59C22×C411yescharacteristic
102C42×C59C2×D411yescharacteristic
103C42×C59C2×D411yescharacteristic
104#11745664—28no—
105#11745664—28no—
106#11745664—44no—
107C2×C59⋊C8—28no—
108C2×C59⋊C8—24no—
109C2×C59⋊C8—24no—
110C23×C59—22no—
111C23×C59—41no—
112C23×C59—41no—
113C23×C59#9511yescharacteristic
114C23×C59#9511yescharacteristic
115C23×C59C2×C4⋊C411yescharacteristic
116C2×C4×C59—22no—
117C2×C4×C59—22no—
118C2×C4×C59—22no—
119C2×C4×C59—22no—
120C2×C4×C59—22no—
121C2×C4×C59—22no—
122C2×C4×C59—22no—
123C2×C4×C59—22no—
124C2×C4×C59—22no—
125C2×C4×C59—22no—
126C2×C4×C59—22no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59#9511yescharacteristic
134C2×C4×C59#9511yescharacteristic
135C2×C4×C59#9511yescharacteristic
136C2×C4×C59#9511yescharacteristic
137C2×C4×C59#9511yescharacteristic
138C2×C4×C59#9511yescharacteristic
139C2×C4×C59#10414yes—
140C2×C4×C59C2×C4211yescharacteristic
141C2×C4×C59C2×C22⋊C411yescharacteristic
142C2×C4×C59C2×C22⋊C411yescharacteristic
143C2×C4×C59C2×C22⋊C411yescharacteristic
144C2×C4×C59C2×C4⋊C411yescharacteristic
145C2×C4×C59C2×C4⋊C411yescharacteristic
146C8×C59—44no—
147C59⋊C8—28no—
148C59⋊C8—44no—
149#7992—591nomaximal, Sylow
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—44no—
159C22×C59#33912yes—
160C22×C59C2×#9511yescharacteristic
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59#33812yes—
170C4×C59#33912yes—
171C4×C59#34412yes—
172C4×C59C2×#10412yes—
173#2920—591no—
174#2920D5911yescharacteristic
175C2×C4×M16—591no—
176#1291—594no—
177C2×C59—22no—
178C2×C59—41no—
179C2×C59—41no—
180C2×C59C2×#33811yescharacteristic
181C2×C59C2×#33911yescharacteristic
182C2×C59C2×#34411yescharacteristic
183C22×M16—1181no—
184C22×C42C2×D5911yescharacteristic
185#432—21no—
186#432—592no—
187#432—1181no—
188#432C2×D5912yes—
189#431—21no—
190#431—592no—
191#431—1181no—
192#431Dic5912yes—
193#423—1181no—
194#423Dic5912yes—
195#407—21no—
196#407—592no—
197C4×M16—21no—
198C4×M16—592no—
199C4×M16—592no—
200C4×M16—1181no—
201C4×M16—1181no—
202C4×M16—1181no—
203C2×#97—1181no—
204C2×C4×C8—592no—
205C59#799211yescharacteristic, complemented, Sylow
206C23×C4Dic11811yescharacteristic
207C23×C4C4×D5911yescharacteristic
208C23×C4C22⋊D5911yescharacteristic
209C2×M16—22no—
210C2×M16—1188no—
211C2×M16—1182no—
212C2×M16—1182no—
213C2×M16—1182no—
214C22×C8—1182no—
215C2×C42Dic11811yescharacteristic
216C2×C42C4×D5911yescharacteristic
217C2×C42C4×D5911yescharacteristic
218C2×C42C4×D5911yescharacteristic
219C2×C42D23611yescharacteristic
220C2×C42D23611yescharacteristic
221C2×C42C2×Dic5911yescharacteristic
222C2×C42C2×Dic5911yescharacteristic
223C2×C42C22⋊D5911yescharacteristic
224C2×C42C22⋊D5911yescharacteristic
225C2×C42C22⋊D5911yescharacteristic
226C2×C42C22×D5911yescharacteristic
227C4⋊C8—22no—
228C4⋊C8—1182no—
229C4⋊C8—1182no—
230C4⋊C8C2×Dic5914yes—
231C22⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—594no—
234C22⋊C8—1182no—
235#97—22no—
236#97—1182no—
237#97—1182no—
238#97—1182no—
239C4×C8—22no—
240C4×C8—594no—
241C4×C8—1182no—
242C4×C8—1182no—
243C24Dic59⋊C411yescharacteristic
244C22×C4—24no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4C4×Dic5911yescharacteristic
248C22×C4C4×Dic5911yescharacteristic
249C22×C4Dic59⋊C411yescharacteristic
250C22×C4Dic59⋊C411yescharacteristic
251C22×C4Dic59⋊C411yescharacteristic
252C22×C4Dic59⋊C411yescharacteristic
253C22×C4Dic59⋊C411yescharacteristic
254C22×C4C4⋊Dic5911yescharacteristic
255C22×C4C4⋊Dic5911yescharacteristic
256C22×C4(C2×D59)⋊C411yescharacteristic
257C22×C4(C2×D59)⋊C411yescharacteristic
258C22×C4(C2×D59)⋊C411yescharacteristic
259C22×C4(C2×D59)⋊C411yescharacteristic
260C22×C4C22⋊Dic5911yescharacteristic
261C22×C4C22⋊Dic5911yescharacteristic
262C22×C4C2×Dic11811yescharacteristic
263C22×C4C2×C4×D5911yescharacteristic
264C22×C4C2×C22⋊D5911yescharacteristic
265M16—44no—
266M16—1188no—
267M16—1188no—
268M16—2364no—
269C2×C8—24no—
270C2×C8—1188no—
271C2×C8—1184no—
272C2×C8—1184no—
273C42C4×Dic5911yescharacteristic
274C42C4×Dic5911yescharacteristic
275C42Dic59⋊C411yescharacteristic
276C42Dic59⋊C411yescharacteristic
277C42C4⋊Dic5911yescharacteristic
278C42C4⋊Dic5911yescharacteristic
279C42(C2×D59)⋊C411yescharacteristic
280C42(C2×D59)⋊C411yescharacteristic
281C42(C2×D59)⋊C411yescharacteristic
282C42(C2×D59)⋊C411yescharacteristic
283C42C22⋊Dic5911yescharacteristic
284C42C22⋊Dic5911yescharacteristic
285C42C2×C4×D5911yescharacteristic
286C42C2×D23611yescharacteristic
287C42C22×Dic5911yescharacteristic
288C42C2×C22⋊D5911yescharacteristic
289C23—22no—
290C23—41no—
291C23—41no—
292C23C59⋊#9511yescharacteristic
293C23C59⋊#9511yescharacteristic
294C23C2×Dic59⋊C411yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4C59⋊#9511yescharacteristic
313C2×C4C59⋊#9511yescharacteristic
314C2×C4C59⋊#9511yescharacteristic
315C2×C4C59⋊#9511yescharacteristic
316C2×C4C59⋊#9511yescharacteristic
317C2×C4C59⋊#9511yescharacteristic
318C2×C4#1427365414yes—
319C2×C4C2×C4×Dic5911yescharacteristic
320C2×C4C2×(C2×D59)⋊C411yescharacteristic
321C2×C4C2×(C2×D59)⋊C411yescharacteristic
322C2×C4C2×C22⋊Dic5911yescharacteristic
323C2×C4C2×Dic59⋊C411yescharacteristic
324C2×C4C2×C4⋊Dic5911yescharacteristic
325C8—44no—
326C8—1188no—
327C8—2364no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—44no—
337C22#1683716112yes—
338C22C2×C59⋊#9511yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4C59⋊#33812yes—
348C4#1683716112yes—
349C4#1683717412yes—
350C4C2×#1427365412yes—
351C2—22no—
352C2—41no—
353C2—41no—
354C2C2×C59⋊#33811yescharacteristic
355C2C2×#1683716111yescharacteristic
356C2C2×#1683717411yescharacteristic
subgroupG/H
centerC2×C4C59⋊#95
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC59×#2920C2
socleC22×C59C2×#95
prime radicalC24×C59C4⋊C4
cosocleC2×C42×C59C23
hypercenter#2920D59
hypocenterC59#7992
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
3. #21421967C2semidirect
205. C59#7992semidirect

Maximal subgroups

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

subgroupindex
#214327292
C2×C4×#117456642
#214219672
C59×#29202
#799259