Finite Group Databasebeta

← #28477190

Subgroups — #28477190

Order 15104.

530 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21423858C211yesmaximal, characteristic
2C2×#16837157C211yesmaximal, characteristic
3#21421919C212yesmaximal, complemented
4#21421919C212yesmaximal, complemented
5C59×#2851C211yesmaximal, characteristic
6C23×C59⋊C8—21no—
7C2×C22⋊(C59⋊C8)—21no—
8C2×#14273638—21no—
9#16837157—21no—
10#16837157C2212yes—
11#16837157C2212yes—
12C2×#125×C59C411yescharacteristic
13C22×C42×C59C2211yescharacteristic
14C59×#389C2211yescharacteristic
15C59×#389C2211yescharacteristic
16C59×#387—21no—
17C59×#387—21no—
18C59×#385—21no—
19C59×#385—21no—
20C59×#382C411yescharacteristic
21C59×#380C411yescharacteristic
22C59×#380C411yescharacteristic
23C22×C59⋊C8—24no—
24C22×C59⋊C8—22no—
25C22×C59⋊C8—22no—
26C22×C59⋊C8—42no—
27C22×C59⋊C8—42no—
28C22⋊(C59⋊C8)—24no—
29#14273638—42no—
30C23×C4×C59C2×C411yescharacteristic
31C23×C4×C59D411yescharacteristic
32C23×C4×C59D411yescharacteristic
33#125×C59—42no—
34C2×C4⋊C4×C59—21no—
35C2×C4⋊C4×C59—21no—
36C2×C4⋊C4×C59—21no—
37C2×C4⋊C4×C59—21no—
38C2×C4⋊C4×C59C2×C411yescharacteristic
39C2×C4⋊C4×C59C2×C411yescharacteristic
40C2×C4⋊C4×C59C2×C411yescharacteristic
41C2×C4⋊C4×C59C2×C411yescharacteristic
42C2×C22⋊C4×C59—21no—
43C2×C22⋊C4×C59—21no—
44C2×C42×C59—42no—
45C2×C42×C59C2×C411yescharacteristic
46C2×C42×C59D411yescharacteristic
47C2×C42×C59D411yescharacteristic
48C2×C42×C59C2311yescharacteristic
49#95×C59—21no—
50#95×C59—21no—
51#95×C59—21no—
52#95×C59—21no—
53#95×C59—21no—
54#95×C59—21no—
55C24×C59C22⋊C411yescharacteristic
56C22×C4×C59—22no—
57C22×C4×C59—22no—
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—22no—
61C22×C4×C59—22no—
62C22×C4×C59—22no—
63C22×C4×C59—22no—
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—41no—
69C22×C4×C59—41no—
70C22×C4×C59C22⋊C411yescharacteristic
71C22×C4×C59C22⋊C411yescharacteristic
72C22×C4×C59C22⋊C411yescharacteristic
73C22×C4×C59C22×C411yescharacteristic
74C22×C4×C59C2×D411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C4⋊C4×C59—22no—
77C4⋊C4×C59—22no—
78C4⋊C4×C59—42no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—42no—
82C4⋊C4×C59—42no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C22⋊C4×C59—42no—
86C22⋊C4×C59—42no—
87C42×C59—22no—
88C42×C59—22no—
89C42×C59—41no—
90C42×C59—41no—
91C2×C59⋊C8—24no—
92C2×C59⋊C8—24no—
93C2×C59⋊C8—42no—
94C2×C59⋊C8—48no—
95C2×C59⋊C8—42no—
96C2×C59⋊C8—42no—
97C2×C59⋊C8—42no—
98C23×C59—21no—
99C23×C59—21no—
100C23×C59—21no—
101C23×C59—21no—
102C23×C59#10112yes—
103C23×C59#10412yes—
104C23×C59#10412yes—
105C23×C59C2×C22⋊C411yescharacteristic
106C2×C4×C59—24no—
107C2×C4×C59—24no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—44no—
123C2×C4×C59—44no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
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—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59#9912yes—
137C2×C4×C59#13112yes—
138C2×C4×C59#13512yes—
139C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C59#13711yescharacteristic
141C59⋊C8—44no—
142C59⋊C8—44no—
143#7691—591nomaximal, Sylow
144C22×C59—22no—
145C22×C59—22no—
146C22×C59—22no—
147C22×C59—22no—
148C22×C59—22no—
149C22×C59—22no—
150C22×C59#33014yes—
151C22×C59#40811yescharacteristic
152C22×C59C2×#9911yescharacteristic
153C22×C59C2×#10111yescharacteristic
154C22×C59#41611yescharacteristic
155C22×C59#41711yescharacteristic
156C22×C59C2×#10411yescharacteristic
157C22×C59C2×#10411yescharacteristic
158C4×C59—22no—
159C4×C59—22no—
160C4×C59—21no—
161C4×C59—22no—
162C4×C59—21no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59—81no—
166C4×C59—81no—
167C4×C59—81no—
168C4×C59—81no—
169#2851D5911yescharacteristic
170#1749—591no—
171C2×#336—591no—
172#1271—592no—
173#1271—592no—
174C2×C59—24no—
175C2×C59#147211yescharacteristic
176C2×C59#148311yescharacteristic
177C2×C59#149411yescharacteristic
178C2×C59#150111yescharacteristic
179C2×C59#150411yescharacteristic
180C2×C59C2×#33011yescharacteristic
181C2×C59#155211yescharacteristic
182C23×C8—1181no—
183C2×#125Dic5911yescharacteristic
184C22×C42C2×D5911yescharacteristic
185C2×C22⋊C8—1181no—
186C2×#97—1181no—
187#389C2×D5911yescharacteristic
188#389C2×D5911yescharacteristic
189#387—21no—
190#387—21no—
191#385—21no—
192#385—21no—
193#382Dic5911yescharacteristic
194#380Dic5911yescharacteristic
195#380Dic5911yescharacteristic
196#336—592no—
197#336—592no—
198#336—1181no—
199C59#769111yescharacteristic, complemented, Sylow
200C23×C4C2×Dic5911yescharacteristic
201C23×C4C22⋊D5911yescharacteristic
202C23×C4C22⋊D5911yescharacteristic
203C22×C8—1184no—
204C22×C8—1182no—
205C22×C8—1182no—
206C22×C8—2362no—
207C22×C8—2362no—
208#125—42no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×Dic5911yescharacteristic
214C2×C4⋊C4C2×Dic5911yescharacteristic
215C2×C4⋊C4C2×Dic5911yescharacteristic
216C2×C4⋊C4C2×Dic5911yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C42—42no—
220C2×C42C2×Dic5911yescharacteristic
221C2×C42C22⋊D5911yescharacteristic
222C2×C42C22⋊D5911yescharacteristic
223C2×C42C22×D5911yescharacteristic
224C22⋊C8—1184no—
225#97—2362no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232C24C22⋊Dic5911yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4C22⋊Dic5911yescharacteristic
248C22×C4C22⋊Dic5911yescharacteristic
249C22×C4C22⋊Dic5911yescharacteristic
250C22×C4C22×Dic5911yescharacteristic
251C22×C4C2×C22⋊D5911yescharacteristic
252C22×C4C2×C22⋊D5911yescharacteristic
253C2×C8—1184no—
254C2×C8—1184no—
255C2×C8—2362no—
256C2×C8—2368no—
257C2×C8—2362no—
258C2×C8—2362no—
259C2×C8—2362no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C42—22no—
272C42—22no—
273C42—41no—
274C42—41no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23#1427364612yes—
280C23#1427365412yes—
281C23#1427365412yes—
282C23C2×C22⋊Dic5911yescharacteristic
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4#1427364212yes—
314C2×C4#1427373412yes—
315C2×C4#1427374712yes—
316C2×C4#1427375211yescharacteristic
317C2×C4#1427375711yescharacteristic
318C8—2364no—
319C8—2364no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22#1683714414yes—
327C22#1683736911yescharacteristic
328C22C2×#1427364211yescharacteristic
329C22C2×#1427364611yescharacteristic
330C22#1683739811yescharacteristic
331C22#1683740311yescharacteristic
332C22C2×#1427365411yescharacteristic
333C22C2×#1427365411yescharacteristic
334C4—21no—
335C4—22no—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C2—24no—
346C2#2142246011yescharacteristic
347C2#2142250911yescharacteristic
348C2#2142255611yescharacteristic
349C2#2142258711yescharacteristic
350C2#2142260011yescharacteristic
351C2C2×#1683714411yescharacteristic
352C2#2142279611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2851C2
socleC23×C59C2×C22⋊C4
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenter#2851D59
hypocenterC59#7691
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. #21421919C2semidirect
4. #21421919C2semidirect
199. C59#7691semidirect

Maximal subgroups

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

subgroupindex
#214238582
C2×#168371572
#214219192
C59×#28512
#769159