Finite Group Databasebeta

← #28477188

Subgroups — #28477188

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#21432406C211yesmaximal, characteristic
2#21423858C211yesmaximal, characteristic
3#21421920C212yesmaximal, complemented
4#21421918C212yesmaximal, complemented
5C2×C59×#336C211yesmaximal, characteristic
6C2×#14273719C411yescharacteristic
7C2×C22⋊(C59⋊C8)—21no—
8C2×#14273638—21no—
9#16837300C2211yescharacteristic
10#16837300C2211yescharacteristic
11#16837286—21no—
12#16837286—21no—
13#16837275—21no—
14#16837275—21no—
15#16837268C411yescharacteristic
16#16837262C411yescharacteristic
17#16837262C411yescharacteristic
18#16837157C2212yes—
19C23×C8×C59—21no—
20C22×C42×C59C2211yescharacteristic
21C59×#336—21no—
22C59×#336C2212yes—
23C22×C59⋊C8—22no—
24#14273719—42no—
25C2×C4⋊Dic59C2×C411yescharacteristic
26C2×C4⋊Dic59C2×C411yescharacteristic
27C2×C4⋊Dic59C2×C411yescharacteristic
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×Dic59⋊C4—21no—
30C2×Dic59⋊C4—21no—
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×C22⋊Dic59—21no—
34C2×C22⋊Dic59—21no—
35C22⋊(C59⋊C8)—24no—
36#14273638—42no—
37C59⋊#95—21no—
38C59⋊#95—21no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C23×C4×C59C2×C411yescharacteristic
44C23×C4×C59D411yescharacteristic
45C23×C4×C59D411yescharacteristic
46C22×C8×C59—24no—
47C22×C8×C59—22no—
48C22×C8×C59—42no—
49C22×C8×C59—42no—
50C2×C42×C59—42no—
51C2×C42×C59C2×C411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C2×C42×C59D411yescharacteristic
54C2×C42×C59C2311yescharacteristic
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—41no—
65C22×C4×C59—41no—
66C22×C4×C59C22⋊C411yescharacteristic
67C22×C4×C59C22⋊C411yescharacteristic
68C22×C4×C59C22⋊C411yescharacteristic
69C22×C4×C59C22×C411yescharacteristic
70C22×C4×C59C2×D411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×Dic59—21no—
73C22×Dic59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76C2×C8×C59—24no—
77C2×C8×C59—48no—
78C2×C8×C59—42no—
79C2×C8×C59—42no—
80C42×C59—22no—
81C42×C59—22no—
82C42×C59—41no—
83C42×C59—41no—
84C22⋊Dic59—42no—
85C22⋊Dic59—42no—
86C4⋊Dic59—22no—
87C4⋊Dic59—22no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90Dic59⋊C4—42no—
91Dic59⋊C4—42no—
92Dic59⋊C4—42no—
93Dic59⋊C4—41no—
94Dic59⋊C4—41no—
95C2×C59⋊C8—24no—
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#9912yes—
125C2×C4×C59#13112yes—
126C2×C4×C59#13512yes—
127C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C59#13711yescharacteristic
129C2×Dic59—41no—
130C2×Dic59—41no—
131C2×Dic59—41no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C8×C59—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—
165Dic59—81no—
166Dic59—81no—
167Dic59—81no—
168Dic59—81no—
169#2851—591no—
170#1749—591no—
171C2×#336D5911yescharacteristic
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—21no—
183C2×#125—591no—
184C22×C42C2×D5911yescharacteristic
185C2×C22⋊C8—1181no—
186C2×#97—1181no—
187#389—591no—
188#389—591no—
189#387—1181no—
190#387—1181no—
191#385—1181no—
192#385—1181no—
193#382—591no—
194#380—591no—
195#380—591no—
196#336—21no—
197#336—592no—
198#336C2×D5912yes—
199C59#769111yescharacteristic, complemented, Sylow
200C23×C4C4×D5911yescharacteristic
201C23×C4D23611yescharacteristic
202C23×C4C22⋊D5911yescharacteristic
203C22×C8—24no—
204C22×C8—22no—
205C22×C8—42no—
206C22×C8—42no—
207C22×C8—1182no—
208#125—2362no—
209C2×C4⋊C4—591no—
210C2×C4⋊C4—591no—
211C2×C4⋊C4—591no—
212C2×C4⋊C4—591no—
213C2×C4⋊C4—1181no—
214C2×C4⋊C4—1181no—
215C2×C4⋊C4—1181no—
216C2×C4⋊C4—1181no—
217C2×C22⋊C4—1181no—
218C2×C22⋊C4—1181no—
219C2×C42—42no—
220C2×C42C4×D5911yescharacteristic
221C2×C42D23611yescharacteristic
222C2×C42C22⋊D5911yescharacteristic
223C2×C42C22×D5911yescharacteristic
224C22⋊C8—1184no—
225#97—2362no—
226#95—1181no—
227#95—1181no—
228#95—1181no—
229#95—1181no—
230#95—1181no—
231#95—1181no—
232C24(C2×D59)⋊C411yescharacteristic
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—41no—
242C22×C4—41no—
243C22×C4—1181no—
244C22×C4—1181no—
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4(C2×D59)⋊C411yescharacteristic
248C22×C4(C2×D59)⋊C411yescharacteristic
249C22×C4(C2×D59)⋊C411yescharacteristic
250C22×C4C2×C4×D5911yescharacteristic
251C22×C4C2×D23611yescharacteristic
252C22×C4C2×C22⋊D5911yescharacteristic
253C2×C8—24no—
254C2×C8—48no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—1184no—
258C2×C8—2362no—
259C2×C8—2362no—
260C4⋊C4—1182no—
261C4⋊C4—1182no—
262C4⋊C4—2361no—
263C4⋊C4—2361no—
264C4⋊C4—2362no—
265C4⋊C4—2362no—
266C4⋊C4—2362no—
267C4⋊C4—2361no—
268C4⋊C4—2361no—
269C22⋊C4—2362no—
270C22⋊C4—2362no—
271C42—22no—
272C42—22no—
273C42—41no—
274C42—41no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23#1427364512yes—
280C23#1427365312yes—
281C23#1427365512yes—
282C23C2×(C2×D59)⋊C411yescharacteristic
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—2361no—
302C2×C4—2361no—
303C2×C4—2361no—
304C2×C4—2361no—
305C2×C4—2361no—
306C2×C4—2361no—
307C2×C4—2361no—
308C2×C4—2361no—
309C2×C4—2361no—
310C2×C4—2361no—
311C2×C4—2361no—
312C2×C4—2361no—
313C2×C4#1427364112yes—
314C2×C4#1427373312yes—
315C2×C4#1427374912yes—
316C2×C4#1427375311yescharacteristic
317C2×C4#1427375811yescharacteristic
318C8—44no—
319C8—2364no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22#1683714314yes—
327C22#1683736811yescharacteristic
328C22C2×#1427364111yescharacteristic
329C22C2×#1427364511yescharacteristic
330C22#1683739911yescharacteristic
331C22#1683740111yescharacteristic
332C22C2×#1427365311yescharacteristic
333C22C2×#1427365511yescharacteristic
334C4—21no—
335C4—22no—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—4721no—
342C4—4721no—
343C4—4721no—
344C4—4721no—
345C2—24no—
346C2#2142245911yescharacteristic
347C2#2142250711yescharacteristic
348C2#2142255711yescharacteristic
349C2#2142258811yescharacteristic
350C2#2142259811yescharacteristic
351C2C2×#1683714311yescharacteristic
352C2#2142279411yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC2×C59×#336C2
socleC23×C59C2×C22⋊C4
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenterC2×#336D59
hypocenterC59#7691
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. #21421920C2semidirect
4. #21421918C2semidirect
199. C59#7691semidirect

Maximal subgroups

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

subgroupindex
#214324062
#214238582
#214219202
#214219182
C2×C59×#3362
#769159