Finite Group Databasebeta

← #28476901

Subgroups — #28476901

Order 15104.

506 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14273706C211yesmaximal, characteristic
2#21423858C211yesmaximal, characteristic
3#21421921C212yesmaximal, complemented
4#21421918C212yesmaximal, complemented
5C59×#1817C211yesmaximal, characteristic
6C2×#14273706C411yescharacteristic
7C2×C4×Dic118C411yescharacteristic
8C2×C22⋊(C59⋊C8)—21no—
9C2×#14273638—21no—
10#16837308C2211yescharacteristic
11#16837300C2211yescharacteristic
12#16837286—21no—
13#16837275—21no—
14#16837262C411yescharacteristic
15C4×Dic59⋊C4—21no—
16C4×C4⋊Dic59C411yescharacteristic
17C4×C22⋊Dic59—21no—
18#16837157C2212yes—
19C22×C42×C59C2211yescharacteristic
20C2×C22⋊C8×C59—21no—
21C59×#336—21no—
22C59×#336C2212yes—
23C22×Dic118C2×C411yescharacteristic
24C22×C59⋊C8—22no—
25#14273706—22no—
26#14273706—22no—
27C4×Dic118—42no—
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×C4⋊Dic59C2×C411yescharacteristic
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34C2×C22⋊Dic59—21no—
35C2×C22⋊Dic59—21no—
36C2×C4×Dic59—21no—
37C2×C4×Dic59—21no—
38C22⋊(C59⋊C8)—24no—
39#14273638—42no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C23×C4×C59C2×C411yescharacteristic
46C23×C4×C59D411yescharacteristic
47C23×C4×C59D411yescharacteristic
48C22×C8×C59—22no—
49C2×C42×C59—42no—
50C2×C42×C59C2×C411yescharacteristic
51C2×C42×C59D411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C2×C42×C59C2311yescharacteristic
54C22⋊C8×C59—42no—
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—41no—
63C22×C4×C59—41no—
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×Dic118—21no—
77C2×Dic118—41no—
78C2×Dic118—41no—
79C2×Dic118M1612yes—
80C2×C8×C59—42no—
81C2×C8×C59—42no—
82C2×C8×C59—42no—
83C42×C59—22no—
84C42×C59—22no—
85C42×C59—41no—
86C42×C59—41no—
87C22⋊Dic59—24no—
88C22⋊Dic59—42no—
89C4⋊Dic59—21no—
90C4⋊Dic59—41no—
91C4⋊Dic59—41no—
92C4⋊Dic59M1612yes—
93Dic59⋊C4—24no—
94Dic59⋊C4—42no—
95Dic59⋊C4—42no—
96C4×Dic59—42no—
97C4×Dic59—42no—
98C2×C59⋊C8—24no—
99C2×C59⋊C8—42no—
100C2×C59⋊C8—42no—
101C23×C59—21no—
102C23×C59—21no—
103C23×C59—21no—
104C23×C59—21no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59#10412yes—
108C23×C59C2×C22⋊C411yescharacteristic
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—21no—
123C2×C4×C59—44no—
124C2×C4×C59—44no—
125C2×C4×C59—42no—
126C2×C4×C59—42no—
127C2×C4×C59#9912yes—
128C2×C4×C59C2×M1611yescharacteristic
129C2×C4×C59C2×M1611yescharacteristic
130C2×C4×C59#13512yes—
131C2×C4×C59#13712yes—
132C2×Dic59—22no—
133C2×Dic59—22no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144Dic118—42no—
145Dic118—42no—
146C8×C59—82no—
147C59⋊C8—44no—
148#7623—591nomaximal, Sylow
149C22×C59—22no—
150C22×C59—22no—
151C22×C59—22no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59#40711yescharacteristic
157C22×C59C2×#9911yescharacteristic
158C22×C59#41311yescharacteristic
159C22×C59#41611yescharacteristic
160C22×C59#41911yescharacteristic
161C22×C59C2×#10411yescharacteristic
162C22×C59#42111yescharacteristic
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—22no—
166C4×C59—22no—
167C4×C59—22no—
168C4×C59—41no—
169C4×C59—41no—
170Dic59—42no—
171Dic59—42no—
172Dic59—81no—
173Dic59—81no—
174C4×C22⋊Q8—591no—
175#1817D5911yescharacteristic
176#1749—591no—
177#1272—592no—
178#1271—592no—
179C2×C59—42no—
180C2×C59#146511yescharacteristic
181C2×C59#148811yescharacteristic
182C2×C59#149111yescharacteristic
183C2×C59#150111yescharacteristic
184C2×C59#151111yescharacteristic
185C2×C59#153211yescharacteristic
186C2×C59#155411yescharacteristic
187C2×C22⋊Q8—591no—
188C2×C4×Q8—591no—
189C22×C42C2×D5911yescharacteristic
190C2×C22⋊C8—21no—
191C2×C22⋊C8—1181no—
192C2×#97—1181no—
193#391—591no—
194#389—591no—
195#387—1181no—
196#385—1181no—
197#380—591no—
198C4×C4⋊C4—591no—
199C4×C4⋊C4—1181no—
200C4×C22⋊C4—1181no—
201#336—21no—
202#336—592no—
203#336C2×D5912yes—
204C59#762311yescharacteristic, complemented, Sylow
205C22×Q8—591no—
206C23×C4C4×D5911yescharacteristic
207C23×C4D23611yescharacteristic
208C23×C4C22⋊D5911yescharacteristic
209C22×C8—22no—
210C22×C8—1182no—
211C22⋊Q8—1182no—
212C22⋊Q8—1182no—
213C4×Q8—2362no—
214C2×C4⋊C4—591no—
215C2×C4⋊C4—591no—
216C2×C4⋊C4—591no—
217C2×C4⋊C4—1181no—
218C2×C4⋊C4—1181no—
219C2×C4⋊C4—1181no—
220C2×C22⋊C4—1181no—
221C2×C22⋊C4—1181no—
222C2×C42—42no—
223C2×C42—1181no—
224C2×C42—1181no—
225C2×C42C4×D5911yescharacteristic
226C2×C42D23611yescharacteristic
227C2×C42C22⋊D5911yescharacteristic
228C2×C42C22×D5911yescharacteristic
229C22⋊C8—42no—
230C22⋊C8—1184no—
231#97—2362no—
232#95—1181no—
233#95—1181no—
234#95—1181no—
235#95—1181no—
236#95—1181no—
237C24(C2×D59)⋊C411yescharacteristic
238C2×Q8—592no—
239C2×Q8—1181no—
240C2×Q8—2361no—
241C2×Q8—2361no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4—1181no—
255C22×C4—1181no—
256C22×C4(C2×D59)⋊C411yescharacteristic
257C22×C4(C2×D59)⋊C411yescharacteristic
258C22×C4(C2×D59)⋊C411yescharacteristic
259C22×C4C2×C4×D5911yescharacteristic
260C22×C4C2×D23611yescharacteristic
261C22×C4C2×C22⋊D5911yescharacteristic
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—1184no—
266C2×C8—2362no—
267C2×C8—2362no—
268C4⋊C4—592no—
269C4⋊C4—1184no—
270C4⋊C4—1181no—
271C4⋊C4—2361no—
272C4⋊C4—2361no—
273C4⋊C4—2362no—
274C4⋊C4—2362no—
275C22⋊C4—1184no—
276C22⋊C4—2362no—
277C42—22no—
278C42—22no—
279C42—41no—
280C42—41no—
281C42—2362no—
282C42—2362no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23#1427365312yes—
290C23C2×(C2×D59)⋊C411yescharacteristic
291Q8—2362no—
292Q8—2362no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—1182no—
312C2×C4—1182no—
313C2×C4—2361no—
314C2×C4—2361no—
315C2×C4—2361no—
316C2×C4—2361no—
317C2×C4—2361no—
318C2×C4—2361no—
319C2×C4—2361no—
320C2×C4—2361no—
321C2×C4—2361no—
322C2×C4—2361no—
323C2×C4#1427364112yes—
324C2×C4M16×D5911yescharacteristic
325C2×C4M16×D5911yescharacteristic
326C2×C4#1427374912yes—
327C2×C4#1427375712yes—
328C8—82no—
329C8—2364no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22#1683736511yescharacteristic
338C22C2×#1427364111yescharacteristic
339C22#1683738411yescharacteristic
340C22#1683739911yescharacteristic
341C22#1683741011yescharacteristic
342C22C2×#1427365311yescharacteristic
343C22#1683742011yescharacteristic
344C4—22no—
345C4—22no—
346C4—21no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—4721no—
352C4—4721no—
353C4—2362no—
354C4—2362no—
355C2—42no—
356C2#2142243211yescharacteristic
357C2#2142253111yescharacteristic
358C2#2142254211yescharacteristic
359C2#2142258811yescharacteristic
360C2#2142262811yescharacteristic
361C2#2142271711yescharacteristic
362C2#2142280411yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1817C2
socleC23×C59C2×C22⋊C4
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1817D59
hypocenterC59#7623
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
3. #21421921C2semidirect
4. #21421918C2semidirect
204. C59#7623semidirect

Maximal subgroups

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

subgroupindex
C4×#142737062
#214238582
#214219212
#214219182
C59×#18172
#762359