Finite Group Databasebeta

← #28483748

Subgroups — #28483748

Order 15104.

660 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×#16837332C211yesmaximal, characteristic
2#21424180C212yesmaximal
3C2×#16837128C211yesmaximal, characteristic
4#21421974C212yesmaximal
5C59×#2316C211yesmaximal, characteristic
6C22×C4⋊Dic59C2211yescharacteristic
7C22×Dic59⋊C4—21no—
8C2×C22⋊(C59⋊C8)C2212yes—
9#16837332—22no—
10#16837332C414yescomplemented
11C2×C59⋊#95—21no—
12C2×C59⋊#95C2211yescharacteristic
13#16837164—24no—
14#16837128—22no—
15C2×#117×C59—21no—
16C22×C4⋊C4×C59C2211yescharacteristic
17C59×#389—24no—
18C59×#380—21no—
19C59×#380C2212yes—
20C23×Dic59—21no—
21C23×Dic59—21no—
22C22×C59⋊C8—22no—
23C2×C4⋊Dic59—22no—
24C2×C4⋊Dic59—22no—
25C2×C4⋊Dic59—21no—
26C2×C4⋊Dic59C2×C412yes—
27C2×Dic59⋊C4—24no—
28C2×Dic59⋊C4—42no—
29C2×Dic59⋊C4—42no—
30C22⋊(C59⋊C8)—22no—
31C22⋊(C59⋊C8)—22no—
32C59⋊#95—24no—
33C59⋊#95—21no—
34C59⋊#95C2×C412yes—
35C23×C4×C59D411yescharacteristic
36C23×C4×C59D411yescharacteristic
37C23×C4×C59C2311yescharacteristic
38#117×C59—42no—
39#117×C59—42no—
40C2×C4⋊C4×C59—22no—
41C2×C4⋊C4×C59—22no—
42C2×C4⋊C4×C59—22no—
43C2×C4⋊C4×C59—22no—
44C2×C4⋊C4×C59C2×C412yes—
45C2×C4⋊C4×C59D412yes—
46C2×C4⋊C4×C59D414yes—
47C2×C22⋊C4×C59—22no—
48C2×C42×C59—22no—
49#95×C59—22no—
50#95×C59—22no—
51C24×C59C2×D411yescharacteristic
52C22×C4×C59—21no—
53C22×C4×C59—21no—
54C22×C4×C59—21no—
55C22×C4×C59—21no—
56C22×C4×C59—21no—
57C22×C4×C59—21no—
58C22×C4×C59—24no—
59C22×C4×C59—42no—
60C22×C4×C59—42no—
61C22×C4×C59C22⋊C412yes—
62C22×C4×C59C22⋊C412yes—
63C22×C4×C59D812yes—
64C22×C4×C59SD1612yes—
65C22×C4×C59C22×C411yescharacteristic
66C22×C4×C59C2×D412yes—
67C22×C4×C59C2×D411yescharacteristic
68C22×C4×C59#4112yes—
69C22×Dic59—24no—
70C22×Dic59—22no—
71C22×Dic59—22no—
72C22×Dic59—42no—
73C22×Dic59—41no—
74C22×Dic59—41no—
75C22×Dic59—41no—
76C22×Dic59—41no—
77C22×Dic59—41no—
78C22×Dic59—41no—
79C22×Dic59—41no—
80C22×Dic59—41no—
81C4⋊C4×C59—24no—
82C4⋊C4×C59—24no—
83C4⋊C4×C59—44no—
84C4⋊C4×C59—44no—
85C4⋊C4×C59—82no—
86C22⋊C4×C59—42no—
87C22⋊C4×C59—42no—
88C42×C59—44no—
89C4⋊Dic59—24no—
90C4⋊Dic59—42no—
91Dic59⋊C4—48no—
92C2×C59⋊C8—44no—
93C2×C59⋊C8—42no—
94C23×C59—22no—
95C23×C59—22no—
96C23×C59C2×C22⋊C411yescharacteristic
97C23×C59#12011yescharacteristic
98C23×C59#12311yescharacteristic
99C23×C59C2×D811yescharacteristic
100C23×C59C2×SD1611yescharacteristic
101C23×C59AGL(1,ℤ/8)11yescharacteristic
102C23×C59#13711yescharacteristic
103C2×C4×C59—22no—
104C2×C4×C59—22no—
105C2×C4×C59—22no—
106C2×C4×C59—22no—
107C2×C4×C59—24no—
108C2×C4×C59—22no—
109C2×C4×C59—22no—
110C2×C4×C59—22no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—42no—
114C2×C4×C59—42no—
115C2×C4×C59—42no—
116C2×C4×C59—44no—
117C2×C4×C59—44no—
118C2×C4×C59—44no—
119C2×C4×C59—81no—
120C2×C4×C59#10214yes—
121C2×C4×C59C4×D412yes—
122C2×C4×C59#12112yes—
123C2×Dic59—24no—
124C2×Dic59—44no—
125C2×Dic59—44no—
126C2×Dic59—42no—
127C2×Dic59—42no—
128C2×Dic59—42no—
129C2×Dic59—42no—
130C2×Dic59—42no—
131C2×Dic59—81no—
132C2×Dic59—81no—
133C2×Dic59—81no—
134C2×Dic59—81no—
135C59⋊C8—82no—
136#9027—591nomaximal, Sylow
137C22×C59—22no—
138C22×C59—22no—
139C22×C59—22no—
140C22×C59—22no—
141C22×C59—21no—
142C22×C59—21no—
143C22×C59—21no—
144C22×C59—21no—
145C22×C59#38611yescharacteristic
146C22×C59C2×#10211yescharacteristic
147C22×C59#41711yescharacteristic
148C22×C59#44711yescharacteristic
149C22×C59#44811yescharacteristic
150C22×C59#45612yes—
151C22×C59#45812yes—
152C22×C59#48011yescharacteristic
153C22×C59#48111yescharacteristic
154C4×C59—24no—
155C4×C59—22no—
156C4×C59—22no—
157C4×C59—42no—
158C4×C59—84no—
159Dic59—44no—
160Dic59—82no—
161C2×#398—591no—
162#2316D5911yescharacteristic
163#1823—592no—
164C2×#324—591no—
165#1294—592no—
166C2×C59—21no—
167C2×C59—21no—
168C2×C59—21no—
169C2×C59—21no—
170C2×C59#161012yes—
171C2×C59#161112yes—
172C2×C59#187411yescharacteristic
173C2×C59#188611yescharacteristic
174C2×C59#189011yescharacteristic
175C2×#117—21no—
176C22×C4⋊C4—591no—
177C22×C4⋊C4—1181no—
178C22×C4⋊C4C2×D5911yescharacteristic
179C2×C22⋊C8—592no—
180#398—594no—
181#398—1182no—
182#389—24no—
183#380—21no—
184#380C2×D5912yes—
185C2×#95—591no—
186C2×#95—1181no—
187#340—1184no—
188#324—1182no—
189C59#902711yescharacteristic, complemented, Sylow
190C23×C4—1181no—
191C23×C4—1181no—
192C23×C4C22⋊D5911yescharacteristic
193C23×C4C22⋊D5911yescharacteristic
194C23×C4C22×D5911yescharacteristic
195C22×C8—1182no—
196#117—42no—
197#117—42no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—592no—
203C2×C4⋊C4—1182no—
204C2×C4⋊C4—1182no—
205C2×C4⋊C4—1184no—
206C2×C4⋊C4—1181no—
207C2×C4⋊C4—2362no—
208C2×C4⋊C4—2362no—
209C2×C4⋊C4C4×D5912yes—
210C2×C4⋊C4D23612yes—
211C2×C4⋊C4C22⋊D5914yes—
212C2×C22⋊C4—22no—
213C2×C42—22no—
214C22⋊C8—1182no—
215C22⋊C8—1182no—
216#95—22no—
217#95—22no—
218#95—592no—
219#95—1184no—
220#95—1181no—
221C24C2×C22⋊D5911yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—24no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—1184no—
232C22×C4—1182no—
233C22×C4—1182no—
234C22×C4—2361no—
235C22×C4—2361no—
236C22×C4—2361no—
237C22×C4—2361no—
238C22×C4—2361no—
239C22×C4—2361no—
240C22×C4—2362no—
241C22×C4—2361no—
242C22×C4—2361no—
243C22×C4(C2×D59)⋊C412yes—
244C22×C4(C2×D59)⋊C412yes—
245C22×C4#1174566912yes—
246C22×C4#1174567112yes—
247C22×C4C2×C4×D5911yescharacteristic
248C22×C4C2×D23611yescharacteristic
249C22×C4#1174568512yes—
250C22×C4C2×C22⋊D5912yes—
251C2×C8—2364no—
252C2×C8—2362no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—44no—
256C4⋊C4—44no—
257C4⋊C4—82no—
258C4⋊C4—1184no—
259C4⋊C4—2368no—
260C4⋊C4—2362no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C42—44no—
264C23—22no—
265C23—22no—
266C23C2×(C2×D59)⋊C411yescharacteristic
267C23#1427369611yescharacteristic
268C23#1427371011yescharacteristic
269C23C2×#1174566911yescharacteristic
270C23C2×#1174567111yescharacteristic
271C23#1427375311yescharacteristic
272C23#1427375811yescharacteristic
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—81no—
290C2×C4—1184no—
291C2×C4—4721no—
292C2×C4—4721no—
293C2×C4—4721no—
294C2×C4—4721no—
295C2×C4—2362no—
296C2×C4—2362no—
297C2×C4—2362no—
298C2×C4—2364no—
299C2×C4—2362no—
300C2×C4—2364no—
301C2×C4—2362no—
302C2×C4#1427364714yes—
303C2×C4C4×C22⋊D5912yes—
304C2×C4#1427370112yes—
305C8—4722no—
306C22—22no—
307C22—22no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—22no—
314C22#1683728111yescharacteristic
315C22C2×#1427364711yescharacteristic
316C22#1683740111yescharacteristic
317C22#1683753611yescharacteristic
318C22#1683754111yescharacteristic
319C22#1683758512yes—
320C22#1683759212yes—
321C22#1683771511yescharacteristic
322C22#1683772011yescharacteristic
323C4—24no—
324C4—22no—
325C4—22no—
326C4—42no—
327C4—84no—
328C4—4722no—
329C4—2364no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2#2142309912yes—
335C2#2142310412yes—
336C2#2142441311yescharacteristic
337C2#2142448911yescharacteristic
338C2#2142450911yescharacteristic
subgroupG/H
centerC23#14273696
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#2316C2
socleC23×C59#120
prime radicalC24×C59C2×D4
cosocleC23×C4×C59C23
hypercenter#2316D59
hypocenterC59#9027
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
10. #16837332C4semidirect
189. C59#9027semidirect

Maximal subgroups

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

subgroupindex
C2×#168373322
#214241802
C2×#168371282
#214219742
C59×#23162
#902759