Finite Group Databasebeta

← #28499602

Subgroups — #28499602

Order 15104.

396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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
1#21424176C211yesmaximal, characteristic
2C2×#16837128C211yesmaximal, characteristic
3#21422123C212yesmaximal, complemented
4#21422102C212yesmaximal, complemented
5C59×#2484C211yesmaximal, characteristic
6#16837366—21no—
7C2×C22⋊(C59⋊C8)—21no—
8#16837171—21no—
9#16837171C2212yes—
10#16837128—21no—
11#16837128C2212yes—
12C2×#117×C59C411yescharacteristic
13C22×C4⋊C4×C59C2211yescharacteristic
14C59×#400C411yescharacteristic
15C59×#400C2211yescharacteristic
16C59×#398C411yescharacteristic
17C59×#398C2211yescharacteristic
18C59×#387—21no—
19C59×#387—21no—
20C59×#385—21no—
21C59×#381—21no—
22C59×#381C411yescharacteristic
23C2×#11745664—22no—
24C22×C59⋊C8—41no—
25C22⋊(C59⋊C8)—22no—
26C22⋊(C59⋊C8)—41no—
27C22⋊(C59⋊C8)—41no—
28C22⋊(C59⋊C8)—41no—
29C23×C4×C59C2×C411yescharacteristic
30C23×C4×C59D411yescharacteristic
31C23×C4×C59D411yescharacteristic
32#117×C59—41no—
33#117×C59—41no—
34C2×C4⋊C4×C59—21no—
35C2×C4⋊C4×C59—21no—
36C2×C4⋊C4×C59—41no—
37C2×C4⋊C4×C59—41no—
38C2×C4⋊C4×C59C2×C411yescharacteristic
39C2×C4⋊C4×C59C2×C411yescharacteristic
40C2×C4⋊C4×C59C2×C411yescharacteristic
41C2×C4⋊C4×C59D411yescharacteristic
42C2×C4⋊C4×C59D411yescharacteristic
43C2×C4⋊C4×C59C2311yescharacteristic
44C2×C22⋊C4×C59—21no—
45C2×C22⋊C4×C59—21no—
46C2×C42×C59—21no—
47#95×C59—21no—
48#95×C59—21no—
49#95×C59—21no—
50#95×C59—21no—
51#95×C59—21no—
52#95×C59—21no—
53#95×C59—21no—
54#95×C59C2×C411yescharacteristic
55#95×C59C2×C411yescharacteristic
56C24×C59C22⋊C411yescharacteristic
57C22×C4×C59—21no—
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59—21no—
62C22×C4×C59—21no—
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—42no—
70C22×C4×C59—42no—
71C22×C4×C59C22⋊C411yescharacteristic
72C22×C4×C59C22⋊C411yescharacteristic
73C22×C4×C59C22⋊C411yescharacteristic
74C22×C4×C59C22×C411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C22×C4×C59C2×D411yescharacteristic
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—42no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—42no—
85C22⋊C4×C59—42no—
86C22⋊C4×C59—41no—
87C22⋊C4×C59—41no—
88C42×C59—42no—
89#11745664—42no—
90#11745664—42no—
91C2×C59⋊C8—42no—
92C2×C59⋊C8—42no—
93C2×C59⋊C8—82no—
94C23×C59—22no—
95C23×C59—21no—
96C23×C59—21no—
97C23×C59—41no—
98C23×C59#9911yescharacteristic
99C23×C59#9911yescharacteristic
100C23×C59C2×C22⋊C411yescharacteristic
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—42no—
111C2×C4×C59—42no—
112C2×C4×C59—42no—
113C2×C4×C59—42no—
114C2×C4×C59—42no—
115C2×C4×C59—41no—
116C2×C4×C59—41no—
117C2×C4×C59—41no—
118C2×C4×C59—41no—
119C2×C4×C59—41no—
120C2×C4×C59—41no—
121C2×C4×C59—41no—
122C2×C4×C59—41no—
123C2×C4×C59—42no—
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—81no—
131C2×C4×C59#13512yes—
132C59⋊C8—82no—
133C59⋊C8—82no—
134#11850—591nomaximal, Sylow
135C22×C59—21no—
136C22×C59—21no—
137C22×C59—21no—
138C22×C59—21no—
139C22×C59—21no—
140C22×C59—21no—
141C22×C59—21no—
142C22×C59—42no—
143C22×C59—42no—
144C22×C59#35212yes—
145C22×C59C2×#9911yescharacteristic
146C22×C59#41611yescharacteristic
147C22×C59#42111yescharacteristic
148C4×C59—22no—
149C4×C59—41no—
150C4×C59—41no—
151C4×C59—41no—
152C4×C59—41no—
153C4×C59—41no—
154C4×C59—81no—
155C4×C59—81no—
156C4×C59—81no—
157C4×C59—81no—
158#2484D5911yescharacteristic
159#1821—591no—
160C2×#324—591no—
161#1353—592no—
162#1346—592no—
163C2×C59—21no—
164C2×C59—21no—
165C2×C59—22no—
166C2×C59—41no—
167C2×C59#151611yescharacteristic
168C2×C59C2×#35211yescharacteristic
169C2×C59#213311yescharacteristic
170C2×#117Dic5911yescharacteristic
171C22×C4⋊C4C2×D5911yescharacteristic
172#407—1181no—
173C2×C22⋊C8—1181no—
174#400Dic5911yescharacteristic
175#400C2×D5911yescharacteristic
176#398Dic5911yescharacteristic
177#398C2×D5911yescharacteristic
178#387—21no—
179#387—21no—
180#385—21no—
181#381—21no—
182#381Dic5911yescharacteristic
183#343—592no—
184#343—1181no—
185#324—592no—
186#324—1181no—
187C59#1185011yescharacteristic, complemented, Sylow
188C23×C4C2×Dic5911yescharacteristic
189C23×C4C22⋊D5911yescharacteristic
190C23×C4C22⋊D5911yescharacteristic
191C2×M16—1182no—
192C22×C8—2361no—
193#117—41no—
194#117—41no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4C2×Dic5911yescharacteristic
200C2×C4⋊C4C2×Dic5911yescharacteristic
201C2×C4⋊C4C2×Dic5911yescharacteristic
202C2×C4⋊C4C22⋊D5911yescharacteristic
203C2×C4⋊C4C22⋊D5911yescharacteristic
204C2×C4⋊C4C22×D5911yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C42—21no—
208C22⋊C8—1182no—
209C22⋊C8—2361no—
210C22⋊C8—2361no—
211C22⋊C8—2361no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95C2×Dic5911yescharacteristic
220#95C2×Dic5911yescharacteristic
221C24C22⋊Dic5911yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4C22⋊Dic5911yescharacteristic
237C22×C4C22⋊Dic5911yescharacteristic
238C22×C4C22⋊Dic5911yescharacteristic
239C22×C4C22×Dic5911yescharacteristic
240C22×C4C2×C22⋊D5911yescharacteristic
241C22×C4C2×C22⋊D5911yescharacteristic
242M16—2362no—
243M16—2362no—
244C2×C8—4722no—
245C2×C8—2362no—
246C2×C8—2362no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C42—42no—
259C23—21no—
260C23—21no—
261C23—22no—
262C23—41no—
263C23#1427364211yescharacteristic
264C23#1427364211yescharacteristic
265C23C2×C22⋊Dic5911yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4#1427374712yes—
297C8—4722no—
298C8—4722no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—42no—
307C22—42no—
308C22#1683719212yes—
309C22C2×#1427364211yescharacteristic
310C22#1683739811yescharacteristic
311C22#1683741911yescharacteristic
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—41no—
326C2#2142265211yescharacteristic
327C2C2×#1683719211yescharacteristic
328C2#2142578511yescharacteristic
subgroupG/H
centerC22C2×#14273642
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#2484C2
socleC22×C59C2×#99
prime radicalC24×C59C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#2484D59
hypocenterC59#11850
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
3. #21422123C2semidirect
4. #21422102C2semidirect
187. C59#11850semidirect

Maximal subgroups

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

subgroupindex
#214241762
C2×#168371282
#214221232
#214221022
C59×#24842
#1185059