Finite Group Databasebeta

← #28484687

Subgroups — #28484687

Order 15104.

436 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 103 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#21429972C211yesmaximal, characteristic
2C4×#14273646C211yesmaximal, characteristic
3#21422699C212yesmaximal
4#21421962C212yesmaximal
5C59×#2983C211yesmaximal, characteristic
6C2×#14273719C2211yescharacteristic
7C2×#14273646—21no—
8C4×#11745664C2212yes—
9#16837341C411yescharacteristic
10#16837341C411yescharacteristic
11#16837340—21no—
12#16837332C411yescharacteristic
13#16837332C411yescharacteristic
14#16837321—21no—
15#16837286—21no—
16#16837286—21no—
17#16837270C2211yescharacteristic
18#16837171—21no—
19#16837143—24no—
20C2×C4×Q8×C59C2211yescharacteristic
21C59×#446—24no—
22C59×#432—21no—
23C59×#432C2212yes—
24C59×#431—21no—
25C2×#11745664—22no—
26#14273719—22no—
27#14273719—22no—
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×Dic59⋊C4—21no—
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34#14273646—24no—
35#14273638—22no—
36C4×C59⋊C8—22no—
37C59⋊#95—21no—
38C59⋊#95—21no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95C2×C411yescharacteristic
46C59⋊#95C2×C411yescharacteristic
47C22×Q8×C59D411yescharacteristic
48C4×Q8×C59—22no—
49C4×Q8×C59—22no—
50C2×C4⋊C4×C59C2×C411yescharacteristic
51C2×C4⋊C4×C59C2×C411yescharacteristic
52C2×C4⋊C4×C59D411yescharacteristic
53C2×C42×C59D411yescharacteristic
54C2×C42×C59D411yescharacteristic
55C2×C42×C59C2311yescharacteristic
56C4⋊C8×C59—22no—
57C4⋊C8×C59—22no—
58C4⋊C8×C59—22no—
59C22⋊C8×C59—22no—
60#97×C59—22no—
61#97×C59D414yes—
62C4×C8×C59—22no—
63C2×Q8×C59—22no—
64C2×Q8×C59—22no—
65C2×Q8×C59—41no—
66C22×C4×C59C22⋊C411yescharacteristic
67C22×C4×C59C22⋊C411yescharacteristic
68C22×C4×C59C22⋊C411yescharacteristic
69C22×C4×C59C22⋊C411yescharacteristic
70C22×C4×C59C22×C411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×Dic59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76C22×Dic59—21no—
77C2×C8×C59—24no—
78C4⋊C4×C59—22no—
79C4⋊C4×C59—22no—
80C4⋊C4×C59—22no—
81C42×C59—21no—
82C42×C59—21no—
83C42×C59—21no—
84C42×C59—21no—
85C42×C59C2×D412yes—
86C42×C59#4112yes—
87C4⋊Dic59—22no—
88C4⋊Dic59—22no—
89Dic59⋊C4—42no—
90Dic59⋊C4—42no—
91Dic59⋊C4—41no—
92Dic59⋊C4—42no—
93Dic59⋊C4—41no—
94#11745664—24no—
95#11745664—42no—
96C2×C59⋊C8—42no—
97C23×C59C2×C22⋊C411yescharacteristic
98Q8×C59—44no—
99C2×C4×C59—21no—
100C2×C4×C59—21no—
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—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59#10412yes—
113C2×C4×C59C4×D412yes—
114C2×C4×C59#12011yescharacteristic
115C2×C4×C59#12112yes—
116C2×C4×C59#12311yescharacteristic
117C2×Dic59—41no—
118C2×Dic59—41no—
119C2×Dic59—41no—
120C2×Dic59—41no—
121C2×Dic59—42no—
122C2×Dic59—41no—
123C2×Dic59—41no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C8×C59—44no—
129C59⋊C8—44no—
130#9190—591nomaximal, Sylow
131C22×C59—21no—
132C22×C59—21no—
133C22×C59#38611yescharacteristic
134C22×C59C2×#10411yescharacteristic
135C22×C59#42111yescharacteristic
136C4×C59—22no—
137C4×C59—22no—
138C4×C59—21no—
139C4×C59—21no—
140C4×C59—22no—
141C4×C59—41no—
142C4×C59—41no—
143C4×C59—41no—
144Dic59—81no—
145Dic59—81no—
146Dic59—81no—
147Dic59—81no—
148#2983D5911yescharacteristic
149#2634—591no—
150C4×#101—591no—
151#1528—592no—
152#1288—592no—
153C2×C59—21no—
154C2×C59—21no—
155C2×C59#187111yescharacteristic
156C2×C59#191211yescharacteristic
157C2×C59#191511yescharacteristic
158C2×#125—591no—
159C2×C4×Q8C2×D5911yescharacteristic
160#446—24no—
161#432—21no—
162#432C2×D5912yes—
163#431—21no—
164C2×#101—1181no—
165C4×M16—592no—
166#400—591no—
167#400—591no—
168#400—1181no—
169#398—591no—
170#398—591no—
171#395—1181no—
172#387—1181no—
173#387—1181no—
174#383—591no—
175#343—1181no—
176#330—1184no—
177C59#919011yescharacteristic, complemented, Sylow
178C22×Q8D23611yescharacteristic
179C2×M16—1182no—
180#125—1182no—
181#125—1182no—
182C4×Q8—22no—
183C4×Q8—22no—
184C2×C4⋊C4—591no—
185C2×C4⋊C4—591no—
186C2×C4⋊C4—1181no—
187C2×C4⋊C4—1181no—
188C2×C4⋊C4—1181no—
189C2×C4⋊C4—1181no—
190C2×C4⋊C4C4×D5911yescharacteristic
191C2×C4⋊C4C4×D5911yescharacteristic
192C2×C4⋊C4D23611yescharacteristic
193C2×C42C22⋊D5911yescharacteristic
194C2×C42C22⋊D5911yescharacteristic
195C2×C42C22×D5911yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—22no—
198C4⋊C8—22no—
199#101—1184no—
200C22⋊C8—22no—
201#97—22no—
202#97—1182no—
203#97C22⋊D5914yes—
204C4×C8—22no—
205C4×C8—1182no—
206#95—591no—
207#95—591no—
208#95—1181no—
209#95—1181no—
210#95—1181no—
211#95—1181no—
212#95—1181no—
213#95—1181no—
214#95—1181no—
215#95—1181no—
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—41no—
219C22×C4—1181no—
220C22×C4—1181no—
221C22×C4—1181no—
222C22×C4—1181no—
223C22×C4(C2×D59)⋊C411yescharacteristic
224C22×C4(C2×D59)⋊C411yescharacteristic
225C22×C4(C2×D59)⋊C411yescharacteristic
226C22×C4(C2×D59)⋊C411yescharacteristic
227C22×C4C2×C4×D5911yescharacteristic
228C22×C4C2×D23611yescharacteristic
229C22×C4C2×C22⋊D5911yescharacteristic
230M16—1184no—
231M16—2362no—
232C2×C8—24no—
233C2×C8—2362no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—1182no—
238C4⋊C4—1182no—
239C4⋊C4—2362no—
240C4⋊C4—2362no—
241C4⋊C4—2361no—
242C4⋊C4—2362no—
243C4⋊C4—2361no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42#1174568512yes—
249C42C2×C22⋊D5912yes—
250C23C2×(C2×D59)⋊C411yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—2361no—
266C2×C4—2361no—
267C2×C4—2361no—
268C2×C4—2361no—
269C2×C4—2362no—
270C2×C4—2361no—
271C2×C4—2361no—
272C2×C4—2361no—
273C2×C4—2361no—
274C2×C4—2361no—
275C2×C4—2361no—
276C2×C4#1427365312yes—
277C2×C4C4×C22⋊D5912yes—
278C2×C4#1427369611yescharacteristic
279C2×C4#1427370112yes—
280C2×C4#1427371011yescharacteristic
281C8—44no—
282C8—2364no—
283C22—21no—
284C22—21no—
285C22#1683728111yescharacteristic
286C22C2×#1427365311yescharacteristic
287C22#1683741811yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—4721no—
297C4—4721no—
298C4—4721no—
299C4—4721no—
300C2—21no—
301C2—21no—
302C2#2142439811yescharacteristic
303C2#2142463311yescharacteristic
304C2#2142464811yescharacteristic
subgroupG/H
centerC22#16837281
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2983C2
socleC22×C59#386
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#2983D59
hypocenterC59#9190
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
177. C59#9190semidirect

Maximal subgroups

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

subgroupindex
#214299722
C4×#142736462
#214226992
#214219622
C59×#29832
#919059