Finite Group Databasebeta

← #28483761

Subgroups — #28483761

Order 15104.

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

normal subgroups only

This group has 484 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#21433181C211yesmaximal, characteristic
2#21427387C211yesmaximal, characteristic
3#21422544C212yesmaximal
4#21421990C212yesmaximal
5C4×#101×C59C211yesmaximal, characteristic
6C2×C4×Dic118C2211yescharacteristic
7#16837533—24no—
8#16837459—21no—
9#16837459C2212yes—
10#16837455—21no—
11#16837333—21no—
12#16837332C411yescharacteristic
13#16837332C411yescharacteristic
14#16837322C411yescharacteristic
15#16837322C411yescharacteristic
16#16837321—21no—
17C4×Dic59⋊C4—21no—
18C4×Dic59⋊C4—21no—
19#16837248C2211yescharacteristic
20#16837134—24no—
21C2×C4×Q8×C59C2211yescharacteristic
22C2×#101×C59—21no—
23C4×M16×C59C2212yes—
24C59×#343—21no—
25C22×Dic118C2×C411yescharacteristic
26C4×Dic118—22no—
27C4×Dic118—22no—
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×Dic59⋊C4—21no—
30C2×Dic59⋊C4—21no—
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34C2×C4×Dic59—21no—
35C2×C4×Dic59—21no—
36C4⋊(C59⋊C8)—22no—
37C4⋊(C59⋊C8)—22no—
38C4⋊(C59⋊C8)D414yes—
39C22⋊(C59⋊C8)—22no—
40#14273638—22no—
41#14273638—22no—
42C4×C59⋊C8—22no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95C2×C411yescharacteristic
49C59⋊#95C2×C411yescharacteristic
50C22×Q8×C59D411yescharacteristic
51C2×M16×C59—22no—
52C4×Q8×C59—22no—
53C4×Q8×C59—22no—
54C2×C4⋊C4×C59C2×C411yescharacteristic
55C2×C4⋊C4×C59C2×C411yescharacteristic
56C2×C4⋊C4×C59D411yescharacteristic
57C2×C42×C59D411yescharacteristic
58C2×C42×C59D411yescharacteristic
59C2×C42×C59C2311yescharacteristic
60#101×C59—24no—
61#97×C59—22no—
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×Dic118—22no—
78C2×Dic118—42no—
79M16×C59—24no—
80M16×C59—42no—
81C2×C8×C59—42no—
82C4⋊C4×C59—22no—
83C4⋊C4×C59—22no—
84C4⋊C4×C59—22no—
85C42×C59—21no—
86C42×C59—21no—
87C42×C59—21no—
88C42×C59—21no—
89C42×C59C2×D412yes—
90C42×C59#4112yes—
91C4⋊Dic59—22no—
92Dic59⋊C4—42no—
93Dic59⋊C4—42no—
94Dic59⋊C4—42no—
95Dic59⋊C4—42no—
96Dic59⋊C4—42no—
97C4×Dic59—24no—
98C4×Dic59—41no—
99C4×Dic59—41no—
100C2×C59⋊C8—24no—
101C23×C59C2×C22⋊C411yescharacteristic
102Q8×C59—44no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—22no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—41no—
114C2×C4×C59—41no—
115C2×C4×C59—41no—
116C2×C4×C59#10412yes—
117C2×C4×C59C4×D412yes—
118C2×C4×C59#12011yescharacteristic
119C2×C4×C59#12112yes—
120C2×C4×C59#12311yescharacteristic
121C2×Dic59—22no—
122C2×Dic59—22no—
123C2×Dic59—22no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C2×Dic59—41no—
129C2×Dic59—41no—
130C2×Dic59—41no—
131C2×Dic59—41no—
132C2×Dic59—41no—
133Dic118—24no—
134Dic118—42no—
135C8×C59—44no—
136C59⋊C8—44no—
137#9030—591nomaximal, Sylow
138C22×C59—21no—
139C22×C59—21no—
140C22×C59#38611yescharacteristic
141C22×C59C2×#10411yescharacteristic
142C22×C59#42111yescharacteristic
143C4×C59—22no—
144C4×C59—22no—
145C4×C59—21no—
146C4×C59—22no—
147C4×C59—41no—
148C4×C59—41no—
149C4×C59—41no—
150C4×C59#45612yes—
151Dic59—42no—
152Dic59—42no—
153Dic59—42no—
154Dic59—81no—
155#2983—591no—
156#2399—591no—
157C4×#101D5911yescharacteristic
158#1491—592no—
159#1300—592no—
160C2×C59—21no—
161C2×C59—21no—
162C2×C59#187111yescharacteristic
163C2×C59#188611yescharacteristic
164C2×C59#189111yescharacteristic
165C2×C4×Q8—591no—
166C2×C4×Q8C2×D5911yescharacteristic
167#446—1184no—
168#432—592no—
169#432—1181no—
170#431—1181no—
171C2×#101—21no—
172C4×M16C2×D5912yes—
173#398—591no—
174#398—591no—
175#398—1181no—
176#395—591no—
177#395—591no—
178#395—1181no—
179C4×C4⋊C4—1181no—
180C4×C4⋊C4—1181no—
181#376—591no—
182#343—21no—
183Q8⋊C8—1184no—
184C59#903011yescharacteristic, complemented, Sylow
185C22×Q8—591no—
186C22×Q8C22⋊D5911yescharacteristic
187C2×M16—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—1182no—
191C4×Q8—1182no—
192C2×C4⋊C4—591no—
193C2×C4⋊C4—1181no—
194C2×C4⋊C4—1181no—
195C2×C4⋊C4—1181no—
196C2×C4⋊C4—1181no—
197C2×C4⋊C4—1181no—
198C2×C4⋊C4C4×D5911yescharacteristic
199C2×C4⋊C4C4×D5911yescharacteristic
200C2×C4⋊C4C22⋊D5911yescharacteristic
201C2×C42—1181no—
202C2×C42—1181no—
203C2×C42D23611yescharacteristic
204C2×C42D23611yescharacteristic
205C2×C42C22×D5911yescharacteristic
206C4⋊C8—594no—
207C4⋊C8—1182no—
208C4⋊C8—1182no—
209#101—24no—
210C22⋊C8—1182no—
211#97—22no—
212#97—1182no—
213#97—1182no—
214C4×C8—22no—
215C4×C8—1182no—
216#95—591no—
217#95—591no—
218#95—1181no—
219#95—1181no—
220#95—1181no—
221#95—1181no—
222#95—1181no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—1182no—
227C2×Q8—2362no—
228C22×C4—1181no—
229C22×C4—1181no—
230C22×C4—1181no—
231C22×C4—1181no—
232C22×C4(C2×D59)⋊C411yescharacteristic
233C22×C4(C2×D59)⋊C411yescharacteristic
234C22×C4(C2×D59)⋊C411yescharacteristic
235C22×C4(C2×D59)⋊C411yescharacteristic
236C22×C4C2×C4×D5911yescharacteristic
237C22×C4C2×D23611yescharacteristic
238C22×C4C2×C22⋊D5911yescharacteristic
239M16—24no—
240M16—42no—
241C2×C8—42no—
242C2×C8—1184no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—1182no—
247C4⋊C4—2362no—
248C4⋊C4—2362no—
249C4⋊C4—2362no—
250C4⋊C4—2362no—
251C4⋊C4—2362no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—1184no—
257C42—2361no—
258C42—2361no—
259C42D4×D5912yes—
260C42#1174568712yes—
261C23C2×(C2×D59)⋊C411yescharacteristic
262Q8—44no—
263Q8—1184no—
264Q8—2362no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—1182no—
279C2×C4—1182no—
280C2×C4—1182no—
281C2×C4—2361no—
282C2×C4—2361no—
283C2×C4—2361no—
284C2×C4—2361no—
285C2×C4—2361no—
286C2×C4—2361no—
287C2×C4—2361no—
288C2×C4—2361no—
289C2×C4—2361no—
290C2×C4#1427365512yes—
291C2×C4(C22⋊D59)⋊C412yes—
292C2×C4#1427369711yescharacteristic
293C2×C4#1427369912yes—
294C2×C4#1427371111yescharacteristic
295C8—44no—
296C8—2364no—
297C22—21no—
298C22—21no—
299C22#1683727911yescharacteristic
300C22C2×#1427365511yescharacteristic
301C22#1683742011yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—4721no—
310C4—2362no—
311C4—2362no—
312C4—2362no—
313C4#1683758712yes—
314C2—21no—
315C2—21no—
316C2#2142439611yescharacteristic
317C2#2142448711yescharacteristic
318C2#2142451211yescharacteristic
subgroupG/H
centerC2×C4#14273697
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC4×#101×C59C2
socleC22×C59#386
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenterC4×#101D59
hypocenterC59#9030
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
184. C59#9030semidirect

Maximal subgroups

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

subgroupindex
#214331812
#214273872
#214225442
#214219902
C4×#101×C592
#903059