Finite Group Databasebeta

← #28483763

Subgroups — #28483763

Order 15104.

484 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 107 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#21427387C211yesmaximal, characteristic
2C4×#14273646C211yesmaximal, characteristic
3#21422542C212yesmaximal
4#21421988C212yesmaximal
5C59×#2983C211yesmaximal, characteristic
6C2×C4×Dic118C2211yescharacteristic
7C2×#14273646—21no—
8C4×#11745664C2212yes—
9#16837333—21no—
10#16837332C411yescharacteristic
11#16837332C411yescharacteristic
12#16837322C411yescharacteristic
13#16837322C411yescharacteristic
14#16837321—21no—
15C4×Dic59⋊C4—21no—
16C4×Dic59⋊C4—21no—
17#16837248C2211yescharacteristic
18#16837171—21no—
19#16837132—24no—
20C2×C4×Q8×C59C2211yescharacteristic
21C59×#446—24no—
22C59×#432—21no—
23C59×#432C2212yes—
24C59×#431—21no—
25C22×Dic118C2×C411yescharacteristic
26C2×#11745664—22no—
27C4×Dic118—22no—
28C4×Dic118—22no—
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×Dic59⋊C4—21no—
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34C2×Dic59⋊C4—21no—
35C2×C4×Dic59—21no—
36C2×C4×Dic59—21no—
37#14273646—24no—
38#14273638—22no—
39C4×C59⋊C8—22no—
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×C59D414yes—
59C22⋊C8×C59—22no—
60#97×C59—22no—
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—
79C2×C8×C59—24no—
80C4⋊C4×C59—22no—
81C4⋊C4×C59—22no—
82C4⋊C4×C59—22no—
83C42×C59—21no—
84C42×C59—21no—
85C42×C59—21no—
86C42×C59—21no—
87C42×C59C2×D412yes—
88C42×C59#4112yes—
89C4⋊Dic59—22no—
90Dic59⋊C4—42no—
91Dic59⋊C4—42no—
92Dic59⋊C4—42no—
93Dic59⋊C4—42no—
94Dic59⋊C4—42no—
95C4×Dic59—24no—
96C4×Dic59—41no—
97C4×Dic59—41no—
98#11745664—24no—
99#11745664—42no—
100C2×C59⋊C8—42no—
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#2983D5911yescharacteristic
156#2399—591no—
157C4×#101—591no—
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—24no—
168#432—21no—
169#432C2×D5912yes—
170#431—21no—
171C2×#101—1181no—
172C4×M16—592no—
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—1181no—
183Q8⋊C8—1184no—
184C59#903011yescharacteristic, complemented, Sylow
185C22×Q8—591no—
186C22×Q8D23611yescharacteristic
187C2×M16—1182no—
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⋊C4D23611yescharacteristic
201C2×C42—1181no—
202C2×C42—1181no—
203C2×C42C22⋊D5911yescharacteristic
204C2×C42C22⋊D5911yescharacteristic
205C2×C42C22×D5911yescharacteristic
206C4⋊C8—22no—
207C4⋊C8—22no—
208C4⋊C8C22⋊D5914yes—
209#101—1184no—
210C22⋊C8—22no—
211#97—22no—
212#97—22no—
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—1184no—
240M16—2362no—
241C2×C8—24no—
242C2×C8—2362no—
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—
259C42#1174568512yes—
260C42C2×C22⋊D5912yes—
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#1427365312yes—
291C2×C4C4×C22⋊D5912yes—
292C2×C4#1427369611yescharacteristic
293C2×C4#1427370112yes—
294C2×C4#1427371011yescharacteristic
295C8—44no—
296C8—2364no—
297C22—21no—
298C22—21no—
299C22#1683728111yescharacteristic
300C22C2×#1427365311yescharacteristic
301C22#1683741811yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—4721no—
310C4—2362no—
311C4—2362no—
312C4—2362no—
313C4#1683758512yes—
314C2—21no—
315C2—21no—
316C2#2142439811yescharacteristic
317C2#2142448911yescharacteristic
318C2#2142451411yescharacteristic
subgroupG/H
centerC2×C4#14273696
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2983C2
socleC22×C59#386
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#2983D59
hypocenterC59#9030
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

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
#214273872
C4×#142736462
#214225422
#214219882
C59×#29832
#903059