Finite Group Databasebeta

← #28482302

Subgroups — #28482302

Order 15104.

384 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 95 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#21427061C211yesmaximal, characteristic
2C4×#14273646C211yesmaximal, characteristic
3#21421988C212yesmaximal
4#21421962C212yesmaximal
5C59×#1467C211yesmaximal, characteristic
6C2×#14273646—21no—
7C4×#11745664C2212yes—
8#16837309—21no—
9#16837288—21no—
10#16837288—21no—
11#16837270C411yescharacteristic
12#16837270C2211yescharacteristic
13#16837268C411yescharacteristic
14C4⋊C4×Dic59—21no—
15C4×C4⋊Dic59C411yescharacteristic
16#16837248C411yescharacteristic
17#16837248C2211yescharacteristic
18#16837171—21no—
19C2×C4×Q8×C59C2211yescharacteristic
20C59×#432C2212yes—
21C59×#324—21no—
22C59×#324—21no—
23C2×#11745664—22no—
24C2×C4⋊Dic59—21no—
25C2×C4⋊Dic59—21no—
26C2×C4×Dic59—21no—
27C2×C4×Dic59—21no—
28C2×C4×Dic59—21no—
29#14273646—24no—
30#14273638—22no—
31C4×C59⋊C8—22no—
32C59⋊#95—21no—
33C59⋊#95—21no—
34C59⋊#95—21no—
35C59⋊#95—21no—
36C59⋊#95—21no—
37C59⋊#95—21no—
38C59⋊#95—21no—
39C59⋊#95C2×C411yescharacteristic
40C59⋊#95C2×C411yescharacteristic
41C59⋊#95C2×C411yescharacteristic
42C59⋊#95C2×C411yescharacteristic
43C22×Q8×C59D411yescharacteristic
44C4×Q8×C59—22no—
45C4×Q8×C59—22no—
46C2×C4⋊C4×C59D411yescharacteristic
47C2×C4⋊C4×C59D411yescharacteristic
48C2×C4⋊C4×C59D411yescharacteristic
49C2×C42×C59C2×C411yescharacteristic
50C2×C42×C59C2×C411yescharacteristic
51C2×C42×C59C2311yescharacteristic
52C4⋊C8×C59—22no—
53C22⋊C8×C59—22no—
54#97×C59—22no—
55C2×Q8×C59—22no—
56C2×Q8×C59—22no—
57C2×Q8×C59—41no—
58C22×C4×C59C22⋊C411yescharacteristic
59C22×C4×C59C22⋊C411yescharacteristic
60C22×C4×C59C22⋊C411yescharacteristic
61C22×C4×C59C22⋊C411yescharacteristic
62C22×C4×C59C22×C411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C22×C4×C59C2×D411yescharacteristic
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—21no—
68C22×Dic59—21no—
69C2×C8×C59—42no—
70C4⋊C4×C59—22no—
71C4⋊C4×C59—22no—
72C4⋊C4×C59—22no—
73C42×C59—21no—
74C42×C59—21no—
75C42×C59—21no—
76C42×C59—21no—
77C42×C59#4112yes—
78C42×C59#4112yes—
79C4⋊Dic59—42no—
80C4⋊Dic59—42no—
81C4×Dic59—42no—
82C4×Dic59—42no—
83C4×Dic59—42no—
84#11745664—24no—
85#11745664—42no—
86C2×C59⋊C8—42no—
87C23×C59C2×C22⋊C411yescharacteristic
88Q8×C59—44no—
89C2×C4×C59—21no—
90C2×C4×C59—21no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—41no—
99C2×C4×C59—41no—
100C2×C4×C59—41no—
101C2×C4×C59—41no—
102C2×C4×C59#10412yes—
103C2×C4×C59#11711yescharacteristic
104C2×C4×C59#11711yescharacteristic
105C2×C4×C59#12312yes—
106C2×C4×C59#12312yes—
107C2×Dic59—22no—
108C2×Dic59—41no—
109C2×Dic59—41no—
110C2×Dic59—41no—
111C2×Dic59—41no—
112C2×Dic59—41no—
113C2×Dic59—41no—
114C2×Dic59—41no—
115C2×Dic59—41no—
116C2×Dic59—41no—
117C2×Dic59—41no—
118C2×Dic59—41no—
119C8×C59—82no—
120C59⋊C8—44no—
121#8774—591nomaximal, Sylow
122C22×C59—21no—
123C22×C59—21no—
124C22×C59#38111yescharacteristic
125C22×C59C2×#10411yescharacteristic
126C22×C59#42111yescharacteristic
127C4×C59—22no—
128C4×C59—22no—
129C4×C59—22no—
130C4×C59—21no—
131C4×C59—21no—
132C4×C59—41no—
133C4×C59—41no—
134C4×C59—41no—
135Dic59—42no—
136Dic59—81no—
137Dic59—81no—
138Dic59—81no—
139#2356—591no—
140C4×#101—591no—
141#1467D5911yescharacteristic
142#1300—592no—
143#1288—592no—
144C2×C59—21no—
145C2×C59—21no—
146C2×C59#182611yescharacteristic
147C2×C59#182711yescharacteristic
148C2×C59#183011yescharacteristic
149C2×C4×Q8C2×D5911yescharacteristic
150#432C2×D5912yes—
151C2×#101—1181no—
152C4×M16—592no—
153#391—1181no—
154#387—1181no—
155#387—1181no—
156#383—591no—
157#383—591no—
158#382—591no—
159C4×C4⋊C4—591no—
160C4×C4⋊C4—1181no—
161#376—591no—
162#376—591no—
163#343—1181no—
164#324—21no—
165#324—21no—
166C59#877411yescharacteristic, complemented, Sylow
167C22×Q8D23611yescharacteristic
168C2×M16—1182no—
169C4×Q8—22no—
170C4×Q8—22no—
171C2×C4⋊C4—1181no—
172C2×C4⋊C4—1181no—
173C2×C4⋊C4D23611yescharacteristic
174C2×C4⋊C4C22⋊D5911yescharacteristic
175C2×C4⋊C4C22⋊D5911yescharacteristic
176C2×C42—1181no—
177C2×C42—1181no—
178C2×C42—1181no—
179C2×C42C4×D5911yescharacteristic
180C2×C42C4×D5911yescharacteristic
181C2×C42C22×D5911yescharacteristic
182C4⋊C8—22no—
183#101—1184no—
184C22⋊C8—22no—
185#97—22no—
186#97—1182no—
187C4×C8—1182no—
188#95—591no—
189#95—591no—
190#95—591no—
191#95—591no—
192#95—1181no—
193#95—1181no—
194#95—1181no—
195#95—1181no—
196#95—1181no—
197#95—1181no—
198#95—1181no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—41no—
202C22×C4—1181no—
203C22×C4—1181no—
204C22×C4—1181no—
205C22×C4—1181no—
206C22×C4(C2×D59)⋊C411yescharacteristic
207C22×C4(C2×D59)⋊C411yescharacteristic
208C22×C4(C2×D59)⋊C411yescharacteristic
209C22×C4(C2×D59)⋊C411yescharacteristic
210C22×C4C2×C4×D5911yescharacteristic
211C22×C4C2×D23611yescharacteristic
212C22×C4C2×C22⋊D5911yescharacteristic
213M16—1184no—
214M16—2362no—
215C2×C8—42no—
216C2×C8—2362no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—2362no—
221C4⋊C4—2362no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—2362no—
227C42—2362no—
228C42—2362no—
229C42#1174568712yes—
230C42#1174568712yes—
231C23C2×(C2×D59)⋊C411yescharacteristic
232Q8—44no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—1182no—
247C2×C4—2361no—
248C2×C4—2361no—
249C2×C4—2361no—
250C2×C4—2361no—
251C2×C4—2361no—
252C2×C4—2361no—
253C2×C4—2361no—
254C2×C4—2361no—
255C2×C4—2361no—
256C2×C4—2361no—
257C2×C4—2361no—
258C2×C4#1427365312yes—
259C2×C4#1427368311yescharacteristic
260C2×C4#1427368311yescharacteristic
261C2×C4#1427370812yes—
262C2×C4#1427371112yes—
263C8—82no—
264C8—2364no—
265C22—21no—
266C22—21no—
267C22#1683726311yescharacteristic
268C22C2×#1427365311yescharacteristic
269C22#1683741811yescharacteristic
270C4—22no—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—4721no—
279C4—4721no—
280C4—4721no—
281C4—2362no—
282C2—21no—
283C2—21no—
284C2#2142419311yescharacteristic
285C2#2142419711yescharacteristic
286C2#2142420811yescharacteristic
subgroupG/H
centerC22#16837263
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1467C2
socleC22×C59#381
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1467D59
hypocenterC59#8774
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
166. C59#8774semidirect

Maximal subgroups

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

subgroupindex
#214270612
C4×#142736462
#214219882
#214219622
C59×#14672
#877459