Finite Group Databasebeta

← #28482305

Subgroups — #28482305

Order 15104.

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

normal subgroups only

This group has 384 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
1C4×#14273646C211yesmaximal, characteristic
2#21422440C211yesmaximal, characteristic
3#21421989C212yesmaximal
4#21421960C212yesmaximal
5C59×#2356C211yesmaximal, characteristic
6#16837459C2212yes—
7C2×#14273646—21no—
8C4×#11745664C2212yes—
9#16837171—21no—
10#16837128—21no—
11#16837128—21no—
12C2×C4×Q8×C59C2211yescharacteristic
13C59×#391—21no—
14C59×#387—21no—
15C59×#387—21no—
16C59×#383C411yescharacteristic
17C59×#383C2211yescharacteristic
18C59×#382C411yescharacteristic
19C4×C4⋊C4×C59—21no—
20C4×C4⋊C4×C59C411yescharacteristic
21C59×#376C411yescharacteristic
22C59×#376C2211yescharacteristic
23C2×#11745664—22no—
24C4⋊(C59⋊C8)—22no—
25#14273646—24no—
26C22⋊(C59⋊C8)—22no—
27#14273638—22no—
28#14273638—22no—
29C4×C59⋊C8—22no—
30C22×Q8×C59D411yescharacteristic
31C4×Q8×C59—22no—
32C4×Q8×C59—22no—
33C2×C4⋊C4×C59—21no—
34C2×C4⋊C4×C59—21no—
35C2×C4⋊C4×C59D411yescharacteristic
36C2×C4⋊C4×C59D411yescharacteristic
37C2×C4⋊C4×C59D411yescharacteristic
38C2×C42×C59—21no—
39C2×C42×C59—21no—
40C2×C42×C59—21no—
41C2×C42×C59C2×C411yescharacteristic
42C2×C42×C59C2×C411yescharacteristic
43C2×C42×C59C2311yescharacteristic
44#95×C59—21no—
45#95×C59—21no—
46#95×C59—21no—
47#95×C59—21no—
48#95×C59—21no—
49#95×C59—21no—
50#95×C59—21no—
51#95×C59C2×C411yescharacteristic
52#95×C59C2×C411yescharacteristic
53#95×C59C2×C411yescharacteristic
54#95×C59C2×C411yescharacteristic
55C2×Q8×C59—22no—
56C2×Q8×C59—22no—
57C2×Q8×C59—41no—
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59—21no—
62C22×C4×C59C22⋊C411yescharacteristic
63C22×C4×C59C22⋊C411yescharacteristic
64C22×C4×C59C22⋊C411yescharacteristic
65C22×C4×C59C22⋊C411yescharacteristic
66C22×C4×C59C22×C411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×C4×C59C2×D411yescharacteristic
69C4⋊C4×C59—22no—
70C4⋊C4×C59—22no—
71C4⋊C4×C59—22no—
72C4⋊C4×C59—42no—
73C4⋊C4×C59—42no—
74C42×C59—21no—
75C42×C59—21no—
76C42×C59—21no—
77C42×C59—21no—
78C42×C59—42no—
79C42×C59—42no—
80C42×C59—42no—
81C42×C59#4112yes—
82C42×C59#4112yes—
83#11745664—24no—
84#11745664—42no—
85C2×C59⋊C8—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—22no—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
99C2×C4×C59—41no—
100C2×C4×C59—41no—
101C2×C4×C59—41no—
102C2×C4×C59—41no—
103C2×C4×C59—41no—
104C2×C4×C59—41no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59#10412yes—
115C2×C4×C59#11711yescharacteristic
116C2×C4×C59#11711yescharacteristic
117C2×C4×C59#12312yes—
118C2×C4×C59#12312yes—
119C59⋊C8—44no—
120C59⋊C8—82no—
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—42no—
133C4×C59—41no—
134C4×C59—41no—
135C4×C59—41no—
136C4×C59—81no—
137C4×C59—81no—
138C4×C59—81no—
139#2356D5911yescharacteristic
140C4×#101—591no—
141#1467—591no—
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#432—592no—
151C2×#101—1181no—
152C4×M16—592no—
153#391—21no—
154#387—21no—
155#387—21no—
156#383Dic5911yescharacteristic
157#383C2×D5911yescharacteristic
158#382Dic5911yescharacteristic
159C4×C4⋊C4—21no—
160C4×C4⋊C4Dic5911yescharacteristic
161#376Dic5911yescharacteristic
162#376C2×D5911yescharacteristic
163#343—1181no—
164#324—1181no—
165#324—1181no—
166C59#877411yescharacteristic, complemented, Sylow
167C22×Q8C22⋊D5911yescharacteristic
168C2×M16—1182no—
169C4×Q8—22no—
170C4×Q8—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C22⋊D5911yescharacteristic
174C2×C4⋊C4C22⋊D5911yescharacteristic
175C2×C4⋊C4C22⋊D5911yescharacteristic
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42C2×Dic5911yescharacteristic
180C2×C42C2×Dic5911yescharacteristic
181C2×C42C22×D5911yescharacteristic
182C4⋊C8—1182no—
183#101—1184no—
184C22⋊C8—1182no—
185#97—1182no—
186#97—1182no—
187C4×C8—1182no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95C2×Dic5911yescharacteristic
196#95C2×Dic5911yescharacteristic
197#95C2×Dic5911yescharacteristic
198#95C2×Dic5911yescharacteristic
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—41no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4C22⋊Dic5911yescharacteristic
207C22×C4C22⋊Dic5911yescharacteristic
208C22×C4C22⋊Dic5911yescharacteristic
209C22×C4C22⋊Dic5911yescharacteristic
210C22×C4C22×Dic5911yescharacteristic
211C22×C4C2×C22⋊D5911yescharacteristic
212C22×C4C2×C22⋊D5911yescharacteristic
213M16—1184no—
214M16—2362no—
215C2×C8—2362no—
216C2×C8—2362no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—42no—
227C42—42no—
228C42—42no—
229C42#1174568512yes—
230C42#1174568512yes—
231C23C2×C22⋊Dic5911yescharacteristic
232Q8—44no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4#1427365412yes—
259C2×C4#1427368611yescharacteristic
260C2×C4#1427368611yescharacteristic
261C2×C4#1427371012yes—
262C2×C4#1427371012yes—
263C8—4722no—
264C8—2364no—
265C22—21no—
266C22—21no—
267C22#1683726511yescharacteristic
268C22C2×#1427365411yescharacteristic
269C22#1683741911yescharacteristic
270C4—22no—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—41no—
277C4—41no—
278C4—41no—
279C4—81no—
280C4—81no—
281C4—81no—
282C2—21no—
283C2—21no—
284C2#2142419511yescharacteristic
285C2#2142420011yescharacteristic
286C2#2142421011yescharacteristic
subgroupG/H
centerC22#16837265
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2356C2
socleC22×C59#381
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#2356D59
hypocenterC59#8774
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2356

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
C4×#142736462
#214224402
#214219892
#214219602
C59×#23562
#877459