Finite Group Databasebeta

← #28499442

Subgroups — #28499442

Order 15104.

368 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 79 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#21429917C211yesmaximal, characteristic
2#21424179C211yesmaximal, characteristic
3#21422124C214yesmaximal, complemented
4C59×#1464C211yesmaximal, characteristic
5C2×#14273727C411yescharacteristic
6#16837366—21no—
7#16837341C2212yes—
8#16837338C412yes—
9#16837322—21no—
10#16837314—21no—
11#16837300—21no—
12#16837268C411yescharacteristic
13#16837262—21no—
14#16837171—21no—
15#16837171C2212yes—
16C2×#117×C59C2211yescharacteristic
17C59×#432—21no—
18C59×#324C2212yes—
19C59×#323—21no—
20C22×Dic118—21no—
21C2×#11745664—22no—
22#14273727—41no—
23#14273727—41no—
24C2×C4⋊Dic59—21no—
25C2×C4⋊Dic59—21no—
26C2×C4⋊Dic59C2×C412yes—
27C2×Dic59⋊C4—22no—
28C2×C22⋊Dic59—22no—
29C22⋊(C59⋊C8)—41no—
30C22⋊(C59⋊C8)—41no—
31C59⋊#95—21no—
32C59⋊#95—22no—
33C59⋊#95—22no—
34C59⋊#95C2×C412yes—
35C23×C4×C59D411yescharacteristic
36#117×C59—41no—
37#117×C59—41no—
38C2×C4⋊C4×C59D411yescharacteristic
39C2×C4⋊C4×C59C2311yescharacteristic
40C2×C22⋊C4×C59C2×C411yescharacteristic
41C2×C22⋊C4×C59D411yescharacteristic
42C2×C42×C59C2×C411yescharacteristic
43C2×C42×C59D411yescharacteristic
44C4⋊C8×C59—41no—
45C22⋊C8×C59—22no—
46#97×C59—41no—
47C24×C59C22⋊C411yescharacteristic
48C22×C4×C59—21no—
49C22×C4×C59—21no—
50C22×C4×C59—22no—
51C22×C4×C59—41no—
52C22×C4×C59C22⋊C411yescharacteristic
53C22×C4×C59C22⋊C411yescharacteristic
54C22×C4×C59C22⋊C411yescharacteristic
55C22×C4×C59C22×C411yescharacteristic
56C22×C4×C59C2×D411yescharacteristic
57C22×C4×C59C2×D411yescharacteristic
58C22×Dic59—22no—
59C22×Dic59—22no—
60C2×Dic118—42no—
61C2×Dic118—82no—
62C2×C8×C59—42no—
63C4⋊C4×C59—41no—
64C4⋊C4×C59—41no—
65C22⋊C4×C59—41no—
66C22⋊C4×C59—41no—
67C42×C59—21no—
68C42×C59—21no—
69C42×C59—21no—
70C42×C59—21no—
71C22⋊Dic59—82no—
72C4⋊Dic59—42no—
73C4⋊Dic59—41no—
74C4⋊Dic59—41no—
75C4⋊Dic59—42no—
76Dic59⋊C4—82no—
77#11745664—42no—
78#11745664—42no—
79C2×C59⋊C8—42no—
80C23×C59—21no—
81C23×C59—21no—
82C23×C59—21no—
83C23×C59—41no—
84C23×C59—41no—
85C23×C59C2×C22⋊C411yescharacteristic
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59—21no—
90C2×C4×C59—21no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—42no—
95C2×C4×C59—42no—
96C2×C4×C59—41no—
97C2×C4×C59—41no—
98C2×C4×C59—41no—
99C2×C4×C59—41no—
100C2×C4×C59#9911yescharacteristic
101C2×C4×C59#9911yescharacteristic
102C2×C4×C59#13712yes—
103C2×Dic59—42no—
104C2×Dic59—42no—
105C2×Dic59—42no—
106C2×Dic59—42no—
107C2×Dic59—42no—
108C2×Dic59—42no—
109Dic118—84no—
110C8×C59—82no—
111C59⋊C8—82no—
112#11818—591nomaximal, Sylow
113C22×C59—21no—
114C22×C59—21no—
115C22×C59—42no—
116C22×C59—41no—
117C22×C59—41no—
118C22×C59—41no—
119C22×C59—81no—
120C22×C59C2×#9911yescharacteristic
121C22×C59#41911yescharacteristic
122C22×C59#42111yescharacteristic
123C4×C59—22no—
124C4×C59—21no—
125C4×C59—21no—
126C4×C59—41no—
127C4×C59—41no—
128C4×C59—41no—
129C4×C59—41no—
130Dic59—82no—
131Dic59—82no—
132#2628—591no—
133#1822—591no—
134#1464D5911yescharacteristic
135#1353—594no—
136C2×C59—21no—
137C2×C59—21no—
138C2×C59—81no—
139C2×C59#151111yescharacteristic
140C2×C59#212311yescharacteristic
141C2×C59#213411yescharacteristic
142C2×C4⋊Q8—591no—
143C2×#117C2×D5911yescharacteristic
144#432—21no—
145#407—1181no—
146#400—592no—
147#399—592no—
148#395—1181no—
149#393—1181no—
150#389—1181no—
151#382—591no—
152#380—1181no—
153#343—592no—
154#343—1181no—
155#324C2×D5912yes—
156#323—21no—
157C59#1181811yescharacteristic, complemented, Sylow
158C22×Q8—1181no—
159C23×C4D23611yescharacteristic
160C2×M16—1182no—
161C4⋊Q8—2361no—
162C4⋊Q8—2361no—
163#117—41no—
164#117—41no—
165C2×C4⋊C4—592no—
166C2×C4⋊C4—1182no—
167C2×C4⋊C4—1181no—
168C2×C4⋊C4—1181no—
169C2×C4⋊C4D23611yescharacteristic
170C2×C4⋊C4C22×D5911yescharacteristic
171C2×C22⋊C4—1182no—
172C2×C22⋊C4C4×D5911yescharacteristic
173C2×C22⋊C4C22⋊D5911yescharacteristic
174C2×C42C4×D5911yescharacteristic
175C2×C42C22⋊D5911yescharacteristic
176C4⋊C8—41no—
177C22⋊C8—22no—
178C22⋊C8—2361no—
179C22⋊C8—2361no—
180#97—41no—
181#95—592no—
182#95—1181no—
183#95—1182no—
184#95—1182no—
185C24(C2×D59)⋊C411yescharacteristic
186C2×Q8—4722no—
187C2×Q8—2362no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—41no—
192C22×C4—1182no—
193C22×C4—1182no—
194C22×C4(C2×D59)⋊C411yescharacteristic
195C22×C4(C2×D59)⋊C411yescharacteristic
196C22×C4(C2×D59)⋊C411yescharacteristic
197C22×C4C2×C4×D5911yescharacteristic
198C22×C4C2×D23611yescharacteristic
199C22×C4C2×C22⋊D5911yescharacteristic
200M16—2362no—
201M16—2362no—
202C2×C8—42no—
203C2×C8—2362no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—4722no—
207C4⋊C4—2362no—
208C4⋊C4—2362no—
209C4⋊C4—2361no—
210C4⋊C4—2361no—
211C22⋊C4—41no—
212C22⋊C4—41no—
213C22⋊C4—4722no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×(C2×D59)⋊C411yescharacteristic
224Q8—4724no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—2362no—
240C2×C4—2362no—
241C2×C4—2362no—
242C2×C4—2362no—
243C2×C4—2362no—
244C2×C4—2362no—
245C2×C4#1427364111yescharacteristic
246C2×C4#1427364111yescharacteristic
247C2×C4#1427376012yes—
248C8—82no—
249C8—4722no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#1427364111yescharacteristic
258C22#1683741211yescharacteristic
259C22#1683741811yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—4722no—
268C4—4722no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#2142263011yescharacteristic
273C2#2142574911yescharacteristic
274C2#2142578711yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#1464C2
socleC22×C59C2×#99
prime radicalC24×C59C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#1464D59
hypocenterC59#11818
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #21422124C2semidirect
157. C59#11818semidirect

Maximal subgroups

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

subgroupindex
#214299172
#214241792
#214221242
C59×#14642
#1181859