Finite Group Databasebeta

← #28477787

Subgroups — #28477787

Order 15104.

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

normal subgroups only

This group has 478 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#21425624C211yesmaximal, characteristic
2#21425567C212yesmaximal, complemented
3#21421919C212yesmaximal, complemented
4#21421917C211yesmaximal, characteristic
5C59×#2683C211yesmaximal, characteristic
6C2×#14273660—22no—
7C2×#14273660—21no—
8C2×#14273648—21no—
9#16837272C2211yescharacteristic
10#16837164—22no—
11#16837157C2212yes—
12#16837157C2211yescharacteristic
13C2×C22⋊Q8×C59—22no—
14C59×#396—22no—
15C59×#395—21no—
16C59×#390C2211yescharacteristic
17C59×#389C2212yes—
18C59×#386—21no—
19C22×C59⋊C8—21no—
20C22×C59⋊C8—22no—
21C2×C4⋊Dic59—21no—
22C2×C4⋊Dic59—22no—
23#14273660—42no—
24#14273660—44no—
25#14273648—42no—
26C22×Q8×C59—21no—
27C22×D4×C59D411yescharacteristic
28C23×C4×C59—21no—
29C22⋊Q8×C59—44no—
30C22⋊Q8×C59—44no—
31C2×C4⋊C4×C59—22no—
32C2×C4⋊C4×C59—22no—
33C2×C4⋊C4×C59D412yes—
34C2×C4⋊C4×C59D412yes—
35C2×C4⋊C4×C59D411yescharacteristic
36C2×C22⋊C4×C59—22no—
37C2×C22⋊C4×C59—22no—
38C2×C22⋊C4×C59—21no—
39C2×C42×C59C2311yescharacteristic
40#95×C59—21no—
41#95×C59—22no—
42C24×C59—21no—
43C2×Q8×C59—44no—
44C2×Q8×C59—81no—
45C2×D4×C59—21no—
46C2×D4×C59—41no—
47C2×D4×C59—41no—
48C2×D4×C59Q1612yes—
49C22×C4×C59—22no—
50C22×C4×C59—22no—
51C22×C4×C59—21no—
52C22×C4×C59—44no—
53C22×C4×C59—81no—
54C22×C4×C59C2×D412yes—
55C22×C4×C59C2×D411yescharacteristic
56C22×Dic59—41no—
57C4⋊C4×C59—22no—
58C4⋊C4×C59—44no—
59C4⋊C4×C59—42no—
60C4⋊C4×C59—41no—
61C4⋊C4×C59—42no—
62C4⋊C4×C59—42no—
63C4⋊C4×C59D814yes—
64C22⋊C4×C59—44no—
65C22⋊C4×C59—42no—
66C22⋊C4×C59—42no—
67C22⋊C4×C59—81no—
68C42×C59—41no—
69C4⋊Dic59—41no—
70C4⋊Dic59—41no—
71C4⋊Dic59—42no—
72C4⋊Dic59—42no—
73C2×C59⋊C8—22no—
74C2×C59⋊C8—24no—
75C2×C59⋊C8—42no—
76C2×C59⋊C8—41no—
77C2×C59⋊C8—42no—
78C2×C59⋊C8—41no—
79C23×C59—22no—
80C23×C59—42no—
81C23×C59—41no—
82C23×C59—42no—
83C23×C59—41no—
84C23×C59#12011yescharacteristic
85Q8×C59—84no—
86D4×C59—42no—
87D4×C59—81no—
88C2×C4×C59—21no—
89C2×C4×C59—22no—
90C2×C4×C59—22no—
91C2×C4×C59—21no—
92C2×C4×C59—24no—
93C2×C4×C59—42no—
94C2×C4×C59—42no—
95C2×C4×C59—42no—
96C2×C4×C59—42no—
97C2×C4×C59—41no—
98C2×C4×C59—42no—
99C2×C4×C59—42no—
100C2×C4×C59—84no—
101C2×C4×C59C2×D812yes—
102C2×C4×C59C2×Q1611yescharacteristic
103C2×C4×C59AGL(1,ℤ/8)12yes—
104C2×C4×C59#13711yescharacteristic
105C2×Dic59—82no—
106C2×Dic59—81no—
107C59⋊C8—44no—
108C59⋊C8—42no—
109#7797—591nomaximal, Sylow
110C22×C59—42no—
111C22×C59—44no—
112C22×C59—82no—
113C22×C59—81no—
114C22×C59—81no—
115C22×C59#44712yes—
116C22×C59#45111yescharacteristic
117C22×C59#45311yescharacteristic
118C22×C59#45612yes—
119C22×C59#45811yescharacteristic
120C4×C59—22no—
121C4×C59—22no—
122C4×C59—21no—
123C4×C59—21no—
124C4×C59—44no—
125C4×C59—82no—
126C4×C59—81no—
127Dic59—161no—
128#2683D5911yescharacteristic
129#2093—591no—
130#2083—592no—
131#1271—592no—
132#1270—591no—
133C2×C59—82no—
134C2×C59#161012yes—
135C2×C59#161411yescharacteristic
136C2×C59#161911yescharacteristic
137C2×C59#164912yes—
138C2×C59#166011yescharacteristic
139C2×C22⋊Q8—22no—
140C2×#107—1182no—
141C2×#107—1181no—
142C2×#102—1181no—
143#396—22no—
144#395—21no—
145#390C2×D5911yescharacteristic
146#389C2×D5912yes—
147#386—21no—
148#384—591no—
149#340—1182no—
150#336—592no—
151#336—591no—
152C59#779711yescharacteristic, complemented, Sylow
153C22×Q8—21no—
154C22×D4C22⋊D5911yescharacteristic
155C23×C4—21no—
156C22×C8—1182no—
157C22×C8—1181no—
158C22⋊Q8—44no—
159C22⋊Q8—44no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—1182no—
163C2×C4⋊C4—1181no—
164C2×C4⋊C4C22⋊D5912yes—
165C2×C4⋊C4C22⋊D5912yes—
166C2×C4⋊C4C22⋊D5911yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—21no—
170C2×C42C22×D5911yescharacteristic
171#107—2362no—
172#107—2364no—
173#102—2362no—
174#95—21no—
175#95—22no—
176C24—21no—
177C2×Q8—44no—
178C2×Q8—81no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4#1174567212yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—44no—
187C22×C4—81no—
188C22×C4—2361no—
189C22×C4C2×C22⋊D5912yes—
190C22×C4C2×C22⋊D5911yescharacteristic
191C2×C8—1182no—
192C2×C8—1184no—
193C2×C8—2362no—
194C2×C8—2361no—
195C2×C8—2362no—
196C2×C8—2361no—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—44no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—2361no—
204C4⋊C4—2361no—
205C4⋊C4—2362no—
206C4⋊C4—2362no—
207C4⋊C4#1174566914yes—
208C22⋊C4—44no—
209C22⋊C4—42no—
210C22⋊C4—42no—
211C22⋊C4—81no—
212C42—41no—
213C23—22no—
214C23—42no—
215C23—41no—
216C23—42no—
217C23—41no—
218C23#1427369611yescharacteristic
219Q8—84no—
220D4—42no—
221D4—81no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4—4722no—
236C2×C4—4721no—
237C2×C4C2×#1174566912yes—
238C2×C4C2×#1174567211yescharacteristic
239C2×C4#1427375312yes—
240C2×C4#1427375811yescharacteristic
241C8—2362no—
242C8—2364no—
243C22—42no—
244C22—44no—
245C22—81no—
246C22—81no—
247C22—82no—
248C22#1683753612yes—
249C22#1683755811yescharacteristic
250C22#1683757011yescharacteristic
251C22#1683758512yes—
252C22#1683759211yescharacteristic
253C4—21no—
254C4—21no—
255C4—22no—
256C4—22no—
257C4—44no—
258C4—81no—
259C4—82no—
260C4—9441no—
261C2—82no—
262C2#2142309912yes—
263C2#2142312111yescharacteristic
264C2#2142315011yescharacteristic
265C2#2142334512yes—
266C2#2142340711yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2683C2
socleC23×C59#120
prime radicalC22×D4×C59D4
hypercenter#2683D59
hypocenterC59#7797
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2683

Complements

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

NH ≅ G/Ntype
2. #21425567C2semidirect
3. #21421919C2semidirect
152. C59#7797semidirect

Maximal subgroups

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

subgroupindex
#214256242
#214255672
#214219192
#214219172
C59×#26832
#779759