Finite Group Databasebeta

← #28509048

Subgroups — #28509048

Order 15104.

318 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 71 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#21434441C211yesmaximal, characteristic
2#21425781C211yesmaximal, characteristic
3#21422268C214yesmaximal, complemented
4C59×#2132C211yesmaximal, characteristic
5#16837959C411yescharacteristic
6#16837770C2212yes—
7#16837766C412yes—
8#16837761—21no—
9#16837761—21no—
10#16837398—21no—
11#16837398—21no—
12#16837386—21no—
13C2×#14273638C411yescharacteristic
14#16837201C2212yes—
15#16837199—21no—
16C59×#532C2211yescharacteristic
17C59×#413—21no—
18C59×#356C2212yes—
19C59×#355—21no—
20C2×#11745664—41no—
21C22×C59⋊C8—21no—
22#14273727—21no—
23#14273719C2×C412yes—
24#14273706—41no—
25C4×Dic118—41no—
26#14273686—21no—
27#14273651—22no—
28#14273651—22no—
29#14273648—22no—
30#14273648—22no—
31#14273646—22no—
32#14273644—41no—
33#14273638—21no—
34#14273638C2×C412yes—
35C2×#41×C59D411yescharacteristic
36C2×#41×C59D411yescharacteristic
37C2×M16×C59—41no—
38C4⋊Q8×C59C2311yescharacteristic
39#127×C59C2×C411yescharacteristic
40#124×C59D411yescharacteristic
41#124×C59D411yescharacteristic
42#121×C59—41no—
43C4×D4×C59—41no—
44C2×C42×C59C2×C411yescharacteristic
45#101×C59—22no—
46#100×C59—41no—
47#41×C59—41no—
48#41×C59—41no—
49#41×C59—41no—
50#41×C59—41no—
51C2×Q8×C59C2×D411yescharacteristic
52C2×Q8×C59C2×D411yescharacteristic
53C2×D4×C59—21no—
54C2×D4×C59—21no—
55C2×D4×C59—41no—
56C2×D4×C59C22⋊C411yescharacteristic
57C2×D4×C59C22⋊C411yescharacteristic
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59C22⋊C411yescharacteristic
62C2×Dic118—41no—
63M16×C59—42no—
64M16×C59—81no—
65C2×C8×C59—81no—
66C4⋊C4×C59—41no—
67C22⋊C4×C59—41no—
68C22⋊C4×C59—41no—
69C42×C59—21no—
70C42×C59C22⋊C411yescharacteristic
71C42×C59C22×C411yescharacteristic
72C22⋊Dic59—41no—
73C4⋊Dic59—22no—
74C4⋊Dic59—41no—
75Dic59⋊C4—42no—
76C4×Dic59—41no—
77#11745664—42no—
78#11745664—81no—
79C2×C59⋊C8—22no—
80C2×C59⋊C8—41no—
81C2×C59⋊C8—41no—
82C2×C59⋊C8—81no—
83C23×C59—21no—
84C23×C59—21no—
85C23×C59#9911yescharacteristic
86Q8×C59—41no—
87Q8×C59—41no—
88D4×C59—41no—
89D4×C59—41no—
90D4×C59—81no—
91D4×C59—81no—
92D4×C59—82no—
93C2×C4×C59—21no—
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—81no—
104C2×C4×C59#9911yescharacteristic
105C2×C4×C59C2×C22⋊C411yescharacteristic
106C2×Dic59—42no—
107Dic118—82no—
108C8×C59—82no—
109C59⋊C8—42no—
110C59⋊C8—82no—
111#13598—591nomaximal, Sylow
112C22×C59—21no—
113C22×C59—41no—
114C22×C59—41no—
115C22×C59—41no—
116C22×C59—81no—
117C22×C59—81no—
118C22×C59C2×#9911yescharacteristic
119C4×C59—21no—
120C4×C59—41no—
121C4×C59—41no—
122C4×C59—41no—
123C4×C59—41no—
124C4×C59#35411yescharacteristic
125C4×C59#35411yescharacteristic
126Dic59—82no—
127#3135—591no—
128#2132—591no—
129#2132D5911yescharacteristic
130#1413—594no—
131C2×C59—21no—
132C2×C59—41no—
133C2×C59—81no—
134C2×C59—81no—
135C2×C59C2×#35411yescharacteristic
136#533—591no—
137#532C2×D5911yescharacteristic
138#491—592no—
139#490—592no—
140#489—1181no—
141#489—1181no—
142#416—1181no—
143#416—1181no—
144#413—21no—
145#413—1181no—
146C2×#97—591no—
147#356—592no—
148#356C2×D5912yes—
149#355—21no—
150#355—1181no—
151C59#1359811yescharacteristic, complemented, Sylow
152C2×#41D23611yescharacteristic
153C2×#41C22⋊D5911yescharacteristic
154C2×M16—41no—
155C2×M16—2361no—
156C22×C8—1181no—
157C4⋊Q8—1181no—
158C4⋊Q8C22×D5911yescharacteristic
159#127C4×D5911yescharacteristic
160#125—592no—
161#124D23611yescharacteristic
162#124C22⋊D5911yescharacteristic
163C22⋊Q8—2361no—
164#121—41no—
165C4×Q8—2361no—
166C4×D4—41no—
167#117—1181no—
168C2×C42C4×D5911yescharacteristic
169#103—1182no—
170#103—1182no—
171#102—1182no—
172#102—1182no—
173#101—22no—
174#101—1182no—
175#100—41no—
176#100—2361no—
177#97—592no—
178#97—1181no—
179#41—41no—
180#41—41no—
181#41—41no—
182#41—41no—
183C2×Q8—2361no—
184C2×Q8C2×D23611yescharacteristic
185C2×Q8C2×C22⋊D5911yescharacteristic
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4(C2×D59)⋊C411yescharacteristic
190C2×D4(C2×D59)⋊C411yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4(C2×D59)⋊C411yescharacteristic
195M16—42no—
196M16—81no—
197M16—4721no—
198M16—2362no—
199C2×C8—81no—
200C2×C8—1182no—
201C2×C8—4721no—
202C2×C8—2361no—
203C2×C8—2361no—
204C4⋊C4—41no—
205C4⋊C4—1182no—
206C4⋊C4—2362no—
207C4⋊C4—2361no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—2361no—
211C42—21no—
212C42—2361no—
213C42(C2×D59)⋊C411yescharacteristic
214C42C2×C4×D5911yescharacteristic
215C23—21no—
216C23—21no—
217C23#1427364111yescharacteristic
218Q8—41no—
219Q8—41no—
220Q8—4722no—
221D4—41no—
222D4—41no—
223D4—81no—
224D4—81no—
225D4—82no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—81no—
237C2×C4—2362no—
238C2×C4#1427364111yescharacteristic
239C2×C4C2×(C2×D59)⋊C411yescharacteristic
240C8—82no—
241C8—4722no—
242C8—2362no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—81no—
248C22—81no—
249C22C2×#1427364111yescharacteristic
250C4—21no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—4722no—
256C4#1683719611yescharacteristic
257C4#1683719611yescharacteristic
258C2—21no—
259C2—41no—
260C2—81no—
261C2—81no—
262C2C2×#1683719611yescharacteristic
subgroupG/H
centerC4#16837196
commutatorC42×C59C22×C4
FrattiniC4⋊Q8C22×D59
FittingC59×#2132C2
socleC2×C59C2×#354
prime radicalC59×#532C22
cosocleC4⋊Q8×C59C23
hypercenter#2132D59
hypocenterC59#13598
LCSG ▷ C42×C59 ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
3. #21422268C2semidirect
151. C59#13598semidirect

Maximal subgroups

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

subgroupindex
#214344412
#214257812
#214222682
C59×#21322
#1359859