Finite Group Databasebeta

← #28492759

Subgroups — #28492759

Order 15104.

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

normal subgroups only

This group has 408 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#21435406C211yesmaximal, characteristic
2#21422789C212yesmaximal, complemented
3#21422603C212yesmaximal, complemented
4#21421966C211yesmaximal, characteristic, complemented
5C59×#1843C211yesmaximal, characteristic, complemented
6#16837952C2212yes—
7#16837683—22no—
8#16837638—22no—
9#16837598—22no—
10#16837459C2212yes—
11#16837150—22no—
12#16837145—22no—
13#16837135—24no—
14C2×C4⋊C8×C59—22no—
15C2×C4⋊C8×C59C2211yescharacteristic
16C2×C4⋊C8×C59C2211yescharacteristic
17C59×#376C2211yescharacteristic
18C2×#11745685—22no—
19C2×D472—22no—
20#14273727D412yes—
21#14273724D412yes—
22#14273715—22no—
23#14273701—22no—
24#14273701—22no—
25C4×D236—22no—
26C4×D236—22no—
27#14273661—22no—
28C4⋊(C59⋊C8)—22no—
29#14273649—24no—
30C22⋊(C59⋊C8)—22no—
31#14273638—22no—
32C22×C8×C59—21no—
33C22×C8×C59D412yes—
34C2×C42×C59—21no—
35C2×C42×C59C2311yescharacteristic
36C4⋊C8×C59—22no—
37C4⋊C8×C59—22no—
38C4⋊C8×C59—44no—
39#95×C59—21no—
40#95×C59D412yes—
41C22×C4×C59—22no—
42C22×C4×C59C2×D411yescharacteristic
43C22×C4×C59C2×D411yescharacteristic
44C22×C4×C59#4111yescharacteristic
45C2×C22⋊D59—42no—
46#11745685—84no—
47C2×D236—22no—
48C2×D236—22no—
49C2×D236—22no—
50C2×C4×D59—42no—
51C2×Dic118—22no—
52C2×C8×C59—22no—
53C2×C8×C59—42no—
54C2×C8×C59—42no—
55C2×C8×C59—41no—
56C42×C59—22no—
57C42×C59—22no—
58C42×C59C2×D412yes—
59C42×C59#4112yes—
60(C2×D59)⋊C4—42no—
61(C2×D59)⋊C4—42no—
62C4⋊Dic59—22no—
63C4⋊Dic59—22no—
64C2×C59⋊C8—42no—
65D472—82no—
66C23×C59#12111yescharacteristic
67C22×D59—42no—
68C2×C4×C59—22no—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—24no—
72C2×C4×C59—41no—
73C2×C4×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59#12011yescharacteristic
76C2×C4×C59#12112yes—
77C2×C4×C59#12312yes—
78C2×C4×C59#12411yescharacteristic
79C22⋊D59—84no—
80C2×Dic59—42no—
81D236—42no—
82D236—42no—
83D236—82no—
84D236—82no—
85C4×D59—84no—
86Dic118—82no—
87C8×C59—42no—
88C8×C59—81no—
89C59⋊C8—82no—
90#10512—591nomaximal, Sylow
91C22×C59—21no—
92C22×C59—21no—
93C22×C59#39411yescharacteristic
94C22×C59#47212yes—
95C2×D59—82no—
96C2×D59—82no—
97C2×D59—82no—
98C4×C59—22no—
99C4×C59—21no—
100C4×C59—22no—
101C4×C59—44no—
102C4×C59#45311yescharacteristic
103C4×C59#45611yescharacteristic
104Dic59—82no—
105#3245—591no—
106#1843D5911yescharacteristic, complemented
107#1551—592no—
108#1505—592no—
109#1290—591no—
110C2×C59—22no—
111C2×C59#203911yescharacteristic
112C2×C59#204511yescharacteristic
113C2×C59#205311yescharacteristic
114D59—162no—
115#532—592no—
116#474—1182no—
117#466—1182no—
118#459—1182no—
119#432—592no—
120C2×C4⋊C8—22no—
121C2×C4⋊C8C2×D5911yescharacteristic
122C2×C4⋊C8C2×D5911yescharacteristic
123#376C2×D5911yescharacteristic
124#333—1182no—
125#331—1182no—
126#327—1184no—
127C59#1051211yescharacteristic, complemented, Sylow
128C2×#41—1182no—
129C2×D8—1182no—
130C22×C8—21no—
131C22×C8C22⋊D5912yes—
132C4⋊Q8—592no—
133#127—592no—
134#124—1182no—
135#121—1182no—
136#121—1182no—
137C4×D4—1182no—
138C4×D4—1182no—
139C2×C42—21no—
140C2×C42C22×D5911yescharacteristic
141#107—1182no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—44no—
145C4⋊C8—1182no—
146#102—1184no—
147C22⋊C8—1182no—
148#97—1182no—
149#95—21no—
150#95D23612yes—
151#41—4724no—
152C2×Q8—1182no—
153C2×D4—1182no—
154C2×D4—1182no—
155C2×D4—1182no—
156C2×D4—2362no—
157C22×C4—22no—
158C22×C4—2362no—
159C22×C4C2×D23611yescharacteristic
160C22×C4#1174568511yescharacteristic
161C22×C4C2×C22⋊D5911yescharacteristic
162D8—4722no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—41no—
167C2×C8—2362no—
168C4⋊C4—1182no—
169C4⋊C4—1182no—
170C22⋊C4—2362no—
171C22⋊C4—2362no—
172C42—22no—
173C42—22no—
174C42D4×D5912yes—
175C42#1174568912yes—
176C23—2362no—
177C23#1427370111yescharacteristic
178Q8—4722no—
179D4—4722no—
180D4—4722no—
181D4—4724no—
182D4—2362no—
183D4—2362no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—41no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—4724no—
192C2×C4—2362no—
193C2×C4#1427369511yescharacteristic
194C2×C4#1427370212yes—
195C2×C4#1427371212yes—
196C2×C4#1427371611yescharacteristic
197C8—42no—
198C8—81no—
199C8—4722no—
200C22—21no—
201C22—21no—
202C22—4722no—
203C22—4722no—
204C22—4722no—
205C22#1683731911yescharacteristic
206C22#1683767212yes—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—44no—
211C4—4722no—
212C4#1683756911yescharacteristic
213C4#1683758411yescharacteristic
214C2—22no—
215C2—9442no—
216C2#2142532011yescharacteristic
217C2#2142535211yescharacteristic
218C2#2142540211yescharacteristic
subgroupG/H
centerC22#16837319
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1843C2
socleC22×C59#394
prime radical#21435406C2
hypercenter#1843D59
hypocenterC59#10512
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1843

Complements

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

NH ≅ G/Ntype
2. #21422789C2semidirect
3. #21422603C2semidirect
4. #21421966C2semidirect
5. C59×#1843C2semidirect
106. #1843D59semidirect
127. C59#10512semidirect

Maximal subgroups

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

subgroupindex
#214354062
#214227892
#214226032
#214219662
C59×#18432
#1051259