Finite Group Databasebeta

← #28493187

Subgroups — #28493187

Order 15104.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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#21432368C211yesmaximal, characteristic
2#21424265C211yesmaximal, characteristic
3#21424264C212yesmaximal
4#21421978C212yesmaximal
5C59×#1295C211yesmaximal, characteristic
6C2×#14273661—22no—
7C2×#14273660—21no—
8C2×#14273659—22no—
9C2×#14273658—21no—
10C2×#14273638C2211yescharacteristic
11#16837344—22no—
12#16837341—21no—
13#16837323—22no—
14#16837322—21no—
15#16837272C2211yescharacteristic
16#16837268C2212yes—
17C2×#97×C59C2212yes—
18C59×#382C2211yescharacteristic
19C22×Dic118—21no—
20C22×C59⋊C8—21no—
21C2×C4⋊Dic59—21no—
22C2×C4⋊Dic59—22no—
23C2×C4⋊Dic59—21no—
24C2×C4⋊Dic59D412yes—
25C2×C4⋊Dic59D412yes—
26C2×Dic59⋊C4—22no—
27#14273661—44no—
28#14273660—42no—
29#14273659—44no—
30#14273658—42no—
31#14273638—21no—
32#14273638Q812yescomplemented
33C59⋊#95—21no—
34C59⋊#95—22no—
35C59⋊#95—21no—
36C59⋊#95—22no—
37C59⋊#95—22no—
38C22×C8×C59—22no—
39C2×C4⋊C4×C59D411yescharacteristic
40C2×C4⋊C4×C59D411yescharacteristic
41C2×C42×C59C2311yescharacteristic
42#97×C59—22no—
43#97×C59Q814yescomplemented
44#95×C59—22no—
45C22×C4×C59—21no—
46C22×C4×C59—21no—
47C22×C4×C59C2×D411yescharacteristic
48C22×C4×C59C2×D412yes—
49C22×Dic59—22no—
50C22×Dic59—22no—
51C22×Dic59—41no—
52C2×Dic118—82no—
53C2×Dic118—81no—
54C2×C8×C59—24no—
55C2×C8×C59—24no—
56C2×C8×C59—24no—
57C4⋊C4×C59—41no—
58C4⋊C4×C59—41no—
59C42×C59C2×Q812yes—
60C42×C59C2×Q811yescharacteristic
61C42×C59#4111yescharacteristic
62C4⋊Dic59—42no—
63C4⋊Dic59—42no—
64C4⋊Dic59—41no—
65C4⋊Dic59—42no—
66C4⋊Dic59—41no—
67C4⋊Dic59—42no—
68C4⋊Dic59—81no—
69Dic59⋊C4—82no—
70C2×C59⋊C8—22no—
71C2×C59⋊C8—22no—
72C2×C59⋊C8—22no—
73C23×C59#12011yescharacteristic
74C2×C4×C59—21no—
75C2×C4×C59—22no—
76C2×C4×C59—21no—
77C2×C4×C59—22no—
78C2×C4×C59—42no—
79C2×C4×C59—41no—
80C2×C4×C59—41no—
81C2×C4×C59—42no—
82C2×C4×C59C22⋊Q812yes—
83C2×C4×C59C22⋊Q811yescharacteristic
84C2×C4×C59C4⋊Q812yes—
85C2×C4×C59C4⋊Q811yescharacteristic
86C2×Dic59—42no—
87C2×Dic59—42no—
88C2×Dic59—42no—
89C2×Dic59—42no—
90C2×Dic59—42no—
91C2×Dic59—42no—
92C2×Dic59—82no—
93C2×Dic59—81no—
94Dic118—84no—
95C8×C59—28no—
96C59⋊C8—24no—
97#10583—591nomaximal, Sylow
98C22×C59#39511yescharacteristic
99C22×C59#45312yes—
100C22×C59#45311yescharacteristic
101C22×C59#45612yes—
102C22×C59#45611yescharacteristic
103C4×C59—21no—
104C4×C59—22no—
105C4×C59—22no—
106C4×C59—21no—
107C4×C59—81no—
108C4×C59—81no—
109Dic59—82no—
110Dic59—82no—
111Dic59—161no—
112#2844—591no—
113#1847—592no—
114#1847—591no—
115#1295—592no—
116#1295D5911yescharacteristic
117C2×C59#165511yescharacteristic
118C2×C59#166011yescharacteristic
119C2×C59#166012yes—
120C2×C59#206012yes—
121C2×C59#206011yescharacteristic
122C2×#107—1182no—
123C2×#107—1181no—
124C2×#106—1182no—
125C2×#106—1181no—
126C2×#97—591no—
127C2×#97C2×D5912yes—
128#400—1182no—
129#400—1181no—
130#395—1182no—
131#395—1181no—
132#384—591no—
133#382—592no—
134#382C2×D5911yescharacteristic
135C59#1058311yescharacteristic, complemented, Sylow
136C22×Q8—1181no—
137C22×C8—22no—
138C22×C8—1181no—
139C2×C4⋊C4—592no—
140C2×C4⋊C4—592no—
141C2×C4⋊C4—1182no—
142C2×C4⋊C4—1181no—
143C2×C4⋊C4—1181no—
144C2×C4⋊C4—1182no—
145C2×C4⋊C4D23611yescharacteristic
146C2×C4⋊C4D23611yescharacteristic
147C2×C42C22×D5911yescharacteristic
148#107—2362no—
149#107—2364no—
150#106—2362no—
151#106—2364no—
152#97—22no—
153#97—592no—
154#97—1181no—
155#97Dic11814yescomplemented
156#95—22no—
157#95—1182no—
158#95—1181no—
159#95—1181no—
160#95—1182no—
161#95—1182no—
162C2×Q8—4722no—
163C2×Q8—4721no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—1182no—
167C22×C4—1182no—
168C22×C4—2361no—
169C22×C4C2×D23611yescharacteristic
170C22×C4D4×D5912yes—
171C2×C8—24no—
172C2×C8—24no—
173C2×C8—24no—
174C2×C8—1182no—
175C2×C8—1182no—
176C2×C8—1182no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—4722no—
180C4⋊C4—4721no—
181C4⋊C4—2362no—
182C4⋊C4—2361no—
183C4⋊C4—2362no—
184C4⋊C4—2361no—
185C4⋊C4—2362no—
186C4⋊C4—2362no—
187C42C2×Dic11812yes—
188C42#1174568711yescharacteristic
189C42Q8×D5911yescharacteristic
190C23#1427369711yescharacteristic
191Q8—4724no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—4722no—
201C2×C4—4721no—
202C2×C4—2362no—
203C2×C4—2362no—
204C2×C4—2362no—
205C2×C4—2362no—
206C2×C4—2362no—
207C2×C4—2362no—
208C2×C4#1427370412yes—
209C2×C4#1427370711yescharacteristic
210C2×C4#1427372612yes—
211C2×C4#1427372711yescharacteristic
212C8—28no—
213C8—1184no—
214C22#1683732311yescharacteristic
215C22#1683757112yes—
216C22#1683757211yescharacteristic
217C22#1683758612yes—
218C22#1683758711yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—81no—
224C4—81no—
225C4—9441no—
226C4—4722no—
227C4—4722no—
228C2#2142338611yescharacteristic
229C2#2142340811yescharacteristic
230C2#2142340912yes—
231C2#2142544012yes—
232C2#2142544211yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1295C2
socle, prime radicalC23×C59#120
hypercenter#1295D59
hypocenterC59#10583
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
32. #14273638Q8semidirect
43. #97×C59Q8semidirect
135. C59#10583semidirect
155. #97Dic118semidirect

Maximal subgroups

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

subgroupindex
#214323682
#214242652
#214242642
#214219782
C59×#12952
#1058359