Finite Group Databasebeta

← #28493679

Subgroups — #28493679

Order 15104.

320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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#21425035C211yesmaximal, characteristic
2#21424270C211yesmaximal, characteristic
3#21422866C211yesmaximal, characteristic
4#21422526C211yesmaximal, characteristic
5#21422524C211yesmaximal, characteristic
6#21421926C211yesmaximal, characteristic
7C59×#1570C211yesmaximal, characteristic
8C2×C4×Dic118C2211yescharacteristic
9#16837455C2211yescharacteristic
10C2×#14273662—22no—
11#16837426C2211yescharacteristic
12C2×#14273638C2211yescharacteristic
13#16837156—22no—
14#16837152—22no—
15#16837134—22no—
16#16837132—22no—
17C59×#431C2211yescharacteristic
18C59×#423C2211yescharacteristic
19C2×C4⋊C8×C59C2211yescharacteristic
20C59×#334—22no—
21C22×Dic118Q811yescharacteristic
22C2×#11745664—21no—
23C22×C59⋊C8D412yes—
24C4×Dic118—21no—
25C4×Dic118—21no—
26C4×Dic118—21no—
27C4×Dic118—21no—
28C2×C4⋊Dic59Q811yescharacteristic
29C2×Dic59⋊C4—21no—
30C2×C4×Dic59—21no—
31#14273662—44no—
32C4⋊(C59⋊C8)—21no—
33C4⋊(C59⋊C8)—21no—
34C4⋊(C59⋊C8)—21no—
35C22⋊(C59⋊C8)—21no—
36#14273638—21no—
37#14273638—21no—
38C4×C59⋊C8D412yes—
39C2×M16×C59—21no—
40C22×C8×C59—21no—
41C2×C42×C59C2311yescharacteristic
42C4⋊C8×C59—21no—
43C4⋊C8×C59—21no—
44C4⋊C8×C59—21no—
45C4⋊C8×C59—21no—
46C4⋊C8×C59—21no—
47C22⋊C8×C59—21no—
48C4×C8×C59D412yes—
49C22×C4×C59C2×D411yescharacteristic
50C22×C4×C59C2×Q811yescharacteristic
51C22×C4×C59#4111yescharacteristic
52C22×Dic59—21no—
53C22×Dic59—21no—
54C2×Dic118—21no—
55C2×Dic118—21no—
56C2×Dic118—42no—
57M16×C59—42no—
58C2×C8×C59—22no—
59C2×C8×C59—41no—
60C2×C8×C59—41no—
61C2×C8×C59—42no—
62C42×C59C2×D411yescharacteristic
63C42×C59C2×D411yescharacteristic
64C42×C59#4111yescharacteristic
65C42×C59#4111yescharacteristic
66C4⋊Dic59—21no—
67C4⋊Dic59—21no—
68Dic59⋊C4—41no—
69Dic59⋊C4—41no—
70C4×Dic59—41no—
71C4×Dic59—41no—
72#11745664—42no—
73C2×C59⋊C8—22no—
74C2×C59⋊C8—22no—
75C2×C59⋊C8—22no—
76C2×C59⋊C8—41no—
77C2×C59⋊C8SD1614yes—
78C23×C59C22⋊Q811yescharacteristic
79C2×C4×C59—41no—
80C2×C4×C59—41no—
81C2×C4×C59C22⋊Q811yescharacteristic
82C2×C4×C59C22⋊Q811yescharacteristic
83C2×C4×C59#12311yescharacteristic
84C2×C4×C59#12311yescharacteristic
85C2×C4×C59#12311yescharacteristic
86C2×C4×C59#12711yescharacteristic
87C2×C4×C59C2×SD1612yes—
88C2×C4×C59#13712yes—
89C2×Dic59—22no—
90C2×Dic59—41no—
91C2×Dic59—41no—
92C2×Dic59—42no—
93C2×Dic59—41no—
94Dic118—22no—
95Dic118—22no—
96Dic118—41no—
97Dic118—41no—
98C8×C59—42no—
99C8×C59—81no—
100C8×C59—81no—
101C59⋊C8—24no—
102C59⋊C8—42no—
103C59⋊C8—81no—
104#10663—591nomaximal, Sylow
105C22×C59—21no—
106C22×C59—21no—
107C22×C59#39911yescharacteristic
108C22×C59#47512yes—
109C4×C59—21no—
110C4×C59—21no—
111C4×C59—21no—
112C4×C59—21no—
113C4×C59#48312yes—
114C4×C59#49211yescharacteristic
115C4×C59#49711yescharacteristic
116Dic59—42no—
117Dic59—81no—
118#1985—591no—
119#1849—591no—
120#1570—591no—
121#1570D5911yescharacteristic
122#1487—591no—
123#1487—591no—
124#1275—591no—
125C2×C59—22no—
126C2×C59#209111yescharacteristic
127C2×C59#209611yescharacteristic
128C2×C59#209811yescharacteristic
129C2×C4×Q8—591no—
130#431—591no—
131#431C2×D5911yescharacteristic
132C2×#108—1182no—
133#423—591no—
134#423C2×D5911yescharacteristic
135C2×C4⋊C8C2×D5911yescharacteristic
136C2×#97—591no—
137#336—1182no—
138#334—22no—
139#334—1182no—
140Q8⋊C8—1182no—
141Q8⋊C8—1182no—
142C59#1066311yescharacteristic, complemented, Sylow
143C22×Q8—591no—
144C2×M16—21no—
145C2×M16—1181no—
146C22×C8—21no—
147C22×C8—592no—
148C4×Q8—1181no—
149C4×Q8—1181no—
150C4×Q8—1181no—
151C4×Q8—1181no—
152C2×C4⋊C4—591no—
153C2×C4⋊C4—1181no—
154C2×C42—1181no—
155C2×C42C22×D5911yescharacteristic
156#108—2364no—
157C4⋊C8—21no—
158C4⋊C8—21no—
159C4⋊C8—21no—
160C4⋊C8—21no—
161C4⋊C8—21no—
162C4⋊C8—1181no—
163C4⋊C8—1181no—
164C4⋊C8—1181no—
165C22⋊C8—21no—
166C22⋊C8—1181no—
167#97—1181no—
168#97—1181no—
169C4×C8—592no—
170C4×C8C22⋊D5912yes—
171C2×Q8—1181no—
172C2×Q8—1181no—
173C2×Q8—2362no—
174C22×C4—1181no—
175C22×C4—1181no—
176C22×C4#1174568511yescharacteristic
177C22×C4D4×D5911yescharacteristic
178C22×C4Q8×D5911yescharacteristic
179M16—42no—
180M16—2362no—
181C2×C8—22no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8—594no—
186C2×C8—1182no—
187C2×C8—1182no—
188C2×C8—1182no—
189C2×C8—2361no—
190C4⋊C4—1181no—
191C4⋊C4—1181no—
192C4⋊C4—2361no—
193C4⋊C4—2361no—
194C42—2361no—
195C42—2361no—
196C42#1174568511yescharacteristic
197C42D4×D5911yescharacteristic
198C42#1174568911yescharacteristic
199C42C2×C22⋊D5911yescharacteristic
200C23#1427370511yescharacteristic
201Q8—1182no—
202Q8—1182no—
203Q8—2361no—
204Q8—2361no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—1182no—
208C2×C4—2362no—
209C2×C4—2361no—
210C2×C4—2361no—
211C2×C4—2361no—
212C2×C4#1427370311yescharacteristic
213C2×C4#1427370511yescharacteristic
214C2×C4#1427371011yescharacteristic
215C2×C4#1427371211yescharacteristic
216C2×C4#1427371211yescharacteristic
217C2×C4#1427372311yescharacteristic
218C2×C4SD16×D5912yes—
219C2×C4#1427375612yes—
220C8—42no—
221C8—81no—
222C8—81no—
223C8—1184no—
224C8—4721no—
225C8—2362no—
226C22—21no—
227C22—21no—
228C22#1683733711yescharacteristic
229C22#1683768612yes—
230C4—21no—
231C4—21no—
232C4—21no—
233C4—21no—
234C4—4721no—
235C4—2362no—
236C4#1683773412yes—
237C4#1683777311yescharacteristic
238C4#1683779311yescharacteristic
239C2—22no—
240C2#2142561111yescharacteristic
241C2#2142563611yescharacteristic
242C2#2142565211yescharacteristic
subgroupG/H
centerC2×C4#14273723
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1570C2
socleC22×C59#399
prime radicalC23×C59C22⋊Q8
hypercenter#1570D59
hypocenterC59#10663
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
142. C59#10663semidirect

Maximal subgroups

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

subgroupindex
#214250352
#214242702
#214228662
#214225262
#214225242
#214219262
C59×#15702
#1066359