Finite Group Databasebeta

← #28488368

Subgroups — #28488368

Order 15104.

418 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 127 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#21425086C211yesmaximal, characteristic
2#21424941C211yesmaximal, characteristic
3#21422855C211yesmaximal, characteristic
4#21422777C211yesmaximal, characteristic
5#21422768C211yesmaximal, characteristic
6#21422385C211yesmaximal, characteristic
7C2×C59×#487C211yesmaximal, characteristic
8#16837455C2211yescharacteristic
9#16837426C2211yescharacteristic
10#16837426C2211yescharacteristic
11C2×#14273646—22no—
12C4×#11745664C2211yescharacteristic
13#16837171—22no—
14#16837155—22no—
15#16837151—22no—
16#16837148—22no—
17#16837124—21no—
18#16837123—21no—
19C2×C4⋊Q8×C59C2211yescharacteristic
20C2×C4⋊Q8×C59C2211yescharacteristic
21C59×#487—21no—
22C59×#487—21no—
23C59×#487—22no—
24C2×#103×C59C414yes—
25C2×C4×C8×C59C2211yescharacteristic
26C2×#11745664—21no—
27C2×#11745664—21no—
28C2×#11745664D412yes—
29C4⋊(C59⋊C8)—21no—
30C4⋊(C59⋊C8)—21no—
31C4⋊(C59⋊C8)—21no—
32C4⋊(C59⋊C8)—21no—
33C4⋊(C59⋊C8)D412yes—
34#14273646—44no—
35C22⋊(C59⋊C8)—21no—
36#14273638—21no—
37C4×C59⋊C8—21no—
38C4×C59⋊C8—21no—
39C22×Q8×C59—21no—
40C22×Q8×C59C2×C412yes—
41C22×C8×C59C2×C412yes—
42C4⋊Q8×C59—21no—
43C4⋊Q8×C59—21no—
44C4⋊Q8×C59—21no—
45C4⋊Q8×C59—21no—
46C4⋊Q8×C59—21no—
47C4⋊Q8×C59—21no—
48C4⋊Q8×C59—21no—
49C4⋊Q8×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59C2×C412yes—
54C2×C42×C59C2311yescharacteristic
55#103×C59—24no—
56#103×C59—24no—
57C4×C8×C59D411yescharacteristic
58C4×C8×C59D411yescharacteristic
59C4×C8×C59D412yes—
60C2×Q8×C59—22no—
61C2×Q8×C59—22no—
62C2×Q8×C59—44no—
63C2×Q8×C59—41no—
64C2×Q8×C59—41no—
65C2×Q8×C59—42no—
66C2×Q8×C59—42no—
67C22×C4×C59—22no—
68C22×C4×C59—22no—
69C22×C4×C59C22×C411yescharacteristic
70C22×C4×C59C2×D411yescharacteristic
71C22×C4×C59#4111yescharacteristic
72C2×C8×C59—42no—
73C2×C8×C59C22⋊C412yes—
74C2×C8×C59C22⋊C412yes—
75C4⋊C4×C59—22no—
76C4⋊C4×C59—22no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C42×C59C2×D411yescharacteristic
84C42×C59C2×D411yescharacteristic
85C42×C59C2×D411yescharacteristic
86C42×C59#4111yescharacteristic
87#11745664—22no—
88#11745664—22no—
89#11745664—42no—
90#11745664—42no—
91C2×C59⋊C8—22no—
92C2×C59⋊C8—22no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8—41no—
95C23×C59C4×D411yescharacteristic
96Q8×C59—44no—
97Q8×C59—82no—
98Q8×C59—82no—
99Q8×C59—81no—
100Q8×C59—81no—
101C2×C4×C59—22no—
102C2×C4×C59—22no—
103C2×C4×C59—42no—
104C2×C4×C59—42no—
105C2×C4×C59—44no—
106C2×C4×C59—82no—
107C2×C4×C59C2×C22⋊C411yescharacteristic
108C2×C4×C59C4×D411yescharacteristic
109C2×C4×C59#12111yescharacteristic
110C2×C4×C59#12111yescharacteristic
111C2×C4×C59#12411yescharacteristic
112C2×C4×C59#12711yescharacteristic
113C2×C4×C59AGL(1,ℤ/8)12yes—
114C2×C4×C59#13712yes—
115C8×C59—22no—
116C8×C59—22no—
117C59⋊C8—42no—
118C59⋊C8—42no—
119C59⋊C8—81no—
120C59⋊C8—81no—
121#9809—591nomaximal, Sylow
122C22×C59—21no—
123C22×C59—21no—
124C22×C59#39011yescharacteristic
125C22×C59#44012yes—
126C4×C59—21no—
127C4×C59—21no—
128C4×C59—82no—
129C4×C59—82no—
130C4×C59#41312yes—
131C4×C59#46812yes—
132C4×C59#47312yes—
133C4×C59#49611yescharacteristic
134C4×C59#49711yescharacteristic
135C2×#487D5911yescharacteristic
136#1997—591no—
137#1966—591no—
138#1567—591no—
139#1548—591no—
140#1546—591no—
141#1451—591no—
142C2×C59—22no—
143C2×C59#196711yescharacteristic
144C2×C59#197311yescharacteristic
145C2×C59#197911yescharacteristic
146C2×C4⋊Q8C2×D5911yescharacteristic
147C2×C4⋊Q8C2×D5911yescharacteristic
148#487—21no—
149#487—21no—
150#487—22no—
151#431—591no—
152#423—591no—
153#423—591no—
154C2×#103Dic5914yes—
155C2×#101—1182no—
156C4×M16—591no—
157C2×C4×C8C2×D5911yescharacteristic
158#343—1182no—
159#335—1182no—
160#333—1182no—
161#332—1182no—
162#322—1181no—
163#322—1181no—
164C59#980911yescharacteristic, complemented, Sylow
165C22×Q8—21no—
166C22×Q8C2×Dic5912yes—
167C2×M16—592no—
168C2×M16—1181no—
169C2×M16—1181no—
170C22×C8C2×Dic5912yes—
171C4⋊Q8—21no—
172C4⋊Q8—21no—
173C4⋊Q8—21no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4C2×Dic5912yes—
183C2×C42C22×D5911yescharacteristic
184C4⋊C8—592no—
185C4⋊C8—1181no—
186C4⋊C8—1181no—
187C4⋊C8—1181no—
188C4⋊C8—1181no—
189#103—24no—
190#103—24no—
191#101—2364no—
192C22⋊C8—1181no—
193#97—1181no—
194C4×C8—1181no—
195C4×C8—1181no—
196C4×C8C22⋊D5911yescharacteristic
197C4×C8C22⋊D5911yescharacteristic
198C4×C8C22⋊D5912yes—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—44no—
202C2×Q8—41no—
203C2×Q8—41no—
204C2×Q8—42no—
205C2×Q8—42no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4D4×D5911yescharacteristic
209C22×C4#1174568711yescharacteristic
210C22×C4C22×Dic5911yescharacteristic
211M16—1182no—
212M16—1182no—
213M16—2362no—
214M16—2362no—
215C2×C8—42no—
216C2×C8—1182no—
217C2×C8—1182no—
218C2×C8—2361no—
219C2×C8—2361no—
220C2×C8C22⋊Dic5912yes—
221C2×C8C22⋊Dic5912yes—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C42D4×D5911yescharacteristic
231C42#1174568711yescharacteristic
232C42C2×C22⋊D5911yescharacteristic
233C42C2×C22⋊D5911yescharacteristic
234C23D4×Dic5911yescharacteristic
235Q8—44no—
236Q8—82no—
237Q8—82no—
238Q8—81no—
239Q8—81no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—44no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—82no—
246C2×C4C2×C22⋊Dic5911yescharacteristic
247C2×C4D4×Dic5911yescharacteristic
248C2×C4#1427369811yescharacteristic
249C2×C4#1427369811yescharacteristic
250C2×C4#1427371411yescharacteristic
251C2×C4#1427372311yescharacteristic
252C2×C4#1427375412yes—
253C2×C4#1427375612yes—
254C8—22no—
255C8—22no—
256C8—4721no—
257C8—4721no—
258C8—2362no—
259C8—2362no—
260C22—21no—
261C22—21no—
262C22#1683730511yescharacteristic
263C22#1683750312yes—
264C4—21no—
265C4—21no—
266C4—82no—
267C4—82no—
268C4#1683738612yes—
269C4#1683764512yes—
270C4#1683767412yes—
271C4#1683778811yescharacteristic
272C4#1683779311yescharacteristic
273C2—22no—
274C2#2142494611yescharacteristic
275C2#2142497911yescharacteristic
276C2#2142501211yescharacteristic
subgroupG/H
centerC22#16837305
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC2×C59×#487C2
socleC22×C59#390
prime radicalC23×C59C4×D4
cosocleC2×C42×C59C23
hypercenterC2×#487D59
hypocenterC59#9809
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
164. C59#9809semidirect

Maximal subgroups

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

subgroupindex
#214250862
#214249412
#214228552
#214227772
#214227682
#214223852
C2×C59×#4872
#980959