Finite Group Databasebeta

← #28483352

Subgroups — #28483352

Order 15104.

558 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 119 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#21433137C211yesmaximal, characteristic
2C4×#14273714C211yesmaximal, characteristic
3#21422492C212yesmaximal, complemented
4#21421928C212yesmaximal, complemented
5C59×#1460C211yesmaximal, characteristic
6C2×#14273714C411yescharacteristic
7C2×C4×Dic118C2211yescharacteristic
8#16837480—24no—
9#16837455C2212yes—
10#16837366—22no—
11#16837307C411yescharacteristic
12#16837305C411yescharacteristic
13#16837296—22no—
14#16837267C411yescharacteristic
15C4×C22⋊Dic59—22no—
16C42×Dic59C2211yescharacteristic
17#16837134—24no—
18C2×C4×D4×C59C2211yescharacteristic
19C59×#431C2212yes—
20C59×#323—22no—
21C22×Dic118C2×C411yescharacteristic
22C2×#11745664—24no—
23#14273714—22no—
24#14273714—22no—
25C4×Dic118—22no—
26C4×Dic118—22no—
27C2×C4⋊Dic59C2×C411yescharacteristic
28C2×Dic59⋊C4—21no—
29C2×C22⋊Dic59—22no—
30C2×C22⋊Dic59—22no—
31C2×C4×Dic59—21no—
32C2×C4×Dic59—21no—
33C2×C4×Dic59—21no—
34C2×C4×Dic59C2×C411yescharacteristic
35C2×C4×Dic59C2×C411yescharacteristic
36C4⋊(C59⋊C8)D414yes—
37C22⋊(C59⋊C8)—24no—
38C22⋊(C59⋊C8)—22no—
39C4×C59⋊C8—22no—
40C59⋊#95—22no—
41C59⋊#95—22no—
42C22×D4×C59C2×C411yescharacteristic
43C23×C4×C59D412yes—
44C4×D4×C59—22no—
45C4×D4×C59—22no—
46C2×C4⋊C4×C59C2×C411yescharacteristic
47C2×C22⋊C4×C59D412yes—
48C2×C42×C59C2311yescharacteristic
49C4⋊C8×C59—22no—
50C22⋊C8×C59—22no—
51C4×C8×C59—22no—
52C24×C59C22⋊C412yes—
53C2×D4×C59—22no—
54C2×D4×C59—21no—
55C2×D4×C59—21no—
56C2×D4×C59—22no—
57C22×C4×C59—22no—
58C22×C4×C59—22no—
59C22×C4×C59—44no—
60C22×C4×C59C22⋊C412yes—
61C22×C4×C59C22×C411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C22×Dic59—21no—
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—21no—
68C2×Dic118—22no—
69C2×Dic118—22no—
70C2×Dic118—21no—
71C2×Dic118M1612yescomplemented
72C2×C8×C59—42no—
73C4⋊C4×C59—22no—
74C22⋊C4×C59—24no—
75C42×C59C2×D412yes—
76C42×C59#4112yes—
77C22⋊Dic59—28no—
78C22⋊Dic59—44no—
79C4⋊Dic59—22no—
80Dic59⋊C4—42no—
81C4×Dic59—21no—
82C4×Dic59—22no—
83C4×Dic59—42no—
84C4×Dic59—42no—
85C4×Dic59—41no—
86C4×Dic59—41no—
87C4×Dic59M1612yescomplemented
88#11745664—84no—
89C2×C59⋊C8—24no—
90C23×C59—22no—
91C23×C59—22no—
92C23×C59—22no—
93C23×C59—42no—
94C23×C59—42no—
95C23×C59C2×C22⋊C411yescharacteristic
96D4×C59—42no—
97D4×C59—42no—
98C2×C4×C59—22no—
99C2×C4×C59—22no—
100C2×C4×C59—41no—
101C2×C4×C59—44no—
102C2×C4×C59—42no—
103C2×C4×C59—82no—
104C2×C4×C59C4×D412yes—
105C2×C4×C59#12011yescharacteristic
106C2×C4×C59#12112yes—
107C2×C4×C59#12311yescharacteristic
108C2×C4×C59C2×M1611yescharacteristic
109C2×C4×C59C2×M1611yescharacteristic
110C2×C4×C59#13112yes—
111C2×Dic59—22no—
112C2×Dic59—22no—
113C2×Dic59—22no—
114C2×Dic59—41no—
115C2×Dic59—41no—
116C2×Dic59—41no—
117C2×Dic59—41no—
118C2×Dic59—41no—
119C2×Dic59—41no—
120C2×Dic59—42no—
121C2×Dic59—41no—
122Dic118—24no—
123Dic118—42no—
124C8×C59—82no—
125C59⋊C8—44no—
126#8961—591nomaximal, Sylow
127C22×C59—21no—
128C22×C59—21no—
129C22×C59—44no—
130C22×C59—42no—
131C22×C59—42no—
132C22×C59—42no—
133C22×C59—82no—
134C22×C59#38611yescharacteristic
135C22×C59#40711yescharacteristic
136C22×C59#40811yescharacteristic
137C4×C59—22no—
138C4×C59—21no—
139C4×C59—42no—
140C4×C59#43512yes—
141C4×C59#43612yes—
142C4×C59#45512yes—
143Dic59—42no—
144Dic59—42no—
145Dic59—42no—
146Dic59—81no—
147#2975—591no—
148C4×#124—591no—
149#1479—592no—
150#1460D5911yescharacteristic
151#1276—592no—
152C2×C59—21no—
153C2×C59—21no—
154C2×C59—82no—
155C2×C59#187011yescharacteristic
156C2×C59#188411yescharacteristic
157C2×C59#188511yescharacteristic
158C2×#124—591no—
159C2×C4×Q8—591no—
160C2×C4×D4C2×D5911yescharacteristic
161#436—1184no—
162#431—592no—
163#431C2×D5912yes—
164#407—1182no—
165#391—591no—
166#390—591no—
167#388—1182no—
168#382—591no—
169C4×C22⋊C4—1182no—
170C43—591no—
171Q8⋊C8—1184no—
172#323—22no—
173C59#896111yescharacteristic, complemented, Sylow
174C22×Q8—591no—
175C22×D4C4×D5911yescharacteristic
176C23×C4D23612yes—
177C2×M16—1184no—
178#124—1182no—
179#124—1182no—
180C4×Q8—1182no—
181C4×Q8—1182no—
182C4×D4—22no—
183C4×D4—22no—
184C2×C4⋊C4—591no—
185C2×C4⋊C4—1181no—
186C2×C4⋊C4C4×D5911yescharacteristic
187C2×C22⋊C4—1182no—
188C2×C22⋊C4—1182no—
189C2×C22⋊C4C22⋊D5912yes—
190C2×C42—591no—
191C2×C42—591no—
192C2×C42—1181no—
193C2×C42—1181no—
194C2×C42—1181no—
195C2×C42C22×D5911yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—594no—
198C22⋊C8—22no—
199C22⋊C8—1184no—
200C22⋊C8—1182no—
201C4×C8—22no—
202C4×C8—1182no—
203#95—1182no—
204#95—1182no—
205C24(C2×D59)⋊C412yes—
206C2×Q8—592no—
207C2×Q8—1181no—
208C2×Q8—1182no—
209C2×Q8—1182no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—44no—
217C22×C4—1181no—
218C22×C4—1181no—
219C22×C4—1181no—
220C22×C4—1181no—
221C22×C4(C2×D59)⋊C412yes—
222C22×C4C2×C4×D5911yescharacteristic
223C22×C4C2×D23611yescharacteristic
224C22×C4C2×C22⋊D5911yescharacteristic
225M16—4724no—
226C2×C8—42no—
227C2×C8—1184no—
228C4⋊C4—22no—
229C4⋊C4—1182no—
230C4⋊C4—2362no—
231C22⋊C4—24no—
232C22⋊C4—1188no—
233C22⋊C4—2364no—
234C42—592no—
235C42—1181no—
236C42—1182no—
237C42—2362no—
238C42—2362no—
239C42—2361no—
240C42—2361no—
241C42D4×D5912yes—
242C42#1174568712yes—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—42no—
247C23—42no—
248C23C2×(C2×D59)⋊C411yescharacteristic
249Q8—1184no—
250Q8—2362no—
251D4—42no—
252D4—42no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—82no—
259C2×C4—1182no—
260C2×C4—1182no—
261C2×C4—1182no—
262C2×C4—2362no—
263C2×C4—2361no—
264C2×C4—2361no—
265C2×C4—2361no—
266C2×C4—2361no—
267C2×C4—2361no—
268C2×C4—2361no—
269C2×C4—2361no—
270C2×C4(C22⋊D59)⋊C412yes—
271C2×C4#1427369711yescharacteristic
272C2×C4#1427369912yes—
273C2×C4#1427371111yescharacteristic
274C2×C4M16×D5911yescharacteristic
275C2×C4M16×D5911yescharacteristic
276C2×C4#1427373312yes—
277C8—82no—
278C8—2364no—
279C22—21no—
280C22—21no—
281C22—44no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—82no—
286C22#1683727911yescharacteristic
287C22#1683736511yescharacteristic
288C22#1683736811yescharacteristic
289C4—22no—
290C4—21no—
291C4—42no—
292C4—4721no—
293C4—2362no—
294C4—2362no—
295C4—2362no—
296C4#1683747612yes—
297C4#1683747712yes—
298C4#1683758212yes—
299C2—21no—
300C2—21no—
301C2—82no—
302C2#2142439111yescharacteristic
303C2#2142447711yescharacteristic
304C2#2142448211yescharacteristic
subgroupG/H
centerC2×C4#14273697
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1460C2
socleC22×C59#386
prime radicalC22×D4×C59C2×C4
cosocleC2×C42×C59C23
hypercenter#1460D59
hypocenterC59#8961
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #21422492C2semidirect
4. #21421928C2semidirect
71. C2×Dic118M16semidirect
87. C4×Dic59M16semidirect
173. C59#8961semidirect

Maximal subgroups

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

subgroupindex
#214331372
C4×#142737142
#214224922
#214219282
C59×#14602
#896159