Finite Group Databasebeta

← #28499334

Subgroups — #28499334

Order 15104.

444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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#21429272C211yesmaximal, characteristic
2C4×#14273644C211yesmaximal, characteristic
3#21422127C212yesmaximal, complemented
4#21422124C212yesmaximal, complemented
5C59×#1465C211yesmaximal, characteristic
6C2×#14273706C411yescharacteristic
7C2×#14273644—21no—
8C4×#11745664—21no—
9#16837341C2211yescharacteristic
10#16837338C411yescharacteristic
11#16837322C2211yescharacteristic
12#16837314C411yescharacteristic
13#16837286—21no—
14#16837282—21no—
15#16837275—21no—
16#16837260—21no—
17C2×C59⋊#95C411yescharacteristic
18#16837171C2212yes—
19C2×C4×D4×C59C2211yescharacteristic
20C59×#407—21no—
21C59×#324C2212yes—
22C59×#323—21no—
23C22×Dic118C2×C411yescharacteristic
24C23×Dic59—21no—
25C2×#11745664—22no—
26#14273706—41no—
27#14273706—41no—
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×Dic59⋊C4—21no—
30C2×Dic59⋊C4—21no—
31C2×Dic59⋊C4—21no—
32C2×C22⋊Dic59—21no—
33C2×C22⋊Dic59—21no—
34C2×C22⋊Dic59—21no—
35#14273644—24no—
36#14273638—41no—
37C4×C59⋊C8—41no—
38C59⋊#95—21no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95C2×C411yescharacteristic
44C59⋊#95C2×C411yescharacteristic
45C22×D4×C59D411yescharacteristic
46C23×C4×C59C2×C411yescharacteristic
47C23×C4×C59D411yescharacteristic
48C2×M16×C59—41no—
49C4×D4×C59—41no—
50C4×D4×C59—41no—
51C2×C4⋊C4×C59C2311yescharacteristic
52C2×C22⋊C4×C59C2×C411yescharacteristic
53C2×C22⋊C4×C59D411yescharacteristic
54C2×C42×C59D411yescharacteristic
55C22⋊C8×C59—22no—
56C22⋊C8×C59—41no—
57C24×C59C22⋊C411yescharacteristic
58C24×C59C22⋊C411yescharacteristic
59C2×D4×C59—22no—
60C2×D4×C59—22no—
61C2×D4×C59—41no—
62C22×C4×C59—21no—
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59—81no—
67C22×C4×C59—81no—
68C22×C4×C59C22⋊C411yescharacteristic
69C22×C4×C59C22⋊C411yescharacteristic
70C22×C4×C59C22×C411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×Dic59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76C22×Dic59—21no—
77C22×Dic59—42no—
78C22×Dic59—42no—
79C22×Dic59—81no—
80C2×Dic118—41no—
81C2×Dic118—81no—
82M16×C59—82no—
83C2×C8×C59—42no—
84C4⋊C4×C59—41no—
85C22⋊C4×C59—41no—
86C22⋊C4×C59—41no—
87C42×C59—21no—
88C42×C59—21no—
89C22⋊Dic59—42no—
90C22⋊Dic59—42no—
91C22⋊Dic59—81no—
92C4⋊Dic59—41no—
93Dic59⋊C4—42no—
94Dic59⋊C4—41no—
95Dic59⋊C4—41no—
96Dic59⋊C4—81no—
97#11745664—24no—
98#11745664—42no—
99C2×C59⋊C8—42no—
100C23×C59—21no—
101C23×C59—21no—
102C23×C59—21no—
103C23×C59—21no—
104C23×C59—21no—
105C23×C59—41no—
106C23×C59—41no—
107C23×C59—41no—
108C23×C59—41no—
109C23×C59#10412yes—
110C23×C59C2×C22⋊C411yescharacteristic
111D4×C59—44no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—41no—
118C2×C4×C59—42no—
119C2×C4×C59—41no—
120C2×C4×C59—41no—
121C2×C4×C59—41no—
122C2×C4×C59—81no—
123C2×C4×C59—81no—
124C2×C4×C59—81no—
125C2×C4×C59#9911yescharacteristic
126C2×C4×C59#9911yescharacteristic
127C2×C4×C59#13712yes—
128C2×Dic59—22no—
129C2×Dic59—41no—
130C2×Dic59—41no—
131C2×Dic59—41no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—84no—
141Dic118—82no—
142C8×C59—82no—
143C59⋊C8—44no—
144#11793—591nomaximal, Sylow
145C22×C59—21no—
146C22×C59—21no—
147C22×C59—22no—
148C22×C59—42no—
149C22×C59—42no—
150C22×C59—42no—
151C22×C59—41no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—81no—
157C22×C59C2×#9911yescharacteristic
158C22×C59#41911yescharacteristic
159C22×C59C2×#10411yescharacteristic
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—22no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59—41no—
166Dic59—42no—
167Dic59—81no—
168Dic59—81no—
169Dic59—81no—
170#2564—591no—
171C4×#100—591no—
172#1465D5911yescharacteristic
173#1354—592no—
174#1353—592no—
175C2×C59—21no—
176C2×C59—21no—
177C2×C59—42no—
178C2×C59—81no—
179C2×C59#150811yescharacteristic
180C2×C59#212111yescharacteristic
181C2×C59#213211yescharacteristic
182C2×C22⋊Q8—591no—
183C2×C4×D4C2×D5911yescharacteristic
184C2×#100—1181no—
185#407—21no—
186C4×M16—1181no—
187#400—591no—
188#399—591no—
189#395—591no—
190#393—591no—
191#387—1181no—
192#386—1181no—
193#385—1181no—
194#380—1181no—
195C2×#95—591no—
196#343—592no—
197#324C2×D5912yes—
198#323—21no—
199C59#1179311yescharacteristic, complemented, Sylow
200C22×Q8—591no—
201C22×D4D23611yescharacteristic
202C23×C4—1181no—
203C23×C4C4×D5911yescharacteristic
204C23×C4C22⋊D5911yescharacteristic
205C2×M16—41no—
206C2×M16—1182no—
207C22⋊Q8—2361no—
208C22⋊Q8—2361no—
209C4×D4—41no—
210C4×D4—41no—
211C2×C4⋊C4—591no—
212C2×C4⋊C4—1181no—
213C2×C4⋊C4—1181no—
214C2×C4⋊C4—1181no—
215C2×C4⋊C4C22×D5911yescharacteristic
216C2×C22⋊C4—1181no—
217C2×C22⋊C4—1181no—
218C2×C22⋊C4—1181no—
219C2×C22⋊C4C4×D5911yescharacteristic
220C2×C22⋊C4C22⋊D5911yescharacteristic
221C2×C42D23611yescharacteristic
222#100—1184no—
223C22⋊C8—22no—
224C22⋊C8—41no—
225#97—2361no—
226C4×C8—2361no—
227#95—591no—
228#95—591no—
229#95—1181no—
230#95—1181no—
231#95—1181no—
232#95—1181no—
233#95—1181no—
234C24(C2×D59)⋊C411yescharacteristic
235C24(C2×D59)⋊C411yescharacteristic
236C2×Q8—4721no—
237C2×Q8—2361no—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—41no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4—1181no—
248C22×C4—1181no—
249C22×C4—1181no—
250C22×C4—1181no—
251C22×C4—4721no—
252C22×C4—2362no—
253C22×C4—2362no—
254C22×C4(C2×D59)⋊C411yescharacteristic
255C22×C4(C2×D59)⋊C411yescharacteristic
256C22×C4C2×C4×D5911yescharacteristic
257C22×C4C2×D23611yescharacteristic
258C22×C4C2×C22⋊D5911yescharacteristic
259M16—82no—
260M16—1184no—
261M16—2362no—
262C2×C8—42no—
263C2×C8—2362no—
264C4⋊C4—41no—
265C4⋊C4—4721no—
266C4⋊C4—2361no—
267C4⋊C4—2362no—
268C4⋊C4—2361no—
269C4⋊C4—2361no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—4721no—
273C22⋊C4—2362no—
274C22⋊C4—2362no—
275C42—21no—
276C42—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23#1427365312yes—
287C23C2×(C2×D59)⋊C411yescharacteristic
288Q8—4722no—
289D4—44no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—1182no—
304C2×C4—4724no—
305C2×C4—2361no—
306C2×C4—2361no—
307C2×C4—2361no—
308C2×C4—2361no—
309C2×C4—2361no—
310C2×C4—2361no—
311C2×C4—2361no—
312C2×C4—2361no—
313C2×C4—2361no—
314C2×C4—2361no—
315C2×C4—2361no—
316C2×C4#1427364111yescharacteristic
317C2×C4#1427364111yescharacteristic
318C2×C4#1427376012yes—
319C8—82no—
320C8—2364no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22C2×#1427364111yescharacteristic
334C22#1683741211yescharacteristic
335C22C2×#1427365311yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—4721no—
343C4—4721no—
344C4—4721no—
345C4—2362no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2#2142261711yescharacteristic
351C2#2142574011yescharacteristic
352C2#2142577911yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#1465C2
socleC22×C59C2×#99
prime radicalC22×D4×C59D4
cosocleC2×C4⋊C4×C59C23
hypercenter#1465D59
hypocenterC59#11793
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #21422127C2semidirect
4. #21422124C2semidirect
199. C59#11793semidirect

Maximal subgroups

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

subgroupindex
#214292722
C4×#142736442
#214221272
#214221242
C59×#14652
#1179359