Finite Group Databasebeta

← #28499084

Subgroups — #28499084

Order 15104.

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

normal subgroups only

This group has 420 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#21430013C211yesmaximal, characteristic
2C4×#14273644C211yesmaximal, characteristic
3#21422127C212yesmaximal, complemented
4#21422103C212yesmaximal, complemented
5C59×#1459C211yesmaximal, characteristic
6C2×#14273706C411yescharacteristic
7C2×#14273644—21no—
8C4×#11745664—21no—
9#16837332C2211yescharacteristic
10#16837330—21no—
11#16837327C411yescharacteristic
12#16837322C2211yescharacteristic
13#16837316—21no—
14#16837314C411yescharacteristic
15#16837286—21no—
16#16837275—21no—
17#16837265C411yescharacteristic
18#16837171C2212yes—
19C2×C4×D4×C59C2211yescharacteristic
20C2×C22⋊C8×C59—21no—
21C59×#324C2212yes—
22C59×#323—21no—
23C22×Dic118C2×C411yescharacteristic
24C2×#11745664—22no—
25#14273706—41no—
26#14273706—41no—
27C2×C4⋊Dic59C2×C411yescharacteristic
28C2×Dic59⋊C4—21no—
29C2×Dic59⋊C4—21no—
30C2×Dic59⋊C4—21no—
31C2×C22⋊Dic59—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
48C22×C8×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—
77C2×Dic118—41no—
78C2×Dic118—81no—
79C2×C8×C59—42no—
80C2×C8×C59—82no—
81C4⋊C4×C59—41no—
82C22⋊C4×C59—41no—
83C22⋊C4×C59—41no—
84C42×C59—21no—
85C42×C59—21no—
86C22⋊Dic59—42no—
87C22⋊Dic59—42no—
88C22⋊Dic59—81no—
89C22⋊Dic59—81no—
90C4⋊Dic59—41no—
91Dic59⋊C4—41no—
92Dic59⋊C4—41no—
93Dic59⋊C4—42no—
94Dic59⋊C4—81no—
95#11745664—24no—
96#11745664—42no—
97C2×C59⋊C8—42no—
98C23×C59—21no—
99C23×C59—21no—
100C23×C59—21no—
101C23×C59—21no—
102C23×C59—21no—
103C23×C59—41no—
104C23×C59—41no—
105C23×C59—41no—
106C23×C59—41no—
107C23×C59#10412yes—
108C23×C59C2×C22⋊C411yescharacteristic
109D4×C59—44no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—41no—
116C2×C4×C59—42no—
117C2×C4×C59—41no—
118C2×C4×C59—41no—
119C2×C4×C59—41no—
120C2×C4×C59—81no—
121C2×C4×C59—81no—
122C2×C4×C59—81no—
123C2×C4×C59#9911yescharacteristic
124C2×C4×C59#9911yescharacteristic
125C2×C4×C59#13512yes—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C2×Dic59—41no—
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—
138Dic118—82no—
139C8×C59—82no—
140C59⋊C8—44no—
141#11739—591nomaximal, Sylow
142C22×C59—21no—
143C22×C59—21no—
144C22×C59—22no—
145C22×C59—42no—
146C22×C59—41no—
147C22×C59—41no—
148C22×C59—41no—
149C22×C59—41no—
150C22×C59—41no—
151C22×C59—81no—
152C22×C59—81no—
153C22×C59—81no—
154C22×C59C2×#9911yescharacteristic
155C22×C59#41611yescharacteristic
156C22×C59C2×#10411yescharacteristic
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—22no—
160C4×C59—41no—
161C4×C59—41no—
162C4×C59—41no—
163Dic59—81no—
164Dic59—81no—
165Dic59—81no—
166Dic59—81no—
167#2638—591no—
168C4×#100—591no—
169#1459D5911yescharacteristic
170#1354—592no—
171#1346—592no—
172C2×C59—21no—
173C2×C59—21no—
174C2×C59—42no—
175C2×C59—81no—
176C2×C59#150111yescharacteristic
177C2×C59#212111yescharacteristic
178C2×C59#213511yescharacteristic
179C2×C22⋊Q8—591no—
180C2×C4×D4C2×D5911yescharacteristic
181C2×#100—1181no—
182C2×C22⋊C8—21no—
183C4×M16—1181no—
184#398—591no—
185#397—591no—
186#397—1181no—
187#395—591no—
188#394—1181no—
189#393—591no—
190#387—1181no—
191#385—1181no—
192#381—591no—
193#343—592no—
194#324C2×D5912yes—
195#323—21no—
196C59#1173911yescharacteristic, complemented, Sylow
197C22×Q8—591no—
198C22×D4D23611yescharacteristic
199C23×C4C4×D5911yescharacteristic
200C23×C4C22⋊D5911yescharacteristic
201C2×M16—1182no—
202C22×C8—41no—
203C22⋊Q8—2361no—
204C22⋊Q8—2361no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—591no—
208C2×C4⋊C4—1181no—
209C2×C4⋊C4—1181no—
210C2×C4⋊C4—1181no—
211C2×C4⋊C4C22×D5911yescharacteristic
212C2×C22⋊C4—1181no—
213C2×C22⋊C4—1181no—
214C2×C22⋊C4—1181no—
215C2×C22⋊C4—1181no—
216C2×C22⋊C4C4×D5911yescharacteristic
217C2×C22⋊C4C22⋊D5911yescharacteristic
218C2×C42D23611yescharacteristic
219#100—1184no—
220C22⋊C8—22no—
221C22⋊C8—41no—
222#97—2361no—
223C4×C8—2361no—
224#95—591no—
225#95—591no—
226#95—1181no—
227#95—1181no—
228#95—1181no—
229#95—1181no—
230#95—1181no—
231C24(C2×D59)⋊C411yescharacteristic
232C24(C2×D59)⋊C411yescharacteristic
233C2×Q8—4721no—
234C2×Q8—2361no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4—1181no—
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4—1181no—
248C22×C4(C2×D59)⋊C411yescharacteristic
249C22×C4(C2×D59)⋊C411yescharacteristic
250C22×C4C2×C4×D5911yescharacteristic
251C22×C4C2×D23611yescharacteristic
252C22×C4C2×C22⋊D5911yescharacteristic
253M16—1184no—
254M16—2362no—
255C2×C8—42no—
256C2×C8—82no—
257C2×C8—2362no—
258C4⋊C4—41no—
259C4⋊C4—4721no—
260C4⋊C4—2361no—
261C4⋊C4—2361no—
262C4⋊C4—2361no—
263C4⋊C4—2362no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—4721no—
267C22⋊C4—4721no—
268C22⋊C4—2362no—
269C22⋊C4—2362no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#1427365312yes—
282C23C2×(C2×D59)⋊C411yescharacteristic
283Q8—4722no—
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—2361no—
299C2×C4—2361no—
300C2×C4—2361no—
301C2×C4—2361no—
302C2×C4—2361no—
303C2×C4—2361no—
304C2×C4—2361no—
305C2×C4—2361no—
306C2×C4—2361no—
307C2×C4—2361no—
308C2×C4—2361no—
309C2×C4—2361no—
310C2×C4#1427364111yescharacteristic
311C2×C4#1427364111yescharacteristic
312C2×C4#1427374912yes—
313C8—82no—
314C8—2364no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C2×#1427364111yescharacteristic
328C22#1683739911yescharacteristic
329C22C2×#1427365311yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—4721no—
337C4—4721no—
338C4—4721no—
339C4—4721no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#2142258811yescharacteristic
345C2#2142574011yescharacteristic
346C2#2142579011yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#1459C2
socleC22×C59C2×#99
prime radicalC22×D4×C59D4
cosocleC2×C4⋊C4×C59C23
hypercenter#1459D59
hypocenterC59#11739
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #21422127C2semidirect
4. #21422103C2semidirect
196. C59#11739semidirect

Maximal subgroups

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

subgroupindex
#214300132
C4×#142736442
#214221272
#214221032
C59×#14592
#1173959