Finite Group Databasebeta

← #28484682

Subgroups — #28484682

Order 15104.

502 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 103 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#21429964C211yesmaximal, characteristic
2C4×#14273644C211yesmaximal, characteristic
3#21422699C212yesmaximal, complemented
4#21421962C212yesmaximal, complemented
5C59×#2973C211yesmaximal, characteristic
6C2×#14273719C2211yescharacteristic
7C2×#14273644—21no—
8C4×#11745664C2212yes—
9#16837338C411yescharacteristic
10#16837338C411yescharacteristic
11#16837333—21no—
12#16837327C411yescharacteristic
13#16837327C411yescharacteristic
14#16837316—21no—
15#16837275—21no—
16#16837275—21no—
17#16837270C2211yescharacteristic
18#16837171—21no—
19#16837143—24no—
20C2×C4×D4×C59C2211yescharacteristic
21C59×#435—24no—
22C59×#432C2212yes—
23C59×#407—21no—
24C2×C22⋊C8×C59—21no—
25C2×#11745664—22no—
26#14273719—22no—
27#14273719—22no—
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×Dic59⋊C4—21no—
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34C2×C22⋊Dic59—21no—
35C2×C22⋊Dic59—21no—
36C2×C22⋊Dic59—21no—
37C2×C22⋊Dic59—21no—
38#14273644—24no—
39#14273638—22no—
40C4×C59⋊C8—22no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95C2×C411yescharacteristic
46C59⋊#95C2×C411yescharacteristic
47C22×D4×C59D411yescharacteristic
48C23×C4×C59D411yescharacteristic
49C23×C4×C59D411yescharacteristic
50C2×M16×C59—22no—
51C22×C8×C59—22no—
52C4×D4×C59—22no—
53C4×D4×C59—22no—
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C22⋊C4×C59C2×C411yescharacteristic
56C2×C22⋊C4×C59C2×C411yescharacteristic
57C2×C42×C59C2311yescharacteristic
58C4⋊C8×C59—22no—
59C22⋊C8×C59—22no—
60C22⋊C8×C59—22no—
61C22⋊C8×C59—22no—
62#97×C59D414yes—
63C24×C59C22⋊C411yescharacteristic
64C24×C59C22⋊C411yescharacteristic
65C2×D4×C59—22no—
66C2×D4×C59—22no—
67C2×D4×C59—41no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—81no—
73C22×C4×C59—81no—
74C22×C4×C59C22⋊C411yescharacteristic
75C22×C4×C59C22⋊C411yescharacteristic
76C22×C4×C59C22×C411yescharacteristic
77C22×C4×C59C2×D411yescharacteristic
78C22×C4×C59C2×D411yescharacteristic
79C22×Dic59—21no—
80C22×Dic59—21no—
81C22×Dic59—21no—
82C22×Dic59—21no—
83M16×C59—82no—
84C2×C8×C59—24no—
85C2×C8×C59—82no—
86C4⋊C4×C59—22no—
87C22⋊C4×C59—22no—
88C22⋊C4×C59—22no—
89C42×C59C2×D412yes—
90C42×C59#4112yes—
91C22⋊Dic59—42no—
92C22⋊Dic59—42no—
93C22⋊Dic59—81no—
94C22⋊Dic59—81no—
95C4⋊Dic59—22no—
96C4⋊Dic59—22no—
97Dic59⋊C4—41no—
98Dic59⋊C4—42no—
99Dic59⋊C4—41no—
100Dic59⋊C4—81no—
101Dic59⋊C4—81no—
102#11745664—24no—
103#11745664—42no—
104C2×C59⋊C8—42no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—41no—
111C23×C59—41no—
112C23×C59—41no—
113C23×C59—41no—
114C23×C59#10412yes—
115C23×C59C2×C22⋊C411yescharacteristic
116D4×C59—44no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—41no—
122C2×C4×C59—41no—
123C2×C4×C59—42no—
124C2×C4×C59—42no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—81no—
128C2×C4×C59—81no—
129C2×C4×C59C4×D412yes—
130C2×C4×C59#12011yescharacteristic
131C2×C4×C59#12112yes—
132C2×C4×C59#12311yescharacteristic
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145C8×C59—44no—
146C59⋊C8—44no—
147#9189—591nomaximal, Sylow
148C22×C59—21no—
149C22×C59—21no—
150C22×C59—22no—
151C22×C59—42no—
152C22×C59—42no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—81no—
159C22×C59—81no—
160C22×C59#38611yescharacteristic
161C22×C59C2×#10411yescharacteristic
162C22×C59#42111yescharacteristic
163C4×C59—22no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—22no—
167C4×C59—41no—
168C4×C59—41no—
169Dic59—81no—
170Dic59—81no—
171Dic59—81no—
172Dic59—81no—
173#2973D5911yescharacteristic
174#2633—591no—
175C4×#100—591no—
176#1528—592no—
177#1288—592no—
178C2×C59—21no—
179C2×C59—21no—
180C2×C59—42no—
181C2×C59—81no—
182C2×C59#187111yescharacteristic
183C2×C59#191111yescharacteristic
184C2×C59#191511yescharacteristic
185C2×#125—591no—
186C2×C4×D4C2×D5911yescharacteristic
187#435—24no—
188#432C2×D5912yes—
189C2×#100—1181no—
190#407—21no—
191C2×C22⋊C8—21no—
192C4×M16—592no—
193#399—591no—
194#399—591no—
195#398—1181no—
196#397—591no—
197#397—591no—
198#394—1181no—
199#385—1181no—
200#385—1181no—
201#383—591no—
202#343—1181no—
203#330—1184no—
204C59#918911yescharacteristic, complemented, Sylow
205C22×D4D23611yescharacteristic
206C23×C4C22⋊D5911yescharacteristic
207C23×C4C22⋊D5911yescharacteristic
208C2×M16—22no—
209C2×M16—1182no—
210C22×C8—22no—
211#125—1182no—
212#125—1182no—
213C4×D4—22no—
214C4×D4—22no—
215C2×C4⋊C4—591no—
216C2×C4⋊C4—591no—
217C2×C4⋊C4—1181no—
218C2×C4⋊C4—1181no—
219C2×C4⋊C4—1181no—
220C2×C4⋊C4—1181no—
221C2×C4⋊C4D23611yescharacteristic
222C2×C22⋊C4—1181no—
223C2×C22⋊C4—1181no—
224C2×C22⋊C4—1181no—
225C2×C22⋊C4—1181no—
226C2×C22⋊C4C4×D5911yescharacteristic
227C2×C22⋊C4C4×D5911yescharacteristic
228C2×C42C22×D5911yescharacteristic
229C4⋊C8—22no—
230#100—1184no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234#97—1182no—
235#97C22⋊D5914yes—
236C4×C8—1182no—
237#95—591no—
238#95—591no—
239#95—1181no—
240#95—1181no—
241#95—1181no—
242#95—1181no—
243C24(C2×D59)⋊C411yescharacteristic
244C24(C2×D59)⋊C411yescharacteristic
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4—1181no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4—1181no—
258C22×C4(C2×D59)⋊C411yescharacteristic
259C22×C4(C2×D59)⋊C411yescharacteristic
260C22×C4C2×C4×D5911yescharacteristic
261C22×C4C2×D23611yescharacteristic
262C22×C4C2×C22⋊D5911yescharacteristic
263M16—82no—
264M16—1184no—
265M16—2362no—
266C2×C8—24no—
267C2×C8—82no—
268C2×C8—2362no—
269C4⋊C4—22no—
270C4⋊C4—1182no—
271C4⋊C4—1182no—
272C4⋊C4—4721no—
273C4⋊C4—4721no—
274C4⋊C4—2361no—
275C4⋊C4—2362no—
276C4⋊C4—2361no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—4721no—
280C22⋊C4—4721no—
281C22⋊C4—2362no—
282C22⋊C4—2362no—
283C42#1174568512yes—
284C42C2×C22⋊D5912yes—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#1427365312yes—
295C23C2×(C2×D59)⋊C411yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—2361no—
310C2×C4—2361no—
311C2×C4—2361no—
312C2×C4—2361no—
313C2×C4—2361no—
314C2×C4—2361no—
315C2×C4—2361no—
316C2×C4—2361no—
317C2×C4—2361no—
318C2×C4—2361no—
319C2×C4—2361no—
320C2×C4—2361no—
321C2×C4C4×C22⋊D5912yes—
322C2×C4#1427369611yescharacteristic
323C2×C4#1427370112yes—
324C2×C4#1427371011yescharacteristic
325C8—44no—
326C8—2364no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#1683728111yescharacteristic
340C22C2×#1427365311yescharacteristic
341C22#1683741811yescharacteristic
342C4—22no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—4721no—
349C4—4721no—
350C4—4721no—
351C4—4721no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2#2142439811yescharacteristic
357C2#2142462811yescharacteristic
358C2#2142464811yescharacteristic
subgroupG/H
centerC22#16837281
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2973C2
socleC22×C59#386
prime radicalC22×D4×C59D4
cosocleC2×C42×C59C23
hypercenter#2973D59
hypocenterC59#9189
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
3. #21422699C2semidirect
4. #21421962C2semidirect
204. C59#9189semidirect

Maximal subgroups

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

subgroupindex
#214299642
C4×#142736442
#214226992
#214219622
C59×#29732
#918959