Finite Group Databasebeta

← #28498263

Subgroups — #28498263

Order 15104.

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

normal subgroups only

This group has 440 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#21428584C211yesmaximal, characteristic
2#21422426C211yesmaximal, characteristic, complemented
3#21422039C212yesmaximal, complemented
4#21422027C212yesmaximal, complemented
5C2×C59×#324C211yesmaximal, characteristic, complemented
6C2×#14273701C411yescharacteristic
7#16837366—21no—
8#16837328—21no—
9#16837328—21no—
10#16837303C411yescharacteristic
11#16837303C2211yescharacteristic
12#16837281—21no—
13#16837281—21no—
14#16837267C411yescharacteristic
15#16837267C2211yescharacteristic
16C4×C22⋊Dic59C411yescharacteristic
17#16837128—21no—
18#16837128C2212yes—
19C22×C4⋊C4×C59C2211yescharacteristic
20C2×C22⋊C8×C59—21no—
21C59×#324—21no—
22C59×#324C2212yes—
23C22×D236C2×C411yescharacteristic
24C22×C22⋊D59—21no—
25C2×#11745664—41no—
26#14273701—41no—
27#14273701—41no—
28C2×C4⋊Dic59C2×C411yescharacteristic
29C2×C22⋊Dic59—21no—
30C2×(C2×D59)⋊C4—21no—
31C2×(C2×D59)⋊C4—21no—
32C2×(C2×D59)⋊C4—21no—
33C2×(C2×D59)⋊C4—21no—
34C2×(C2×D59)⋊C4—21no—
35C2×C4×Dic59C2×C411yescharacteristic
36C2×C4×Dic59C2×C411yescharacteristic
37C22⋊(C59⋊C8)—22no—
38C22⋊(C59⋊C8)—41no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C23×C4×C59C2×C411yescharacteristic
45C23×C4×C59D411yescharacteristic
46C23×C4×C59D411yescharacteristic
47C22×C8×C59—41no—
48C2×C4⋊C4×C59—41no—
49C2×C4⋊C4×C59—41no—
50C2×C4⋊C4×C59C2×C411yescharacteristic
51C2×C4⋊C4×C59D411yescharacteristic
52C2×C4⋊C4×C59D411yescharacteristic
53C2×C4⋊C4×C59C2311yescharacteristic
54C22⋊C8×C59—22no—
55C22⋊C8×C59—41no—
56C24×C59C22⋊C411yescharacteristic
57C23×D59—21no—
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59—21no—
62C22×C4×C59—21no—
63C22×C4×C59—21no—
64C22×C4×C59—22no—
65C22×C4×C59—41no—
66C22×C4×C59—81no—
67C22×C4×C59—81no—
68C22×C4×C59C22⋊C411yescharacteristic
69C22×C4×C59C22⋊C411yescharacteristic
70C22×C4×C59C22⋊C411yescharacteristic
71C22×C4×C59C22×C411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×C4×C59C2×D411yescharacteristic
74C2×C22⋊D59—42no—
75C2×C22⋊D59—42no—
76C2×C22⋊D59—41no—
77C2×C22⋊D59—41no—
78C22×Dic59—21no—
79C22×Dic59—21no—
80C22×Dic59—21no—
81C2×D236—22no—
82C2×D236—41no—
83C2×D236—41no—
84C2×C8×C59—42no—
85C2×C8×C59—82no—
86C4⋊C4×C59—41no—
87C4⋊C4×C59—41no—
88C4⋊C4×C59—41no—
89C4⋊C4×C59—41no—
90C22⋊Dic59—42no—
91(C2×D59)⋊C4—42no—
92(C2×D59)⋊C4—81no—
93(C2×D59)⋊C4—81no—
94(C2×D59)⋊C4—81no—
95(C2×D59)⋊C4—81no—
96C4⋊Dic59—41no—
97C4×Dic59—22no—
98C4×Dic59—41no—
99#11745664—82no—
100C2×C59⋊C8—42no—
101C23×C59—22no—
102C23×C59—21no—
103C23×C59—21no—
104C23×C59—41no—
105C23×C59#9911yescharacteristic
106C23×C59#9911yescharacteristic
107C23×C59C2×C22⋊C411yescharacteristic
108C22×D59—41no—
109C22×D59—41no—
110C22×D59—41no—
111C22×D59—41no—
112C22×D59—41no—
113C22×D59—41no—
114C22×D59—41no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—42no—
125C2×C4×C59—42no—
126C2×C4×C59—42no—
127C2×C4×C59—42no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—41no—
131C2×C4×C59—41no—
132C2×C4×C59—81no—
133C2×C4×C59—81no—
134C2×C4×C59#13112yes—
135C22⋊D59—82no—
136C22⋊D59—82no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146D236—82no—
147C8×C59—82no—
148C59⋊C8—82no—
149#11553—591nomaximal, Sylow
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—42no—
158C22×C59—42no—
159C22×C59#35512yes—
160C22×C59#40811yescharacteristic
161C22×C59C2×#9911yescharacteristic
162C22×C59#41311yescharacteristic
163C2×D59—81no—
164C2×D59—81no—
165C2×D59—81no—
166C2×D59—81no—
167C2×D59—81no—
168C2×D59—81no—
169C2×D59—81no—
170C4×C59—22no—
171C4×C59—41no—
172C4×C59—41no—
173C4×C59—41no—
174C4×C59—41no—
175C4×C59—41no—
176Dic59—81no—
177Dic59—81no—
178Dic59—81no—
179#2504—591no—
180#1463—591no—
181C2×#324D5911yescharacteristic, complemented
182#1324—592no—
183#1318—592no—
184C2×C59—21no—
185C2×C59—21no—
186C2×C59—22no—
187C2×C59—41no—
188C2×C59#146811yescharacteristic
189C2×C59#212711yescharacteristic
190C2×C59C2×#35511yescharacteristic
191D59—161no—
192C2×#121—591no—
193C22×C4⋊C4C2×D5911yescharacteristic
194#407—1181no—
195C2×C22⋊C8—21no—
196#397—1181no—
197#397—1181no—
198#390—591no—
199#390—591no—
200#386—1181no—
201#386—1181no—
202#382—591no—
203#382—591no—
204C4×C22⋊C4—591no—
205#324—21no—
206#324—592no—
207#324—1181no—
208#324C2×D5912yes—
209C59#1155311yescharacteristic, complemented, Sylow
210C22×D4—591no—
211C22×D4—1181no—
212C23×C4C4×D5911yescharacteristic
213C23×C4D23611yescharacteristic
214C23×C4C22⋊D5911yescharacteristic
215C2×M16—2361no—
216C22×C8—41no—
217#121—2361no—
218#121—2361no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—591no—
222C2×C4⋊C4C4×D5911yescharacteristic
223C2×C4⋊C4D23611yescharacteristic
224C2×C4⋊C4C22⋊D5911yescharacteristic
225C2×C4⋊C4C22×D5911yescharacteristic
226C2×C22⋊C4—1181no—
227C2×C22⋊C4—1181no—
228C2×C22⋊C4—1181no—
229C2×C22⋊C4—1181no—
230C2×C22⋊C4—1181no—
231C2×C22⋊C4—1181no—
232C2×C42—591no—
233C2×C42—591no—
234C22⋊C8—22no—
235C22⋊C8—41no—
236C22⋊C8—1182no—
237C22⋊C8—2361no—
238#95—1181no—
239#95—1181no—
240#95—1181no—
241#95—1181no—
242#95—1181no—
243C24—1181no—
244C24(C2×D59)⋊C411yescharacteristic
245C2×D4—1182no—
246C2×D4—2361no—
247C2×D4—2361no—
248C2×D4—2362no—
249C2×D4—2362no—
250C2×D4—2361no—
251C2×D4—2361no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—1181no—
263C22×C4—1181no—
264C22×C4—1181no—
265C22×C4(C2×D59)⋊C411yescharacteristic
266C22×C4(C2×D59)⋊C411yescharacteristic
267C22×C4(C2×D59)⋊C411yescharacteristic
268C22×C4C2×C4×D5911yescharacteristic
269C22×C4C2×D23611yescharacteristic
270C22×C4C2×C22⋊D5911yescharacteristic
271M16—4722no—
272C2×C8—42no—
273C2×C8—82no—
274C2×C8—2362no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—2361no—
280C22⋊C4—4721no—
281C22⋊C4—4721no—
282C22⋊C4—4721no—
283C22⋊C4—4721no—
284C22⋊C4—2362no—
285C22⋊C4—2362no—
286C42—1182no—
287C42—2361no—
288C23—21no—
289C23—22no—
290C23—21no—
291C23—41no—
292C23—2361no—
293C23—2361no—
294C23—2361no—
295C23—2361no—
296C23—2361no—
297C23—2361no—
298C23—2361no—
299C23#1427364111yescharacteristic
300C23#1427364111yescharacteristic
301C23C2×(C2×D59)⋊C411yescharacteristic
302D4—4722no—
303D4—4722no—
304D4—4722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—2361no—
325C2×C4—2361no—
326C2×C4—2361no—
327C2×C4—2361no—
328C2×C4—2361no—
329C2×C4—2361no—
330C2×C4—2361no—
331C2×C4—2361no—
332C2×C4—2361no—
333C2×C4#1427373312yes—
334C8—82no—
335C8—4722no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—42no—
345C22—4721no—
346C22—4721no—
347C22—4721no—
348C22—4721no—
349C22—4721no—
350C22—4721no—
351C22—4721no—
352C22#1683719812yes—
353C22#1683736811yescharacteristic
354C22C2×#1427364111yescharacteristic
355C22#1683738411yescharacteristic
356C4—22no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—4721no—
363C4—4721no—
364C4—4721no—
365C2—21no—
366C2—21no—
367C2—22no—
368C2—41no—
369C2—9441no—
370C2#2142244211yescharacteristic
371C2#2142576311yescharacteristic
372C2C2×#1683719811yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC2×C59×#324C2
socleC22×C59C2×#99
prime radicalC2×#14273701C4
cosocleC2×C4⋊C4×C59C23
hypercenterC2×#324D59
hypocenterC59#11553
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #21422426C2semidirect
3. #21422039C2semidirect
4. #21422027C2semidirect
5. C2×C59×#324C2semidirect
181. C2×#324D59semidirect
209. C59#11553semidirect

Maximal subgroups

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

subgroupindex
#214285842
#214224262
#214220392
#214220272
C2×C59×#3242
#1155359