Finite Group Databasebeta

← #28477960

Subgroups — #28477960

Order 15104.

418 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 81 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#21431025C211yesmaximal, characteristic
2#21425660C211yesmaximal, characteristic, complemented
3#21425659C211yesmaximal, characteristic, complemented
4#21425628C211yesmaximal, characteristic
5#21421920C211yesmaximal, characteristic, complemented
6#21421916C211yesmaximal, characteristic
7C59×#1271C211yesmaximal, characteristic, complemented
8C2×#14273712—21no—
9C2×#14273659—21no—
10C2×#14273649—21no—
11#16837335—21no—
12#16837329—21no—
13#16837328—21no—
14#16837304C2211yescharacteristic
15#16837300C2211yescharacteristic
16#16837276—21no—
17#16837273—21no—
18#16837272C2211yescharacteristic
19#16837165—21no—
20#16837165—21no—
21#16837164—21no—
22#16837164—21no—
23#16837157C2211yescharacteristic
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×D236D411yescharacteristic
28C22×C4×D59—21no—
29C22×C59⋊C8—21no—
30#14273712—42no—
31#14273712—42no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59D411yescharacteristic
36C2×C4⋊Dic59D411yescharacteristic
37C2×C4⋊Dic59D411yescharacteristic
38C2×Dic59⋊C4—21no—
39C2×Dic59⋊C4—21no—
40C2×(C2×D59)⋊C4—21no—
41C2×(C2×D59)⋊C4—21no—
42C2×(C2×D59)⋊C4—21no—
43C2×(C2×D59)⋊C4—21no—
44C2×(C2×D59)⋊C4—21no—
45#14273659—42no—
46#14273649—42no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C22×C8×C59—21no—
52C22×C8×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C4⋊C4×C59D411yescharacteristic
56C2×C42×C59C2311yescharacteristic
57#95×C59—21no—
58C23×D59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C22×Dic59—21no—
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—41no—
68C2×D236—21no—
69C2×D236—41no—
70C2×D236—41no—
71C2×D236SD1612yes—
72C2×C4×D59—42no—
73C2×C4×D59—81no—
74C2×C4×D59—81no—
75C2×C8×C59—22no—
76C2×C8×C59—41no—
77C2×C8×C59—41no—
78C2×C8×C59—41no—
79C2×C8×C59—41no—
80C2×C8×C59—41no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C42×C59—41no—
87(C2×D59)⋊C4—42no—
88(C2×D59)⋊C4—42no—
89(C2×D59)⋊C4—42no—
90(C2×D59)⋊C4—41no—
91(C2×D59)⋊C4—41no—
92(C2×D59)⋊C4—41no—
93(C2×D59)⋊C4—41no—
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59—41no—
97C4⋊Dic59—41no—
98C4⋊Dic59—41no—
99C4⋊Dic59—41no—
100C4⋊Dic59—42no—
101C4⋊Dic59—42no—
102Dic59⋊C4—41no—
103Dic59⋊C4—41no—
104Dic59⋊C4—81no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8—41no—
108C23×C59#12011yescharacteristic
109C22×D59—22no—
110C22×D59—41no—
111C22×D59—41no—
112C22×D59—41no—
113C22×D59—41no—
114C22×D59—41no—
115C22×D59—41no—
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—41no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59C2×SD1611yescharacteristic
129C2×C4×C59#13511yescharacteristic
130C2×C4×C59#13511yescharacteristic
131C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C59#13711yescharacteristic
133C2×C4×C59#13711yescharacteristic
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—81no—
144C2×Dic59—81no—
145C2×Dic59—81no—
146D236—42no—
147D236—81no—
148C4×D59—84no—
149C8×C59—42no—
150C8×C59—81no—
151C59⋊C8—81no—
152#7824—591nomaximal, Sylow
153C22×C59#45011yescharacteristic
154C22×C59#45211yescharacteristic
155C22×C59#45211yescharacteristic
156C22×C59#45311yescharacteristic
157C22×C59#45411yescharacteristic
158C22×C59#45411yescharacteristic
159C22×C59#45811yescharacteristic
160C2×D59—42no—
161C2×D59—42no—
162C2×D59—42no—
163C2×D59—81no—
164C2×D59—81no—
165C2×D59—81no—
166C2×D59—81no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—81no—
174C4×C59—81no—
175Dic59—81no—
176Dic59—81no—
177Dic59—81no—
178Dic59—161no—
179#2724—591no—
180#2100—591no—
181#2100—591no—
182#2094—591no—
183#1271—591no—
184#1271D5911yescharacteristic, complemented
185#1270—591no—
186C2×C59#161311yescharacteristic
187C2×C59#161511yescharacteristic
188C2×C59#161511yescharacteristic
189C2×C59#163011yescharacteristic
190C2×C59#163511yescharacteristic
191C2×C59#163511yescharacteristic
192C2×C59#165711yescharacteristic
193D59—82no—
194C2×#123—1181no—
195C2×#106—1181no—
196C2×#102—1181no—
197#398—1181no—
198#397—1181no—
199#397—1181no—
200#390—591no—
201#389—591no—
202#389C2×D5911yescharacteristic
203#385—1181no—
204#385—1181no—
205#384—591no—
206#340—1181no—
207#340—1181no—
208#340—1181no—
209#340—1181no—
210#336—591no—
211#336C2×D5911yescharacteristic
212#336C2×D5911yescharacteristic
213C59#782411yescharacteristic, complemented, Sylow
214C22×D4—591no—
215C23×C4—1181no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—1181no—
219#123—2362no—
220#123—2362no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—591no—
223C2×C4⋊C4—591no—
224C2×C4⋊C4—591no—
225C2×C4⋊C4—1181no—
226C2×C4⋊C4—1181no—
227C2×C4⋊C4—1181no—
228C2×C4⋊C4—1181no—
229C2×C4⋊C4—1181no—
230C2×C4⋊C4D23611yescharacteristic
231C2×C4⋊C4D23611yescharacteristic
232C2×C22⋊C4—1181no—
233C2×C22⋊C4—1181no—
234C2×C22⋊C4—1181no—
235C2×C22⋊C4—1181no—
236C2×C22⋊C4—1181no—
237C2×C42C22×D5911yescharacteristic
238#106—2362no—
239#102—2362no—
240#95—21no—
241#95—1181no—
242#95—1181no—
243#95—1181no—
244#95—1181no—
245C24—1181no—
246C2×D4—592no—
247C2×D4—1181no—
248C2×D4—2361no—
249C2×D4—2361no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4—1181no—
255C22×C4—4721no—
256C22×C4—4721no—
257C22×C4—2362no—
258C22×C4—2361no—
259C22×C4C2×D23611yescharacteristic
260C22×C4D4×D5911yescharacteristic
261C22×C4D4×D5911yescharacteristic
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—2361no—
269C2×C8—2361no—
270C2×C8—2361no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—4721no—
279C4⋊C4—2361no—
280C4⋊C4—2361no—
281C4⋊C4—2362no—
282C4⋊C4—2362no—
283C4⋊C4—2361no—
284C4⋊C4—2361no—
285C4⋊C4—2361no—
286C4⋊C4—2361no—
287C22⋊C4—2362no—
288C22⋊C4—2362no—
289C22⋊C4—2362no—
290C22⋊C4—2361no—
291C22⋊C4—2361no—
292C22⋊C4—2361no—
293C22⋊C4—2361no—
294C42—41no—
295C23—1182no—
296C23—2361no—
297C23—2361no—
298C23—2361no—
299C23—2361no—
300C23—2361no—
301C23—2361no—
302C23#1427369711yescharacteristic
303D4—4721no—
304D4—2362no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—4724no—
318C2×C4—4721no—
319C2×C4—4721no—
320C2×C4—4721no—
321C2×C4—2361no—
322C2×C4—2361no—
323C2×C4—2361no—
324C2×C4—2361no—
325C2×C4—2361no—
326C2×C4—2361no—
327C2×C4—2361no—
328C2×C4—2361no—
329C2×C4—2361no—
330C2×C4SD16×D5911yescharacteristic
331C2×C4#1427374811yescharacteristic
332C2×C4#1427374911yescharacteristic
333C2×C4#1427375111yescharacteristic
334C2×C4#1427375911yescharacteristic
335C2×C4#1427376011yescharacteristic
336C8—42no—
337C8—81no—
338C8—4721no—
339C22—4721no—
340C22—4721no—
341C22—4721no—
342C22—4721no—
343C22—2362no—
344C22—2362no—
345C22—2362no—
346C22#1683755411yescharacteristic
347C22#1683756611yescharacteristic
348C22#1683756711yescharacteristic
349C22#1683757111yescharacteristic
350C22#1683757611yescharacteristic
351C22#1683757711yescharacteristic
352C22#1683759311yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—81no—
360C4—81no—
361C4—9441no—
362C4—4721no—
363C4—4721no—
364C4—4721no—
365C2—4722no—
366C2#2142311711yescharacteristic
367C2#2142312911yescharacteristic
368C2#2142313011yescharacteristic
369C2#2142321911yescharacteristic
370C2#2142324811yescharacteristic
371C2#2142325011yescharacteristic
372C2#2142339611yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1271C2
socleC23×C59#120
prime radicalC22×D236D4
hypercenter#1271D59
hypocenterC59#7824
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #21425660C2semidirect
3. #21425659C2semidirect
5. #21421920C2semidirect
7. C59×#1271C2semidirect
184. #1271D59semidirect
213. C59#7824semidirect

Maximal subgroups

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

subgroupindex
#214310252
#214256602
#214256592
#214256282
#214219202
#214219162
C59×#12712
#782459