Finite Group Databasebeta

← #28477758

Subgroups — #28477758

Order 15104.

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

normal subgroups only

This group has 420 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#21431056C211yesmaximal, characteristic
2#21425625C211yesmaximal, characteristic
3#21425573C211yesmaximal, characteristic, complemented
4#21421919C211yesmaximal, characteristic, complemented
5#21421918C211yesmaximal, characteristic, complemented
6#21421916C211yesmaximal, characteristic
7C59×#2083C211yesmaximal, characteristic, complemented
8C2×#14273722—21no—
9C2×#14273660—21no—
10C2×#14273658—21no—
11C2×#14273647—21no—
12#16837337—21no—
13#16837324—21no—
14#16837320—21no—
15#16837304C2211yescharacteristic
16#16837300C2211yescharacteristic
17#16837299—21no—
18#16837292—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C2×#107×C59—21no—
23C59×#389C2211yescharacteristic
24C59×#384C2211yescharacteristic
25C59×#340—21no—
26C59×#336C2211yescharacteristic
27C22×D236D411yescharacteristic
28C22×C59⋊C8—21no—
29C22×C59⋊C8—21no—
30#14273722—42no—
31#14273722—42no—
32C2×C4⋊Dic59D411yescharacteristic
33C2×C4⋊Dic59D411yescharacteristic
34C2×C4⋊Dic59D411yescharacteristic
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4—21no—
37C2×Dic59⋊C4—21no—
38C2×(C2×D59)⋊C4—21no—
39C2×(C2×D59)⋊C4—21no—
40C2×(C2×D59)⋊C4—21no—
41C2×(C2×D59)⋊C4—21no—
42C2×(C2×D59)⋊C4—21no—
43C2×(C2×D59)⋊C4—21no—
44C2×C4×Dic59—21no—
45#14273660—42no—
46#14273658—42no—
47#14273647—42no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C22×C8×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59D411yescharacteristic
56C2×C4⋊C4×C59D411yescharacteristic
57C2×C42×C59C2311yescharacteristic
58#107×C59—42no—
59#95×C59—21no—
60C23×D59—21no—
61C22×C4×C59—21no—
62C22×C4×C59—21no—
63C22×C4×C59—41no—
64C22×C4×C59C2×D411yescharacteristic
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×Dic59—21no—
68C22×Dic59—21no—
69C22×Dic59—21no—
70C2×D236—21no—
71C2×D236—21no—
72C2×D236—41no—
73C2×D236—41no—
74C2×C8×C59—22no—
75C2×C8×C59—41no—
76C2×C8×C59—41no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59—41no—
87C4⋊C4×C59—41no—
88C42×C59—41no—
89(C2×D59)⋊C4—42no—
90(C2×D59)⋊C4—42no—
91(C2×D59)⋊C4—41no—
92(C2×D59)⋊C4—41no—
93(C2×D59)⋊C4—41no—
94(C2×D59)⋊C4—41no—
95(C2×D59)⋊C4—81no—
96(C2×D59)⋊C4—81no—
97C4⋊Dic59—21no—
98C4⋊Dic59—41no—
99C4⋊Dic59—41no—
100C4⋊Dic59D812yes—
101Dic59⋊C4—42no—
102Dic59⋊C4—41no—
103Dic59⋊C4—41no—
104Dic59⋊C4—81no—
105C4×Dic59—42no—
106C2×C59⋊C8—22no—
107C2×C59⋊C8—22no—
108C2×C59⋊C8—41no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8—41no—
111C2×C59⋊C8—41no—
112C23×C59#12011yescharacteristic
113C22×D59—41no—
114C22×D59—41no—
115C22×D59—41no—
116C22×D59—41no—
117C22×D59—41no—
118C22×D59—41no—
119C22×D59—41no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
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—81no—
135C2×C4×C59C2×D811yescharacteristic
136C2×C4×C59#13511yescharacteristic
137C2×C4×C59#13511yescharacteristic
138C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C59#13711yescharacteristic
141C2×Dic59—22no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C2×Dic59—41no—
149C2×Dic59—41no—
150D236—42no—
151D236—81no—
152C8×C59—42no—
153C59⋊C8—42no—
154C59⋊C8—42no—
155#7793—591nomaximal, Sylow
156C22×C59#44711yescharacteristic
157C22×C59#44911yescharacteristic
158C22×C59#45211yescharacteristic
159C22×C59#45311yescharacteristic
160C22×C59#45611yescharacteristic
161C22×C59#45611yescharacteristic
162C22×C59#45811yescharacteristic
163C2×D59—81no—
164C2×D59—81no—
165C2×D59—81no—
166C2×D59—81no—
167C2×D59—81no—
168C2×D59—81no—
169C2×D59—81no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—21no—
174C4×C59—21no—
175C4×C59—21no—
176C4×C59—81no—
177C4×C59—81no—
178C4×C59—161no—
179Dic59—42no—
180Dic59—81no—
181Dic59—81no—
182#2727—591no—
183#2093—591no—
184#2084—591no—
185#2083D5911yescharacteristic, complemented
186#1271—591no—
187#1271—591no—
188#1270—591no—
189C2×C59#160911yescharacteristic
190C2×C59#161011yescharacteristic
191C2×C59#161811yescharacteristic
192C2×C59#162111yescharacteristic
193C2×C59#164711yescharacteristic
194C2×C59#165211yescharacteristic
195C2×C59#166011yescharacteristic
196D59—161no—
197C2×#126—1181no—
198C2×#107—21no—
199C2×#107—1181no—
200C2×#106—1181no—
201C2×#102—1181no—
202#399—1181no—
203#396—1181no—
204#394—1181no—
205#390—591no—
206#389—591no—
207#389—1181no—
208#389C2×D5911yescharacteristic
209#388—1181no—
210#384C2×D5911yescharacteristic
211#340—21no—
212#340—1181no—
213#336—591no—
214#336—591no—
215#336C2×D5911yescharacteristic
216C59#779311yescharacteristic, complemented, Sylow
217C22×D4—591no—
218C22×C8—21no—
219C22×C8—1181no—
220C22×C8—1181no—
221#126—2362no—
222#126—2362no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—591no—
228C2×C4⋊C4—591no—
229C2×C4⋊C4—591no—
230C2×C4⋊C4—1181no—
231C2×C4⋊C4—1181no—
232C2×C4⋊C4—1181no—
233C2×C4⋊C4C22⋊D5911yescharacteristic
234C2×C4⋊C4C22⋊D5911yescharacteristic
235C2×C22⋊C4—1181no—
236C2×C22⋊C4—1181no—
237C2×C22⋊C4—1181no—
238C2×C22⋊C4—1181no—
239C2×C22⋊C4—1181no—
240C2×C22⋊C4—1181no—
241C2×C42—1181no—
242C2×C42C22×D5911yescharacteristic
243#107—42no—
244#107—2362no—
245#106—2362no—
246#102—2362no—
247#95—21no—
248#95—1181no—
249#95—1181no—
250C24—1181no—
251C2×D4—1181no—
252C2×D4—1181no—
253C2×D4—2361no—
254C2×D4—2361no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—1181no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4D4×D5911yescharacteristic
262C22×C4D4×D5911yescharacteristic
263C22×C4C2×C22⋊D5911yescharacteristic
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—1182no—
268C2×C8—1182no—
269C2×C8—2361no—
270C2×C8—2361no—
271C2×C8—2361no—
272C2×C8—2361no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—592no—
285C4⋊C4—1181no—
286C4⋊C4—4721no—
287C4⋊C4—2361no—
288C4⋊C4—2361no—
289C4⋊C4—2362no—
290C4⋊C4—2361no—
291C4⋊C4—2361no—
292C22⋊C4—4721no—
293C22⋊C4—4721no—
294C22⋊C4—2362no—
295C22⋊C4—2362no—
296C22⋊C4—2361no—
297C22⋊C4—2361no—
298C22⋊C4—2361no—
299C22⋊C4—2361no—
300C42—41no—
301C42—2362no—
302C23—2361no—
303C23—2361no—
304C23—2361no—
305C23—2361no—
306C23—2361no—
307C23—2361no—
308C23—2361no—
309C23#1427369511yescharacteristic
310D4—4721no—
311D4—2362no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—1182no—
328C2×C4—2361no—
329C2×C4—2361no—
330C2×C4—2361no—
331C2×C4—2361no—
332C2×C4—2361no—
333C2×C4—2361no—
334C2×C4—2361no—
335C2×C4—2361no—
336C2×C4D8×D5911yescharacteristic
337C2×C4#1427374711yescharacteristic
338C2×C4#1427375011yescharacteristic
339C2×C4#1427375111yescharacteristic
340C2×C4#1427375311yescharacteristic
341C2×C4#1427375911yescharacteristic
342C8—42no—
343C8—2362no—
344C8—2362no—
345C22—4721no—
346C22—4721no—
347C22—4721no—
348C22—4721no—
349C22—4721no—
350C22—4721no—
351C22—4721no—
352C22#1683753411yescharacteristic
353C22#1683754511yescharacteristic
354C22#1683756311yescharacteristic
355C22#1683756811yescharacteristic
356C22#1683758311yescharacteristic
357C22#1683758411yescharacteristic
358C22#1683759111yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—81no—
366C4—81no—
367C4—161no—
368C4—4721no—
369C4—4721no—
370C4—2362no—
371C2—9441no—
372C2#2142309111yescharacteristic
373C2#2142309711yescharacteristic
374C2#2142314311yescharacteristic
375C2#2142316011yescharacteristic
376C2#2142332811yescharacteristic
377C2#2142336411yescharacteristic
378C2#2142340611yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2083C2
socleC23×C59#120
prime radicalC22×D236D4
hypercenter#2083D59
hypocenterC59#7793
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
3. #21425573C2semidirect
4. #21421919C2semidirect
5. #21421918C2semidirect
7. C59×#2083C2semidirect
185. #2083D59semidirect
216. C59#7793semidirect

Maximal subgroups

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

subgroupindex
#214310562
#214256252
#214255732
#214219192
#214219182
#214219162
C59×#20832
#779359