Finite Group Databasebeta

← #28477152

Subgroups — #28477152

Order 15104.

432 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 109 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#21432455C211yesmaximal, characteristic
2#21423948C211yesmaximal, characteristic
3#21423840C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#1271C211yesmaximal, characteristic
8C2×#14273717—21no—
9C2×Dic59⋊C8—21no—
10C2×#14273637—21no—
11C2×C8×Dic59—21no—
12#16837301C411yescharacteristic
13#16837300C2211yescharacteristic
14#16837299—21no—
15#16837298C411yescharacteristic
16#16837297—21no—
17#16837271C411yescharacteristic
18#16837271C411yescharacteristic
19#16837266—21no—
20C42×Dic59C2211yescharacteristic
21#16837157C2211yescharacteristic
22#16837157C2211yescharacteristic
23#16837156—21no—
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29#14273717—42no—
30#14273717—42no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59C2×C411yescharacteristic
33C2×C4⋊Dic59C2×C411yescharacteristic
34C2×Dic59⋊C4—21no—
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4—21no—
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×Dic59⋊C4—21no—
40C2×C4×Dic59C2×C411yescharacteristic
41C2×C4×Dic59C2×C411yescharacteristic
42C2×C4×Dic59D411yescharacteristic
43C2×C4×Dic59D411yescharacteristic
44C2×C4×Dic59D411yescharacteristic
45C2×C4×Dic59D411yescharacteristic
46Dic59⋊C8—24no—
47#14273637—42no—
48C8×Dic59—24no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C59⋊#95—21no—
52C22×C8×C59—21no—
53C22×C8×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59C2×C411yescharacteristic
56C2×C4⋊C4×C59C2×C411yescharacteristic
57C2×C42×C59C2311yescharacteristic
58#95×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—21no—
61C22×C4×C59C22×C411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C22×Dic59—21no—
65C22×Dic59—21no—
66C22×Dic59C22⋊C411yescharacteristic
67C22×Dic59C22⋊C411yescharacteristic
68C22×Dic59C22⋊C411yescharacteristic
69C22×Dic59C22⋊C411yescharacteristic
70C2×C8×C59—22no—
71C2×C8×C59—22no—
72C2×C8×C59—41no—
73C2×C8×C59—41no—
74C2×C8×C59—41no—
75C2×C8×C59—41no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C42×C59—41no—
82C4⋊Dic59—21no—
83C4⋊Dic59—21no—
84C4⋊Dic59—42no—
85C4⋊Dic59—41no—
86Dic59⋊C4—42no—
87Dic59⋊C4—42no—
88Dic59⋊C4—42no—
89Dic59⋊C4—41no—
90Dic59⋊C4—41no—
91Dic59⋊C4—42no—
92Dic59⋊C4—42no—
93C4×Dic59—21no—
94C4×Dic59—21no—
95C4×Dic59—21no—
96C4×Dic59—21no—
97C4×Dic59—22no—
98C4×Dic59—22no—
99C4×Dic59—22no—
100C4×Dic59SD1612yes—
101C4×Dic59Q1612yes—
102C2×C59⋊C8—22no—
103C2×C59⋊C8—22no—
104C2×C59⋊C8—41no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8—41no—
108C23×C59C2×C22⋊C411yescharacteristic
109C2×C4×C59—21no—
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—41no—
117C2×C4×C59—41no—
118C2×C4×C59—41no—
119C2×C4×C59—41no—
120C2×C4×C59—41no—
121C2×C4×C59#13111yescharacteristic
122C2×C4×C59#13111yescharacteristic
123C2×C4×C59C2×SD1611yescharacteristic
124C2×C4×C59C2×Q1611yescharacteristic
125C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59#10112yes—
141C2×Dic59#10312yes—
142C2×Dic59#10312yes—
143C2×Dic59#10412yes—
144C2×Dic59#10412yes—
145C8×C59—42no—
146C8×C59—42no—
147C59⋊C8—42no—
148C59⋊C8—42no—
149#7683—591nomaximal, Sylow
150C22×C59#40811yescharacteristic
151C22×C59#41011yescharacteristic
152C22×C59C2×#10111yescharacteristic
153C22×C59C2×#10311yescharacteristic
154C22×C59#41811yescharacteristic
155C22×C59C2×#10411yescharacteristic
156C22×C59C2×#10411yescharacteristic
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—81no—
164C4×C59—81no—
165Dic59—22no—
166Dic59—22no—
167Dic59—41no—
168Dic59—81no—
169Dic59—81no—
170Dic59#33014yes—
171#2859—591no—
172#1767—591no—
173#1744—591no—
174#1271—591no—
175#1271—591no—
176#1271—591no—
177#1271D5911yescharacteristic
178C2×C59#147011yescharacteristic
179C2×C59#148411yescharacteristic
180C2×C59#149311yescharacteristic
181C2×C59#150311yescharacteristic
182C2×C59#150511yescharacteristic
183C2×C59C2×#33011yescharacteristic
184C2×C59#154911yescharacteristic
185C2×#125—1181no—
186C2×C4⋊C8—1181no—
187C2×#97—1181no—
188C2×C4×C8—1181no—
189#389—591no—
190#389—591no—
191#389—591no—
192#389—1181no—
193#389—1181no—
194#389C2×D5911yescharacteristic
195#384—591no—
196#384—591no—
197#382—1181no—
198C43—591no—
199#336—591no—
200#336—591no—
201#336—1181no—
202#336C2×D5911yescharacteristic
203#336C2×D5911yescharacteristic
204C59#768311yescharacteristic, complemented, Sylow
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—1181no—
208C22×C8—1181no—
209#125—2362no—
210#125—2362no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—591no—
213C2×C4⋊C4—591no—
214C2×C4⋊C4—1181no—
215C2×C4⋊C4—1181no—
216C2×C4⋊C4—1181no—
217C2×C4⋊C4—1181no—
218C2×C4⋊C4—1181no—
219C2×C4⋊C4—1181no—
220C2×C4⋊C4—1181no—
221C2×C4⋊C4C4×D5911yescharacteristic
222C2×C4⋊C4C4×D5911yescharacteristic
223C2×C42—591no—
224C2×C42—591no—
225C2×C42—591no—
226C2×C42—591no—
227C2×C42—591no—
228C2×C42—591no—
229C2×C42C22×D5911yescharacteristic
230C4⋊C8—1184no—
231#97—2362no—
232C4×C8—1184no—
233#95—21no—
234#95—1181no—
235#95—1181no—
236#95—1181no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—591no—
240C22×C4—591no—
241C22×C4—591no—
242C22×C4—591no—
243C22×C4—1181no—
244C22×C4—1181no—
245C22×C4C2×C4×D5911yescharacteristic
246C22×C4D4×D5911yescharacteristic
247C22×C4D4×D5911yescharacteristic
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—1182no—
255C2×C8—1182no—
256C2×C8—2361no—
257C2×C8—2361no—
258C2×C8—2361no—
259C2×C8—2361no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—1181no—
266C4⋊C4—1181no—
267C4⋊C4—2361no—
268C4⋊C4—2362no—
269C4⋊C4—2362no—
270C4⋊C4—2362no—
271C4⋊C4—2362no—
272C4⋊C4—2362no—
273C4⋊C4—2362no—
274C4⋊C4—2361no—
275C4⋊C4—2361no—
276C42—41no—
277C42—592no—
278C42—592no—
279C42—1182no—
280C42—1182no—
281C42—1182no—
282C42—1181no—
283C42—1181no—
284C42—1181no—
285C42—1181no—
286C23C22⋊C4×D5911yescharacteristic
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—592no—
300C2×C4—592no—
301C2×C4—592no—
302C2×C4—592no—
303C2×C4—592no—
304C2×C4—1181no—
305C2×C4—1181no—
306C2×C4—1181no—
307C2×C4—1181no—
308C2×C4—1181no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—2361no—
312C2×C4—2361no—
313C2×C4—2361no—
314C2×C4—2361no—
315C2×C4—2361no—
316C2×C4—2361no—
317C2×C4#1427373311yescharacteristic
318C2×C4#1427373511yescharacteristic
319C2×C4SD16×D5911yescharacteristic
320C2×C4Q16×D5911yescharacteristic
321C2×C4#1427375111yescharacteristic
322C2×C4#1427375411yescharacteristic
323C8—42no—
324C8—42no—
325C8—2362no—
326C8—2362no—
327C22#1683736711yescharacteristic
328C22#1683737411yescharacteristic
329C22#101×D5911yescharacteristic
330C22#103×D5911yescharacteristic
331C22#1683740511yescharacteristic
332C22#104×D5911yescharacteristic
333C22#104×D5911yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—81no—
341C4—81no—
342C4—594no—
343C4—1182no—
344C4—1182no—
345C4—4721no—
346C4—4721no—
347C4—2361no—
348C2#2142245011yescharacteristic
349C2#2142251111yescharacteristic
350C2#2142254911yescharacteristic
351C2#2142259311yescharacteristic
352C2#2142260211yescharacteristic
353C2#330×D5911yescharacteristic
354C2#2142277911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1271C2
socle, prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1271D59
hypocenterC59#7683
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
204. C59#7683semidirect

Maximal subgroups

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

subgroupindex
#214324552
#214239482
#214238402
#214219202
#214219192
#214219182
C59×#12712
#768359