Finite Group Databasebeta

← #28477614

Subgroups — #28477614

Order 15104.

416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 85 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#21431047C211yesmaximal, characteristic
2#21425421C211yesmaximal, characteristic
3#21425339C211yesmaximal, characteristic
4#21421919C211yesmaximal, characteristic
5#21421918C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#2058C211yesmaximal, characteristic
8C2×#14273718—21no—
9C2×#14273660—21no—
10C2×#14273651—21no—
11C2×#14273651—21no—
12#16837335—21no—
13#16837335—21no—
14#16837334—21no—
15#16837300C2211yescharacteristic
16#16837300C2211yescharacteristic
17#16837299—21no—
18#16837288—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C2×C4⋊Q8×C59C2211yescharacteristic
23C2×#106×C59—21no—
24C59×#389C2211yescharacteristic
25C59×#340—21no—
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29#14273718—42no—
30#14273718—42no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59D411yescharacteristic
34C2×C4⋊Dic59D411yescharacteristic
35C2×C4⋊Dic59D411yescharacteristic
36C2×C4⋊Dic59D411yescharacteristic
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×Dic59⋊C4—21no—
40C2×Dic59⋊C4—21no—
41C2×C4×Dic59—21no—
42#14273660—42no—
43#14273651—42no—
44#14273651—42no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C22×Q8×C59—21no—
51C22×C8×C59—21no—
52C4⋊Q8×C59—42no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59—21no—
55C2×C4⋊C4×C59—21no—
56C2×C4⋊C4×C59D411yescharacteristic
57C2×C4⋊C4×C59D411yescharacteristic
58C2×C42×C59C2311yescharacteristic
59#106×C59—42no—
60#95×C59—21no—
61C2×Q8×C59—22no—
62C2×Q8×C59—41no—
63C2×Q8×C59—41no—
64C2×Q8×C59—41no—
65C2×Q8×C59—41no—
66C2×Q8×C59—41no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—41no—
70C22×C4×C59C2×D411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×Dic59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76C22×Dic59—21no—
77C2×C8×C59—22no—
78C2×C8×C59—41no—
79C2×C8×C59—41no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—22no—
82C4⋊C4×C59—22no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59—41no—
87C4⋊C4×C59—41no—
88C4⋊C4×C59Q1612yes—
89C42×C59—41no—
90C4⋊Dic59—21no—
91C4⋊Dic59—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59—42no—
94C4⋊Dic59—42no—
95C4⋊Dic59—41no—
96C4⋊Dic59—41no—
97C4⋊Dic59SD1612yes—
98Dic59⋊C4—42no—
99Dic59⋊C4—41no—
100Dic59⋊C4—41no—
101Dic59⋊C4—41no—
102Dic59⋊C4—41no—
103Dic59⋊C4—81no—
104C4×Dic59—42no—
105C2×C59⋊C8—22no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8—41no—
108C2×C59⋊C8—41no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8—41no—
111C23×C59#12011yescharacteristic
112Q8×C59—42no—
113Q8×C59—42no—
114Q8×C59—81no—
115Q8×C59—81no—
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—22no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—42no—
129C2×C4×C59—81no—
130C2×C4×C59—81no—
131C2×C4×C59C2×SD1611yescharacteristic
132C2×C4×C59C2×Q1611yescharacteristic
133C2×C4×C59#13511yescharacteristic
134C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C59#13711yescharacteristic
137C2×Dic59—22no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C2×Dic59—41no—
149C8×C59—42no—
150C59⋊C8—42no—
151C59⋊C8—81no—
152#7772—591nomaximal, Sylow
153C22×C59#44911yescharacteristic
154C22×C59#45011yescharacteristic
155C22×C59#45111yescharacteristic
156C22×C59#45411yescharacteristic
157C22×C59#45611yescharacteristic
158C22×C59#45611yescharacteristic
159C22×C59B(4,𝔽2)11yescharacteristic
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—42no—
167C4×C59—82no—
168C4×C59—81no—
169Dic59—42no—
170Dic59—81no—
171Dic59—81no—
172Dic59—81no—
173#2726—591no—
174#2058D5911yescharacteristic
175#2057—591no—
176#2043—591no—
177#1271—591no—
178#1271—591no—
179#1271—591no—
180C2×C59#159711yescharacteristic
181C2×C59#160411yescharacteristic
182C2×C59#160511yescharacteristic
183C2×C59#163711yescharacteristic
184C2×C59#164811yescharacteristic
185C2×C59#165411yescharacteristic
186C2×C59#166311yescharacteristic
187C2×C4⋊Q8C2×D5911yescharacteristic
188C2×#125—1181no—
189C2×#107—1181no—
190C2×#106—21no—
191C2×#103—1181no—
192C2×#103—1181no—
193#398—1181no—
194#398—1181no—
195#398—1181no—
196#389—591no—
197#389—591no—
198#389—1181no—
199#389C2×D5911yescharacteristic
200#387—1181no—
201#340—21no—
202#340—1181no—
203#336—591no—
204#336—591no—
205#336C2×D5911yescharacteristic
206C59#777211yescharacteristic, complemented, Sylow
207C22×Q8—21no—
208C22×C8—21no—
209C22×C8—1181no—
210C22×C8—1181no—
211C4⋊Q8—42no—
212#125—2362no—
213#125—2362no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—591no—
218C2×C4⋊C4—591no—
219C2×C4⋊C4—591no—
220C2×C4⋊C4—591no—
221C2×C4⋊C4—1181no—
222C2×C4⋊C4—1181no—
223C2×C4⋊C4—1181no—
224C2×C4⋊C4—1181no—
225C2×C4⋊C4—1181no—
226C2×C4⋊C4—1181no—
227C2×C4⋊C4C22⋊D5911yescharacteristic
228C2×C4⋊C4C22⋊D5911yescharacteristic
229C2×C42—1181no—
230C2×C42C22×D5911yescharacteristic
231#107—2362no—
232#106—42no—
233#103—2362no—
234#103—2362no—
235#95—21no—
236#95—1181no—
237#95—1181no—
238#95—1181no—
239#95—1181no—
240#95—1181no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—1181no—
251C22×C4—1181no—
252C22×C4—1181no—
253C22×C4—1181no—
254C22×C4D4×D5911yescharacteristic
255C22×C4D4×D5911yescharacteristic
256C22×C4C2×C22⋊D5911yescharacteristic
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—1182no—
261C2×C8—2361no—
262C2×C8—2361no—
263C2×C8—2361no—
264C2×C8—2361no—
265C2×C8—2361no—
266C4⋊C4—21no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—592no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—4721no—
279C4⋊C4—2361no—
280C4⋊C4—2361no—
281C4⋊C4—2362no—
282C4⋊C4—2362no—
283C4⋊C4—2362no—
284C4⋊C4—2361no—
285C4⋊C4—2361no—
286C4⋊C4—2361no—
287C4⋊C4—2361no—
288C4⋊C4#1174567212yes—
289C42—41no—
290C42—2362no—
291C23#1427369511yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—1182no—
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×C4—2361no—
322C2×C4—2361no—
323C2×C4SD16×D5911yescharacteristic
324C2×C4C2×#1174567211yescharacteristic
325C2×C4#1427374811yescharacteristic
326C2×C4#1427375411yescharacteristic
327C2×C4#1427375411yescharacteristic
328C2×C4#1427375711yescharacteristic
329C8—42no—
330C8—4721no—
331C8—2362no—
332C22#1683754611yescharacteristic
333C22#1683755111yescharacteristic
334C22#1683755711yescharacteristic
335C22#1683757311yescharacteristic
336C22#1683758311yescharacteristic
337C22#1683758411yescharacteristic
338C22#1683758811yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—82no—
347C4—81no—
348C4—4721no—
349C4—4721no—
350C4—4721no—
351C4—2362no—
352C2#2142302411yescharacteristic
353C2#2142306311yescharacteristic
354C2#2142306911yescharacteristic
355C2#2142326011yescharacteristic
356C2#2142333711yescharacteristic
357C2#2142337711yescharacteristic
358C2#2142342311yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2058C2
socle, prime radicalC23×C59#120
hypercenter#2058D59
hypocenterC59#7772
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
206. C59#7772semidirect

Maximal subgroups

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

subgroupindex
#214310472
#214254212
#214253392
#214219192
#214219182
C59×#20582
#777259