Finite Group Databasebeta

← #28477573

Subgroups — #28477573

Order 15104.

436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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#21425429C211yesmaximal, characteristic
2#21425342C211yesmaximal, characteristic
3#21425237C211yesmaximal, characteristic
4#21421922C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421919C211yesmaximal, characteristic
7C59×#2734C211yesmaximal, characteristic
8C2×#14273727C2211yescharacteristic
9C2×#14273658—21no—
10C2×#14273651—21no—
11C2×#14273650—21no—
12C2×#14273650—21no—
13#16837164—21no—
14#16837164—21no—
15#16837157C2211yescharacteristic
16#16837157C2211yescharacteristic
17#16837157C2211yescharacteristic
18C2×C4⋊Q8×C59—21no—
19C59×#398—21no—
20C59×#395—21no—
21C59×#395—21no—
22C59×#391C2211yescharacteristic
23C59×#389C2211yescharacteristic
24C59×#389C2211yescharacteristic
25C59×#387—21no—
26C59×#387—21no—
27C22×Dic118—21no—
28C22×C59⋊C8—21no—
29C22×C59⋊C8—21no—
30C22×C59⋊C8—21no—
31#14273727—42no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34#14273658—42no—
35#14273651—42no—
36#14273650—42no—
37#14273650—42no—
38C22×Q8×C59—21no—
39C22×Q8×C59D411yescharacteristic
40C4⋊Q8×C59—42no—
41C4⋊Q8×C59—42no—
42C2×C4⋊C4×C59—21no—
43C2×C4⋊C4×C59—21no—
44C2×C4⋊C4×C59—21no—
45C2×C4⋊C4×C59—21no—
46C2×C4⋊C4×C59—21no—
47C2×C4⋊C4×C59D411yescharacteristic
48C2×C4⋊C4×C59D411yescharacteristic
49C2×C4⋊C4×C59D411yescharacteristic
50C2×C4⋊C4×C59D411yescharacteristic
51C2×C4⋊C4×C59D411yescharacteristic
52C2×C42×C59—21no—
53C2×C42×C59C2311yescharacteristic
54#95×C59—21no—
55#95×C59—21no—
56#95×C59—21no—
57#95×C59—21no—
58#95×C59—21no—
59#95×C59—21no—
60#95×C59—21no—
61C2×Q8×C59—21no—
62C2×Q8×C59—42no—
63C2×Q8×C59—41no—
64C2×Q8×C59—41no—
65C2×Q8×C59—81no—
66C2×Q8×C59—81no—
67C2×Q8×C59SD1612yes—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59C2×D411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C22×C4×C59C2×D411yescharacteristic
77C22×Dic59—41no—
78C2×Dic118—22no—
79C2×Dic118—41no—
80C2×Dic118—41no—
81C2×Dic118—41no—
82C2×Dic118—41no—
83C2×Dic118—41no—
84C4⋊C4×C59—21no—
85C4⋊C4×C59—21no—
86C4⋊C4×C59—42no—
87C4⋊C4×C59—42no—
88C4⋊C4×C59—41no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—41no—
91C4⋊C4×C59—41no—
92C4⋊C4×C59—41no—
93C4⋊C4×C59—41no—
94C4⋊C4×C59—41no—
95C4⋊C4×C59—81no—
96C4⋊C4×C59SD1612yes—
97C4⋊C4×C59Q1612yes—
98C42×C59—41no—
99C42×C59—42no—
100C4⋊Dic59—22no—
101C4⋊Dic59—22no—
102C4⋊Dic59—41no—
103C4⋊Dic59—41no—
104C2×C59⋊C8—22no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8—41no—
108C2×C59⋊C8—41no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8—41no—
111C2×C59⋊C8—41no—
112C2×C59⋊C8—41no—
113C23×C59#12011yescharacteristic
114Q8×C59—42no—
115Q8×C59—81no—
116Q8×C59—84no—
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—22no—
124C2×C4×C59—22no—
125C2×C4×C59—22no—
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—41no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—41no—
139C2×C4×C59—41no—
140C2×C4×C59—41no—
141C2×C4×C59C2×SD1611yescharacteristic
142C2×C4×C59C2×SD1611yescharacteristic
143C2×C4×C59C2×Q1611yescharacteristic
144C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C59#13711yescharacteristic
146C2×C4×C59#13711yescharacteristic
147C2×Dic59—42no—
148C2×Dic59—81no—
149C2×Dic59—81no—
150Dic118—42no—
151Dic118—42no—
152Dic118—81no—
153Dic118—81no—
154C59⋊C8—42no—
155C59⋊C8—81no—
156C59⋊C8—81no—
157#7766—591nomaximal, Sylow
158C22×C59#44811yescharacteristic
159C22×C59#45011yescharacteristic
160C22×C59#45111yescharacteristic
161C22×C59#45411yescharacteristic
162C22×C59#45511yescharacteristic
163C22×C59#45611yescharacteristic
164C22×C59B(4,𝔽2)11yescharacteristic
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—21no—
171C4×C59—42no—
172C4×C59—42no—
173C4×C59—42no—
174C4×C59—81no—
175C4×C59—81no—
176C4×C59—81no—
177Dic59—82no—
178#2734D5911yescharacteristic
179#2058—591no—
180#2043—591no—
181#2024—591no—
182#1272—591no—
183#1271—591no—
184#1271—591no—
185C2×C59#159911yescharacteristic
186C2×C59#160111yescharacteristic
187C2×C59#160511yescharacteristic
188C2×C59#163711yescharacteristic
189C2×C59#164511yescharacteristic
190C2×C59#165111yescharacteristic
191C2×C59#166411yescharacteristic
192C2×C4⋊Q8—21no—
193C2×C4⋊Q8—591no—
194C2×#106—1181no—
195C2×#103—1181no—
196C2×#103—1181no—
197C2×#103—1181no—
198#398—21no—
199#395—21no—
200#395—21no—
201#391C2×D5911yescharacteristic
202#389C2×D5911yescharacteristic
203#389C2×D5911yescharacteristic
204#387—21no—
205#387—21no—
206#340—1181no—
207#340—1181no—
208#336—591no—
209#336—591no—
210#336—591no—
211C59#776611yescharacteristic, complemented, Sylow
212C22×Q8—21no—
213C22×Q8—1181no—
214C22×Q8C22⋊D5911yescharacteristic
215C22×C8—1181no—
216C22×C8—1181no—
217C22×C8—1181no—
218C4⋊Q8—42no—
219C4⋊Q8—42no—
220C4⋊Q8—2362no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—1181no—
227C2×C4⋊C4—1181no—
228C2×C4⋊C4C22⋊D5911yescharacteristic
229C2×C4⋊C4C22⋊D5911yescharacteristic
230C2×C4⋊C4C22⋊D5911yescharacteristic
231C2×C4⋊C4C22⋊D5911yescharacteristic
232C2×C4⋊C4C22⋊D5911yescharacteristic
233C2×C42—21no—
234C2×C42C22×D5911yescharacteristic
235#106—2362no—
236#103—2362no—
237#103—2362no—
238#103—2362no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—21no—
246C2×Q8—21no—
247C2×Q8—42no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—81no—
251C2×Q8—81no—
252C2×Q8—1182no—
253C2×Q8—2361no—
254C2×Q8—2361no—
255C2×Q8—2361no—
256C2×Q8—2361no—
257C2×Q8—2361no—
258C2×Q8#1174567012yes—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—2361no—
266C22×C4C2×C22⋊D5911yescharacteristic
267C22×C4C2×C22⋊D5911yescharacteristic
268C22×C4C2×C22⋊D5911yescharacteristic
269C2×C8—1182no—
270C2×C8—2361no—
271C2×C8—2361no—
272C2×C8—2361no—
273C2×C8—2361no—
274C2×C8—2361no—
275C2×C8—2361no—
276C2×C8—2361no—
277C2×C8—2361no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—81no—
290C4⋊C4—1182no—
291C4⋊C4—1182no—
292C4⋊C4—2361no—
293C4⋊C4—2361no—
294C4⋊C4#1174567112yes—
295C4⋊C4#1174567212yes—
296C42—41no—
297C42—42no—
298C23#1427369611yescharacteristic
299Q8—42no—
300Q8—81no—
301Q8—84no—
302Q8—4721no—
303Q8—4721no—
304Q8—2362no—
305Q8—2362no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—4721no—
331C2×C4—4721no—
332C2×C4—2362no—
333C2×C4C2×#1174567111yescharacteristic
334C2×C4C2×#1174567011yescharacteristic
335C2×C4C2×#1174567211yescharacteristic
336C2×C4#1427375311yescharacteristic
337C2×C4#1427375811yescharacteristic
338C2×C4#1427375811yescharacteristic
339C8—4721no—
340C8—4721no—
341C8—2362no—
342C22#1683754111yescharacteristic
343C22#1683755311yescharacteristic
344C22#1683755811yescharacteristic
345C22#1683757511yescharacteristic
346C22#1683758011yescharacteristic
347C22#1683758511yescharacteristic
348C22#1683758911yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—42no—
357C4—42no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—4722no—
362C2#2142303611yescharacteristic
363C2#2142304811yescharacteristic
364C2#2142307011yescharacteristic
365C2#2142326111yescharacteristic
366C2#2142331711yescharacteristic
367C2#2142335911yescharacteristic
368C2#2142343011yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2734C2
socle, prime radicalC23×C59#120
hypercenter#2734D59
hypocenterC59#7766
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2734

Complements

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

NH ≅ G/Ntype
211. C59#7766semidirect

Maximal subgroups

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

subgroupindex
#214254292
#214253422
#214252372
#214219222
#214219192
C59×#27342
#776659