Finite Group Databasebeta

← #28477699

Subgroups — #28477699

Order 15104.

436 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 91 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#21425424C211yesmaximal, characteristic
2#21425237C211yesmaximal, characteristic
3#21425195C211yesmaximal, characteristic
4#21421922C211yesmaximal, characteristic
5#21421922C211yesmaximal, characteristic
6#21421919C211yesmaximal, characteristic
7C59×#2806C211yesmaximal, characteristic
8C22×#11745672—21no—
9C2×#14273727C2211yescharacteristic
10C2×#14273660—21no—
11C2×#14273651—21no—
12C2×#14273650—21no—
13#16837164—21no—
14#16837164—21no—
15#16837157C2211yescharacteristic
16#16837157C2211yescharacteristic
17#16837157C2211yescharacteristic
18C59×#398—21no—
19C59×#398—21no—
20C59×#395—21no—
21C59×#391—21no—
22C59×#391C2211yescharacteristic
23C59×#391C2211yescharacteristic
24C59×#389—21no—
25C59×#389C2211yescharacteristic
26C59×#387—21no—
27C22×Dic118—21no—
28C2×#11745672—42no—
29C2×#11745672—42no—
30C2×#11745672—42no—
31C22×C59⋊C8—21no—
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34#14273727—42no—
35C2×C4⋊Dic59—21no—
36C2×C4⋊Dic59—21no—
37#14273660—42no—
38#14273651—42no—
39#14273650—42no—
40C22×Q8×C59D411yescharacteristic
41C22×Q8×C59D411yescharacteristic
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×C42×C59—21no—
52C2×C42×C59C2311yescharacteristic
53#95×C59—21no—
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—21no—
63C2×Q8×C59—21no—
64C2×Q8×C59—41no—
65C2×Q8×C59—41no—
66C2×Q8×C59—41no—
67C2×Q8×C59—41no—
68C2×Q8×C59Q1612yescomplemented
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59C2×D411yescharacteristic
76C22×C4×C59C2×D411yescharacteristic
77C22×C4×C59C2×D411yescharacteristic
78C22×Dic59—41no—
79C2×Dic118—22no—
80C2×Dic118—41no—
81C2×Dic118—41no—
82C2×Dic118—41no—
83C2×Dic118—41no—
84C2×Dic118—41no—
85C4⋊C4×C59—21no—
86C4⋊C4×C59—41no—
87C4⋊C4×C59—41no—
88C4⋊C4×C59—41no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—41no—
91C4⋊C4×C59—81no—
92C4⋊C4×C59—81no—
93C4⋊C4×C59—81no—
94C4⋊C4×C59—81no—
95C4⋊C4×C59Q1612yescomplemented
96C42×C59—41no—
97C42×C59—81no—
98#11745672—48no—
99C4⋊Dic59—22no—
100C4⋊Dic59—22no—
101C4⋊Dic59—41no—
102C4⋊Dic59—41no—
103C2×C59⋊C8—22no—
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—
112C23×C59#12011yescharacteristic
113Q8×C59—42no—
114Q8×C59—42no—
115Q8×C59—81no—
116Q8×C59—81no—
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—41no—
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×Q1611yescharacteristic
142C2×C4×C59C2×Q1611yescharacteristic
143C2×C4×C59#13511yescharacteristic
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—42no—
156C59⋊C8—81no—
157#7784—591nomaximal, Sylow
158C22×C59#44911yescharacteristic
159C22×C59#45111yescharacteristic
160C22×C59#45111yescharacteristic
161C22×C59#45311yescharacteristic
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—81no—
174C4×C59—81no—
175C4×C59—81no—
176C4×C59—81no—
177Dic59—82no—
178#2806D5911yescharacteristic
179#2057—591no—
180#2024—591no—
181#2016—591no—
182#1272—591no—
183#1272—591no—
184#1271—591no—
185C2×C59#160011yescharacteristic
186C2×C59#160211yescharacteristic
187C2×C59#160511yescharacteristic
188C2×C59#163311yescharacteristic
189C2×C59#164411yescharacteristic
190C2×C59#164811yescharacteristic
191C2×C59#166111yescharacteristic
192C22×Q16—1181no—
193C2×C4⋊Q8—591no—
194C2×#107—1181no—
195C2×#103—1181no—
196C2×#103—1181no—
197#398—21no—
198#398—21no—
199#395—21no—
200#391—21no—
201#391C2×D5911yescharacteristic
202#391C2×D5911yescharacteristic
203#389—21no—
204#389C2×D5911yescharacteristic
205#387—21no—
206#340—1181no—
207#340—1181no—
208#336—591no—
209#336—591no—
210#336—591no—
211C59#778411yescharacteristic, complemented, Sylow
212C22×Q8—1181no—
213C22×Q8C22⋊D5911yescharacteristic
214C22×Q8C22⋊D5911yescharacteristic
215C2×Q16—2362no—
216C2×Q16—2362no—
217C2×Q16—2362no—
218C22×C8—1181no—
219C22×C8—1181no—
220C22×C8—1181no—
221C4⋊Q8—2362no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—1181no—
228C2×C4⋊C4—1181no—
229C2×C4⋊C4C22⋊D5911yescharacteristic
230C2×C4⋊C4C22⋊D5911yescharacteristic
231C2×C4⋊C4C22⋊D5911yescharacteristic
232C2×C4⋊C4C22⋊D5911yescharacteristic
233C2×C42—21no—
234C2×C42C22×D5911yescharacteristic
235#107—2362no—
236#103—2362no—
237#103—2362no—
238#95—21no—
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—21no—
248C2×Q8—21no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—1182no—
254C2×Q8—2361no—
255C2×Q8—2361no—
256C2×Q8—2361no—
257C2×Q8—2361no—
258C2×Q8—2361no—
259C2×Q8#1174567212yescomplemented
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—2361no—
267C22×C4C2×C22⋊D5911yescharacteristic
268C22×C4C2×C22⋊D5911yescharacteristic
269C22×C4C2×C22⋊D5911yescharacteristic
270Q16—2368no—
271C2×C8—1182no—
272C2×C8—1182no—
273C2×C8—2361no—
274C2×C8—2361no—
275C2×C8—2361no—
276C2×C8—2361no—
277C2×C8—2361no—
278C2×C8—2361no—
279C2×C8—2361no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C4⋊C4—1182no—
291C4⋊C4—1182no—
292C4⋊C4—2361no—
293C4⋊C4—2361no—
294C4⋊C4#1174567212yescomplemented
295C42—41no—
296C42—81no—
297C23#1427369611yescharacteristic
298Q8—42no—
299Q8—42no—
300Q8—81no—
301Q8—81no—
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—41no—
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×#1174567211yescharacteristic
334C2×C4C2×#1174567211yescharacteristic
335C2×C4#1427374711yescharacteristic
336C2×C4#1427375211yescharacteristic
337C2×C4#1427375811yescharacteristic
338C2×C4#1427375811yescharacteristic
339C8—4721no—
340C8—2362no—
341C8—2362no—
342C22#1683754711yescharacteristic
343C22#1683755811yescharacteristic
344C22#1683755811yescharacteristic
345C22#1683757011yescharacteristic
346C22#1683758011yescharacteristic
347C22#1683758511yescharacteristic
348C22#1683758911yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—42no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—4722no—
362C2#2142304211yescharacteristic
363C2#2142305311yescharacteristic
364C2#2142307011yescharacteristic
365C2#2142323611yescharacteristic
366C2#2142331011yescharacteristic
367C2#2142333811yescharacteristic
368C2#2142341311yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2806C2
socle, prime radicalC23×C59#120
hypercenter#2806D59
hypocenterC59#7784
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2806

Complements

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

NH ≅ G/Ntype
68. C2×Q8×C59Q16semidirect
95. C4⋊C4×C59Q16semidirect
211. C59#7784semidirect
259. C2×Q8#11745672semidirect
294. C4⋊C4#11745672semidirect

Maximal subgroups

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

subgroupindex
#214254242
#214252372
#214251952
#214219222
#214219192
C59×#28062
#778459