Finite Group Databasebeta

← #28477635

Subgroups — #28477635

Order 15104.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#21432087C211yesmaximal, characteristic
2#21425426C211yesmaximal, characteristic
3#21425339C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#2057C211yesmaximal, characteristic
8C2×#14273658—21no—
9C2×#14273651—21no—
10C2×#14273651—21no—
11#16837342—21no—
12#16837341—21no—
13#16837340—21no—
14#16837300C2211yescharacteristic
15#16837300C2211yescharacteristic
16#16837289—21no—
17#16837288—21no—
18#16837283—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C2×C4⋊Q8×C59C2211yescharacteristic
23C2×#107×C59—21no—
24C59×#389C2211yescharacteristic
25C59×#340—21no—
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29C2×C4⋊Dic59D411yescharacteristic
30C2×C4⋊Dic59D411yescharacteristic
31C2×C4⋊Dic59D411yescharacteristic
32C2×C4⋊Dic59D411yescharacteristic
33C2×Dic59⋊C4—21no—
34C2×Dic59⋊C4—21no—
35C2×C4×Dic59—21no—
36#14273658—42no—
37#14273651—42no—
38#14273651—42no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C22×Q8×C59—21no—
49C22×C8×C59—21no—
50C4⋊Q8×C59—42no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C4⋊C4×C59D411yescharacteristic
56C2×C42×C59C2311yescharacteristic
57#107×C59—42no—
58#95×C59—21no—
59C2×Q8×C59—22no—
60C2×Q8×C59—41no—
61C2×Q8×C59—41no—
62C2×Q8×C59—41no—
63C2×Q8×C59—41no—
64C2×Q8×C59—41no—
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—41no—
68C22×C4×C59C2×D411yescharacteristic
69C22×C4×C59C2×D411yescharacteristic
70C22×C4×C59C2×D411yescharacteristic
71C22×Dic59—21no—
72C22×Dic59—21no—
73C22×Dic59—21no—
74C22×Dic59—21no—
75C2×C8×C59—22no—
76C2×C8×C59—41no—
77C2×C8×C59—41no—
78C4⋊C4×C59—22no—
79C4⋊C4×C59—22no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59—41no—
87C42×C59—41no—
88C4⋊Dic59—21no—
89C4⋊Dic59—21no—
90C4⋊Dic59—21no—
91C4⋊Dic59—21no—
92C4⋊Dic59—41no—
93C4⋊Dic59—41no—
94Dic59⋊C4—41no—
95Dic59⋊C4—41no—
96Dic59⋊C4—41no—
97Dic59⋊C4—41no—
98C4×Dic59—81no—
99C2×C59⋊C8—22no—
100C2×C59⋊C8—41no—
101C2×C59⋊C8—41no—
102C2×C59⋊C8—41no—
103C2×C59⋊C8—41no—
104C2×C59⋊C8—41no—
105C23×C59#12011yescharacteristic
106Q8×C59—42no—
107Q8×C59—42no—
108Q8×C59—81no—
109Q8×C59—81no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—41no—
117C2×C4×C59—41no—
118C2×C4×C59—41no—
119C2×C4×C59—41no—
120C2×C4×C59—41no—
121C2×C4×C59—41no—
122C2×C4×C59—42no—
123C2×C4×C59—81no—
124C2×C4×C59—81no—
125C2×C4×C59#13511yescharacteristic
126C2×C4×C59#13511yescharacteristic
127C2×C4×C59#13511yescharacteristic
128C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C59#13711yescharacteristic
130C2×C4×C59#13711yescharacteristic
131C2×Dic59—41no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C8×C59—42no—
144C59⋊C8—42no—
145C59⋊C8—81no—
146#7775—591nomaximal, Sylow
147C22×C59#44911yescharacteristic
148C22×C59#45211yescharacteristic
149C22×C59#45211yescharacteristic
150C22×C59#45411yescharacteristic
151C22×C59#45611yescharacteristic
152C22×C59#45611yescharacteristic
153C22×C59B(4,𝔽2)11yescharacteristic
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—81no—
161C4×C59—82no—
162C4×C59—81no—
163Dic59—81no—
164Dic59—81no—
165Dic59—81no—
166Dic59—81no—
167#2810—591no—
168#2058—591no—
169#2057D5911yescharacteristic
170#2043—591no—
171#1271—591no—
172#1271—591no—
173#1271—591no—
174C2×C59#159711yescharacteristic
175C2×C59#160311yescharacteristic
176C2×C59#160311yescharacteristic
177C2×C59#163811yescharacteristic
178C2×C59#165011yescharacteristic
179C2×C59#165211yescharacteristic
180C2×C59#166311yescharacteristic
181C2×C4⋊Q8C2×D5911yescharacteristic
182C2×#107—21no—
183C2×#106—1181no—
184C2×#103—1181no—
185C2×#103—1181no—
186#400—1181no—
187#400—1181no—
188#400—1181no—
189#389—591no—
190#389—591no—
191#389C2×D5911yescharacteristic
192#387—1181no—
193#387—1181no—
194#387—1181no—
195#340—21no—
196#340—1181no—
197#336—591no—
198#336—591no—
199#336C2×D5911yescharacteristic
200C59#777511yescharacteristic, complemented, Sylow
201C22×Q8—21no—
202C22×C8—21no—
203C22×C8—1181no—
204C22×C8—1181no—
205C4⋊Q8—42no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—591no—
210C2×C4⋊C4—591no—
211C2×C4⋊C4—591no—
212C2×C4⋊C4—591no—
213C2×C4⋊C4—1181no—
214C2×C4⋊C4—1181no—
215C2×C4⋊C4C22⋊D5911yescharacteristic
216C2×C4⋊C4C22⋊D5911yescharacteristic
217C2×C42—1181no—
218C2×C42C22×D5911yescharacteristic
219#107—42no—
220#106—2362no—
221#103—2362no—
222#103—2362no—
223#95—21no—
224#95—1181no—
225#95—1181no—
226#95—1181no—
227#95—1181no—
228#95—1181no—
229#95—1181no—
230#95—1181no—
231#95—1181no—
232#95—1181no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—1181no—
243C22×C4—1181no—
244C22×C4—1181no—
245C22×C4—1181no—
246C22×C4D4×D5911yescharacteristic
247C22×C4D4×D5911yescharacteristic
248C22×C4C2×C22⋊D5911yescharacteristic
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—1182no—
253C2×C8—2361no—
254C2×C8—2361no—
255C2×C8—2361no—
256C2×C8—2361no—
257C2×C8—2361no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—2361no—
272C4⋊C4—2361no—
273C4⋊C4—2361no—
274C4⋊C4—2361no—
275C4⋊C4—2361no—
276C4⋊C4—2361no—
277C42—41no—
278C42—4721no—
279C23#1427369511yescharacteristic
280Q8—42no—
281Q8—42no—
282Q8—81no—
283Q8—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—2361no—
300C2×C4—2361no—
301C2×C4—2361no—
302C2×C4—2361no—
303C2×C4—2361no—
304C2×C4—2361no—
305C2×C4—2361no—
306C2×C4—2361no—
307C2×C4—2361no—
308C2×C4—2361no—
309C2×C4—2361no—
310C2×C4—2361no—
311C2×C4#1427374611yescharacteristic
312C2×C4#1427374711yescharacteristic
313C2×C4#1427375011yescharacteristic
314C2×C4#1427375111yescharacteristic
315C2×C4#1427375811yescharacteristic
316C2×C4#1427375911yescharacteristic
317C8—42no—
318C8—4721no—
319C8—2362no—
320C22#1683754411yescharacteristic
321C22#1683756211yescharacteristic
322C22#1683756311yescharacteristic
323C22#1683757311yescharacteristic
324C22#1683758311yescharacteristic
325C22#1683758411yescharacteristic
326C22#1683758811yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4—81no—
335C4—82no—
336C4—4721no—
337C4—4721no—
338C4—4721no—
339C4—4721no—
340C2#2142302211yescharacteristic
341C2#2142305711yescharacteristic
342C2#2142305811yescharacteristic
343C2#2142326711yescharacteristic
344C2#2142334911yescharacteristic
345C2#2142336511yescharacteristic
346C2#2142342311yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2057C2
socle, prime radicalC23×C59#120
hypercenter#2057D59
hypocenterC59#7775
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
200. C59#7775semidirect

Maximal subgroups

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

subgroupindex
#214320872
#214254262
#214253392
#214219202
#214219192
#214219182
C59×#20572
#777559