Finite Group Databasebeta

← #28477690

Subgroups — #28477690

Order 15104.

424 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 81 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#21432046C211yesmaximal, characteristic
2#21425426C211yesmaximal, characteristic
3#21425196C211yesmaximal, characteristic
4#21421921C211yesmaximal, characteristic
5#21421920C211yesmaximal, characteristic
6#21421919C211yesmaximal, characteristic
7C59×#2057C211yesmaximal, characteristic
8C22×#11745672—21no—
9C2×#14273658—21no—
10C2×#14273651—21no—
11#16837344—21no—
12#16837340—21no—
13#16837322—21no—
14#16837308C2211yescharacteristic
15#16837300C2211yescharacteristic
16#16837297—21no—
17#16837288—21no—
18#16837287—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C2×C4⋊Q8×C59C2211yescharacteristic
23C2×#107×C59—21no—
24C59×#389C2211yescharacteristic
25C59×#340—21no—
26C59×#336C2211yescharacteristic
27C22×Dic118D411yescharacteristic
28C2×#11745672—42no—
29C2×#11745672—42no—
30C2×#11745672—42no—
31C22×C59⋊C8—21no—
32C22×C59⋊C8—21no—
33C2×C4⋊Dic59D411yescharacteristic
34C2×C4⋊Dic59D411yescharacteristic
35C2×C4⋊Dic59D411yescharacteristic
36C2×Dic59⋊C4—21no—
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×C4×Dic59—21no—
40#14273658—42no—
41#14273651—42no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
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#107×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×Dic118—21no—
78C2×Dic118—21no—
79C2×Dic118—41no—
80C2×Dic118—41no—
81C2×C8×C59—22no—
82C2×C8×C59—41no—
83C2×C8×C59—41no—
84C4⋊C4×C59—22no—
85C4⋊C4×C59—22no—
86C4⋊C4×C59—21no—
87C4⋊C4×C59—21no—
88C4⋊C4×C59—41no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—41no—
91C4⋊C4×C59—41no—
92C4⋊C4×C59—41no—
93C42×C59—41no—
94#11745672—48no—
95C4⋊Dic59—21no—
96C4⋊Dic59—41no—
97C4⋊Dic59—41no—
98C4⋊Dic59Q1612yescomplemented
99Dic59⋊C4—41no—
100Dic59⋊C4—41no—
101Dic59⋊C4—81no—
102Dic59⋊C4—81no—
103C4×Dic59—81no—
104C2×C59⋊C8—22no—
105C2×C59⋊C8—22no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8—41no—
108C2×C59⋊C8—41no—
109C2×C59⋊C8—41no—
110C23×C59#12011yescharacteristic
111Q8×C59—42no—
112Q8×C59—42no—
113Q8×C59—81no—
114Q8×C59—81no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—41no—
122C2×C4×C59—41no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—42no—
128C2×C4×C59—81no—
129C2×C4×C59—81no—
130C2×C4×C59C2×Q1611yescharacteristic
131C2×C4×C59#13511yescharacteristic
132C2×C4×C59#13511yescharacteristic
133C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C59#13711yescharacteristic
135C2×C4×C59#13711yescharacteristic
136C2×Dic59—22no—
137C2×Dic59—41no—
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—
148Dic118—42no—
149Dic118—81no—
150C8×C59—42no—
151C59⋊C8—42no—
152C59⋊C8—42no—
153#7783—591nomaximal, Sylow
154C22×C59#44911yescharacteristic
155C22×C59#45111yescharacteristic
156C22×C59#45211yescharacteristic
157C22×C59#45311yescharacteristic
158C22×C59#45611yescharacteristic
159C22×C59#45611yescharacteristic
160C22×C59B(4,𝔽2)11yescharacteristic
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—81no—
168C4×C59—82no—
169C4×C59—81no—
170Dic59—42no—
171Dic59—81no—
172Dic59—81no—
173Dic59—81no—
174#2805—591no—
175#2058—591no—
176#2057D5911yescharacteristic
177#2016—591no—
178#1272—591no—
179#1271—591no—
180#1271—591no—
181C2×C59#160011yescharacteristic
182C2×C59#160311yescharacteristic
183C2×C59#160511yescharacteristic
184C2×C59#163211yescharacteristic
185C2×C59#164811yescharacteristic
186C2×C59#165211yescharacteristic
187C2×C59#166011yescharacteristic
188C22×Q16—1181no—
189C2×C4⋊Q8C2×D5911yescharacteristic
190C2×#107—21no—
191C2×#106—1181no—
192C2×#103—1181no—
193#400—1181no—
194#400—1181no—
195#395—1181no—
196#391—591no—
197#389—591no—
198#389—1181no—
199#389C2×D5911yescharacteristic
200#387—1181no—
201#387—1181no—
202#340—21no—
203#340—1181no—
204#336—591no—
205#336—591no—
206#336C2×D5911yescharacteristic
207C59#778311yescharacteristic, complemented, Sylow
208C22×Q8—21no—
209C22×Q8—591no—
210C2×Q16—2362no—
211C2×Q16—2362no—
212C2×Q16—2362no—
213C22×C8—21no—
214C22×C8—1181no—
215C22×C8—1181no—
216C4⋊Q8—42no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—591no—
221C2×C4⋊C4—591no—
222C2×C4⋊C4—591no—
223C2×C4⋊C4—1181no—
224C2×C4⋊C4—1181no—
225C2×C4⋊C4—1181no—
226C2×C4⋊C4C22⋊D5911yescharacteristic
227C2×C4⋊C4C22⋊D5911yescharacteristic
228C2×C42—1181no—
229C2×C42C22×D5911yescharacteristic
230#107—42no—
231#106—2362no—
232#103—2362no—
233#95—21no—
234#95—1181no—
235#95—1181no—
236#95—1181no—
237#95—1181no—
238#95—1181no—
239#95—1181no—
240#95—1181no—
241#95—1181no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—1181no—
249C2×Q8—1181no—
250C2×Q8—2361no—
251C2×Q8—2361no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4—1181no—
258C22×C4—1181no—
259C22×C4D4×D5911yescharacteristic
260C22×C4D4×D5911yescharacteristic
261C22×C4C2×C22⋊D5911yescharacteristic
262Q16—2368no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—1182no—
267C2×C8—1182no—
268C2×C8—2361no—
269C2×C8—2361no—
270C2×C8—2361no—
271C2×C8—2361no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—592no—
282C4⋊C4—1181no—
283C4⋊C4—4721no—
284C4⋊C4—4721no—
285C4⋊C4—2361no—
286C4⋊C4—2361no—
287C4⋊C4—2361no—
288C4⋊C4—2361no—
289C42—41no—
290C42—4721no—
291C23#1427369511yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296Q8—4721no—
297Q8—2362no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—1182no—
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×C4—2361no—
324C2×C4—2361no—
325C2×C4Q16×D5911yescharacteristic
326C2×C4#1427374611yescharacteristic
327C2×C4#1427374711yescharacteristic
328C2×C4#1427375111yescharacteristic
329C2×C4#1427375811yescharacteristic
330C2×C4#1427375911yescharacteristic
331C8—42no—
332C8—2362no—
333C8—2362no—
334C22#1683754411yescharacteristic
335C22#1683755611yescharacteristic
336C22#1683756211yescharacteristic
337C22#1683756811yescharacteristic
338C22#1683758311yescharacteristic
339C22#1683758411yescharacteristic
340C22#1683758811yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—81no—
348C4—81no—
349C4—82no—
350C4—4721no—
351C4—4721no—
352C4—4721no—
353C4—2362no—
354C2#2142303911yescharacteristic
355C2#2142305711yescharacteristic
356C2#2142306811yescharacteristic
357C2#2142322911yescharacteristic
358C2#2142333511yescharacteristic
359C2#2142336511yescharacteristic
360C2#2142340611yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2057C2
socle, prime radicalC23×C59#120
hypercenter#2057D59
hypocenterC59#7783
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
98. C4⋊Dic59Q16semidirect
207. C59#7783semidirect

Maximal subgroups

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

subgroupindex
#214320462
#214254262
#214251962
#214219212
#214219202
#214219192
C59×#20572
#778359