Finite Group Databasebeta

← #28477231

Subgroups — #28477231

Order 15104.

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

normal subgroups only

This group has 394 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#21432455C211yesmaximal, characteristic
2#21424238C211yesmaximal, characteristic
3#21423843C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#1271C211yesmaximal, characteristic
8C2×#14273717—21no—
9C2×#14273637—21no—
10#16837301C411yescharacteristic
11#16837300C2211yescharacteristic
12#16837299—21no—
13#16837298C411yescharacteristic
14#16837297—21no—
15#16837271C411yescharacteristic
16#16837271C411yescharacteristic
17#16837266—21no—
18C42×Dic59C2211yescharacteristic
19#16837157C2211yescharacteristic
20#16837157C2211yescharacteristic
21#16837156—21no—
22#16837156—21no—
23#16837156—21no—
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29#14273717—42no—
30#14273717—42no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59C2×C411yescharacteristic
33C2×C4⋊Dic59C2×C411yescharacteristic
34C2×Dic59⋊C4—21no—
35C2×Dic59⋊C4—21no—
36C2×Dic59⋊C4—21no—
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×Dic59⋊C4—21no—
40C2×C4×Dic59C2×C411yescharacteristic
41C2×C4×Dic59C2×C411yescharacteristic
42C2×C4×Dic59D411yescharacteristic
43C2×C4×Dic59D411yescharacteristic
44C2×C4×Dic59D411yescharacteristic
45C2×C4×Dic59D411yescharacteristic
46#14273637—24no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C22×C8×C59—21no—
51C22×C8×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59C2×C411yescharacteristic
54C2×C4⋊C4×C59C2×C411yescharacteristic
55C2×C42×C59C2311yescharacteristic
56#95×C59—21no—
57C22×C4×C59—21no—
58C22×C4×C59—21no—
59C22×C4×C59C22×C411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×Dic59—21no—
63C22×Dic59—21no—
64C22×Dic59C22⋊C411yescharacteristic
65C22×Dic59C22⋊C411yescharacteristic
66C22×Dic59C22⋊C411yescharacteristic
67C22×Dic59C22⋊C411yescharacteristic
68C2×C8×C59—22no—
69C2×C8×C59—41no—
70C2×C8×C59—41no—
71C2×C8×C59—41no—
72C2×C8×C59—41no—
73C2×C8×C59—41no—
74C4⋊C4×C59—21no—
75C4⋊C4×C59—21no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C42×C59—41no—
80C4⋊Dic59—21no—
81C4⋊Dic59—21no—
82C4⋊Dic59—42no—
83C4⋊Dic59—41no—
84Dic59⋊C4—42no—
85Dic59⋊C4—42no—
86Dic59⋊C4—42no—
87Dic59⋊C4—42no—
88Dic59⋊C4—41no—
89Dic59⋊C4—41no—
90Dic59⋊C4—42no—
91C4×Dic59—21no—
92C4×Dic59—21no—
93C4×Dic59—21no—
94C4×Dic59—21no—
95C4×Dic59—21no—
96C4×Dic59—21no—
97C4×Dic59—22no—
98C4×Dic59—22no—
99C4×Dic59—41no—
100C2×C59⋊C8—22no—
101C2×C59⋊C8—41no—
102C2×C59⋊C8—41no—
103C2×C59⋊C8—41no—
104C2×C59⋊C8—41no—
105C2×C59⋊C8—41no—
106C23×C59C2×C22⋊C411yescharacteristic
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—41no—
114C2×C4×C59—41no—
115C2×C4×C59—41no—
116C2×C4×C59—41no—
117C2×C4×C59—41no—
118C2×C4×C59—41no—
119C2×C4×C59#13111yescharacteristic
120C2×C4×C59#13111yescharacteristic
121C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C59#13711yescharacteristic
124C2×C4×C59#13711yescharacteristic
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59#10112yes—
142C2×Dic59#10412yes—
143C8×C59—42no—
144C8×C59—81no—
145C59⋊C8—42no—
146C59⋊C8—81no—
147#7700—591nomaximal, Sylow
148C22×C59#40811yescharacteristic
149C22×C59#41011yescharacteristic
150C22×C59C2×#10111yescharacteristic
151C22×C59#41811yescharacteristic
152C22×C59#41911yescharacteristic
153C22×C59C2×#10411yescharacteristic
154C22×C59#42111yescharacteristic
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—81no—
162C4×C59—81no—
163Dic59—22no—
164Dic59—22no—
165Dic59—41no—
166Dic59—41no—
167Dic59—81no—
168Dic59—81no—
169#2859—591no—
170#1839—591no—
171#1745—591no—
172#1271—591no—
173#1271—591no—
174#1271—591no—
175#1271D5911yescharacteristic
176C2×C59#147011yescharacteristic
177C2×C59#148511yescharacteristic
178C2×C59#149611yescharacteristic
179C2×C59#150511yescharacteristic
180C2×C59#151511yescharacteristic
181C2×C59#152811yescharacteristic
182C2×C59#155611yescharacteristic
183C2×#125—1181no—
184C2×#97—1181no—
185#389—591no—
186#389—591no—
187#389—591no—
188#389—1181no—
189#389—1181no—
190#389C2×D5911yescharacteristic
191#384—591no—
192#384—591no—
193#382—1181no—
194C43—591no—
195#336—591no—
196#336—591no—
197#336—1181no—
198#336—1181no—
199#336—1181no—
200#336C2×D5911yescharacteristic
201#336C2×D5911yescharacteristic
202C59#770011yescharacteristic, complemented, Sylow
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—1181no—
206C22×C8—1181no—
207#125—2362no—
208#125—2362no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—591no—
211C2×C4⋊C4—591no—
212C2×C4⋊C4—1181no—
213C2×C4⋊C4—1181no—
214C2×C4⋊C4—1181no—
215C2×C4⋊C4—1181no—
216C2×C4⋊C4—1181no—
217C2×C4⋊C4—1181no—
218C2×C4⋊C4—1181no—
219C2×C4⋊C4C4×D5911yescharacteristic
220C2×C4⋊C4C4×D5911yescharacteristic
221C2×C42—591no—
222C2×C42—591no—
223C2×C42—591no—
224C2×C42—591no—
225C2×C42—591no—
226C2×C42—591no—
227C2×C42C22×D5911yescharacteristic
228#97—1184no—
229#95—21no—
230#95—1181no—
231#95—1181no—
232#95—1181no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—591no—
236C22×C4—591no—
237C22×C4—591no—
238C22×C4—591no—
239C22×C4—1181no—
240C22×C4—1181no—
241C22×C4C2×C4×D5911yescharacteristic
242C22×C4D4×D5911yescharacteristic
243C22×C4D4×D5911yescharacteristic
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—1182no—
251C2×C8—2361no—
252C2×C8—2361no—
253C2×C8—2361no—
254C2×C8—2361no—
255C2×C8—2361no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—1181no—
262C4⋊C4—1181no—
263C4⋊C4—2361no—
264C4⋊C4—2362no—
265C4⋊C4—2362no—
266C4⋊C4—2362no—
267C4⋊C4—2362no—
268C4⋊C4—2362no—
269C4⋊C4—2362no—
270C4⋊C4—2361no—
271C4⋊C4—2361no—
272C42—41no—
273C42—1182no—
274C42—1182no—
275C42—1181no—
276C42—1181no—
277C42—1181no—
278C42—1181no—
279C42—1181no—
280C42—1181no—
281C42—2361no—
282C23C22⋊C4×D5911yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—592no—
296C2×C4—592no—
297C2×C4—1181no—
298C2×C4—1181no—
299C2×C4—1181no—
300C2×C4—1181no—
301C2×C4—1181no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—1181no—
305C2×C4—1181no—
306C2×C4—1181no—
307C2×C4—2361no—
308C2×C4—2361no—
309C2×C4—2361no—
310C2×C4—2361no—
311C2×C4—2361no—
312C2×C4—2361no—
313C2×C4#1427373311yescharacteristic
314C2×C4#1427373511yescharacteristic
315C2×C4#1427375111yescharacteristic
316C2×C4#1427375411yescharacteristic
317C2×C4#1427375611yescharacteristic
318C2×C4#1427375911yescharacteristic
319C8—42no—
320C8—81no—
321C8—4721no—
322C8—2362no—
323C22#1683736711yescharacteristic
324C22#1683737411yescharacteristic
325C22#101×D5911yescharacteristic
326C22#1683740511yescharacteristic
327C22#1683740911yescharacteristic
328C22#104×D5911yescharacteristic
329C22#1683741711yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—1182no—
339C4—1182no—
340C4—4721no—
341C4—4721no—
342C4—2361no—
343C4—2361no—
344C2#2142245011yescharacteristic
345C2#2142251511yescharacteristic
346C2#2142256311yescharacteristic
347C2#2142260211yescharacteristic
348C2#2142264511yescharacteristic
349C2#2142269611yescharacteristic
350C2#2142281111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1271C2
socle, prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1271D59
hypocenterC59#7700
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
202. C59#7700semidirect

Maximal subgroups

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

subgroupindex
#214324552
#214242382
#214238432
#214219202
#214219192
#214219182
C59×#12712
#770059