Finite Group Databasebeta

← #28476705

Subgroups — #28476705

Order 15104.

568 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426577C211yesmaximal, characteristic
2#21424163C211yesmaximal, characteristic
3#336×D59C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic, complemented
5#21421919C211yesmaximal, characteristic, complemented
6#21421918C211yesmaximal, characteristic, complemented
7C59×#1271C211yesmaximal, characteristic, complemented
8C22×C8×D59—21no—
9C2×#14273685C411yescharacteristic
10C2×#14273685C411yescharacteristic
11C2×C42×D59C2211yescharacteristic
12C2×(C2×D59)⋊C8—21no—
13#16837301C411yescharacteristic
14#16837300C2211yescharacteristic
15#16837298C411yescharacteristic
16#16837276—21no—
17#16837273—21no—
18C4⋊C4×Dic59—21no—
19#16837253—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22#16837156—21no—
23#16837156—21no—
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×C4×D59C2×C411yescharacteristic
28C22×C4×D59D411yescharacteristic
29C22×C4×D59D411yescharacteristic
30C22×C59⋊C8—21no—
31C22×C59⋊C8—21no—
32C2×C8×D59—24no—
33C2×C8×D59—42no—
34C2×C8×D59—42no—
35#14273685—22no—
36#14273685—42no—
37#14273685C814yescomplemented
38C2×C4⋊Dic59—21no—
39C2×C4⋊Dic59C2×C411yescharacteristic
40C2×C4⋊Dic59C2×C411yescharacteristic
41C2×Dic59⋊C4—21no—
42C2×Dic59⋊C4—21no—
43C2×(C2×D59)⋊C4—21no—
44C2×(C2×D59)⋊C4—21no—
45C2×C4×Dic59—21no—
46C2×C4×Dic59—21no—
47C2×C4×Dic59C2×C411yescharacteristic
48C2×C4×Dic59D411yescharacteristic
49C2×C4×Dic59D411yescharacteristic
50C42×D59—42no—
51(C2×D59)⋊C8—42no—
52C59⋊#95—21no—
53C59⋊#95—21no—
54C59⋊#95—21no—
55C22×C8×C59—21no—
56C22×C8×C59—21no—
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59C2×C411yescharacteristic
59C2×C4⋊C4×C59C2×C411yescharacteristic
60C2×C42×C59C2311yescharacteristic
61#95×C59—21no—
62C23×D59C22⋊C411yescharacteristic
63C22×C4×C59—21no—
64C22×C4×C59—21no—
65C22×C4×C59C22×C411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×Dic59—21no—
69C22×Dic59—21no—
70C22×Dic59C22⋊C411yescharacteristic
71C22×Dic59C22⋊C411yescharacteristic
72C22×Dic59C22⋊C411yescharacteristic
73C2×C4×D59—22no—
74C2×C4×D59—22no—
75C2×C4×D59—22no—
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59—22no—
79C2×C4×D59—22no—
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82C2×C4×D59—41no—
83C2×C4×D59C2×C812yes—
84C2×C4×D59M1612yes—
85C2×C8×C59—22no—
86C2×C8×C59—41no—
87C2×C8×C59—41no—
88C2×C8×C59—41no—
89C2×C8×C59—41no—
90C2×C8×C59—41no—
91C4⋊C4×C59—21no—
92C4⋊C4×C59—41no—
93C4⋊C4×C59—41no—
94C4⋊C4×C59—41no—
95C4⋊C4×C59C2×C812yescomplemented
96C42×C59—41no—
97(C2×D59)⋊C4—24no—
98(C2×D59)⋊C4—42no—
99C4⋊Dic59—21no—
100C4⋊Dic59—42no—
101C4⋊Dic59—41no—
102C4⋊Dic59C2×C812yescomplemented
103Dic59⋊C4—41no—
104Dic59⋊C4—41no—
105Dic59⋊C4—42no—
106C4×Dic59—24no—
107C4×Dic59—41no—
108C4×Dic59—41no—
109C4×Dic59—41no—
110C4×Dic59—42no—
111C2×C59⋊C8—22no—
112C2×C59⋊C8—41no—
113C2×C59⋊C8—41no—
114C2×C59⋊C8—41no—
115C2×C59⋊C8—41no—
116C2×C59⋊C8—41no—
117C8×D59—48no—
118C23×C59C2×C22⋊C411yescharacteristic
119C22×D59—21no—
120C22×D59—21no—
121C22×D59—21no—
122C22×D59—21no—
123C22×D59C22⋊C812yes—
124C22×D59#9912yes—
125C22×D59#10112yes—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—22no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59C22×C811yescharacteristic
139C2×C4×C59C2×M1611yescharacteristic
140C2×C4×C59#13511yescharacteristic
141C2×C4×C59#13511yescharacteristic
142C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C59#13711yescharacteristic
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—22no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152C2×Dic59—41no—
153C2×Dic59—41no—
154C2×Dic59—41no—
155C2×Dic59—41no—
156C2×Dic59—41no—
157C2×Dic59C22⋊C812yes—
158C2×Dic59#10412yes—
159C4×D59—24no—
160C4×D59—24no—
161C4×D59—24no—
162C4×D59—24no—
163C4×D59—42no—
164C4×D59—42no—
165C8×C59—42no—
166C8×C59—81no—
167C59⋊C8—42no—
168C59⋊C8—81no—
169#7579—591nomaximal, Sylow
170C22×C59C2×C22⋊C811yescharacteristic
171C22×C59C2×#9911yescharacteristic
172C22×C59C2×#10111yescharacteristic
173C22×C59#41611yescharacteristic
174C22×C59#41711yescharacteristic
175C22×C59C2×#10411yescharacteristic
176C22×C59#42111yescharacteristic
177C2×D59—22no—
178C2×D59—22no—
179C2×D59—22no—
180C2×D59—22no—
181C2×D59—22no—
182C2×D59—22no—
183C2×D59#32414yes—
184C4×C59—21no—
185C4×C59—21no—
186C4×C59—21no—
187C4×C59—21no—
188C4×C59—21no—
189C4×C59—21no—
190C4×C59—42no—
191C4×C59—81no—
192Dic59—22no—
193Dic59—22no—
194Dic59—42no—
195Dic59—41no—
196Dic59—81no—
197#2296—591no—
198#1817—591no—
199C2×#336—591no—
200#1271—591no—
201#1271—591no—
202#1271—591no—
203#1271D5911yescharacteristic, complemented
204C2×C59C2×#32411yescharacteristic
205C2×C59#147611yescharacteristic
206C2×C59#147711yescharacteristic
207C2×C59#150411yescharacteristic
208C2×C59#151611yescharacteristic
209C2×C59#153111yescharacteristic
210C2×C59#155211yescharacteristic
211D59—24no—
212C23×C8—1181no—
213C2×#117—591no—
214C2×#117—591no—
215C22×C42—591no—
216C2×C22⋊C8—1181no—
217#389—591no—
218#389—591no—
219#389—591no—
220#389C2×D5911yescharacteristic
221#385—1181no—
222#385—1181no—
223C4×C4⋊C4—1181no—
224C4×C4⋊C4—1181no—
225#336—591no—
226#336—591no—
227#336—1181no—
228#336—1181no—
229#336C2×D5911yescharacteristic
230#336C2×D5911yescharacteristic
231C59#757911yescharacteristic, complemented, Sylow
232C23×C4—591no—
233C23×C4—591no—
234C23×C4—591no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—1184no—
238C22×C8—1181no—
239C22×C8—1181no—
240C22×C8—2362no—
241C22×C8—2362no—
242#117—594no—
243#117—1182no—
244#117—2362no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—591no—
247C2×C4⋊C4—591no—
248C2×C4⋊C4—1181no—
249C2×C4⋊C4—1181no—
250C2×C4⋊C4—1181no—
251C2×C4⋊C4C4×D5911yescharacteristic
252C2×C4⋊C4C4×D5911yescharacteristic
253C2×C22⋊C4—1181no—
254C2×C22⋊C4—1181no—
255C2×C42—591no—
256C2×C42—591no—
257C2×C42—591no—
258C2×C42—1181no—
259C2×C42—1181no—
260C2×C42—2362no—
261C2×C42C22×D5911yescharacteristic
262C22⋊C8—2362no—
263#95—21no—
264#95—1181no—
265#95—1181no—
266#95—1181no—
267C24—591no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—591no—
271C22×C4—591no—
272C22×C4—592no—
273C22×C4—592no—
274C22×C4—591no—
275C22×C4—1182no—
276C22×C4—1182no—
277C22×C4—1182no—
278C22×C4—1182no—
279C22×C4—1182no—
280C22×C4—1181no—
281C22×C4—1181no—
282C22×C4—1181no—
283C22×C4—1181no—
284C22×C4—1181no—
285C22×C4—1181no—
286C22×C4—2361no—
287C22×C4C2×C4×D5911yescharacteristic
288C22×C4D4×D5911yescharacteristic
289C22×C4D4×D5911yescharacteristic
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—1182no—
297C2×C8—2368no—
298C2×C8—2361no—
299C2×C8—2361no—
300C2×C8—2361no—
301C2×C8—2361no—
302C2×C8—2361no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—592no—
308C4⋊C4—1181no—
309C4⋊C4—2361no—
310C4⋊C4—2362no—
311C4⋊C4—2362no—
312C4⋊C4—2361no—
313C4⋊C4—2361no—
314C4⋊C4C8×D5912yescomplemented
315C22⋊C4—1184no—
316C22⋊C4—2362no—
317C42—41no—
318C42—1184no—
319C42—2361no—
320C42—2361no—
321C42—2361no—
322C42—2362no—
323C23—592no—
324C23—592no—
325C23—592no—
326C23—1181no—
327C23—1181no—
328C23—1181no—
329C23—1181no—
330C23C22⋊C4×D5911yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—592no—
344C2×C4—592no—
345C2×C4—1184no—
346C2×C4—1184no—
347C2×C4—1184no—
348C2×C4—1184no—
349C2×C4—1181no—
350C2×C4—1181no—
351C2×C4—1181no—
352C2×C4—1181no—
353C2×C4—1181no—
354C2×C4—1181no—
355C2×C4—1182no—
356C2×C4—1181no—
357C2×C4—2362no—
358C2×C4—2362no—
359C2×C4—2361no—
360C2×C4—2361no—
361C2×C4—2361no—
362C2×C4—2361no—
363C2×C4—2361no—
364C2×C4C2×C8×D5911yescharacteristic
365C2×C4M16×D5911yescharacteristic
366C2×C4#1427374811yescharacteristic
367C2×C4#1427375011yescharacteristic
368C2×C4#1427375111yescharacteristic
369C2×C4#1427375611yescharacteristic
370C8—42no—
371C8—81no—
372C8—4721no—
373C8—2362no—
374C22—594no—
375C22—1182no—
376C22—1182no—
377C22—1182no—
378C22—1182no—
379C22—1182no—
380C22—1182no—
381C22C22⋊C8×D5911yescharacteristic
382C22#99×D5911yescharacteristic
383C22#101×D5911yescharacteristic
384C22#1683739711yescharacteristic
385C22#1683740011yescharacteristic
386C22#104×D5911yescharacteristic
387C22#1683741711yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—1182no—
397C4—1182no—
398C4—4721no—
399C4—2361no—
400C4—2362no—
401C2—1184no—
402C2#324×D5911yescharacteristic
403C2#2142247711yescharacteristic
404C2#2142248011yescharacteristic
405C2#2142259711yescharacteristic
406C2#2142265111yescharacteristic
407C2#2142270911yescharacteristic
408C2#2142279511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC2×C4×C59C22×C8
FrattiniC2×C42C22×D59
FittingC59×#1271C2
socleC23×C59C2×C22⋊C4
prime radicalC23×D59C22⋊C4
cosocleC2×C42×C59C23
hypercenter#1271D59
hypocenterC59#7579
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #21421920C2semidirect
5. #21421919C2semidirect
6. #21421918C2semidirect
7. C59×#1271C2semidirect
37. #14273685C8semidirect
95. C4⋊C4×C59C2×C8semidirect
102. C4⋊Dic59C2×C8semidirect
203. #1271D59semidirect
231. C59#7579semidirect
314. C4⋊C4C8×D59semidirect

Maximal subgroups

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

subgroupindex
#214265772
#214241632
#336×D592
#214219202
#214219192
#214219182
C59×#12712
#757959