Finite Group Databasebeta

← #28476767

Subgroups — #28476767

Order 15104.

566 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#389×D59C211yesmaximal, characteristic
2#21424163C211yesmaximal, characteristic
3#21424163C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic, complemented
5#21421919C211yesmaximal, characteristic, complemented
6#21421918C211yesmaximal, characteristic, complemented
7C59×#1271C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D59—21no—
9C2×C4⋊C4×D59C411yescharacteristic
10C2×C4⋊C4×D59C411yescharacteristic
11C2×C42×D59C2211yescharacteristic
12C2×(C2×D59)⋊C8—21no—
13C2×(C2×D59)⋊C8—21no—
14#16837301C411yescharacteristic
15#16837300C2211yescharacteristic
16#16837299—21no—
17#16837298C411yescharacteristic
18#16837297—21no—
19#95×D59—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22#16837156—21no—
23#16837156—21no—
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×C4×D59—21no—
28C22×C4×D59—21no—
29C22×C4×D59C2×C411yescharacteristic
30C22×C4×D59D411yescharacteristic
31C22×C4×D59D411yescharacteristic
32C22×C59⋊C8—21no—
33C22×C59⋊C8—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59C2×C411yescharacteristic
36C2×C4⋊Dic59C2×C411yescharacteristic
37C2×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×Dic59⋊C4—21no—
40C2×Dic59⋊C4—21no—
41C4⋊C4×D59—22no—
42C4⋊C4×D59—42no—
43C4⋊C4×D59—42no—
44C4⋊C4×D59—42no—
45C4⋊C4×D59C814yescomplemented
46C2×C4×Dic59C2×C411yescharacteristic
47C2×C4×Dic59D411yescharacteristic
48C2×C4×Dic59D411yescharacteristic
49C42×D59—42no—
50(C2×D59)⋊C8—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—24no—
76C2×C4×D59—22no—
77C2×C4×D59—22no—
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×C4×D59—21no—
82C2×C4×D59—41no—
83C2×C4×D59—41no—
84C2×C4×D59—42no—
85C2×C4×D59—42no—
86C2×C4×D59—42no—
87C2×C4×D59—42no—
88C2×C4×D59—42no—
89C2×C4×D59C2×C812yes—
90C2×C4×D59M1612yes—
91C2×C8×C59—41no—
92C2×C8×C59—41no—
93C2×C8×C59—41no—
94C2×C8×C59—41no—
95C2×C8×C59—41no—
96C2×C8×C59—41no—
97C4⋊C4×C59—21no—
98C4⋊C4×C59—41no—
99C4⋊C4×C59—41no—
100C4⋊C4×C59—41no—
101C4⋊C4×C59C2×C812yes—
102C42×C59—41no—
103C4⋊Dic59—21no—
104C4⋊Dic59—42no—
105C4⋊Dic59—41no—
106C4⋊Dic59C2×C812yes—
107Dic59⋊C4—24no—
108Dic59⋊C4—42no—
109Dic59⋊C4—42no—
110Dic59⋊C4—41no—
111Dic59⋊C4—41no—
112C4×Dic59—41no—
113C4×Dic59—41no—
114C4×Dic59—41no—
115C2×C59⋊C8—41no—
116C2×C59⋊C8—41no—
117C2×C59⋊C8—41no—
118C2×C59⋊C8—41no—
119C2×C59⋊C8—41no—
120C2×C59⋊C8—41no—
121C23×C59C2×C22⋊C411yescharacteristic
122C22×D59—21no—
123C22×D59—21no—
124C22×D59—21no—
125C22×D59—21no—
126C22×D59C22⋊C812yes—
127C22×D59#9912yes—
128C22×D59#10112yes—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—22no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—41no—
139C2×C4×C59—41no—
140C2×C4×C59—41no—
141C2×C4×C59C22×C811yescharacteristic
142C2×C4×C59C2×M1611yescharacteristic
143C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C59#13711yescharacteristic
146C2×C4×C59#13711yescharacteristic
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—22no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—21no—
156C2×Dic59—41no—
157C2×Dic59—41no—
158C2×Dic59—41no—
159C2×Dic59—41no—
160C2×Dic59—41no—
161C2×Dic59C22⋊C812yes—
162C4×D59—24no—
163C4×D59—24no—
164C4×D59—42no—
165C4×D59—42no—
166C4×D59—42no—
167C4×D59—42no—
168C4×D59—48no—
169C4×D59—84no—
170C8×C59—81no—
171C8×C59—81no—
172C59⋊C8—81no—
173C59⋊C8—81no—
174#7593—591nomaximal, Sylow
175C22×C59C2×C22⋊C811yescharacteristic
176C22×C59C2×#9911yescharacteristic
177C22×C59C2×#10111yescharacteristic
178C22×C59#41811yescharacteristic
179C22×C59#41911yescharacteristic
180C22×C59#42111yescharacteristic
181C22×C59#42111yescharacteristic
182C2×D59—22no—
183C2×D59—22no—
184C2×D59—22no—
185C2×D59—22no—
186C2×D59—22no—
187C2×D59—22no—
188C2×D59#32414yes—
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—21no—
192C4×C59—21no—
193C4×C59—21no—
194C4×C59—21no—
195C4×C59—42no—
196C4×C59—81no—
197Dic59—22no—
198Dic59—42no—
199Dic59—41no—
200Dic59—41no—
201Dic59—81no—
202C2×#389—591no—
203#1817—591no—
204#1817—591no—
205#1271—591no—
206#1271—591no—
207#1271—591no—
208#1271D5911yescharacteristic, complemented
209C2×C59C2×#32411yescharacteristic
210C2×C59#147811yescharacteristic
211C2×C59#147911yescharacteristic
212C2×C59#151011yescharacteristic
213C2×C59#151111yescharacteristic
214C2×C59#153411yescharacteristic
215C2×C59#155611yescharacteristic
216D59—24no—
217C22×C4⋊C4—591no—
218C22×C4⋊C4—591no—
219C22×C4⋊C4—1181no—
220C22×C42—591no—
221C2×C22⋊C8—1181no—
222C2×C22⋊C8—1181no—
223#389—591no—
224#389—591no—
225#389—591no—
226#389—1181no—
227#389—1181no—
228#389C2×D5911yescharacteristic
229C2×#95—1181no—
230#336—591no—
231#336—591no—
232#336—1181no—
233#336—1181no—
234#336C2×D5911yescharacteristic
235#336C2×D5911yescharacteristic
236C59#759311yescharacteristic, complemented, Sylow
237C23×C4—591no—
238C23×C4—591no—
239C23×C4—591no—
240C23×C4—1181no—
241C23×C4—1181no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—1181no—
245C22×C8—1181no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—591no—
248C2×C4⋊C4—594no—
249C2×C4⋊C4—591no—
250C2×C4⋊C4—1182no—
251C2×C4⋊C4—1181no—
252C2×C4⋊C4—1181no—
253C2×C4⋊C4—1181no—
254C2×C4⋊C4—1181no—
255C2×C4⋊C4—1181no—
256C2×C4⋊C4—2362no—
257C2×C4⋊C4—2362no—
258C2×C4⋊C4—2362no—
259C2×C4⋊C4C4×D5911yescharacteristic
260C2×C4⋊C4C4×D5911yescharacteristic
261C2×C42—591no—
262C2×C42—591no—
263C2×C42—591no—
264C2×C42—2362no—
265C2×C42C22×D5911yescharacteristic
266C22⋊C8—2362no—
267C22⋊C8—2362no—
268#95—21no—
269#95—1181no—
270#95—1181no—
271#95—1181no—
272C24—591no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—591no—
276C22×C4—592no—
277C22×C4—592no—
278C22×C4—591no—
279C22×C4—591no—
280C22×C4—1182no—
281C22×C4—1182no—
282C22×C4—1182no—
283C22×C4—1182no—
284C22×C4—1184no—
285C22×C4—1181no—
286C22×C4—1181no—
287C22×C4—1181no—
288C22×C4—1181no—
289C22×C4—1181no—
290C22×C4—1181no—
291C22×C4—2361no—
292C22×C4—2361no—
293C22×C4—2362no—
294C22×C4—2362no—
295C22×C4—2362no—
296C22×C4—2362no—
297C22×C4—2362no—
298C22×C4C2×C4×D5911yescharacteristic
299C22×C4D4×D5911yescharacteristic
300C22×C4D4×D5911yescharacteristic
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—2361no—
308C2×C8—2361no—
309C2×C8—2361no—
310C2×C8—2361no—
311C2×C8—2361no—
312C2×C8—2361no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—592no—
318C4⋊C4—1184no—
319C4⋊C4—1181no—
320C4⋊C4—2361no—
321C4⋊C4—2362no—
322C4⋊C4—2362no—
323C4⋊C4—2362no—
324C4⋊C4—2361no—
325C4⋊C4—2361no—
326C4⋊C4C8×D5912yes—
327C42—41no—
328C42—2361no—
329C42—2361no—
330C42—2361no—
331C23—592no—
332C23—592no—
333C23—592no—
334C23—1181no—
335C23—1181no—
336C23—1181no—
337C23—1181no—
338C23C22⋊C4×D5911yescharacteristic
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—592no—
352C2×C4—1184no—
353C2×C4—1184no—
354C2×C4—1181no—
355C2×C4—1181no—
356C2×C4—1181no—
357C2×C4—1181no—
358C2×C4—1181no—
359C2×C4—1181no—
360C2×C4—1182no—
361C2×C4—1181no—
362C2×C4—1181no—
363C2×C4—4724no—
364C2×C4—2362no—
365C2×C4—2362no—
366C2×C4—2362no—
367C2×C4—2362no—
368C2×C4—2368no—
369C2×C4—2361no—
370C2×C4—2361no—
371C2×C4—2361no—
372C2×C4—2361no—
373C2×C4—2361no—
374C2×C4C2×C8×D5911yescharacteristic
375C2×C4M16×D5911yescharacteristic
376C2×C4#1427375111yescharacteristic
377C2×C4#1427375411yescharacteristic
378C2×C4#1427375611yescharacteristic
379C2×C4#1427375911yescharacteristic
380C8—81no—
381C8—81no—
382C8—4721no—
383C8—4721no—
384C22—594no—
385C22—1182no—
386C22—1182no—
387C22—1182no—
388C22—1182no—
389C22—1182no—
390C22—1182no—
391C22C22⋊C8×D5911yescharacteristic
392C22#99×D5911yescharacteristic
393C22#101×D5911yescharacteristic
394C22#1683740511yescharacteristic
395C22#1683740911yescharacteristic
396C22#1683741711yescharacteristic
397C22#1683741711yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—42no—
405C4—81no—
406C4—1182no—
407C4—4721no—
408C4—2361no—
409C4—2361no—
410C4—2362no—
411C2—1184no—
412C2#324×D5911yescharacteristic
413C2#2142248511yescharacteristic
414C2#2142248911yescharacteristic
415C2#2142262311yescharacteristic
416C2#2142262711yescharacteristic
417C2#2142272111yescharacteristic
418C2#2142281111yescharacteristic
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#7593
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
45. C4⋊C4×D59C8semidirect
208. #1271D59semidirect
236. C59#7593semidirect

Maximal subgroups

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

subgroupindex
#389×D592
#214241632
#214219202
#214219192
#214219182
C59×#12712
#759359