Finite Group Databasebeta

← #28491732

Subgroups — #28491732

Order 15104.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429132C211yesmaximal, characteristic, complemented
2#21425022C211yesmaximal, characteristic
3#21425022C211yesmaximal, characteristic
4#21424901C211yesmaximal, characteristic
5#21421935C211yesmaximal, characteristic, complemented
6#21421935C211yesmaximal, characteristic, complemented
7C59×#1296C211yesmaximal, characteristic, complemented
8C2×#14273724C2211yescharacteristic
9C2×#14273718—21no—
10C2×#14273649—21no—
11C2×#14273649—21no—
12C2×#14273649—21no—
13C2×#14273649—21no—
14C2×#14273647—22no—
15C2×C4×C59⋊C8C2211yescharacteristic
16#16837335—22no—
17#16837301—21no—
18#16837298—21no—
19#16837271—21no—
20C4×C4⋊Dic59C2211yescharacteristic
21C4×C4⋊Dic59C2211yescharacteristic
22C2×C4⋊C8×C59C2211yescharacteristic
23C2×C4⋊C8×C59C2211yescharacteristic
24C59×#384C2211yescharacteristic
25C22×D236—21no—
26C22×D236—21no—
27C22×D236—21no—
28C22×C59⋊C8—21no—
29#14273724—21no—
30#14273724—21no—
31#14273724—21no—
32#14273724Q812yes—
33#14273718—42no—
34#14273718—42no—
35C2×C4⋊Dic59—22no—
36C2×C4⋊Dic59D411yescharacteristic
37C2×C4⋊Dic59D411yescharacteristic
38C2×C4⋊Dic59D411yescharacteristic
39C2×C4⋊Dic59D411yescharacteristic
40C2×Dic59⋊C4—22no—
41C2×Dic59⋊C4—22no—
42C2×C4×Dic59—21no—
43C2×C4×Dic59—21no—
44#14273649—42no—
45#14273649—42no—
46#14273649—42no—
47#14273649—42no—
48#14273647—44no—
49C4×C59⋊C8—21no—
50C4×C59⋊C8—21no—
51C59⋊#95—22no—
52C59⋊#95—21no—
53C59⋊#95—21no—
54C22×C8×C59—21no—
55C22×C8×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59D412yes—
59C2×C42×C59C2311yescharacteristic
60C4⋊C8×C59—21no—
61C4⋊C8×C59—21no—
62C4⋊C8×C59—21no—
63C4⋊C8×C59—21no—
64C23×D59—41no—
65C22×C4×C59—22no—
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59C2×D411yescharacteristic
68C22×C4×C59C2×D411yescharacteristic
69C22×Dic59—21no—
70C22×Dic59—21no—
71C22×Dic59—21no—
72C22×Dic59—21no—
73C2×D236—22no—
74C2×D236—22no—
75C2×D236—22no—
76C2×D236—42no—
77C2×D236—42no—
78C2×D236—41no—
79C2×D236—41no—
80C2×D236—41no—
81C2×D236—41no—
82C2×D236—41no—
83C2×D236—41no—
84C2×D236—41no—
85C2×D236—41no—
86C2×D236—41no—
87C2×D236—41no—
88C2×D236—41no—
89C2×C8×C59—41no—
90C2×C8×C59—41no—
91C2×C8×C59—41no—
92C2×C8×C59—41no—
93C2×C8×C59—41no—
94C2×C8×C59—41no—
95C4⋊C4×C59—42no—
96C4⋊C4×C59—41no—
97C4⋊C4×C59—41no—
98C4⋊C4×C59—41no—
99C4⋊C4×C59—41no—
100C42×C59C2×Q811yescharacteristic
101C42×C59#4111yescharacteristic
102C42×C59#4111yescharacteristic
103C42×C59#4111yescharacteristic
104C4⋊Dic59—21no—
105C4⋊Dic59—21no—
106C4⋊Dic59—21no—
107C4⋊Dic59—21no—
108C4⋊Dic59—21no—
109C4⋊Dic59—21no—
110C4⋊Dic59—44no—
111C4⋊Dic59D812yes—
112C4⋊Dic59SD1612yes—
113Dic59⋊C4—44no—
114Dic59⋊C4—82no—
115C4×Dic59—41no—
116C4×Dic59—41no—
117C4×Dic59—41no—
118C4×Dic59—41no—
119C2×C59⋊C8—22no—
120C2×C59⋊C8—41no—
121C2×C59⋊C8—41no—
122C23×C59#12011yescharacteristic
123C22×D59—42no—
124C22×D59—81no—
125C22×D59—81no—
126C22×D59—81no—
127C22×D59—81no—
128C22×D59—81no—
129C22×D59—81no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—42no—
133C2×C4×C59—42no—
134C2×C4×C59—42no—
135C2×C4×C59C22⋊Q811yescharacteristic
136C2×C4×C59C22⋊Q811yescharacteristic
137C2×C4×C59C22⋊Q811yescharacteristic
138C2×C4×C59#12411yescharacteristic
139C2×C4×C59#12411yescharacteristic
140C2×C4×C59#12411yescharacteristic
141C2×C4×C59C2×D811yescharacteristic
142C2×C4×C59C2×SD1611yescharacteristic
143C2×C4×C59#13511yescharacteristic
144C2×C4×C59#13511yescharacteristic
145C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C59#13711yescharacteristic
149C2×Dic59—22no—
150C2×Dic59—22no—
151C2×Dic59—41no—
152C2×Dic59—41no—
153C2×Dic59—41no—
154C2×Dic59—41no—
155C2×Dic59—41no—
156C2×Dic59—41no—
157C2×Dic59—41no—
158C2×Dic59—41no—
159C2×Dic59—41no—
160C2×Dic59—41no—
161D236—44no—
162D236—42no—
163D236—42no—
164D236—42no—
165D236—42no—
166D236—82no—
167D236—81no—
168D236—81no—
169D236—81no—
170D236—81no—
171C8×C59—81no—
172C8×C59—81no—
173C59⋊C8—42no—
174#10354—591nomaximal, Sylow
175C22×C59#39311yescharacteristic
176C22×C59#44711yescharacteristic
177C22×C59#44811yescharacteristic
178C22×C59#44911yescharacteristic
179C22×C59#44911yescharacteristic
180C22×C59#45311yescharacteristic
181C22×C59#45411yescharacteristic
182C2×D59—82no—
183C2×D59—82no—
184C2×D59—82no—
185C2×D59—161no—
186C2×D59—161no—
187C2×D59—161no—
188C2×D59—161no—
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—82no—
192C4×C59#47411yescharacteristic
193C4×C59#47611yescharacteristic
194C4×C59#47811yescharacteristic
195C4×C59#47811yescharacteristic
196C4×C59#48611yescharacteristic
197C4×C59#48811yescharacteristic
198C4×C59#48911yescharacteristic
199C4×C59#49011yescharacteristic
200Dic59—42no—
201Dic59—42no—
202Dic59—81no—
203Dic59—81no—
204#2552—591no—
205#1982—591no—
206#1982—591no—
207#1957—591no—
208#1296D5911yescharacteristic, complemented
209#1279—591no—
210#1279—591no—
211C2×C59#162111yescharacteristic
212C2×C59#162211yescharacteristic
213C2×C59#162511yescharacteristic
214C2×C59#162611yescharacteristic
215C2×C59#202311yescharacteristic
216C2×C59#202511yescharacteristic
217C2×C59#202711yescharacteristic
218D59—162no—
219C2×#127—591no—
220C2×#125—1181no—
221C2×C4⋊C8C2×D5911yescharacteristic
222C2×C4⋊C8C2×D5911yescharacteristic
223C2×#102—1181no—
224C2×#102—1181no—
225C2×#102—1181no—
226C2×#102—1181no—
227C2×#102—1182no—
228C2×C4×C8—591no—
229#398—1182no—
230#389—1181no—
231#389—1181no—
232#384—1181no—
233#384C2×D5911yescharacteristic
234C4×C4⋊C4—591no—
235C4×C4⋊C4—591no—
236C59#1035411yescharacteristic, complemented, Sylow
237C22×D4—1181no—
238C22×D4—1181no—
239C22×D4—1181no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—1181no—
243#127—592no—
244#127—1181no—
245#127—1181no—
246#127—1181no—
247#125—2362no—
248#125—2362no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—591no—
252C2×C4⋊C4—591no—
253C2×C4⋊C4—591no—
254C2×C4⋊C4—591no—
255C2×C4⋊C4—1182no—
256C2×C4⋊C4—1182no—
257C2×C4⋊C4—1182no—
258C2×C4⋊C4D23612yes—
259C2×C42—1181no—
260C2×C42—1181no—
261C2×C42C22×D5911yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266#102—2364no—
267#102—2362no—
268#102—2362no—
269#102—2362no—
270#102—2362no—
271C4×C8—1181no—
272C4×C8—1181no—
273#95—1182no—
274#95—1181no—
275#95—1181no—
276C24—2361no—
277C2×D4—1182no—
278C2×D4—1182no—
279C2×D4—1182no—
280C2×D4—2362no—
281C2×D4—2362no—
282C2×D4—2361no—
283C2×D4—2361no—
284C2×D4—2361no—
285C2×D4—2361no—
286C2×D4—2361no—
287C2×D4—2361no—
288C2×D4—2361no—
289C2×D4—2361no—
290C2×D4—2361no—
291C2×D4—2361no—
292C2×D4—2361no—
293C22×C4—22no—
294C22×C4—1181no—
295C22×C4—1181no—
296C22×C4—1181no—
297C22×C4—1181no—
298C22×C4C2×D23611yescharacteristic
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—1182no—
308C2×C8—2361no—
309C2×C8—2361no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—592no—
316C4⋊C4—592no—
317C4⋊C4—1181no—
318C4⋊C4—1181no—
319C4⋊C4—1181no—
320C4⋊C4—1181no—
321C4⋊C4—1181no—
322C4⋊C4—1181no—
323C4⋊C4—4722no—
324C4⋊C4—2364no—
325C4⋊C4—2364no—
326C42—2361no—
327C42—2361no—
328C42—2361no—
329C42—2361no—
330C42#1174568511yescharacteristic
331C42#1174568511yescharacteristic
332C42#1174568711yescharacteristic
333C42Q8×D5911yescharacteristic
334C23—4721no—
335C23—4721no—
336C23—4721no—
337C23—4721no—
338C23—4721no—
339C23—4721no—
340C23—2362no—
341C23#1427369711yescharacteristic
342D4—4722no—
343D4—4721no—
344D4—4721no—
345D4—4721no—
346D4—4721no—
347D4—2364no—
348D4—2362no—
349D4—2362no—
350D4—2362no—
351D4—2362no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—1182no—
358C2×C4—1182no—
359C2×C4—2361no—
360C2×C4—2361no—
361C2×C4—2361no—
362C2×C4—2361no—
363C2×C4—2361no—
364C2×C4—2361no—
365C2×C4—2361no—
366C2×C4—2361no—
367C2×C4—2361no—
368C2×C4—2361no—
369C2×C4#1427370511yescharacteristic
370C2×C4#1427370511yescharacteristic
371C2×C4#1427370711yescharacteristic
372C2×C4#1427371311yescharacteristic
373C2×C4#1427371311yescharacteristic
374C2×C4#1427371511yescharacteristic
375C2×C4D8×D5911yescharacteristic
376C2×C4SD16×D5911yescharacteristic
377C2×C4#1427374811yescharacteristic
378C2×C4#1427375011yescharacteristic
379C2×C4#1427375111yescharacteristic
380C2×C4#1427375411yescharacteristic
381C2×C4#1427375411yescharacteristic
382C2×C4#1427375911yescharacteristic
383C8—81no—
384C8—81no—
385C8—2362no—
386C22—9441no—
387C22—9441no—
388C22—9441no—
389C22—9441no—
390C22—4722no—
391C22—4722no—
392C22—4722no—
393C22#1683731511yescharacteristic
394C22#1683753711yescharacteristic
395C22#1683754211yescharacteristic
396C22#1683754811yescharacteristic
397C22#1683755011yescharacteristic
398C22#1683757211yescharacteristic
399C22#1683757711yescharacteristic
400C4—21no—
401C4—21no—
402C4—82no—
403C4—4721no—
404C4—4721no—
405C4—2362no—
406C4—2362no—
407C4#1683768111yescharacteristic
408C4#1683769111yescharacteristic
409C4#1683770111yescharacteristic
410C4#1683770511yescharacteristic
411C4#1683774711yescharacteristic
412C4#1683775811yescharacteristic
413C4#1683776311yescharacteristic
414C4#1683776511yescharacteristic
415C2—9442no—
416C2#2142316211yescharacteristic
417C2#2142316911yescharacteristic
418C2#2142318611yescharacteristic
419C2#2142319311yescharacteristic
420C2#2142523111yescharacteristic
421C2#2142524111yescharacteristic
422C2#2142525311yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1296C2
socleC23×C59#120
prime radicalC2×#14273724C22
hypercenter#1296D59
hypocenterC59#10354
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
1. #21429132C2semidirect
5. #21421935C2semidirect
6. #21421935C2semidirect
7. C59×#1296C2semidirect
208. #1296D59semidirect
236. C59#10354semidirect

Maximal subgroups

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

subgroupindex
#214291322
#214250222
#214249012
#214219352
C59×#12962
#1035459