Finite Group Databasebeta

← #28492510

Subgroups — #28492510

Order 15104.

506 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
1C2×#16837608C211yesmaximal, characteristic
2#21425056C211yesmaximal, characteristic, complemented
3#21424889C211yesmaximal, characteristic
4#21424093C211yesmaximal, characteristic
5C2×#16837154C211yesmaximal, characteristic, complemented
6C2×#16837147C211yesmaximal, characteristic, complemented
7C59×#1296C211yesmaximal, characteristic, complemented
8C22×#11745660—21no—
9C2×#14273727C2211yescharacteristic
10C2×C4×D236C2211yescharacteristic
11#16837608—22no—
12#16837608—22no—
13C2×C4⋊(C59⋊C8)C2211yescharacteristic
14C2×#14273652—21no—
15C2×#14273647—21no—
16C2×(C2×D59)⋊C8—21no—
17C2×(C2×D59)⋊C8—21no—
18C2×C4×C59⋊C8C2211yescharacteristic
19#16837164—21no—
20#16837164—21no—
21#16837164—21no—
22#16837154—22no—
23#16837147—22no—
24C2×C4⋊C8×C59C2211yescharacteristic
25C2×C4⋊C8×C59C2211yescharacteristic
26C59×#384C2211yescharacteristic
27C22×Dic118—21no—
28C22×D236D411yescharacteristic
29C22×C4×D59—21no—
30C2×#11745660—24no—
31C2×#11745660—42no—
32C2×#11745660—42no—
33C22×C59⋊C8—21no—
34C22×C59⋊C8D411yescharacteristic
35C22×C59⋊C8D411yescharacteristic
36#14273727—21no—
37#14273727—21no—
38#14273727—21no—
39#14273727D412yes—
40C4×D236—21no—
41C4×D236—21no—
42C4×D236—21no—
43C4×D236—21no—
44C2×C4⋊Dic59—21no—
45C2×C4⋊Dic59—21no—
46C2×C4⋊Dic59D411yescharacteristic
47C2×(C2×D59)⋊C4—21no—
48C4⋊(C59⋊C8)—21no—
49C4⋊(C59⋊C8)—21no—
50#14273652—24no—
51#14273647—42no—
52(C2×D59)⋊C8—42no—
53(C2×D59)⋊C8—42no—
54C4×C59⋊C8—21no—
55C4×C59⋊C8—21no—
56C22×C8×C59—21no—
57C22×C8×C59—21no—
58C2×C4⋊C4×C59—21no—
59C2×C4⋊C4×C59—21no—
60C2×C4⋊C4×C59—21no—
61C2×C42×C59C2311yescharacteristic
62C4⋊C8×C59—21no—
63C4⋊C8×C59—21no—
64C4⋊C8×C59—21no—
65C4⋊C8×C59D412yes—
66C23×D59—21no—
67C22×C4×C59—41no—
68C22×C4×C59C2×D411yescharacteristic
69C22×C4×C59C2×D411yescharacteristic
70C22×C4×C59#4111yescharacteristic
71C22×Dic59—21no—
72C22×Dic59—41no—
73C2×D236—21no—
74C2×D236—21no—
75C2×D236—21no—
76C2×D236—21no—
77C2×D236—21no—
78C2×D236D812yes—
79C2×C4×D59—41no—
80C2×C4×D59—41no—
81C2×C4×D59—41no—
82C2×C4×D59—41no—
83C2×C4×D59—41no—
84C2×C4×D59—41no—
85C2×Dic118—22no—
86C2×Dic118—41no—
87C2×Dic118—41no—
88C2×Dic118—41no—
89C2×Dic118—41no—
90C2×Dic118—41no—
91C2×C8×C59—22no—
92C2×C8×C59—41no—
93C2×C8×C59—41no—
94C2×C8×C59—41no—
95C2×C8×C59—41no—
96C2×C8×C59—41no—
97C4⋊C4×C59—41no—
98C4⋊C4×C59—41no—
99C4⋊C4×C59—41no—
100C4⋊C4×C59—41no—
101C4⋊C4×C59—81no—
102C42×C59C2×D411yescharacteristic
103C42×C59C2×D411yescharacteristic
104C42×C59#4111yescharacteristic
105C42×C59#4111yescharacteristic
106(C2×D59)⋊C4—41no—
107(C2×D59)⋊C4—41no—
108C4⋊Dic59—21no—
109C4⋊Dic59—22no—
110C4⋊Dic59—22no—
111C4⋊Dic59—21no—
112C4⋊Dic59—41no—
113C4⋊Dic59—41no—
114C2×C59⋊C8—21no—
115C2×C59⋊C8—21no—
116C2×C59⋊C8—21no—
117C2×C59⋊C8—21no—
118C2×C59⋊C8—21no—
119C2×C59⋊C8—41no—
120C2×C59⋊C8—41no—
121C2×C59⋊C8—41no—
122C2×C59⋊C8SD1612yescomplemented
123#11745660—48no—
124C23×C59#12111yescharacteristic
125C22×D59—22no—
126C22×D59—41no—
127C22×D59—41no—
128C22×D59—41no—
129C22×D59—41no—
130C22×D59—41no—
131C22×D59—41no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—81no—
135C2×C4×C59—81no—
136C2×C4×C59—81no—
137C2×C4×C59#12011yescharacteristic
138C2×C4×C59#12111yescharacteristic
139C2×C4×C59#12111yescharacteristic
140C2×C4×C59#12311yescharacteristic
141C2×C4×C59#12311yescharacteristic
142C2×C4×C59#12411yescharacteristic
143C2×C4×C59C2×D811yescharacteristic
144C2×C4×C59C2×SD1611yescharacteristic
145C2×C4×C59#13511yescharacteristic
146C2×C4×C59#13511yescharacteristic
147C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C59#13711yescharacteristic
150C2×C4×C59#13711yescharacteristic
151C2×Dic59—42no—
152C2×Dic59—41no—
153C2×Dic59—41no—
154C2×Dic59—41no—
155C2×Dic59—81no—
156C2×Dic59—81no—
157D236—22no—
158D236—22no—
159D236—41no—
160D236—41no—
161C4×D59—81no—
162C4×D59—81no—
163C4×D59—81no—
164C4×D59—81no—
165Dic118—42no—
166Dic118—42no—
167Dic118—81no—
168Dic118—81no—
169C8×C59—42no—
170C8×C59—81no—
171C59⋊C8—22no—
172C59⋊C8—41no—
173C59⋊C8—81no—
174#10476—591nomaximal, Sylow
175C22×C59#39411yescharacteristic
176C22×C59#46111yescharacteristic
177C22×C59#46311yescharacteristic
178C22×C59#46611yescharacteristic
179C22×C59#46811yescharacteristic
180C22×C59#47111yescharacteristic
181C22×C59#47311yescharacteristic
182C2×D59—42no—
183C2×D59—42no—
184C2×D59—42no—
185C2×D59—81no—
186C2×D59—81no—
187C2×D59—81no—
188C2×D59—81no—
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—161no—
192C4×C59#44711yescharacteristic
193C4×C59#45211yescharacteristic
194C4×C59#46011yescharacteristic
195C4×C59#46411yescharacteristic
196C4×C59#46511yescharacteristic
197C4×C59#46811yescharacteristic
198C4×C59#48011yescharacteristic
199C4×C59#48211yescharacteristic
200Dic59—81no—
201Dic59—82no—
202C2×#461—591no—
203#1990—591no—
204#1954—591no—
205#1802—591no—
206C2×#335—591no—
207C2×#332—591no—
208#1296D5911yescharacteristic, complemented
209C2×C59#167311yescharacteristic
210C2×C59#168111yescharacteristic
211C2×C59#169111yescharacteristic
212C2×C59#169911yescharacteristic
213C2×C59#203311yescharacteristic
214C2×C59#205211yescharacteristic
215C2×C59#205511yescharacteristic
216D59—82no—
217C22×SD16—1181no—
218C2×C4⋊Q8—591no—
219C2×C4×D4—591no—
220#461—1182no—
221#461—1182no—
222C2×C4⋊C8—591no—
223C2×C4⋊C8C2×D5911yescharacteristic
224C2×C4⋊C8C2×D5911yescharacteristic
225C2×#103—1181no—
226C2×#102—1181no—
227C2×C22⋊C8—1181no—
228C2×C22⋊C8—1181no—
229C2×C4×C8—591no—
230#384C2×D5911yescharacteristic
231#340—1181no—
232#340—1181no—
233#340—1181no—
234#335—1182no—
235#332—1182no—
236C59#1047611yescharacteristic, complemented, Sylow
237C22×Q8—1181no—
238C22×D4—591no—
239C23×C4—1181no—
240C2×SD16—1184no—
241C2×SD16—2362no—
242C2×SD16—2362no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—591no—
246C22×C8—591no—
247C22×C8—1181no—
248C4⋊Q8—592no—
249C4⋊Q8—1181no—
250C4⋊Q8—1181no—
251C4⋊Q8—1181no—
252C4×D4—1181no—
253C4×D4—1181no—
254C4×D4—1181no—
255C4×D4—1181no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—591no—
260C2×C4⋊C4—1181no—
261C2×C4⋊C4—1181no—
262C2×C22⋊C4—1181no—
263C2×C42C22×D5911yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—1181no—
268C4⋊C8—1181no—
269C4⋊C8D23612yes—
270#103—1184no—
271#102—2362no—
272C22⋊C8—2362no—
273C22⋊C8—2362no—
274C4×C8—1181no—
275C4×C8—1181no—
276C24—1181no—
277C2×Q8—1182no—
278C2×Q8—2361no—
279C2×Q8—2361no—
280C2×Q8—2361no—
281C2×Q8—2361no—
282C2×Q8—2361no—
283C2×D4—592no—
284C2×D4—1181no—
285C2×D4—1181no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4—1181no—
289C22×C4—41no—
290C22×C4—1181no—
291C22×C4—2361no—
292C22×C4—2361no—
293C22×C4—2361no—
294C22×C4—2361no—
295C22×C4—2361no—
296C22×C4—2361no—
297C22×C4—2361no—
298C22×C4#1174568511yescharacteristic
299C22×C4D4×D5911yescharacteristic
300C22×C4D4×D5911yescharacteristic
301SD16—2368no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—592no—
309C2×C8—1181no—
310C2×C8—1181no—
311C2×C8—1181no—
312C2×C8—1181no—
313C2×C8—1181no—
314C2×C8—2361no—
315C2×C8—2361no—
316C2×C8—2361no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—81no—
322C4⋊C4—1181no—
323C4⋊C4—1182no—
324C4⋊C4—1181no—
325C4⋊C4—1182no—
326C4⋊C4—2361no—
327C4⋊C4—2361no—
328C22⋊C4—2361no—
329C22⋊C4—2361no—
330C42C2×D23611yescharacteristic
331C42#1174568511yescharacteristic
332C42D4×D5911yescharacteristic
333C42#1174568911yescharacteristic
334C23—1182no—
335C23—2361no—
336C23—2361no—
337C23—2361no—
338C23—2361no—
339C23—2361no—
340C23—2361no—
341C23#1427370011yescharacteristic
342Q8—4721no—
343Q8—4721no—
344Q8—2362no—
345Q8—2362no—
346D4—1182no—
347D4—1182no—
348D4—2361no—
349D4—2361no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—4721no—
356C2×C4—4721no—
357C2×C4—4721no—
358C2×C4—4721no—
359C2×C4—4721no—
360C2×C4—4721no—
361C2×C4—2361no—
362C2×C4—2362no—
363C2×C4—2361no—
364C2×C4—2361no—
365C2×C4#1427369711yescharacteristic
366C2×C4#1427370011yescharacteristic
367C2×C4#1427370211yescharacteristic
368C2×C4#1427371211yescharacteristic
369C2×C4#1427371211yescharacteristic
370C2×C4#1427371511yescharacteristic
371C2×C4D8×D5911yescharacteristic
372C2×C4SD16×D5911yescharacteristic
373C2×C4#1427374811yescharacteristic
374C2×C4#1427374811yescharacteristic
375C2×C4#1427375111yescharacteristic
376C2×C4#1427375411yescharacteristic
377C2×C4#1427375911yescharacteristic
378C2×C4#1427375911yescharacteristic
379C8—42no—
380C8—81no—
381C8—1182no—
382C8—4721no—
383C8—2361no—
384C22—4721no—
385C22—4721no—
386C22—4721no—
387C22—4721no—
388C22—2362no—
389C22—2362no—
390C22—2362no—
391C22#1683732011yescharacteristic
392C22#1683760611yescharacteristic
393C22#1683761611yescharacteristic
394C22#1683763711yescharacteristic
395C22#1683765111yescharacteristic
396C22#1683766411yescharacteristic
397C22#1683767611yescharacteristic
398C4—21no—
399C4—21no—
400C4—161no—
401C4—4721no—
402C4—4722no—
403C4#1683753711yescharacteristic
404C4#1683756711yescharacteristic
405C4#1683760111yescharacteristic
406C4#1683762711yescharacteristic
407C4#1683763211yescharacteristic
408C4#1683764911yescharacteristic
409C4#1683771711yescharacteristic
410C4#1683772811yescharacteristic
411C2—4722no—
412C2#2142348411yescharacteristic
413C2#2142353211yescharacteristic
414C2#2142359811yescharacteristic
415C2#2142364211yescharacteristic
416C2#2142528111yescharacteristic
417C2#2142539811yescharacteristic
418C2#2142541511yescharacteristic
subgroupG/H
centerC23#14273700
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1296C2
socleC23×C59#121
prime radicalC22×D236D4
hypercenter#1296D59
hypocenterC59#10476
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
2. #21425056C2semidirect
5. C2×#16837154C2semidirect
6. C2×#16837147C2semidirect
7. C59×#1296C2semidirect
122. C2×C59⋊C8SD16semidirect
208. #1296D59semidirect
236. C59#10476semidirect

Maximal subgroups

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

subgroupindex
C2×#168376082
#214250562
#214248892
#214240932
C2×#168371542
C2×#168371472
C59×#12962
#1047659