Finite Group Databasebeta

← #28746171

Subgroups — #28746171

Order 15104.

516 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21436499C211yesmaximal, characteristic, complemented
2#21436444C211yesmaximal, characteristic, complemented
3#21426382C211yesmaximal, characteristic, complemented
4#21426288C211yesmaximal, characteristic, complemented
5#21426282C211yesmaximal, characteristic, complemented
6#21426282C211yesmaximal, characteristic, complemented
7#21426277C211yesmaximal, characteristic, complemented
8#21426254C211yesmaximal, characteristic, complemented
9#21426244C211yesmaximal, characteristic, complemented
10#21426199C211yesmaximal, characteristic, complemented
11#21426182C211yesmaximal, characteristic, complemented
12#21425973C211yesmaximal, characteristic, complemented
13#21425884C211yesmaximal, characteristic, complemented
14C2×#16837230C211yesmaximal, characteristic, complemented
15C59×#2168C211yesmaximal, characteristic, complemented
16#16838098—21no—
17#16838056—21no—
18C2×D944C2211yescharacteristic
19#16837807C2211yescharacteristic
20#16837804C2211yescharacteristic
21#16837727—21no—
22#16837721—21no—
23#16837716—21no—
24#16837716—21no—
25#16837703—21no—
26#16837683—21no—
27#16837638C2211yescharacteristic
28#16837638C2211yescharacteristic
29#16837638C2211yescharacteristic
30#16837638C2211yescharacteristic
31C4×D472C2211yescharacteristic
32C4×D472C2211yescharacteristic
33#16837440C2211yescharacteristic
34C2×#14273661C2211yescharacteristic
35C2×#14273661C2211yescharacteristic
36C2×#14273661C2211yescharacteristic
37#16837230C2211yescharacteristic
38#16837230C2211yescharacteristic
39#16837230C2211yescharacteristic
40#16837230C2211yescharacteristic
41#16837230C2211yescharacteristic
42#16837230C2211yescharacteristic
43#16837228C2211yescharacteristic
44#16837228C2211yescharacteristic
45#16837228C2211yescharacteristic
46#16837204C2211yescharacteristic
47#16837204C2211yescharacteristic
48#16837204C2211yescharacteristic
49#16837204C2211yescharacteristic
50#16837204C2211yescharacteristic
51#16837204C2211yescharacteristic
52C2×M32×C59C2211yescharacteristic
53C22×C16×C59C2211yescharacteristic
54C8×D4×C59C2211yescharacteristic
55C59×C4⋊C16C2211yescharacteristic
56C59×C22⋊C16C2211yescharacteristic
57C59×C22⋊C16C2211yescharacteristic
58C59×#346C2211yescharacteristic
59C2×#11745687—41no—
60C2×D472C2311yescharacteristic
61C2×D472C2311yescharacteristic
62#14273727—21no—
63#14273722—41no—
64#14273719—21no—
65#14273711—41no—
66#14273711—41no—
67#14273709—41no—
68#14273707—41no—
69#14273701—21no—
70#14273701—21no—
71#14273701—21no—
72#14273701—21no—
73#14273699—41no—
74C4×D236—21no—
75C4×D236—21no—
76(C22⋊D59)⋊C4—41no—
77#14273686—21no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59—21no—
80C2×C4⋊Dic59—21no—
81D944—22no—
82#14273661—21no—
83#14273661—21no—
84#14273661—21no—
85#14273661—21no—
86#14273661C2311yescharacteristic
87#14273661C2311yescharacteristic
88#14273661C2311yescharacteristic
89#14273661C2311yescharacteristic
90#14273661C2311yescharacteristic
91#14273661C2311yescharacteristic
92#14273659—21no—
93#14273659—21no—
94#14273649—21no—
95#14273649—21no—
96#14273649—21no—
97#14273649—21no—
98#14273649—21no—
99#14273649—21no—
100C22×C8×C59C2311yescharacteristic
101C22×C8×C59C2311yescharacteristic
102C4×D4×C59D411yescharacteristic
103M32×C59—22no—
104C2×C16×C59—22no—
105C2×C16×C59C2311yescharacteristic
106C2×C16×C59C2311yescharacteristic
107C2×C16×C59C2311yescharacteristic
108C2×C16×C59C2311yescharacteristic
109C4⋊C8×C59D411yescharacteristic
110C22⋊C8×C59D411yescharacteristic
111C22⋊C8×C59D411yescharacteristic
112C4×C8×C59C2311yescharacteristic
113C2×D4×C59D811yescharacteristic
114C22×C4×C59C2×D411yescharacteristic
115C22×C4×C59C2×D411yescharacteristic
116C2×C22⋊D59—41no—
117C2×C22⋊D59—41no—
118C2×C22⋊D59—41no—
119C2×C22⋊D59—41no—
120C22×Dic59—41no—
121C22×Dic59—41no—
122C22×Dic59—41no—
123#11745687—84no—
124C2×D236—21no—
125C2×D236—21no—
126C2×C4×D59—41no—
127C2×C4×D59—41no—
128C2×Dic118—41no—
129C2×C8×C59—21no—
130C2×C8×C59—21no—
131C2×C8×C59—21no—
132C2×C8×C59—21no—
133C2×C8×C59C2×D411yescharacteristic
134C2×C8×C59C2×D411yescharacteristic
135C2×C8×C59C2×D411yescharacteristic
136C2×C8×C59C2411yescharacteristic
137C4⋊C4×C59D811yescharacteristic
138C22⋊C4×C59D811yescharacteristic
139C22⋊C4×C59D811yescharacteristic
140C42×C59C2×D411yescharacteristic
141C22⋊Dic59—41no—
142(C2×D59)⋊C4—41no—
143(C2×D59)⋊C4—41no—
144(C2×D59)⋊C4—41no—
145(C2×D59)⋊C4—41no—
146(C2×D59)⋊C4—41no—
147(C2×D59)⋊C4—41no—
148C4⋊Dic59—21no—
149C4⋊Dic59—21no—
150C4⋊Dic59—21no—
151C4⋊Dic59—21no—
152C4⋊Dic59—21no—
153C4⋊Dic59—21no—
154C4⋊Dic59—41no—
155C4⋊Dic59—41no—
156C4⋊Dic59—41no—
157C4⋊Dic59—41no—
158Dic59⋊C4—41no—
159Dic59⋊C4—41no—
160C4×Dic59—41no—
161D472—21no—
162D472—21no—
163D472—21no—
164D472—21no—
165C16×C59—21no—
166C16×C59—21no—
167C16×C59—21no—
168C16×C59#4112yescomplemented
169C23×C59C2×D811yescharacteristic
170C23×C59C2×D811yescharacteristic
171C22×D59—41no—
172C22×D59—41no—
173D4×C59—22no—
174C2×C4×C59—21no—
175C2×C4×C59—21no—
176C2×C4×C59—21no—
177C2×C4×C59—21no—
178C2×C4×C59C2×D811yescharacteristic
179C2×C4×C59C2×D811yescharacteristic
180C2×C4×C59C2×D811yescharacteristic
181C2×C4×C59C2×D811yescharacteristic
182C2×C4×C59C22×D411yescharacteristic
183C22⋊D59—82no—
184C22⋊D59—82no—
185C22⋊D59—82no—
186C22⋊D59—161no—
187C2×Dic59—41no—
188C2×Dic59—41no—
189C2×Dic59—41no—
190C2×Dic59—41no—
191C2×Dic59—41no—
192C2×Dic59—41no—
193C2×Dic59—82no—
194C2×Dic59—82no—
195C2×Dic59—161no—
196D236—41no—
197D236—41no—
198D236—41no—
199D236—41no—
200C4×D59—82no—
201C4×D59—161no—
202Dic118—82no—
203C8×C59—21no—
204C8×C59—21no—
205C8×C59—21no—
206C8×C59C2×#4111yescharacteristic
207C8×C592−1+411yescharacteristic
208#33912—591nomaximal, Sylow
209C22×C59—21no—
210C22×C59—21no—
211C22×C59—21no—
212C22×C59—21no—
213C22×C59—21no—
214C22×C59#50912yes—
215C22×C59C22×D811yescharacteristic
216C2×D59—81no—
217C2×D59—81no—
218C2×D59—81no—
219C2×D59—81no—
220C2×D59—81no—
221C2×D59—81no—
222C4×C59—21no—
223C4×C59—21no—
224C4×C59—21no—
225C4×C59—21no—
226C4×C59#54711yescharacteristic
227C4×C59#57811yescharacteristic
228Dic59—81no—
229Dic59—81no—
230Dic59—81no—
231Dic59—81no—
232Dic59—81no—
233Dic59—81no—
234#3339—591no—
235#3334—591no—
236#2255—591no—
237#2234—591no—
238#2233—591no—
239#2233—591no—
240#2232—591no—
241#2228—591no—
242#2226—591no—
243#2218—591no—
244#2215—591no—
245#2177—591no—
246#2168D5911yescharacteristic, complemented
247#2159—591no—
248C2×#367—591no—
249C2×C59—22no—
250C2×C59—41no—
251C2×C59#333411yescharacteristic
252C2×C59C2×#50911yescharacteristic
253C2×C59#341611yescharacteristic
254D59—161no—
255D59—161no—
256#553—1181no—
257#547—1181no—
258C2×D16—591no—
259C2×M32C2×D5911yescharacteristic
260C22×C16C2×D5911yescharacteristic
261#500—591no—
262#499—591no—
263#482—1181no—
264#481—1181no—
265#480—1181no—
266#480—1181no—
267#478—1181no—
268#474—1181no—
269#466—591no—
270#466—591no—
271#466—591no—
272#466—591no—
273C4×D8—591no—
274C4×D8—591no—
275C8×D4C2×D5911yescharacteristic
276#427—591no—
277C2×#107—591no—
278C2×#107—591no—
279C2×#107—591no—
280#367—591no—
281#367—591no—
282#367—591no—
283#367—591no—
284#367—591no—
285#367—591no—
286#366—591no—
287#366—591no—
288#366—591no—
289C4⋊C16C2×D5911yescharacteristic
290#357—591no—
291#357—591no—
292#357—591no—
293#357—591no—
294#357—591no—
295#357—591no—
296C22⋊C16C2×D5911yescharacteristic
297C22⋊C16C2×D5911yescharacteristic
298#346C2×D5911yescharacteristic
299C59#3391211yescharacteristic, complemented, Sylow
300C2×#41—2361no—
301C2×D8—591no—
302C2×D8—591no—
303C22×C8C22×D5911yescharacteristic
304C22×C8C22×D5911yescharacteristic
305C4⋊Q8—1181no—
306#126—2361no—
307#125—1181no—
308#123—2361no—
309#123—2361no—
310#123—2361no—
311C22⋊Q8—2361no—
312#121—1181no—
313#121—1181no—
314#121—1181no—
315#121—1181no—
316#121—2361no—
317C4×D4—1181no—
318C4×D4—1181no—
319C4×D4—2361no—
320C4×D4D23611yescharacteristic
321#117—1181no—
322C2×C4⋊C4—1181no—
323C2×C4⋊C4—1181no—
324C2×C4⋊C4—1181no—
325D16—1182no—
326M32—22no—
327C2×C16—22no—
328C2×C16C22×D5911yescharacteristic
329C2×C16C22×D5911yescharacteristic
330C2×C16C22×D5911yescharacteristic
331C2×C16C22×D5911yescharacteristic
332#107—591no—
333#107—591no—
334#107—591no—
335#107—591no—
336#107—591no—
337#107—591no—
338#107—1181no—
339#107—1181no—
340#107—1181no—
341#107—1181no—
342#106—1181no—
343#106—1181no—
344C4⋊C8D23611yescharacteristic
345#102—1181no—
346#102—1181no—
347#102—1181no—
348#102—1181no—
349#102—1181no—
350#102—1181no—
351C22⋊C8D23611yescharacteristic
352C22⋊C8D23611yescharacteristic
353C4×C8C22×D5911yescharacteristic
354#41—4724no—
355C2×Q8—2361no—
356C2×D4—1181no—
357C2×D4—1181no—
358C2×D4—2361no—
359C2×D4—2361no—
360C2×D4—2361no—
361C2×D4—2361no—
362C2×D4D47211yescharacteristic
363C22×C4—2361no—
364C22×C4—2361no—
365C22×C4—2361no—
366C22×C4—2361no—
367C22×C4—2361no—
368C22×C4C2×D23611yescharacteristic
369C22×C4C2×D23611yescharacteristic
370D8—1181no—
371D8—1181no—
372D8—1181no—
373D8—1181no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8C2×D23611yescharacteristic
379C2×C8C2×D23611yescharacteristic
380C2×C8C2×D23611yescharacteristic
381C2×C8C23×D5911yescharacteristic
382C4⋊C4—1181no—
383C4⋊C4—1181no—
384C4⋊C4—1181no—
385C4⋊C4—1181no—
386C4⋊C4—1181no—
387C4⋊C4—1181no—
388C4⋊C4—2361no—
389C4⋊C4—2361no—
390C4⋊C4—2361no—
391C4⋊C4—2361no—
392C4⋊C4—2361no—
393C4⋊C4—2361no—
394C4⋊C4D47211yescharacteristic
395C22⋊C4—2361no—
396C22⋊C4—2361no—
397C22⋊C4—2361no—
398C22⋊C4—2361no—
399C22⋊C4—2361no—
400C22⋊C4—2361no—
401C22⋊C4—2361no—
402C22⋊C4D47211yescharacteristic
403C22⋊C4D47211yescharacteristic
404C42—2361no—
405C42C2×D23611yescharacteristic
406C16—21no—
407C16—21no—
408C16—21no—
409C16#1174568712yescomplemented
410C23—2361no—
411C23—2361no—
412C23C2×D47211yescharacteristic
413C23C2×D47211yescharacteristic
414Q8—4722no—
415D4—22no—
416D4—9441no—
417D4—4722no—
418D4—4722no—
419D4—4722no—
420D4—2361no—
421D4—2361no—
422D4—2361no—
423D4—2361no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—9441no—
429C2×C4—9441no—
430C2×C4—4722no—
431C2×C4—4722no—
432C2×C4—4722no—
433C2×C4—2361no—
434C2×C4—2361no—
435C2×C4—2361no—
436C2×C4—2361no—
437C2×C4—2361no—
438C2×C4—2361no—
439C2×C4C2×D47211yescharacteristic
440C2×C4C2×D47211yescharacteristic
441C2×C4C2×D47211yescharacteristic
442C2×C4C2×D47211yescharacteristic
443C2×C4C22×D23611yescharacteristic
444C8—21no—
445C8—21no—
446C8—21no—
447C8C2×#1174568711yescharacteristic
448C8#1427377411yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—4721no—
455C22—4721no—
456C22—4721no—
457C22—4721no—
458C22—4721no—
459C22—4721no—
460C22#1683784012yes—
461C22C22×D47211yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—4721no—
467C4—4721no—
468C4—4721no—
469C4—4721no—
470C4—4721no—
471C4—4721no—
472C4#1683805611yescharacteristic
473C4#1683821911yescharacteristic
474C2—22no—
475C2—41no—
476C2—9441no—
477C2—9441no—
478C2#2143644411yescharacteristic
479C2C2×#1683784011yescharacteristic
480C2#2143724411yescharacteristic
subgroupG/H
centerC22C22×D472
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2168C2
socleC22×C59C22×D8
hypercenter#2168D59
hypocenterC59#33912
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. #21436499C2semidirect
2. #21436444C2semidirect
3. #21426382C2semidirect
4. #21426288C2semidirect
5. #21426282C2semidirect
6. #21426282C2semidirect
7. #21426277C2semidirect
8. #21426254C2semidirect
9. #21426244C2semidirect
10. #21426199C2semidirect
11. #21426182C2semidirect
12. #21425973C2semidirect
13. #21425884C2semidirect
14. C2×#16837230C2semidirect
15. C59×#2168C2semidirect
168. C16×C59#41semidirect
246. #2168D59semidirect
299. C59#33912semidirect
409. C16#11745687semidirect

Maximal subgroups

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

subgroupindex
#214364992
#214364442
#214263822
#214262882
#214262822
#214262772
#214262542
#214262442
#214261992
#214261822
#214259732
#214258842
C2×#168372302
C59×#21682
#3391259