Finite Group Databasebeta

← #28746261

Subgroups — #28746261

Order 15104.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21436499C211yesmaximal, characteristic
2#21436465C211yesmaximal, characteristic, complemented
3#21426375C211yesmaximal, characteristic, complemented
4#21426305C211yesmaximal, characteristic, complemented
5#21426294C211yesmaximal, characteristic, complemented
6#21426288C211yesmaximal, characteristic, complemented
7#21426282C211yesmaximal, characteristic, complemented
8#21426261C211yesmaximal, characteristic, complemented
9#21426254C211yesmaximal, characteristic, complemented
10#21426209C211yesmaximal, characteristic, complemented
11#21426209C211yesmaximal, characteristic, complemented
12C4×#14273672C211yesmaximal, characteristic, complemented
13#21425884C211yesmaximal, characteristic, complemented
14#21425884C211yesmaximal, characteristic, complemented
15C59×#2169C211yesmaximal, characteristic, complemented
16#16838098—21no—
17#16838092—21no—
18C2×#14273672C2211yescharacteristic
19#16837804C2211yescharacteristic
20#16837804C2211yescharacteristic
21#16837744—21no—
22#16837733—21no—
23#16837727—21no—
24#16837721—21no—
25#16837710—21no—
26#16837703—21no—
27#16837643C2211yescharacteristic
28#16837643C2211yescharacteristic
29#16837638C2211yescharacteristic
30#16837638C2211yescharacteristic
31C4×Dic236C2211yescharacteristic
32C4×D472C2211yescharacteristic
33#16837440C2211yescharacteristic
34#16837440C2211yescharacteristic
35C2×#14273661C2211yescharacteristic
36C2×#14273661C2211yescharacteristic
37#16837230C2211yescharacteristic
38#16837230C2211yescharacteristic
39#16837230C2211yescharacteristic
40#16837230C2211yescharacteristic
41#16837230C2211yescharacteristic
42#16837228C2211yescharacteristic
43#16837228C2211yescharacteristic
44#16837228C2211yescharacteristic
45#16837228C2211yescharacteristic
46#16837207C2211yescharacteristic
47#16837207C2211yescharacteristic
48#16837207C2211yescharacteristic
49#16837204C2211yescharacteristic
50#16837204C2211yescharacteristic
51#16837204C2211yescharacteristic
52C2×M32×C59C2211yescharacteristic
53C2×M32×C59C2211yescharacteristic
54C8×D4×C59C2211yescharacteristic
55C59×C4⋊C16C2211yescharacteristic
56C59×C22⋊C16C2211yescharacteristic
57C59×C22⋊C16C2211yescharacteristic
58C4×C16×C59C2211yescharacteristic
59C2×Dic236C2311yescharacteristic
60C2×D472C2311yescharacteristic
61#14273722—41no—
62#14273720—41no—
63#14273719—21no—
64#14273719—21no—
65#14273717—41no—
66#14273709—41no—
67#14273708—41no—
68#14273706—21no—
69#14273706—21no—
70#14273701—21no—
71#14273701—21no—
72#14273699—41no—
73C4×Dic118—21no—
74C4×D236—21no—
75(C22⋊D59)⋊C4—41no—
76#14273686—21no—
77#14273686—21no—
78#14273683—41no—
79C2×C4⋊Dic59—21no—
80C2×C4⋊Dic59—21no—
81#14273672—22no—
82#14273661—21no—
83#14273661—21no—
84#14273661C2311yescharacteristic
85#14273661C2311yescharacteristic
86#14273661C2311yescharacteristic
87#14273661C2311yescharacteristic
88#14273661C2311yescharacteristic
89#14273661C2311yescharacteristic
90#14273659—21no—
91#14273659—21no—
92#14273659—21no—
93#14273659—21no—
94#14273652—21no—
95#14273652—21no—
96#14273652—21no—
97#14273649—21no—
98#14273649—21no—
99#14273649—21no—
100C22×C8×C59C2311yescharacteristic
101C22×C8×C59C2311yescharacteristic
102C4×D4×C59D411yescharacteristic
103M32×C59—22no—
104M32×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—
118C22×Dic59—41no—
119C22×Dic59—41no—
120C2×D236—21no—
121C2×C4×D59—41no—
122C2×Dic118—21no—
123C2×C8×C59—21no—
124C2×C8×C59—21no—
125C2×C8×C59—21no—
126C2×C8×C59—21no—
127C2×C8×C59C2×D411yescharacteristic
128C2×C8×C59C2×D411yescharacteristic
129C2×C8×C59C2×D411yescharacteristic
130C2×C8×C59C2411yescharacteristic
131C4⋊C4×C59D811yescharacteristic
132C22⋊C4×C59D811yescharacteristic
133C22⋊C4×C59D811yescharacteristic
134C42×C59C2×D411yescharacteristic
135C22⋊Dic59—41no—
136C22⋊Dic59—41no—
137C22⋊Dic59—41no—
138C22⋊Dic59—41no—
139(C2×D59)⋊C4—41no—
140(C2×D59)⋊C4—41no—
141(C2×D59)⋊C4—41no—
142C4⋊Dic59—21no—
143C4⋊Dic59—21no—
144C4⋊Dic59—21no—
145C4⋊Dic59—21no—
146C4⋊Dic59—21no—
147C4⋊Dic59—21no—
148C4⋊Dic59—41no—
149C4⋊Dic59—41no—
150Dic59⋊C4—41no—
151Dic59⋊C4—41no—
152Dic59⋊C4—41no—
153Dic59⋊C4—41no—
154Dic59⋊C4—41no—
155Dic59⋊C4—41no—
156Dic59⋊C4—41no—
157C4×Dic59—41no—
158C4×Dic59—41no—
159C4×Dic59—41no—
160Dic236—21no—
161Dic236—21no—
162D472—21no—
163D472—21no—
164C16×C59—21no—
165C16×C59—21no—
166C16×C59—21no—
167C16×C59#4112yes—
168C23×C59C2×D811yescharacteristic
169C23×C59C2×D811yescharacteristic
170C22×D59—41no—
171D4×C59—41no—
172C2×C4×C59—21no—
173C2×C4×C59—21no—
174C2×C4×C59—21no—
175C2×C4×C59—21no—
176C2×C4×C59C2×D811yescharacteristic
177C2×C4×C59C2×D811yescharacteristic
178C2×C4×C59C2×D811yescharacteristic
179C2×C4×C59C2×D811yescharacteristic
180C2×C4×C59C22×D411yescharacteristic
181C22⋊D59—82no—
182C22⋊D59—161no—
183C2×Dic59—41no—
184C2×Dic59—41no—
185C2×Dic59—41no—
186C2×Dic59—41no—
187C2×Dic59—41no—
188C2×Dic59—41no—
189C2×Dic59—41no—
190C2×Dic59—82no—
191C2×Dic59—161no—
192D236—41no—
193D236—41no—
194C4×D59—161no—
195Dic118—41no—
196Dic118—41no—
197C8×C59—21no—
198C8×C59—21no—
199C8×C59—21no—
200C8×C59C2×#4111yescharacteristic
201C8×C592−1+411yescharacteristic
202#33918—591nomaximal, Sylow
203C22×C59—21no—
204C22×C59—21no—
205C22×C59—21no—
206C22×C59—21no—
207C22×C59—21no—
208C22×C59—21no—
209C22×C59C22×D811yescharacteristic
210C2×D59—81no—
211C2×D59—81no—
212C2×D59—81no—
213C4×C59—21no—
214C4×C59—21no—
215C4×C59—21no—
216C4×C59—21no—
217C4×C59#54711yescharacteristic
218C4×C59#57811yescharacteristic
219Dic59—81no—
220Dic59—81no—
221Dic59—81no—
222Dic59—81no—
223Dic59—81no—
224Dic59—81no—
225Dic59—81no—
226#3339—591no—
227#3336—591no—
228#2253—591no—
229#2237—591no—
230#2235—591no—
231#2234—591no—
232#2233—591no—
233#2229—591no—
234#2228—591no—
235#2220—591no—
236#2220—591no—
237C4×SD32—591no—
238#2169D5911yescharacteristic, complemented
239#2159—591no—
240#2159—591no—
241C2×C59—41no—
242C2×C59—41no—
243C2×C59#333411yescharacteristic
244C2×C59#341411yescharacteristic
245C2×C59#341611yescharacteristic
246D59—161no—
247#553—1181no—
248#552—1181no—
249C2×SD32—591no—
250C2×M32C2×D5911yescharacteristic
251C2×M32C2×D5911yescharacteristic
252#499—591no—
253#499—591no—
254#485—1181no—
255#483—1181no—
256#482—1181no—
257#481—1181no—
258#479—1181no—
259#478—1181no—
260#467—591no—
261#467—591no—
262#466—591no—
263#466—591no—
264C4×Q16—591no—
265C4×D8—591no—
266C8×D4C2×D5911yescharacteristic
267#427—591no—
268#427—591no—
269C2×#107—591no—
270C2×#107—591no—
271#367—591no—
272#367—591no—
273#367—591no—
274#367—591no—
275#367—591no—
276#366—591no—
277#366—591no—
278#366—591no—
279#366—591no—
280C4⋊C16C2×D5911yescharacteristic
281#358—591no—
282#358—591no—
283#358—591no—
284#357—591no—
285#357—591no—
286#357—591no—
287C22⋊C16C2×D5911yescharacteristic
288C22⋊C16C2×D5911yescharacteristic
289C4×C16C2×D5911yescharacteristic
290C59#3391811yescharacteristic, complemented, Sylow
291C2×Q16—591no—
292C2×D8—591no—
293C22×C8C22×D5911yescharacteristic
294C22×C8C22×D5911yescharacteristic
295#126—2361no—
296#126—2361no—
297#125—1181no—
298#125—1181no—
299#125—2361no—
300#123—2361no—
301#123—2361no—
302C22⋊Q8—1181no—
303C22⋊Q8—1181no—
304#121—1181no—
305#121—1181no—
306#121—2361no—
307C4×Q8—1181no—
308C4×D4—1181no—
309C4×D4—2361no—
310C4×D4D23611yescharacteristic
311#117—1181no—
312#117—1181no—
313#117—2361no—
314C2×C4⋊C4—1181no—
315C2×C4⋊C4—1181no—
316SD32—1182no—
317M32—22no—
318M32—22no—
319C2×C16C22×D5911yescharacteristic
320C2×C16C22×D5911yescharacteristic
321C2×C16C22×D5911yescharacteristic
322C2×C16C22×D5911yescharacteristic
323#107—591no—
324#107—591no—
325#107—591no—
326#107—591no—
327#107—591no—
328#107—591no—
329#107—1181no—
330#107—1181no—
331#106—1181no—
332#106—1181no—
333#106—1181no—
334#106—1181no—
335C4⋊C8D23611yescharacteristic
336#103—1181no—
337#103—1181no—
338#103—1181no—
339#102—1181no—
340#102—1181no—
341#102—1181no—
342C22⋊C8D23611yescharacteristic
343C22⋊C8D23611yescharacteristic
344C4×C8C22×D5911yescharacteristic
345C2×Q8—1181no—
346C2×D4—1181no—
347C2×D4—2361no—
348C2×D4—2361no—
349C2×D4D47211yescharacteristic
350C22×C4—2361no—
351C22×C4—2361no—
352C22×C4—2361no—
353C22×C4C2×D23611yescharacteristic
354C22×C4C2×D23611yescharacteristic
355Q16—1181no—
356Q16—1181no—
357D8—1181no—
358D8—1181no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8C2×D23611yescharacteristic
364C2×C8C2×D23611yescharacteristic
365C2×C8C2×D23611yescharacteristic
366C2×C8C23×D5911yescharacteristic
367C4⋊C4—1181no—
368C4⋊C4—1181no—
369C4⋊C4—1181no—
370C4⋊C4—1181no—
371C4⋊C4—1181no—
372C4⋊C4—1181no—
373C4⋊C4—2361no—
374C4⋊C4—2361no—
375C4⋊C4—2361no—
376C4⋊C4—2361no—
377C4⋊C4—2361no—
378C4⋊C4—2361no—
379C4⋊C4—2361no—
380C4⋊C4—2361no—
381C4⋊C4—2361no—
382C4⋊C4D47211yescharacteristic
383C22⋊C4—2361no—
384C22⋊C4—2361no—
385C22⋊C4—2361no—
386C22⋊C4—2361no—
387C22⋊C4—2361no—
388C22⋊C4—2361no—
389C22⋊C4—2361no—
390C22⋊C4D47211yescharacteristic
391C22⋊C4D47211yescharacteristic
392C42—2361no—
393C42—2361no—
394C42—2361no—
395C42C2×D23611yescharacteristic
396C16—21no—
397C16—21no—
398C16—21no—
399C16#1174568712yes—
400C23—2361no—
401C23C2×D47211yescharacteristic
402C23C2×D47211yescharacteristic
403Q8—2361no—
404Q8—2361no—
405D4—41no—
406D4—9441no—
407D4—4722no—
408D4—2361no—
409D4—2361no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—9441no—
415C2×C4—9441no—
416C2×C4—4722no—
417C2×C4—2361no—
418C2×C4—2361no—
419C2×C4—2361no—
420C2×C4—2361no—
421C2×C4—2361no—
422C2×C4—2361no—
423C2×C4—2361no—
424C2×C4C2×D47211yescharacteristic
425C2×C4C2×D47211yescharacteristic
426C2×C4C2×D47211yescharacteristic
427C2×C4C2×D47211yescharacteristic
428C2×C4C22×D23611yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8C2×#1174568711yescharacteristic
433C8#1427377411yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—4721no—
441C22—4721no—
442C22—4721no—
443C22C22×D47211yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—4721no—
449C4—4721no—
450C4—4721no—
451C4—4721no—
452C4—4721no—
453C4—4721no—
454C4—4721no—
455C4#1683805611yescharacteristic
456C4#1683821911yescharacteristic
457C2—41no—
458C2—41no—
459C2—9441no—
460C2#2143644411yescharacteristic
461C2#2143723211yescharacteristic
462C2#2143724411yescharacteristic
subgroupG/H
centerC22C22×D472
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2169C2
socleC22×C59C22×D8
prime radical#21436499C2
hypercenter#2169D59
hypocenterC59#33918
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2169

Complements

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

NH ≅ G/Ntype
2. #21436465C2semidirect
3. #21426375C2semidirect
4. #21426305C2semidirect
5. #21426294C2semidirect
6. #21426288C2semidirect
7. #21426282C2semidirect
8. #21426261C2semidirect
9. #21426254C2semidirect
10. #21426209C2semidirect
11. #21426209C2semidirect
12. C4×#14273672C2semidirect
13. #21425884C2semidirect
14. #21425884C2semidirect
15. C59×#2169C2semidirect
238. #2169D59semidirect
290. C59#33918semidirect

Maximal subgroups

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

subgroupindex
#214364992
#214364652
#214263752
#214263052
#214262942
#214262882
#214262822
#214262612
#214262542
#214262092
C4×#142736722
#214258842
C59×#21692
#3391859