Finite Group Databasebeta

← #28558760

Subgroups — #28558760

Order 15104.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21434172C211yesmaximal, characteristic
2#21433176C211yesmaximal, characteristic, complemented
3#21422972C211yesmaximal, characteristic, complemented
4#21422965C211yesmaximal, characteristic, complemented
5#21422944C211yesmaximal, characteristic, complemented
6#21422937C211yesmaximal, characteristic, complemented
7#21422913C211yesmaximal, characteristic, complemented
8#21422908C211yesmaximal, characteristic, complemented
9C8×#11745672C211yesmaximal, characteristic, complemented
10C8×#11745670C211yesmaximal, characteristic, complemented
11#21422887C211yesmaximal, characteristic, complemented
12#21422524C211yesmaximal, characteristic, complemented
13#21422504C211yesmaximal, characteristic
14#21422396C211yesmaximal, characteristic, complemented
15C59×#2993C211yesmaximal, characteristic
16C2×C4×Dic118C2211yescharacteristic
17#16837730C411yescharacteristic
18#16837713C411yescharacteristic
19#16837706C411yescharacteristic
20#16837706C411yescharacteristic
21#16837621C411yescharacteristic
22#16837621C411yescharacteristic
23#16837557C411yescharacteristic
24#16837540C411yescharacteristic
25C8×Dic118C2211yescharacteristic
26C8×Dic118C2211yescharacteristic
27C8×Dic118C2211yescharacteristic
28C8×Dic118C2211yescharacteristic
29#16837526—21no—
30#16837526—21no—
31C4×#11745672C2211yescharacteristic
32C4×#11745672C2211yescharacteristic
33C4×#11745670C2211yescharacteristic
34C4×#11745670C2211yescharacteristic
35#16837455C2211yescharacteristic
36#16837455C2211yescharacteristic
37#16837455C2211yescharacteristic
38#16837452—21no—
39#16837452—21no—
40#16837154C2211yescharacteristic
41#16837154C2211yescharacteristic
42#16837152C2211yescharacteristic
43#16837152C2211yescharacteristic
44Q8⋊(C59⋊C8)C2211yescharacteristic
45Q8⋊(C59⋊C8)C2211yescharacteristic
46#16837132C2211yescharacteristic
47#16837132C2211yescharacteristic
48#16837132C2211yescharacteristic
49#16837132C2211yescharacteristic
50D4⋊(C59⋊C8)C2211yescharacteristic
51D4⋊(C59⋊C8)C2211yescharacteristic
52#16837124C2211yescharacteristic
53#16837124C2211yescharacteristic
54#16837123C2211yescharacteristic
55C8×C59⋊C8C2211yescharacteristic
56C59×#529C2211yescharacteristic
57C59×#446C2211yescharacteristic
58C8×Q8×C59C2211yescharacteristic
59C59×#436—21no—
60C59×#436C2211yescharacteristic
61C59×#435—21no—
62C8×D4×C59C2211yescharacteristic
63C59×#433—21no—
64C59×#431C2211yescharacteristic
65C59×#424—21no—
66C59×#423C2211yescharacteristic
67C22×Dic118C2×C411yescharacteristic
68C2×#11745672C2×C411yescharacteristic
69C2×#11745672C2×C411yescharacteristic
70C2×#11745670C2×C411yescharacteristic
71C2×#11745670C2×C411yescharacteristic
72C4×Dic118—21no—
73C4×Dic118—21no—
74C4×Dic118C2×C411yescharacteristic
75C4×Dic118C2×C411yescharacteristic
76C4×Dic118C2311yescharacteristic
77C4×Dic118C2311yescharacteristic
78C2×C4⋊Dic59C2×C411yescharacteristic
79C2×Dic59⋊C4—21no—
80C2×C4×Dic59—21no—
81#14273660C2×C411yescharacteristic
82#14273660C2×C411yescharacteristic
83#14273658C2×C411yescharacteristic
84#14273658C2×C411yescharacteristic
85C4⋊(C59⋊C8)—21no—
86C4⋊(C59⋊C8)C2×C411yescharacteristic
87C4⋊(C59⋊C8)C2×C411yescharacteristic
88C4⋊(C59⋊C8)C2311yescharacteristic
89C4⋊(C59⋊C8)C2311yescharacteristic
90Dic59⋊C8—21no—
91Dic59⋊C8—21no—
92Dic59⋊C8—21no—
93Dic59⋊C8—21no—
94#14273651C2×C411yescharacteristic
95#14273651C2×C411yescharacteristic
96#14273650C2×C411yescharacteristic
97#14273650C2×C411yescharacteristic
98#14273650C2×C411yescharacteristic
99#14273650C2×C411yescharacteristic
100#14273648C2×C411yescharacteristic
101#14273648C2×C411yescharacteristic
102C22⋊(C59⋊C8)—21no—
103C22⋊(C59⋊C8)—21no—
104C22⋊(C59⋊C8)C2×C411yescharacteristic
105C22⋊(C59⋊C8)C2×C411yescharacteristic
106C4×C59⋊C8—21no—
107C4×C59⋊C8C2311yescharacteristic
108C4×C59⋊C8C2311yescharacteristic
109C4×C59⋊C8C2311yescharacteristic
110C4×C59⋊C8C2311yescharacteristic
111C8×Dic59—21no—
112C8×Dic59—21no—
113C8×Dic59—21no—
114C8×Dic59—21no—
115C2×M16×C59—21no—
116C2×M16×C59—21no—
117C22×C8×C59—21no—
118#126×C59—21no—
119#125×C59C2×C411yescharacteristic
120#124×C59C2×C411yescharacteristic
121#123×C59—21no—
122C22⋊Q8×C59C2×C411yescharacteristic
123#121×C59C2×C411yescharacteristic
124C4×Q8×C59C2311yescharacteristic
125C4×D4×C59—21no—
126C4×D4×C59C2311yescharacteristic
127#117×C59—21no—
128C2×C42×C59C2311yescharacteristic
129C4⋊C8×C59—21no—
130C4⋊C8×C59—21no—
131C4⋊C8×C59—21no—
132C4⋊C8×C59D411yescharacteristic
133C4⋊C8×C59D411yescharacteristic
134C4⋊C8×C59C2311yescharacteristic
135C4⋊C8×C59C2311yescharacteristic
136C22⋊C8×C59—21no—
137C22⋊C8×C59—21no—
138C22⋊C8×C59D411yescharacteristic
139C22⋊C8×C59D411yescharacteristic
140#97×C59—21no—
141C4×C8×C59—21no—
142C4×C8×C59C2311yescharacteristic
143C4×C8×C59C2311yescharacteristic
144C2×Q8×C59C22×C411yescharacteristic
145C2×D4×C59—21no—
146C2×D4×C59C22×C411yescharacteristic
147C22×C4×C59—21no—
148C22×C4×C59C22×C411yescharacteristic
149C22×C4×C59C2×D411yescharacteristic
150C22×C4×C59#4111yescharacteristic
151C22×Dic59—21no—
152C22×Dic59—21no—
153C2×Dic118—21no—
154C2×Dic118—22no—
155C2×Dic118—22no—
156C2×Dic118C22×C411yescharacteristic
157C2×Dic118C22×C411yescharacteristic
158M16×C59—81no—
159M16×C59—81no—
160C2×C8×C59—21no—
161C2×C8×C59—21no—
162C2×C8×C59—81no—
163C2×C8×C59C2×D411yescharacteristic
164C2×C8×C59C2×D411yescharacteristic
165C2×C8×C59C2×D411yescharacteristic
166C2×C8×C59C2×D411yescharacteristic
167C4⋊C4×C59—21no—
168C4⋊C4×C59—21no—
169C4⋊C4×C59—21no—
170C4⋊C4×C59—21no—
171C4⋊C4×C59C22×C411yescharacteristic
172C4⋊C4×C59C22×C411yescharacteristic
173C22⋊C4×C59—21no—
174C22⋊C4×C59—21no—
175C22⋊C4×C59—21no—
176C22⋊C4×C59—21no—
177C22⋊C4×C59—21no—
178C42×C59—21no—
179C42×C59C22×C411yescharacteristic
180C42×C59C2×D411yescharacteristic
181C42×C59#4111yescharacteristic
182C42×C59C2411yescharacteristic
183#11745672—22no—
184#11745672—22no—
185#11745670—22no—
186#11745670—22no—
187C4⋊Dic59—21no—
188C4⋊Dic59C22×C411yescharacteristic
189C4⋊Dic59C22×C411yescharacteristic
190Dic59⋊C4—21no—
191Dic59⋊C4—21no—
192Dic59⋊C4—21no—
193Dic59⋊C4—21no—
194C4×Dic59—21no—
195C4×Dic59—21no—
196C4×Dic59—21no—
197C4×Dic59—21no—
198C2×C59⋊C8—21no—
199C2×C59⋊C8—21no—
200C2×C59⋊C8—21no—
201C2×C59⋊C8—21no—
202C2×C59⋊C8C22×C411yescharacteristic
203C2×C59⋊C8C22×C411yescharacteristic
204C2×C59⋊C8C22×C411yescharacteristic
205C2×C59⋊C8C22×C411yescharacteristic
206C23×C59—21no—
207C23×C59C4×D411yescharacteristic
208Q8×C59—21no—
209Q8×C59—21no—
210D4×C59—21no—
211D4×C59—21no—
212D4×C59—81no—
213C2×C4×C59—21no—
214C2×C4×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59—21no—
217C2×C4×C59—21no—
218C2×C4×C59—21no—
219C2×C4×C59—21no—
220C2×C4×C59—41no—
221C2×C4×C59—41no—
222C2×C4×C59—41no—
223C2×C4×C59C4×D411yescharacteristic
224C2×C4×C59C4×D411yescharacteristic
225C2×C4×C59C4×D411yescharacteristic
226C2×C4×C59C23×C411yescharacteristic
227C2×C4×C59C22×D411yescharacteristic
228C2×C4×C59C2×#4111yescharacteristic
229C2×Dic59—24no—
230C2×Dic59—21no—
231C2×Dic59—21no—
232C2×Dic59—21no—
233C2×Dic59—21no—
234C2×Dic59—81no—
235Dic118—24no—
236Dic118—21no—
237Dic118—21no—
238Dic118#13112yes—
239Dic118#13112yes—
240C8×C59—21no—
241C8×C59—21no—
242C8×C59—21no—
243C8×C59—21no—
244C8×C59—41no—
245C8×C59—41no—
246C59⋊C8—21no—
247C59⋊C8—21no—
248C59⋊C8—21no—
249C59⋊C8—21no—
250C59⋊C8—41no—
251C59⋊C8—41no—
252C59⋊C8—41no—
253C59⋊C8—41no—
254#17919—591nomaximal, Sylow
255C22×C59—21no—
256C22×C59—21no—
257C22×C59—21no—
258C22×C59—41no—
259C22×C59—41no—
260C22×C59—41no—
261C22×C59C2×C4×D411yescharacteristic
262C4×C59—21no—
263C4×C59—21no—
264C4×C59—21no—
265C4×C59—21no—
266C4×C59—41no—
267C4×C59—41no—
268C4×C59—41no—
269C4×C59C2×#13111yescharacteristic
270C4×C59C2×#13111yescharacteristic
271C4×C59#57711yescharacteristic
272C4×C59#57811yescharacteristic
273Dic59—22no—
274Dic59—22no—
275Dic59—41no—
276Dic59—41no—
277#3108—591no—
278#2993D5911yescharacteristic
279#2982—591no—
280#1588—591no—
281#1587—591no—
282#1584—591no—
283#1583—591no—
284#1579—591no—
285SD16⋊C8—591no—
286C8×Q16—591no—
287C8×SD16—591no—
288#1574—591no—
289#1487—591no—
290#1482—591no—
291#1454—591no—
292C2×C59—41no—
293C2×C59—81no—
294C2×C59#292911yescharacteristic
295C2×C59#294711yescharacteristic
296C2×C59#295711yescharacteristic
297#529C2×D5911yescharacteristic
298C2×C4×Q8—591no—
299#483—591no—
300#480—591no—
301#479—591no—
302#479—591no—
303#464—591no—
304#464—591no—
305#451—591no—
306#448—591no—
307#446C2×D5911yescharacteristic
308C8×Q8—591no—
309C8×Q8—591no—
310C8×Q8—591no—
311C8×Q8—591no—
312C8×Q8—1181no—
313C8×Q8—1181no—
314C8×Q8C2×D5911yescharacteristic
315C4×Q16—591no—
316C4×Q16—591no—
317C4×SD16—591no—
318C4×SD16—591no—
319#436—21no—
320#436C2×D5911yescharacteristic
321#435—21no—
322C8×D4C2×D5911yescharacteristic
323#433—21no—
324#431—591no—
325#431—591no—
326#431—591no—
327#431—1181no—
328#431—1181no—
329#431C2×D5911yescharacteristic
330#424—21no—
331#423C2×D5911yescharacteristic
332#335—591no—
333#335—591no—
334#334—591no—
335#334—591no—
336Q8⋊C8—591no—
337Q8⋊C8—591no—
338Q8⋊C8—591no—
339Q8⋊C8—591no—
340Q8⋊C8—591no—
341Q8⋊C8—591no—
342D4⋊C8—591no—
343D4⋊C8—591no—
344#322—591no—
345#322—591no—
346#322—591no—
347C82—591no—
348C59#1791911yescharacteristic, complemented, Sylow
349C22×Q8—591no—
350C2×Q16—591no—
351C2×Q16—591no—
352C2×SD16—591no—
353C2×SD16—591no—
354C2×M16—21no—
355C2×M16—21no—
356C22×C8—21no—
357#126—21no—
358#125C4×D5911yescharacteristic
359#124C4×D5911yescharacteristic
360#123—21no—
361C22⋊Q8C4×D5911yescharacteristic
362#121C4×D5911yescharacteristic
363C4×Q8—591no—
364C4×Q8—591no—
365C4×Q8—591no—
366C4×Q8—591no—
367C4×Q8—1181no—
368C4×Q8—1181no—
369C4×Q8C22×D5911yescharacteristic
370C4×D4—21no—
371C4×D4C22×D5911yescharacteristic
372#117—21no—
373C2×C4⋊C4—591no—
374C2×C4⋊C4—1181no—
375C2×C42—1181no—
376C2×C42C22×D5911yescharacteristic
377#107—591no—
378#107—591no—
379#106—591no—
380#106—591no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—591no—
385C4⋊C8—591no—
386C4⋊C8—591no—
387C4⋊C8—591no—
388C4⋊C8—1181no—
389C4⋊C8—1181no—
390C4⋊C8—1181no—
391C4⋊C8—1181no—
392C4⋊C8—1181no—
393C4⋊C8C22⋊D5911yescharacteristic
394C4⋊C8C22⋊D5911yescharacteristic
395C4⋊C8C22×D5911yescharacteristic
396C4⋊C8C22×D5911yescharacteristic
397#103—591no—
398#103—591no—
399#103—591no—
400#103—591no—
401#103—591no—
402#103—591no—
403#102—591no—
404#102—591no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—591no—
408C22⋊C8—591no—
409C22⋊C8—1181no—
410C22⋊C8—1181no—
411C22⋊C8C22⋊D5911yescharacteristic
412C22⋊C8C22⋊D5911yescharacteristic
413#97—21no—
414C4×C8—21no—
415C4×C8—591no—
416C4×C8—591no—
417C4×C8—591no—
418C4×C8—591no—
419C4×C8—1181no—
420C4×C8—1181no—
421C4×C8—1181no—
422C4×C8—1181no—
423C4×C8—1181no—
424C4×C8C22×D5911yescharacteristic
425C4×C8C22×D5911yescharacteristic
426C2×Q8—591no—
427C2×Q8—591no—
428C2×Q8—1182no—
429C2×Q8—1182no—
430C2×Q8—1181no—
431C2×Q8C2×C4×D5911yescharacteristic
432C2×D4—21no—
433C2×D4C2×C4×D5911yescharacteristic
434C22×C4—21no—
435C22×C4—1181no—
436C22×C4—1181no—
437C22×C4C2×C4×D5911yescharacteristic
438C22×C4#1174568511yescharacteristic
439C22×C4C2×C22⋊D5911yescharacteristic
440Q16—1182no—
441Q16—1182no—
442SD16—1182no—
443SD16—1182no—
444M16—81no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—591no—
450C2×C8—591no—
451C2×C8—591no—
452C2×C8—591no—
453C2×C8—1181no—
454C2×C8—1181no—
455C2×C8—1181no—
456C2×C8—1181no—
457C2×C8C2×C22⋊D5911yescharacteristic
458C2×C8C2×C22⋊D5911yescharacteristic
459C2×C8C2×C22⋊D5911yescharacteristic
460C2×C8C2×C22⋊D5911yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—591no—
466C4⋊C4—591no—
467C4⋊C4—1181no—
468C4⋊C4—1181no—
469C4⋊C4—1181no—
470C4⋊C4—1181no—
471C4⋊C4—1181no—
472C4⋊C4C2×C4×D5911yescharacteristic
473C4⋊C4C2×C4×D5911yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—21no—
480C42—1181no—
481C42—1181no—
482C42—1181no—
483C42—1181no—
484C42C2×C4×D5911yescharacteristic
485C42#1174568511yescharacteristic
486C42C2×C22⋊D5911yescharacteristic
487C42C23×D5911yescharacteristic
488C23—21no—
489C23C4×C22⋊D5911yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—592no—
493Q8—592no—
494Q8—1184no—
495Q8—1181no—
496Q8—1181no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—1184no—
511C2×C4—1181no—
512C2×C4—1181no—
513C2×C4—1181no—
514C2×C4—1181no—
515C2×C4—4721no—
516C2×C4C4×C22⋊D5911yescharacteristic
517C2×C4C4×C22⋊D5911yescharacteristic
518C2×C4C4×C22⋊D5911yescharacteristic
519C2×C4C22×C4×D5911yescharacteristic
520C2×C4C22×C22⋊D5911yescharacteristic
521C2×C4C2×#1174568511yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—1181no—
529C8—1181no—
530C8—1181no—
531C8—1181no—
532C8—2361no—
533C8—2361no—
534C8—2361no—
535C8—2361no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×C4×C22⋊D5911yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—1182no—
551C4—1182no—
552C4—2361no—
553C4—2361no—
554C4#131×D5911yescharacteristic
555C4#131×D5911yescharacteristic
556C4#1683821311yescharacteristic
557C4#1683821711yescharacteristic
558C2—41no—
559C2—81no—
560C2#2143278811yescharacteristic
561C2#2143293511yescharacteristic
562C2#2143301111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC59×#2993C2
socleC22×C59C2×C4×D4
prime radical#121×C59C2×C4
cosocleC42×C59C24
hypercenter#2993D59
hypocenterC59#17919
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #21433176C2semidirect
3. #21422972C2semidirect
4. #21422965C2semidirect
5. #21422944C2semidirect
6. #21422937C2semidirect
7. #21422913C2semidirect
8. #21422908C2semidirect
9. C8×#11745672C2semidirect
10. C8×#11745670C2semidirect
11. #21422887C2semidirect
12. #21422524C2semidirect
14. #21422396C2semidirect
348. C59#17919semidirect

Maximal subgroups

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

subgroupindex
#214341722
#214331762
#214229722
#214229652
#214229442
#214229372
#214229132
#214229082
C8×#117456722
C8×#117456702
#214228872
#214225242
#214225042
#214223962
C59×#29932
#1791959