Finite Group Databasebeta

← #28496490

Subgroups — #28496490

Order 15104.

922 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837408C211yesmaximal, characteristic
2C2×#16837406C211yesmaximal, characteristic
3C22×#14273643C211yesmaximal, characteristic
4C2×#16837173C211yesmaximal, characteristic, complemented
5#21423822C211yesmaximal, characteristic, complemented
6#21423805C211yesmaximal, characteristic, complemented
7C59×#1742C211yesmaximal, characteristic, complemented
8C23×D236C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C22×#11745664C2211yescharacteristic
11C2×#14273686C2211yescharacteristic
12#16837408—22no—
13#16837408C414yescomplemented
14#16837406—22no—
15#16837406—22no—
16C2×#14273649—22no—
17C2×#14273647—22no—
18C2×#14273643—22no—
19C2×#14273643—22no—
20C2×#14273643—22no—
21#16837173—22no—
22#16837166—22no—
23#16837161—22no—
24C22×M16×C59C2211yescharacteristic
25C22×M16×C59C2211yescharacteristic
26C2×#117×C59C2211yescharacteristic
27C59×#343—22no—
28C24×D59—21no—
29C22×D236—21no—
30C22×D236—21no—
31C22×D236—21no—
32C22×D236—21no—
33C22×D236—21no—
34C22×D236—21no—
35C22×D236—21no—
36C22×D236—21no—
37C22×D236—21no—
38C22×D236—21no—
39C22×D236—21no—
40C22×D236C2×C412yes—
41C22×D236D412yes—
42C22×D236D412yes—
43C2×#11745664—21no—
44C2×#11745664—21no—
45C2×#11745664—21no—
46C2×#11745664—21no—
47C2×#11745664—21no—
48C2×#11745664—21no—
49C2×#11745664—21no—
50C2×#11745664—21no—
51C2×#11745664—21no—
52C2×#11745664—21no—
53C2×#11745664D412yes—
54C2×#11745664D412yes—
55C22×C59⋊C8—21no—
56C22×C59⋊C8—21no—
57#14273686—21no—
58#14273686—21no—
59#14273686—21no—
60#14273686C2×C412yes—
61C2×C4⋊Dic59—21no—
62C2×C22⋊Dic59—21no—
63C2×C4×Dic59—21no—
64#14273649—28no—
65#14273647—28no—
66#14273643—28no—
67C23×C4×C59C2311yescharacteristic
68C2×M16×C59—21no—
69C2×M16×C59—21no—
70C2×M16×C59—21no—
71C2×M16×C59—21no—
72C2×M16×C59—21no—
73C2×M16×C59—21no—
74C2×M16×C59—21no—
75C2×M16×C59—21no—
76C2×M16×C59—21no—
77C2×M16×C59—21no—
78C2×M16×C59C2×C412yes—
79C2×M16×C59D412yes—
80C22×C8×C59—21no—
81C22×C8×C59—21no—
82#117×C59—21no—
83#117×C59—21no—
84#117×C59—21no—
85#117×C59—21no—
86C2×C4⋊C4×C59D412yes—
87C2×C22⋊C4×C59—21no—
88C2×C42×C59—21no—
89C24×C59#4111yescharacteristic
90C23×D59—22no—
91C23×D59—22no—
92C23×D59—22no—
93C23×D59—41no—
94C23×D59—41no—
95C23×D59—41no—
96C23×D59—41no—
97C23×D59—84no—
98C22×C4×C59—22no—
99C22×C4×C59C22×C411yescharacteristic
100C22×C4×C59C2×D411yescharacteristic
101C22×C4×C59C2×D411yescharacteristic
102C22×C4×C59C2×D411yescharacteristic
103C22×C4×C59C2×D411yescharacteristic
104C22×C4×C59C2×D411yescharacteristic
105C22×C4×C59C2×D411yescharacteristic
106C22×C4×C59#4111yescharacteristic
107C22×C4×C59#4111yescharacteristic
108C22×C4×C59#4111yescharacteristic
109C22×C4×C59#4111yescharacteristic
110C22×C4×C59#4111yescharacteristic
111C22×C4×C59#4111yescharacteristic
112C22×C4×C59#4111yescharacteristic
113C22×Dic59—41no—
114C2×D236—22no—
115C2×D236—22no—
116C2×D236—22no—
117C2×D236—22no—
118C2×D236—22no—
119C2×D236—22no—
120C2×D236—22no—
121C2×D236—22no—
122C2×D236—22no—
123C2×D236—22no—
124C2×D236—22no—
125C2×D236—22no—
126C2×D236—22no—
127C2×D236—22no—
128C2×D236—22no—
129C2×D236—41no—
130C2×D236—41no—
131C2×D236—41no—
132C2×D236—41no—
133C2×D236—41no—
134C2×D236—41no—
135C2×D236—41no—
136C2×D236—41no—
137C2×D236—41no—
138C2×D236—41no—
139C2×D236—41no—
140C2×D236—41no—
141C2×D236C22⋊C414yes—
142M16×C59—22no—
143M16×C59—22no—
144M16×C59—22no—
145M16×C59—22no—
146M16×C59—41no—
147M16×C59—41no—
148M16×C59—41no—
149M16×C59—41no—
150C2×C8×C59—22no—
151C2×C8×C59—22no—
152C2×C8×C59—41no—
153C2×C8×C59—41no—
154C2×C8×C59—41no—
155C2×C8×C59—41no—
156C4⋊C4×C59—22no—
157C4⋊C4×C59—22no—
158C22⋊C4×C59—41no—
159C22⋊C4×C59—41no—
160C42×C59—41no—
161C42×C59—41no—
162C22⋊Dic59—22no—
163C22⋊Dic59—41no—
164C4⋊Dic59—22no—
165C4⋊Dic59—41no—
166C4×Dic59—22no—
167C4×Dic59—41no—
168#11745664—22no—
169#11745664—22no—
170#11745664—22no—
171#11745664—22no—
172#11745664—41no—
173#11745664—41no—
174#11745664—41no—
175#11745664—41no—
176C2×C59⋊C8—22no—
177C2×C59⋊C8—22no—
178C2×C59⋊C8—41no—
179C2×C59⋊C8—41no—
180C2×C59⋊C8—41no—
181C2×C59⋊C8—41no—
182C23×C59—42no—
183C23×C59C4×D411yescharacteristic
184C23×C59#12111yescharacteristic
185C23×C59#12311yescharacteristic
186C23×C59#12311yescharacteristic
187C23×C59#12411yescharacteristic
188C23×C59#12611yescharacteristic
189C23×C59#12611yescharacteristic
190C22×D59—24no—
191C22×D59—42no—
192C22×D59—42no—
193C22×D59—42no—
194C22×D59—42no—
195C22×D59—42no—
196C22×D59—42no—
197C22×D59—84no—
198C22×D59—84no—
199C22×D59—84no—
200C22×D59—84no—
201C22×D59—84no—
202C22×D59—84no—
203C22×D59—84no—
204C2×C4×C59—42no—
205C2×C4×C59—82no—
206C2×C4×C59C2×C22⋊C411yescharacteristic
207C2×C4×C59#11711yescharacteristic
208C2×C4×C59#11711yescharacteristic
209C2×C4×C59C4×D411yescharacteristic
210C2×C4×C59C4×D411yescharacteristic
211C2×C4×C59C4×D411yescharacteristic
212C2×C4×C59#12011yescharacteristic
213C2×C4×C59#12011yescharacteristic
214C2×C4×C59#12111yescharacteristic
215C2×C4×C59#12111yescharacteristic
216C2×C4×C59#12111yescharacteristic
217C2×C4×C59#12111yescharacteristic
218C2×C4×C59#12111yescharacteristic
219C2×C4×C59#12111yescharacteristic
220C2×C4×C59#12111yescharacteristic
221C2×C4×C59#12311yescharacteristic
222C2×C4×C59#12311yescharacteristic
223C2×C4×C59#12311yescharacteristic
224C2×C4×C59#12311yescharacteristic
225C2×C4×C59#12311yescharacteristic
226C2×C4×C59#12311yescharacteristic
227C2×C4×C59#12311yescharacteristic
228C2×C4×C59#12311yescharacteristic
229C2×C4×C59#12411yescharacteristic
230C2×C4×C59#12411yescharacteristic
231C2×C4×C59#12411yescharacteristic
232C2×C4×C59#12611yescharacteristic
233C2×C4×C59#12611yescharacteristic
234C2×Dic59—42no—
235C2×Dic59—82no—
236D236—24no—
237D236—24no—
238D236—42no—
239D236—42no—
240D236—42no—
241D236—42no—
242D236—42no—
243D236—42no—
244C8×C59—42no—
245C8×C59—42no—
246C59⋊C8—42no—
247C59⋊C8—42no—
248#11187—591nomaximal, Sylow
249C22×C59—22no—
250C22×C59—22no—
251C22×C59—22no—
252C22×C59—41no—
253C22×C59—41no—
254C22×C59—41no—
255C22×C59—41no—
256C22×C59#38611yescharacteristic
257C22×C59#38811yescharacteristic
258C22×C59#38811yescharacteristic
259C22×C59#39411yescharacteristic
260C22×C59#39711yescharacteristic
261C22×C59#39711yescharacteristic
262C22×C59#39711yescharacteristic
263C2×D59—44no—
264C2×D59—84no—
265C2×D59—84no—
266C2×D59—84no—
267C2×D59—84no—
268C2×D59—84no—
269C2×D59—84no—
270C2×D59—84no—
271C4×C59—82no—
272C4×C59#38111yescharacteristic
273C4×C59#38611yescharacteristic
274C4×C59#38811yescharacteristic
275C4×C59#38811yescharacteristic
276C4×C59#39411yescharacteristic
277C4×C59#39411yescharacteristic
278C4×C59#39411yescharacteristic
279C4×C59#39711yescharacteristic
280Dic59—82no—
281C2×#418—591no—
282C2×#418—591no—
283C22×#100—591no—
284C2×#344—591no—
285#1742D5911yescharacteristic, complemented
286#1738—591no—
287#1733—591no—
288C2×C59—21no—
289C2×C59—21no—
290C2×C59—21no—
291C2×C59—21no—
292C2×C59—21no—
293C2×C59—21no—
294C2×C59#144011yescharacteristic
295C2×C59#204812yes—
296D59—84no—
297C23×D4—591no—
298C22×M16—591no—
299C22×M16—591no—
300C22×M16C2×D5911yescharacteristic
301C22×M16C2×D5911yescharacteristic
302C2×#117—591no—
303C2×#117C2×D5911yescharacteristic
304#418—594no—
305#418—1182no—
306#418—1182no—
307#418—1182no—
308C2×#102—1182no—
309C2×#102—1182no—
310C2×#100—1182no—
311C2×#100—1182no—
312C2×#100—1182no—
313#344—1182no—
314#343—22no—
315#341—1182no—
316#339—1182no—
317C59#1118711yescharacteristic, complemented, Sylow
318C25—1181no—
319C22×D4—592no—
320C22×D4—592no—
321C22×D4—592no—
322C22×D4—1181no—
323C22×D4—1181no—
324C22×D4—1181no—
325C22×D4—1181no—
326C22×D4—1181no—
327C22×D4—1181no—
328C22×D4—1181no—
329C22×D4—1181no—
330C22×D4—1181no—
331C22×D4—1181no—
332C22×D4—1181no—
333C23×C4C22×D5911yescharacteristic
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—592no—
345C2×M16—592no—
346C2×M16—1181no—
347C2×M16—1181no—
348C2×M16—1181no—
349C2×M16—1181no—
350C2×M16—1181no—
351C2×M16—1181no—
352C2×M16—1181no—
353C2×M16—1181no—
354C2×M16—1181no—
355C2×M16—1181no—
356C2×M16C4×D5912yes—
357C2×M16D23612yes—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—1181no—
361C22×C8—1181no—
362#117—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—592no—
367#117—1181no—
368#117—1181no—
369#117—1181no—
370C2×C4⋊C4—1181no—
371C2×C4⋊C4C22⋊D5912yes—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—1181no—
374C2×C42—21no—
375C2×C42—1181no—
376#102—1188no—
377#102—1188no—
378#100—1188no—
379C24—1182no—
380C24—1182no—
381C24—1182no—
382C24—4724no—
383C24—2361no—
384C24—2361no—
385C24—2361no—
386C24—2361no—
387C24#1174568511yescharacteristic
388C2×D4—594no—
389C2×D4—1182no—
390C2×D4—1182no—
391C2×D4—1182no—
392C2×D4—1182no—
393C2×D4—1182no—
394C2×D4—1182no—
395C2×D4—1182no—
396C2×D4—1182no—
397C2×D4—1182no—
398C2×D4—1182no—
399C2×D4—1182no—
400C2×D4—1182no—
401C2×D4—1182no—
402C2×D4—1182no—
403C2×D4—1182no—
404C2×D4—2361no—
405C2×D4—2361no—
406C2×D4—2361no—
407C2×D4—2361no—
408C2×D4—2361no—
409C2×D4—2361no—
410C2×D4—2361no—
411C2×D4—2361no—
412C2×D4—2361no—
413C2×D4—2361no—
414C2×D4—2361no—
415C2×D4—2361no—
416C22×C4—22no—
417C22×C4—2361no—
418C22×C4C2×C4×D5911yescharacteristic
419C22×C4C2×D23611yescharacteristic
420C22×C4#1174568511yescharacteristic
421C22×C4#1174568511yescharacteristic
422C22×C4#1174568511yescharacteristic
423C22×C4D4×D5911yescharacteristic
424C22×C4D4×D5911yescharacteristic
425C22×C4D4×D5911yescharacteristic
426C22×C4D4×D5911yescharacteristic
427C22×C4#1174568711yescharacteristic
428C22×C4#1174568711yescharacteristic
429C22×C4#1174568911yescharacteristic
430C22×C4#1174568911yescharacteristic
431C22×C4C2×C22⋊D5911yescharacteristic
432M16—22no—
433M16—22no—
434M16—22no—
435M16—22no—
436M16—41no—
437M16—41no—
438M16—41no—
439M16—41no—
440M16—1182no—
441M16—1182no—
442M16—1182no—
443M16—1182no—
444M16—2361no—
445M16—2361no—
446M16—2361no—
447M16—2361no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—41no—
451C2×C8—41no—
452C2×C8—41no—
453C2×C8—41no—
454C2×C8—1182no—
455C2×C8—1182no—
456C2×C8—2361no—
457C2×C8—2361no—
458C2×C8—2361no—
459C2×C8—2361no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—1182no—
463C4⋊C4—2361no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—1182no—
467C22⋊C4—2361no—
468C42—41no—
469C42—41no—
470C42—1182no—
471C42—2361no—
472C23—42no—
473C23—1184no—
474C23—4724no—
475C23—4724no—
476C23—4724no—
477C23—4724no—
478C23—4724no—
479C23—4724no—
480C23—4724no—
481C23—2362no—
482C23—2362no—
483C23—2362no—
484C23—2362no—
485C23—2362no—
486C23—2362no—
487C23C4×D23611yescharacteristic
488C23#1427370011yescharacteristic
489C23#1427371011yescharacteristic
490C23#1427371211yescharacteristic
491C23#1427371311yescharacteristic
492C23#1427372111yescharacteristic
493C23#1427372211yescharacteristic
494D4—1184no—
495D4—1184no—
496D4—2362no—
497D4—2362no—
498D4—2362no—
499D4—2362no—
500D4—2362no—
501D4—2362no—
502C2×C4—42no—
503C2×C4—82no—
504C2×C4—4722no—
505C2×C4—2362no—
506C2×C4C22⋊C4×D5911yescharacteristic
507C2×C4#1427368411yescharacteristic
508C2×C4#1427368511yescharacteristic
509C2×C4(C22⋊D59)⋊C411yescharacteristic
510C2×C4C4×C22⋊D5911yescharacteristic
511C2×C4#1427368911yescharacteristic
512C2×C4#1427369511yescharacteristic
513C2×C4#1427369711yescharacteristic
514C2×C4#1427369811yescharacteristic
515C2×C4#1427369911yescharacteristic
516C2×C4#1427370011yescharacteristic
517C2×C4#1427370011yescharacteristic
518C2×C4#1427370111yescharacteristic
519C2×C4#1427370211yescharacteristic
520C2×C4#1427370211yescharacteristic
521C2×C4#1427370911yescharacteristic
522C2×C4#1427370911yescharacteristic
523C2×C4#1427370911yescharacteristic
524C2×C4#1427371111yescharacteristic
525C2×C4#1427371211yescharacteristic
526C2×C4#1427371211yescharacteristic
527C2×C4#1427371211yescharacteristic
528C2×C4#1427371211yescharacteristic
529C2×C4#1427371311yescharacteristic
530C2×C4#1427371511yescharacteristic
531C2×C4#1427371611yescharacteristic
532C2×C4#1427372211yescharacteristic
533C2×C4#1427372211yescharacteristic
534C8—42no—
535C8—42no—
536C8—2362no—
537C8—2362no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—4724no—
546C22—4724no—
547C22—4724no—
548C22—4724no—
549C22—4724no—
550C22—4724no—
551C22—4724no—
552C22—2364no—
553C22#1683728011yescharacteristic
554C22#1683729311yescharacteristic
555C22#1683729411yescharacteristic
556C22#1683731711yescharacteristic
557C22#1683732811yescharacteristic
558C22#1683733111yescharacteristic
559C22#1683733111yescharacteristic
560C4—82no—
561C4—4722no—
562C4#1683726411yescharacteristic
563C4#1683727811yescharacteristic
564C4#1683729111yescharacteristic
565C4#1683729211yescharacteristic
566C4#1683731811yescharacteristic
567C4#1683731911yescharacteristic
568C4#1683732011yescharacteristic
569C4#1683732911yescharacteristic
570C2—21no—
571C2—21no—
572C2—21no—
573C2—21no—
574C2—21no—
575C2—21no—
576C2—4724no—
577C2#2142234411yescharacteristic
578C2#2142536912yes—
subgroupG/H
centerC22#16837317
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#1742C2
socleC22×C59#394
prime radicalC23×D236C22
cosocleC23×C4×C59C23
hypercenter#1742D59
hypocenterC59#11187
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1742

Complements

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

NH ≅ G/Ntype
4. C2×#16837173C2semidirect
5. #21423822C2semidirect
6. #21423805C2semidirect
7. C59×#1742C2semidirect
13. #16837408C4semidirect
285. #1742D59semidirect
317. C59#11187semidirect

Maximal subgroups

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

subgroupindex
C2×#168374082
C2×#168374062
C22×#142736432
C2×#168371732
#214238222
#214238052
C59×#17422
#1118759