Finite Group Databasebeta

← #28631086

Subgroups — #28631086

Order 15104.

956 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837658C211yesmaximal, characteristic, complemented
2C2×#16837658C211yesmaximal, characteristic, complemented
3C2×#16837480C211yesmaximal, characteristic
4C2×#16837442C211yesmaximal, characteristic, complemented
5#21427525C211yesmaximal, characteristic
6#21425488C211yesmaximal, characteristic, complemented
7#21425477C211yesmaximal, characteristic, complemented
8#21425296C211yesmaximal, characteristic, complemented
9#21425292C211yesmaximal, characteristic, complemented
10#21424956C211yesmaximal, characteristic, complemented
11#21424821C211yesmaximal, characteristic, complemented
12#21424409C211yesmaximal, characteristic, complemented
13#21424403C211yesmaximal, characteristic, complemented
14#21424127C211yesmaximal, characteristic, complemented
15C59×#2417C211yesmaximal, characteristic
16C22×#11745672C2211yescharacteristic
17C22×#11745664C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C2×#14273706C2211yescharacteristic
20C2×#14273706C2211yescharacteristic
21C2×#14273686C2211yescharacteristic
22#16837658—24no—
23#16837658—24no—
24#16837480—24no—
25#16837442—24no—
26C2×#14273660C2211yescharacteristic
27C2×#14273660C2211yescharacteristic
28C2×#14273658C2211yescharacteristic
29C2×#14273658C2211yescharacteristic
30C2×#14273658C2211yescharacteristic
31C2×C4⋊(C59⋊C8)C2211yescharacteristic
32C2×#14273651C2211yescharacteristic
33C2×#14273651C2211yescharacteristic
34C2×#14273651C2211yescharacteristic
35C2×#14273650C2211yescharacteristic
36C2×#14273650C2211yescharacteristic
37C2×#14273650C2211yescharacteristic
38C2×C22⋊(C59⋊C8)C2211yescharacteristic
39C2×C22⋊(C59⋊C8)C2211yescharacteristic
40C2×C4×C59⋊C8C2211yescharacteristic
41#16837330—21no—
42#16837316—21no—
43#16837308C2211yescharacteristic
44#16837300C2211yescharacteristic
45#16837297—21no—
46#16837296—21no—
47#16837262C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52C2×C22⋊Q8×C59C2211yescharacteristic
53C2×C22⋊Q8×C59C2211yescharacteristic
54C2×C4×D4×C59C2211yescharacteristic
55C22×C4⋊C4×C59C2211yescharacteristic
56C59×#398—21no—
57C59×#396—21no—
58C59×#391C2211yescharacteristic
59C59×#389C2211yescharacteristic
60C59×#386—21no—
61C59×#380—21no—
62C59×#380C2211yescharacteristic
63C22×Dic118C2311yescharacteristic
64C2×#11745672—22no—
65C2×#11745672—22no—
66C2×#11745672—22no—
67C2×#11745664—22no—
68C2×#11745664—22no—
69C2×#11745664—22no—
70C2×#11745664—22no—
71C2×#11745664—22no—
72C2×#11745664D414yes—
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77#14273706—22no—
78#14273706—22no—
79#14273706—22no—
80#14273706—41no—
81#14273686—22no—
82#14273686—41no—
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×Dic59⋊C4—21no—
87C2×Dic59⋊C4—21no—
88C2×Dic59⋊C4—21no—
89C2×C22⋊Dic59—21no—
90C2×C22⋊Dic59—21no—
91C2×C22⋊Dic59—21no—
92C2×C22⋊Dic59—21no—
93C2×C4×Dic59—21no—
94#14273660—22no—
95#14273660—22no—
96#14273658—22no—
97#14273658—22no—
98#14273658D414yescomplemented
99C4⋊(C59⋊C8)—22no—
100#14273651—22no—
101#14273651—22no—
102#14273651—41no—
103#14273650—22no—
104#14273650—22no—
105#14273650—41no—
106C22⋊(C59⋊C8)—22no—
107C22⋊(C59⋊C8)—22no—
108C4×C59⋊C8—22no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C22×Q8×C59C2311yescharacteristic
114C22×D4×C59D411yescharacteristic
115C23×C4×C59—21no—
116C23×C4×C59C2311yescharacteristic
117C23×C4×C59C2311yescharacteristic
118C22⋊Q8×C59—22no—
119C22⋊Q8×C59—22no—
120C22⋊Q8×C59—22no—
121C22⋊Q8×C59—41no—
122C4×D4×C59—22no—
123C4×D4×C59—22no—
124C2×C4⋊C4×C59—22no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59—21no—
127C2×C4⋊C4×C59—21no—
128C2×C4⋊C4×C59—21no—
129C2×C4⋊C4×C59—41no—
130C2×C4⋊C4×C59D411yescharacteristic
131C2×C4⋊C4×C59C2311yescharacteristic
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C4⋊C4×C59C2311yescharacteristic
134C2×C22⋊C4×C59—21no—
135C2×C22⋊C4×C59—21no—
136C2×C22⋊C4×C59—21no—
137C2×C22⋊C4×C59D411yescharacteristic
138C2×C22⋊C4×C59D411yescharacteristic
139C2×C42×C59C2311yescharacteristic
140#95×C59—21no—
141#95×C59—21no—
142#95×C59—21no—
143#95×C59—21no—
144C24×C59C2×D411yescharacteristic
145C24×C59C2×D411yescharacteristic
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×D4×C59—22no—
153C2×D4×C59—22no—
154C2×D4×C59—41no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—42no—
170C22×C4×C59—42no—
171C22×C4×C59—81no—
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D412yes—
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59#4112yes—
178C22×C4×C59C2411yescharacteristic
179C22×Dic59—21no—
180C22×Dic59—21no—
181C22×Dic59—21no—
182C22×Dic59—21no—
183C2×Dic118—21no—
184C2×Dic118—21no—
185C2×Dic118—21no—
186C2×Dic118—21no—
187C2×Dic118—21no—
188C2×Dic118—21no—
189C4⋊C4×C59—22no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59—21no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—42no—
196C4⋊C4×C59—42no—
197C4⋊C4×C59—42no—
198C4⋊C4×C59—81no—
199C4⋊C4×C59C2×D412yes—
200C22⋊C4×C59—22no—
201C22⋊C4×C59—22no—
202C22⋊C4×C59—42no—
203C22⋊C4×C59—42no—
204C22⋊C4×C59—81no—
205C42×C59—21no—
206C42×C59—21no—
207C22⋊Dic59—42no—
208C22⋊Dic59—42no—
209C22⋊Dic59—42no—
210C22⋊Dic59—42no—
211#11745672—44no—
212C4⋊Dic59—21no—
213C4⋊Dic59—21no—
214C4⋊Dic59—21no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59C2×D412yes—
218Dic59⋊C4—42no—
219Dic59⋊C4—42no—
220Dic59⋊C4—42no—
221C4×Dic59—42no—
222#11745664—28no—
223#11745664—44no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8C2×D412yes—
233C2×C59⋊C8C2×D412yes—
234C2×C59⋊C8C2×D412yes—
235C2×C59⋊C8#4112yes—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59—21no—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59#12112yes—
250C23×C59C22×D411yescharacteristic
251Q8×C59—41no—
252Q8×C59—41no—
253Q8×C59—41no—
254Q8×C59—41no—
255D4×C59—44no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—22no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—41no—
272C2×C4×C59—41no—
273C2×C4×C59—41no—
274C2×C4×C59—41no—
275C2×C4×C59—41no—
276C2×C4×C59—41no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—84no—
287C2×C4×C59#12112yes—
288C2×C4×C59#13712yes—
289C2×C4×C59C22×D411yescharacteristic
290C2×C4×C59C22×D411yescharacteristic
291C2×C4×C59C2×#4111yescharacteristic
292C2×C4×C59C2×#4111yescharacteristic
293C2×C4×C59H(5,𝔽2)11yescharacteristic
294C2×C4×C592−1+411yescharacteristic
295C2×Dic59—22no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307Dic118—41no—
308Dic118—41no—
309Dic118—41no—
310Dic118—41no—
311C59⋊C8—22no—
312C59⋊C8—41no—
313C59⋊C8—41no—
314C59⋊C8#12114yes—
315#24793—591nomaximal, Sylow
316C22×C59—22no—
317C22×C59—22no—
318C22×C59—22no—
319C22×C59—41no—
320C22×C59—41no—
321C22×C59—41no—
322C22×C59—41no—
323C22×C59—41no—
324C22×C59—41no—
325C22×C59—41no—
326C22×C59—41no—
327C22×C59—41no—
328C22×C59—41no—
329C22×C59—41no—
330C22×C59C2×#12111yescharacteristic
331C22×C59D4211yescharacteristic
332C22×C59#54711yescharacteristic
333C22×C59C2×#13711yescharacteristic
334C22×C59#57511yescharacteristic
335C22×C59#57711yescharacteristic
336C22×C59#57811yescharacteristic
337C4×C59—22no—
338C4×C59—22no—
339C4×C59—41no—
340C4×C59—42no—
341C4×C59—41no—
342C4×C59—81no—
343C4×C59—81no—
344C4×C59—81no—
345C4×C59C2×#12111yescharacteristic
346C4×C59#53711yescharacteristic
347C4×C59#54811yescharacteristic
348C4×C59#55311yescharacteristic
349Dic59—42no—
350Dic59—81no—
351Dic59—81no—
352Dic59—81no—
353C2×#470—591no—
354C2×#470—591no—
355C2×#436—591no—
356C2×#428—591no—
357#2417D5911yescharacteristic
358#2415—591no—
359#2068—591no—
360#2066—591no—
361#2036—591no—
362#2035—591no—
363#1969—591no—
364#1941—591no—
365#1873—591no—
366#1872—591no—
367#1809—591no—
368C2×C59—42no—
369C2×C59—81no—
370C2×C59#241611yescharacteristic
371C2×C59#305611yescharacteristic
372C2×C59#306311yescharacteristic
373C2×C59#327511yescharacteristic
374C2×C59#327611yescharacteristic
375C2×C59#335211yescharacteristic
376C2×C59#335611yescharacteristic
377C22×Q16—591no—
378C22×M16—591no—
379C22×M16—591no—
380C2×C22⋊Q8—591no—
381C2×C22⋊Q8—591no—
382C2×C22⋊Q8C2×D5911yescharacteristic
383C2×C22⋊Q8C2×D5911yescharacteristic
384C2×C4×D4C2×D5911yescharacteristic
385C2×#117—591no—
386C22×C4⋊C4C2×D5911yescharacteristic
387#470—1184no—
388#470—1184no—
389#436—1184no—
390#428—1184no—
391C2×#107—591no—
392C2×#107—591no—
393C2×#106—591no—
394C2×#106—591no—
395C2×#106—591no—
396C2×C4⋊C8—591no—
397C2×#103—591no—
398C2×#103—591no—
399C2×#103—591no—
400C2×#103—591no—
401C2×#103—591no—
402C2×#103—591no—
403C2×C22⋊C8—591no—
404C2×C22⋊C8—591no—
405C2×C4×C8—591no—
406#398—21no—
407#397—1181no—
408#396—21no—
409#394—1181no—
410#391—591no—
411#391C2×D5911yescharacteristic
412#389—591no—
413#389—1181no—
414#389C2×D5911yescharacteristic
415#388—1181no—
416#386—21no—
417#380—21no—
418#380—591no—
419#380C2×D5911yescharacteristic
420#340—591no—
421#340—591no—
422#340—591no—
423#340—591no—
424C59#2479311yescharacteristic, complemented, Sylow
425C22×Q8—591no—
426C22×Q8C22×D5911yescharacteristic
427C22×D4C22⋊D5911yescharacteristic
428C23×C4—21no—
429C23×C4C22×D5911yescharacteristic
430C23×C4C22×D5911yescharacteristic
431C2×Q16—1182no—
432C2×Q16—1182no—
433C2×Q16—1182no—
434C2×M16—594no—
435C2×M16—1182no—
436C2×M16—1182no—
437C2×M16—1182no—
438C2×M16—1182no—
439C2×M16—1182no—
440C22×C8—591no—
441C22×C8—591no—
442C22×C8—591no—
443C22×C8—591no—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—41no—
448C22⋊Q8—1182no—
449C22⋊Q8—1182no—
450C22⋊Q8—1182no—
451C22⋊Q8—2361no—
452C4×D4—22no—
453C4×D4—22no—
454#117—1182no—
455#117—2361no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—591no—
463C2×C4⋊C4—591no—
464C2×C4⋊C4—591no—
465C2×C4⋊C4—1181no—
466C2×C4⋊C4—1181no—
467C2×C4⋊C4—1181no—
468C2×C4⋊C4C22⋊D5911yescharacteristic
469C2×C4⋊C4C22×D5911yescharacteristic
470C2×C4⋊C4C22×D5911yescharacteristic
471C2×C4⋊C4C22×D5911yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—1181no—
476C2×C22⋊C4—1181no—
477C2×C22⋊C4—1181no—
478C2×C22⋊C4—1181no—
479C2×C22⋊C4C22⋊D5911yescharacteristic
480C2×C22⋊C4C22⋊D5911yescharacteristic
481C2×C42—1181no—
482C2×C42C22×D5911yescharacteristic
483#107—1182no—
484#107—1182no—
485#106—594no—
486#106—1182no—
487#106—1182no—
488C4⋊C8—1182no—
489#103—1182no—
490#103—1182no—
491#103—1182no—
492#103—1182no—
493#103—2361no—
494#103—2361no—
495C22⋊C8—1182no—
496C22⋊C8—1182no—
497C4×C8—1182no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—1181no—
503#95—1181no—
504#95—1181no—
505#95—1181no—
506C24C2×C22⋊D5911yescharacteristic
507C24C2×C22⋊D5911yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—1181no—
515C2×Q8—1181no—
516C2×Q8—1181no—
517C2×Q8—1181no—
518C2×Q8—1181no—
519C2×Q8—1181no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4—1181no—
541C22×C4—1181no—
542C22×C4—1181no—
543C22×C4—1181no—
544C22×C4D4×D5912yes—
545C22×C4#1174568712yes—
546C22×C4C2×C22⋊D5911yescharacteristic
547C22×C4C2×C22⋊D5911yescharacteristic
548C22×C4C2×C22⋊D5911yescharacteristic
549C22×C4C2×C22⋊D5911yescharacteristic
550C22×C4C23×D5911yescharacteristic
551Q16—2364no—
552M16—1188no—
553M16—2364no—
554C2×C8—592no—
555C2×C8—592no—
556C2×C8—592no—
557C2×C8—592no—
558C2×C8—1181no—
559C2×C8—1181no—
560C2×C8—1181no—
561C2×C8—1181no—
562C2×C8—1181no—
563C2×C8—1181no—
564C2×C8—1181no—
565C2×C8—1181no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—81no—
576C4⋊C4—592no—
577C4⋊C4—1181no—
578C4⋊C4—1181no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4—1181no—
582C4⋊C4—2362no—
583C4⋊C4—2362no—
584C4⋊C4—2362no—
585C4⋊C4D4×D5912yes—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—81no—
591C22⋊C4—2362no—
592C22⋊C4—2362no—
593C22⋊C4—2362no—
594C22⋊C4—2362no—
595C42—21no—
596C42—21no—
597C42—2362no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23#1427369912yes—
612C23C22×C22⋊D5911yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—2361no—
618Q8—2361no—
619Q8—2361no—
620Q8—2361no—
621D4—44no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—84no—
653C2×C4—1182no—
654C2×C4—2361no—
655C2×C4—2361no—
656C2×C4—2361no—
657C2×C4—2361no—
658C2×C4—2361no—
659C2×C4—2361no—
660C2×C4—2361no—
661C2×C4—2361no—
662C2×C4—2361no—
663C2×C4—2361no—
664C2×C4—2361no—
665C2×C4#1427369912yes—
666C2×C4#1427375812yes—
667C2×C4C2×D4×D5911yescharacteristic
668C2×C4C2×D4×D5911yescharacteristic
669C2×C4#41×D5911yescharacteristic
670C2×C4C2×#1174568711yescharacteristic
671C2×C4#1427377211yescharacteristic
672C2×C4#1427377411yescharacteristic
673C8—594no—
674C8—1182no—
675C8—2361no—
676C8—2361no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22C2×#1427369911yescharacteristic
692C22D4×C22⋊D5911yescharacteristic
693C22#1683805111yescharacteristic
694C22C2×#1427375811yescharacteristic
695C22#1683820011yescharacteristic
696C22#1683821311yescharacteristic
697C22#1683821711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—4721no—
707C4—4721no—
708C4—4721no—
709C4—2362no—
710C4#121×D5911yescharacteristic
711C4#1683797911yescharacteristic
712C4#1683805811yescharacteristic
713C4#1683809511yescharacteristic
714C2—42no—
715C2—81no—
716C2#2142753311yescharacteristic
717C2#2143372211yescharacteristic
718C2#2143378911yescharacteristic
719C2#2143572311yescharacteristic
720C2#2143574211yescharacteristic
721C2#2143666511yescharacteristic
722C2#2143671111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2417C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
hypercenter#2417D59
hypocenterC59#24793
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

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

NH ≅ G/Ntype
1. C2×#16837658C2semidirect
2. C2×#16837658C2semidirect
4. C2×#16837442C2semidirect
6. #21425488C2semidirect
7. #21425477C2semidirect
8. #21425296C2semidirect
9. #21425292C2semidirect
10. #21424956C2semidirect
11. #21424821C2semidirect
12. #21424409C2semidirect
13. #21424403C2semidirect
14. #21424127C2semidirect
98. #14273658D4semidirect
424. C59#24793semidirect

Maximal subgroups

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

subgroupindex
C2×#168376582
C2×#168374802
C2×#168374422
#214275252
#214254882
#214254772
#214252962
#214252922
#214249562
#214248212
#214244092
#214244032
#214241272
C59×#24172
#2479359