Finite Group Databasebeta

← #28646001

Subgroups — #28646001

Order 15104.

1004 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837687C211yesmaximal, characteristic, complemented
2C2×#16837403C211yesmaximal, characteristic
3#21427798C211yesmaximal, characteristic, complemented
4#21425629C211yesmaximal, characteristic, complemented
5#21425484C211yesmaximal, characteristic, complemented
6#21425470C211yesmaximal, characteristic, complemented
7#21425232C211yesmaximal, characteristic, complemented
8#21424364C211yesmaximal, characteristic, complemented
9#21424350C211yesmaximal, characteristic, complemented
10#21424288C211yesmaximal, characteristic, complemented
11#21424281C211yesmaximal, characteristic, complemented
12#21424127C211yesmaximal, characteristic, complemented
13#21424101C211yesmaximal, characteristic, complemented
14#21424036C211yesmaximal, characteristic
15C59×#2341C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C2×#14273727C2211yescharacteristic
18C2×#14273704—21no—
19C22×C4⋊Dic59C2211yescharacteristic
20#16837687—24no—
21C2×#14273660C2211yescharacteristic
22C2×#14273658C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×#14273658C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×C4⋊(C59⋊C8)C2211yescharacteristic
27#16837403—24no—
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273651C2211yescharacteristic
32C2×#14273648C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×#14273648C2211yescharacteristic
35C2×#14273648C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37#16837334—21no—
38#16837323—21no—
39#16837300C2211yescharacteristic
40#16837300C2211yescharacteristic
41#16837277—21no—
42#16837272C2211yescharacteristic
43#16837262C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50C22×#41×C59C2211yescharacteristic
51C2×C4×Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic
53C59×#390—21no—
54C59×#390—21no—
55C59×#390C2211yescharacteristic
56C59×#390C2211yescharacteristic
57C59×#380—21no—
58C59×#380C2211yescharacteristic
59C4×C22⋊C4×C59—21no—
60C4×C22⋊C4×C59C2211yescharacteristic
61C22×Dic118—21no—
62C23×Dic59—21no—
63C2×#11745664—22no—
64C2×#11745664—22no—
65C2×#11745664—41no—
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70#14273727—22no—
71#14273727—41no—
72#14273704—44no—
73C2×C4⋊Dic59—22no—
74C2×C4⋊Dic59—21no—
75C2×C4⋊Dic59—21no—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—21no—
78C2×C4⋊Dic59—41no—
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×Dic59⋊C4—21no—
84C2×Dic59⋊C4—21no—
85C2×C22⋊Dic59—21no—
86#14273660—41no—
87#14273658—22no—
88#14273658—22no—
89#14273658—41no—
90C4⋊(C59⋊C8)—22no—
91C4⋊(C59⋊C8)—41no—
92#14273651—22no—
93#14273651—22no—
94#14273651—22no—
95#14273651D414yes—
96#14273648—22no—
97#14273648—22no—
98#14273648—41no—
99#14273648—41no—
100C22⋊(C59⋊C8)—22no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C2×#41×C59—22no—
105C2×#41×C59—22no—
106C2×#41×C59—22no—
107C2×#41×C59—41no—
108C2×#41×C59—41no—
109C2×#41×C59Q814yescomplemented
110C22×Q8×C59C2311yescharacteristic
111C22×D4×C59—21no—
112C22×D4×C59C2311yescharacteristic
113C23×C4×C59—21no—
114C23×C4×C59C2311yescharacteristic
115C4×Q8×C59—22no—
116C4×Q8×C59—22no—
117C4×Q8×C59—41no—
118C4×Q8×C59—41no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59D411yescharacteristic
129C2×C22⋊C4×C59D411yescharacteristic
130C2×C42×C59—21no—
131C2×C42×C59—21no—
132C2×C42×C59C2311yescharacteristic
133C2×C42×C59C2311yescharacteristic
134#95×C59—21no—
135#95×C59D411yescharacteristic
136#95×C59D411yescharacteristic
137C24×C59—21no—
138C24×C59C2×D411yescharacteristic
139#41×C59—28no—
140#41×C59—44no—
141#41×C59—44no—
142#41×C59—44no—
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59C2×D412yes—
147C2×Q8×C59C2×Q812yes—
148C2×Q8×C59#4112yes—
149C2×D4×C59—24no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—42no—
156C2×D4×C59—42no—
157C2×D4×C59C2×Q812yes—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—24no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—42no—
167C22×C4×C59—42no—
168C22×C4×C59C2×D411yescharacteristic
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×Q812yes—
174C22×C4×C59#4112yes—
175C22×C4×C59C2411yescharacteristic
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—21no—
180C22×Dic59—42no—
181C22×Dic59—42no—
182C22×Dic59—81no—
183C2×Dic118—42no—
184C2×Dic118—42no—
185C2×Dic118—81no—
186C4⋊C4×C59—21no—
187C4⋊C4×C59—21no—
188C4⋊C4×C59—21no—
189C4⋊C4×C59—21no—
190C4⋊C4×C59—42no—
191C4⋊C4×C59—42no—
192C22⋊C4×C59—22no—
193C22⋊C4×C59—22no—
194C22⋊C4×C59—42no—
195C22⋊C4×C59—42no—
196C22⋊C4×C59—81no—
197C22⋊C4×C59—81no—
198C22⋊C4×C59—81no—
199C42×C59—21no—
200C42×C59—21no—
201C42×C59—21no—
202C42×C59—21no—
203C42×C59—42no—
204C42×C59—42no—
205C22⋊Dic59—42no—
206C4⋊Dic59—21no—
207C4⋊Dic59—21no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59—21no—
213C4⋊Dic59—42no—
214C4⋊Dic59—42no—
215C4⋊Dic59—42no—
216C4⋊Dic59—81no—
217C4⋊Dic59C2×D412yes—
218Dic59⋊C4—42no—
219Dic59⋊C4—42no—
220#11745664—44no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
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—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—22no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59C22⋊Q812yes—
247C23×C59C22×D411yescharacteristic
248Q8×C59—22no—
249Q8×C59—22no—
250Q8×C59—22no—
251Q8×C59C22⋊Q814yescomplemented
252D4×C59—22no—
253D4×C59—22no—
254D4×C59—48no—
255D4×C59—41no—
256D4×C59—41no—
257C2×C4×C59—22no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—22no—
261C2×C4×C59—21no—
262C2×C4×C59—22no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—48no—
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×C59C22⋊Q812yes—
284C2×C4×C59AGL(1,ℤ/8)12yes—
285C2×C4×C59#13712yes—
286C2×C4×C59C22×D411yescharacteristic
287C2×C4×C59C22×Q811yescharacteristic
288C2×C4×C59C2×#4111yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59H(5,𝔽2)11yescharacteristic
291C2×C4×C59H(5,𝔽2)11yescharacteristic
292C2×Dic59—22no—
293C2×Dic59—41no—
294C2×Dic59—41no—
295C2×Dic59—41no—
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—84no—
305Dic118—84no—
306C59⋊C8—22no—
307C59⋊C8—41no—
308C59⋊C8—41no—
309C59⋊C8—41no—
310#25967—591nomaximal, Sylow
311C22×C59—22no—
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—41no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—42no—
319C22×C59—42no—
320C22×C59—42no—
321C22×C59—81no—
322C22×C59—81no—
323C22×C59—81no—
324C22×C59—81no—
325C22×C59C2×C22⋊Q811yescharacteristic
326C22×C59D4211yescharacteristic
327C22×C59#54611yescharacteristic
328C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C59C2×#13711yescharacteristic
330C22×C59#57711yescharacteristic
331C22×C59#57711yescharacteristic
332C4×C59—22no—
333C4×C59—24no—
334C4×C59—22no—
335C4×C59—22no—
336C4×C59—41no—
337C4×C59—41no—
338C4×C59—81no—
339C4×C59—81no—
340C4×C59C2×C22⋊Q811yescharacteristic
341C4×C59#54311yescharacteristic
342C4×C59#54611yescharacteristic
343C4×C59#55111yescharacteristic
344Dic59—42no—
345Dic59—81no—
346Dic59—81no—
347Dic59—81no—
348C2×#475—591no—
349C2×#417—591no—
350#2440—591no—
351#2341D5911yescharacteristic
352#2094—591no—
353#2067—591no—
354#2065—591no—
355#2023—591no—
356#1865—591no—
357#1863—591no—
358#1853—591no—
359#1851—591no—
360#1809—591no—
361#1803—591no—
362#1788—591no—
363C2×C59—42no—
364C2×C59—82no—
365C2×C59#243711yescharacteristic
366C2×C59#307911yescharacteristic
367C2×C59#308411yescharacteristic
368C2×C59#326511yescharacteristic
369C2×C59#327811yescharacteristic
370C2×C59#331611yescharacteristic
371C2×C59#333211yescharacteristic
372C22×#41C2×D5911yescharacteristic
373C22×M16—591no—
374C2×C4⋊Q8—591no—
375C2×C22⋊Q8—1181no—
376C2×C4×Q8C2×D5911yescharacteristic
377C2×C4×Q8C2×D5911yescharacteristic
378C22×C4⋊C4—591no—
379#475—1184no—
380C2×#107—591no—
381C2×#106—591no—
382C2×#106—591no—
383C2×#106—591no—
384C2×C4⋊C8—591no—
385C2×C4⋊C8—591no—
386#417—1184no—
387C2×#103—591no—
388C2×#103—591no—
389C2×#103—591no—
390C2×#103—591no—
391C2×#102—591no—
392C2×#102—591no—
393C2×#102—591no—
394C2×#102—591no—
395C2×C22⋊C8—591no—
396#398—1181no—
397#395—1181no—
398#390—21no—
399#390—21no—
400#390C2×D5911yescharacteristic
401#390C2×D5911yescharacteristic
402#389—591no—
403#389—591no—
404#385—1181no—
405#384—591no—
406#380—21no—
407#380—591no—
408#380C2×D5911yescharacteristic
409C4×C22⋊C4—21no—
410C4×C22⋊C4C2×D5911yescharacteristic
411#340—591no—
412#340—591no—
413#340—591no—
414#340—591no—
415#336—591no—
416#336—591no—
417C59#2596711yescharacteristic, complemented, Sylow
418C2×#41—22no—
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—41no—
422C2×#41—41no—
423C2×#41Dic11814yescomplemented
424C22×Q8—1181no—
425C22×Q8C22×D5911yescharacteristic
426C22×D4—21no—
427C22×D4C22×D5911yescharacteristic
428C23×C4—21no—
429C23×C4—1181no—
430C23×C4C22×D5911yescharacteristic
431C2×M16—1182no—
432C2×M16—1182no—
433C2×M16—2361no—
434C22×C8—591no—
435C22×C8—591no—
436C22×C8—591no—
437C22×C8—591no—
438C4⋊Q8—1182no—
439C4⋊Q8—2361no—
440C22⋊Q8—2364no—
441C4×Q8—22no—
442C4×Q8—22no—
443C4×Q8—41no—
444C4×Q8—41no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—591no—
448C2×C4⋊C4—591no—
449C2×C4⋊C4—591no—
450C2×C4⋊C4—591no—
451C2×C4⋊C4—1182no—
452C2×C4⋊C4—1181no—
453C2×C4⋊C4—1181no—
454C2×C4⋊C4—1181no—
455C2×C4⋊C4—1181no—
456C2×C4⋊C4—1181no—
457C2×C4⋊C4—1181no—
458C2×C4⋊C4—2361no—
459C2×C4⋊C4C22×D5911yescharacteristic
460C2×C4⋊C4C22×D5911yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1181no—
467C2×C22⋊C4C22⋊D5911yescharacteristic
468C2×C22⋊C4C22⋊D5911yescharacteristic
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C22×D5911yescharacteristic
472C2×C42C22×D5911yescharacteristic
473#107—2361no—
474#106—1182no—
475#106—1182no—
476#106—2361no—
477C4⋊C8—1182no—
478C4⋊C8—2361no—
479#103—594no—
480#103—1182no—
481#103—1182no—
482#103—1182no—
483#102—1182no—
484#102—1182no—
485#102—2361no—
486#102—2361no—
487C22⋊C8—1182no—
488#95—21no—
489#95—1181no—
490#95—1181no—
491#95—1181no—
492#95C22⋊D5911yescharacteristic
493#95C22⋊D5911yescharacteristic
494C24—21no—
495C24C2×C22⋊D5911yescharacteristic
496#41—28no—
497#41—44no—
498#41—44no—
499#41—44no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—4721no—
504C2×Q8—2362no—
505C2×Q8—2362no—
506C2×Q8C2×Dic11812yes—
507C2×Q8D4×D5912yes—
508C2×Q8#1174568712yes—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4C2×Dic11812yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—1181no—
529C22×C4—1181no—
530C22×C4—1181no—
531C22×C4—1181no—
532C22×C4—4721no—
533C22×C4—2362no—
534C22×C4—2362no—
535C22×C4C2×Dic11812yes—
536C22×C4#1174568512yes—
537C22×C4C2×C22⋊D5911yescharacteristic
538C22×C4C2×C22⋊D5911yescharacteristic
539C22×C4C2×C22⋊D5911yescharacteristic
540C22×C4C2×C22⋊D5911yescharacteristic
541C22×C4C2×C22⋊D5911yescharacteristic
542C22×C4C23×D5911yescharacteristic
543M16—2364no—
544C2×C8—592no—
545C2×C8—1181no—
546C2×C8—1181no—
547C2×C8—1181no—
548C2×C8—1181no—
549C2×C8—1181no—
550C2×C8—1181no—
551C2×C8—1181no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—592no—
563C4⋊C4—1181no—
564C4⋊C4—1181no—
565C4⋊C4—1181no—
566C4⋊C4—1181no—
567C4⋊C4—1181no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—4721no—
571C4⋊C4—2362no—
572C4⋊C4—2362no—
573C4⋊C4—2362no—
574C4⋊C4—2362no—
575C4⋊C4—2362no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—2362no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—42no—
589C42—42no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23#1427370612yes—
604C23C22×C22⋊D5911yescharacteristic
605Q8—22no—
606Q8—22no—
607Q8—22no—
608Q8—4724no—
609Q8#1427370414yescomplemented
610D4—22no—
611D4—22no—
612D4—48no—
613D4—41no—
614D4—41no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—1182no—
642C2×C4—4724no—
643C2×C4—2361no—
644C2×C4—2361no—
645C2×C4—2361no—
646C2×C4—2361no—
647C2×C4—2361no—
648C2×C4—2361no—
649C2×C4—2361no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4#1427370612yes—
655C2×C4#1427375212yes—
656C2×C4#1427375712yes—
657C2×C4C2×D4×D5911yescharacteristic
658C2×C4C22×Dic11811yescharacteristic
659C2×C4C2×#1174568711yescharacteristic
660C2×C4C2×#1174568511yescharacteristic
661C2×C4#1427377211yescharacteristic
662C2×C4#1427377211yescharacteristic
663C8—1182no—
664C8—2361no—
665C8—2361no—
666C8—2361no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#1427370611yescharacteristic
682C22D4×C22⋊D5911yescharacteristic
683C22#1683804611yescharacteristic
684C22C2×#1427375211yescharacteristic
685C22C2×#1427375711yescharacteristic
686C22#1683821011yescharacteristic
687C22#1683821311yescharacteristic
688C4—22no—
689C4—24no—
690C4—22no—
691C4—22no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4—4721no—
697C4—4721no—
698C4—4721no—
699C4—2362no—
700C4C2×#1427370411yescharacteristic
701C4#1683802811yescharacteristic
702C4#1683804211yescharacteristic
703C4#1683807811yescharacteristic
704C2—42no—
705C2—82no—
706C2#2142775711yescharacteristic
707C2#2143391111yescharacteristic
708C2#2143395811yescharacteristic
709C2#2143559211yescharacteristic
710C2#2143576211yescharacteristic
711C2#2143620711yescharacteristic
712C2#2143642311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2341C2
socleC23×C59C22×D4
prime radicalC22×#41×C59C22
hypercenter#2341D59
hypocenterC59#25967
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
1. C2×#16837687C2semidirect
3. #21427798C2semidirect
4. #21425629C2semidirect
5. #21425484C2semidirect
6. #21425470C2semidirect
7. #21425232C2semidirect
8. #21424364C2semidirect
9. #21424350C2semidirect
10. #21424288C2semidirect
11. #21424281C2semidirect
12. #21424127C2semidirect
13. #21424101C2semidirect
109. C2×#41×C59Q8semidirect
251. Q8×C59C22⋊Q8semidirect
417. C59#25967semidirect
423. C2×#41Dic118semidirect
609. Q8#14273704semidirect

Maximal subgroups

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

subgroupindex
C2×#168376872
C2×#168374032
#214277982
#214256292
#214254842
#214254702
#214252322
#214243642
#214243502
#214242882
#214242812
#214241272
#214241012
#214240362
C59×#23412
#2596759