Finite Group Databasebeta

← #28632444

Subgroups — #28632444

Order 15104.

988 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×#16837541C211yesmaximal, characteristic
2C2×C4×#11745671C211yesmaximal, characteristic, complemented
3#21427588C211yesmaximal, characteristic
4#21425644C211yesmaximal, characteristic, complemented
5#21425532C211yesmaximal, characteristic, complemented
6#21425411C211yesmaximal, characteristic, complemented
7#21425278C211yesmaximal, characteristic
8#21424775C211yesmaximal, characteristic, complemented
9#21424704C211yesmaximal, characteristic, complemented
10#21424451C211yesmaximal, characteristic, complemented
11#21424433C211yesmaximal, characteristic, complemented
12#21424350C211yesmaximal, characteristic, complemented
13#21424111C211yesmaximal, characteristic, complemented
14#21424031C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C59C211yesmaximal, characteristic, complemented
16C22×#11745671C2211yescharacteristic
17C22×#11745671C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20#16837541—24no—
21C4×#11745671—24no—
22C2×#14273660C2211yescharacteristic
23C2×#14273658C2211yescharacteristic
24C2×C4⋊(C59⋊C8)C2211yescharacteristic
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273651C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C4×C59⋊C8C2211yescharacteristic
36#16837331—21no—
37#16837317—21no—
38#16837304C2211yescharacteristic
39#16837300C2211yescharacteristic
40#16837278—21no—
41#16837268C2211yescharacteristic
42#16837264—21no—
43#16837262C2211yescharacteristic
44#16837164C2211yescharacteristic
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50C23×Q8×C59C2211yescharacteristic
51C2×C4×Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic
53C59×#391—21no—
54C59×#391—21no—
55C59×#391C2211yescharacteristic
56C59×#391C2211yescharacteristic
57C59×#380—21no—
58C59×#380C2211yescharacteristic
59C4×C22⋊C4×C59—21no—
60C4×C22⋊C4×C59C2211yescharacteristic
61C22×D236C2311yescharacteristic
62C22×C22⋊D59—21no—
63C22×C4×D59—21no—
64C2×#11745671—22no—
65C2×#11745671—22no—
66C2×#11745671—22no—
67C2×#11745671—22no—
68C2×#11745671—41no—
69C2×#11745671D414yes—
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74#14273701—22no—
75#14273701—41no—
76C4×D236—22no—
77C4×D236—41no—
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×Dic59⋊C4—21no—
82C2×C22⋊Dic59—21no—
83C2×(C2×D59)⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×(C2×D59)⋊C4—21no—
87#14273660—41no—
88#14273658—22no—
89C4⋊(C59⋊C8)—41no—
90#14273651—22no—
91#14273651—22no—
92#14273651—22no—
93#14273651—22no—
94#14273651—22no—
95#14273651—41no—
96#14273647—22no—
97#14273647—41no—
98C22⋊(C59⋊C8)—22no—
99C22⋊(C59⋊C8)—41no—
100C4×C59⋊C8—22no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C59⋊#95—21no—
105C22×Q8×C59—22no—
106C22×Q8×C59—22no—
107C22×Q8×C59—21no—
108C22×Q8×C59—22no—
109C22×Q8×C59—22no—
110C22×Q8×C59—41no—
111C22×Q8×C59—41no—
112C22×Q8×C59C2311yescharacteristic
113C22×Q8×C59C2311yescharacteristic
114C23×C4×C59—21no—
115C23×C4×C59C2311yescharacteristic
116C4×Q8×C59—22no—
117C4×Q8×C59—22no—
118C4×Q8×C59—41no—
119C4×Q8×C59—41no—
120C2×C4⋊C4×C59—21no—
121C2×C4⋊C4×C59—21no—
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59D411yescharacteristic
126C2×C22⋊C4×C59D411yescharacteristic
127C2×C42×C59—21no—
128C2×C42×C59—21no—
129C2×C42×C59C2311yescharacteristic
130C2×C42×C59C2311yescharacteristic
131#95×C59—21no—
132#95×C59—21no—
133#95×C59—21no—
134#95×C59—21no—
135#95×C59—21no—
136#95×C59D411yescharacteristic
137#95×C59D411yescharacteristic
138C24×C59C2×D411yescharacteristic
139C23×D59—21no—
140C2×Q8×C59—24no—
141C2×Q8×C59—21no—
142C2×Q8×C59—21no—
143C2×Q8×C59—21no—
144C2×Q8×C59—21no—
145C2×Q8×C59—21no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—42no—
150C2×Q8×C59—42no—
151C2×Q8×C59—44no—
152C2×Q8×C59—44no—
153C2×Q8×C59—44no—
154C2×Q8×C59—44no—
155C2×Q8×C59C2×D412yes—
156C2×Q8×C59#4112yes—
157C2×Q8×C59#4112yes—
158C2×Q8×C59#4112yes—
159C22×C4×C59—21no—
160C22×C4×C59—24no—
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—21no—
170C22×C4×C59—42no—
171C22×C4×C59—42no—
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2411yescharacteristic
178C2×C22⋊D59—42no—
179C2×C22⋊D59—42no—
180C2×C22⋊D59—81no—
181C22×Dic59—21no—
182C22×Dic59—21no—
183C22×Dic59—21no—
184C2×D236—21no—
185C2×D236—21no—
186C2×D236—21no—
187C2×D236—21no—
188C2×D236—21no—
189C2×D236C2×D412yes—
190C2×C4×D59—42no—
191C2×C4×D59—42no—
192C2×C4×D59—81no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—42no—
198C4⋊C4×C59—42no—
199C22⋊C4×C59—22no—
200C22⋊C4×C59—22no—
201C22⋊C4×C59—42no—
202C42×C59—21no—
203C42×C59—21no—
204C42×C59—21no—
205C42×C59—21no—
206C42×C59—42no—
207C42×C59—42no—
208C22⋊Dic59—81no—
209#11745671—28no—
210#11745671—44no—
211(C2×D59)⋊C4—42no—
212(C2×D59)⋊C4—42no—
213(C2×D59)⋊C4—81no—
214(C2×D59)⋊C4—81no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221Dic59⋊C4—81no—
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⋊C8—21no—
233C2×C59⋊C8C2×D412yes—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—21no—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59#13512yes—
241C23×C59C22×D411yescharacteristic
242C22×D59—22no—
243C22×D59—41no—
244C22×D59—41no—
245C22×D59—41no—
246C22×D59—41no—
247C22×D59—41no—
248C22×D59—41no—
249Q8×C59—22no—
250Q8×C59—22no—
251Q8×C59—22no—
252Q8×C59—22no—
253Q8×C59—22no—
254Q8×C59—48no—
255Q8×C59—41no—
256Q8×C59—41no—
257Q8×C59#12314yes—
258C2×C4×C59—22no—
259C2×C4×C59—21no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—21no—
263C2×C4×C59—22no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
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×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59#13712yes—
290C2×C4×C59C22×D411yescharacteristic
291C2×C4×C59C2×#4111yescharacteristic
292C2×C4×C59C2×#4111yescharacteristic
293C2×C4×C59C2×#4111yescharacteristic
294C2×C4×C59H(5,𝔽2)11yescharacteristic
295C2×C4×C59H(5,𝔽2)11yescharacteristic
296C22⋊D59—84no—
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—
306D236—22no—
307D236—22no—
308D236—41no—
309D236—41no—
310C4×D59—84no—
311C59⋊C8—22no—
312C59⋊C8—41no—
313C59⋊C8—41no—
314C59⋊C8—41no—
315#24894—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#52511yescharacteristic
324C22×C59D4211yescharacteristic
325C22×C59#54611yescharacteristic
326C22×C59C2×#13511yescharacteristic
327C22×C59C2×#13711yescharacteristic
328C22×C59#57711yescharacteristic
329C22×C59#57711yescharacteristic
330C2×D59—42no—
331C2×D59—42no—
332C2×D59—42no—
333C2×D59—81no—
334C2×D59—81no—
335C2×D59—81no—
336C2×D59—81no—
337C4×C59—24no—
338C4×C59—22no—
339C4×C59—41no—
340C4×C59—41no—
341C4×C59—42no—
342C4×C59—41no—
343C4×C59—41no—
344C4×C59—81no—
345C4×C59—81no—
346C4×C59C2×#12311yescharacteristic
347C4×C59#53811yescharacteristic
348C4×C59#54611yescharacteristic
349C4×C59#55111yescharacteristic
350Dic59—81no—
351Dic59—81no—
352Dic59—81no—
353C2×#448—591no—
354C2×C4×SD16—591no—
355#2420—591no—
356Q8×C22⋊C4D5911yescharacteristic, complemented
357#2097—591no—
358#2077—591no—
359#2055—591no—
360#2033—591no—
361#1933—591no—
362#1923—591no—
363#1880—591no—
364#1877—591no—
365#1863—591no—
366#1805—591no—
367#1787—591no—
368C2×C59—42no—
369C2×C59#241811yescharacteristic
370C2×C59#310811yescharacteristic
371C2×C59#312611yescharacteristic
372C2×C59#326611yescharacteristic
373C2×C59#328211yescharacteristic
374C2×C59#330111yescharacteristic
375C2×C59#332911yescharacteristic
376D59—82no—
377C23×Q8C2×D5911yescharacteristic
378C22×SD16—591no—
379C22×SD16—591no—
380C2×#121—591no—
381C2×C4×Q8C2×D5911yescharacteristic
382C2×C4×Q8C2×D5911yescharacteristic
383C2×C4×D4—591no—
384#448—1184no—
385C4×SD16—1184no—
386C2×#107—591no—
387C2×#106—591no—
388C2×C4⋊C8—591no—
389C2×#103—591no—
390C2×#103—591no—
391C2×#103—591no—
392C2×#103—591no—
393C2×#103—591no—
394C2×#103—591no—
395C2×#102—591no—
396C2×#102—591no—
397C2×C22⋊C8—591no—
398C2×C22⋊C8—591no—
399C2×C4×C8—591no—
400#397—1181no—
401#394—1181no—
402#391—21no—
403#391—21no—
404#391C2×D5911yescharacteristic
405#391C2×D5911yescharacteristic
406#390—591no—
407#389—591no—
408#386—1181no—
409#382—591no—
410#381—1181no—
411#380—21no—
412#380—591no—
413#380C2×D5911yescharacteristic
414C4×C22⋊C4—21no—
415C4×C22⋊C4C2×D5911yescharacteristic
416#340—591no—
417#340—591no—
418#340—591no—
419#340—591no—
420#336—591no—
421#336—591no—
422C59#2489411yescharacteristic, complemented, Sylow
423C22×Q8—22no—
424C22×Q8—22no—
425C22×Q8—21no—
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—41no—
429C22×Q8—41no—
430C22×Q8C22×D5911yescharacteristic
431C22×Q8C22×D5911yescharacteristic
432C22×D4—591no—
433C22×D4—1181no—
434C23×C4—21no—
435C23×C4—1181no—
436C23×C4C22×D5911yescharacteristic
437C2×SD16—594no—
438C2×SD16—1182no—
439C2×SD16—1182no—
440C2×SD16—1182no—
441C2×SD16—1182no—
442C2×SD16—2361no—
443C22×C8—591no—
444C22×C8—591no—
445C22×C8—591no—
446C22×C8—591no—
447#121—1182no—
448#121—2361no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—41no—
452C4×Q8—41no—
453C4×D4—1182no—
454C4×D4—2361no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—591no—
458C2×C4⋊C4—591no—
459C2×C4⋊C4—591no—
460C2×C4⋊C4—1181no—
461C2×C4⋊C4C22×D5911yescharacteristic
462C2×C4⋊C4C22×D5911yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—1181no—
465C2×C22⋊C4—1181no—
466C2×C22⋊C4—1181no—
467C2×C22⋊C4—1181no—
468C2×C22⋊C4—1181no—
469C2×C22⋊C4C22⋊D5911yescharacteristic
470C2×C22⋊C4C22⋊D5911yescharacteristic
471C2×C42—21no—
472C2×C42—21no—
473C2×C42C22×D5911yescharacteristic
474C2×C42C22×D5911yescharacteristic
475#107—2361no—
476#106—1182no—
477C4⋊C8—2361no—
478#103—1182no—
479#103—1182no—
480#103—1182no—
481#103—1182no—
482#103—1182no—
483#103—2361no—
484#102—1182no—
485#102—2361no—
486C22⋊C8—1182no—
487C22⋊C8—2361no—
488C4×C8—1182no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—1181no—
495#95—1181no—
496#95—1181no—
497#95—1181no—
498#95C22⋊D5911yescharacteristic
499#95C22⋊D5911yescharacteristic
500C24—1181no—
501C24C2×C22⋊D5911yescharacteristic
502C2×Q8—24no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8#1174568512yes—
518C2×Q8#1174568512yes—
519C2×Q8D4×D5912yes—
520C2×Q8#1174568712yes—
521C2×D4—592no—
522C2×D4—1181no—
523C2×D4—1181no—
524C2×D4—1181no—
525C2×D4—1181no—
526C2×D4—1181no—
527C2×D4—4721no—
528C2×D4—2362no—
529C2×D4—2362no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—1181no—
544C22×C4—1181no—
545C22×C4—1181no—
546C22×C4—4721no—
547C22×C4—2362no—
548C22×C4—2362no—
549C22×C4C2×C22⋊D5911yescharacteristic
550C22×C4C2×C22⋊D5911yescharacteristic
551C22×C4C2×C22⋊D5911yescharacteristic
552C22×C4C2×C22⋊D5911yescharacteristic
553C22×C4C2×C22⋊D5911yescharacteristic
554C22×C4C23×D5911yescharacteristic
555SD16—1188no—
556SD16—2364no—
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—
566C2×C8—1181no—
567C2×C8—1181no—
568C2×C8—1181no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—1181no—
576C4⋊C4—1181no—
577C4⋊C4—1181no—
578C4⋊C4—1181no—
579C4⋊C4—1181no—
580C4⋊C4—1181no—
581C4⋊C4—4721no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—42no—
585C22⋊C4—4721no—
586C22⋊C4—4721no—
587C22⋊C4—4721no—
588C22⋊C4—2362no—
589C22⋊C4—2362no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—42no—
595C42—42no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—1182no—
603C23—2361no—
604C23—2361no—
605C23—2361no—
606C23—2361no—
607C23—2361no—
608C23—2361no—
609C23#1427374712yes—
610C23C22×C22⋊D5911yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8—48no—
617Q8—41no—
618Q8—41no—
619Q8#1427370914yes—
620D4—1182no—
621D4—1182no—
622D4—4724no—
623D4—2361no—
624D4—2361no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—48no—
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—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—4724no—
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—2361no—
666C2×C4#1427375812yes—
667C2×C4C2×D4×D5911yescharacteristic
668C2×C4C2×#1174568711yescharacteristic
669C2×C4C2×#1174568511yescharacteristic
670C2×C4C2×#1174568511yescharacteristic
671C2×C4#1427377211yescharacteristic
672C2×C4#1427377211yescharacteristic
673C8—1182no—
674C8—2361no—
675C8—2361no—
676C8—2361no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—4721no—
685C22—4721no—
686C22—4721no—
687C22—4721no—
688C22—2362no—
689C22—2362no—
690C22—2362no—
691C22#1683791311yescharacteristic
692C22D4×C22⋊D5911yescharacteristic
693C22#1683804611yescharacteristic
694C22C2×#1427374711yescharacteristic
695C22C2×#1427375811yescharacteristic
696C22#1683821011yescharacteristic
697C22#1683821011yescharacteristic
698C4—24no—
699C4—22no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—4721no—
708C4—4721no—
709C4—4721no—
710C4C2×#1427370911yescharacteristic
711C4#1683799011yescharacteristic
712C4#1683804211yescharacteristic
713C4#1683807811yescharacteristic
714C2—42no—
715C2—4722no—
716C2#2142755811yescharacteristic
717C2#2143417611yescharacteristic
718C2#2143438711yescharacteristic
719C2#2143560711yescharacteristic
720C2#2143580411yescharacteristic
721C2#2143599811yescharacteristic
722C2#2143639011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingQ8×C22⋊C4×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273701C22
hypercenterQ8×C22⋊C4D59
hypocenterC59#24894
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745671C2semidirect
4. #21425644C2semidirect
5. #21425532C2semidirect
6. #21425411C2semidirect
8. #21424775C2semidirect
9. #21424704C2semidirect
10. #21424451C2semidirect
11. #21424433C2semidirect
12. #21424350C2semidirect
13. #21424111C2semidirect
14. #21424031C2semidirect
15. Q8×C22⋊C4×C59C2semidirect
356. Q8×C22⋊C4D59semidirect
422. C59#24894semidirect

Maximal subgroups

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

subgroupindex
C2×#168375412
C2×C4×#117456712
#214275882
#214256442
#214255322
#214254112
#214252782
#214247752
#214247042
#214244512
#214244332
#214243502
#214241112
#214240312
Q8×C22⋊C4×C592
#2489459