Finite Group Databasebeta

← C2×#21436866 #29468472

Subgroups — C2×#21436866 #29468472

Order 15104.

1874 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×#16838137C211yesmaximal, characteristic
2C2×#16838130C211yesmaximal, characteristic, complemented
3#21436866C2116yesmaximal, direct product factor
4C2×#16837767C211yesmaximal, characteristic
5C2×#16837762C211yesmaximal, characteristic, complemented
6C2×#16837757C211yesmaximal, characteristic, complemented
7C2×#16837710C211yesmaximal, characteristic, complemented
8C2×#16837703C211yesmaximal, characteristic, complemented
9C2×#16837693C211yesmaximal, characteristic, complemented
10C2×#16837625C211yesmaximal, characteristic, complemented
11C2×#16837625C211yesmaximal, characteristic, complemented
12C2×#16837603C211yesmaximal, characteristic
13C2×#16837510C211yesmaximal, characteristic, complemented
14C2×#16837504C211yesmaximal, characteristic, complemented
15C2×C4×#11745660C211yesmaximal, characteristic, complemented
16C2×C59×#446C211yesmaximal, characteristic, complemented
17C22×Dic236C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20#16838137—24no—
21#16838137C2218yes—
22#16838130—24no—
23#16838130C2218yescomplemented
24C2×#14273727C2211yescharacteristic
25C2×#14273725—21no—
26C2×#14273724C2211yescharacteristic
27C2×#14273719C2211yescharacteristic
28C2×#14273719C2211yescharacteristic
29C2×#14273717—21no—
30C2×#14273717—21no—
31C2×#14273716—21no—
32C2×#14273715C2211yescharacteristic
33C2×#14273715C2211yescharacteristic
34C2×#14273712—21no—
35C2×#14273712—21no—
36C2×C4×Dic118C2211yescharacteristic
37C2×C4×Dic118C2211yescharacteristic
38C2×C4×Dic118C2211yescharacteristic
39C2×C4×Dic118C2211yescharacteristic
40C2×#14273692—21no—
41C2×C4×D236C2211yescharacteristic
42C2×C4×D236C2211yescharacteristic
43C2×#14273689—21no—
44#16837767C2218yes—
45#16837762C2218yescomplemented
46#16837757C2218yescomplemented
47#16837710C2218yescomplemented
48#16837703C2218yescomplemented
49#16837693C2218yescomplemented
50#16837625C2218yescomplemented
51#16837625C2218yescomplemented
52#16837603C2218yes—
53#16837510C2218yescomplemented
54#16837504C2218yescomplemented
55C4×#11745660C2218yescomplemented
56C2×#14273661C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273659C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C2×C4×Q8×C59C2211yescharacteristic
70C59×#446C2218yescomplemented
71C2×C4⋊C8×C59C2211yescharacteristic
72C2×C4⋊C8×C59C2211yescharacteristic
73C2×C4⋊C8×C59C2211yescharacteristic
74C2×#97×C59C2211yescharacteristic
75C2×#97×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×Dic118C2311yescharacteristic
80C22×D236—21no—
81C22×D236—21no—
82C22×D236C2311yescharacteristic
83C22×D236C2311yescharacteristic
84C22×C4×D59—21no—
85C22×C4×D59—21no—
86C2×Dic236—24no—
87C2×Dic236C2314yes—
88C2×#11745660—24no—
89C2×#11745660—24no—
90C2×#11745660C2314yes—
91C2×#11745660C2314yes—
92#14273727—22no—
93#14273727C2314yes—
94#14273725—28no—
95#14273724—22no—
96#14273724C2314yes—
97#14273719—22no—
98#14273719—22no—
99#14273719C2314yes—
100#14273719C2314yes—
101#14273717—28no—
102#14273717—28no—
103#14273716—28no—
104#14273715—22no—
105#14273715—22no—
106#14273715C2314yes—
107#14273715C2314yes—
108#14273712—28no—
109#14273712—28no—
110C4×Dic118—22no—
111C4×Dic118—22no—
112C4×Dic118—22no—
113C4×Dic118—22no—
114C4×Dic118C2314yes—
115C4×Dic118C2314yes—
116C4×Dic118C2314yes—
117C4×Dic118C2314yes—
118#14273692—28no—
119C4×D236—22no—
120C4×D236—22no—
121C4×D236C2314yes—
122C4×D236C2314yes—
123#14273689—28no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59—21no—
147#14273661C2314yes—
148#14273659C2314yes—
149#14273659C2314yes—
150#14273652C2314yes—
151#14273652C2314yes—
152#14273652C2314yes—
153#14273652C2314yes—
154#14273649C2314yes—
155#14273649C2314yes—
156#14273649C2314yes—
157#14273649C2314yes—
158#14273649C2314yes—
159#14273649C2314yes—
160C22×Q8×C59D411yescharacteristic
161C22×C8×C59C2311yescharacteristic
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C4×Q8×C59D414yes—
166C4×Q8×C59C2314yes—
167C2×C4⋊C4×C59D411yescharacteristic
168C2×C4⋊C4×C59D411yescharacteristic
169C2×C4⋊C4×C59D411yescharacteristic
170C2×C42×C59C2311yescharacteristic
171C2×C42×C59C2311yescharacteristic
172C2×C42×C59C2311yescharacteristic
173C4⋊C8×C59C2314yes—
174C4⋊C8×C59C2314yes—
175C4⋊C8×C59C2314yes—
176#97×C59C2314yes—
177#97×C59C2314yes—
178C4×C8×C59C2314yes—
179C23×D59—21no—
180C23×D59—21no—
181C2×Q8×C59—42no—
182C2×Q8×C59C2×D414yes—
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2411yescharacteristic
190C22×Dic59—21no—
191C22×Dic59—21no—
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59—21no—
196C2×D236—22no—
197C2×D236—22no—
198C2×D236—22no—
199C2×D236—22no—
200C2×D236—24no—
201C2×D236—21no—
202C2×D236—21no—
203C2×D236—24no—
204C2×D236—44no—
205C2×D236—82no—
206C2×D236C2412yes—
207C2×D236C2412yes—
208C2×C4×D59—24no—
209C2×C4×D59—24no—
210C2×C4×D59—82no—
211C2×C4×D59—82no—
212C2×Dic118—21no—
213C2×Dic118—22no—
214C2×Dic118—22no—
215C2×Dic118—22no—
216C2×Dic118—24no—
217C2×Dic118—21no—
218C2×Dic118—44no—
219C2×Dic118#4114yes—
220C2×Dic118C2412yes—
221C2×Dic118C2412yes—
222C2×C8×C59—22no—
223C2×C8×C59—22no—
224C2×C8×C59—22no—
225C2×C8×C59—22no—
226C2×C8×C59C2412yes—
227C2×C8×C59C2412yes—
228C2×C8×C59C2412yes—
229C2×C8×C59C2412yes—
230C4⋊C4×C59C2×D414yes—
231C4⋊C4×C59C2×D414yes—
232C4⋊C4×C59C2×D414yes—
233C42×C59C2×D412yes—
234C42×C59C2×D412yes—
235C42×C59C2×D412yes—
236C42×C59C2412yes—
237C42×C59C2412yes—
238C42×C59C2412yes—
239(C2×D59)⋊C4—24no—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4—24no—
245C4⋊Dic59—24no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—21no—
250C4⋊Dic59C2412yes—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253C4⋊Dic59C2412yes—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262C4×Dic59—24no—
263C4×Dic59—24no—
264C4×Dic59—24no—
265C4×Dic59—24no—
266Dic236—28no—
267#11745660—28no—
268#11745660—28no—
269C23×C59C22×D411yescharacteristic
270C22×D59—22no—
271C22×D59—22no—
272C22×D59—42no—
273C22×D59—42no—
274C22×D59—42no—
275C22×D59—42no—
276C22×D59—42no—
277C22×D59—42no—
278Q8×C59—44no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59C22×D412yes—
286C2×C4×C59C22×D412yes—
287C2×C4×C59C22×D412yes—
288C2×C4×C59C22×D412yes—
289C2×C4×C59C22×D412yes—
290C2×C4×C59C22×D412yes—
291C2×C4×C59C22×D411yescharacteristic
292C2×C4×C59C2×#4112yes—
293C2×C4×C592−1+412yes—
294C2×C4×C59C2511yescharacteristic
295C2×Dic59—24no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—42no—
303C2×Dic59—42no—
304C2×Dic59—42no—
305C2×Dic59—42no—
306C2×Dic59—42no—
307D236—22no—
308D236—22no—
309D236—22no—
310D236—22no—
311D236—48no—
312D236—42no—
313D236—42no—
314D236—84no—
315C4×D59—84no—
316C4×D59—84no—
317Dic118—24no—
318Dic118—22no—
319Dic118—22no—
320Dic118—22no—
321Dic118—48no—
322Dic118—42no—
323Dic118C2×#4114yes—
324C8×C59—22no—
325C8×C59—22no—
326C8×C59—22no—
327C8×C59—22no—
328C2×#3371—591nomaximal, Sylow
329C22×C59#54812yes—
330C22×C59#57512yes—
331C22×C59#57712yes—
332C22×C59C23×D411yescharacteristic
333C2×D59—42no—
334C2×D59—42no—
335C2×D59—42no—
336C2×D59—42no—
337C2×D59—42no—
338C2×D59—42no—
339C2×D59—84no—
340C2×D59—84no—
341C4×C59—22no—
342C4×C59—22no—
343C4×C59—22no—
344C4×C59—22no—
345C4×C59—22no—
346C4×C59—22no—
347C4×C59#54812yes—
348C4×C59C22×#4111yescharacteristic
349C4×C59C2×2−1+411yescharacteristic
350Dic59—24no—
351Dic59—42no—
352Dic59—42no—
353Dic59—42no—
354Dic59—42no—
355Dic59—42no—
356C2×#559—591no—
357C2×#557—591no—
358#3371—5916no—
359C2×#490—591no—
360C2×#489—591no—
361C2×#488—591no—
362C2×#479—591no—
363C2×#478—591no—
364C2×#476—591no—
365C2×#464—591no—
366C2×#464—591no—
367C2×#460—591no—
368C2×#446D5911yescharacteristic, complemented
369C2×#441—591no—
370C2×#440—591no—
371C2×C4×SD16—591no—
372C2×C59#337114yescomplemented
373C2×C59C2×#54811yescharacteristic
374C2×C59C2×#57511yescharacteristic
375C2×C59C2×#57711yescharacteristic
376D59—82no—
377D59—82no—
378C22×Q16—591no—
379C22×SD16—591no—
380C22×SD16—591no—
381#559—598no—
382#559—1184no—
383#557—598no—
384#557—1184no—
385C2×C4⋊Q8—591no—
386C2×C4⋊Q8—1181no—
387C2×#127—591no—
388C2×#125—591no—
389C2×#125—591no—
390C2×#125—1181no—
391C2×#125—1181no—
392C2×#124—591no—
393C2×#124—591no—
394C2×#124—1181no—
395C2×#123—1181no—
396C2×#123—1181no—
397C2×C4×Q8—591no—
398C2×C4×Q8—591no—
399C2×C4×Q8—591no—
400C2×C4×Q8—591no—
401C2×C4×Q8—1181no—
402C2×C4×Q8C2×D5911yescharacteristic
403C2×C4×D4—591no—
404C2×C4×D4—591no—
405C2×C4×D4—1181no—
406#490—598no—
407#489—598no—
408#488—598no—
409#479—598no—
410#478—598no—
411#476—598no—
412#464—598no—
413#464—598no—
414#460—598no—
415#446C2×D5918yescomplemented
416#441—598no—
417#440—598no—
418C4×SD16—598no—
419C2×#107—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×C4⋊C8C2×D5911yescharacteristic
423C2×C4⋊C8C2×D5911yescharacteristic
424C2×C4⋊C8C2×D5911yescharacteristic
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#102—591no—
430C2×#102—591no—
431C2×#102—591no—
432C2×#102—591no—
433C2×#102—591no—
434C2×#102—591no—
435C2×#97C2×D5911yescharacteristic
436C2×#97C2×D5911yescharacteristic
437C2×C4×C8C2×D5911yescharacteristic
438C59C2×#337111yescharacteristic, complemented, Sylow
439C22×Q8—591no—
440C22×Q8—591no—
441C22×Q8—1181no—
442C22×Q8D23611yescharacteristic
443C22×D4—591no—
444C22×D4—591no—
445C22×D4—1181no—
446C22×D4—1181no—
447C23×C4—1181no—
448C23×C4—1181no—
449C2×Q16—594no—
450C2×Q16—1184no—
451C2×SD16—594no—
452C2×SD16—594no—
453C2×SD16—1184no—
454C2×SD16—1184no—
455C22×C8C22×D5911yescharacteristic
456C22×C8C22×D5911yescharacteristic
457C22×C8C22×D5911yescharacteristic
458C22×C8C22×D5911yescharacteristic
459C4⋊Q8—594no—
460C4⋊Q8—1188no—
461C4⋊Q8—1182no—
462#127—594no—
463#127—1182no—
464#125—594no—
465#125—594no—
466#125—1188no—
467#125—1188no—
468#125—1182no—
469#125—1182no—
470#124—594no—
471#124—594no—
472#124—1188no—
473#124—1182no—
474#124—1182no—
475#123—1188no—
476#123—1188no—
477C4×Q8—594no—
478C4×Q8—594no—
479C4×Q8—594no—
480C4×Q8—594no—
481C4×Q8—1188no—
482C4×Q8—1182no—
483C4×Q8—1182no—
484C4×Q8—1182no—
485C4×Q8—1182no—
486C4×Q8D23614yes—
487C4×Q8C22×D5914yes—
488C4×D4—594no—
489C4×D4—594no—
490C4×D4—1188no—
491C4×D4—1182no—
492C4×D4—1182no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4D23611yescharacteristic
507C2×C4⋊C4D23611yescharacteristic
508C2×C4⋊C4D23611yescharacteristic
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C42—1181no—
516C2×C42—1181no—
517C2×C42—1181no—
518C2×C42—1181no—
519C2×C42C22×D5911yescharacteristic
520C2×C42C22×D5911yescharacteristic
521C2×C42C22×D5911yescharacteristic
522#107—594no—
523#106—594no—
524#106—594no—
525C4⋊C8C22×D5914yes—
526C4⋊C8C22×D5914yes—
527C4⋊C8C22×D5914yes—
528#103—594no—
529#103—594no—
530#103—594no—
531#103—594no—
532#102—594no—
533#102—594no—
534#102—594no—
535#102—594no—
536#102—594no—
537#102—594no—
538#97C22×D5914yes—
539#97C22×D5914yes—
540C4×C8C22×D5914yes—
541C24—1181no—
542C24—1181no—
543C2×Q8—42no—
544C2×Q8—594no—
545C2×Q8—592no—
546C2×Q8—592no—
547C2×Q8—1181no—
548C2×Q8—1181no—
549C2×Q8—1184no—
550C2×Q8—1182no—
551C2×Q8—1182no—
552C2×Q8—1182no—
553C2×Q8—2364no—
554C2×Q8C2×D23614yes—
555C2×D4—592no—
556C2×D4—592no—
557C2×D4—1184no—
558C2×D4—1184no—
559C2×D4—1181no—
560C2×D4—1181no—
561C2×D4—1182no—
562C2×D4—1182no—
563C2×D4—1182no—
564C2×D4—1182no—
565C2×D4—4722no—
566C2×D4—2364no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4—1181no—
571C22×C4—1181no—
572C22×C4—1181no—
573C22×C4—1184no—
574C22×C4—1184no—
575C22×C4—4722no—
576C22×C4—4722no—
577C22×C4C2×D23611yescharacteristic
578C22×C4C2×D23611yescharacteristic
579C22×C4C2×D23611yescharacteristic
580C22×C4C2×D23611yescharacteristic
581C22×C4C2×D23611yescharacteristic
582C22×C4C2×D23611yescharacteristic
583C22×C4C23×D5911yescharacteristic
584Q16—1188no—
585SD16—1188no—
586SD16—1188no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8C23×D5912yes—
592C2×C8C23×D5912yes—
593C2×C8C23×D5912yes—
594C2×C8C23×D5912yes—
595C4⋊C4—592no—
596C4⋊C4—592no—
597C4⋊C4—592no—
598C4⋊C4—592no—
599C4⋊C4—1181no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4C2×D23614yes—
613C4⋊C4C2×D23614yes—
614C4⋊C4C2×D23614yes—
615C22⋊C4—1184no—
616C22⋊C4—1184no—
617C22⋊C4—1184no—
618C22⋊C4—1184no—
619C22⋊C4—1184no—
620C22⋊C4—1184no—
621C42—1184no—
622C42—1184no—
623C42—1184no—
624C42—1184no—
625C42C2×D23612yes—
626C42C2×D23612yes—
627C42C2×D23612yes—
628C42C23×D5912yes—
629C42C23×D5912yes—
630C42C23×D5912yes—
631C23—1182no—
632C23—1182no—
633C23—2362no—
634C23—2362no—
635C23—2362no—
636C23—2362no—
637C23—2362no—
638C23—2362no—
639C23C22×D23611yescharacteristic
640Q8—44no—
641Q8—594no—
642Q8—1182no—
643Q8—1184no—
644Q8—1182no—
645Q8—1182no—
646Q8—2368no—
647Q8—2362no—
648D4—1182no—
649D4—1182no—
650D4—1182no—
651D4—1182no—
652D4—4724no—
653D4—2368no—
654D4—2362no—
655D4—2362no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—1182no—
663C2×C4—1184no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—4724no—
670C2×C4—4724no—
671C2×C4—2362no—
672C2×C4—2362no—
673C2×C4—2362no—
674C2×C4—2362no—
675C2×C4—2362no—
676C2×C4C22×D23612yes—
677C2×C4C22×D23612yes—
678C2×C4C22×D23612yes—
679C2×C4C22×D23612yes—
680C2×C4C22×D23612yes—
681C2×C4C22×D23612yes—
682C2×C4C22×D23611yescharacteristic
683C2×C4#41×D5912yes—
684C2×C4#1427377512yes—
685C2×C4C24×D5911yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C22—4724no—
691C22—4724no—
692C22—2362no—
693C22—2362no—
694C22—2362no—
695C22—2362no—
696C22—2362no—
697C22—2362no—
698C22#1683806412yes—
699C22#1683820212yes—
700C22#1683821412yes—
701C22C23×D23611yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—1184no—
709C4—2362no—
710C4—2362no—
711C4—2362no—
712C4—2362no—
713C4—2362no—
714C4#1683806412yes—
715C4C2×#41×D5911yescharacteristic
716C4C2×#1427377511yescharacteristic
717C2—4722no—
718C2—4722no—
719C2#2143686614yesdirect product factor
720C2C2×#1683806411yescharacteristic
721C2C2×#1683820211yescharacteristic
722C2C2×#1683821411yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#446C2
socleC23×C59C22×D4
prime radicalC2×#14273724C22
hypercenterC2×#446D59
hypocenterC59C2×#3371
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#16838130C2semidirect
3. #21436866C2direct (N × H)
5. C2×#16837762C2semidirect
6. C2×#16837757C2semidirect
7. C2×#16837710C2semidirect
8. C2×#16837703C2semidirect
9. C2×#16837693C2semidirect
10. C2×#16837625C2semidirect
11. C2×#16837625C2semidirect
13. C2×#16837510C2semidirect
14. C2×#16837504C2semidirect
15. C2×C4×#11745660C2semidirect
16. C2×C59×#446C2semidirect
23. #16838130C22semidirect
45. #16837762C22semidirect
46. #16837757C22semidirect
47. #16837710C22semidirect
48. #16837703C22semidirect
49. #16837693C22semidirect
50. #16837625C22semidirect
51. #16837625C22semidirect
53. #16837510C22semidirect
54. #16837504C22semidirect
55. C4×#11745660C22semidirect
70. C59×#446C22semidirect
368. C2×#446D59semidirect
372. C2×C59#3371semidirect
415. #446C2×D59semidirect
438. C59C2×#3371semidirect
719. C2#21436866direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381372
C2×#168381302
#214368662
C2×#168377672
C2×#168377622
C2×#168377572
C2×#168377102
C2×#168377032
C2×#168376932
C2×#168376252
C2×#168376032
C2×#168375102
C2×#168375042
C2×C4×#117456602
C2×C59×#4462
C2×#337159