Finite Group Databasebeta

← C2×#21430113 #28755367

Subgroups — C2×#21430113 #28755367

Order 15104.

2026 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21430113C2116yesmaximal, direct product factor
2C2×#16837344C211yesmaximal, characteristic, complemented
3C2×#16837341C211yesmaximal, characteristic, complemented
4C2×#16837331C211yesmaximal, characteristic
5C2×#16837329C211yesmaximal, characteristic
6C2×#16837324C211yesmaximal, characteristic
7C2×#16837323C211yesmaximal, characteristic, complemented
8C2×#16837315C211yesmaximal, characteristic
9C2×#16837307C211yesmaximal, characteristic, complemented
10C2×#16837294C211yesmaximal, characteristic
11C2×#16837292C211yesmaximal, characteristic
12C2×#16837291C211yesmaximal, characteristic
13C2×#16837289C211yesmaximal, characteristic, complemented
14C2×#16837285C211yesmaximal, characteristic, complemented
15C2×#16837253C211yesmaximal, characteristic, complemented
16C2×C59×#400C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×C4⋊Dic59C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34#16837344C2218yescomplemented
35#16837341C2218yescomplemented
36#16837331C2218yes—
37#16837329C2218yes—
38#16837324C2218yes—
39#16837323C2218yescomplemented
40#16837315C2218yes—
41#16837307C2218yescomplemented
42#16837294C2218yes—
43#16837292C2218yes—
44#16837291C2218yes—
45#16837289C2218yescomplemented
46#16837285C2218yescomplemented
47#16837253C2218yescomplemented
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C22×C4⋊C4×C59C2211yescharacteristic
60C22×C4⋊C4×C59C2211yescharacteristic
61C59×#400C2218yescomplemented
62C2×#95×C59C2211yescharacteristic
63C2×#95×C59C2211yescharacteristic
64C2×#95×C59C2211yescharacteristic
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C24×D59C2311yescharacteristic
68C22×Dic118—24no—
69C22×Dic118—42no—
70C22×Dic118—42no—
71C22×Dic118C2314yes—
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C2×C4⋊Dic59—24no—
80C2×C4⋊Dic59—42no—
81C2×C4⋊Dic59—42no—
82C2×C4⋊Dic59C2314yes—
83C2×C4⋊Dic59C2314yes—
84C2×C4⋊Dic59C2314yes—
85C2×Dic59⋊C4—24no—
86C2×Dic59⋊C4—24no—
87C2×Dic59⋊C4—24no—
88C2×Dic59⋊C4C2314yes—
89C2×Dic59⋊C4C2314yes—
90C2×Dic59⋊C4C2314yes—
91C2×(C2×D59)⋊C4—24no—
92C2×(C2×D59)⋊C4—24no—
93C2×(C2×D59)⋊C4—24no—
94C2×(C2×D59)⋊C4—42no—
95C2×(C2×D59)⋊C4—42no—
96C2×(C2×D59)⋊C4—42no—
97C2×(C2×D59)⋊C4—42no—
98C2×(C2×D59)⋊C4C2314yes—
99C2×(C2×D59)⋊C4C2314yes—
100C2×(C2×D59)⋊C4C2314yes—
101C2×(C2×D59)⋊C4C2314yes—
102C2×(C2×D59)⋊C4C2314yes—
103C2×(C2×D59)⋊C4C2314yes—
104C2×(C2×D59)⋊C4C2314yes—
105C2×C4×Dic59—24no—
106C2×C4×Dic59—42no—
107C2×C4×Dic59—42no—
108C2×C4×Dic59C2314yes—
109C2×C4×Dic59C2314yes—
110C2×C4×Dic59C2314yes—
111C59⋊#95C2314yes—
112C59⋊#95C2314yes—
113C59⋊#95C2314yes—
114C59⋊#95C2314yes—
115C59⋊#95C2314yes—
116C59⋊#95C2314yes—
117C59⋊#95C2314yes—
118C59⋊#95C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C59⋊#95C2314yes—
122C23×C4×C59C2311yescharacteristic
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C2×C4⋊C4×C59—42no—
130C2×C4⋊C4×C59—42no—
131C2×C4⋊C4×C59C2314yes—
132C2×C4⋊C4×C59C2314yes—
133#95×C59C2314yes—
134#95×C59C2314yes—
135#95×C59C2314yes—
136#95×C59C2314yes—
137#95×C59C2314yes—
138C24×C59C2411yescharacteristic
139C23×D59—22no—
140C23×D59—22no—
141C23×D59—22no—
142C23×D59—22no—
143C23×D59—22no—
144C23×D59—22no—
145C23×D59—22no—
146C23×D59C2412yes—
147C22×C4×C59—22no—
148C22×C4×C59—22no—
149C22×C4×C59—22no—
150C22×C4×C59—22no—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59—22no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
163C22×C4×C59—22no—
164C22×C4×C59—22no—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59#4114yes—
168C22×C4×C59C2412yes—
169C22×C4×C59C2412yes—
170C22×C4×C59C2412yes—
171C22×C4×C59C2412yes—
172C22×C4×C59C2412yes—
173C22×C4×C59C2412yes—
174C22×C4×C59C2412yes—
175C22×Dic59—22no—
176C22×Dic59—22no—
177C22×Dic59—22no—
178C22×Dic59—22no—
179C22×Dic59—22no—
180C22×Dic59—22no—
181C22×Dic59—22no—
182C22×Dic59—22no—
183C22×Dic59—22no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59—22no—
187C22×Dic59—22no—
188C22×Dic59—22no—
189C22×Dic59—22no—
190C22×Dic59—22no—
191C22×Dic59—22no—
192C22×Dic59—22no—
193C22×Dic59—22no—
194C22×Dic59#4114yes—
195C22×Dic59#4114yes—
196C22×Dic59C2412yes—
197C22×Dic59C2412yes—
198C22×Dic59C2412yes—
199C22×Dic59C2412yes—
200C22×Dic59C2412yes—
201C22×Dic59C2412yes—
202C22×Dic59C2412yes—
203C2×Dic118—28no—
204C2×Dic118—44no—
205C2×Dic118—44no—
206C2×Dic118—416no—
207C4⋊C4×C59—44no—
208C4⋊C4×C59—44no—
209(C2×D59)⋊C4—28no—
210(C2×D59)⋊C4—28no—
211(C2×D59)⋊C4—28no—
212(C2×D59)⋊C4—44no—
213(C2×D59)⋊C4—44no—
214(C2×D59)⋊C4—44no—
215(C2×D59)⋊C4—44no—
216C4⋊Dic59—28no—
217C4⋊Dic59—44no—
218C4⋊Dic59—44no—
219Dic59⋊C4—28no—
220Dic59⋊C4—28no—
221Dic59⋊C4—28no—
222C4×Dic59—28no—
223C4×Dic59—44no—
224C4×Dic59—44no—
225C23×C59C2×#4112yes—
226C23×C59C2×#4112yes—
227C23×C59C2×#4112yes—
228C23×C59H(5,𝔽2)12yes—
229C23×C59H(5,𝔽2)12yes—
230C23×C592−1+412yes—
231C23×C592−1+412yes—
232C23×C59C2511yescharacteristic
233C22×D59—22no—
234C22×D59—22no—
235C22×D59—22no—
236C22×D59—22no—
237C22×D59—22no—
238C22×D59—22no—
239C22×D59—22no—
240C22×D59—44no—
241C22×D59—44no—
242C22×D59—44no—
243C22×D59—44no—
244C22×D59—44no—
245C22×D59—44no—
246C22×D59—44no—
247C2×C4×C59—28no—
248C2×C4×C59—22no—
249C2×C4×C59—22no—
250C2×C4×C59—22no—
251C2×C4×C59—22no—
252C2×C4×C59—22no—
253C2×C4×C59—22no—
254C2×C4×C59—22no—
255C2×C4×C59—22no—
256C2×C4×C59—22no—
257C2×C4×C59—22no—
258C2×C4×C59—22no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—44no—
269C2×C4×C59—44no—
270C2×C4×C59—44no—
271C2×C4×C59—44no—
272C2×C4×C59—44no—
273C2×C4×C59—44no—
274C2×C4×C59C2×#4114yes—
275C2×Dic59—28no—
276C2×Dic59—28no—
277C2×Dic59—22no—
278C2×Dic59—22no—
279C2×Dic59—22no—
280C2×Dic59—22no—
281C2×Dic59—22no—
282C2×Dic59—22no—
283C2×Dic59—22no—
284C2×Dic59—22no—
285C2×Dic59—22no—
286C2×Dic59—22no—
287C2×Dic59—22no—
288C2×Dic59—22no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—22no—
292C2×Dic59—22no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—44no—
297C2×Dic59—44no—
298C2×Dic59—44no—
299C2×Dic59—44no—
300C2×Dic59—44no—
301C2×Dic59C2×#4114yes—
302C2×Dic59C2×#4114yes—
303Dic118—416no—
304C2×#2650—591nomaximal, Sylow
305C22×C59#52914yes—
306C22×C59#53814yes—
307C22×C59#53914yes—
308C22×C59#54114yes—
309C22×C59#54214yes—
310C22×C59#54214yes—
311C22×C59#54214yes—
312C22×C59C22×#4111yescharacteristic
313C22×C59C22×#4111yescharacteristic
314C22×C59C22×#4111yescharacteristic
315C22×C59C2×H(5,𝔽2)11yescharacteristic
316C22×C59C2×H(5,𝔽2)11yescharacteristic
317C22×C59C2×2−1+411yescharacteristic
318C22×C59C2×2−1+411yescharacteristic
319C2×D59—42no—
320C2×D59—42no—
321C2×D59—42no—
322C2×D59—42no—
323C2×D59—42no—
324C2×D59—42no—
325C2×D59—42no—
326C2×D59—88no—
327C4×C59—24no—
328C4×C59—42no—
329C4×C59—42no—
330C4×C59—42no—
331C4×C59—42no—
332C4×C59—42no—
333C4×C59—42no—
334Dic59—24no—
335Dic59—24no—
336Dic59—42no—
337Dic59—42no—
338Dic59—42no—
339Dic59—42no—
340Dic59—42no—
341#2650—5916no—
342C2×#400—591no—
343C2×#400—591no—
344C2×#400D5911yescharacteristic, complemented
345C2×#397—591no—
346C2×#397—591no—
347C2×#396—591no—
348C2×#395—591no—
349C2×#393—591no—
350C2×#391—591no—
351C2×#388—591no—
352C2×#388—591no—
353C2×#388—591no—
354C2×#387—591no—
355C2×#387—591no—
356C2×C4×C4⋊C4—591no—
357C2×C59#265018yescomplemented
358C2×C59C2×#52911yescharacteristic
359C2×C59C2×#53811yescharacteristic
360C2×C59C2×#53911yescharacteristic
361C2×C59C2×#54111yescharacteristic
362C2×C59C2×#54211yescharacteristic
363C2×C59C2×#54211yescharacteristic
364C2×C59C2×#54211yescharacteristic
365D59—82no—
366C23×Q8—591no—
367C22×C4⋊C4—591no—
368C22×C4⋊C4—591no—
369C22×C4⋊C4—591no—
370C22×C4⋊C4—591no—
371C22×C4⋊C4—591no—
372C22×C4⋊C4—591no—
373C22×C4⋊C4C2×D5911yescharacteristic
374C22×C4⋊C4C2×D5911yescharacteristic
375C22×C22⋊C4—591no—
376C22×C22⋊C4—591no—
377C22×C22⋊C4—591no—
378C22×C22⋊C4—591no—
379C22×C22⋊C4—591no—
380C22×C22⋊C4—591no—
381C22×C22⋊C4—591no—
382C22×C42—591no—
383C22×C42—591no—
384C22×C42—591no—
385#400—598no—
386#400—598no—
387#400C2×D5918yescomplemented
388#397—598no—
389#397—598no—
390#396—598no—
391#395—598no—
392#393—598no—
393#391—598no—
394#388—598no—
395#388—598no—
396#388—598no—
397#387—598no—
398#387—598no—
399C4×C4⋊C4—598no—
400C2×#95—591no—
401C2×#95—591no—
402C2×#95—591no—
403C2×#95—591no—
404C2×#95—591no—
405C2×#95—591no—
406C2×#95—591no—
407C2×#95—591no—
408C2×#95—591no—
409C2×#95—591no—
410C2×#95—591no—
411C2×#95C2×D5911yescharacteristic
412C2×#95C2×D5911yescharacteristic
413C2×#95C2×D5911yescharacteristic
414C2×#95C2×D5911yescharacteristic
415C2×#95C2×D5911yescharacteristic
416C59C2×#265011yescharacteristic, complemented, Sylow
417C25—591no—
418C22×Q8—594no—
419C22×Q8—1184no—
420C22×Q8—2362no—
421C22×Q8—2362no—
422C23×C4—591no—
423C23×C4—591no—
424C23×C4—591no—
425C23×C4—591no—
426C23×C4—591no—
427C23×C4—591no—
428C23×C4—591no—
429C23×C4C22×D5911yescharacteristic
430C23×C4C22×D5911yescharacteristic
431C23×C4C22×D5911yescharacteristic
432C23×C4C22×D5911yescharacteristic
433C23×C4C22×D5911yescharacteristic
434C23×C4C22×D5911yescharacteristic
435C23×C4C22×D5911yescharacteristic
436C2×C4⋊C4—42no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—594no—
439C2×C4⋊C4—594no—
440C2×C4⋊C4—594no—
441C2×C4⋊C4—594no—
442C2×C4⋊C4—594no—
443C2×C4⋊C4—594no—
444C2×C4⋊C4—1184no—
445C2×C4⋊C4—1184no—
446C2×C4⋊C4—1184no—
447C2×C4⋊C4—1184no—
448C2×C4⋊C4—2362no—
449C2×C4⋊C4—2362no—
450C2×C4⋊C4C22×D5914yes—
451C2×C4⋊C4C22×D5914yes—
452C2×C22⋊C4—594no—
453C2×C22⋊C4—594no—
454C2×C22⋊C4—594no—
455C2×C22⋊C4—594no—
456C2×C22⋊C4—594no—
457C2×C22⋊C4—594no—
458C2×C22⋊C4—594no—
459C2×C22⋊C4—1184no—
460C2×C22⋊C4—1184no—
461C2×C22⋊C4—1184no—
462C2×C22⋊C4—2362no—
463C2×C22⋊C4—2362no—
464C2×C22⋊C4—2362no—
465C2×C22⋊C4—2362no—
466C2×C42—594no—
467C2×C42—594no—
468C2×C42—594no—
469C2×C42—1184no—
470C2×C42—2362no—
471C2×C42—2362no—
472#95—594no—
473#95—594no—
474#95—594no—
475#95—594no—
476#95—594no—
477#95—594no—
478#95—594no—
479#95—594no—
480#95—594no—
481#95—594no—
482#95—594no—
483#95C22×D5914yes—
484#95C22×D5914yes—
485#95C22×D5914yes—
486#95C22×D5914yes—
487#95C22×D5914yes—
488C24—592no—
489C24—1182no—
490C24—1182no—
491C24—1182no—
492C24—1182no—
493C24—1182no—
494C24—1182no—
495C24—1182no—
496C24C23×D5911yescharacteristic
497C2×Q8—1188no—
498C2×Q8—2364no—
499C2×Q8—2364no—
500C2×Q8—23616no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—594no—
522C22×C4—594no—
523C22×C4—592no—
524C22×C4—592no—
525C22×C4—592no—
526C22×C4—592no—
527C22×C4—592no—
528C22×C4—592no—
529C22×C4—592no—
530C22×C4—1182no—
531C22×C4—1182no—
532C22×C4—1182no—
533C22×C4—1182no—
534C22×C4—1182no—
535C22×C4—1182no—
536C22×C4—1182no—
537C22×C4—1182no—
538C22×C4—1182no—
539C22×C4—1182no—
540C22×C4—1182no—
541C22×C4—1182no—
542C22×C4—1182no—
543C22×C4—1182no—
544C22×C4—1182no—
545C22×C4—1182no—
546C22×C4—1182no—
547C22×C4—1182no—
548C22×C4—1182no—
549C22×C4#1174568914yes—
550C22×C4C23×D5912yes—
551C22×C4C23×D5912yes—
552C22×C4C23×D5912yes—
553C22×C4C23×D5912yes—
554C22×C4C23×D5912yes—
555C22×C4C23×D5912yes—
556C22×C4C23×D5912yes—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—1188no—
560C4⋊C4—1188no—
561C4⋊C4—1188no—
562C4⋊C4—1188no—
563C4⋊C4—2364no—
564C4⋊C4—2364no—
565C22⋊C4—1188no—
566C22⋊C4—1188no—
567C22⋊C4—1188no—
568C22⋊C4—2364no—
569C22⋊C4—2364no—
570C22⋊C4—2364no—
571C22⋊C4—2364no—
572C42—1188no—
573C42—2364no—
574C42—2364no—
575C23—1182no—
576C23—1182no—
577C23—1182no—
578C23—1182no—
579C23—1182no—
580C23—1182no—
581C23—1182no—
582C23—2364no—
583C23—2364no—
584C23—2364no—
585C23—2364no—
586C23—2364no—
587C23—2364no—
588C23—2364no—
589C23#41×D5912yes—
590C23#41×D5912yes—
591C23C2×#1174568912yes—
592C23#1427377212yes—
593C23#1427377312yes—
594C23#1427377412yes—
595C23#1427377412yes—
596C23C24×D5911yescharacteristic
597Q8—23616no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—28no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—594no—
626C2×C4—594no—
627C2×C4—1188no—
628C2×C4—1182no—
629C2×C4—1182no—
630C2×C4—1182no—
631C2×C4—1182no—
632C2×C4—1188no—
633C2×C4—1182no—
634C2×C4—1182no—
635C2×C4—1182no—
636C2×C4—1182no—
637C2×C4—1182no—
638C2×C4—1182no—
639C2×C4—1182no—
640C2×C4—1182no—
641C2×C4—1182no—
642C2×C4—1182no—
643C2×C4—1182no—
644C2×C4—1182no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—1182no—
648C2×C4—2364no—
649C2×C4—2364no—
650C2×C4—2364no—
651C2×C4—2364no—
652C2×C4—2364no—
653C2×C4C2×#1174568914yes—
654C22—4728no—
655C22—2362no—
656C22—2362no—
657C22—2362no—
658C22—2362no—
659C22—2362no—
660C22—2362no—
661C22—2362no—
662C22#1683793714yes—
663C22#1683799214yes—
664C22#1683799314yes—
665C22#1683801514yes—
666C22#1683801614yes—
667C22#1683801814yes—
668C22#1683802014yes—
669C22C2×#41×D5911yescharacteristic
670C22C2×#41×D5911yescharacteristic
671C22C22×#1174568911yescharacteristic
672C22C2×#1427377211yescharacteristic
673C22C2×#1427377311yescharacteristic
674C22C2×#1427377411yescharacteristic
675C22C2×#1427377411yescharacteristic
676C4—24no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—42no—
683C4—1184no—
684C4—1184no—
685C4—2362no—
686C4—2362no—
687C4—2362no—
688C4—2362no—
689C4—2362no—
690C2—4722no—
691C2#2143011318yesdirect product factor
692C2C2×#1683793711yescharacteristic
693C2C2×#1683799211yescharacteristic
694C2C2×#1683799311yescharacteristic
695C2C2×#1683801511yescharacteristic
696C2C2×#1683801611yescharacteristic
697C2C2×#1683801811yescharacteristic
698C2C2×#1683802011yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#400C2
socleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#400D59
hypocenterC59C2×#2650
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #21430113C2direct (N × H)
2. C2×#16837344C2semidirect
3. C2×#16837341C2semidirect
7. C2×#16837323C2semidirect
9. C2×#16837307C2semidirect
13. C2×#16837289C2semidirect
14. C2×#16837285C2semidirect
15. C2×#16837253C2semidirect
16. C2×C59×#400C2semidirect
34. #16837344C22semidirect
35. #16837341C22semidirect
39. #16837323C22semidirect
41. #16837307C22semidirect
45. #16837289C22semidirect
46. #16837285C22semidirect
47. #16837253C22semidirect
61. C59×#400C22semidirect
344. C2×#400D59semidirect
357. C2×C59#2650semidirect
387. #400C2×D59semidirect
416. C59C2×#2650semidirect
691. C2#21430113direct (N × H)

Maximal subgroups

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

subgroupindex
#214301132
C2×#168373442
C2×#168373412
C2×#168373312
C2×#168373292
C2×#168373242
C2×#168373232
C2×#168373152
C2×#168373072
C2×#168372942
C2×#168372922
C2×#168372912
C2×#168372892
C2×#168372852
C2×#168372532
C2×C59×#4002
C2×#265059