Finite Group Databasebeta

← C2×#21438627 #29496058

Subgroups — C2×#21438627 #29496058

Order 15104.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438627C2132yesmaximal, direct product factor
2C2×#16838156C212yesmaximal, complemented
3C2×#16838146C212yesmaximal, complemented
4C2×#16838112C212yesmaximal, complemented
5C2×#16838098C212yesmaximal, complemented
6C2×#16838098C212yesmaximal, complemented
7C2×#16838056C212yesmaximal, complemented
8C2×#16838050C214yesmaximal, complemented
9C2×#16838030C212yesmaximal, complemented
10C2×#16838007C212yesmaximal, complemented
11C2×#16838001C212yesmaximal, complemented
12C2×#16837993C214yesmaximal, complemented
13C2×#16837979C212yesmaximal, complemented
14C2×#16837952C211yesmaximal, characteristic, complemented
15C22×#14273719C211yesmaximal, characteristic, complemented
16C2×C59×#529C211yesmaximal, characteristic, complemented
17C22×#11745685C2212yes—
18C22×#11745687C2214yes—
19#16838156C22132yescomplemented
20#16838146C22132yescomplemented
21#16838112C22132yescomplemented
22#16838098C22132yescomplemented
23#16838098C22132yescomplemented
24#16838056C22132yescomplemented
25#16838050C22164yescomplemented
26#16838030C22132yescomplemented
27#16838007C22132yescomplemented
28#16838001C22132yescomplemented
29#16837993C22164yescomplemented
30#16837979C22132yescomplemented
31#16837952C22116yescomplemented
32C2×#14273727C2211yescharacteristic
33C2×#14273727C2212yes—
34C2×#14273726C2214yes—
35C2×#14273724C2211yescharacteristic
36C2×#14273722C2214yes—
37C2×#14273722C2214yes—
38C2×#14273719C2212yes—
39C2×#14273719C2212yes—
40C2×#14273719C2212yes—
41C2×#14273719C2212yes—
42C2×#14273719C2212yes—
43C2×#14273719C22116yescomplemented
44C2×#14273718C2214yes—
45C2×#14273715C2212yes—
46C2×#14273712C2214yes—
47C2×#14273712C2214yes—
48C2×#14273711C2214yes—
49C2×#14273711C2214yes—
50C2×#14273709C2214yes—
51C2×#14273709C2214yes—
52C2×#14273707C2214yes—
53C2×#14273705C2214yes—
54C2×#14273705C2214yes—
55C2×#14273704C2214yes—
56C2×#14273704C2214yes—
57C2×#14273703C2214yes—
58C2×#14273701C2212yes—
59C2×#14273701C2212yes—
60C2×#14273701C2212yes—
61C2×#14273701C2212yes—
62C2×#14273700C2214yes—
63C2×#14273700C2214yes—
64C2×#14273699C2214yes—
65C2×#14273699C2214yes—
66C2×C4×D236C2212yes—
67C2×C4×D236C2212yes—
68C2×C4×D236C2212yes—
69C2×C4×D236C2212yes—
70C2×(C22⋊D59)⋊C4C2214yes—
71C2×(C22⋊D59)⋊C4C2214yes—
72C2×#14273686C2212yes—
73C22×C4⋊Dic59C2212yes—
74C22×C4⋊Dic59C2211yescharacteristic
75C22×C4⋊Dic59C2211yescharacteristic
76C22×Dic59⋊C4C2212yes—
77C22×Dic59⋊C4C2212yes—
78C2×C4⋊C4×D59C2214yes—
79C59×#529C22116yescomplemented
80C2×#126×C59C2212yes—
81C2×#125×C59C2211yescharacteristic
82C2×#124×C59C2211yescharacteristic
83C2×#123×C59C2212yes—
84C2×C22⋊Q8×C59C2211yescharacteristic
85C2×#121×C59C2211yescharacteristic
86C2×C4×Q8×C59C2211yescharacteristic
87C2×C4×D4×C59C2212yes—
88C2×C4×D4×C59C2211yescharacteristic
89C2×#117×C59C2212yes—
90C22×C42×C59C2211yescharacteristic
91C2×#11745685—48no—
92C2×#11745685C23116yes—
93C2×#11745687—416no—
94C2×#11745687C23132yes—
95C22×Dic118C2312yes—
96C22×Dic118C2314yes—
97C22×D236C2312yes—
98C22×D236C2312yes—
99C22×D236C2312yes—
100C22×C22⋊D59C2314yes—
101C22×C22⋊D59C2314yes—
102C22×C22⋊D59C2314yes—
103C23×Dic59C2312yes—
104C23×Dic59C2312yes—
105C23×Dic59C2314yes—
106C22×C4×D59C2314yes—
107C22×C4×D59C2314yes—
108C22×C4×D59C2314yes—
109#14273727C2318yes—
110#14273727C23116yes—
111#14273726C23132yes—
112#14273724C2318yes—
113#14273722C23132yes—
114#14273722C23132yes—
115#14273719C23116yes—
116#14273719C23116yes—
117#14273719C23116yes—
118#14273719C23116yes—
119#14273719C23116yes—
120#14273718C23132yes—
121#14273715C23116yes—
122#14273712C23132yes—
123#14273712C23132yes—
124#14273711C23132yes—
125#14273711C23132yes—
126#14273709C23132yes—
127#14273709C23132yes—
128#14273707C23132yes—
129#14273705C23132yes—
130#14273705C23132yes—
131#14273704C23132yes—
132#14273704C23132yes—
133#14273703C23132yes—
134#14273701C23116yes—
135#14273701C23116yes—
136#14273701C23116yes—
137#14273701C23116yes—
138#14273700C23132yes—
139#14273700C23132yes—
140#14273699C23132yes—
141#14273699C23132yes—
142C4×D236C23116yes—
143C4×D236C23116yes—
144C4×D236C23116yes—
145C4×D236C23116yes—
146(C22⋊D59)⋊C4C23132yes—
147(C22⋊D59)⋊C4C23132yes—
148#14273686C23116yes—
149C2×C4⋊Dic59C2312yes—
150C2×C4⋊Dic59C2312yes—
151C2×C4⋊Dic59C2312yes—
152C2×C4⋊Dic59C2312yes—
153C2×C4⋊Dic59C2314yes—
154C2×C4⋊Dic59C2312yes—
155C2×C4⋊Dic59C2314yes—
156C2×C4⋊Dic59C2312yes—
157C2×C4⋊Dic59C2318yes—
158C2×C4⋊Dic59C2318yes—
159C2×C4⋊Dic59C23116yes—
160C2×Dic59⋊C4C2314yes—
161C2×Dic59⋊C4C2314yes—
162C2×Dic59⋊C4C2314yes—
163C2×Dic59⋊C4C2314yes—
164C2×Dic59⋊C4C2314yes—
165C2×Dic59⋊C4C2314yes—
166C2×Dic59⋊C4C23116yes—
167C2×Dic59⋊C4C23116yes—
168C4⋊C4×D59C23132yes—
169C2×C22⋊Dic59C2314yes—
170C2×(C2×D59)⋊C4C2314yes—
171C2×(C2×D59)⋊C4C2314yes—
172C2×(C2×D59)⋊C4C2314yes—
173C2×(C2×D59)⋊C4C2314yes—
174C2×(C2×D59)⋊C4C2314yes—
175C2×(C2×D59)⋊C4C2314yes—
176C2×C4×Dic59C2314yes—
177C22×Q8×C59C2311yescharacteristic
178C22×D4×C59C2312yes—
179C22×D4×C59C2311yescharacteristic
180C23×C4×C59C2311yescharacteristic
181C23×C4×C59C2312yes—
182C23×C4×C59C2311yescharacteristic
183C23×C4×C59C2311yescharacteristic
184#126×C59C23116yes—
185#125×C59C2318yes—
186#124×C59C2318yes—
187#123×C59C23116yes—
188C22⋊Q8×C59C2318yes—
189#121×C59C2318yes—
190C4×Q8×C59C2318yes—
191C4×D4×C59C23116yes—
192C4×D4×C59C2318yes—
193#117×C59C23116yes—
194C2×C4⋊C4×C59C2311yescharacteristic
195C2×C4⋊C4×C59C2312yes—
196C2×C4⋊C4×C59C2312yes—
197C2×C4⋊C4×C59C2312yes—
198C2×C4⋊C4×C59C2312yes—
199C2×C4⋊C4×C59C2311yescharacteristic
200C2×C22⋊C4×C59C2312yes—
201C2×C22⋊C4×C59C2312yes—
202C2×C22⋊C4×C59C2312yes—
203C2×C22⋊C4×C59C2312yes—
204C2×C22⋊C4×C59C2312yes—
205C2×C42×C59C2311yescharacteristic
206C2×C42×C59C2311yescharacteristic
207C2×C42×C59C2311yescharacteristic
208C2×C42×C59C2311yescharacteristic
209C2×C42×C59C2312yes—
210C2×C42×C59C2318yes—
211C24×C59C2412yes—
212C24×C59C2411yescharacteristic
213C23×D59C2414yes—
214C2×Q8×C59—42no—
215C2×Q8×C59C2414yes—
216C2×D4×C59—28no—
217C2×D4×C59—42no—
218C2×D4×C59C2418yes—
219C2×D4×C59C2414yes—
220C22×C4×C59—24no—
221C22×C4×C59—24no—
222C22×C4×C59—28no—
223C22×C4×C59—42no—
224C22×C4×C59C2411yescharacteristic
225C22×C4×C59C2411yescharacteristic
226C22×C4×C59C2411yescharacteristic
227C22×C4×C59C2411yescharacteristic
228C22×C4×C59C2411yescharacteristic
229C22×C4×C59C2414yes—
230C22×C4×C59C2414yes—
231C22×C4×C59C2412yes—
232C22×C4×C59C2412yes—
233C22×C4×C59C2412yes—
234C22×C4×C59C2418yes—
235C22×C4×C59C2414yes—
236C22×C4×C59C2411yescharacteristic
237C2×C22⋊D59—216no—
238C2×C22⋊D59—48no—
239C2×C22⋊D59—48no—
240C2×C22⋊D59C24116yes—
241C2×C22⋊D59C24116yes—
242C2×C22⋊D59C24116yes—
243C22×Dic59—28no—
244C22×Dic59—44no—
245C22×Dic59—48no—
246C22×Dic59C2414yes—
247C22×Dic59C2414yes—
248C22×Dic59C2414yes—
249C22×Dic59C2418yes—
250C22×Dic59C2418yes—
251C22×Dic59C24116yes—
252#11745687—464no—
253#11745685—432no—
254C2×D236—28no—
255C2×D236—44no—
256C2×D236—44no—
257C2×D236C2418yes—
258C2×D236C2418yes—
259C2×D236C2418yes—
260C2×C4×D59—48no—
261C2×C4×D59—48no—
262C2×C4×D59—48no—
263C2×C4×D59C24116yes—
264C2×C4×D59C24116yes—
265C2×C4×D59C24116yes—
266C2×Dic118—48no—
267C2×Dic118—44no—
268C2×Dic118C2418yes—
269C2×Dic118C24116yes—
270C4⋊C4×C59C2418yes—
271C4⋊C4×C59C2418yes—
272C4⋊C4×C59C2414yes—
273C4⋊C4×C59C2418yes—
274C4⋊C4×C59C2414yes—
275C4⋊C4×C59C2418yes—
276C22⋊C4×C59C2418yes—
277C22⋊C4×C59C2418yes—
278C22⋊C4×C59C2418yes—
279C22⋊C4×C59C2418yes—
280C22⋊C4×C59C2418yes—
281C42×C59C2414yes—
282C42×C59C2414yes—
283C42×C59C2414yes—
284C42×C59C2414yes—
285C42×C59C2418yes—
286C22⋊Dic59C24116yes—
287(C2×D59)⋊C4C24116yes—
288(C2×D59)⋊C4C24116yes—
289(C2×D59)⋊C4C24116yes—
290(C2×D59)⋊C4C24116yes—
291(C2×D59)⋊C4C24116yes—
292(C2×D59)⋊C4C24116yes—
293C4⋊Dic59C24116yes—
294C4⋊Dic59C2418yes—
295C4⋊Dic59C2418yes—
296C4⋊Dic59C2418yes—
297C4⋊Dic59C2418yes—
298C4⋊Dic59C24116yes—
299C4⋊Dic59C2418yes—
300C4⋊Dic59C2418yes—
301Dic59⋊C4C24116yes—
302Dic59⋊C4C24116yes—
303Dic59⋊C4C24116yes—
304Dic59⋊C4C24116yes—
305Dic59⋊C4C24116yes—
306Dic59⋊C4C24116yes—
307C4×Dic59C24116yes—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—24no—
311C23×C59—24no—
312C23×C59—24no—
313C23×C59H(5,𝔽2)14yes—
314C23×C59C2514yes—
315C23×C59C2512yes—
316C23×C59C2511yescharacteristic
317C22×D59—28no—
318C22×D59—28no—
319C22×D59—28no—
320C22×D59C2518yes—
321Q8×C59—44no—
322D4×C59—216no—
323D4×C59—44no—
324C2×C4×C59—24no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—28no—
328C2×C4×C59—22no—
329C2×C4×C59—24no—
330C2×C4×C59—24no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—28no—
334C2×C4×C59—216no—
335C2×C4×C59—44no—
336C2×C4×C592−1+414yes—
337C2×C4×C59C2514yes—
338C2×C4×C59C2512yes—
339C2×C4×C59C2512yes—
340C2×C4×C59C2512yes—
341C2×C4×C59C2512yes—
342C2×C4×C59C2514yes—
343C2×C4×C59C2514yes—
344C2×C4×C59C2512yes—
345C2×C4×C59C2512yes—
346C22⋊D59—232no—
347C22⋊D59—416no—
348C22⋊D59—416no—
349C2×Dic59—28no—
350C2×Dic59—28no—
351C2×Dic59—216no—
352C2×Dic59—28no—
353C2×Dic59—416no—
354C2×Dic59—48no—
355C2×Dic59C2518yes—
356C2×Dic59C2518yes—
357C2×Dic59C2518yes—
358D236—216no—
359D236—48no—
360D236—48no—
361C4×D59—416no—
362C4×D59—416no—
363C4×D59—416no—
364Dic118—48no—
365Dic118—416no—
366C2×#3559—591nomaximal, Sylow
367C22×C59—22no—
368C22×C59—22no—
369C22×C59—28no—
370C22×C59—24no—
371C22×C59—24no—
372C22×C59—24no—
373C22×C59—48no—
374C22×C59C2×H(5,𝔽2)14yes—
375C22×C59C2×H(5,𝔽2)12yes—
376C22×C59C2×2−1+412yes—
377C22×C59#58512yes—
378C22×C59C2611yescharacteristic
379C2×D59—28no—
380C2×D59—28no—
381C2×D59—28no—
382C2×D59—416no—
383C4×C59—24no—
384C4×C59—22no—
385C4×C59—22no—
386C4×C59—24no—
387C4×C59—22no—
388C4×C59—24no—
389C4×C59—22no—
390C4×C59—22no—
391C4×C59C2×2−1+414yes—
392Dic59—28no—
393Dic59—28no—
394Dic59—28no—
395#3559—5932no—
396C2×#563—592no—
397C2×#562—592no—
398C2×#554—592no—
399C2×#553—592no—
400C2×#553—592no—
401C2×#547—594no—
402C2×#547—592no—
403C2×#544—592no—
404C2×#540—592no—
405C2×#539—594no—
406C2×#539—592no—
407C2×#537—592no—
408C2×#532—591no—
409C2×#529D5911yescharacteristic, complemented
410C22×#125—591no—
411C2×C59—24no—
412C2×C59—44no—
413C2×C59#355914yescomplemented
414C2×C59C22×H(5,𝔽2)11yescharacteristic
415C2×C59C22×2−1+411yescharacteristic
416C2×C59C2×#58511yescharacteristic
417D59—48no—
418C22×#41—594no—
419C22×#41—592no—
420#563—5932no—
421#562—5932no—
422#554—5932no—
423#553—5932no—
424#553—5932no—
425#547—5964no—
426#547—5932no—
427#544—5932no—
428#540—5932no—
429#539—5964no—
430#539—5932no—
431#537—5932no—
432#532—5916no—
433C2×C4⋊Q8—594no—
434C2×C4⋊Q8—591no—
435C2×C4⋊Q8—592no—
436C2×#127—591no—
437#529C2×D59116yescomplemented
438C2×#126—594no—
439C2×#126—594no—
440C2×#126C2×D5912yes—
441C2×#125—594no—
442C2×#125—592no—
443C2×#125—592no—
444C2×#125—592no—
445C2×#125—592no—
446C2×#125—592no—
447C2×#125—5916no—
448C2×#125C2×D5911yescharacteristic
449C2×#124—592no—
450C2×#124C2×D5911yescharacteristic
451C2×#123—594no—
452C2×#123—594no—
453C2×#123—594no—
454C2×#123—594no—
455C2×#123—594no—
456C2×#123—594no—
457C2×#123C2×D5912yes—
458C2×C22⋊Q8—594no—
459C2×C22⋊Q8—594no—
460C2×C22⋊Q8—594no—
461C2×C22⋊Q8—594no—
462C2×C22⋊Q8—594no—
463C2×C22⋊Q8—594no—
464C2×C22⋊Q8C2×D5911yescharacteristic
465C2×#121—594no—
466C2×#121—594no—
467C2×#121—592no—
468C2×#121—592no—
469C2×#121—592no—
470C2×#121—592no—
471C2×#121—594no—
472C2×#121—594no—
473C2×#121C2×D5911yescharacteristic
474C2×C4×Q8C2×D5911yescharacteristic
475C2×C4×D4—594no—
476C2×C4×D4—594no—
477C2×C4×D4—592no—
478C2×C4×D4—592no—
479C2×C4×D4—592no—
480C2×C4×D4—592no—
481C2×C4×D4C2×D5912yes—
482C2×C4×D4C2×D5911yescharacteristic
483C2×#117—592no—
484C2×#117C2×D5912yes—
485C22×C4⋊C4—592no—
486C22×C4⋊C4—592no—
487C22×C4⋊C4—591no—
488C22×C4⋊C4—591no—
489C22×C4⋊C4—592no—
490C22×C4⋊C4—594no—
491C22×C42C2×D5911yescharacteristic
492C59C2×#355911yescharacteristic, complemented, Sylow
493C2×#41—5932no—
494C2×#41—5916no—
495C2×#41—2368no—
496C2×#41—23616no—
497C22×Q8—594no—
498C22×Q8—592no—
499C22×Q8C22×D5911yescharacteristic
500C22×D4—594no—
501C22×D4—594no—
502C22×D4—594no—
503C22×D4—592no—
504C22×D4—592no—
505C22×D4—592no—
506C22×D4C22×D5912yes—
507C22×D4C22×D5911yescharacteristic
508C23×C4—592no—
509C23×C4—592no—
510C23×C4—594no—
511C23×C4—594no—
512C23×C4—594no—
513C23×C4—594no—
514C23×C4C22×D5911yescharacteristic
515C23×C4C22×D5911yescharacteristic
516C23×C4C22×D5912yes—
517C23×C4C22×D5911yescharacteristic
518C4⋊Q8—5932no—
519C4⋊Q8—598no—
520C4⋊Q8—5916no—
521#127—598no—
522#126—5932no—
523#126—5932no—
524#126C22×D59116yes—
525#125—5932no—
526#125—5916no—
527#125—5916no—
528#125—5916no—
529#125—5916no—
530#125—5916no—
531#125C22×D5918yes—
532#124—5916no—
533#124C22×D5918yes—
534#123—5932no—
535#123—5932no—
536#123—5932no—
537#123—5932no—
538#123—5932no—
539#123—5932no—
540#123C22×D59116yes—
541C22⋊Q8—5932no—
542C22⋊Q8—5932no—
543C22⋊Q8—5932no—
544C22⋊Q8—5932no—
545C22⋊Q8—5932no—
546C22⋊Q8—5932no—
547C22⋊Q8C22×D5918yes—
548#121—5932no—
549#121—5932no—
550#121—5916no—
551#121—5916no—
552#121—5916no—
553#121—5916no—
554#121—5932no—
555#121—5932no—
556#121C22×D5918yes—
557C4×Q8C22×D5918yes—
558C4×D4—5932no—
559C4×D4—5932no—
560C4×D4—5916no—
561C4×D4—5916no—
562C4×D4—5916no—
563C4×D4—5916no—
564C4×D4C22×D59116yes—
565C4×D4C22×D5918yes—
566#117—5916no—
567#117C22×D59116yes—
568C2×C4⋊C4—592no—
569C2×C4⋊C4—594no—
570C2×C4⋊C4—592no—
571C2×C4⋊C4—592no—
572C2×C4⋊C4—594no—
573C2×C4⋊C4—594no—
574C2×C4⋊C4—594no—
575C2×C4⋊C4—594no—
576C2×C4⋊C4—592no—
577C2×C4⋊C4—594no—
578C2×C4⋊C4—594no—
579C2×C4⋊C4—592no—
580C2×C4⋊C4—5916no—
581C2×C4⋊C4—5916no—
582C2×C4⋊C4—598no—
583C2×C4⋊C4—598no—
584C2×C4⋊C4—5916no—
585C2×C4⋊C4—592no—
586C2×C4⋊C4—594no—
587C2×C4⋊C4—5932no—
588C2×C4⋊C4C22×D5912yes—
589C2×C4⋊C4C22×D5912yes—
590C2×C4⋊C4C22×D5912yes—
591C2×C4⋊C4C22×D5912yes—
592C2×C4⋊C4C22×D5911yescharacteristic
593C2×C4⋊C4C22×D5911yescharacteristic
594C2×C22⋊C4—594no—
595C2×C22⋊C4—594no—
596C2×C22⋊C4—594no—
597C2×C22⋊C4—594no—
598C2×C22⋊C4—594no—
599C2×C22⋊C4—594no—
600C2×C22⋊C4—594no—
601C2×C22⋊C4C22×D5912yes—
602C2×C22⋊C4C22×D5912yes—
603C2×C22⋊C4C22×D5912yes—
604C2×C22⋊C4C22×D5912yes—
605C2×C22⋊C4C22×D5912yes—
606C2×C42—594no—
607C2×C42C22×D5911yescharacteristic
608C2×C42C22×D5912yes—
609C2×C42C22×D5911yescharacteristic
610C2×C42C22×D5911yescharacteristic
611C2×C42C22×D5911yescharacteristic
612C2×C42C22×D5918yes—
613C24—594no—
614C24C23×D5912yes—
615C24C23×D5911yescharacteristic
616#41—23632no—
617#41—23664no—
618C2×Q8—42no—
619C2×Q8—5916no—
620C2×Q8—598no—
621C2×Q8—2364no—
622C2×Q8—2368no—
623C2×Q8C23×D5914yes—
624C2×D4—28no—
625C2×D4—42no—
626C2×D4—5916no—
627C2×D4—5916no—
628C2×D4—5916no—
629C2×D4—598no—
630C2×D4—598no—
631C2×D4—598no—
632C2×D4—11816no—
633C2×D4—1188no—
634C2×D4—2364no—
635C2×D4—2364no—
636C2×D4—2368no—
637C2×D4—2368no—
638C2×D4C23×D5918yes—
639C2×D4C23×D5914yes—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—28no—
643C22×C4—42no—
644C22×C4—598no—
645C22×C4—594no—
646C22×C4—594no—
647C22×C4—594no—
648C22×C4—598no—
649C22×C4—5916no—
650C22×C4—5916no—
651C22×C4—5916no—
652C22×C4—5916no—
653C22×C4—1188no—
654C22×C4—2368no—
655C22×C4—2368no—
656C22×C4—2368no—
657C22×C4—2368no—
658C22×C4—2364no—
659C22×C4C23×D5914yes—
660C22×C4C23×D5914yes—
661C22×C4C23×D5918yes—
662C22×C4C23×D5912yes—
663C22×C4C23×D5911yescharacteristic
664C22×C4C23×D5911yescharacteristic
665C22×C4C23×D5911yescharacteristic
666C22×C4C23×D5911yescharacteristic
667C22×C4C23×D5911yescharacteristic
668C22×C4C23×D5912yes—
669C22×C4C23×D5912yes—
670C22×C4C23×D5914yes—
671C22×C4C23×D5911yescharacteristic
672C4⋊C4—598no—
673C4⋊C4—5916no—
674C4⋊C4—598no—
675C4⋊C4—598no—
676C4⋊C4—5916no—
677C4⋊C4—5916no—
678C4⋊C4—5916no—
679C4⋊C4—5916no—
680C4⋊C4—598no—
681C4⋊C4—5916no—
682C4⋊C4—5916no—
683C4⋊C4—598no—
684C4⋊C4—598no—
685C4⋊C4—5916no—
686C4⋊C4C23×D5918yes—
687C4⋊C4C23×D5918yes—
688C4⋊C4C23×D5918yes—
689C4⋊C4C23×D5918yes—
690C4⋊C4C23×D5914yes—
691C4⋊C4C23×D5914yes—
692C22⋊C4—5916no—
693C22⋊C4—5916no—
694C22⋊C4—5916no—
695C22⋊C4—5916no—
696C22⋊C4—5916no—
697C22⋊C4—5916no—
698C22⋊C4—5916no—
699C22⋊C4C23×D5918yes—
700C22⋊C4C23×D5918yes—
701C22⋊C4C23×D5918yes—
702C22⋊C4C23×D5918yes—
703C22⋊C4C23×D5918yes—
704C42—5916no—
705C42C23×D5914yes—
706C42C23×D5914yes—
707C42C23×D5914yes—
708C42C23×D5914yes—
709C42C23×D5918yes—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—598no—
716C23—1188no—
717C23—1188no—
718C23—1188no—
719C23#1427377314yes—
720C23C24×D5914yes—
721C23C24×D5912yes—
722C23C24×D5911yescharacteristic
723Q8—44no—
724Q8—2368no—
725Q8—23616no—
726D4—216no—
727D4—44no—
728D4—11832no—
729D4—11816no—
730D4—2368no—
731D4—2368no—
732D4—23616no—
733D4—23616no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—216no—
745C2×C4—44no—
746C2×C4—598no—
747C2×C4—598no—
748C2×C4—598no—
749C2×C4—1188no—
750C2×C4—11816no—
751C2×C4—1188no—
752C2×C4—1188no—
753C2×C4—23616no—
754C2×C4—23616no—
755C2×C4—23616no—
756C2×C4—2368no—
757C2×C4—23616no—
758C2×C4#1427377414yes—
759C2×C4C24×D5914yes—
760C2×C4C24×D5912yes—
761C2×C4C24×D5912yes—
762C2×C4C24×D5912yes—
763C2×C4C24×D5912yes—
764C2×C4C24×D5912yes—
765C2×C4C24×D5914yes—
766C2×C4C24×D5914yes—
767C2×C4C24×D5912yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—48no—
775C22—1188no—
776C22—1188no—
777C22—1188no—
778C22—23616no—
779C22C2×#1427377314yes—
780C22C2×#1427377312yes—
781C22C2×#1427377412yes—
782C22#1683823812yes—
783C22C25×D5911yescharacteristic
784C4—22no—
785C4—22no—
786C4—24no—
787C4—24no—
788C4—22no—
789C4—22no—
790C4—22no—
791C4—24no—
792C4—1188no—
793C4—1188no—
794C4—1188no—
795C4C2×#1427377414yes—
796C2—24no—
797C2—44no—
798C2—2368no—
799C2#2143862714yesdirect product factor
800C2C22×#1427377311yescharacteristic
801C2C22×#1427377411yescharacteristic
802C2C2×#1683823811yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#529C2
socleC23×C59C25
hypercenterC2×#529D59
hypocenterC59C2×#3559
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #21438627C2direct (N × H)
2. C2×#16838156C2semidirect
3. C2×#16838146C2semidirect
4. C2×#16838112C2semidirect
5. C2×#16838098C2semidirect
6. C2×#16838098C2semidirect
7. C2×#16838056C2semidirect
8. C2×#16838050C2semidirect
9. C2×#16838030C2semidirect
10. C2×#16838007C2semidirect
11. C2×#16838001C2semidirect
12. C2×#16837993C2semidirect
13. C2×#16837979C2semidirect
14. C2×#16837952C2semidirect
15. C22×#14273719C2semidirect
16. C2×C59×#529C2semidirect
19. #16838156C22semidirect
20. #16838146C22semidirect
21. #16838112C22semidirect
22. #16838098C22semidirect
23. #16838098C22semidirect
24. #16838056C22semidirect
25. #16838050C22semidirect
26. #16838030C22semidirect
27. #16838007C22semidirect
28. #16838001C22semidirect
29. #16837993C22semidirect
30. #16837979C22semidirect
31. #16837952C22semidirect
43. C2×#14273719C22semidirect
79. C59×#529C22semidirect
409. C2×#529D59semidirect
413. C2×C59#3559semidirect
437. #529C2×D59semidirect
492. C59C2×#3559semidirect
799. C2#21438627direct (N × H)

Maximal subgroups

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

subgroupindex
#214386272
C2×#168381562
C2×#168381462
C2×#168381122
C2×#168380982
C2×#168380562
C2×#168380502
C2×#168380302
C2×#168380072
C2×#168380012
C2×#168379932
C2×#168379792
C2×#168379522
C22×#142737192
C2×C59×#5292
C2×#355959