Finite Group Databasebeta

← C2×#21459677 #30588086

Subgroups — C2×#21459677 #30588086

Order 15616.

7130 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459677C2132yesmaximal, direct product factor
2C2×#16840495C212yesmaximal, complemented
3C2×#16840490C212yesmaximal, complemented
4C2×#16840484C212yesmaximal, complemented
5C2×#16840482C212yesmaximal, complemented
6C2×#16840480C212yesmaximal, complemented
7C2×#16840467C212yesmaximal, complemented
8C2×#16840451C212yesmaximal, complemented
9C2×#16840447C212yesmaximal, complemented
10C2×#16840354C214yesmaximal, complemented
11C2×#16840338C211yesmaximal, characteristic, complemented
12C2×#16840333C211yesmaximal, characteristic, complemented
13C2×#16840315C211yesmaximal, characteristic, complemented
14C2×#16840308C211yesmaximal, characteristic
15C2×#16840292C214yesmaximal, complemented
16C2×#16840243C211yesmaximal, characteristic, complemented
17C22×#14519742C211yesmaximal, characteristic, complemented
18C2×C61×#520C211yesmaximal, characteristic, complemented
19C22×#11758222C2211yescharacteristic
20C23×Dic122C2211yescharacteristic
21#16840495C22132yescomplemented
22#16840490C22132yescomplemented
23#16840484C22132yescomplemented
24#16840482C22132yescomplemented
25#16840480C22132yescomplemented
26#16840467C22132yescomplemented
27#16840451C22132yescomplemented
28#16840447C22132yescomplemented
29#16840354C22164yescomplemented
30#16840338C22116yescomplemented
31#16840333C22116yescomplemented
32#16840315C22116yescomplemented
33#16840308C22116yes—
34C2×#14519777C2212yes—
35C2×#14519776C2211yescharacteristic
36C2×#14519776C2211yescharacteristic
37C2×#14519775C2211yescharacteristic
38C2×#14519775C2212yes—
39C2×#14519773C2211yescharacteristic
40#16840292C22164yescomplemented
41C2×#14519772C2214yes—
42C2×#14519771C2214yes—
43C2×#14519770C2214yes—
44C2×#14519770C2214yes—
45C2×#14519769C2214yes—
46C2×#14519768C2211yescharacteristic
47C2×#14519768C2211yescharacteristic
48C2×#14519767C2214yes—
49C2×#14519767C2214yes—
50C2×#14519766C2211yescharacteristic
51C2×#14519765C2212yes—
52C2×#14519764C2211yescharacteristic
53C2×#14519764C2212yes—
54C2×#14519763C2214yes—
55C2×#14519761C2214yes—
56C2×#14519760C2214yes—
57C2×#14519759C2214yes—
58C2×#14519758C2214yes—
59C2×#14519757C2212yes—
60C2×#14519757C2212yes—
61C2×#14519756C2212yes—
62C2×#14519756C2212yes—
63C2×#14519756C2214yes—
64C2×#14519755C2214yes—
65C2×#14519754C2212yes—
66C2×#14519754C2212yes—
67C2×#14519749C2212yes—
68C2×#14519749C2212yes—
69#16840243C22116yescomplemented
70C2×C4×Dic122C2214yes—
71C2×C4×Dic122C2212yes—
72C2×C4×Dic122C2212yes—
73C2×#14519742C2212yes—
74C2×#14519742C2212yes—
75C2×#14519742C2212yes—
76C2×#14519742C2212yes—
77C2×#14519742C2212yes—
78C2×#14519742C22116yescomplemented
79C2×#14519739C2212yes—
80C2×C4×C22⋊D61C2214yes—
81C2×C4×C22⋊D61C2212yes—
82C2×C4×C22⋊D61C2214yes—
83C2×C4×C22⋊D61C2212yes—
84C2×#14519736C2211yescharacteristic
85C2×#14519736C2214yes—
86C2×#14519735C2212yes—
87C2×#14519734C2214yes—
88C22×#11758196C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C22×C4×Dic61C2212yes—
91C22×C4×Dic61C2211yescharacteristic
92C22×#41×C61C2211yescharacteristic
93C61×#520C22116yescomplemented
94C2×C4×Q8×C61C2212yes—
95C2×C4×D4×C61C2214yes—
96C2×C4×D4×C61C2212yes—
97C2×#117×C61C2212yes—
98C2×#117×C61C2211yescharacteristic
99C22×C4⋊C4×C61C2211yescharacteristic
100C22×C4⋊C4×C61C2212yes—
101C2×#11758222—28no—
102C2×#11758222C2318yes—
103C22×Dic122—28no—
104C22×Dic122C2312yes—
105C22×Dic122C2312yes—
106C22×Dic122C2311yescharacteristic
107C22×Dic122C2318yes—
108C22×Dic122C2312yes—
109C22×Dic122C2312yes—
110C22×D244C2311yescharacteristic
111C22×C22⋊D61C2312yes—
112C22×C22⋊D61C2312yes—
113C22×C22⋊D61C2312yes—
114C23×Dic61C2311yescharacteristic
115C23×Dic61C2312yes—
116C23×Dic61C2311yescharacteristic
117C22×C4×D61C2312yes—
118C22×C4×D61C2314yes—
119#14519777C23116yes—
120#14519776C2318yes—
121#14519776C2318yes—
122#14519775C23116yes—
123#14519775C2318yes—
124#14519773C2318yes—
125#14519772C23132yes—
126#14519771C23132yes—
127#14519770C23132yes—
128#14519770C23132yes—
129#14519769C23132yes—
130#14519768C2318yes—
131#14519768C2318yes—
132#14519767C23132yes—
133#14519767C23132yes—
134#14519766C2318yes—
135#14519765C23116yes—
136#14519764C2318yes—
137#14519764C23116yes—
138#14519763C23132yes—
139#14519761C23132yes—
140#14519760C23132yes—
141#14519759C23132yes—
142#14519758C23132yes—
143#14519757C23116yes—
144#14519757C23116yes—
145#14519756C23116yes—
146#14519756C23132yes—
147#14519756C23116yes—
148#14519755C23132yes—
149#14519754C23116yes—
150#14519754C23116yes—
151#14519749C23116yes—
152#14519749C23116yes—
153C4×Dic122C23132yes—
154C4×Dic122C23116yes—
155C4×Dic122C23116yes—
156#14519742C23116yes—
157#14519742C23116yes—
158#14519742C23116yes—
159#14519742C23116yes—
160#14519742C23116yes—
161#14519739C23116yes—
162C4×C22⋊D61C23116yes—
163C4×C22⋊D61C23116yes—
164C4×C22⋊D61C23132yes—
165C4×C22⋊D61C23132yes—
166#14519736C23132yes—
167#14519736C2318yes—
168#14519735C23116yes—
169#14519734C23132yes—
170C2×C4⋊Dic61C2311yescharacteristic
171C2×C4⋊Dic61C2311yescharacteristic
172C2×C4⋊Dic61C2312yes—
173C2×C4⋊Dic61C2314yes—
174C2×C4⋊Dic61C2312yes—
175C2×C4⋊Dic61C2314yes—
176C2×#11758196C2314yes—
177C2×#11758196C2314yes—
178C2×#11758196C2314yes—
179C2×#11758196C23116yes—
180C2×#11758196C2312yes—
181C2×#11758196C2314yes—
182C2×#11758196C2312yes—
183C2×#11758196C2312yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2314yes—
188C4⋊C4×D61C23116yes—
189C2×C22⋊Dic61C2312yes—
190C2×C22⋊Dic61C2312yes—
191C2×C22⋊Dic61C2314yes—
192C2×C22⋊Dic61C2312yes—
193C2×C22⋊Dic61C2314yes—
194C2×#11758198C2312yes—
195C2×#11758198C2314yes—
196C2×#11758198C2314yes—
197C2×#11758198C2312yes—
198C2×#11758198C2314yes—
199C2×C4×Dic61C2314yes—
200C2×C4×Dic61C2311yescharacteristic
201C2×C4×Dic61C2311yescharacteristic
202C2×C4×Dic61C2314yes—
203C2×C4×Dic61C2311yescharacteristic
204C2×C4×Dic61C2311yescharacteristic
205C2×C4×Dic61C23116yes—
206C2×C4×Dic61C2318yes—
207C2×C4×Dic61C2314yes—
208C2×C4×Dic61C2312yes—
209C2×#41×C61—28no—
210C2×#41×C61C2318yes—
211C22×Q8×C61C2311yescharacteristic
212C22×D4×C61C2312yes—
213C22×D4×C61C2311yescharacteristic
214C23×C4×C61C2312yes—
215C23×C4×C61C2312yes—
216C23×C4×C61C2314yes—
217C23×C4×C61C2311yescharacteristic
218C4×Q8×C61C23116yes—
219C4×D4×C61C23116yes—
220C4×D4×C61C23132yes—
221#117×C61C23116yes—
222#117×C61C2318yes—
223C2×C4⋊C4×C61C2312yes—
224C2×C4⋊C4×C61C23116yes—
225C2×C4⋊C4×C61C2312yes—
226C2×C4⋊C4×C61C2318yes—
227C2×C4⋊C4×C61C2314yes—
228C2×C4⋊C4×C61C2311yescharacteristic
229C2×C4⋊C4×C61C2311yescharacteristic
230C2×C22⋊C4×C61C2312yes—
231C2×C22⋊C4×C61C2314yes—
232C2×C42×C61C2314yes—
233C2×C42×C61C2312yes—
234C24×C61C2412yes—
235C24×C61C2411yescharacteristic
236C23×D61C2412yes—
237#41×C61—232no—
238C2×Q8×C61—24no—
239C2×Q8×C61C2414yes—
240C2×D4×C61—28no—
241C2×D4×C61—24no—
242C2×D4×C61C2418yes—
243C2×D4×C61C2414yes—
244C22×C4×C61—28no—
245C22×C4×C61—48no—
246C22×C4×C61—44no—
247C22×C4×C61#4118yes—
248C22×C4×C61C2414yes—
249C22×C4×C61C2412yes—
250C22×C4×C61C2412yes—
251C22×C4×C61C2412yes—
252C22×C4×C61C2418yes—
253C22×C4×C61C2418yes—
254C22×C4×C61C24116yes—
255C22×C4×C61C2411yescharacteristic
256C22×C4×C61C2411yescharacteristic
257C22×C4×C61C2414yes—
258C2×C22⋊D61—28no—
259C2×C22⋊D61—28no—
260C2×C22⋊D61—44no—
261C2×C22⋊D61C2418yes—
262C2×C22⋊D61C2418yes—
263C2×C22⋊D61C2418yes—
264C22×Dic61—28no—
265C22×Dic61—24no—
266C22×Dic61—42no—
267C22×Dic61C2412yes—
268C22×Dic61C2412yes—
269C22×Dic61C2411yescharacteristic
270C22×Dic61C2411yescharacteristic
271C22×Dic61C2414yes—
272C22×Dic61C2418yes—
273C22×Dic61C2411yescharacteristic
274C22×Dic61C2414yes—
275C22×Dic61C2412yes—
276C22×Dic61C2414yes—
277C22×Dic61C2411yescharacteristic
278#11758222—232no—
279C2×D244—24no—
280C2×D244C2414yes—
281C2×C4×D61—28no—
282C2×C4×D61—48no—
283C2×C4×D61C2418yes—
284C2×C4×D61C24116yes—
285C2×Dic122—28no—
286C2×Dic122—28no—
287C2×Dic122—232no—
288C2×Dic122—24no—
289C2×Dic122—28no—
290C2×Dic122—44no—
291C2×Dic122C2418yes—
292C2×Dic122C2418yes—
293C2×Dic122C2414yes—
294C2×Dic122C2418yes—
295C2×Dic122C2418yes—
296C4⋊C4×C61C2418yes—
297C4⋊C4×C61C2414yes—
298C4⋊C4×C61C2418yes—
299C4⋊C4×C61C24116yes—
300C4⋊C4×C61C2414yes—
301C22⋊C4×C61C2418yes—
302C22⋊C4×C61C24116yes—
303C42×C61C24116yes—
304C42×C61C2418yes—
305C22⋊Dic61C2418yes—
306C22⋊Dic61C2418yes—
307C22⋊Dic61C24116yes—
308C22⋊Dic61C2418yes—
309C22⋊Dic61C24116yes—
310#11758198C2418yes—
311#11758198C24116yes—
312#11758198C24116yes—
313#11758198C2418yes—
314#11758198C24116yes—
315C4⋊Dic61C2414yes—
316C4⋊Dic61C2414yes—
317C4⋊Dic61C2418yes—
318C4⋊Dic61C24116yes—
319C4⋊Dic61C2418yes—
320C4⋊Dic61C24116yes—
321#11758196C24116yes—
322#11758196C24116yes—
323#11758196C24116yes—
324#11758196C2418yes—
325#11758196C24116yes—
326#11758196C2418yes—
327#11758196C2418yes—
328#11758196C2418yes—
329#11758196C2418yes—
330#11758196C2418yes—
331#11758196C24116yes—
332C4×Dic61C24116yes—
333C4×Dic61C2414yes—
334C4×Dic61C2414yes—
335C4×Dic61C24116yes—
336C4×Dic61C2414yes—
337C4×Dic61C2414yes—
338C4×Dic61C24116yes—
339C4×Dic61C2418yes—
340C23×C61—22no—
341C23×C61—22no—
342C23×C61—24no—
343C23×C61—24no—
344C23×C61—24no—
345C23×C61C2×#4114yes—
346C23×C61C2514yes—
347C23×C61C2512yes—
348C23×C61C2511yescharacteristic
349C22×D61—24no—
350C22×D61—24no—
351C22×D61—24no—
352C22×D61C2514yes—
353Q8×C61—28no—
354D4×C61—216no—
355D4×C61—28no—
356C2×C4×C61—24no—
357C2×C4×C61—24no—
358C2×C4×C61—24no—
359C2×C4×C61—28no—
360C2×C4×C61—216no—
361C2×C4×C61—416no—
362C2×C4×C61—48no—
363C2×C4×C61C2×#4114yes—
364C2×C4×C61C2×#4114yes—
365C2×C4×C61C2×#41116yes—
366C2×C4×C61C2518yes—
367C2×C4×C61C2514yes—
368C2×C4×C61C2514yes—
369C2×C4×C61C2514yes—
370C2×C4×C61C2512yes—
371C2×C4×C61C2512yes—
372C22⋊D61—216no—
373C22⋊D61—216no—
374C22⋊D61—48no—
375C2×Dic61—216no—
376C2×Dic61—28no—
377C2×Dic61—24no—
378C2×Dic61—24no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—24no—
382C2×Dic61—22no—
383C2×Dic61—28no—
384C2×Dic61—44no—
385C2×Dic612−1+414yes—
386C2×Dic61C2512yes—
387C2×Dic61C2514yes—
388C2×Dic61C2512yes—
389C2×Dic61C2512yes—
390C2×Dic61C2514yes—
391C2×Dic61C2518yes—
392C2×Dic61C2514yes—
393C2×Dic61C2512yes—
394D244—28no—
395C4×D61—216no—
396C4×D61—416no—
397Dic122—216no—
398Dic122—216no—
399Dic122—28no—
400Dic122—216no—
401Dic122—48no—
402C2×#3507—611nomaximal, Sylow
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—28no—
406C22×C61—24no—
407C22×C61—24no—
408C22×C61—24no—
409C22×C61—48no—
410C22×C61C22×#4114yes—
411C22×C61C22×#4112yes—
412C22×C61C2×2−1+412yes—
413C22×C61#58512yes—
414C22×C61C2611yescharacteristic
415C2×D61—24no—
416C2×D61—24no—
417C2×D61—24no—
418C2×D61—48no—
419C4×C61—24no—
420C4×C61—24no—
421C4×C61—24no—
422C4×C61—28no—
423C4×C61C22×#4114yes—
424C4×C61C22×#4114yes—
425Dic61—28no—
426Dic61—24no—
427Dic61—24no—
428Dic61—22no—
429Dic61—22no—
430Dic61—24no—
431Dic61—22no—
432Dic61C2×2−1+414yes—
433#3507—6132no—
434C2×#559—612no—
435C2×#557—612no—
436C2×#556—612no—
437C2×#556—612no—
438C2×#556—612no—
439C2×#554—612no—
440C2×#552—612no—
441C2×#552—612no—
442C2×#539—614no—
443C2×#536—611no—
444C2×#536—611no—
445C2×#533—611no—
446C2×#532—611no—
447C2×#529—614no—
448C2×#520—611no—
449C2×#520D6111yescharacteristic, complemented
450C22×C4×Q8—611no—
451C2×C61—24no—
452C2×C61—44no—
453C2×C61#350714yescomplemented
454C2×C61C23×#4111yescharacteristic
455C2×C61C22×2−1+411yescharacteristic
456C2×C61C2×#58511yescharacteristic
457D61—44no—
458C22×#41—611no—
459C22×#41C2×D6111yescharacteristic
460C23×Q8—611no—
461#559—6132no—
462#557—6132no—
463#556—6132no—
464#556—6132no—
465#556—6132no—
466#554—6132no—
467#552—6132no—
468#552—6132no—
469#539—6164no—
470#536—6116no—
471#536—6116no—
472#533—6116no—
473#532—6116no—
474C2×C4⋊Q8—611no—
475C2×C4⋊Q8—612no—
476C2×C4⋊Q8—611no—
477C2×C4⋊Q8—611no—
478C2×C4⋊Q8—612no—
479C2×#127—611no—
480#529—6164no—
481C2×#126—614no—
482C2×#126—614no—
483C2×#126—614no—
484C2×#126—614no—
485C2×#125—614no—
486C2×#125—614no—
487C2×#125—611no—
488C2×#125—611no—
489C2×#125—614no—
490C2×#124—611no—
491C2×#124—611no—
492C2×#124—612no—
493C2×#124—614no—
494C2×#124—612no—
495C2×#123—614no—
496C2×#123—614no—
497C2×#123—614no—
498C2×#123—614no—
499C2×C22⋊Q8—612no—
500C2×C22⋊Q8—612no—
501C2×C22⋊Q8—614no—
502C2×C22⋊Q8—614no—
503C2×C22⋊Q8—612no—
504C2×C22⋊Q8—612no—
505C2×C22⋊Q8—612no—
506C2×C22⋊Q8—612no—
507C2×#121—612no—
508C2×#121—612no—
509#520—6116no—
510#520C2×D61116yescomplemented
511C2×C4×Q8—612no—
512C2×C4×Q8—612no—
513C2×C4×Q8—612no—
514C2×C4×Q8—612no—
515C2×C4×Q8—612no—
516C2×C4×Q8—6116no—
517C2×C4×Q8—614no—
518C2×C4×Q8—612no—
519C2×C4×Q8—612no—
520C2×C4×Q8C2×D6112yes—
521C2×C4×D4—614no—
522C2×C4×D4—614no—
523C2×C4×D4—612no—
524C2×C4×D4—612no—
525C2×C4×D4—612no—
526C2×C4×D4C2×D6114yes—
527C2×C4×D4C2×D6112yes—
528C2×#117—611no—
529C2×#117—614no—
530C2×#117—612no—
531C2×#117—614no—
532C2×#117C2×D6111yescharacteristic
533C2×#117C2×D6112yes—
534C22×C4⋊C4—612no—
535C22×C4⋊C4—612no—
536C22×C4⋊C4C2×D6111yescharacteristic
537C22×C4⋊C4C2×D6112yes—
538C22×C42—612no—
539C22×C42—611no—
540C61C2×#350711yescharacteristic, complemented, Sylow
541C2×#41—28no—
542C2×#41—618no—
543C2×#41—1228no—
544C2×#41C22×D6118yes—
545C22×Q8—612no—
546C22×Q8—612no—
547C22×Q8—612no—
548C22×Q8—611no—
549C22×Q8—618no—
550C22×Q8—612no—
551C22×Q8—1228no—
552C22×Q8C22×D6111yescharacteristic
553C22×D4—612no—
554C22×D4—612no—
555C22×D4—612no—
556C22×D4—611no—
557C22×D4C22×D6112yes—
558C22×D4C22×D6111yescharacteristic
559C23×C4—612no—
560C23×C4—611no—
561C23×C4—611no—
562C23×C4—612no—
563C23×C4—614no—
564C23×C4C22×D6112yes—
565C23×C4C22×D6112yes—
566C23×C4C22×D6114yes—
567C23×C4C22×D6111yescharacteristic
568C4⋊Q8—618no—
569C4⋊Q8—6116no—
570C4⋊Q8—618no—
571C4⋊Q8—618no—
572C4⋊Q8—6116no—
573#127—618no—
574#126—6132no—
575#126—6132no—
576#126—6132no—
577#126—6132no—
578#125—6132no—
579#125—618no—
580#125—618no—
581#125—6132no—
582#125—6132no—
583#124—618no—
584#124—618no—
585#124—6116no—
586#124—6132no—
587#124—6116no—
588#123—6132no—
589#123—6132no—
590#123—6132no—
591#123—6132no—
592C22⋊Q8—6116no—
593C22⋊Q8—6116no—
594C22⋊Q8—6132no—
595C22⋊Q8—6116no—
596C22⋊Q8—6116no—
597C22⋊Q8—6132no—
598C22⋊Q8—6116no—
599C22⋊Q8—6116no—
600#121—6116no—
601#121—6116no—
602C4×Q8—6116no—
603C4×Q8—6116no—
604C4×Q8—6116no—
605C4×Q8—6116no—
606C4×Q8—6116no—
607C4×Q8—6132no—
608C4×Q8—6116no—
609C4×Q8—6116no—
610C4×Q8C22×D61116yes—
611C4×D4—6132no—
612C4×D4—6132no—
613C4×D4—6116no—
614C4×D4—6116no—
615C4×D4—6116no—
616C4×D4C22×D61132yes—
617C4×D4C22×D61116yes—
618#117—618no—
619#117—6132no—
620#117—6116no—
621#117—6132no—
622#117C22×D6118yes—
623#117C22×D61116yes—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—614no—
626C2×C4⋊C4—614no—
627C2×C4⋊C4—614no—
628C2×C4⋊C4—6116no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4—612no—
631C2×C4⋊C4—612no—
632C2×C4⋊C4—614no—
633C2×C4⋊C4—614no—
634C2×C4⋊C4—612no—
635C2×C4⋊C4—612no—
636C2×C4⋊C4—612no—
637C2×C4⋊C4—612no—
638C2×C4⋊C4—612no—
639C2×C4⋊C4—614no—
640C2×C4⋊C4—614no—
641C2×C4⋊C4—612no—
642C2×C4⋊C4—6116no—
643C2×C4⋊C4C22×D6112yes—
644C2×C4⋊C4C22×D6111yescharacteristic
645C2×C4⋊C4C22×D6112yes—
646C2×C4⋊C4C22×D6114yes—
647C2×C4⋊C4C22×D6118yes—
648C2×C4⋊C4C22×D61116yes—
649C2×C4⋊C4C22×D6111yescharacteristic
650C2×C22⋊C4—612no—
651C2×C22⋊C4—612no—
652C2×C22⋊C4—614no—
653C2×C22⋊C4—612no—
654C2×C22⋊C4—614no—
655C2×C22⋊C4—612no—
656C2×C22⋊C4—614no—
657C2×C22⋊C4—614no—
658C2×C22⋊C4—612no—
659C2×C22⋊C4—614no—
660C2×C22⋊C4C22×D6112yes—
661C2×C22⋊C4C22×D6114yes—
662C2×C42—614no—
663C2×C42—614no—
664C2×C42—612no—
665C2×C42—611no—
666C2×C42—611no—
667C2×C42—614no—
668C2×C42—611no—
669C2×C42—611no—
670C2×C42—6116no—
671C2×C42—618no—
672C2×C42C22×D6114yes—
673C2×C42C22×D6112yes—
674C24—612no—
675C24C23×D6112yes—
676C24C23×D6111yescharacteristic
677#41—232no—
678#41—12232no—
679C2×Q8—24no—
680C2×Q8—618no—
681C2×Q8—618no—
682C2×Q8—618no—
683C2×Q8—614no—
684C2×Q8—618no—
685C2×Q8—1228no—
686C2×Q8—1228no—
687C2×Q8—1228no—
688C2×Q8—12232no—
689C2×Q8—1224no—
690C2×Q8—2444no—
691C2×Q8C23×D6114yes—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—618no—
695C2×D4—618no—
696C2×D4—618no—
697C2×D4—614no—
698C2×D4—1228no—
699C2×D4—1228no—
700C2×D4—1224no—
701C2×D4—2444no—
702C2×D4C23×D6118yes—
703C2×D4C23×D6114yes—
704C22×C4—28no—
705C22×C4—44no—
706C22×C4—48no—
707C22×C4—611no—
708C22×C4—614no—
709C22×C4—618no—
710C22×C4—611no—
711C22×C4—612no—
712C22×C4—614no—
713C22×C4—611no—
714C22×C4—612no—
715C22×C4—611no—
716C22×C4—612no—
717C22×C4—614no—
718C22×C4—618no—
719C22×C4—6116no—
720C22×C4—1224no—
721C22×C4—1228no—
722C22×C4—1228no—
723C22×C4—2448no—
724C22×C4—2442no—
725C22×C4#1175822218yes—
726C22×C4C23×D6118yes—
727C22×C4C23×D6114yes—
728C22×C4C23×D6112yes—
729C22×C4C23×D6112yes—
730C22×C4C23×D6112yes—
731C22×C4C23×D6118yes—
732C22×C4C23×D61116yes—
733C22×C4C23×D6114yes—
734C22×C4C23×D6111yescharacteristic
735C22×C4C23×D6111yescharacteristic
736C4⋊C4—614no—
737C4⋊C4—6116no—
738C4⋊C4—6116no—
739C4⋊C4—6116no—
740C4⋊C4—618no—
741C4⋊C4—6116no—
742C4⋊C4—618no—
743C4⋊C4—618no—
744C4⋊C4—618no—
745C4⋊C4—618no—
746C4⋊C4—6116no—
747C4⋊C4—618no—
748C4⋊C4—614no—
749C4⋊C4—618no—
750C4⋊C4—6116no—
751C4⋊C4—618no—
752C4⋊C4—6116no—
753C4⋊C4C23×D6118yes—
754C4⋊C4C23×D6114yes—
755C4⋊C4C23×D6118yes—
756C4⋊C4C23×D61116yes—
757C4⋊C4C23×D6114yes—
758C22⋊C4—618no—
759C22⋊C4—618no—
760C22⋊C4—6116no—
761C22⋊C4—618no—
762C22⋊C4—6116no—
763C22⋊C4—618no—
764C22⋊C4—6116no—
765C22⋊C4—6116no—
766C22⋊C4—618no—
767C22⋊C4—6116no—
768C22⋊C4C23×D6118yes—
769C22⋊C4C23×D61116yes—
770C42—6116no—
771C42—614no—
772C42—614no—
773C42—6116no—
774C42—614no—
775C42—614no—
776C42—6116no—
777C42—618no—
778C42C23×D61116yes—
779C42C23×D6118yes—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—614no—
786C23—1224no—
787C23—1224no—
788C23—1224no—
789C23C2×#1175822214yes—
790C23C24×D6114yes—
791C23C24×D6112yes—
792C23C24×D6111yescharacteristic
793Q8—28no—
794Q8—12216no—
795Q8—12216no—
796Q8—12216no—
797Q8—1228no—
798Q8—2448no—
799D4—216no—
800D4—28no—
801D4—12216no—
802D4—12216no—
803D4—1228no—
804D4—2448no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—216no—
810C2×C4—48no—
811C2×C4—416no—
812C2×C4—614no—
813C2×C4—612no—
814C2×C4—612no—
815C2×C4—614no—
816C2×C4—618no—
817C2×C4—612no—
818C2×C4—614no—
819C2×C4—612no—
820C2×C4—614no—
821C2×C4—1228no—
822C2×C4—1224no—
823C2×C4—12216no—
824C2×C4—1228no—
825C2×C4—1222no—
826C2×C4—1224no—
827C2×C4—1224no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—12216no—
831C2×C4—24416no—
832C2×C4—2444no—
833C2×C4C2×#1175822214yes—
834C2×C4C2×#1175822214yes—
835C2×C4C2×#11758222116yes—
836C2×C4C24×D6118yes—
837C2×C4C24×D6114yes—
838C2×C4C24×D6114yes—
839C2×C4C24×D6114yes—
840C2×C4C24×D6112yes—
841C2×C4C24×D6112yes—
842C22—22no—
843C22—22no—
844C22—28no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—48no—
849C22—1224no—
850C22—1224no—
851C22—1224no—
852C22—2448no—
853C22C22×#1175822214yes—
854C22C22×#1175822212yes—
855C222−1+4×D6112yes—
856C22#1684059712yes—
857C22C25×D6111yescharacteristic
858C4—24no—
859C4—24no—
860C4—28no—
861C4—24no—
862C4—614no—
863C4—1224no—
864C4—1228no—
865C4—1222no—
866C4—1224no—
867C4—1224no—
868C4—1222no—
869C4—1222no—
870C4C22×#1175822214yes—
871C4C22×#1175822214yes—
872C2—24no—
873C2—44no—
874C2—2444no—
875C2#2145967714yesdirect product factor
876C2C23×#1175822211yescharacteristic
877C2C2×2−1+4×D6111yescharacteristic
878C2C2×#1684059711yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#520C2
socleC23×C61C25
prime radicalC2×#16840308C2
hypercenterC2×#520D61
hypocenterC61C2×#3507
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #21459677C2direct (N × H)
2. C2×#16840495C2semidirect
3. C2×#16840490C2semidirect
4. C2×#16840484C2semidirect
5. C2×#16840482C2semidirect
6. C2×#16840480C2semidirect
7. C2×#16840467C2semidirect
8. C2×#16840451C2semidirect
9. C2×#16840447C2semidirect
10. C2×#16840354C2semidirect
11. C2×#16840338C2semidirect
12. C2×#16840333C2semidirect
13. C2×#16840315C2semidirect
15. C2×#16840292C2semidirect
16. C2×#16840243C2semidirect
17. C22×#14519742C2semidirect
18. C2×C61×#520C2semidirect
21. #16840495C22semidirect
22. #16840490C22semidirect
23. #16840484C22semidirect
24. #16840482C22semidirect
25. #16840480C22semidirect
26. #16840467C22semidirect
27. #16840451C22semidirect
28. #16840447C22semidirect
29. #16840354C22semidirect
30. #16840338C22semidirect
31. #16840333C22semidirect
32. #16840315C22semidirect
40. #16840292C22semidirect
69. #16840243C22semidirect
78. C2×#14519742C22semidirect
93. C61×#520C22semidirect
449. C2×#520D61semidirect
453. C2×C61#3507semidirect
510. #520C2×D61semidirect
540. C61C2×#3507semidirect
875. C2#21459677direct (N × H)

Maximal subgroups

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

subgroupindex
#214596772
C2×#168404952
C2×#168404902
C2×#168404842
C2×#168404822
C2×#168404802
C2×#168404672
C2×#168404512
C2×#168404472
C2×#168403542
C2×#168403382
C2×#168403332
C2×#168403152
C2×#168403082
C2×#168402922
C2×#168402432
C22×#145197422
C2×C61×#5202
C2×#350761