Finite Group Databasebeta

← C2×#21460290 #30587642

Subgroups — C2×#21460290 #30587642

Order 15616.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21460290C2132yesmaximal, direct product factor
2C2×#16840508C214yesmaximal, complemented
3C2×#16840497C211yesmaximal, characteristic, complemented
4C2×#16840497C212yesmaximal, complemented
5C2×#16840490C211yesmaximal, characteristic, complemented
6C2×#16840472C212yesmaximal, complemented
7C2×#16840434C211yesmaximal, characteristic, complemented
8C2×Q8×D244C211yesmaximal, characteristic, complemented
9C2×#16840422C212yesmaximal, complemented
10C2×#16840414C212yesmaximal, complemented
11C2×#16840386C212yesmaximal, complemented
12C2×#16840383C212yesmaximal, complemented
13C2×#16840367C212yesmaximal, complemented
14C2×#16840360C214yesmaximal, complemented
15C2×#16840337C212yesmaximal, complemented
16C2×#16840312C211yesmaximal, characteristic, complemented
17C2×#16840296C211yesmaximal, characteristic, complemented
18C2×C61×#533C211yesmaximal, characteristic, complemented
19C22×#11758226C2212yes—
20C22×#11758222C2212yes—
21C22×Q8×D61C2212yes—
22#16840508C22164yescomplemented
23#16840497C22132yescomplemented
24#16840497C22116yescomplemented
25#16840490C22116yescomplemented
26#16840472C22132yescomplemented
27#16840434C22116yescomplemented
28Q8×D244C22116yescomplemented
29#16840422C22132yescomplemented
30#16840414C22132yescomplemented
31#16840386C22132yescomplemented
32#16840383C22132yescomplemented
33#16840367C22132yescomplemented
34#16840360C22164yescomplemented
35#16840337C22132yescomplemented
36#16840312C22116yescomplemented
37C2×#14519777C2212yes—
38C2×#14519777C2211yescharacteristic
39C2×#14519775C2212yes—
40C2×#14519774C2211yescharacteristic
41C2×#14519774C2212yes—
42#16840296C22116yescomplemented
43C2×#14519772C2214yes—
44C2×#14519771C2212yes—
45C2×#14519769C2211yescharacteristic
46C2×#14519769C2212yes—
47C2×#14519767C2214yes—
48C2×#14519766C2214yes—
49C2×#14519766C2212yes—
50C2×#14519765C2212yes—
51C2×#14519765C2211yescharacteristic
52C2×#14519765C2212yes—
53C2×#14519763C2214yes—
54C2×#14519762C2214yes—
55C2×#14519762C2214yes—
56C2×#14519762C2214yes—
57C2×#14519762C2214yes—
58C2×#14519762C2214yes—
59C2×#14519760C2212yes—
60C2×#14519759C2214yes—
61C2×#14519757C2212yes—
62C2×#14519757C2214yes—
63C2×#14519756C2211yescharacteristic
64C2×#14519755C2214yes—
65C2×#14519755C2214yes—
66C2×#14519755C2214yes—
67C2×#14519753C2214yes—
68C2×#14519752C2212yes—
69C2×#14519752C2214yes—
70C2×#14519751C2211yescharacteristic
71C2×#14519751C2212yes—
72C2×#14519751C2212yes—
73C2×#14519750C2214yes—
74C2×#14519750C2214yes—
75C2×C4×Dic122C2211yescharacteristic
76C2×C4×Dic122C2212yes—
77C2×#14519742C2212yes—
78C2×C4×D244C2211yescharacteristic
79C2×C4×D244C2212yes—
80C2×C4×D244C2212yes—
81C2×C4×D244C2212yes—
82C2×C4×D244C2212yes—
83C2×C4×D244C2212yes—
84C2×#14519739C2212yes—
85C2×#14519739C2214yes—
86C2×C4×C22⋊D61C2212yes—
87C2×#14519734C2212yes—
88C2×C4⋊C4×D61C2214yes—
89C61×#533C22116yescomplemented
90C2×C4⋊Q8×C61C2211yescharacteristic
91C2×C4⋊Q8×C61C2211yescharacteristic
92C2×#125×C61C2212yes—
93C2×C22⋊Q8×C61C2211yescharacteristic
94C2×C22⋊Q8×C61C2211yescharacteristic
95C2×C22⋊Q8×C61C2212yes—
96C2×C4×Q8×C61C2211yescharacteristic
97C2×C4×Q8×C61C2211yescharacteristic
98C2×C4×Q8×C61C2212yes—
99C2×#117×C61C2212yes—
100C22×C42×C61C2211yescharacteristic
101C2×#11758226—48no—
102C2×#11758226C23116yes—
103C2×#11758222—48no—
104C2×#11758222C23116yes—
105C22×Dic122C2312yes—
106C22×Dic122C2311yescharacteristic
107C22×Dic122C2314yes—
108C2×Q8×D61—48no—
109C2×Q8×D61C23116yes—
110C22×D244C2312yes—
111C22×D244C2311yescharacteristic
112C22×D244C2312yes—
113C22×D244C2314yes—
114C22×D244C2312yes—
115C22×D244C2314yes—
116C22×C22⋊D61C2312yes—
117C22×C22⋊D61C2314yes—
118C22×C4×D61C2312yes—
119C22×C4×D61C2314yes—
120C22×C4×D61C2314yes—
121C22×C4×D61C2314yes—
122C22×C4×D61C2314yes—
123#14519777C23116yes—
124#14519777C2318yes—
125#14519775C23116yes—
126#14519774C2318yes—
127#14519774C23116yes—
128#14519772C23132yes—
129#14519771C23116yes—
130#14519769C2318yes—
131#14519769C23116yes—
132#14519767C23132yes—
133#14519766C23132yes—
134#14519766C23116yes—
135#14519765C2318yes—
136#14519765C23116yes—
137#14519765C23116yes—
138#14519763C23132yes—
139#14519762C23132yes—
140#14519762C23132yes—
141#14519762C23132yes—
142#14519762C23132yes—
143#14519762C23132yes—
144#14519760C23116yes—
145#14519759C23132yes—
146#14519757C23132yes—
147#14519757C23116yes—
148#14519756C2318yes—
149#14519755C23132yes—
150#14519755C23132yes—
151#14519755C23132yes—
152#14519753C23132yes—
153#14519752C23132yes—
154#14519752C23116yes—
155#14519751C23116yes—
156#14519751C2318yes—
157#14519751C23116yes—
158#14519750C23132yes—
159#14519750C23132yes—
160C4×Dic122C2318yes—
161C4×Dic122C23116yes—
162#14519742C23116yes—
163C4×D244C23116yes—
164C4×D244C23116yes—
165C4×D244C23116yes—
166C4×D244C23116yes—
167C4×D244C2318yes—
168C4×D244C23116yes—
169#14519739C23132yes—
170#14519739C23116yes—
171C4×C22⋊D61C23116yes—
172#14519734C23116yes—
173C2×C4⋊Dic61C2314yes—
174C2×C4⋊Dic61C2311yescharacteristic
175C2×C4⋊Dic61C2311yescharacteristic
176C2×C4⋊Dic61C2312yes—
177C2×C4⋊Dic61C2312yes—
178C2×#11758196C2312yes—
179C2×#11758196C2314yes—
180C2×#11758196C2312yes—
181C2×#11758196C2312yes—
182C2×#11758196C2314yes—
183C2×#11758196C2314yes—
184C2×#11758196C2312yes—
185C4⋊C4×D61C23132yes—
186C2×C22⋊Dic61C2312yes—
187C2×#11758198C2312yes—
188C2×#11758198C2312yes—
189C2×#11758198C2312yes—
190C2×#11758198C2314yes—
191C2×#11758198C2314yes—
192C2×#11758198C2314yes—
193C2×#11758198C2314yes—
194C2×#11758198C2314yes—
195C2×#11758198C2314yes—
196C2×#11758198C2314yes—
197C2×#11758198C2312yes—
198C2×C4×Dic61C2312yes—
199C2×C4×Dic61C2314yes—
200C22×Q8×C61C2311yescharacteristic
201C22×Q8×C61C2311yescharacteristic
202C22×Q8×C61C2312yes—
203C23×C4×C61C2311yescharacteristic
204C23×C4×C61C2311yescharacteristic
205C23×C4×C61C2311yescharacteristic
206C4⋊Q8×C61C2318yes—
207C4⋊Q8×C61C2318yes—
208#125×C61C23116yes—
209C22⋊Q8×C61C23116yes—
210C22⋊Q8×C61C2318yes—
211C22⋊Q8×C61C2318yes—
212C4×Q8×C61C23116yes—
213C4×Q8×C61C2318yes—
214C4×Q8×C61C2318yes—
215#117×C61C23116yes—
216C2×C4⋊C4×C61C2311yescharacteristic
217C2×C4⋊C4×C61C2311yescharacteristic
218C2×C4⋊C4×C61C2312yes—
219C2×C4⋊C4×C61C2312yes—
220C2×C4⋊C4×C61C2312yes—
221C2×C4⋊C4×C61C2312yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C2312yes—
224C2×C4⋊C4×C61C2312yes—
225C2×C22⋊C4×C61C2312yes—
226C2×C22⋊C4×C61C2312yes—
227C2×C42×C61C2311yescharacteristic
228C2×C42×C61C2318yes—
229C2×C42×C61C2311yescharacteristic
230C2×C42×C61C2312yes—
231C2×C42×C61C2311yescharacteristic
232C2×C42×C61C2312yes—
233C2×C42×C61C2311yescharacteristic
234C24×C61C2411yescharacteristic
235C23×D61C2412yes—
236C23×D61C2414yes—
237C2×Q8×C61—24no—
238C2×Q8×C61—24no—
239C2×Q8×C61—44no—
240C2×Q8×C61C2414yes—
241C2×Q8×C61C2414yes—
242C2×Q8×C61C2418yes—
243C22×C4×C61—24no—
244C22×C4×C61—24no—
245C22×C4×C61—42no—
246C22×C4×C61C2411yescharacteristic
247C22×C4×C61C2412yes—
248C22×C4×C61C2412yes—
249C22×C4×C61C2412yes—
250C22×C4×C61C2411yescharacteristic
251C22×C4×C61C2412yes—
252C22×C4×C61C2414yes—
253C22×C4×C61C2411yescharacteristic
254C22×C4×C61C2411yescharacteristic
255C22×C4×C61C2414yes—
256C22×C4×C61C2414yes—
257C22×C4×C61C2411yescharacteristic
258C22×C4×C61C2411yescharacteristic
259C2×C22⋊D61—44no—
260C2×C22⋊D61—48no—
261C2×C22⋊D61C24116yes—
262C2×C22⋊D61C2418yes—
263C22×Dic61C2412yes—
264C22×Dic61C2414yes—
265C22×Dic61C2412yes—
266C22×Dic61C2412yes—
267#11758226—432no—
268Q8×D61—432no—
269#11758222—432no—
270C2×D244—28no—
271C2×D244—24no—
272C2×D244—28no—
273C2×D244—44no—
274C2×D244—48no—
275C2×D244—48no—
276C2×D244C2418yes—
277C2×D244C2418yes—
278C2×D244C2414yes—
279C2×D244C24116yes—
280C2×D244C24116yes—
281C2×D244C2418yes—
282C2×C4×D61—28no—
283C2×C4×D61—48no—
284C2×C4×D61—48no—
285C2×C4×D61—48no—
286C2×C4×D61—48no—
287C2×C4×D61C2418yes—
288C2×C4×D61C24116yes—
289C2×C4×D61C24116yes—
290C2×C4×D61C24116yes—
291C2×C4×D61C24116yes—
292C2×Dic122—28no—
293C2×Dic122—24no—
294C2×Dic122—48no—
295C2×Dic122C2418yes—
296C2×Dic122C2414yes—
297C2×Dic122C24116yes—
298C4⋊C4×C61C2418yes—
299C4⋊C4×C61C2418yes—
300C4⋊C4×C61C2418yes—
301C4⋊C4×C61C2418yes—
302C4⋊C4×C61C2418yes—
303C4⋊C4×C61C2418yes—
304C4⋊C4×C61C2414yes—
305C4⋊C4×C61C2414yes—
306C4⋊C4×C61C2418yes—
307C22⋊C4×C61C2418yes—
308C22⋊C4×C61C2418yes—
309C42×C61C2414yes—
310C42×C61C2414yes—
311C42×C61C2414yes—
312C42×C61C2414yes—
313C42×C61C2418yes—
314C42×C61C2418yes—
315C22⋊Dic61C2418yes—
316#11758198C2418yes—
317#11758198C2418yes—
318#11758198C2418yes—
319#11758198C24116yes—
320#11758198C24116yes—
321#11758198C24116yes—
322#11758198C24116yes—
323#11758198C24116yes—
324#11758198C24116yes—
325#11758198C24116yes—
326#11758198C2418yes—
327C4⋊Dic61C24116yes—
328C4⋊Dic61C2414yes—
329C4⋊Dic61C2414yes—
330C4⋊Dic61C2418yes—
331C4⋊Dic61C2418yes—
332#11758196C2418yes—
333#11758196C24116yes—
334#11758196C2418yes—
335#11758196C2418yes—
336#11758196C24116yes—
337#11758196C24116yes—
338#11758196C2418yes—
339C4×Dic61C2418yes—
340C4×Dic61C24116yes—
341C23×C61—22no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61C2512yes—
345C23×C61C2511yescharacteristic
346C22×D61—24no—
347C22×D61—28no—
348C22×D61—24no—
349C22×D61—28no—
350C22×D61—28no—
351C22×D61—24no—
352C22×D61C2514yes—
353C22×D61C2518yes—
354Q8×C61—28no—
355Q8×C61—28no—
356Q8×C61—48no—
357C2×C4×C61—24no—
358C2×C4×C61—22no—
359C2×C4×C61—24no—
360C2×C4×C61—22no—
361C2×C4×C61—24no—
362C2×C4×C61—22no—
363C2×C4×C61—24no—
364C2×C4×C61—22no—
365C2×C4×C61—28no—
366C2×C4×C61—28no—
367C2×C4×C61—44no—
368C2×C4×C61H(5,𝔽2)14yes—
369C2×C4×C612−1+414yes—
370C2×C4×C61C2514yes—
371C2×C4×C61C2514yes—
372C2×C4×C61C2512yes—
373C2×C4×C61C2512yes—
374C2×C4×C61C2512yes—
375C2×C4×C61C2512yes—
376C2×C4×C61C2514yes—
377C2×C4×C61C2514yes—
378C2×C4×C61C2512yes—
379C2×C4×C61C2512yes—
380C22⋊D61—416no—
381C22⋊D61—48no—
382C2×Dic61—28no—
383C2×Dic61—24no—
384C2×Dic61—24no—
385C2×Dic61—24no—
386C2×Dic61C2514yes—
387C2×Dic61C2514yes—
388C2×Dic61C2518yes—
389C2×Dic61C2514yes—
390D244—216no—
391D244—216no—
392D244—28no—
393D244—48no—
394D244—416no—
395D244—416no—
396C4×D61—216no—
397C4×D61—416no—
398C4×D61—416no—
399C4×D61—416no—
400C4×D61—416no—
401Dic122—216no—
402Dic122—28no—
403Dic122—416no—
404C2×#3554—611nomaximal, Sylow
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—22no—
408C22×C61—44no—
409C22×C61C2×H(5,𝔽2)12yes—
410C22×C61C2×2−1+412yes—
411C22×C61#58512yes—
412C22×C61C2611yescharacteristic
413C2×D61—24no—
414C2×D61—28no—
415C2×D61—24no—
416C2×D61—28no—
417C2×D61—28no—
418C2×D61—24no—
419C2×D61—48no—
420C2×D61—416no—
421C4×C61—24no—
422C4×C61—22no—
423C4×C61—24no—
424C4×C61—22no—
425C4×C61—24no—
426C4×C61—22no—
427C4×C61—24no—
428C4×C61—22no—
429C4×C61C2×H(5,𝔽2)14yes—
430C4×C61C2×2−1+414yes—
431Dic61—28no—
432Dic61—24no—
433Dic61—24no—
434Dic61—24no—
435#3554—6132no—
436C2×#562—614no—
437C2×#559—612no—
438C2×#559—611no—
439C2×#557—611no—
440C2×#554—612no—
441C2×#550—611no—
442C2×D4×Q8—611no—
443C2×#548—612no—
444C2×#547—612no—
445C2×#542—612no—
446C2×#542—612no—
447C2×#540—612no—
448C2×#539—614no—
449C2×#536—612no—
450C2×#533D6111yescharacteristic, complemented
451C2×#532—611no—
452C2×#529—611no—
453C2×C61—42no—
454C2×C61#355414yescomplemented
455C2×C61C22×H(5,𝔽2)11yescharacteristic
456C2×C61C22×2−1+411yescharacteristic
457C2×C61C2×#58511yescharacteristic
458D61—44no—
459D61—48no—
460C22×#41—612no—
461C22×#41—612no—
462C23×Q8—612no—
463#562—6164no—
464#559—6132no—
465#559—6116no—
466#557—6116no—
467#554—6132no—
468#550—6116no—
469D4×Q8—6116no—
470#548—6132no—
471#547—6132no—
472#542—6132no—
473#542—6132no—
474#540—6132no—
475#539—6164no—
476#536—6132no—
477#533C2×D61116yescomplemented
478#532—6116no—
479C2×C4⋊Q8—612no—
480C2×C4⋊Q8—611no—
481C2×C4⋊Q8—612no—
482C2×C4⋊Q8C2×D6111yescharacteristic
483C2×C4⋊Q8C2×D6111yescharacteristic
484C2×#127—611no—
485C2×#127—612no—
486#529—6116no—
487C2×#126—614no—
488C2×#126—612no—
489C2×#125—614no—
490C2×#125—611no—
491C2×#125—612no—
492C2×#125C2×D6112yes—
493C2×#124—612no—
494C2×#124—614no—
495C2×#124—614no—
496C2×#124—611no—
497C2×#124—612no—
498C2×#124—612no—
499C2×#123—612no—
500C2×#123—614no—
501C2×#123—614no—
502C2×#123—614no—
503C2×#123—614no—
504C2×#123—614no—
505C2×#123—614no—
506C2×C22⋊Q8—614no—
507C2×C22⋊Q8—611no—
508C2×C22⋊Q8—614no—
509C2×C22⋊Q8—614no—
510C2×C22⋊Q8—614no—
511C2×C22⋊Q8—614no—
512C2×C22⋊Q8—612no—
513C2×C22⋊Q8C2×D6111yescharacteristic
514C2×C22⋊Q8C2×D6111yescharacteristic
515C2×C22⋊Q8C2×D6112yes—
516C2×#121—611no—
517C2×#121—612no—
518C2×#121—612no—
519C2×#121—614no—
520C2×#121—612no—
521C2×#121—614no—
522C2×#121—614no—
523C2×C4×Q8—612no—
524C2×C4×Q8—611no—
525C2×C4×Q8—612no—
526C2×C4×Q8C2×D6111yescharacteristic
527C2×C4×Q8C2×D6111yescharacteristic
528C2×C4×Q8C2×D6112yes—
529C2×C4×D4—612no—
530C2×C4×D4—614no—
531C2×C4×D4—612no—
532C2×C4×D4—611no—
533C2×C4×D4—612no—
534C2×C4×D4—612no—
535C2×C4×D4—612no—
536C2×C4×D4—612no—
537C2×C4×D4—612no—
538C2×#117—612no—
539C2×#117C2×D6112yes—
540C22×C4⋊C4—614no—
541C22×C42C2×D6111yescharacteristic
542C61C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—6116no—
544C2×#41—6116no—
545C2×#41—2448no—
546C2×#41—2448no—
547C22×Q8—6116no—
548C22×Q8—611no—
549C22×Q8—612no—
550C22×Q8—614no—
551C22×Q8—2448no—
552C22×Q8C22×D6111yescharacteristic
553C22×Q8C22×D6111yescharacteristic
554C22×Q8C22×D6112yes—
555C22×D4—612no—
556C22×D4—614no—
557C22×D4—611no—
558C22×D4—612no—
559C22×D4—612no—
560C22×D4—612no—
561C22×D4—614no—
562C22×D4—614no—
563C23×C4—612no—
564C23×C4—614no—
565C23×C4—614no—
566C23×C4—614no—
567C23×C4—614no—
568C23×C4C22×D6111yescharacteristic
569C23×C4C22×D6111yescharacteristic
570C23×C4C22×D6111yescharacteristic
571C4⋊Q8—6116no—
572C4⋊Q8—618no—
573C4⋊Q8—6116no—
574C4⋊Q8C22×D6118yes—
575C4⋊Q8C22×D6118yes—
576#127—618no—
577#127—6116no—
578#126—6132no—
579#126—6116no—
580#125—6132no—
581#125—618no—
582#125—6116no—
583#125C22×D61116yes—
584#124—6116no—
585#124—6132no—
586#124—6132no—
587#124—618no—
588#124—6116no—
589#124—6116no—
590#123—6116no—
591#123—6132no—
592#123—6132no—
593#123—6132no—
594#123—6132no—
595#123—6132no—
596#123—6132no—
597C22⋊Q8—6132no—
598C22⋊Q8—618no—
599C22⋊Q8—6132no—
600C22⋊Q8—6132no—
601C22⋊Q8—6132no—
602C22⋊Q8—6132no—
603C22⋊Q8—6116no—
604C22⋊Q8C22×D6118yes—
605C22⋊Q8C22×D6118yes—
606C22⋊Q8C22×D61116yes—
607#121—618no—
608#121—6116no—
609#121—6116no—
610#121—6132no—
611#121—6116no—
612#121—6132no—
613#121—6132no—
614C4×Q8—6116no—
615C4×Q8—618no—
616C4×Q8—6116no—
617C4×Q8C22×D6118yes—
618C4×Q8C22×D6118yes—
619C4×Q8C22×D61116yes—
620C4×D4—6116no—
621C4×D4—6132no—
622C4×D4—6116no—
623C4×D4—618no—
624C4×D4—6116no—
625C4×D4—6116no—
626C4×D4—6116no—
627C4×D4—6116no—
628C4×D4—6116no—
629#117—6116no—
630#117C22×D61116yes—
631C2×C4⋊C4—612no—
632C2×C4⋊C4—614no—
633C2×C4⋊C4—614no—
634C2×C4⋊C4—612no—
635C2×C4⋊C4—612no—
636C2×C4⋊C4—611no—
637C2×C4⋊C4—611no—
638C2×C4⋊C4—612no—
639C2×C4⋊C4—612no—
640C2×C4⋊C4—614no—
641C2×C4⋊C4—614no—
642C2×C4⋊C4—612no—
643C2×C4⋊C4—6132no—
644C2×C4⋊C4C22×D6112yes—
645C2×C4⋊C4C22×D6112yes—
646C2×C4⋊C4C22×D6112yes—
647C2×C4⋊C4C22×D6112yes—
648C2×C4⋊C4C22×D6111yescharacteristic
649C2×C4⋊C4C22×D6111yescharacteristic
650C2×C4⋊C4C22×D6112yes—
651C2×C4⋊C4C22×D6112yes—
652C2×C4⋊C4C22×D6112yes—
653C2×C22⋊C4—612no—
654C2×C22⋊C4—612no—
655C2×C22⋊C4—612no—
656C2×C22⋊C4—612no—
657C2×C22⋊C4—612no—
658C2×C22⋊C4—614no—
659C2×C22⋊C4—614no—
660C2×C22⋊C4—614no—
661C2×C22⋊C4—614no—
662C2×C22⋊C4—614no—
663C2×C22⋊C4—614no—
664C2×C22⋊C4—614no—
665C2×C22⋊C4C22×D6112yes—
666C2×C22⋊C4C22×D6112yes—
667C2×C42—612no—
668C2×C42—614no—
669C2×C42C22×D6111yescharacteristic
670C2×C42C22×D6112yes—
671C2×C42C22×D6112yes—
672C2×C42C22×D6111yescharacteristic
673C2×C42C22×D6111yescharacteristic
674C2×C42C22×D6111yescharacteristic
675C2×C42C22×D6118yes—
676C24—612no—
677C24—614no—
678C24C23×D6111yescharacteristic
679#41—24432no—
680#41—24432no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—44no—
684C2×Q8—614no—
685C2×Q8—618no—
686C2×Q8—6116no—
687C2×Q8—1228no—
688C2×Q8—1224no—
689C2×Q8—2448no—
690C2×Q8—24432no—
691C2×Q8C23×D6114yes—
692C2×Q8C23×D6114yes—
693C2×Q8C23×D6118yes—
694C2×D4—618no—
695C2×D4—6116no—
696C2×D4—614no—
697C2×D4—618no—
698C2×D4—618no—
699C2×D4—618no—
700C2×D4—6116no—
701C2×D4—6116no—
702C2×D4—1228no—
703C2×D4—1224no—
704C2×D4—1228no—
705C2×D4—2448no—
706C2×D4—2444no—
707C2×D4—2448no—
708C2×D4—2448no—
709C2×D4—2444no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—42no—
713C22×C4—612no—
714C22×C4—612no—
715C22×C4—614no—
716C22×C4—612no—
717C22×C4—618no—
718C22×C4—6116no—
719C22×C4—6116no—
720C22×C4—6116no—
721C22×C4—6116no—
722C22×C4—1228no—
723C22×C4—2448no—
724C22×C4—2448no—
725C22×C4—2448no—
726C22×C4—2448no—
727C22×C4C23×D6114yes—
728C22×C4C23×D6114yes—
729C22×C4C23×D6112yes—
730C22×C4C23×D6111yescharacteristic
731C22×C4C23×D6111yescharacteristic
732C22×C4C23×D6111yescharacteristic
733C22×C4C23×D6111yescharacteristic
734C22×C4C23×D6112yes—
735C22×C4C23×D6112yes—
736C22×C4C23×D6112yes—
737C22×C4C23×D6114yes—
738C22×C4C23×D6111yescharacteristic
739C22×C4C23×D6111yescharacteristic
740C4⋊C4—618no—
741C4⋊C4—6116no—
742C4⋊C4—6116no—
743C4⋊C4—618no—
744C4⋊C4—618no—
745C4⋊C4—6116no—
746C4⋊C4—6116no—
747C4⋊C4—618no—
748C4⋊C4—614no—
749C4⋊C4—614no—
750C4⋊C4—618no—
751C4⋊C4—618no—
752C4⋊C4C23×D6118yes—
753C4⋊C4C23×D6118yes—
754C4⋊C4C23×D6118yes—
755C4⋊C4C23×D6118yes—
756C4⋊C4C23×D6114yes—
757C4⋊C4C23×D6114yes—
758C4⋊C4C23×D6118yes—
759C4⋊C4C23×D6118yes—
760C4⋊C4C23×D6118yes—
761C22⋊C4—618no—
762C22⋊C4—618no—
763C22⋊C4—618no—
764C22⋊C4—618no—
765C22⋊C4—618no—
766C22⋊C4—6116no—
767C22⋊C4—6116no—
768C22⋊C4—6116no—
769C22⋊C4—6116no—
770C22⋊C4—6116no—
771C22⋊C4—6116no—
772C22⋊C4—6116no—
773C22⋊C4C23×D6118yes—
774C22⋊C4C23×D6118yes—
775C42—618no—
776C42—6116no—
777C42C23×D6114yes—
778C42C23×D6114yes—
779C42C23×D6114yes—
780C42C23×D6114yes—
781C42C23×D6118yes—
782C42C23×D6118yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—614no—
787C23—618no—
788C23—1224no—
789C23—1228no—
790C23—1224no—
791C23—1228no—
792C23—1228no—
793C23—1224no—
794C23C24×D6112yes—
795C23C24×D6111yescharacteristic
796Q8—28no—
797Q8—28no—
798Q8—48no—
799Q8—12216no—
800Q8—1228no—
801Q8—24416no—
802D4—12216no—
803D4—1228no—
804D4—12216no—
805D4—2448no—
806D4—24416no—
807D4—24416no—
808D4—2448no—
809D4—24416no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—614no—
822C2×C4—614no—
823C2×C4—618no—
824C2×C4—614no—
825C2×C4—1224no—
826C2×C4—1228no—
827C2×C4—1224no—
828C2×C4—1224no—
829C2×C4—12216no—
830C2×C4—24416no—
831C2×C4—24416no—
832C2×C4—24416no—
833C2×C4—24416no—
834C2×C4#1451982314yes—
835C2×C4#1451982514yes—
836C2×C4C24×D6114yes—
837C2×C4C24×D6112yes—
838C2×C4C24×D6112yes—
839C2×C4C24×D6112yes—
840C2×C4C24×D6112yes—
841C2×C4C24×D6114yes—
842C2×C4C24×D6114yes—
843C2×C4C24×D6114yes—
844C2×C4C24×D6112yes—
845C2×C4C24×D6112yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—1224no—
851C22—1228no—
852C22—1224no—
853C22—1228no—
854C22—1228no—
855C22—1224no—
856C22—2448no—
857C22—24416no—
858C22C2×#1451982312yes—
859C22C2×#1451982512yes—
860C22#1684059812yes—
861C22C25×D6111yescharacteristic
862C4—22no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—24no—
870C4—1224no—
871C4—1228no—
872C4—1224no—
873C4—1224no—
874C4C2×#1451982314yes—
875C4C2×#1451982514yes—
876C2—42no—
877C2—2444no—
878C2—2448no—
879C2#2146029014yesdirect product factor
880C2C22×#1451982311yescharacteristic
881C2C22×#1451982511yescharacteristic
882C2C2×#1684059811yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#533C2
socleC23×C61C25
hypercenterC2×#533D61
hypocenterC61C2×#3554
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #21460290C2direct (N × H)
2. C2×#16840508C2semidirect
3. C2×#16840497C2semidirect
4. C2×#16840497C2semidirect
5. C2×#16840490C2semidirect
6. C2×#16840472C2semidirect
7. C2×#16840434C2semidirect
8. C2×Q8×D244C2semidirect
9. C2×#16840422C2semidirect
10. C2×#16840414C2semidirect
11. C2×#16840386C2semidirect
12. C2×#16840383C2semidirect
13. C2×#16840367C2semidirect
14. C2×#16840360C2semidirect
15. C2×#16840337C2semidirect
16. C2×#16840312C2semidirect
17. C2×#16840296C2semidirect
18. C2×C61×#533C2semidirect
22. #16840508C22semidirect
23. #16840497C22semidirect
24. #16840497C22semidirect
25. #16840490C22semidirect
26. #16840472C22semidirect
27. #16840434C22semidirect
28. Q8×D244C22semidirect
29. #16840422C22semidirect
30. #16840414C22semidirect
31. #16840386C22semidirect
32. #16840383C22semidirect
33. #16840367C22semidirect
34. #16840360C22semidirect
35. #16840337C22semidirect
36. #16840312C22semidirect
42. #16840296C22semidirect
89. C61×#533C22semidirect
450. C2×#533D61semidirect
454. C2×C61#3554semidirect
477. #533C2×D61semidirect
542. C61C2×#3554semidirect
879. C2#21460290direct (N × H)

Maximal subgroups

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

subgroupindex
#214602902
C2×#168405082
C2×#168404972
C2×#168404902
C2×#168404722
C2×#168404342
C2×Q8×D2442
C2×#168404222
C2×#168404142
C2×#168403862
C2×#168403832
C2×#168403672
C2×#168403602
C2×#168403372
C2×#168403122
C2×#168402962
C2×C61×#5332
C2×#355461