Finite Group Databasebeta

← C2×#21460284 #30587638

Subgroups — C2×#21460284 #30587638

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#21460284C2132yesmaximal, direct product factor
2C2×#16840507C214yesmaximal, complemented
3C2×#16840498C211yesmaximal, characteristic, complemented
4C2×#16840495C212yesmaximal, complemented
5C2×#16840487C211yesmaximal, characteristic, complemented
6C2×#16840471C212yesmaximal, complemented
7C2×#16840432C211yesmaximal, characteristic, complemented
8C2×#16840427C211yesmaximal, characteristic, complemented
9C2×#16840419C212yesmaximal, complemented
10C2×#16840411C212yesmaximal, complemented
11C2×#16840381C212yesmaximal, complemented
12C2×#16840379C212yesmaximal, complemented
13C2×#16840365C212yesmaximal, complemented
14C2×#16840354C214yesmaximal, complemented
15C2×#16840332C212yesmaximal, complemented
16C2×#16840319C211yesmaximal, characteristic, complemented
17C2×#16840296C211yesmaximal, characteristic, complemented
18C2×C61×#532C211yesmaximal, characteristic, complemented
19C22×#11758224C2212yes—
20C22×Q8×D61C2212yes—
21#16840507C22164yescomplemented
22#16840498C22116yescomplemented
23#16840495C22132yescomplemented
24#16840487C22116yescomplemented
25#16840471C22132yescomplemented
26#16840432C22116yescomplemented
27#16840427C22116yescomplemented
28#16840419C22132yescomplemented
29#16840411C22132yescomplemented
30#16840381C22132yescomplemented
31#16840379C22132yescomplemented
32#16840365C22132yescomplemented
33#16840354C22164yescomplemented
34#16840332C22132yescomplemented
35#16840319C22116yescomplemented
36C2×#14519777C2211yescharacteristic
37C2×#14519777C2211yescharacteristic
38C2×#14519776C2212yes—
39C2×#14519775C2212yes—
40C2×#14519773C2212yes—
41#16840296C22116yescomplemented
42C2×#14519771C2212yes—
43C2×#14519770C2214yes—
44C2×#14519769C2211yescharacteristic
45C2×#14519769C2212yes—
46C2×#14519768C2212yes—
47C2×#14519767C2214yes—
48C2×#14519765C2211yescharacteristic
49C2×#14519764C2212yes—
50C2×#14519764C2214yes—
51C2×#14519764C2212yes—
52C2×#14519763C2214yes—
53C2×#14519761C2214yes—
54C2×#14519760C2214yes—
55C2×#14519760C2212yes—
56C2×#14519759C2214yes—
57C2×#14519759C2214yes—
58C2×#14519758C2214yes—
59C2×#14519758C2214yes—
60C2×#14519756C2211yescharacteristic
61C2×#14519756C2211yescharacteristic
62C2×#14519756C2214yes—
63C2×#14519756C2211yescharacteristic
64C2×#14519756C2212yes—
65C2×#14519755C2214yes—
66C2×#14519754C2214yes—
67C2×#14519754C2214yes—
68C2×#14519754C2214yes—
69C2×#14519753C2212yes—
70C2×#14519751C2211yescharacteristic
71C2×#14519749C2214yes—
72C2×#14519749C2214yes—
73C2×#14519748C2212yes—
74C2×#14519748C2214yes—
75C2×Q8×Dic61C2212yes—
76C2×C4×Dic122C2211yescharacteristic
77C2×C4×Dic122C2211yescharacteristic
78C2×C4×Dic122C2211yescharacteristic
79C2×C4×Dic122C2212yes—
80C2×#14519742C2212yes—
81C2×C4×D244C2211yescharacteristic
82C2×D4×Dic61C2212yes—
83C2×D4×Dic61C2212yes—
84C2×D4×Dic61C2212yes—
85C2×#14519739C2212yes—
86C2×C4×C22⋊D61C2212yes—
87C2×C4×C22⋊D61C2214yes—
88C2×#14519736C2212yes—
89C2×#14519734C2212yes—
90C22×#11758196C2214yes—
91C22×#41×C61C2212yes—
92C61×#532C22116yescomplemented
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×#127×C61C2211yescharacteristic
95C2×#124×C61C2212yes—
96C2×#121×C61C2212yes—
97C2×#121×C61C2212yes—
98C2×C4×D4×C61C2212yes—
99C2×C4×D4×C61C2212yes—
100C22×C42×C61C2211yescharacteristic
101C2×#11758224—48no—
102C2×#11758224C23116yes—
103C22×Dic122C2311yescharacteristic
104C22×Dic122C2311yescharacteristic
105C22×Dic122C2311yescharacteristic
106C22×Dic122C2312yes—
107C22×Dic122C2314yes—
108C2×Q8×D61—48no—
109C2×Q8×D61C23116yes—
110C22×D244C2311yescharacteristic
111C22×C22⋊D61C2312yes—
112C22×C22⋊D61C2314yes—
113C22×C22⋊D61C2314yes—
114C23×Dic61C2314yes—
115C23×Dic61C2314yes—
116C22×C4×D61C2312yes—
117C22×C4×D61C2314yes—
118#14519777C2318yes—
119#14519777C2318yes—
120#14519776C23116yes—
121#14519775C23116yes—
122#14519773C23116yes—
123#14519771C23116yes—
124#14519770C23132yes—
125#14519769C2318yes—
126#14519769C23116yes—
127#14519768C23116yes—
128#14519767C23132yes—
129#14519765C2318yes—
130#14519764C23116yes—
131#14519764C23116yes—
132#14519764C23132yes—
133#14519763C23132yes—
134#14519761C23132yes—
135#14519760C23132yes—
136#14519760C23116yes—
137#14519759C23132yes—
138#14519759C23132yes—
139#14519758C23132yes—
140#14519758C23132yes—
141#14519756C23132yes—
142#14519756C23116yes—
143#14519756C2318yes—
144#14519756C2318yes—
145#14519756C2318yes—
146#14519755C23132yes—
147#14519754C23132yes—
148#14519754C23132yes—
149#14519754C23132yes—
150#14519753C23116yes—
151#14519751C2318yes—
152#14519749C23132yes—
153#14519749C23132yes—
154#14519748C23132yes—
155#14519748C23116yes—
156Q8×Dic61C23116yes—
157C4×Dic122C23116yes—
158C4×Dic122C2318yes—
159C4×Dic122C2318yes—
160C4×Dic122C2318yes—
161#14519742C23116yes—
162C4×D244C2318yes—
163D4×Dic61C23116yes—
164D4×Dic61C23116yes—
165D4×Dic61C23116yes—
166#14519739C23116yes—
167C4×C22⋊D61C23132yes—
168C4×C22⋊D61C23116yes—
169#14519736C23116yes—
170#14519734C23116yes—
171C2×C4⋊Dic61C2312yes—
172C2×C4⋊Dic61C2312yes—
173C2×C4⋊Dic61C2311yescharacteristic
174C2×C4⋊Dic61C2311yescharacteristic
175C2×C4⋊Dic61C2311yescharacteristic
176C2×C4⋊Dic61C2311yescharacteristic
177C2×C4⋊Dic61C2312yes—
178C2×C4⋊Dic61C2314yes—
179C2×#11758196C2312yes—
180C2×#11758196C2312yes—
181C2×#11758196C23132yes—
182C2×#11758196C2314yes—
183C2×#11758196C2314yes—
184C2×#11758196C2312yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2314yes—
188C2×#11758196C2312yes—
189C2×#11758196C2312yes—
190C2×#11758196C2312yes—
191C2×C22⋊Dic61C2312yes—
192C2×C22⋊Dic61C2312yes—
193C2×C22⋊Dic61C2314yes—
194C2×C22⋊Dic61C2312yes—
195C2×C22⋊Dic61C2314yes—
196C2×C22⋊Dic61C2314yes—
197C2×C22⋊Dic61C2314yes—
198C2×#11758198C2312yes—
199C2×#11758198C2312yes—
200C2×#11758198C2312yes—
201C2×#11758198C2314yes—
202C2×#11758198C2312yes—
203C2×C4×Dic61C2312yes—
204C2×C4×Dic61C2312yes—
205C2×C4×Dic61C2312yes—
206C2×C4×Dic61C2314yes—
207C2×#41×C61—48no—
208C2×#41×C61C23116yes—
209C22×Q8×C61C2312yes—
210C22×D4×C61C2312yes—
211C22×D4×C61C2312yes—
212C22×D4×C61C2312yes—
213C22×D4×C61C2314yes—
214C23×C4×C61C2311yescharacteristic
215C23×C4×C61C2311yescharacteristic
216C23×C4×C61C2314yes—
217C23×C4×C61C2311yescharacteristic
218C4⋊Q8×C61C2318yes—
219#127×C61C2318yes—
220#124×C61C23116yes—
221#121×C61C23116yes—
222#121×C61C23116yes—
223C4×D4×C61C23116yes—
224C4×D4×C61C23116yes—
225C2×C4⋊C4×C61C2312yes—
226C2×C4⋊C4×C61C2312yes—
227C2×C22⋊C4×C61C2314yes—
228C2×C22⋊C4×C61C2314yes—
229C2×C42×C61C2311yescharacteristic
230C2×C42×C61C2318yes—
231C2×C42×C61C2311yescharacteristic
232C2×C42×C61C2311yescharacteristic
233C2×C42×C61C2311yescharacteristic
234C24×C61C2414yes—
235C24×C61C2411yescharacteristic
236C23×D61C2412yes—
237#41×C61—432no—
238C2×Q8×C61—28no—
239C2×Q8×C61C2418yes—
240C2×D4×C61—28no—
241C2×D4×C61—28no—
242C2×D4×C61—44no—
243C2×D4×C61—48no—
244C2×D4×C61C2418yes—
245C2×D4×C61C2418yes—
246C2×D4×C61C2418yes—
247C2×D4×C61C24116yes—
248C22×C4×C61—24no—
249C22×C4×C61—24no—
250C22×C4×C61—42no—
251C22×C4×C61—48no—
252C22×C4×C61C2414yes—
253C22×C4×C61C2411yescharacteristic
254C22×C4×C61C2411yescharacteristic
255C22×C4×C61C2411yescharacteristic
256C22×C4×C61C2414yes—
257C22×C4×C61C2411yescharacteristic
258C22×C4×C61C2414yes—
259C22×C4×C61C2414yes—
260C22×C4×C61C24116yes—
261C22×C4×C61C2411yescharacteristic
262C22×C4×C61C2411yescharacteristic
263C2×C22⋊D61—48no—
264C2×C22⋊D61—44no—
265C2×C22⋊D61—48no—
266C2×C22⋊D61C24116yes—
267C2×C22⋊D61C2418yes—
268C2×C22⋊D61C24116yes—
269C22×Dic61—48no—
270C22×Dic61—48no—
271C22×Dic61C2412yes—
272C22×Dic61C2412yes—
273C22×Dic61C2412yes—
274C22×Dic61C2412yes—
275C22×Dic61C2412yes—
276C22×Dic61C2412yes—
277C22×Dic61C2412yes—
278C22×Dic61C24116yes—
279C22×Dic61C24116yes—
280Q8×D61—432no—
281#11758224—432no—
282C2×D244—24no—
283C2×D244C2414yes—
284C2×C4×D61—28no—
285C2×C4×D61—48no—
286C2×C4×D61C2418yes—
287C2×C4×D61C24116yes—
288C2×Dic122—24no—
289C2×Dic122—24no—
290C2×Dic122—24no—
291C2×Dic122—48no—
292C2×Dic122—44no—
293C2×Dic122C2414yes—
294C2×Dic122C2414yes—
295C2×Dic122C2414yes—
296C2×Dic122C24116yes—
297C2×Dic122C2418yes—
298C4⋊C4×C61C2418yes—
299C4⋊C4×C61C2418yes—
300C22⋊C4×C61C24116yes—
301C22⋊C4×C61C24116yes—
302C42×C61C2414yes—
303C42×C61C2414yes—
304C42×C61C2414yes—
305C42×C61C2414yes—
306C22⋊Dic61C2418yes—
307C22⋊Dic61C2418yes—
308C22⋊Dic61C24116yes—
309C22⋊Dic61C2418yes—
310C22⋊Dic61C24116yes—
311C22⋊Dic61C24116yes—
312C22⋊Dic61C24116yes—
313#11758198C2418yes—
314#11758198C2418yes—
315#11758198C2418yes—
316#11758198C24116yes—
317#11758198C2418yes—
318C4⋊Dic61C2418yes—
319C4⋊Dic61C2418yes—
320C4⋊Dic61C2414yes—
321C4⋊Dic61C2414yes—
322C4⋊Dic61C2414yes—
323C4⋊Dic61C2414yes—
324C4⋊Dic61C2418yes—
325C4⋊Dic61C24116yes—
326#11758196C2418yes—
327#11758196C2418yes—
328#11758196C24116yes—
329#11758196C24116yes—
330#11758196C2418yes—
331#11758196C2418yes—
332#11758196C2418yes—
333#11758196C24116yes—
334#11758196C2418yes—
335#11758196C2418yes—
336#11758196C2418yes—
337C4×Dic61C2418yes—
338C4×Dic61C2418yes—
339C4×Dic61C2418yes—
340C4×Dic61C24116yes—
341C23×C61—28no—
342C23×C61—22no—
343C23×C61—22no—
344C23×C61—28no—
345C23×C61—28no—
346C23×C61—22no—
347C23×C61C2512yes—
348C23×C61C2518yes—
349C23×C61C2511yescharacteristic
350C22×D61—24no—
351C22×D61—24no—
352C22×D61—24no—
353C22×D61C2514yes—
354Q8×C61—216no—
355D4×C61—216no—
356D4×C61—216no—
357D4×C61—48no—
358D4×C61—416no—
359C2×C4×C61—28no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—28no—
365C2×C4×C61—28no—
366C2×C4×C61—44no—
367C2×C4×C61—416no—
368C2×C4×C61H(5,𝔽2)14yes—
369C2×C4×C612−1+414yes—
370C2×C4×C61C2518yes—
371C2×C4×C61C2512yes—
372C2×C4×C61C2512yes—
373C2×C4×C61C2512yes—
374C2×C4×C61C2512yes—
375C2×C4×C61C2512yes—
376C2×C4×C61C2512yes—
377C22⋊D61—416no—
378C22⋊D61—416no—
379C22⋊D61—48no—
380C2×Dic61—24no—
381C2×Dic61—24no—
382C2×Dic61—24no—
383C2×Dic61—24no—
384C2×Dic61—24no—
385C2×Dic61—24no—
386C2×Dic61—24no—
387C2×Dic61—416no—
388C2×Dic61—416no—
389C2×Dic61C2514yes—
390C2×Dic61C2514yes—
391C2×Dic61C2514yes—
392C2×Dic61C2514yes—
393C2×Dic61C2514yes—
394C2×Dic61C2514yes—
395C2×Dic61C2514yes—
396D244—28no—
397C4×D61—216no—
398C4×D61—416no—
399Dic122—28no—
400Dic122—28no—
401Dic122—28no—
402Dic122—48no—
403Dic122—416no—
404C2×#3554—611nomaximal, Sylow
405C22×C61—28no—
406C22×C61—22no—
407C22×C61—22no—
408C22×C61—28no—
409C22×C61—28no—
410C22×C61—22no—
411C22×C61—416no—
412C22×C61—44no—
413C22×C61C2×H(5,𝔽2)12yes—
414C22×C61C2×2−1+412yes—
415C22×C61#58512yes—
416C22×C61C2611yescharacteristic
417C2×D61—24no—
418C2×D61—24no—
419C2×D61—24no—
420C2×D61—48no—
421C4×C61—28no—
422C4×C61—22no—
423C4×C61—22no—
424C4×C61—22no—
425C4×C61—22no—
426C4×C61C2×H(5,𝔽2)14yes—
427C4×C61C2×2−1+414yes—
428Dic61—24no—
429Dic61—24no—
430Dic61—24no—
431Dic61—24no—
432Dic61—24no—
433Dic61—24no—
434Dic61—24no—
435#3554—6132no—
436C2×#562—614no—
437C2×#559—611no—
438C2×#559—612no—
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×#533—611no—
451C2×#532D6111yescharacteristic, complemented
452C2×#529—611no—
453C2×C61—48no—
454C2×C61—42no—
455C2×C61#355414yescomplemented
456C2×C61C22×H(5,𝔽2)11yescharacteristic
457C2×C61C22×2−1+411yescharacteristic
458C2×C61C2×#58511yescharacteristic
459D61—44no—
460C22×#41—612no—
461C22×#41C2×D6112yes—
462C23×Q8—612no—
463#562—6164no—
464#559—6116no—
465#559—6132no—
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#533—6116no—
478#532C2×D61116yescomplemented
479C2×C4⋊Q8—612no—
480C2×C4⋊Q8—612no—
481C2×C4⋊Q8—611no—
482C2×C4⋊Q8—611no—
483C2×C4⋊Q8C2×D6111yescharacteristic
484C2×#127—612no—
485C2×#127C2×D6111yescharacteristic
486#529—6116no—
487C2×#126—614no—
488C2×#126—612no—
489C2×#125—614no—
490C2×#125—612no—
491C2×#125—611no—
492C2×#125—612no—
493C2×#124—612no—
494C2×#124—614no—
495C2×#124—612no—
496C2×#124—614no—
497C2×#124—611no—
498C2×#124C2×D6112yes—
499C2×#123—614no—
500C2×#123—614no—
501C2×#123—612no—
502C2×#123—614no—
503C2×#123—614no—
504C2×#123—614no—
505C2×#123—614no—
506C2×C22⋊Q8—612no—
507C2×C22⋊Q8—611no—
508C2×C22⋊Q8—611no—
509C2×C22⋊Q8—611no—
510C2×C22⋊Q8—612no—
511C2×C22⋊Q8—614no—
512C2×C22⋊Q8—614no—
513C2×C22⋊Q8—614no—
514C2×C22⋊Q8—614no—
515C2×C22⋊Q8—614no—
516C2×#121—614no—
517C2×#121—612no—
518C2×#121—614no—
519C2×#121—614no—
520C2×#121—611no—
521C2×#121C2×D6112yes—
522C2×#121C2×D6112yes—
523C2×C4×Q8—612no—
524C2×C4×Q8—612no—
525C2×C4×Q8—611no—
526C2×C4×Q8—611no—
527C2×C4×Q8—611no—
528C2×C4×Q8—612no—
529C2×C4×D4—612no—
530C2×C4×D4—612no—
531C2×C4×D4—612no—
532C2×C4×D4—612no—
533C2×C4×D4—614no—
534C2×C4×D4—612no—
535C2×C4×D4—611no—
536C2×C4×D4C2×D6112yes—
537C2×C4×D4C2×D6112yes—
538C2×#117—612no—
539C2×#117—612no—
540C22×C4⋊C4—614no—
541C22×C42C2×D6111yescharacteristic
542C61C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—48no—
544C2×#41—6116no—
545C2×#41—2448no—
546C2×#41C22×D61116yes—
547C22×Q8—6116no—
548C22×Q8—611no—
549C22×Q8—611no—
550C22×Q8—611no—
551C22×Q8—612no—
552C22×Q8—614no—
553C22×Q8—2448no—
554C22×Q8C22×D6112yes—
555C22×D4—612no—
556C22×D4—614no—
557C22×D4—614no—
558C22×D4—611no—
559C22×D4C22×D6112yes—
560C22×D4C22×D6112yes—
561C22×D4C22×D6112yes—
562C22×D4C22×D6114yes—
563C23×C4—614no—
564C23×C4—614no—
565C23×C4—612no—
566C23×C4—614no—
567C23×C4C22×D6111yescharacteristic
568C23×C4C22×D6111yescharacteristic
569C23×C4C22×D6114yes—
570C23×C4C22×D6111yescharacteristic
571C4⋊Q8—6116no—
572C4⋊Q8—6116no—
573C4⋊Q8—618no—
574C4⋊Q8—618no—
575C4⋊Q8C22×D6118yes—
576#127—6116no—
577#127C22×D6118yes—
578#126—6132no—
579#126—6116no—
580#125—6132no—
581#125—6116no—
582#125—618no—
583#125—6116no—
584#124—6116no—
585#124—6132no—
586#124—6116no—
587#124—6132no—
588#124—618no—
589#124C22×D61116yes—
590#123—6132no—
591#123—6132no—
592#123—6116no—
593#123—6132no—
594#123—6132no—
595#123—6132no—
596#123—6132no—
597C22⋊Q8—6116no—
598C22⋊Q8—618no—
599C22⋊Q8—618no—
600C22⋊Q8—618no—
601C22⋊Q8—6116no—
602C22⋊Q8—6132no—
603C22⋊Q8—6132no—
604C22⋊Q8—6132no—
605C22⋊Q8—6132no—
606C22⋊Q8—6132no—
607#121—6132no—
608#121—6132no—
609#121—6132no—
610#121—6116no—
611#121—618no—
612#121C22×D61116yes—
613#121C22×D61116yes—
614C4×Q8—6116no—
615C4×Q8—6116no—
616C4×Q8—618no—
617C4×Q8—618no—
618C4×Q8—618no—
619C4×Q8—6116no—
620C4×D4—6116no—
621C4×D4—6116no—
622C4×D4—6116no—
623C4×D4—6116no—
624C4×D4—6132no—
625C4×D4—6116no—
626C4×D4—618no—
627C4×D4C22×D61116yes—
628C4×D4C22×D61116yes—
629#117—6116no—
630#117—6116no—
631C2×C4⋊C4—612no—
632C2×C4⋊C4—612no—
633C2×C4⋊C4—614no—
634C2×C4⋊C4—614no—
635C2×C4⋊C4—6132no—
636C2×C4⋊C4—612no—
637C2×C4⋊C4—612no—
638C2×C4⋊C4—612no—
639C2×C4⋊C4—612no—
640C2×C4⋊C4—611no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—612no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—612no—
646C2×C4⋊C4—614no—
647C2×C4⋊C4—612no—
648C2×C4⋊C4—612no—
649C2×C4⋊C4—614no—
650C2×C4⋊C4—612no—
651C2×C4⋊C4C22×D6112yes—
652C2×C4⋊C4C22×D6112yes—
653C2×C22⋊C4—612no—
654C2×C22⋊C4—612no—
655C2×C22⋊C4—614no—
656C2×C22⋊C4—614no—
657C2×C22⋊C4—612no—
658C2×C22⋊C4—614no—
659C2×C22⋊C4—614no—
660C2×C22⋊C4—612no—
661C2×C22⋊C4—612no—
662C2×C22⋊C4—612no—
663C2×C22⋊C4—612no—
664C2×C22⋊C4—614no—
665C2×C22⋊C4C22×D6114yes—
666C2×C22⋊C4C22×D6114yes—
667C2×C42—612no—
668C2×C42—612no—
669C2×C42—612no—
670C2×C42—614no—
671C2×C42C22×D6111yescharacteristic
672C2×C42C22×D6111yescharacteristic
673C2×C42C22×D6111yescharacteristic
674C2×C42C22×D6111yescharacteristic
675C2×C42C22×D6118yes—
676C24—612no—
677C24C23×D6111yescharacteristic
678C24C23×D6114yes—
679#41—432no—
680#41—24432no—
681C2×Q8—28no—
682C2×Q8—614no—
683C2×Q8—614no—
684C2×Q8—614no—
685C2×Q8—618no—
686C2×Q8—6116no—
687C2×Q8—1224no—
688C2×Q8—1224no—
689C2×Q8—1224no—
690C2×Q8—2444no—
691C2×Q8—2448no—
692C2×Q8—24432no—
693C2×Q8C23×D6118yes—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—48no—
697C2×D4—44no—
698C2×D4—618no—
699C2×D4—6116no—
700C2×D4—6116no—
701C2×D4—614no—
702C2×D4—1224no—
703C2×D4—2448no—
704C2×D4—2444no—
705C2×D4—2448no—
706C2×D4C23×D6118yes—
707C2×D4C23×D6118yes—
708C2×D4C23×D6118yes—
709C2×D4C23×D61116yes—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—48no—
713C22×C4—42no—
714C22×C4—612no—
715C22×C4—612no—
716C22×C4—612no—
717C22×C4—612no—
718C22×C4—612no—
719C22×C4—612no—
720C22×C4—612no—
721C22×C4—6116no—
722C22×C4—6116no—
723C22×C4—618no—
724C22×C4—6116no—
725C22×C4—1228no—
726C22×C4—2448no—
727C22×C4—2448no—
728C22×C4—2448no—
729C22×C4C23×D6114yes—
730C22×C4C23×D6114yes—
731C22×C4C23×D6114yes—
732C22×C4C23×D6111yescharacteristic
733C22×C4C23×D6111yescharacteristic
734C22×C4C23×D6111yescharacteristic
735C22×C4C23×D6111yescharacteristic
736C22×C4C23×D6114yes—
737C22×C4C23×D61116yes—
738C22×C4C23×D6111yescharacteristic
739C22×C4C23×D6111yescharacteristic
740C4⋊C4—618no—
741C4⋊C4—618no—
742C4⋊C4—6116no—
743C4⋊C4—6116no—
744C4⋊C4—618no—
745C4⋊C4—618no—
746C4⋊C4—618no—
747C4⋊C4—618no—
748C4⋊C4—618no—
749C4⋊C4—6116no—
750C4⋊C4—618no—
751C4⋊C4—618no—
752C4⋊C4—618no—
753C4⋊C4—614no—
754C4⋊C4—614no—
755C4⋊C4—614no—
756C4⋊C4—614no—
757C4⋊C4—6116no—
758C4⋊C4—618no—
759C4⋊C4C23×D6118yes—
760C4⋊C4C23×D6118yes—
761C22⋊C4—618no—
762C22⋊C4—618no—
763C22⋊C4—6116no—
764C22⋊C4—6116no—
765C22⋊C4—618no—
766C22⋊C4—6116no—
767C22⋊C4—6116no—
768C22⋊C4—618no—
769C22⋊C4—618no—
770C22⋊C4—618no—
771C22⋊C4—618no—
772C22⋊C4—6116no—
773C22⋊C4C23×D61116yes—
774C22⋊C4C23×D61116yes—
775C42—618no—
776C42—618no—
777C42—618no—
778C42—6116no—
779C42C23×D6114yes—
780C42C23×D6114yes—
781C42C23×D6114yes—
782C42C23×D6114yes—
783C23—22no—
784C23—28no—
785C23—22no—
786C23—28no—
787C23—22no—
788C23—28no—
789C23—614no—
790C23—1224no—
791C23—1224no—
792C23—1224no—
793C23C24×D6112yes—
794C23C24×D6118yes—
795C23C24×D6111yescharacteristic
796Q8—216no—
797Q8—1228no—
798Q8—1228no—
799Q8—1228no—
800Q8—2448no—
801Q8—24416no—
802D4—216no—
803D4—216no—
804D4—48no—
805D4—416no—
806D4—1228no—
807D4—2448no—
808D4—24416no—
809D4—24416no—
810C2×C4—22no—
811C2×C4—28no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—28no—
817C2×C4—44no—
818C2×C4—416no—
819C2×C4—614no—
820C2×C4—614no—
821C2×C4—614no—
822C2×C4—614no—
823C2×C4—614no—
824C2×C4—614no—
825C2×C4—614no—
826C2×C4—1224no—
827C2×C4—1224no—
828C2×C4—1224no—
829C2×C4—1224no—
830C2×C4—1224no—
831C2×C4—1224no—
832C2×C4—1224no—
833C2×C4—12216no—
834C2×C4—24416no—
835C2×C4—24416no—
836C2×C4—24416no—
837C2×C4#1451982214yes—
838C2×C4#1451982414yes—
839C2×C4C24×D6118yes—
840C2×C4C24×D6112yes—
841C2×C4C24×D6112yes—
842C2×C4C24×D6112yes—
843C2×C4C24×D6112yes—
844C2×C4C24×D6112yes—
845C2×C4C24×D6112yes—
846C22—22no—
847C22—28no—
848C22—22no—
849C22—28no—
850C22—22no—
851C22—28no—
852C22—44no—
853C22—416no—
854C22—1224no—
855C22—1224no—
856C22—1224no—
857C22—2448no—
858C22C2×#1451982212yes—
859C22C2×#1451982412yes—
860C22#1684059812yes—
861C22C25×D6111yescharacteristic
862C4—22no—
863C4—28no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—1224no—
868C4—1224no—
869C4—1224no—
870C4—1224no—
871C4—1224no—
872C4—1224no—
873C4—1224no—
874C4C2×#1451982214yes—
875C4C2×#1451982414yes—
876C2—42no—
877C2—48no—
878C2—2444no—
879C2#2146028414yesdirect product factor
880C2C22×#1451982211yescharacteristic
881C2C22×#1451982411yescharacteristic
882C2C2×#1684059811yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#532C2
socleC23×C61C25
hypercenterC2×#532D61
hypocenterC61C2×#3554
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #21460284C2direct (N × H)
2. C2×#16840507C2semidirect
3. C2×#16840498C2semidirect
4. C2×#16840495C2semidirect
5. C2×#16840487C2semidirect
6. C2×#16840471C2semidirect
7. C2×#16840432C2semidirect
8. C2×#16840427C2semidirect
9. C2×#16840419C2semidirect
10. C2×#16840411C2semidirect
11. C2×#16840381C2semidirect
12. C2×#16840379C2semidirect
13. C2×#16840365C2semidirect
14. C2×#16840354C2semidirect
15. C2×#16840332C2semidirect
16. C2×#16840319C2semidirect
17. C2×#16840296C2semidirect
18. C2×C61×#532C2semidirect
21. #16840507C22semidirect
22. #16840498C22semidirect
23. #16840495C22semidirect
24. #16840487C22semidirect
25. #16840471C22semidirect
26. #16840432C22semidirect
27. #16840427C22semidirect
28. #16840419C22semidirect
29. #16840411C22semidirect
30. #16840381C22semidirect
31. #16840379C22semidirect
32. #16840365C22semidirect
33. #16840354C22semidirect
34. #16840332C22semidirect
35. #16840319C22semidirect
41. #16840296C22semidirect
92. C61×#532C22semidirect
451. C2×#532D61semidirect
455. C2×C61#3554semidirect
478. #532C2×D61semidirect
542. C61C2×#3554semidirect
879. C2#21460284direct (N × H)

Maximal subgroups

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

subgroupindex
#214602842
C2×#168405072
C2×#168404982
C2×#168404952
C2×#168404872
C2×#168404712
C2×#168404322
C2×#168404272
C2×#168404192
C2×#168404112
C2×#168403812
C2×#168403792
C2×#168403652
C2×#168403542
C2×#168403322
C2×#168403192
C2×#168402962
C2×C61×#5322
C2×#355461