Finite Group Databasebeta

← C2×#21460232 #30587824

Subgroups — C2×#21460232 #30587824

Order 15616.

7074 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#21460232C2132yesmaximal, direct product factor
2C2×#16840514C214yesmaximal, complemented
3C2×#16840494C212yesmaximal, complemented
4C2×Q8×Dic122C212yesmaximal, complemented
5C2×#16840486C211yesmaximal, characteristic, complemented
6C2×#16840480C212yesmaximal, complemented
7C2×Q8×D244C211yesmaximal, characteristic, complemented
8C2×D4×Dic122C211yesmaximal, characteristic, complemented
9C2×#16840425C212yesmaximal, complemented
10C2×#16840384C212yesmaximal, complemented
11C2×#16840381C212yesmaximal, complemented
12C2×#16840378C214yesmaximal, complemented
13C2×#16840338C212yesmaximal, complemented
14C2×#16840335C212yesmaximal, complemented
15C2×#16840317C211yesmaximal, characteristic, complemented
16C2×#16840316C211yesmaximal, characteristic, complemented
17C2×#16840309C211yesmaximal, characteristic
18C2×C61×#556C211yesmaximal, characteristic, complemented
19C22×#11758222C2212yes—
20C23×Dic122C2212yes—
21C22×Q8×D61C2212yes—
22#16840514C22164yescomplemented
23#16840494C22132yescomplemented
24Q8×Dic122C22132yescomplemented
25#16840486C22116yescomplemented
26#16840480C22132yescomplemented
27Q8×D244C22116yescomplemented
28D4×Dic122C22116yescomplemented
29#16840425C22132yescomplemented
30#16840384C22132yescomplemented
31#16840381C22132yescomplemented
32#16840378C22164yescomplemented
33#16840338C22132yescomplemented
34#16840335C22132yescomplemented
35#16840317C22116yescomplemented
36#16840316C22116yescomplemented
37#16840309C22116yes—
38C2×#14519777C2211yescharacteristic
39C2×#14519777C2212yes—
40C2×#14519777C2214yes—
41C2×#14519776C2214yes—
42C2×#14519776C2212yes—
43C2×#14519776C2211yescharacteristic
44C2×#14519776C2211yescharacteristic
45C2×#14519776C2214yes—
46C2×#14519775C2211yescharacteristic
47C2×#14519773C2211yescharacteristic
48C2×#14519772C2214yes—
49C2×#14519771C2214yes—
50C2×#14519770C2214yes—
51C2×#14519768C2212yes—
52C2×#14519767C2212yes—
53C2×#14519766C2212yes—
54C2×#14519765C2214yes—
55C2×#14519763C2212yes—
56C2×#14519763C2214yes—
57C2×#14519763C2214yes—
58C2×#14519762C2214yes—
59C2×#14519761C2214yes—
60C2×#14519761C2214yes—
61C2×#14519759C2214yes—
62C2×#14519757C2212yes—
63C2×#14519757C2212yes—
64C2×#14519757C2214yes—
65C2×#14519757C2211yescharacteristic
66C2×#14519757C2212yes—
67C2×#14519756C2212yes—
68C2×#14519755C2214yes—
69C2×#14519755C2212yes—
70C2×#14519754C2214yes—
71C2×#14519754C2214yes—
72C2×#14519753C2211yescharacteristic
73C2×#14519753C2212yes—
74C2×#14519752C2211yescharacteristic
75C2×#14519750C2212yes—
76C2×#14519748C2211yescharacteristic
77C2×Q8×Dic61C2212yes—
78C2×Q8×Dic61C2212yes—
79C2×C4×Dic122C2211yescharacteristic
80C2×C4×Dic122C2212yes—
81C2×C4×Dic122C2214yes—
82C2×#14519742C2212yes—
83C2×C4×D244C2211yescharacteristic
84C2×C4×D244C2212yes—
85C2×D4×Dic61C2212yes—
86C2×C4×C22⋊D61C2212yes—
87C2×#14519737C2214yes—
88C2×#14519735C2212yes—
89C2×#14519735C2212yes—
90C2×#14519734C2212yes—
91C2×C42×D61C2211yescharacteristic
92C61×#556C22116yescomplemented
93C2×C4⋊Q8×C61C2211yescharacteristic
94C2×#126×C61C2214yes—
95C2×#124×C61C2212yes—
96C2×C22⋊Q8×C61C2212yes—
97C2×C4×Q8×C61C2211yescharacteristic
98C2×C4×Q8×C61C2212yes—
99C2×C4×D4×C61C2211yescharacteristic
100C2×#117×C61C2212yes—
101C2×#11758222—48no—
102C2×#11758222C23116yes—
103C22×Dic122—48no—
104C22×Dic122C2312yes—
105C22×Dic122C2312yes—
106C22×Dic122C2311yescharacteristic
107C22×Dic122C2314yes—
108C22×Dic122C2314yes—
109C22×Dic122C2312yes—
110C22×Dic122C23116yes—
111C2×Q8×D61—48no—
112C2×Q8×D61C23116yes—
113C22×D244C2311yescharacteristic
114C22×D244C2312yes—
115C22×C22⋊D61C2312yes—
116C22×C22⋊D61C2312yes—
117C22×C22⋊D61C2312yes—
118C23×Dic61C2314yes—
119C22×C4×D61C2311yescharacteristic
120C22×C4×D61C2311yescharacteristic
121C22×C4×D61C2311yescharacteristic
122C22×C4×D61C2312yes—
123C22×C4×D61C2314yes—
124#14519777C23132yes—
125#14519777C23116yes—
126#14519777C2318yes—
127#14519776C2318yes—
128#14519776C2318yes—
129#14519776C23132yes—
130#14519776C23132yes—
131#14519776C23116yes—
132#14519775C2318yes—
133#14519773C2318yes—
134#14519772C23132yes—
135#14519771C23132yes—
136#14519770C23132yes—
137#14519768C23116yes—
138#14519767C23116yes—
139#14519766C23116yes—
140#14519765C23132yes—
141#14519763C23132yes—
142#14519763C23116yes—
143#14519763C23132yes—
144#14519762C23132yes—
145#14519761C23132yes—
146#14519761C23132yes—
147#14519759C23132yes—
148#14519757C23116yes—
149#14519757C23116yes—
150#14519757C23132yes—
151#14519757C2318yes—
152#14519757C23116yes—
153#14519756C23116yes—
154#14519755C23132yes—
155#14519755C23116yes—
156#14519754C23132yes—
157#14519754C23132yes—
158#14519753C2318yes—
159#14519753C23116yes—
160#14519752C2318yes—
161#14519750C23116yes—
162#14519748C2318yes—
163Q8×Dic61C23116yes—
164Q8×Dic61C23116yes—
165C4×Dic122C23132yes—
166C4×Dic122C2318yes—
167C4×Dic122C23116yes—
168#14519742C23116yes—
169C4×D244C2318yes—
170C4×D244C23116yes—
171D4×Dic61C23116yes—
172C4×C22⋊D61C23116yes—
173#14519737C23132yes—
174#14519735C23116yes—
175#14519735C23116yes—
176#14519734C23116yes—
177C2×C4⋊Dic61C2311yescharacteristic
178C2×C4⋊Dic61C2312yes—
179C2×C4⋊Dic61C2312yes—
180C2×C4⋊Dic61C2311yescharacteristic
181C2×C4⋊Dic61C2314yes—
182C2×C4⋊Dic61C2312yes—
183C2×C4⋊Dic61C2314yes—
184C2×C4⋊Dic61C2314yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2312yes—
188C2×#11758196C2312yes—
189C2×#11758196C2314yes—
190C2×#11758196C2312yes—
191C2×#11758196C2312yes—
192C2×#11758196C2314yes—
193C2×C22⋊Dic61C2312yes—
194C2×C22⋊Dic61C2314yes—
195C2×#11758198C2312yes—
196C2×#11758198C2312yes—
197C2×#11758198C2314yes—
198C2×#11758198C2314yes—
199C2×#11758198C2314yes—
200C2×#11758198C2312yes—
201C2×#11758198C2312yes—
202C2×#11758198C2314yes—
203C2×C4×Dic61C2311yescharacteristic
204C2×C4×Dic61C2311yescharacteristic
205C2×C4×Dic61C2311yescharacteristic
206C2×C4×Dic61C2312yes—
207C2×C4×Dic61C2314yes—
208C2×C4×Dic61C2314yes—
209C42×D61C2318yes—
210C22×Q8×C61C2312yes—
211C22×Q8×C61C2311yescharacteristic
212C22×D4×C61C2311yescharacteristic
213C23×C4×C61C2312yes—
214C4⋊Q8×C61C2318yes—
215#126×C61C23132yes—
216#124×C61C23116yes—
217C22⋊Q8×C61C23116yes—
218C4×Q8×C61C23116yes—
219C4×Q8×C61C2318yes—
220C4×D4×C61C2318yes—
221#117×C61C23116yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C2312yes—
224C2×C4⋊C4×C61C2311yescharacteristic
225C2×C4⋊C4×C61C2312yes—
226C2×C4⋊C4×C61C2314yes—
227C2×C4⋊C4×C61C2311yescharacteristic
228C2×C22⋊C4×C61C2314yes—
229C2×C22⋊C4×C61C2312yes—
230C2×C22⋊C4×C61C2314yes—
231C2×C42×C61C2311yescharacteristic
232C2×C42×C61C2312yes—
233C2×C42×C61C2314yes—
234C24×C61C2412yes—
235C23×D61C2412yes—
236C23×D61C2411yescharacteristic
237C2×Q8×C61—24no—
238C2×Q8×C61—28no—
239C2×Q8×C61C2414yes—
240C2×Q8×C61C2418yes—
241C2×D4×C61—24no—
242C2×D4×C61C2414yes—
243C22×C4×C61—28no—
244C22×C4×C61C2412yes—
245C22×C4×C61C2411yescharacteristic
246C22×C4×C61C2412yes—
247C22×C4×C61C2418yes—
248C22×C4×C61C2412yes—
249C22×C4×C61C2414yes—
250C22×C4×C61C2411yescharacteristic
251C22×C4×C61C2411yescharacteristic
252C2×C22⋊D61—28no—
253C2×C22⋊D61—44no—
254C2×C22⋊D61—44no—
255C2×C22⋊D61C2418yes—
256C2×C22⋊D61C2418yes—
257C2×C22⋊D61C2418yes—
258C22×Dic61—48no—
259C22×Dic61C2414yes—
260C22×Dic61C2411yescharacteristic
261C22×Dic61C2412yes—
262C22×Dic61C2411yescharacteristic
263C22×Dic61C2412yes—
264C22×Dic61C2412yes—
265C22×Dic61C24116yes—
266C22×Dic61C2411yescharacteristic
267Q8×D61—432no—
268#11758222—432no—
269C2×D244—24no—
270C2×D244—44no—
271C2×D244C2414yes—
272C2×D244C2418yes—
273C2×C4×D61—28no—
274C2×C4×D61—24no—
275C2×C4×D61—24no—
276C2×C4×D61—24no—
277C2×C4×D61—48no—
278C2×C4×D61C2418yes—
279C2×C4×D61C2414yes—
280C2×C4×D61C2414yes—
281C2×C4×D61C2414yes—
282C2×C4×D61C24116yes—
283C2×Dic122—28no—
284C2×Dic122—24no—
285C2×Dic122—28no—
286C2×Dic122—432no—
287C2×Dic122—48no—
288C2×Dic122—48no—
289C2×Dic122—44no—
290C2×Dic122C2418yes—
291C2×Dic122C2414yes—
292C2×Dic122C2418yes—
293C2×Dic122C24116yes—
294C2×Dic122C24116yes—
295C2×Dic122C2418yes—
296C4⋊C4×C61C2414yes—
297C4⋊C4×C61C2418yes—
298C4⋊C4×C61C2414yes—
299C4⋊C4×C61C24116yes—
300C4⋊C4×C61C2418yes—
301C4⋊C4×C61C2418yes—
302C22⋊C4×C61C24116yes—
303C22⋊C4×C61C2418yes—
304C22⋊C4×C61C24116yes—
305C42×C61C24116yes—
306C42×C61C2414yes—
307C42×C61C2418yes—
308C22⋊Dic61C2418yes—
309C22⋊Dic61C24116yes—
310#11758198C2418yes—
311#11758198C2418yes—
312#11758198C24116yes—
313#11758198C24116yes—
314#11758198C24116yes—
315#11758198C2418yes—
316#11758198C2418yes—
317#11758198C24116yes—
318C4⋊Dic61C2414yes—
319C4⋊Dic61C2418yes—
320C4⋊Dic61C2418yes—
321C4⋊Dic61C2414yes—
322C4⋊Dic61C24116yes—
323C4⋊Dic61C2418yes—
324C4⋊Dic61C24116yes—
325C4⋊Dic61C24116yes—
326#11758196C2418yes—
327#11758196C2418yes—
328#11758196C2418yes—
329#11758196C2418yes—
330#11758196C24116yes—
331#11758196C2418yes—
332#11758196C2418yes—
333#11758196C24116yes—
334C4×Dic61C2414yes—
335C4×Dic61C2414yes—
336C4×Dic61C2414yes—
337C4×Dic61C2418yes—
338C4×Dic61C24116yes—
339C4×Dic61C24116yes—
340C23×C61—24no—
341C23×C61—24no—
342C23×C61—24no—
343C23×C61C2514yes—
344C23×C61C2511yescharacteristic
345C22×D61—24no—
346C22×D61—22no—
347C22×D61—22no—
348C22×D61—22no—
349C22×D61—24no—
350C22×D61—24no—
351C22×D61C2514yes—
352C22×D61C2512yes—
353Q8×C61—28no—
354Q8×C61—216no—
355D4×C61—28no—
356C2×C4×C61—24no—
357C2×C4×C61—24no—
358C2×C4×C61—24no—
359C2×C4×C61—22no—
360C2×C4×C61—28no—
361C2×C4×C61—216no—
362C2×C4×C61H(5,𝔽2)14yes—
363C2×C4×C612−1+414yes—
364C2×C4×C61C2518yes—
365C2×C4×C61C2512yes—
366C2×C4×C61C2514yes—
367C2×C4×C61C2514yes—
368C2×C4×C61C2514yes—
369C2×C4×C61C2512yes—
370C2×C4×C61C2512yes—
371C22⋊D61—216no—
372C22⋊D61—48no—
373C22⋊D61—48no—
374C2×Dic61—28no—
375C2×Dic61—24no—
376C2×Dic61—24no—
377C2×Dic61—22no—
378C2×Dic61—24no—
379C2×Dic61—22no—
380C2×Dic61—416no—
381C2×Dic612−1+414yes—
382C2×Dic61C2514yes—
383C2×Dic61C2512yes—
384C2×Dic61C2512yes—
385C2×Dic61C2514yes—
386C2×Dic61C2514yes—
387C2×Dic61C2518yes—
388C2×Dic61C2512yes—
389D244—28no—
390D244—48no—
391C4×D61—28no—
392C4×D61—216no—
393C4×D61—28no—
394C4×D61—28no—
395C4×D61—416no—
396Dic122—28no—
397Dic122—216no—
398Dic122—216no—
399Dic122—416no—
400Dic122—48no—
401Dic122—416no—
402C2×#3550—611nomaximal, Sylow
403C22×C61—24no—
404C22×C61—24no—
405C22×C61—24no—
406C22×C61—48no—
407C22×C61C2×H(5,𝔽2)12yes—
408C22×C61C2×2−1+412yes—
409C22×C61C2×2−1+412yes—
410C22×C61C2611yescharacteristic
411C2×D61—24no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—24no—
416C2×D61—24no—
417C2×D61—48no—
418C2×D61—44no—
419C4×C61—24no—
420C4×C61—24no—
421C4×C61—24no—
422C4×C61—22no—
423C4×C61—28no—
424C4×C61C2×H(5,𝔽2)14yes—
425C4×C61C2×2−1+414yes—
426Dic61—28no—
427Dic61—24no—
428Dic61—24no—
429Dic61—22no—
430Dic61—24no—
431Dic61—22no—
432Dic61C2×2−1+414yes—
433#3550—6132no—
434C2×#563—614no—
435C2×#559—612no—
436C2×Q82—612no—
437C2×#556—611no—
438C2×#556—612no—
439C2×#556D6111yescharacteristic, complemented
440C2×D4×Q8—612no—
441C2×D4×Q8—611no—
442C2×D4×Q8—611no—
443C2×#542—614no—
444C2×#542—612no—
445C2×#542—612no—
446C2×#536—612no—
447C2×#536—612no—
448C2×#533—611no—
449C2×#533—611no—
450C2×#532—611no—
451C2×C61—44no—
452C2×C61#355014yescomplemented
453C2×C61C22×H(5,𝔽2)11yescharacteristic
454C2×C61C22×2−1+411yescharacteristic
455C2×C61C22×2−1+411yescharacteristic
456D61—44no—
457D61—42no—
458C22×#41—612no—
459C23×Q8—612no—
460C23×Q8—612no—
461#563—6164no—
462#559—6132no—
463Q82—6132no—
464#556—6116no—
465#556—6132no—
466#556C2×D61116yescomplemented
467D4×Q8—6132no—
468D4×Q8—6116no—
469D4×Q8—6116no—
470#542—6164no—
471#542—6132no—
472#542—6132no—
473#536—6132no—
474#536—6132no—
475#533—6116no—
476#533—6116no—
477#532—6116no—
478C2×C4⋊Q8—611no—
479C2×C4⋊Q8—611no—
480C2×C4⋊Q8—611no—
481C2×C4⋊Q8—614no—
482C2×C4⋊Q8—614no—
483C2×C4⋊Q8—612no—
484C2×C4⋊Q8—611no—
485C2×C4⋊Q8—614no—
486C2×C4⋊Q8—612no—
487C2×C4⋊Q8C2×D6111yescharacteristic
488C2×#127—611no—
489C2×#126—614no—
490C2×#126—614no—
491C2×#126—614no—
492C2×#126C2×D6114yes—
493C2×#125—612no—
494C2×#125—612no—
495C2×#124—612no—
496C2×#124—612no—
497C2×#124—614no—
498C2×#124—614no—
499C2×#124—614no—
500C2×#124C2×D6112yes—
501C2×#123—614no—
502C2×#123—614no—
503C2×#123—614no—
504C2×#123—614no—
505C2×C22⋊Q8—611no—
506C2×C22⋊Q8—612no—
507C2×C22⋊Q8—612no—
508C2×C22⋊Q8—612no—
509C2×C22⋊Q8—614no—
510C2×C22⋊Q8—612no—
511C2×C22⋊Q8—611no—
512C2×C22⋊Q8—612no—
513C2×C22⋊Q8—612no—
514C2×C22⋊Q8—614no—
515C2×C22⋊Q8—614no—
516C2×C22⋊Q8—614no—
517C2×C22⋊Q8C2×D6112yes—
518C2×#121—611no—
519C2×#121—611no—
520C2×#121—612no—
521C2×C4×Q8—612no—
522C2×C4×Q8—612no—
523C2×C4×Q8—612no—
524C2×C4×Q8—611no—
525C2×C4×Q8—612no—
526C2×C4×Q8—614no—
527C2×C4×Q8C2×D6111yescharacteristic
528C2×C4×Q8C2×D6112yes—
529C2×C4×D4—612no—
530C2×C4×D4—612no—
531C2×C4×D4—614no—
532C2×C4×D4—611no—
533C2×C4×D4—612no—
534C2×C4×D4C2×D6111yescharacteristic
535C2×#117—612no—
536C2×#117—612no—
537C2×#117—612no—
538C2×#117C2×D6112yes—
539C22×C42—611no—
540C61C2×#355011yescharacteristic, complemented, Sylow
541C2×#41—6116no—
542C2×#41—2448no—
543C22×Q8—6116no—
544C22×Q8—612no—
545C22×Q8—612no—
546C22×Q8—611no—
547C22×Q8—614no—
548C22×Q8—614no—
549C22×Q8—612no—
550C22×Q8—6116no—
551C22×Q8—2448no—
552C22×Q8—2448no—
553C22×Q8C22×D6112yes—
554C22×Q8C22×D6111yescharacteristic
555C22×D4—612no—
556C22×D4—612no—
557C22×D4—612no—
558C22×D4—611no—
559C22×D4—612no—
560C22×D4C22×D6111yescharacteristic
561C23×C4—614no—
562C23×C4—611no—
563C23×C4—611no—
564C23×C4—612no—
565C23×C4—611no—
566C23×C4—614no—
567C23×C4C22×D6112yes—
568C4⋊Q8—618no—
569C4⋊Q8—618no—
570C4⋊Q8—618no—
571C4⋊Q8—6132no—
572C4⋊Q8—6132no—
573C4⋊Q8—6116no—
574C4⋊Q8—618no—
575C4⋊Q8—6132no—
576C4⋊Q8—6116no—
577C4⋊Q8C22×D6118yes—
578#127—618no—
579#126—6132no—
580#126—6132no—
581#126—6132no—
582#126C22×D61132yes—
583#125—6116no—
584#125—6116no—
585#124—6116no—
586#124—6116no—
587#124—6132no—
588#124—6132no—
589#124—6132no—
590#124C22×D61116yes—
591#123—6132no—
592#123—6132no—
593#123—6132no—
594#123—6132no—
595C22⋊Q8—618no—
596C22⋊Q8—6116no—
597C22⋊Q8—6116no—
598C22⋊Q8—6116no—
599C22⋊Q8—618no—
600C22⋊Q8—6116no—
601C22⋊Q8—6116no—
602C22⋊Q8—6116no—
603C22⋊Q8—6132no—
604C22⋊Q8—6132no—
605C22⋊Q8—6132no—
606C22⋊Q8—6132no—
607C22⋊Q8C22×D61116yes—
608#121—618no—
609#121—618no—
610#121—6116no—
611C4×Q8—6116no—
612C4×Q8—6116no—
613C4×Q8—6116no—
614C4×Q8—618no—
615C4×Q8—6116no—
616C4×Q8—6132no—
617C4×Q8C22×D6118yes—
618C4×Q8C22×D61116yes—
619C4×D4—6116no—
620C4×D4—6116no—
621C4×D4—6132no—
622C4×D4—618no—
623C4×D4—6116no—
624C4×D4C22×D6118yes—
625#117—6116no—
626#117—6116no—
627#117—6116no—
628#117C22×D61116yes—
629C2×C4⋊C4—611no—
630C2×C4⋊C4—612no—
631C2×C4⋊C4—612no—
632C2×C4⋊C4—612no—
633C2×C4⋊C4—612no—
634C2×C4⋊C4—612no—
635C2×C4⋊C4—612no—
636C2×C4⋊C4—611no—
637C2×C4⋊C4—612no—
638C2×C4⋊C4—614no—
639C2×C4⋊C4—614no—
640C2×C4⋊C4—614no—
641C2×C4⋊C4—614no—
642C2×C4⋊C4—612no—
643C2×C4⋊C4—614no—
644C2×C4⋊C4—612no—
645C2×C4⋊C4C22×D6112yes—
646C2×C4⋊C4C22×D6112yes—
647C2×C4⋊C4C22×D6111yescharacteristic
648C2×C4⋊C4C22×D6111yescharacteristic
649C2×C4⋊C4C22×D6112yes—
650C2×C4⋊C4C22×D6114yes—
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—612no—
658C2×C22⋊C4—612no—
659C2×C22⋊C4—614no—
660C2×C22⋊C4—614no—
661C2×C22⋊C4C22×D6114yes—
662C2×C22⋊C4C22×D6114yes—
663C2×C22⋊C4C22×D6112yes—
664C2×C42—614no—
665C2×C42—612no—
666C2×C42—614no—
667C2×C42—611no—
668C2×C42—611no—
669C2×C42—611no—
670C2×C42—618no—
671C2×C42C22×D6112yes—
672C2×C42C22×D6114yes—
673C2×C42C22×D6111yescharacteristic
674C24—612no—
675C24—611no—
676C24C23×D6112yes—
677#41—24432no—
678C2×Q8—24no—
679C2×Q8—28no—
680C2×Q8—618no—
681C2×Q8—618no—
682C2×Q8—614no—
683C2×Q8—6116no—
684C2×Q8—6116no—
685C2×Q8—618no—
686C2×Q8—1228no—
687C2×Q8—1228no—
688C2×Q8—1224no—
689C2×Q8—2448no—
690C2×Q8—2448no—
691C2×Q8—2444no—
692C2×Q8—24432no—
693C2×Q8—24432no—
694C2×Q8C23×D6118yes—
695C2×Q8C23×D6114yes—
696C2×D4—24no—
697C2×D4—618no—
698C2×D4—618no—
699C2×D4—618no—
700C2×D4—614no—
701C2×D4—618no—
702C2×D4—1228no—
703C2×D4—1224no—
704C2×D4—2444no—
705C2×D4—2444no—
706C2×D4—2444no—
707C2×D4C23×D6114yes—
708C22×C4—28no—
709C22×C4—611no—
710C22×C4—612no—
711C22×C4—611no—
712C22×C4—612no—
713C22×C4—611no—
714C22×C4—614no—
715C22×C4—612no—
716C22×C4—6116no—
717C22×C4—614no—
718C22×C4—614no—
719C22×C4—614no—
720C22×C4—618no—
721C22×C4—6116no—
722C22×C4—1224no—
723C22×C4—1228no—
724C22×C4—1224no—
725C22×C4—1224no—
726C22×C4—2448no—
727C22×C4—2448no—
728C22×C4C23×D6118yes—
729C22×C4C23×D6114yes—
730C22×C4C23×D6111yescharacteristic
731C22×C4C23×D6112yes—
732C22×C4C23×D6112yes—
733C22×C4C23×D6112yes—
734C22×C4C23×D6111yescharacteristic
735C22×C4C23×D6111yescharacteristic
736C4⋊C4—618no—
737C4⋊C4—618no—
738C4⋊C4—618no—
739C4⋊C4—618no—
740C4⋊C4—618no—
741C4⋊C4—6116no—
742C4⋊C4—6116no—
743C4⋊C4—618no—
744C4⋊C4—614no—
745C4⋊C4—618no—
746C4⋊C4—618no—
747C4⋊C4—614no—
748C4⋊C4—6116no—
749C4⋊C4—6116no—
750C4⋊C4—6116no—
751C4⋊C4—618no—
752C4⋊C4C23×D6118yes—
753C4⋊C4C23×D6118yes—
754C4⋊C4C23×D6114yes—
755C4⋊C4C23×D6114yes—
756C4⋊C4C23×D6118yes—
757C4⋊C4C23×D61116yes—
758C22⋊C4—618no—
759C22⋊C4—6116no—
760C22⋊C4—618no—
761C22⋊C4—6116no—
762C22⋊C4—618no—
763C22⋊C4—6116no—
764C22⋊C4—618no—
765C22⋊C4—618no—
766C22⋊C4—6116no—
767C22⋊C4—6116no—
768C22⋊C4C23×D61116yes—
769C22⋊C4C23×D61116yes—
770C22⋊C4C23×D6118yes—
771C42—614no—
772C42—614no—
773C42—614no—
774C42—6116no—
775C42—618no—
776C42—6116no—
777C42C23×D6114yes—
778C42C23×D6118yes—
779C42C23×D61116yes—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—614no—
784C23—612no—
785C23—1224no—
786C23—1222no—
787C23—1222no—
788C23—1224no—
789C23—1222no—
790C23—1224no—
791C23C24×D6114yes—
792C23C24×D6111yescharacteristic
793Q8—28no—
794Q8—216no—
795Q8—12216no—
796Q8—1228no—
797Q8—12216no—
798Q8—24416no—
799Q8—24416no—
800Q8—2448no—
801D4—28no—
802D4—12216no—
803D4—1228no—
804D4—2448no—
805D4—2448no—
806D4—2448no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—216no—
813C2×C4—614no—
814C2×C4—612no—
815C2×C4—614no—
816C2×C4—612no—
817C2×C4—614no—
818C2×C4—612no—
819C2×C4—614no—
820C2×C4—618no—
821C2×C4—1228no—
822C2×C4—1222no—
823C2×C4—1224no—
824C2×C4—1228no—
825C2×C4—1224no—
826C2×C4—1224no—
827C2×C4—1222no—
828C2×C4—12216no—
829C2×C4—1228no—
830C2×C4—1228no—
831C2×C4—24416no—
832C2×C4—24416no—
833C2×C4#1451982314yes—
834C2×C4#1451982414yes—
835C2×C4C24×D6118yes—
836C2×C4C24×D6112yes—
837C2×C4C24×D6114yes—
838C2×C4C24×D6114yes—
839C2×C4C24×D6114yes—
840C2×C4C24×D6112yes—
841C2×C4C24×D6112yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—48no—
846C22—1224no—
847C22—1222no—
848C22—1222no—
849C22—1224no—
850C22—1222no—
851C22—1224no—
852C22—2448no—
853C22—2444no—
854C22C2×#1451982312yes—
855C222−1+4×D6112yes—
856C22C2×#1451982412yes—
857C22C25×D6111yescharacteristic
858C4—24no—
859C4—24no—
860C4—22no—
861C4—24no—
862C4—28no—
863C4—614no—
864C4—1222no—
865C4—1224no—
866C4—1228no—
867C4—1224no—
868C4—1224no—
869C4—1222no—
870C4C2×#1451982314yes—
871C4C2×#1451982414yes—
872C2—44no—
873C2—2444no—
874C2—2442no—
875C2#2146023214yesdirect product factor
876C2C22×#1451982311yescharacteristic
877C2C2×2−1+4×D6111yescharacteristic
878C2C22×#1451982411yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#556C2
socleC23×C61C25
prime radicalC2×#16840309C2
hypercenterC2×#556D61
hypocenterC61C2×#3550
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #21460232C2direct (N × H)
2. C2×#16840514C2semidirect
3. C2×#16840494C2semidirect
4. C2×Q8×Dic122C2semidirect
5. C2×#16840486C2semidirect
6. C2×#16840480C2semidirect
7. C2×Q8×D244C2semidirect
8. C2×D4×Dic122C2semidirect
9. C2×#16840425C2semidirect
10. C2×#16840384C2semidirect
11. C2×#16840381C2semidirect
12. C2×#16840378C2semidirect
13. C2×#16840338C2semidirect
14. C2×#16840335C2semidirect
15. C2×#16840317C2semidirect
16. C2×#16840316C2semidirect
18. C2×C61×#556C2semidirect
22. #16840514C22semidirect
23. #16840494C22semidirect
24. Q8×Dic122C22semidirect
25. #16840486C22semidirect
26. #16840480C22semidirect
27. Q8×D244C22semidirect
28. D4×Dic122C22semidirect
29. #16840425C22semidirect
30. #16840384C22semidirect
31. #16840381C22semidirect
32. #16840378C22semidirect
33. #16840338C22semidirect
34. #16840335C22semidirect
35. #16840317C22semidirect
36. #16840316C22semidirect
92. C61×#556C22semidirect
439. C2×#556D61semidirect
452. C2×C61#3550semidirect
466. #556C2×D61semidirect
540. C61C2×#3550semidirect
875. C2#21460232direct (N × H)

Maximal subgroups

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

subgroupindex
#214602322
C2×#168405142
C2×#168404942
C2×Q8×Dic1222
C2×#168404862
C2×#168404802
C2×Q8×D2442
C2×D4×Dic1222
C2×#168404252
C2×#168403842
C2×#168403812
C2×#168403782
C2×#168403382
C2×#168403352
C2×#168403172
C2×#168403162
C2×#168403092
C2×C61×#5562
C2×#355061