Finite Group Databasebeta

← C2×#21459722 #30588382

Subgroups — C2×#21459722 #30588382

Order 15616.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459722C2132yesmaximal, direct product factor
2C2×#16840480C212yesmaximal, complemented
3C2×#16840475C212yesmaximal, complemented
4C2×#16840467C212yesmaximal, complemented
5C2×#16840461C214yesmaximal, complemented
6C2×#16840421C214yesmaximal, complemented
7C2×#16840413C212yesmaximal, complemented
8C2×#16840384C212yesmaximal, complemented
9C2×#16840377C212yesmaximal, complemented
10C2×#16840343C211yesmaximal, characteristic, complemented
11C2×#16840340C211yesmaximal, characteristic, complemented
12C2×#16840316C212yesmaximal, complemented
13C2×#16840309C212yesmaximal, complemented
14C2×#16840308C211yesmaximal, characteristic, complemented
15C22×#14519776C211yesmaximal, characteristic, complemented
16C2×#16840242C211yesmaximal, characteristic, complemented
17C2×#16840230C211yesmaximal, characteristic, complemented
18C2×C61×#520C211yesmaximal, characteristic, complemented
19C22×#11758222C2211yescharacteristic
20C22×#11758222C2211yescharacteristic
21C22×#11758222C2214yes—
22C23×Dic122C2212yes—
23#16840480C22132yescomplemented
24#16840475C22132yescomplemented
25#16840467C22132yescomplemented
26#16840461C22164yescomplemented
27#16840421C22164yescomplemented
28#16840413C22132yescomplemented
29#16840384C22132yescomplemented
30#16840377C22132yescomplemented
31#16840343C22116yescomplemented
32#16840340C22116yescomplemented
33#16840316C22132yescomplemented
34#16840309C22132yescomplemented
35#16840308C22116yescomplemented
36C2×#14519776C2212yes—
37C2×#14519776C2212yes—
38C2×#14519776C2212yes—
39C2×#14519776C2212yes—
40C2×#14519776C22116yescomplemented
41C2×#14519775C2211yescharacteristic
42C2×#14519773C2211yescharacteristic
43C2×#14519771C2214yes—
44C2×#14519770C2214yes—
45C2×#14519767C2214yes—
46C2×#14519766C2211yescharacteristic
47C2×#14519765C2214yes—
48C2×#14519764C2211yescharacteristic
49C2×#14519763C2214yes—
50C2×#14519763C2214yes—
51C2×#14519762C2214yes—
52C2×#14519760C2214yes—
53C2×#14519757C2212yes—
54C2×#14519757C2212yes—
55C2×#14519756C2214yes—
56C2×#14519756C2212yes—
57C2×#14519755C2214yes—
58C2×#14519755C2214yes—
59C2×#14519753C2212yes—
60C2×#14519752C2212yes—
61C2×#14519752C2212yes—
62C2×#14519751C2212yes—
63C2×#14519751C2214yes—
64C2×#14519750C2214yes—
65C2×#14519749C2212yes—
66C2×#14519749C2214yes—
67C2×#14519749C2212yes—
68C2×#14519748C2212yes—
69#16840242C22116yescomplemented
70#16840230C22116yescomplemented
71C2×C4×Dic122C2212yes—
72C2×C4×Dic122C2214yes—
73C2×#14519742C2211yescharacteristic
74C2×#14519742C2211yescharacteristic
75C2×C4×D244C2212yes—
76C2×#14519739C2211yescharacteristic
77C2×#14519739C2211yescharacteristic
78C2×C4×C22⋊D61C2212yes—
79C2×C4×C22⋊D61C2214yes—
80C2×C4×C22⋊D61C2212yes—
81C2×#14519737C2212yes—
82C2×#14519737C2212yes—
83C2×#14519737C2214yes—
84C2×#14519735C2212yes—
85C2×#14519734C2212yes—
86C2×#14519734C2214yes—
87C22×C4⋊Dic61C2211yescharacteristic
88C22×#11758196C2212yes—
89C2×C4⋊C4×D61C2212yes—
90C22×C4×Dic61C2211yescharacteristic
91C2×C42×D61C2212yes—
92C22×#41×C61C2211yescharacteristic
93C61×#520C22116yescomplemented
94C2×C4×Q8×C61C2212yes—
95C2×C4×D4×C61C2214yes—
96C2×C4×D4×C61C2212yes—
97C2×#117×C61C2211yescharacteristic
98C2×#117×C61C2212yes—
99C22×C4⋊C4×C61C2212yes—
100C22×C4⋊C4×C61C2211yescharacteristic
101C2×#11758222—28no—
102C2×#11758222—28no—
103C2×#11758222—416no—
104C2×#11758222C2318yes—
105C2×#11758222C2318yes—
106C2×#11758222C23132yes—
107C22×Dic122—48no—
108C22×Dic122C2311yescharacteristic
109C22×Dic122C2311yescharacteristic
110C22×Dic122C2314yes—
111C22×Dic122C2314yes—
112C22×Dic122C23116yes—
113C22×D244C2311yescharacteristic
114C22×D244C2311yescharacteristic
115C22×D244C2314yes—
116C22×C22⋊D61C2312yes—
117C22×C22⋊D61C2312yes—
118C22×C22⋊D61C2312yes—
119C22×C22⋊D61C2312yes—
120C22×C22⋊D61C2314yes—
121C23×Dic61C2311yescharacteristic
122C23×Dic61C2311yescharacteristic
123C23×Dic61C2312yes—
124C22×C4×D61C2312yes—
125C22×C4×D61C2312yes—
126C22×C4×D61C2312yes—
127C22×C4×D61C2312yes—
128C22×C4×D61C2314yes—
129#14519776C23116yes—
130#14519776C23116yes—
131#14519776C23116yes—
132#14519776C23116yes—
133#14519775C2318yes—
134#14519773C2318yes—
135#14519771C23132yes—
136#14519770C23132yes—
137#14519767C23132yes—
138#14519766C2318yes—
139#14519765C23132yes—
140#14519764C2318yes—
141#14519763C23132yes—
142#14519763C23132yes—
143#14519762C23132yes—
144#14519760C23132yes—
145#14519757C23116yes—
146#14519757C23116yes—
147#14519756C23116yes—
148#14519756C23132yes—
149#14519755C23132yes—
150#14519755C23132yes—
151#14519753C23116yes—
152#14519752C23116yes—
153#14519752C23116yes—
154#14519751C23132yes—
155#14519751C23116yes—
156#14519750C23132yes—
157#14519749C23116yes—
158#14519749C23132yes—
159#14519749C23116yes—
160#14519748C23116yes—
161C4×Dic122C23132yes—
162C4×Dic122C23116yes—
163#14519742C2318yes—
164#14519742C2318yes—
165C4×D244C23116yes—
166#14519739C2318yes—
167#14519739C2318yes—
168C4×C22⋊D61C23132yes—
169C4×C22⋊D61C23116yes—
170C4×C22⋊D61C23116yes—
171#14519737C23116yes—
172#14519737C23132yes—
173#14519737C23116yes—
174#14519735C23116yes—
175#14519734C23132yes—
176#14519734C23116yes—
177C2×C4⋊Dic61C2312yes—
178C2×C4⋊Dic61C2312yes—
179C2×C4⋊Dic61C2318yes—
180C2×C4⋊Dic61C2314yes—
181C2×#11758196C23116yes—
182C2×#11758196C2314yes—
183C2×#11758196C2314yes—
184C2×#11758196C2314yes—
185C2×#11758196C2312yes—
186C2×#11758196C2312yes—
187C2×#11758196C2312yes—
188C2×#11758196C2312yes—
189C2×#11758196C2314yes—
190C4⋊C4×D61C23116yes—
191C2×C22⋊Dic61C2314yes—
192C2×C22⋊Dic61C2312yes—
193C2×C22⋊Dic61C2312yes—
194C2×#11758198C2312yes—
195C2×#11758198C2312yes—
196C2×#11758198C2314yes—
197C2×#11758198C2314yes—
198C2×#11758198C2314yes—
199C2×#11758198C2312yes—
200C2×#11758198C2312yes—
201C2×#11758198C2314yes—
202C2×C4×Dic61C2311yescharacteristic
203C2×C4×Dic61C2312yes—
204C2×C4×Dic61C2312yes—
205C2×C4×Dic61C2311yescharacteristic
206C2×C4×Dic61C2311yescharacteristic
207C2×C4×Dic61C2311yescharacteristic
208C2×C4×Dic61C2318yes—
209C2×C4×Dic61C2314yes—
210C42×D61C23116yes—
211C2×#41×C61—28no—
212C2×#41×C61C2318yes—
213C22×Q8×C61C2311yescharacteristic
214C22×D4×C61C2311yescharacteristic
215C22×D4×C61C2312yes—
216C23×C4×C61C2312yes—
217C23×C4×C61C2312yes—
218C23×C4×C61C2314yes—
219C23×C4×C61C2311yescharacteristic
220C4×Q8×C61C23116yes—
221C4×D4×C61C23132yes—
222C4×D4×C61C23116yes—
223#117×C61C23116yes—
224#117×C61C2318yes—
225C2×C4⋊C4×C61C2311yescharacteristic
226C2×C4⋊C4×C61C23116yes—
227C2×C4⋊C4×C61C2311yescharacteristic
228C2×C4⋊C4×C61C2312yes—
229C2×C4⋊C4×C61C2312yes—
230C2×C4⋊C4×C61C2314yes—
231C2×C4⋊C4×C61C2318yes—
232C2×C22⋊C4×C61C2312yes—
233C2×C22⋊C4×C61C2314yes—
234C2×C42×C61C2312yes—
235C2×C42×C61C2314yes—
236C24×C61C2412yes—
237C24×C61C2411yescharacteristic
238C23×D61C2412yes—
239C23×D61C2412yes—
240#41×C61—232no—
241C2×Q8×C61—24no—
242C2×Q8×C61C2414yes—
243C2×D4×C61—28no—
244C2×D4×C61—24no—
245C2×D4×C61C2414yes—
246C2×D4×C61C2418yes—
247C22×C4×C61—28no—
248C22×C4×C61—44no—
249C22×C4×C61—48no—
250C22×C4×C61#4118yescomplemented
251C22×C4×C61C2412yes—
252C22×C4×C61C2412yes—
253C22×C4×C61C2414yes—
254C22×C4×C61C2412yes—
255C22×C4×C61C2418yes—
256C22×C4×C61C2418yes—
257C22×C4×C61C24116yes—
258C22×C4×C61C2411yescharacteristic
259C22×C4×C61C2411yescharacteristic
260C22×C4×C61C2414yes—
261C2×C22⋊D61—28no—
262C2×C22⋊D61—28no—
263C2×C22⋊D61—28no—
264C2×C22⋊D61—28no—
265C2×C22⋊D61—48no—
266C2×C22⋊D61C2418yes—
267C2×C22⋊D61C2418yes—
268C2×C22⋊D61C2418yes—
269C2×C22⋊D61C2418yes—
270C2×C22⋊D61C24116yes—
271C22×Dic61—24no—
272C22×Dic61—24no—
273C22×Dic61—44no—
274C22×Dic61C2414yes—
275C22×Dic61C2412yes—
276C22×Dic61C2412yes—
277C22×Dic61C2411yescharacteristic
278C22×Dic61C2414yes—
279C22×Dic61C2411yescharacteristic
280C22×Dic61C2414yes—
281C22×Dic61C2418yes—
282C22×Dic61C2411yescharacteristic
283C22×Dic61C2411yescharacteristic
284#11758222—232no—
285#11758222—232no—
286#11758222—464no—
287C2×D244—24no—
288C2×D244—24no—
289C2×D244—48no—
290C2×D244C2414yes—
291C2×D244C2414yes—
292C2×D244C24116yes—
293C2×C4×D61—28no—
294C2×C4×D61—28no—
295C2×C4×D61—28no—
296C2×C4×D61—28no—
297C2×C4×D61—48no—
298C2×C4×D61C2418yes—
299C2×C4×D61C2418yes—
300C2×C4×D61C2418yes—
301C2×C4×D61C2418yes—
302C2×C4×D61C24116yes—
303C2×Dic122—24no—
304C2×Dic122—24no—
305C2×Dic122—216no—
306C2×Dic122—432no—
307C2×Dic122—48no—
308C2×Dic122C24116yes—
309C2×Dic122C2414yes—
310C2×Dic122C2414yes—
311C2×Dic122C24116yes—
312C4⋊C4×C61C2414yes—
313C4⋊C4×C61C2418yes—
314C4⋊C4×C61C2418yes—
315C4⋊C4×C61C24116yes—
316C4⋊C4×C61C2414yes—
317C22⋊C4×C61C2418yes—
318C22⋊C4×C61C24116yes—
319C42×C61C2418yes—
320C42×C61C24116yes—
321C22⋊Dic61C24116yes—
322C22⋊Dic61C2418yes—
323C22⋊Dic61C2418yes—
324#11758198C2418yes—
325#11758198C2418yes—
326#11758198C24116yes—
327#11758198C24116yes—
328#11758198C24116yes—
329#11758198C2418yes—
330#11758198C2418yes—
331#11758198C24116yes—
332C4⋊Dic61C2418yes—
333C4⋊Dic61C2418yes—
334C4⋊Dic61C24116yes—
335#11758196C24116yes—
336#11758196C24116yes—
337#11758196C24116yes—
338#11758196C2418yes—
339#11758196C2418yes—
340#11758196C2418yes—
341#11758196C2418yes—
342#11758196C24116yes—
343C4×Dic61C2414yes—
344C4×Dic61C2418yes—
345C4×Dic61C2418yes—
346C4×Dic61C2414yes—
347C4×Dic61C2414yes—
348C4×Dic61C2414yes—
349C4×Dic61C24116yes—
350C23×C61—22no—
351C23×C61—22no—
352C23×C61—24no—
353C23×C61—24no—
354C23×C61—24no—
355C23×C61C2×#4114yes—
356C23×C61C2514yes—
357C23×C61C2512yes—
358C23×C61C2511yescharacteristic
359C22×D61—24no—
360C22×D61—24no—
361C22×D61—24no—
362C22×D61—24no—
363C22×D61—24no—
364C22×D61—24no—
365C22×D61C2514yes—
366C22×D61C2514yes—
367Q8×C61—28no—
368D4×C61—216no—
369D4×C61—28no—
370C2×C4×C61—24no—
371C2×C4×C61—28no—
372C2×C4×C61—24no—
373C2×C4×C61—24no—
374C2×C4×C61—216no—
375C2×C4×C61—48no—
376C2×C4×C61—416no—
377C2×C4×C61C2×#4114yes—
378C2×C4×C61C2×#4114yes—
379C2×C4×C61C2×#41116yescomplemented
380C2×C4×C61C2514yes—
381C2×C4×C61C2514yes—
382C2×C4×C61C2514yes—
383C2×C4×C61C2518yes—
384C2×C4×C61C2512yes—
385C2×C4×C61C2512yes—
386C22⋊D61—216no—
387C22⋊D61—216no—
388C22⋊D61—216no—
389C22⋊D61—216no—
390C22⋊D61—416no—
391C2×Dic61—24no—
392C2×Dic61—24no—
393C2×Dic61—28no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—28no—
397C2×Dic61—28no—
398C2×Dic61—48no—
399C2×Dic61H(5,𝔽2)14yes—
400C2×Dic612−1+414yes—
401C2×Dic61C2512yes—
402C2×Dic61C2514yes—
403C2×Dic61C2514yes—
404C2×Dic61C2512yes—
405C2×Dic61C2518yes—
406C2×Dic61C2512yes—
407C2×Dic61C2512yes—
408D244—28no—
409D244—28no—
410D244—416no—
411C4×D61—216no—
412C4×D61—216no—
413C4×D61—216no—
414C4×D61—216no—
415C4×D61—416no—
416Dic122—28no—
417Dic122—28no—
418Dic122—232no—
419Dic122—416no—
420C2×#3511—611nomaximal, Sylow
421C22×C61—22no—
422C22×C61—22no—
423C22×C61—28no—
424C22×C61—24no—
425C22×C61—24no—
426C22×C61—24no—
427C22×C61—48no—
428C22×C61C22×#4114yes—
429C22×C61C22×#4112yes—
430C22×C61C2×H(5,𝔽2)12yes—
431C22×C61C2×2−1+412yes—
432C22×C61C2611yescharacteristic
433C2×D61—24no—
434C2×D61—24no—
435C2×D61—24no—
436C2×D61—24no—
437C2×D61—24no—
438C2×D61—24no—
439C2×D61—48no—
440C2×D61—48no—
441C4×C61—24no—
442C4×C61—28no—
443C4×C61—24no—
444C4×C61—24no—
445C4×C61C22×#4114yes—
446C4×C61C22×#4114yes—
447Dic61—24no—
448Dic61—24no—
449Dic61—28no—
450Dic61—22no—
451Dic61—22no—
452Dic61C2×H(5,𝔽2)14yes—
453Dic61C2×2−1+414yes—
454#3511—6132no—
455C2×#556—612no—
456C2×#555—612no—
457C2×#554—612no—
458C2×#553—614no—
459C2×#548—614no—
460C2×#547—612no—
461C2×#542—612no—
462C2×#542—612no—
463C2×#537—611no—
464C2×#537—611no—
465C2×#533—612no—
466C2×#532—611no—
467C2×#532—612no—
468C22×C4⋊Q8—611no—
469C2×#520—611no—
470C2×#520D6111yescharacteristic, complemented
471C2×C4×#41—611no—
472C2×C61—24no—
473C2×C61—44no—
474C2×C61#351114yescomplemented
475C2×C61C23×#4111yescharacteristic
476C2×C61C22×H(5,𝔽2)11yescharacteristic
477C2×C61C22×2−1+411yescharacteristic
478D61—44no—
479D61—44no—
480C22×#41—611no—
481C22×#41—611no—
482C22×#41—614no—
483C22×#41C2×D6111yescharacteristic
484C23×Q8—612no—
485#556—6132no—
486#555—6132no—
487#554—6132no—
488#553—6164no—
489#548—6164no—
490#547—6132no—
491#542—6132no—
492#542—6132no—
493#537—6116no—
494#537—6116no—
495#533—6132no—
496#532—6116no—
497#532—6132no—
498C2×C4⋊Q8—611no—
499C2×C4⋊Q8—612no—
500C2×C4⋊Q8—612no—
501C2×C4⋊Q8—612no—
502C2×C4⋊Q8—612no—
503C2×C4⋊Q8—6116no—
504C2×#127—611no—
505C2×#126—614no—
506C2×#126—614no—
507C2×#125—614no—
508C2×#124—611no—
509C2×#124—611no—
510C2×#124—614no—
511C2×#124—614no—
512C2×#124—614no—
513C2×#123—614no—
514C2×#123—614no—
515C2×C22⋊Q8—612no—
516C2×C22⋊Q8—612no—
517C2×C22⋊Q8—614no—
518C2×C22⋊Q8—614no—
519C2×C22⋊Q8—614no—
520C2×C22⋊Q8—612no—
521C2×C22⋊Q8—612no—
522C2×#121—612no—
523C2×#121—612no—
524C2×#121—612no—
525C2×#121—614no—
526C2×#121—612no—
527C2×#121—614no—
528C2×#121—612no—
529C2×#121—612no—
530C2×#121—614no—
531#520—6116no—
532#520C2×D61116yescomplemented
533C4×#41—6116no—
534C2×C4×Q8—611no—
535C2×C4×Q8—611no—
536C2×C4×Q8—612no—
537C2×C4×Q8—614no—
538C2×C4×Q8C2×D6112yes—
539C2×C4×D4—612no—
540C2×C4×D4—614no—
541C2×C4×D4—612no—
542C2×C4×D4—611no—
543C2×C4×D4—611no—
544C2×C4×D4—612no—
545C2×C4×D4—612no—
546C2×C4×D4—614no—
547C2×C4×D4—612no—
548C2×C4×D4C2×D6112yes—
549C2×C4×D4C2×D6114yes—
550C2×#117—612no—
551C2×#117—612no—
552C2×#117—614no—
553C2×#117C2×D6111yescharacteristic
554C2×#117C2×D6112yes—
555C22×C4⋊C4—612no—
556C22×C4⋊C4—611no—
557C22×C4⋊C4—612no—
558C22×C4⋊C4C2×D6111yescharacteristic
559C22×C4⋊C4C2×D6112yes—
560C22×C42—611no—
561C22×C42—612no—
562C61C2×#351111yescharacteristic, complemented, Sylow
563C2×#41—28no—
564C2×#41—618no—
565C2×#41—618no—
566C2×#41—6132no—
567C2×#41—1228no—
568C2×#41—1228no—
569C2×#41—24416no—
570C2×#41C22×D6118yes—
571C22×Q8—611no—
572C22×Q8—611no—
573C22×Q8—614no—
574C22×Q8—614no—
575C22×Q8—6116no—
576C22×Q8—2448no—
577C22×Q8C22×D6111yescharacteristic
578C22×D4—612no—
579C22×D4—612no—
580C22×D4—612no—
581C22×D4—612no—
582C22×D4—614no—
583C22×D4—611no—
584C22×D4—611no—
585C22×D4—614no—
586C22×D4C22×D6112yes—
587C22×D4C22×D6111yescharacteristic
588C23×C4—611no—
589C23×C4—611no—
590C23×C4—612no—
591C23×C4—612no—
592C23×C4—612no—
593C23×C4—612no—
594C23×C4—612no—
595C23×C4—614no—
596C23×C4C22×D6112yes—
597C23×C4C22×D6112yes—
598C23×C4C22×D6114yes—
599C23×C4C22×D6111yescharacteristic
600C4⋊Q8—618no—
601C4⋊Q8—6116no—
602C4⋊Q8—6116no—
603C4⋊Q8—6116no—
604C4⋊Q8—6116no—
605#127—618no—
606#126—6132no—
607#126—6132no—
608#125—6132no—
609#124—618no—
610#124—618no—
611#124—6132no—
612#124—6132no—
613#124—6132no—
614#123—6132no—
615#123—6132no—
616C22⋊Q8—6116no—
617C22⋊Q8—6116no—
618C22⋊Q8—6132no—
619C22⋊Q8—6116no—
620C22⋊Q8—6132no—
621C22⋊Q8—6116no—
622C22⋊Q8—6132no—
623#121—6116no—
624#121—6116no—
625#121—6116no—
626#121—6132no—
627#121—6116no—
628#121—6132no—
629#121—6116no—
630#121—6116no—
631#121—6132no—
632C4×Q8—618no—
633C4×Q8—618no—
634C4×Q8—6116no—
635C4×Q8—6132no—
636C4×Q8C22×D61116yes—
637C4×D4—6116no—
638C4×D4—6132no—
639C4×D4—6116no—
640C4×D4—618no—
641C4×D4—618no—
642C4×D4—6116no—
643C4×D4—6116no—
644C4×D4—6132no—
645C4×D4—6116no—
646C4×D4C22×D61116yes—
647C4×D4C22×D61132yes—
648#117—6116no—
649#117—6116no—
650#117—6132no—
651#117C22×D6118yes—
652#117C22×D61116yes—
653C2×C4⋊C4—612no—
654C2×C4⋊C4—614no—
655C2×C4⋊C4—612no—
656C2×C4⋊C4—614no—
657C2×C4⋊C4—618no—
658C2×C4⋊C4—614no—
659C2×C4⋊C4—6116no—
660C2×C4⋊C4—612no—
661C2×C4⋊C4—612no—
662C2×C4⋊C4—612no—
663C2×C4⋊C4—612no—
664C2×C4⋊C4—614no—
665C2×C4⋊C4—614no—
666C2×C4⋊C4—6116no—
667C2×C4⋊C4C22×D6111yescharacteristic
668C2×C4⋊C4C22×D6112yes—
669C2×C4⋊C4C22×D6112yes—
670C2×C4⋊C4C22×D6114yes—
671C2×C4⋊C4C22×D6118yes—
672C2×C4⋊C4C22×D61116yes—
673C2×C4⋊C4C22×D6111yescharacteristic
674C2×C22⋊C4—614no—
675C2×C22⋊C4—612no—
676C2×C22⋊C4—612no—
677C2×C22⋊C4—614no—
678C2×C22⋊C4—612no—
679C2×C22⋊C4—612no—
680C2×C22⋊C4—614no—
681C2×C22⋊C4—614no—
682C2×C22⋊C4—614no—
683C2×C22⋊C4—612no—
684C2×C22⋊C4—612no—
685C2×C22⋊C4C22×D6112yes—
686C2×C22⋊C4C22×D6114yes—
687C2×C42—614no—
688C2×C42—611no—
689C2×C42—612no—
690C2×C42—611no—
691C2×C42—611no—
692C2×C42—612no—
693C2×C42—618no—
694C2×C42—611no—
695C2×C42—6116no—
696C2×C42C22×D6112yes—
697C2×C42C22×D6114yes—
698C24—612no—
699C24—612no—
700C24C23×D6112yes—
701C24C23×D6111yescharacteristic
702#41—232no—
703#41—12232no—
704#41—12232no—
705#41—24464no—
706C2×Q8—24no—
707C2×Q8—614no—
708C2×Q8—614no—
709C2×Q8—6116no—
710C2×Q8—6116no—
711C2×Q8—12216no—
712C2×Q8—1224no—
713C2×Q8—1224no—
714C2×Q8—2448no—
715C2×Q8—24432no—
716C2×Q8C23×D6114yes—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—618no—
720C2×D4—618no—
721C2×D4—618no—
722C2×D4—618no—
723C2×D4—6116no—
724C2×D4—614no—
725C2×D4—614no—
726C2×D4—6116no—
727C2×D4—1228no—
728C2×D4—1228no—
729C2×D4—1228no—
730C2×D4—1228no—
731C2×D4—1224no—
732C2×D4—1224no—
733C2×D4—2448no—
734C2×D4—2448no—
735C2×D4C23×D6118yes—
736C2×D4C23×D6114yes—
737C22×C4—28no—
738C22×C4—44no—
739C22×C4—48no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—614no—
743C22×C4—614no—
744C22×C4—611no—
745C22×C4—611no—
746C22×C4—612no—
747C22×C4—612no—
748C22×C4—614no—
749C22×C4—618no—
750C22×C4—618no—
751C22×C4—618no—
752C22×C4—618no—
753C22×C4—618no—
754C22×C4—6116no—
755C22×C4—1228no—
756C22×C4—1228no—
757C22×C4—1224no—
758C22×C4—1224no—
759C22×C4—1228no—
760C22×C4—1228no—
761C22×C4—2448no—
762C22×C4—2444no—
763C22×C4#1175822218yescomplemented
764C22×C4C23×D6118yes—
765C22×C4C23×D6112yes—
766C22×C4C23×D6112yes—
767C22×C4C23×D6112yes—
768C22×C4C23×D6114yes—
769C22×C4C23×D6118yes—
770C22×C4C23×D61116yes—
771C22×C4C23×D6111yescharacteristic
772C22×C4C23×D6111yescharacteristic
773C22×C4C23×D6114yes—
774C4⋊C4—618no—
775C4⋊C4—6116no—
776C4⋊C4—6116no—
777C4⋊C4—6116no—
778C4⋊C4—618no—
779C4⋊C4—618no—
780C4⋊C4—618no—
781C4⋊C4—618no—
782C4⋊C4—618no—
783C4⋊C4—6116no—
784C4⋊C4—6116no—
785C4⋊C4C23×D6114yes—
786C4⋊C4C23×D6118yes—
787C4⋊C4C23×D6118yes—
788C4⋊C4C23×D61116yes—
789C4⋊C4C23×D6114yes—
790C22⋊C4—6116no—
791C22⋊C4—618no—
792C22⋊C4—618no—
793C22⋊C4—6116no—
794C22⋊C4—618no—
795C22⋊C4—618no—
796C22⋊C4—6116no—
797C22⋊C4—6116no—
798C22⋊C4—6116no—
799C22⋊C4—618no—
800C22⋊C4—618no—
801C22⋊C4C23×D6118yes—
802C22⋊C4C23×D61116yes—
803C42—614no—
804C42—614no—
805C42—618no—
806C42—614no—
807C42—614no—
808C42—618no—
809C42—6116no—
810C42C23×D6118yes—
811C42C23×D61116yes—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—614no—
818C23—614no—
819C23—1224no—
820C23—1224no—
821C23—1224no—
822C23—1224no—
823C23—1224no—
824C23—1224no—
825C23C2×#1175822214yes—
826C23C24×D6114yes—
827C23C24×D6112yes—
828C23C24×D6111yescharacteristic
829Q8—28no—
830Q8—12232no—
831Q8—1228no—
832Q8—1228no—
833Q8—24416no—
834D4—216no—
835D4—28no—
836D4—12216no—
837D4—12216no—
838D4—12216no—
839D4—12216no—
840D4—1228no—
841D4—1228no—
842D4—24416no—
843D4—24416no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—416no—
851C2×C4—614no—
852C2×C4—614no—
853C2×C4—612no—
854C2×C4—612no—
855C2×C4—612no—
856C2×C4—612no—
857C2×C4—614no—
858C2×C4—614no—
859C2×C4—618no—
860C2×C4—12216no—
861C2×C4—12216no—
862C2×C4—1228no—
863C2×C4—1228no—
864C2×C4—1224no—
865C2×C4—1224no—
866C2×C4—1222no—
867C2×C4—1228no—
868C2×C4—1222no—
869C2×C4—12216no—
870C2×C4—12216no—
871C2×C4—24416no—
872C2×C4—2448no—
873C2×C4C2×#1175822214yes—
874C2×C4C2×#1175822214yes—
875C2×C4C2×#11758222116yescomplemented
876C2×C4C24×D6114yes—
877C2×C4C24×D6114yes—
878C2×C4C24×D6114yes—
879C2×C4C24×D6118yes—
880C2×C4C24×D6112yes—
881C2×C4C24×D6112yes—
882C22—28no—
883C22—22no—
884C22—22no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—48no—
889C22—1224no—
890C22—1224no—
891C22—1224no—
892C22—1224no—
893C22—1224no—
894C22—1224no—
895C22—2448no—
896C22—2448no—
897C22C22×#1175822214yes—
898C22C22×#1175822212yes—
899C22H(5,𝔽2)×D6112yes—
900C222−1+4×D6112yes—
901C22C25×D6111yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—24no—
906C4—614no—
907C4—614no—
908C4—1224no—
909C4—1224no—
910C4—1222no—
911C4—1228no—
912C4—1222no—
913C4C22×#1175822214yes—
914C4C22×#1175822214yes—
915C2—24no—
916C2—44no—
917C2—2444no—
918C2—2444no—
919C2#2145972214yesdirect product factor
920C2C23×#1175822211yescharacteristic
921C2C2×H(5,𝔽2)×D6111yescharacteristic
922C2C2×2−1+4×D6111yescharacteristic
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#520C2
socleC23×C61C25
hypercenterC2×#520D61
hypocenterC61C2×#3511
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #21459722C2direct (N × H)
2. C2×#16840480C2semidirect
3. C2×#16840475C2semidirect
4. C2×#16840467C2semidirect
5. C2×#16840461C2semidirect
6. C2×#16840421C2semidirect
7. C2×#16840413C2semidirect
8. C2×#16840384C2semidirect
9. C2×#16840377C2semidirect
10. C2×#16840343C2semidirect
11. C2×#16840340C2semidirect
12. C2×#16840316C2semidirect
13. C2×#16840309C2semidirect
14. C2×#16840308C2semidirect
15. C22×#14519776C2semidirect
16. C2×#16840242C2semidirect
17. C2×#16840230C2semidirect
18. C2×C61×#520C2semidirect
23. #16840480C22semidirect
24. #16840475C22semidirect
25. #16840467C22semidirect
26. #16840461C22semidirect
27. #16840421C22semidirect
28. #16840413C22semidirect
29. #16840384C22semidirect
30. #16840377C22semidirect
31. #16840343C22semidirect
32. #16840340C22semidirect
33. #16840316C22semidirect
34. #16840309C22semidirect
35. #16840308C22semidirect
40. C2×#14519776C22semidirect
69. #16840242C22semidirect
70. #16840230C22semidirect
93. C61×#520C22semidirect
250. C22×C4×C61#41semidirect
379. C2×C4×C61C2×#41semidirect
470. C2×#520D61semidirect
474. C2×C61#3511semidirect
532. #520C2×D61semidirect
562. C61C2×#3511semidirect
763. C22×C4#11758222semidirect
875. C2×C4C2×#11758222semidirect
919. C2#21459722direct (N × H)

Maximal subgroups

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

subgroupindex
#214597222
C2×#168404802
C2×#168404752
C2×#168404672
C2×#168404612
C2×#168404212
C2×#168404132
C2×#168403842
C2×#168403772
C2×#168403432
C2×#168403402
C2×#168403162
C2×#168403092
C2×#168403082
C22×#145197762
C2×#168402422
C2×#168402302
C2×C61×#5202
C2×#351161