Finite Group Databasebeta

← C2×#20288627 #28292456

Subgroups — C2×#20288627 #28292456

Order 13568.

7758 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288627C2132yesmaximal, direct product factor
2C2×#16811345C212yesmaximal, complemented
3C2×#16811336C212yesmaximal, complemented
4C2×#16811329C212yesmaximal, complemented
5C2×#16811326C212yesmaximal, complemented
6C2×#16811317C212yesmaximal, complemented
7C2×#16811285C212yesmaximal, complemented
8C2×#16811283C212yesmaximal, complemented
9C2×#16811275C212yesmaximal, complemented
10C2×#16811246C212yesmaximal, complemented
11C2×#16811245C212yesmaximal, complemented
12C2×#16811203C212yesmaximal, complemented
13C2×#16811178C211yesmaximal, characteristic, complemented
14C2×#16811174C211yesmaximal, characteristic, complemented
15C2×#16811174C211yesmaximal, characteristic, complemented
16C2×#16811173C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
18C2×#16811105C212yesmaximal, complemented
19C2×C4×#11719945C211yesmaximal, characteristic, complemented
20C2×C53×#533C211yesmaximal, characteristic, complemented
21C22×#11719949C2212yes—
22C22×#11719949C2212yes—
23C22×#11719945C2211yescharacteristic
24C22×#11719945C2212yes—
25C22×Q8×D53C2212yes—
26#16811345C22132yescomplemented
27#16811336C22132yescomplemented
28#16811329C22132yescomplemented
29#16811326C22132yescomplemented
30#16811317C22132yescomplemented
31#16811285C22132yescomplemented
32#16811283C22132yescomplemented
33#16811275C22132yescomplemented
34#16811246C22132yescomplemented
35#16811245C22132yescomplemented
36#16811203C22132yescomplemented
37#16811178C22116yescomplemented
38#16811174C22116yescomplemented
39#16811174C22116yescomplemented
40#16811173C22116yescomplemented
41C2×#13133217C2211yescharacteristic
42C2×#13133216C2212yes—
43C2×#13133216C2212yes—
44C2×#13133215C2212yes—
45C4⋊Q8×D53C22116yescomplemented
46C2×#13133214C2211yescharacteristic
47C2×#13133212C2214yes—
48C2×#13133211C2214yes—
49C2×#13133208C2212yes—
50C2×#13133206C2212yes—
51C2×#13133206C2212yes—
52C2×#13133205C2212yes—
53C2×#13133205C2214yes—
54C2×#13133203C2214yes—
55C2×#13133202C2214yes—
56C2×#13133199C2214yes—
57C2×#13133197C2212yes—
58C2×#13133197C2214yes—
59C2×#13133195C2214yes—
60C2×#13133195C2214yes—
61C2×#13133193C2212yes—
62C2×#13133192C2212yes—
63C2×#13133192C2214yes—
64C2×#13133192C2212yes—
65C2×#13133192C2212yes—
66C2×#13133192C2212yes—
67C2×#13133191C2212yes—
68C2×#13133191C2212yes—
69C2×#13133190C2214yes—
70C2×#13133190C2214yes—
71#16811105C22132yescomplemented
72C4×#11719945C22116yescomplemented
73C2×Q8×Dic53C2212yes—
74C2×C4×Dic106C2211yescharacteristic
75C2×C4×Dic106C2211yescharacteristic
76C2×#13133182C2212yes—
77C2×C4×D212C2212yes—
78C2×C4×D212C2211yescharacteristic
79C2×C4×D212C2211yescharacteristic
80C2×C4×D212C2214yes—
81C2×C4×D212C2212yes—
82C2×#13133179C2212yes—
83C2×#13133179C2212yes—
84C2×#13133179C2214yes—
85C2×#13133179C2212yes—
86C2×#13133179C2212yes—
87C2×C4×C22⋊D53C2211yescharacteristic
88C2×C4×C22⋊D53C2211yescharacteristic
89C2×C4×C22⋊D53C2211yescharacteristic
90C2×C4×C22⋊D53C2211yescharacteristic
91C2×#13133176C2211yescharacteristic
92C2×#13133175C2212yes—
93C2×#13133174C2214yes—
94C2×#13133174C2211yescharacteristic
95C2×#13133174C2211yescharacteristic
96C2×C4⋊C4×D53C2212yes—
97C2×C4⋊C4×D53C2214yes—
98C2×C4⋊C4×D53C2212yes—
99C2×C42×D53C2211yescharacteristic
100C2×C42×D53C2211yescharacteristic
101C53×#533C22116yescomplemented
102C2×C4⋊Q8×C53C2211yescharacteristic
103C2×C4⋊Q8×C53C2211yescharacteristic
104C2×#125×C53C2212yes—
105C2×C22⋊Q8×C53C2212yes—
106C2×C22⋊Q8×C53C2212yes—
107C2×C4×Q8×C53C2212yes—
108C2×C4×Q8×C53C2212yes—
109C2×#117×C53C2212yes—
110C22×C42×C53C2211yescharacteristic
111C2×#11719949—216no—
112C2×#11719949—48no—
113C2×#11719949C23116yes—
114C2×#11719949C23116yes—
115C2×#11719945—28no—
116C2×#11719945—48no—
117C2×#11719945C2318yes—
118C2×#11719945C23116yes—
119C22×Dic106C2312yes—
120C22×Dic106C2311yescharacteristic
121C22×Dic106C2314yes—
122C2×Q8×D53—48no—
123C2×Q8×D53C23116yes—
124C22×D212C2312yes—
125C22×D212C2314yes—
126C22×D212C2312yes—
127C22×D212C2312yes—
128C22×D212C2311yescharacteristic
129C22×D212C2314yes—
130C22×C22⋊D53C2311yescharacteristic
131C22×C22⋊D53C2311yescharacteristic
132C22×C22⋊D53C2314yes—
133C22×C4×D53C2311yescharacteristic
134C22×C4×D53C2311yescharacteristic
135C22×C4×D53C2311yescharacteristic
136C22×C4×D53C2311yescharacteristic
137C22×C4×D53C2311yescharacteristic
138C22×C4×D53C2314yes—
139C22×C4×D53C2314yes—
140C22×C4×D53C2314yes—
141C22×C4×D53C2314yes—
142C22×C4×D53C2311yescharacteristic
143#13133217C2318yes—
144#13133216C23116yes—
145#13133216C23116yes—
146#13133215C23116yes—
147#13133214C2318yes—
148#13133212C23132yes—
149#13133211C23132yes—
150#13133208C23116yes—
151#13133206C23116yes—
152#13133206C23116yes—
153#13133205C23132yes—
154#13133205C23116yes—
155#13133203C23132yes—
156#13133202C23132yes—
157#13133199C23132yes—
158#13133197C23116yes—
159#13133197C23132yes—
160#13133195C23132yes—
161#13133195C23132yes—
162#13133193C23116yes—
163#13133192C23116yes—
164#13133192C23132yes—
165#13133192C23116yes—
166#13133192C23116yes—
167#13133192C23116yes—
168#13133191C23116yes—
169#13133191C23116yes—
170#13133190C23132yes—
171#13133190C23132yes—
172Q8×Dic53C23116yes—
173C4×Dic106C2318yes—
174C4×Dic106C2318yes—
175#13133182C23116yes—
176C4×D212C2318yes—
177C4×D212C23132yes—
178C4×D212C2318yes—
179C4×D212C23116yes—
180C4×D212C23116yes—
181#13133179C23116yes—
182#13133179C23132yes—
183#13133179C23116yes—
184#13133179C23116yes—
185#13133179C23116yes—
186C4×C22⋊D53C2318yes—
187C4×C22⋊D53C2318yes—
188C4×C22⋊D53C2318yes—
189C4×C22⋊D53C2318yes—
190#13133176C2318yes—
191#13133175C23116yes—
192#13133174C23132yes—
193#13133174C2318yes—
194#13133174C2318yes—
195C2×C4⋊Dic53C2312yes—
196C2×C4⋊Dic53C2312yes—
197C2×C4⋊Dic53C2314yes—
198C2×C4⋊Dic53C2311yescharacteristic
199C2×C4⋊Dic53C2311yescharacteristic
200C2×#11719919C2311yescharacteristic
201C2×#11719919C2314yes—
202C2×#11719919C2314yes—
203C2×#11719919C2311yescharacteristic
204C2×#11719919C2311yescharacteristic
205C2×#11719919C2311yescharacteristic
206C2×#11719919C2314yes—
207C4⋊C4×D53C23132yes—
208C4⋊C4×D53C23116yes—
209C4⋊C4×D53C23116yes—
210C2×C22⋊Dic53C2311yescharacteristic
211C2×C22⋊Dic53C2311yescharacteristic
212C2×#11719921C2311yescharacteristic
213C2×#11719921C2311yescharacteristic
214C2×#11719921C2311yescharacteristic
215C2×#11719921C2311yescharacteristic
216C2×#11719921C2314yes—
217C2×#11719921C2314yes—
218C2×#11719921C2314yes—
219C2×#11719921C2314yes—
220C2×#11719921C2314yes—
221C2×#11719921C2314yes—
222C2×#11719921C2314yes—
223C2×C4×Dic53C2311yescharacteristic
224C2×C4×Dic53C2311yescharacteristic
225C2×C4×Dic53C2311yescharacteristic
226C2×C4×Dic53C2311yescharacteristic
227C2×C4×Dic53C2311yescharacteristic
228C2×C4×Dic53C2311yescharacteristic
229C2×C4×Dic53C2314yes—
230C42×D53C2318yes—
231C42×D53C2318yes—
232C22×Q8×C53C2312yes—
233C22×Q8×C53C2312yes—
234C23×C4×C53C2311yescharacteristic
235C23×C4×C53C2311yescharacteristic
236C23×C4×C53C2311yescharacteristic
237C4⋊Q8×C53C2318yes—
238C4⋊Q8×C53C2318yes—
239#125×C53C23116yes—
240C22⋊Q8×C53C23116yes—
241C22⋊Q8×C53C23116yes—
242C4×Q8×C53C23116yes—
243C4×Q8×C53C23116yes—
244#117×C53C23116yes—
245C2×C4⋊C4×C53C2312yes—
246C2×C4⋊C4×C53C2312yes—
247C2×C4⋊C4×C53C2314yes—
248C2×C4⋊C4×C53C2314yes—
249C2×C4⋊C4×C53C2312yes—
250C2×C4⋊C4×C53C2312yes—
251C2×C22⋊C4×C53C2314yes—
252C2×C42×C53C2311yescharacteristic
253C2×C42×C53C2311yescharacteristic
254C2×C42×C53C2311yescharacteristic
255C2×C42×C53C2311yescharacteristic
256C2×C42×C53C2318yes—
257C2×C42×C53C2314yes—
258C24×C53C2411yescharacteristic
259C23×D53C2414yes—
260C23×D53C2411yescharacteristic
261C23×D53C2411yescharacteristic
262C2×Q8×C53—28no—
263C2×Q8×C53—28no—
264C2×Q8×C53C2418yes—
265C2×Q8×C53C2418yes—
266C22×C4×C53—24no—
267C22×C4×C53—24no—
268C22×C4×C53—24no—
269C22×C4×C53C2411yescharacteristic
270C22×C4×C53C2411yescharacteristic
271C22×C4×C53C2411yescharacteristic
272C22×C4×C53C2414yes—
273C22×C4×C53C2414yes—
274C22×C4×C53C2414yes—
275C22×C4×C53C2414yes—
276C22×C4×C53C2414yes—
277C22×C4×C53C2411yescharacteristic
278C22×C4×C53C2411yescharacteristic
279C22×C4×C53C2411yescharacteristic
280C2×C22⋊D53—24no—
281C2×C22⋊D53—24no—
282C2×C22⋊D53—48no—
283C2×C22⋊D53C2414yes—
284C2×C22⋊D53C2414yes—
285C2×C22⋊D53C24116yes—
286C22×Dic53C2411yescharacteristic
287C22×Dic53C2411yescharacteristic
288C22×Dic53C2411yescharacteristic
289C22×Dic53C2411yescharacteristic
290C22×Dic53C2411yescharacteristic
291C22×Dic53C2414yes—
292C22×Dic53C2411yescharacteristic
293#11719949—264no—
294#11719949—432no—
295Q8×D53—432no—
296#11719945—232no—
297#11719945—432no—
298C2×D212—24no—
299C2×D212—216no—
300C2×D212—28no—
301C2×D212—28no—
302C2×D212—28no—
303C2×D212—48no—
304C2×D212C2418yes—
305C2×D212C24116yes—
306C2×D212C2418yes—
307C2×D212C2418yes—
308C2×D212C2414yes—
309C2×D212C24116yes—
310C2×C4×D53—24no—
311C2×C4×D53—24no—
312C2×C4×D53—24no—
313C2×C4×D53—24no—
314C2×C4×D53—24no—
315C2×C4×D53—216no—
316C2×C4×D53—48no—
317C2×C4×D53—48no—
318C2×C4×D53—48no—
319C2×C4×D53#4118yescomplemented
320C2×C4×D53C2414yes—
321C2×C4×D53C2414yes—
322C2×C4×D53C2414yes—
323C2×C4×D53C2414yes—
324C2×C4×D53C2414yes—
325C2×C4×D53C24116yes—
326C2×C4×D53C24116yes—
327C2×C4×D53C24116yes—
328C2×C4×D53C24116yes—
329C2×C4×D53C2414yes—
330C2×Dic106—28no—
331C2×Dic106—24no—
332C2×Dic106—48no—
333C2×Dic106C2418yes—
334C2×Dic106C2414yes—
335C2×Dic106C24116yes—
336C4⋊C4×C53C2418yes—
337C4⋊C4×C53C2418yes—
338C4⋊C4×C53C24116yes—
339C4⋊C4×C53C24116yes—
340C4⋊C4×C53C2418yes—
341C4⋊C4×C53C2418yes—
342C22⋊C4×C53C24116yes—
343C42×C53C2414yes—
344C42×C53C2414yes—
345C42×C53C2414yes—
346C42×C53C2414yes—
347C42×C53C24116yes—
348C22⋊Dic53C2414yes—
349C22⋊Dic53C2414yes—
350#11719921C2414yes—
351#11719921C2414yes—
352#11719921C2414yes—
353#11719921C2414yes—
354#11719921C24116yes—
355#11719921C24116yes—
356#11719921C24116yes—
357#11719921C24116yes—
358#11719921C24116yes—
359#11719921C24116yes—
360#11719921C24116yes—
361C4⋊Dic53C2418yes—
362C4⋊Dic53C2418yes—
363C4⋊Dic53C24116yes—
364C4⋊Dic53C2414yes—
365C4⋊Dic53C2414yes—
366#11719919C2414yes—
367#11719919C24116yes—
368#11719919C24116yes—
369#11719919C2414yes—
370#11719919C2414yes—
371#11719919C2414yes—
372#11719919C24116yes—
373C4×Dic53C2414yes—
374C4×Dic53C2414yes—
375C4×Dic53C2414yes—
376C4×Dic53C2414yes—
377C4×Dic53C2414yes—
378C4×Dic53C2414yes—
379C4×Dic53C24116yes—
380C23×C53—22no—
381C23×C53—22no—
382C23×C53—22no—
383C23×C53C2512yes—
384C23×C53C2511yescharacteristic
385C22×D53—22no—
386C22×D53—22no—
387C22×D53—28no—
388C22×D53—22no—
389C22×D53—22no—
390C22×D53—28no—
391C22×D53—22no—
392C22×D53—28no—
393C22×D53C2×#4114yes—
394C22×D53C2518yes—
395C22×D53C2512yes—
396C22×D53C2512yes—
397Q8×C53—216no—
398Q8×C53—216no—
399C2×C4×C53—22no—
400C2×C4×C53—28no—
401C2×C4×C53—28no—
402C2×C4×C53—22no—
403C2×C4×C53—22no—
404C2×C4×C53—28no—
405C2×C4×C53—28no—
406C2×C4×C53—28no—
407C2×C4×C53C2×#4114yes—
408C2×C4×C53H(5,𝔽2)14yes—
409C2×C4×C532−1+414yes—
410C2×C4×C53C2518yes—
411C2×C4×C53C2512yes—
412C2×C4×C53C2512yes—
413C2×C4×C53C2518yes—
414C2×C4×C53C2512yes—
415C2×C4×C53C2512yes—
416C2×C4×C53C2512yes—
417C2×C4×C53C2512yes—
418C22⋊D53—28no—
419C22⋊D53—28no—
420C22⋊D53—416no—
421C2×Dic53—22no—
422C2×Dic53—28no—
423C2×Dic53—22no—
424C2×Dic53—22no—
425C2×Dic53—22no—
426C2×Dic53—22no—
427C2×Dic53C2×#4114yes—
428C2×Dic53C2512yes—
429C2×Dic53C2518yes—
430C2×Dic53C2512yes—
431C2×Dic53C2512yes—
432C2×Dic53C2512yes—
433C2×Dic53C2512yes—
434C2×Dic53C2512yes—
435D212—28no—
436D212—232no—
437D212—216no—
438D212—216no—
439D212—216no—
440D212—416no—
441C4×D53—28no—
442C4×D53—28no—
443C4×D53—28no—
444C4×D53—28no—
445C4×D53—28no—
446C4×D53—232no—
447C4×D53—416no—
448C4×D53—416no—
449C4×D53—416no—
450C4×D53C2×#41116yescomplemented
451Dic106—216no—
452Dic106—28no—
453Dic106—416no—
454C2×#3511—531nomaximal, Sylow
455C22×C53—22no—
456C22×C53—22no—
457C22×C53—22no—
458C22×C53—44no—
459C22×C53C22×#4112yes—
460C22×C53C2×H(5,𝔽2)12yes—
461C22×C53C2×2−1+412yes—
462C22×C53C2611yescharacteristic
463C2×D53—22no—
464C2×D53—22no—
465C2×D53—28no—
466C2×D53—28no—
467C2×D53—22no—
468C2×D53—22no—
469C2×D53—28no—
470C2×D53—22no—
471C2×D53—28no—
472C2×D53—416no—
473C2×D53—44no—
474C2×D53C22×#4114yes—
475C4×C53—22no—
476C4×C53—28no—
477C4×C53—28no—
478C4×C53—22no—
479C4×C53—22no—
480C4×C53C22×#4114yes—
481C4×C53C2×H(5,𝔽2)14yes—
482C4×C53C2×2−1+414yes—
483Dic53—22no—
484Dic53—28no—
485Dic53—22no—
486Dic53—22no—
487Dic53—22no—
488Dic53—22no—
489Dic53C22×#4114yes—
490#3511—5332no—
491C2×#556—532no—
492C2×#555—532no—
493C2×#554—532no—
494C2×#553—532no—
495C2×#553—532no—
496C2×#548—532no—
497C2×#548—532no—
498C2×#547—532no—
499C2×#542—532no—
500C2×#542—532no—
501C2×#537—532no—
502C2×#533—531no—
503C2×#533D5311yescharacteristic, complemented
504C2×#532—531no—
505C2×#532—531no—
506C2×#532—531no—
507C22×C4⋊Q8—531no—
508C2×#520—532no—
509C2×C4×#41—531no—
510C2×C53—42no—
511C2×C53#351114yescomplemented
512C2×C53C23×#4111yescharacteristic
513C2×C53C22×H(5,𝔽2)11yescharacteristic
514C2×C53C22×2−1+411yescharacteristic
515D53—24no—
516D53—48no—
517D53—42no—
518C22×#41—532no—
519C22×#41—532no—
520C22×#41—531no—
521C22×#41—532no—
522C23×Q8—532no—
523#556—5332no—
524#555—5332no—
525#554—5332no—
526#553—5332no—
527#553—5332no—
528#548—5332no—
529#548—5332no—
530#547—5332no—
531#542—5332no—
532#542—5332no—
533#537—5332no—
534#533—5316no—
535#533C2×D53116yescomplemented
536#532—5316no—
537#532—5316no—
538#532—5316no—
539C2×C4⋊Q8—532no—
540C2×C4⋊Q8—5316no—
541C2×C4⋊Q8—532no—
542C2×C4⋊Q8—532no—
543C2×C4⋊Q8—531no—
544C2×C4⋊Q8C2×D5311yescharacteristic
545C2×C4⋊Q8C2×D5311yescharacteristic
546C2×#127—531no—
547C2×#126—534no—
548C2×#126—534no—
549C2×#125—532no—
550C2×#125C2×D5312yes—
551C2×#124—532no—
552C2×#124—532no—
553C2×#124—534no—
554C2×#124—532no—
555C2×#124—534no—
556C2×#123—534no—
557C2×#123—534no—
558C2×C22⋊Q8—532no—
559C2×C22⋊Q8—534no—
560C2×C22⋊Q8—534no—
561C2×C22⋊Q8—532no—
562C2×C22⋊Q8—534no—
563C2×C22⋊Q8C2×D5312yes—
564C2×C22⋊Q8C2×D5312yes—
565C2×#121—532no—
566C2×#121—532no—
567C2×#121—532no—
568C2×#121—532no—
569C2×#121—532no—
570C2×#121—532no—
571C2×#121—534no—
572C2×#121—534no—
573C2×#121—534no—
574#520—5332no—
575C4×#41—5316no—
576C2×C4×Q8—532no—
577C2×C4×Q8—532no—
578C2×C4×Q8—531no—
579C2×C4×Q8—531no—
580C2×C4×Q8C2×D5312yes—
581C2×C4×Q8C2×D5312yes—
582C2×C4×D4—531no—
583C2×C4×D4—531no—
584C2×C4×D4—531no—
585C2×C4×D4—531no—
586C2×C4×D4—532no—
587C2×C4×D4—534no—
588C2×C4×D4—532no—
589C2×C4×D4—532no—
590C2×C4×D4—532no—
591C2×C4×D4—531no—
592C2×C4×D4—531no—
593C2×C4×D4—532no—
594C2×C4×D4—534no—
595C2×C4×D4—532no—
596C2×#117—531no—
597C2×#117—532no—
598C2×#117—531no—
599C2×#117—531no—
600C2×#117—534no—
601C2×#117C2×D5312yes—
602C22×C4⋊C4—532no—
603C22×C4⋊C4—534no—
604C22×C4⋊C4—532no—
605C22×C42—531no—
606C22×C42—531no—
607C22×C42C2×D5311yescharacteristic
608C53C2×#351111yescharacteristic, complemented, Sylow
609C2×#41—5316no—
610C2×#41—5316no—
611C2×#41—538no—
612C2×#41—5316no—
613C2×#41—1068no—
614C2×#41—10616no—
615C2×#41—2128no—
616C2×#41—2128no—
617C22×Q8—5316no—
618C22×Q8—531no—
619C22×Q8—532no—
620C22×Q8—534no—
621C22×Q8—2128no—
622C22×Q8C22×D5312yes—
623C22×Q8C22×D5312yes—
624C22×D4—531no—
625C22×D4—531no—
626C22×D4—534no—
627C22×D4—532no—
628C22×D4—534no—
629C22×D4—531no—
630C22×D4—532no—
631C22×D4—532no—
632C22×D4—534no—
633C23×C4—531no—
634C23×C4—531no—
635C23×C4—534no—
636C23×C4—531no—
637C23×C4—531no—
638C23×C4—531no—
639C23×C4—531no—
640C23×C4—534no—
641C23×C4—534no—
642C23×C4—534no—
643C23×C4C22×D5311yescharacteristic
644C23×C4C22×D5311yescharacteristic
645C23×C4C22×D5311yescharacteristic
646C4⋊Q8—5316no—
647C4⋊Q8—5316no—
648C4⋊Q8—5316no—
649C4⋊Q8—538no—
650C4⋊Q8C22×D5318yes—
651C4⋊Q8C22×D5318yes—
652#127—538no—
653#126—5332no—
654#126—5332no—
655#125—5316no—
656#125C22×D53116yes—
657#124—5316no—
658#124—5316no—
659#124—5332no—
660#124—5316no—
661#124—5332no—
662#123—5332no—
663#123—5332no—
664C22⋊Q8—5316no—
665C22⋊Q8—5316no—
666C22⋊Q8—5332no—
667C22⋊Q8—5332no—
668C22⋊Q8—5332no—
669C22⋊Q8C22×D53116yes—
670C22⋊Q8C22×D53116yes—
671#121—5316no—
672#121—5316no—
673#121—5316no—
674#121—5316no—
675#121—5316no—
676#121—5316no—
677#121—5332no—
678#121—5332no—
679#121—5332no—
680C4×Q8—5316no—
681C4×Q8—5316no—
682C4×Q8—538no—
683C4×Q8—538no—
684C4×Q8C22×D53116yes—
685C4×Q8C22×D53116yes—
686C4×D4—538no—
687C4×D4—538no—
688C4×D4—538no—
689C4×D4—538no—
690C4×D4—5316no—
691C4×D4—5332no—
692C4×D4—5316no—
693C4×D4—5316no—
694C4×D4—5316no—
695C4×D4—538no—
696C4×D4—538no—
697C4×D4—5316no—
698C4×D4—5332no—
699C4×D4—5316no—
700#117—538no—
701#117—5316no—
702#117—538no—
703#117—538no—
704#117—5332no—
705#117C22×D53116yes—
706C2×C4⋊C4—531no—
707C2×C4⋊C4—534no—
708C2×C4⋊C4—532no—
709C2×C4⋊C4—532no—
710C2×C4⋊C4—534no—
711C2×C4⋊C4—534no—
712C2×C4⋊C4—531no—
713C2×C4⋊C4—531no—
714C2×C4⋊C4—531no—
715C2×C4⋊C4—531no—
716C2×C4⋊C4—531no—
717C2×C4⋊C4—534no—
718C2×C4⋊C4—5316no—
719C2×C4⋊C4—5332no—
720C2×C4⋊C4—5316no—
721C2×C4⋊C4C22×D5312yes—
722C2×C4⋊C4C22×D5312yes—
723C2×C4⋊C4C22×D5314yes—
724C2×C4⋊C4C22×D5312yes—
725C2×C4⋊C4C22×D5312yes—
726C2×C4⋊C4C22×D5314yes—
727C2×C22⋊C4—531no—
728C2×C22⋊C4—531no—
729C2×C22⋊C4—531no—
730C2×C22⋊C4—531no—
731C2×C22⋊C4—534no—
732C2×C22⋊C4—534no—
733C2×C22⋊C4—531no—
734C2×C22⋊C4—531no—
735C2×C22⋊C4—534no—
736C2×C22⋊C4—534no—
737C2×C22⋊C4—534no—
738C2×C22⋊C4—534no—
739C2×C22⋊C4—534no—
740C2×C22⋊C4C22×D5314yes—
741C2×C42—531no—
742C2×C42—534no—
743C2×C42—531no—
744C2×C42—531no—
745C2×C42—531no—
746C2×C42—531no—
747C2×C42—531no—
748C2×C42—538no—
749C2×C42—538no—
750C2×C42C22×D5311yescharacteristic
751C2×C42C22×D5314yes—
752C2×C42C22×D5311yescharacteristic
753C2×C42C22×D5311yescharacteristic
754C2×C42C22×D5318yes—
755C2×C42C22×D5311yescharacteristic
756C24—531no—
757C24—531no—
758C24—534no—
759C24C23×D5311yescharacteristic
760#41—10632no—
761#41—10664no—
762#41—21232no—
763#41—21232no—
764C2×Q8—28no—
765C2×Q8—28no—
766C2×Q8—534no—
767C2×Q8—538no—
768C2×Q8—5316no—
769C2×Q8—1064no—
770C2×Q8—1068no—
771C2×Q8—2128no—
772C2×Q8—21232no—
773C2×Q8C23×D5318yes—
774C2×Q8C23×D5318yes—
775C2×D4—534no—
776C2×D4—534no—
777C2×D4—5316no—
778C2×D4—538no—
779C2×D4—5316no—
780C2×D4—534no—
781C2×D4—538no—
782C2×D4—538no—
783C2×D4—5316no—
784C2×D4—1064no—
785C2×D4—10616no—
786C2×D4—1064no—
787C2×D4—1064no—
788C2×D4—1068no—
789C2×D4—1068no—
790C2×D4—1068no—
791C2×D4—2128no—
792C2×D4—2128no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—531no—
797C22×C4—538no—
798C22×C4—534no—
799C22×C4—531no—
800C22×C4—531no—
801C22×C4—531no—
802C22×C4—531no—
803C22×C4—531no—
804C22×C4—534no—
805C22×C4—534no—
806C22×C4—534no—
807C22×C4—534no—
808C22×C4—534no—
809C22×C4—534no—
810C22×C4—5316no—
811C22×C4—5316no—
812C22×C4—5316no—
813C22×C4—5316no—
814C22×C4—10616no—
815C22×C4—1064no—
816C22×C4—1064no—
817C22×C4—1064no—
818C22×C4—1064no—
819C22×C4—1064no—
820C22×C4—2128no—
821C22×C4—2128no—
822C22×C4—2128no—
823C22×C4C23×D5314yes—
824C22×C4C23×D5314yes—
825C22×C4C23×D5314yes—
826C22×C4C23×D5314yes—
827C22×C4C23×D5311yescharacteristic
828C22×C4C23×D5311yescharacteristic
829C22×C4C23×D5311yescharacteristic
830C22×C4C23×D5314yes—
831C22×C4C23×D5311yescharacteristic
832C22×C4C23×D5311yescharacteristic
833C22×C4C23×D5311yescharacteristic
834C4⋊C4—534no—
835C4⋊C4—5316no—
836C4⋊C4—538no—
837C4⋊C4—538no—
838C4⋊C4—5316no—
839C4⋊C4—5316no—
840C4⋊C4—534no—
841C4⋊C4—534no—
842C4⋊C4—534no—
843C4⋊C4—534no—
844C4⋊C4—534no—
845C4⋊C4—5316no—
846C4⋊C4C23×D5318yes—
847C4⋊C4C23×D5318yes—
848C4⋊C4C23×D53116yes—
849C4⋊C4C23×D5318yes—
850C4⋊C4C23×D5318yes—
851C4⋊C4C23×D53116yes—
852C22⋊C4—534no—
853C22⋊C4—534no—
854C22⋊C4—534no—
855C22⋊C4—534no—
856C22⋊C4—5316no—
857C22⋊C4—5316no—
858C22⋊C4—534no—
859C22⋊C4—534no—
860C22⋊C4—5316no—
861C22⋊C4—5316no—
862C22⋊C4—5316no—
863C22⋊C4—5316no—
864C22⋊C4—5316no—
865C22⋊C4C23×D53116yes—
866C42—534no—
867C42—534no—
868C42—534no—
869C42—534no—
870C42—534no—
871C42—534no—
872C42—5316no—
873C42C23×D5314yes—
874C42C23×D5314yes—
875C42C23×D5314yes—
876C42C23×D5314yes—
877C42C23×D53116yes—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—534no—
882C23—532no—
883C23—532no—
884C23—538no—
885C23—1062no—
886C23—1062no—
887C23—1068no—
888C23—1062no—
889C23—1062no—
890C23—1068no—
891C23—1062no—
892C23—1068no—
893C23C24×D5312yes—
894C23C24×D5311yescharacteristic
895Q8—216no—
896Q8—216no—
897Q8—1068no—
898Q8—10616no—
899Q8—21216no—
900D4—1068no—
901D4—10632no—
902D4—1068no—
903D4—1068no—
904D4—10616no—
905D4—10616no—
906D4—10616no—
907D4—21216no—
908D4—21216no—
909C2×C4—22no—
910C2×C4—28no—
911C2×C4—22no—
912C2×C4—28no—
913C2×C4—22no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—534no—
918C2×C4—532no—
919C2×C4—5316no—
920C2×C4—532no—
921C2×C4—532no—
922C2×C4—532no—
923C2×C4—532no—
924C2×C4—532no—
925C2×C4—538no—
926C2×C4—10632no—
927C2×C4—1062no—
928C2×C4—1062no—
929C2×C4—1062no—
930C2×C4—1068no—
931C2×C4—1062no—
932C2×C4—1062no—
933C2×C4—1068no—
934C2×C4—1068no—
935C2×C4—1068no—
936C2×C4—1068no—
937C2×C4—1068no—
938C2×C4—21216no—
939C2×C4—21216no—
940C2×C4—21216no—
941C2×C4#41×D5314yes—
942C2×C4#1313326314yes—
943C2×C4#1313326514yes—
944C2×C4C24×D5318yes—
945C2×C4C24×D5312yes—
946C2×C4C24×D5312yes—
947C2×C4C24×D5312yes—
948C2×C4C24×D5318yes—
949C2×C4C24×D5312yes—
950C2×C4C24×D5312yes—
951C2×C4C24×D5312yes—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—44no—
956C22—534no—
957C22—1068no—
958C22—1062no—
959C22—1062no—
960C22—1068no—
961C22—1062no—
962C22—1062no—
963C22—1068no—
964C22—1062no—
965C22—1068no—
966C22—2124no—
967C22—21216no—
968C22C2×#41×D5312yes—
969C22C2×#1313326312yes—
970C22C2×#1313326512yes—
971C22C25×D5311yescharacteristic
972C4—22no—
973C4—28no—
974C4—22no—
975C4—28no—
976C4—22no—
977C4—534no—
978C4—1062no—
979C4—1062no—
980C4—1062no—
981C4—1068no—
982C4—1062no—
983C4—1062no—
984C4C2×#41×D5314yes—
985C4C2×#1313326314yes—
986C4C2×#1313326514yes—
987C2—42no—
988C2—1064no—
989C2—2122no—
990C2—2128no—
991C2#2028862714yesdirect product factor
992C2C22×#41×D5311yescharacteristic
993C2C22×#1313326311yescharacteristic
994C2C22×#1313326511yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#533C2
socleC23×C53C25
hypercenterC2×#533D53
hypocenterC53C2×#3511
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #20288627C2direct (N × H)
2. C2×#16811345C2semidirect
3. C2×#16811336C2semidirect
4. C2×#16811329C2semidirect
5. C2×#16811326C2semidirect
6. C2×#16811317C2semidirect
7. C2×#16811285C2semidirect
8. C2×#16811283C2semidirect
9. C2×#16811275C2semidirect
10. C2×#16811246C2semidirect
11. C2×#16811245C2semidirect
12. C2×#16811203C2semidirect
13. C2×#16811178C2semidirect
14. C2×#16811174C2semidirect
15. C2×#16811174C2semidirect
16. C2×#16811173C2semidirect
17. C2×C4⋊Q8×D53C2semidirect
18. C2×#16811105C2semidirect
19. C2×C4×#11719945C2semidirect
20. C2×C53×#533C2semidirect
26. #16811345C22semidirect
27. #16811336C22semidirect
28. #16811329C22semidirect
29. #16811326C22semidirect
30. #16811317C22semidirect
31. #16811285C22semidirect
32. #16811283C22semidirect
33. #16811275C22semidirect
34. #16811246C22semidirect
35. #16811245C22semidirect
36. #16811203C22semidirect
37. #16811178C22semidirect
38. #16811174C22semidirect
39. #16811174C22semidirect
40. #16811173C22semidirect
45. C4⋊Q8×D53C22semidirect
71. #16811105C22semidirect
72. C4×#11719945C22semidirect
101. C53×#533C22semidirect
319. C2×C4×D53#41semidirect
450. C4×D53C2×#41semidirect
503. C2×#533D53semidirect
511. C2×C53#3511semidirect
535. #533C2×D53semidirect
608. C53C2×#3511semidirect
991. C2#20288627direct (N × H)

Maximal subgroups

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

subgroupindex
#202886272
C2×#168113452
C2×#168113362
C2×#168113292
C2×#168113262
C2×#168113172
C2×#168112852
C2×#168112832
C2×#168112752
C2×#168112462
C2×#168112452
C2×#168112032
C2×#168111782
C2×#168111742
C2×#168111732
C2×C4⋊Q8×D532
C2×#168111052
C2×C4×#117199452
C2×C53×#5332
C2×#351153