Finite Group Databasebeta

← C2×#20289203 #28291812

Subgroups — C2×#20289203 #28291812

Order 13568.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289203C2132yesmaximal, direct product factor
2C2×#16811374C214yesmaximal, complemented
3C2×Q8×Dic106C211yesmaximal, characteristic, complemented
4C2×#16811352C211yesmaximal, characteristic, complemented
5C2×#16811351C212yesmaximal, complemented
6C2×#16811346C212yesmaximal, complemented
7C2×#16811346C211yesmaximal, characteristic, complemented
8C2×#16811344C212yesmaximal, complemented
9C2×#16811333C211yesmaximal, characteristic, complemented
10C2×#16811307C212yesmaximal, complemented
11C2×#16811250C212yesmaximal, complemented
12C2×#16811244C212yesmaximal
13C2×#16811235C212yesmaximal, complemented
14C2×#16811234C212yesmaximal, complemented
15C2×#16811232C214yesmaximal, complemented
16C2×#16811180C211yesmaximal, characteristic, complemented
17C2×#16811157C211yesmaximal, characteristic
18C2×C53×#533C211yesmaximal, characteristic, complemented
19#16811374C22164yescomplemented
20Q8×Dic106C22116yescomplemented
21#16811352C22116yescomplemented
22#16811351C22132yescomplemented
23#16811346C22132yescomplemented
24#16811346C22116yescomplemented
25#16811344C22132yescomplemented
26#16811333C22116yescomplemented
27#16811307C22132yescomplemented
28#16811250C22132yescomplemented
29#16811244C22132yes—
30#16811235C22132yescomplemented
31#16811234C22132yescomplemented
32#16811232C22164yescomplemented
33#16811180C22116yescomplemented
34C2×#13133217C2211yescharacteristic
35C2×#13133217C2211yescharacteristic
36C2×#13133217C2212yes—
37C2×#13133217C2212yes—
38C2×#13133216C2212yes—
39C2×#13133216C2214yes—
40C2×#13133215C2214yes—
41#16811157C22116yes—
42C2×#13133212C2214yes—
43C2×#13133212C2214yes—
44C2×#13133212C2214yes—
45C2×#13133212C2214yes—
46C2×#13133211C2212yes—
47C2×#13133210C2214yes—
48C2×#13133210C2214yes—
49C2×#13133209C2212yes—
50C2×#13133209C2211yescharacteristic
51C2×#13133209C2212yes—
52C2×#13133208C2214yes—
53C2×#13133208C2212yes—
54C2×#13133207C2214yes—
55C2×#13133207C2214yes—
56C2×#13133207C2214yes—
57C2×#13133207C2214yes—
58C2×#13133205C2212yes—
59C2×#13133205C2211yescharacteristic
60C2×#13133203C2214yes—
61C2×#13133200C2212yes—
62C2×#13133199C2214yes—
63C2×#13133196C2212yes—
64C2×#13133196C2212yes—
65C2×#13133196C2211yescharacteristic
66C2×#13133195C2214yes—
67C2×#13133195C2214yes—
68C2×#13133193C2212yes—
69C2×#13133193C2214yes—
70C2×#13133193C2212yes—
71C2×#13133191C2211yescharacteristic
72C2×Q8×Dic53C2212yes—
73C2×Q8×Dic53C2212yes—
74C2×C4×Dic106C2212yes—
75C2×C4×Dic106C2212yes—
76C2×C4×Dic106C2212yes—
77C2×C4×Dic106C2212yes—
78C2×C4×Dic106C2212yes—
79C2×C4×Dic106C2211yescharacteristic
80C2×#13133182C2214yes—
81C2×C4×D212C2212yes—
82C2×C4×D212C2211yescharacteristic
83C2×C4×C22⋊D53C2212yes—
84C2×#13133176C2212yes—
85C2×#13133175C2212yes—
86C2×#13133175C2214yes—
87C2×#13133174C2212yes—
88C2×C4⋊C4×D53C2212yes—
89C53×#533C22116yescomplemented
90C2×C4⋊Q8×C53C2211yescharacteristic
91C2×C4⋊Q8×C53C2211yescharacteristic
92C2×#125×C53C2212yes—
93C2×C22⋊Q8×C53C2211yescharacteristic
94C2×C22⋊Q8×C53C2212yes—
95C2×C22⋊Q8×C53C2211yescharacteristic
96C2×C4×Q8×C53C2212yes—
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×Q8×C53C2211yescharacteristic
99C2×#117×C53C2212yes—
100C22×C42×C53C2211yescharacteristic
101C22×Dic106C2312yes—
102C22×Dic106C2311yescharacteristic
103C22×Dic106C2314yes—
104C22×Dic106C2312yes—
105C22×D212C2311yescharacteristic
106C22×C22⋊D53C2312yes—
107C22×C4×D53C2312yes—
108C22×C4×D53C2314yes—
109#13133217C2318yes—
110#13133217C2318yes—
111#13133217C23116yes—
112#13133217C23116yes—
113#13133216C23116yes—
114#13133216C23132yes—
115#13133215C23132yes—
116#13133212C23132yes—
117#13133212C23132yes—
118#13133212C23132yes—
119#13133212C23132yes—
120#13133211C23116yes—
121#13133210C23132yes—
122#13133210C23132yes—
123#13133209C23116yes—
124#13133209C2318yes—
125#13133209C23116yes—
126#13133208C23116yes—
127#13133208C23132yes—
128#13133207C23132yes—
129#13133207C23132yes—
130#13133207C23132yes—
131#13133207C23132yes—
132#13133205C2318yes—
133#13133205C23116yes—
134#13133203C23132yes—
135#13133200C23116yes—
136#13133199C23132yes—
137#13133196C23116yes—
138#13133196C2318yes—
139#13133196C23116yes—
140#13133195C23132yes—
141#13133195C23132yes—
142#13133193C23116yes—
143#13133193C23116yes—
144#13133193C23132yes—
145#13133191C2318yes—
146Q8×Dic53C23116yes—
147Q8×Dic53C23116yes—
148C4×Dic106C23116yes—
149C4×Dic106C23116yes—
150C4×Dic106C23116yes—
151C4×Dic106C23116yes—
152C4×Dic106C2318yes—
153C4×Dic106C23116yes—
154#13133182C23132yes—
155C4×D212C2318yes—
156C4×D212C23116yes—
157C4×C22⋊D53C23116yes—
158#13133176C23116yes—
159#13133175C23132yes—
160#13133175C23116yes—
161#13133174C23116yes—
162C2×C4⋊Dic53C2312yes—
163C2×C4⋊Dic53C2312yes—
164C2×C4⋊Dic53C2314yes—
165C2×C4⋊Dic53C2311yescharacteristic
166C2×C4⋊Dic53C2312yes—
167C2×C4⋊Dic53C2311yescharacteristic
168C2×C4⋊Dic53C2312yes—
169C2×C4⋊Dic53C2314yes—
170C2×C4⋊Dic53C2314yes—
171C2×#11719919C2314yes—
172C2×#11719919C2312yes—
173C2×#11719919C2312yes—
174C2×#11719919C2312yes—
175C2×#11719919C2314yes—
176C2×#11719919C2314yes—
177C2×#11719919C2314yes—
178C2×#11719919C2314yes—
179C2×#11719919C2314yes—
180C2×#11719919C2314yes—
181C2×#11719919C2312yes—
182C4⋊C4×D53C23116yes—
183C2×C22⋊Dic53C2314yes—
184C2×C22⋊Dic53C2312yes—
185C2×#11719921C2312yes—
186C2×#11719921C2312yes—
187C2×#11719921C2312yes—
188C2×#11719921C2314yes—
189C2×#11719921C2314yes—
190C2×#11719921C2314yes—
191C2×#11719921C2312yes—
192C2×C4×Dic53C2312yes—
193C2×C4×Dic53C2314yes—
194C2×C4×Dic53C2314yes—
195C2×C4×Dic53C2314yes—
196C2×C4×Dic53C2314yes—
197C22×Q8×C53C2311yescharacteristic
198C22×Q8×C53C2311yescharacteristic
199C22×Q8×C53C2312yes—
200C23×C4×C53C2311yescharacteristic
201C23×C4×C53C2311yescharacteristic
202C23×C4×C53C2311yescharacteristic
203C4⋊Q8×C53C2318yes—
204C4⋊Q8×C53C2318yes—
205#125×C53C23116yes—
206C22⋊Q8×C53C2318yes—
207C22⋊Q8×C53C2318yes—
208C22⋊Q8×C53C23116yes—
209C4×Q8×C53C2318yes—
210C4×Q8×C53C23116yes—
211C4×Q8×C53C2318yes—
212#117×C53C23116yes—
213C2×C4⋊C4×C53C2312yes—
214C2×C4⋊C4×C53C2312yes—
215C2×C4⋊C4×C53C2312yes—
216C2×C4⋊C4×C53C2312yes—
217C2×C4⋊C4×C53C2312yes—
218C2×C4⋊C4×C53C2312yes—
219C2×C4⋊C4×C53C2311yescharacteristic
220C2×C4⋊C4×C53C2311yescharacteristic
221C2×C4⋊C4×C53C2312yes—
222C2×C22⋊C4×C53C2312yes—
223C2×C22⋊C4×C53C2312yes—
224C2×C42×C53C2311yescharacteristic
225C2×C42×C53C2311yescharacteristic
226C2×C42×C53C2311yescharacteristic
227C2×C42×C53C2311yescharacteristic
228C2×C42×C53C2318yes—
229C2×C42×C53C2312yes—
230C2×C42×C53C2312yes—
231C24×C53C2411yescharacteristic
232C23×D53C2412yes—
233C2×Q8×C53—24no—
234C2×Q8×C53—24no—
235C2×Q8×C53—44no—
236C2×Q8×C53C2414yes—
237C2×Q8×C53C2414yes—
238C2×Q8×C53C2418yes—
239C22×C4×C53—24no—
240C22×C4×C53—24no—
241C22×C4×C53—42no—
242C22×C4×C53C2411yescharacteristic
243C22×C4×C53C2411yescharacteristic
244C22×C4×C53C2411yescharacteristic
245C22×C4×C53C2411yescharacteristic
246C22×C4×C53C2414yes—
247C22×C4×C53C2414yes—
248C22×C4×C53C2412yes—
249C22×C4×C53C2412yes—
250C22×C4×C53C2412yes—
251C22×C4×C53C2412yes—
252C22×C4×C53C2414yes—
253C22×C4×C53C2411yescharacteristic
254C22×C4×C53C2411yescharacteristic
255C2×C22⋊D53—44no—
256C2×C22⋊D53C2418yes—
257C22×Dic53C2412yes—
258C22×Dic53C2414yes—
259C22×Dic53C2412yes—
260C22×Dic53C2412yes—
261C22×Dic53C2414yes—
262C2×D212—24no—
263C2×D212C2414yes—
264C2×C4×D53—28no—
265C2×C4×D53—48no—
266C2×C4×D53C2418yes—
267C2×C4×D53C24116yes—
268C2×Dic106—28no—
269C2×Dic106—24no—
270C2×Dic106—44no—
271C2×Dic106—48no—
272C2×Dic106C2418yes—
273C2×Dic106C2414yes—
274C2×Dic106C24116yes—
275C2×Dic106C2418yes—
276C4⋊C4×C53C2418yes—
277C4⋊C4×C53C2418yes—
278C4⋊C4×C53C2418yes—
279C4⋊C4×C53C2418yes—
280C4⋊C4×C53C2418yes—
281C4⋊C4×C53C2418yes—
282C4⋊C4×C53C2414yes—
283C4⋊C4×C53C2414yes—
284C4⋊C4×C53C2418yes—
285C22⋊C4×C53C2418yes—
286C22⋊C4×C53C2418yes—
287C42×C53C2414yes—
288C42×C53C2414yes—
289C42×C53C2414yes—
290C42×C53C2414yes—
291C42×C53C2418yes—
292C42×C53C2418yes—
293C22⋊Dic53C24116yes—
294C22⋊Dic53C2418yes—
295#11719921C2418yes—
296#11719921C2418yes—
297#11719921C2418yes—
298#11719921C24116yes—
299#11719921C24116yes—
300#11719921C24116yes—
301#11719921C2418yes—
302C4⋊Dic53C2418yes—
303C4⋊Dic53C2418yes—
304C4⋊Dic53C24116yes—
305C4⋊Dic53C2414yes—
306C4⋊Dic53C2418yes—
307C4⋊Dic53C2414yes—
308C4⋊Dic53C2418yes—
309C4⋊Dic53C24116yes—
310C4⋊Dic53C24116yes—
311#11719919C24116yes—
312#11719919C2418yes—
313#11719919C2418yes—
314#11719919C2418yes—
315#11719919C24116yes—
316#11719919C24116yes—
317#11719919C24116yes—
318#11719919C24116yes—
319#11719919C24116yes—
320#11719919C24116yes—
321#11719919C2418yes—
322C4×Dic53C2418yes—
323C4×Dic53C24116yes—
324C4×Dic53C24116yes—
325C4×Dic53C24116yes—
326C4×Dic53C24116yes—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53C2512yes—
331C23×C53C2511yescharacteristic
332C22×D53—24no—
333C22×D53—24no—
334C22×D53—24no—
335C22×D53C2514yes—
336Q8×C53—28no—
337Q8×C53—28no—
338Q8×C53—48no—
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—24no—
342C2×C4×C53—24no—
343C2×C4×C53—22no—
344C2×C4×C53—24no—
345C2×C4×C53—24no—
346C2×C4×C53—22no—
347C2×C4×C53—28no—
348C2×C4×C53—28no—
349C2×C4×C53—44no—
350C2×C4×C532−1+414yes—
351C2×C4×C532−1+414yes—
352C2×C4×C53C2512yes—
353C2×C4×C53C2514yes—
354C2×C4×C53C2514yes—
355C2×C4×C53C2512yes—
356C2×C4×C53C2512yes—
357C2×C4×C53C2512yes—
358C2×C4×C53C2514yes—
359C2×C4×C53C2514yes—
360C2×C4×C53C2512yes—
361C2×C4×C53C2512yes—
362C22⋊D53—48no—
363C2×Dic53—24no—
364C2×Dic53—28no—
365C2×Dic53—24no—
366C2×Dic53—28no—
367C2×Dic53—24no—
368C2×Dic53C2518yes—
369C2×Dic53C2514yes—
370C2×Dic53C2514yes—
371C2×Dic53C2518yes—
372C2×Dic53C2514yes—
373D212—28no—
374C4×D53—216no—
375C4×D53—416no—
376Dic106—216no—
377Dic106—28no—
378Dic106—48no—
379Dic106—416no—
380C2×#3555—531nomaximal, Sylow
381C22×C53—22no—
382C22×C53—22no—
383C22×C53—22no—
384C22×C53—44no—
385C22×C53C2×2−1+412yes—
386C22×C53C2×2−1+412yes—
387C22×C53#58512yes—
388C22×C53C2611yescharacteristic
389C2×D53—24no—
390C2×D53—24no—
391C2×D53—24no—
392C2×D53—48no—
393C4×C53—22no—
394C4×C53—22no—
395C4×C53—24no—
396C4×C53—24no—
397C4×C53—22no—
398C4×C53—24no—
399C4×C53—24no—
400C4×C53—22no—
401C4×C53C2×2−1+414yes—
402C4×C53C2×2−1+414yes—
403Dic53—24no—
404Dic53—28no—
405Dic53—24no—
406Dic53—28no—
407Dic53—24no—
408#3555—5332no—
409C2×#563—534no—
410C2×Q82—531no—
411C2×#557—532no—
412C2×#557—531no—
413C2×#556—532no—
414C2×#556—532no—
415C2×#556—531no—
416C2×#554—531no—
417C2×#552—532no—
418C2×#544—532no—
419C2×#542—532no—
420C2×#541—532no—
421C2×#541—534no—
422C2×#541—532no—
423C2×#533—531no—
424C2×#533D5311yescharacteristic, complemented
425C2×#529—531no—
426C2×C53—42no—
427C2×C53#355514yescomplemented
428C2×C53C22×2−1+411yescharacteristic
429C2×C53C22×2−1+411yescharacteristic
430C2×C53C2×#58511yescharacteristic
431D53—44no—
432#563—5364no—
433Q82—5316no—
434#557—5332no—
435#557—5316no—
436#556—5332no—
437#556—5332no—
438#556—5316no—
439#554—5316no—
440#552—5332no—
441#544—5332no—
442#542—5332no—
443#541—5332no—
444#541—5364no—
445#541—5332no—
446#533—5316no—
447#533C2×D53116yescomplemented
448C2×C4⋊Q8—534no—
449C2×C4⋊Q8—534no—
450C2×C4⋊Q8—532no—
451C2×C4⋊Q8—531no—
452C2×C4⋊Q8—531no—
453C2×C4⋊Q8—532no—
454C2×C4⋊Q8—532no—
455C2×C4⋊Q8C2×D5311yescharacteristic
456C2×C4⋊Q8C2×D5311yescharacteristic
457#529—5316no—
458C2×#126—534no—
459C2×#126—534no—
460C2×#126—534no—
461C2×#126—534no—
462C2×#126—534no—
463C2×#126—534no—
464C2×#126—532no—
465C2×#125—534no—
466C2×#125—534no—
467C2×#125—534no—
468C2×#125—534no—
469C2×#125—534no—
470C2×#125—532no—
471C2×#125—531no—
472C2×#125—532no—
473C2×#125—532no—
474C2×#125C2×D5312yes—
475C2×#124—534no—
476C2×#124—531no—
477C2×#124—532no—
478C2×#123—532no—
479C2×#123—534no—
480C2×C22⋊Q8—532no—
481C2×C22⋊Q8—532no—
482C2×C22⋊Q8—534no—
483C2×C22⋊Q8—531no—
484C2×C22⋊Q8—532no—
485C2×C22⋊Q8—532no—
486C2×C22⋊Q8—534no—
487C2×C22⋊Q8—534no—
488C2×C22⋊Q8C2×D5311yescharacteristic
489C2×C22⋊Q8C2×D5311yescharacteristic
490C2×C22⋊Q8C2×D5312yes—
491C2×#121—531no—
492C2×C4×Q8—532no—
493C2×C4×Q8—532no—
494C2×C4×Q8—534no—
495C2×C4×Q8—531no—
496C2×C4×Q8—532no—
497C2×C4×Q8—532no—
498C2×C4×Q8—532no—
499C2×C4×Q8—532no—
500C2×C4×Q8—532no—
501C2×C4×Q8C2×D5311yescharacteristic
502C2×C4×Q8C2×D5312yes—
503C2×C4×Q8C2×D5311yescharacteristic
504C2×C4×D4—532no—
505C2×C4×D4—531no—
506C2×C4×D4—532no—
507C2×#117—532no—
508C2×#117—534no—
509C2×#117—532no—
510C2×#117—532no—
511C2×#117C2×D5312yes—
512C22×C4⋊C4—532no—
513C22×C42C2×D5311yescharacteristic
514C53C2×#355511yescharacteristic, complemented, Sylow
515C22×Q8—531no—
516C22×Q8—532no—
517C22×Q8—532no—
518C22×Q8—534no—
519C22×Q8C22×D5311yescharacteristic
520C22×Q8C22×D5311yescharacteristic
521C22×Q8C22×D5312yes—
522C22×D4—532no—
523C22×D4—531no—
524C23×C4—532no—
525C23×C4—534no—
526C23×C4C22×D5311yescharacteristic
527C23×C4C22×D5311yescharacteristic
528C23×C4C22×D5311yescharacteristic
529C4⋊Q8—5332no—
530C4⋊Q8—5332no—
531C4⋊Q8—5316no—
532C4⋊Q8—538no—
533C4⋊Q8—538no—
534C4⋊Q8—5316no—
535C4⋊Q8—5316no—
536C4⋊Q8C22×D5318yes—
537C4⋊Q8C22×D5318yes—
538#126—5332no—
539#126—5332no—
540#126—5332no—
541#126—5332no—
542#126—5332no—
543#126—5332no—
544#126—5316no—
545#125—5332no—
546#125—5332no—
547#125—5332no—
548#125—5332no—
549#125—5332no—
550#125—5316no—
551#125—538no—
552#125—5316no—
553#125—5316no—
554#125C22×D53116yes—
555#124—5332no—
556#124—538no—
557#124—5316no—
558#123—5316no—
559#123—5332no—
560C22⋊Q8—5316no—
561C22⋊Q8—5316no—
562C22⋊Q8—5332no—
563C22⋊Q8—538no—
564C22⋊Q8—5316no—
565C22⋊Q8—5316no—
566C22⋊Q8—5332no—
567C22⋊Q8—5332no—
568C22⋊Q8C22×D5318yes—
569C22⋊Q8C22×D5318yes—
570C22⋊Q8C22×D53116yes—
571#121—538no—
572C4×Q8—5316no—
573C4×Q8—5316no—
574C4×Q8—5332no—
575C4×Q8—538no—
576C4×Q8—5316no—
577C4×Q8—5316no—
578C4×Q8—5316no—
579C4×Q8—5316no—
580C4×Q8—5316no—
581C4×Q8C22×D5318yes—
582C4×Q8C22×D53116yes—
583C4×Q8C22×D5318yes—
584C4×D4—5316no—
585C4×D4—538no—
586C4×D4—5316no—
587#117—5316no—
588#117—5332no—
589#117—5316no—
590#117—5316no—
591#117C22×D53116yes—
592C2×C4⋊C4—532no—
593C2×C4⋊C4—534no—
594C2×C4⋊C4—532no—
595C2×C4⋊C4—532no—
596C2×C4⋊C4—534no—
597C2×C4⋊C4—532no—
598C2×C4⋊C4—531no—
599C2×C4⋊C4—532no—
600C2×C4⋊C4—532no—
601C2×C4⋊C4—531no—
602C2×C4⋊C4—534no—
603C2×C4⋊C4—534no—
604C2×C4⋊C4—534no—
605C2×C4⋊C4—534no—
606C2×C4⋊C4—534no—
607C2×C4⋊C4—532no—
608C2×C4⋊C4—534no—
609C2×C4⋊C4—532no—
610C2×C4⋊C4—534no—
611C2×C4⋊C4—534no—
612C2×C4⋊C4—5316no—
613C2×C4⋊C4C22×D5311yescharacteristic
614C2×C4⋊C4C22×D5312yes—
615C2×C4⋊C4C22×D5311yescharacteristic
616C2×C4⋊C4C22×D5312yes—
617C2×C4⋊C4C22×D5312yes—
618C2×C4⋊C4C22×D5312yes—
619C2×C4⋊C4C22×D5312yes—
620C2×C4⋊C4C22×D5312yes—
621C2×C4⋊C4C22×D5312yes—
622C2×C22⋊C4—534no—
623C2×C22⋊C4—532no—
624C2×C22⋊C4—532no—
625C2×C22⋊C4—532no—
626C2×C22⋊C4—532no—
627C2×C22⋊C4—534no—
628C2×C22⋊C4—534no—
629C2×C22⋊C4—532no—
630C2×C22⋊C4—534no—
631C2×C22⋊C4C22×D5312yes—
632C2×C22⋊C4C22×D5312yes—
633C2×C42—534no—
634C2×C42—532no—
635C2×C42—534no—
636C2×C42—534no—
637C2×C42—534no—
638C2×C42C22×D5311yescharacteristic
639C2×C42C22×D5312yes—
640C2×C42C22×D5312yes—
641C2×C42C22×D5311yescharacteristic
642C2×C42C22×D5311yescharacteristic
643C2×C42C22×D5311yescharacteristic
644C2×C42C22×D5318yes—
645C24—532no—
646C24C23×D5311yescharacteristic
647C2×Q8—24no—
648C2×Q8—24no—
649C2×Q8—44no—
650C2×Q8—534no—
651C2×Q8—538no—
652C2×Q8—538no—
653C2×Q8—5316no—
654C2×Q8—1064no—
655C2×Q8—1068no—
656C2×Q8—2124no—
657C2×Q8—2128no—
658C2×Q8C23×D5314yes—
659C2×Q8C23×D5314yes—
660C2×Q8C23×D5318yes—
661C2×D4—538no—
662C2×D4—534no—
663C2×D4—1064no—
664C2×D4—2124no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—534no—
669C22×C4—532no—
670C22×C4—532no—
671C22×C4—532no—
672C22×C4—534no—
673C22×C4—538no—
674C22×C4—5316no—
675C22×C4—1068no—
676C22×C4—2128no—
677C22×C4C23×D5314yes—
678C22×C4C23×D5314yes—
679C22×C4C23×D5311yescharacteristic
680C22×C4C23×D5312yes—
681C22×C4C23×D5312yes—
682C22×C4C23×D5312yes—
683C22×C4C23×D5311yescharacteristic
684C22×C4C23×D5311yescharacteristic
685C22×C4C23×D5311yescharacteristic
686C22×C4C23×D5312yes—
687C22×C4C23×D5314yes—
688C22×C4C23×D5311yescharacteristic
689C22×C4C23×D5311yescharacteristic
690C4⋊C4—538no—
691C4⋊C4—5316no—
692C4⋊C4—538no—
693C4⋊C4—538no—
694C4⋊C4—5316no—
695C4⋊C4—538no—
696C4⋊C4—534no—
697C4⋊C4—538no—
698C4⋊C4—538no—
699C4⋊C4—534no—
700C4⋊C4—5316no—
701C4⋊C4—5316no—
702C4⋊C4—5316no—
703C4⋊C4—5316no—
704C4⋊C4—5316no—
705C4⋊C4—538no—
706C4⋊C4—5316no—
707C4⋊C4—538no—
708C4⋊C4—5316no—
709C4⋊C4—5316no—
710C4⋊C4C23×D5314yes—
711C4⋊C4C23×D5318yes—
712C4⋊C4C23×D5314yes—
713C4⋊C4C23×D5318yes—
714C4⋊C4C23×D5318yes—
715C4⋊C4C23×D5318yes—
716C4⋊C4C23×D5318yes—
717C4⋊C4C23×D5318yes—
718C4⋊C4C23×D5318yes—
719C22⋊C4—5316no—
720C22⋊C4—538no—
721C22⋊C4—538no—
722C22⋊C4—538no—
723C22⋊C4—538no—
724C22⋊C4—5316no—
725C22⋊C4—5316no—
726C22⋊C4—538no—
727C22⋊C4—5316no—
728C22⋊C4C23×D5318yes—
729C22⋊C4C23×D5318yes—
730C42—5316no—
731C42—538no—
732C42—5316no—
733C42—5316no—
734C42—5316no—
735C42C23×D5314yes—
736C42C23×D5314yes—
737C42C23×D5314yes—
738C42C23×D5314yes—
739C42C23×D5318yes—
740C42C23×D5318yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—534no—
745C23—1064no—
746C23—1064no—
747C23—1064no—
748C23C24×D5312yes—
749C23C24×D5311yescharacteristic
750Q8—28no—
751Q8—28no—
752Q8—48no—
753Q8—1068no—
754Q8—10616no—
755Q8—2128no—
756Q8—21216no—
757D4—1068no—
758D4—2128no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—44no—
770C2×C4—538no—
771C2×C4—534no—
772C2×C4—534no—
773C2×C4—534no—
774C2×C4—538no—
775C2×C4—1064no—
776C2×C4—1068no—
777C2×C4—1064no—
778C2×C4—1068no—
779C2×C4—1064no—
780C2×C4—10616no—
781C2×C4—21216no—
782C2×C4#1313326414yes—
783C2×C4#1313326514yes—
784C2×C4C24×D5312yes—
785C2×C4C24×D5314yes—
786C2×C4C24×D5314yes—
787C2×C4C24×D5314yes—
788C2×C4C24×D5312yes—
789C2×C4C24×D5312yes—
790C2×C4C24×D5312yes—
791C2×C4C24×D5314yes—
792C2×C4C24×D5312yes—
793C2×C4C24×D5312yes—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—1064no—
799C22—1064no—
800C22—1064no—
801C22—2128no—
802C22C2×#1313326412yes—
803C22C2×#1313326512yes—
804C22#1681145912yes—
805C22C25×D5311yescharacteristic
806C4—22no—
807C4—24no—
808C4—24no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—24no—
814C4—1064no—
815C4—1068no—
816C4—1064no—
817C4—1068no—
818C4—1064no—
819C4C2×#1313326414yes—
820C4C2×#1313326514yes—
821C2—42no—
822C2—2124no—
823C2#2028920314yesdirect product factor
824C2C22×#1313326411yescharacteristic
825C2C22×#1313326511yescharacteristic
826C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#533C2
socleC23×C53C25
prime radicalC2×#13133191C22
hypercenterC2×#533D53
hypocenterC53C2×#3555
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #20289203C2direct (N × H)
2. C2×#16811374C2semidirect
3. C2×Q8×Dic106C2semidirect
4. C2×#16811352C2semidirect
5. C2×#16811351C2semidirect
6. C2×#16811346C2semidirect
7. C2×#16811346C2semidirect
8. C2×#16811344C2semidirect
9. C2×#16811333C2semidirect
10. C2×#16811307C2semidirect
11. C2×#16811250C2semidirect
13. C2×#16811235C2semidirect
14. C2×#16811234C2semidirect
15. C2×#16811232C2semidirect
16. C2×#16811180C2semidirect
18. C2×C53×#533C2semidirect
19. #16811374C22semidirect
20. Q8×Dic106C22semidirect
21. #16811352C22semidirect
22. #16811351C22semidirect
23. #16811346C22semidirect
24. #16811346C22semidirect
25. #16811344C22semidirect
26. #16811333C22semidirect
27. #16811307C22semidirect
28. #16811250C22semidirect
30. #16811235C22semidirect
31. #16811234C22semidirect
32. #16811232C22semidirect
33. #16811180C22semidirect
89. C53×#533C22semidirect
424. C2×#533D53semidirect
427. C2×C53#3555semidirect
447. #533C2×D53semidirect
514. C53C2×#3555semidirect
823. C2#20289203direct (N × H)

Maximal subgroups

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

subgroupindex
#202892032
C2×#168113742
C2×Q8×Dic1062
C2×#168113522
C2×#168113512
C2×#168113462
C2×#168113442
C2×#168113332
C2×#168113072
C2×#168112502
C2×#168112442
C2×#168112352
C2×#168112342
C2×#168112322
C2×#168111802
C2×#168111572
C2×C53×#5332
C2×#355553