Finite Group Databasebeta

← C2×#20288538 #28292572

Subgroups — C2×#20288538 #28292572

Order 13568.

6958 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288538C2132yesmaximal, direct product factor
2C2×#16811350C212yesmaximal, complemented
3C2×#16811348C212yesmaximal, complemented
4C2×#16811334C212yesmaximal, complemented
5C2×#16811331C214yesmaximal, complemented
6C2×#16811329C212yesmaximal, complemented
7C2×#16811327C214yesmaximal, complemented
8C2×#16811253C212yesmaximal, complemented
9C2×#16811251C211yesmaximal, characteristic, complemented
10C2×#16811250C212yesmaximal, complemented
11C2×#16811178C212yesmaximal, complemented
12C2×#16811176C211yesmaximal, characteristic, complemented
13C22×#13133208C211yesmaximal, characteristic, complemented
14C2×#125×D53C212yesmaximal, complemented
15C2×#16811104C211yesmaximal, characteristic
16C2×#16811103C211yesmaximal, characteristic
17C2×#16811091C211yesmaximal, characteristic
18C2×C53×#544C211yesmaximal, characteristic, complemented
19C22×#11719945C2211yescharacteristic
20#16811350C22132yescomplemented
21#16811348C22132yescomplemented
22#16811334C22132yescomplemented
23#16811331C22164yescomplemented
24#16811329C22132yescomplemented
25#16811327C22164yescomplemented
26#16811253C22132yescomplemented
27#16811251C22116yescomplemented
28#16811250C22132yescomplemented
29#16811178C22132yescomplemented
30#16811176C22116yescomplemented
31C2×#13133217C2212yes—
32C2×#13133216C2211yescharacteristic
33C2×#13133216C2211yescharacteristic
34C2×#13133216C2212yes—
35C2×#13133216C2214yes—
36C2×#13133215C2214yes—
37C2×#13133209C2212yes—
38C2×#13133208C2211yescharacteristic
39C2×#13133208C2211yescharacteristic
40C2×#13133208C2212yes—
41C2×#13133208C2212yes—
42C2×#13133208C2212yes—
43C2×#13133208C2212yes—
44C2×#13133208C2212yes—
45C2×#13133208C22116yescomplemented
46C2×#13133207C2214yes—
47C2×#13133207C2214yes—
48C2×#13133207C2214yes—
49C2×#13133207C2214yes—
50#125×D53C22132yescomplemented
51C2×#13133197C2214yes—
52C2×#13133197C2214yes—
53C2×#13133195C2214yes—
54C2×#13133195C2214yes—
55C2×#13133194C2212yes—
56C2×#13133194C2212yes—
57C2×#13133194C2214yes—
58C2×#13133193C2214yes—
59C2×#13133193C2214yes—
60#16811104C22116yes—
61#16811103C22116yes—
62#16811091C22116yes—
63C2×Q8×Dic53C2214yes—
64C2×C4×Dic106C2212yes—
65C2×C4×Dic106C2212yes—
66C2×C4×Dic106C2212yes—
67C2×#13133182C2214yes—
68C2×#13133182C2211yescharacteristic
69C2×#13133182C2212yes—
70C2×#13133182C2211yescharacteristic
71C2×C4×D212C2212yes—
72C2×#13133179C2211yescharacteristic
73C2×#13133179C2211yescharacteristic
74C2×#13133179C2212yes—
75C2×C4×C22⋊D53C2214yes—
76C2×#13133177C2212yes—
77C2×#13133177C2212yes—
78C2×#13133177C2214yes—
79C2×#13133176C2211yescharacteristic
80C2×#13133175C2212yes—
81C2×#13133175C2212yes—
82C2×#13133174C2212yes—
83C22×C4⋊Dic53C2211yescharacteristic
84C22×C4⋊Dic53C2212yes—
85C22×#11719919C2212yes—
86C2×C4⋊C4×D53C2212yes—
87C2×C4⋊C4×D53C2212yes—
88C2×C4⋊C4×D53C2214yes—
89C2×C4⋊C4×D53C2214yes—
90C22×C4×Dic53C2211yescharacteristic
91C2×C42×D53C2212yes—
92C53×#544C22116yescomplemented
93C2×C4⋊Q8×C53C2212yes—
94C2×C4⋊Q8×C53C2212yes—
95C2×#125×C53C2212yes—
96C2×#125×C53C2212yes—
97C2×C22⋊Q8×C53C2214yes—
98C2×#117×C53C2211yescharacteristic
99C2×#117×C53C2211yescharacteristic
100C22×C4⋊C4×C53C2211yescharacteristic
101C2×#11719945Q8116yescomplemented
102C2×#11719945C2318yes—
103C22×Dic106C2314yes—
104C22×Dic106C2312yes—
105C22×Dic106C2312yes—
106C22×Dic106C2311yescharacteristic
107C22×D212C2311yescharacteristic
108C22×C22⋊D53C2312yes—
109C23×Dic53C2311yescharacteristic
110C23×Dic53C2311yescharacteristic
111C23×Dic53C2312yes—
112C22×C4×D53C2312yes—
113C22×C4×D53C2312yes—
114C22×C4×D53C2314yes—
115C22×C4×D53C2314yes—
116C22×C4×D53C2312yes—
117#13133217C23116yes—
118#13133216C23116yes—
119#13133216C23132yes—
120#13133216C2318yes—
121#13133216C2318yes—
122#13133215C23132yes—
123#13133209C23116yes—
124#13133208C23116yes—
125#13133208C23116yes—
126#13133208C23116yes—
127#13133208C2318yes—
128#13133208C23116yes—
129#13133208C23116yes—
130#13133208C2318yes—
131#13133207C23132yes—
132#13133207C23132yes—
133#13133207C23132yes—
134#13133207C23132yes—
135#13133197C23132yes—
136#13133197C23132yes—
137#13133195C23132yes—
138#13133195C23132yes—
139#13133194C23116yes—
140#13133194C23132yes—
141#13133194C23116yes—
142#13133193C23132yes—
143#13133193C23132yes—
144Q8×Dic53C23132yes—
145C4×Dic106C23116yes—
146C4×Dic106C23116yes—
147C4×Dic106C23116yes—
148#13133182C23132yes—
149#13133182C2318yes—
150#13133182C2318yes—
151#13133182C23116yes—
152C4×D212C23116yes—
153#13133179C2318yes—
154#13133179C23116yes—
155#13133179C2318yes—
156C4×C22⋊D53C23132yes—
157#13133177C23116yes—
158#13133177C23132yes—
159#13133177C23116yes—
160#13133176C2318yes—
161#13133175C23116yes—
162#13133175C23116yes—
163#13133174C23116yes—
164C2×C4⋊Dic53C2311yescharacteristic
165C2×C4⋊Dic53C2312yes—
166C2×C4⋊Dic53C2312yes—
167C2×C4⋊Dic53C2314yes—
168C2×C4⋊Dic53C23116yes—
169C2×C4⋊Dic53C2312yes—
170C2×C4⋊Dic53C2318yes—
171C2×C4⋊Dic53C2314yes—
172C2×C4⋊Dic53C2311yescharacteristic
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2314yes—
175C2×#11719919C23116yes—
176C2×#11719919C2312yes—
177C2×#11719919C2314yes—
178C2×#11719919C2314yes—
179C2×#11719919C2314yes—
180C2×#11719919C2314yes—
181C2×#11719919C2314yes—
182C2×#11719919C2314yes—
183C2×#11719919C2312yes—
184C2×#11719919C2312yes—
185C2×#11719919C2312yes—
186C2×#11719919C2312yes—
187C2×#11719919C2312yes—
188C4⋊C4×D53C23132yes—
189C4⋊C4×D53C23132yes—
190C4⋊C4×D53C23116yes—
191C4⋊C4×D53C23116yes—
192C2×C22⋊Dic53C2312yes—
193C2×#11719921C2312yes—
194C2×#11719921C2312yes—
195C2×#11719921C2314yes—
196C2×#11719921C2314yes—
197C2×C4×Dic53C2311yescharacteristic
198C2×C4×Dic53C2312yes—
199C2×C4×Dic53C2312yes—
200C2×C4×Dic53C2311yescharacteristic
201C2×C4×Dic53C2311yescharacteristic
202C2×C4×Dic53C2311yescharacteristic
203C2×C4×Dic53C2318yes—
204C2×C4×Dic53C2314yes—
205C2×C4×Dic53C2314yes—
206C2×C4×Dic53C2312yes—
207C42×D53C23116yes—
208C22×Q8×C53C2314yes—
209C23×C4×C53C2312yes—
210C23×C4×C53C2311yescharacteristic
211C4⋊Q8×C53C23116yes—
212C4⋊Q8×C53C23116yes—
213#125×C53C23116yes—
214#125×C53C23116yes—
215C22⋊Q8×C53C23132yes—
216#117×C53C2318yes—
217#117×C53C2318yes—
218C2×C4⋊C4×C53C2312yes—
219C2×C4⋊C4×C53C2312yes—
220C2×C4⋊C4×C53C2318yes—
221C2×C4⋊C4×C53C2311yescharacteristic
222C2×C4⋊C4×C53C2311yescharacteristic
223C2×C4⋊C4×C53C2311yescharacteristic
224C2×C4⋊C4×C53C2311yescharacteristic
225C2×C4⋊C4×C53C2314yes—
226C2×C4⋊C4×C53C2314yes—
227C2×C4⋊C4×C53C2314yes—
228C2×C22⋊C4×C53C2312yes—
229C2×C22⋊C4×C53C2312yes—
230C2×C42×C53C2312yes—
231C2×C42×C53C2312yes—
232C24×C53C2411yescharacteristic
233C23×D53C2412yes—
234C2×Q8×C53—48no—
235C2×Q8×C53C24116yes—
236C22×C4×C53—44no—
237C22×C4×C53C2×Q818yes—
238C22×C4×C53C2412yes—
239C22×C4×C53C2412yes—
240C22×C4×C53C2412yes—
241C22×C4×C53C2412yes—
242C22×C4×C53C2414yes—
243C22×C4×C53C2418yes—
244C22×C4×C53C2411yescharacteristic
245C22×C4×C53C2411yescharacteristic
246C22×C4×C53C2414yes—
247C2×C22⋊D53C2×Q8116yes—
248C2×C22⋊D53C2418yes—
249C22×Dic53—42no—
250C22×Dic53—42no—
251C22×Dic53—44no—
252C22×Dic53C2411yescharacteristic
253C22×Dic53C2411yescharacteristic
254C22×Dic53C2412yes—
255C22×Dic53C2411yescharacteristic
256C22×Dic53C2411yescharacteristic
257C22×Dic53C2414yes—
258C22×Dic53C2412yes—
259C22×Dic53C2414yes—
260C22×Dic53C2414yes—
261C22×Dic53C2418yes—
262C22×Dic53C2412yes—
263#11719945C2×Q8164yescomplemented
264C2×D212C2×Q818yes—
265C2×D212C2414yes—
266C2×C4×D53—48no—
267C2×C4×D53—48no—
268C2×C4×D53—44no—
269C2×C4×D53—44no—
270C2×C4×D53C2×Q8116yes—
271C2×C4×D53C2418yes—
272C2×C4×D53C2418yes—
273C2×C4×D53C24116yes—
274C2×C4×D53C24116yes—
275C2×C4×D53C2418yes—
276C2×Dic106—44no—
277C2×Dic106—48no—
278C2×Dic106—44no—
279C2×Dic106C2×Q818yes—
280C2×Dic106C24116yes—
281C2×Dic106C2418yes—
282C2×Dic106C2418yes—
283C2×Dic106C2414yes—
284C4⋊C4×C53C2418yes—
285C4⋊C4×C53C2418yes—
286C4⋊C4×C53C2414yes—
287C4⋊C4×C53C2414yes—
288C4⋊C4×C53C2414yes—
289C4⋊C4×C53C2414yes—
290C4⋊C4×C53C24116yes—
291C4⋊C4×C53C24116yes—
292C4⋊C4×C53C24116yes—
293C22⋊C4×C53C2418yes—
294C22⋊C4×C53C2418yes—
295C42×C53C2418yes—
296C42×C53C2418yes—
297C22⋊Dic53C2418yes—
298#11719921C2418yes—
299#11719921C2418yes—
300#11719921C24116yes—
301#11719921C24116yes—
302C4⋊Dic53C2414yes—
303C4⋊Dic53C2418yes—
304C4⋊Dic53C2418yes—
305C4⋊Dic53C24116yes—
306C4⋊Dic53C2418yes—
307C4⋊Dic53C24116yes—
308C4⋊Dic53C2414yes—
309C4⋊Dic53C2418yes—
310C4⋊Dic53C24116yes—
311#11719919C2418yes—
312#11719919C24116yes—
313#11719919C24116yes—
314#11719919C24116yes—
315#11719919C24116yes—
316#11719919C24116yes—
317#11719919C24116yes—
318#11719919C2418yes—
319#11719919C2418yes—
320#11719919C2418yes—
321#11719919C2418yes—
322#11719919C2418yes—
323C4×Dic53C2414yes—
324C4×Dic53C2418yes—
325C4×Dic53C2418yes—
326C4×Dic53C2414yes—
327C4×Dic53C2414yes—
328C4×Dic53C2414yes—
329C4×Dic53C24116yes—
330C4×Dic53C24116yes—
331C4×Dic53C2418yes—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53C22×Q814yes—
335C23×C53C2512yes—
336C23×C53C2511yescharacteristic
337C22×D53—24no—
338C22×D53—24no—
339C22×D53C22×Q818yes—
340C22×D53C2514yes—
341Q8×C53—416no—
342C2×C4×C53—24no—
343C2×C4×C53—24no—
344C2×C4×C53—24no—
345C2×C4×C53—28no—
346C2×C4×C53—24no—
347C2×C4×C53—48no—
348C2×C4×C53C22×Q814yes—
349C2×C4×C53C22×Q814yes—
350C2×C4×C53C22×Q8116yes—
351C2×C4×C53C2514yes—
352C2×C4×C53C2514yes—
353C2×C4×C53C2514yes—
354C2×C4×C53C2518yes—
355C2×C4×C53C2514yes—
356C2×C4×C53C2512yes—
357C2×C4×C53C2512yes—
358C22⋊D53C22×Q8132yes—
359C2×Dic53—24no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—24no—
363C2×Dic53—28no—
364C2×Dic53—22no—
365C2×Dic53—22no—
366C2×Dic53—44no—
367C2×Dic53—44no—
368C2×Dic53—48no—
369C2×Dic53C22×Q818yes—
370C2×Dic53C2514yes—
371C2×Dic53C2512yes—
372C2×Dic53C2512yes—
373C2×Dic53C2514yes—
374C2×Dic53C2518yes—
375C2×Dic53C2512yes—
376C2×Dic53C2512yes—
377C2×Dic53C2514yes—
378D212C22×Q8116yes—
379C4×D53—416no—
380C4×D53—416no—
381C4×D53—48no—
382C4×D53—48no—
383C4×D53C22×Q8132yes—
384Dic106—48no—
385Dic106—416no—
386Dic106—48no—
387Dic106C22×Q8116yes—
388C2×#3504—531nomaximal, Sylow
389C22×C53—22no—
390C22×C53—22no—
391C22×C53—28no—
392C22×C53C23×Q814yes—
393C22×C53C23×Q812yes—
394C22×C53#58512yes—
395C22×C53#58512yes—
396C22×C53C2611yescharacteristic
397C2×D53—24no—
398C2×D53—24no—
399C2×D53—216no—
400C2×D53C23×Q818yes—
401C4×C53—24no—
402C4×C53—24no—
403C4×C53—24no—
404C4×C53—28no—
405C4×C53—24no—
406C4×C53C23×Q814yes—
407C4×C53C23×Q814yes—
408Dic53—24no—
409Dic53—22no—
410Dic53—22no—
411Dic53—24no—
412Dic53—28no—
413Dic53—22no—
414Dic53—22no—
415Dic53C23×Q818yes—
416#3504—5332no—
417C2×#557—532no—
418C2×#557—532no—
419C2×#554—532no—
420C2×#554—532no—
421C2×#554—534no—
422C2×#554—534no—
423C2×#544—532no—
424C2×#544—532no—
425C2×#544—531no—
426C2×#544D5311yescharacteristic, complemented
427C2×#533—532no—
428C2×#533—531no—
429C22×#125—532no—
430C22×#125—531no—
431C2×#520—531no—
432C2×#520—531no—
433C2×C4×#41—531no—
434C2×C53—24no—
435C2×C53#350414yescomplemented
436C2×C53C24×Q811yescharacteristic
437C2×C53C2×#58511yescharacteristic
438C2×C53C2×#58511yescharacteristic
439D53—28no—
440C22×#41—531no—
441#557—5332no—
442#557—5332no—
443#554—5332no—
444#554—5332no—
445#554—5364no—
446#554—5364no—
447#544—5332no—
448#544—5332no—
449#544—5316no—
450#544C2×D53116yescomplemented
451#533—5332no—
452#533—5316no—
453C2×C4⋊Q8—534no—
454C2×C4⋊Q8—531no—
455C2×C4⋊Q8—531no—
456C2×C4⋊Q8—534no—
457C2×C4⋊Q8—532no—
458C2×C4⋊Q8—532no—
459C2×C4⋊Q8C2×D5312yes—
460C2×C4⋊Q8C2×D5312yes—
461C2×#125—5332no—
462C2×#125—531no—
463C2×#125—532no—
464C2×#125—532no—
465C2×#125—534no—
466C2×#125—534no—
467C2×#125—532no—
468C2×#125—532no—
469C2×#125—5316no—
470C2×#125—531no—
471C2×#125—534no—
472C2×#125—534no—
473C2×#125—532no—
474C2×#125—532no—
475C2×#125C2×D5312yes—
476C2×#125C2×D5312yes—
477C2×C22⋊Q8—534no—
478C2×C22⋊Q8—534no—
479C2×C22⋊Q8—534no—
480C2×C22⋊Q8—534no—
481C2×C22⋊Q8—534no—
482C2×C22⋊Q8—534no—
483C2×C22⋊Q8—532no—
484C2×C22⋊Q8—532no—
485C2×C22⋊Q8—534no—
486C2×C22⋊Q8C2×D5314yes—
487#520—5316no—
488#520—5316no—
489C4×#41—5316no—
490C2×C4×Q8—534no—
491C2×C4×Q8—531no—
492C2×C4×Q8—531no—
493C2×C4×Q8—532no—
494C2×C4×Q8—534no—
495C2×C4×Q8—532no—
496C2×C4×Q8—532no—
497C2×C4×Q8—532no—
498C2×C4×D4—534no—
499C2×C4×D4—531no—
500C2×C4×D4—531no—
501C2×C4×D4—532no—
502C2×C4×D4—532no—
503C2×C4×D4—532no—
504C2×C4×D4—534no—
505C2×C4×D4—532no—
506C2×#117—531no—
507C2×#117—532no—
508C2×#117—532no—
509C2×#117—532no—
510C2×#117C2×D5311yescharacteristic
511C2×#117C2×D5311yescharacteristic
512C22×C4⋊C4—532no—
513C22×C4⋊C4—531no—
514C22×C4⋊C4—532no—
515C22×C4⋊C4—532no—
516C22×C4⋊C4—532no—
517C22×C4⋊C4—534no—
518C22×C4⋊C4—534no—
519C22×C4⋊C4C2×D5311yescharacteristic
520C22×C42—531no—
521C22×C42—532no—
522C53C2×#350411yescharacteristic, complemented, Sylow
523C2×#41—5316no—
524C2×#41—538no—
525C22×Q8—531no—
526C22×Q8—532no—
527C22×Q8—534no—
528C22×Q8—532no—
529C22×Q8C22×D5314yes—
530C22×D4—532no—
531C22×D4—531no—
532C23×C4—532no—
533C23×C4—532no—
534C23×C4—531no—
535C23×C4—531no—
536C23×C4—534no—
537C23×C4—534no—
538C23×C4—532no—
539C23×C4—532no—
540C23×C4C22×D5312yes—
541C23×C4C22×D5311yescharacteristic
542C4⋊Q8—5332no—
543C4⋊Q8—538no—
544C4⋊Q8—538no—
545C4⋊Q8—5332no—
546C4⋊Q8—5316no—
547C4⋊Q8—5316no—
548C4⋊Q8C22×D53116yes—
549C4⋊Q8C22×D53116yes—
550#125—538no—
551#125—5316no—
552#125—5316no—
553#125—5332no—
554#125—5332no—
555#125—5316no—
556#125—5316no—
557#125—538no—
558#125—5332no—
559#125—5332no—
560#125—5316no—
561#125—5316no—
562#125C22×D53116yes—
563#125C22×D53116yes—
564C22⋊Q8—5332no—
565C22⋊Q8—5332no—
566C22⋊Q8—5332no—
567C22⋊Q8—5332no—
568C22⋊Q8—5332no—
569C22⋊Q8—5332no—
570C22⋊Q8—5316no—
571C22⋊Q8—5316no—
572C22⋊Q8—5332no—
573C22⋊Q8C22×D53132yes—
574C4×Q8—5332no—
575C4×Q8—538no—
576C4×Q8—538no—
577C4×Q8—5316no—
578C4×Q8—5332no—
579C4×Q8—5316no—
580C4×Q8—5316no—
581C4×Q8—5316no—
582C4×D4—5332no—
583C4×D4—538no—
584C4×D4—538no—
585C4×D4—5316no—
586C4×D4—5316no—
587C4×D4—5316no—
588C4×D4—5332no—
589C4×D4—5316no—
590#117—538no—
591#117—5316no—
592#117—5316no—
593#117—5316no—
594#117C22×D5318yes—
595#117C22×D5318yes—
596C2×C4⋊C4—532no—
597C2×C4⋊C4—531no—
598C2×C4⋊C4—534no—
599C2×C4⋊C4—532no—
600C2×C4⋊C4—534no—
601C2×C4⋊C4—532no—
602C2×C4⋊C4—534no—
603C2×C4⋊C4—534no—
604C2×C4⋊C4—532no—
605C2×C4⋊C4—538no—
606C2×C4⋊C4—534no—
607C2×C4⋊C4—534no—
608C2×C4⋊C4—534no—
609C2×C4⋊C4—534no—
610C2×C4⋊C4—5316no—
611C2×C4⋊C4—5316no—
612C2×C4⋊C4—531no—
613C2×C4⋊C4—532no—
614C2×C4⋊C4—532no—
615C2×C4⋊C4—532no—
616C2×C4⋊C4—532no—
617C2×C4⋊C4—532no—
618C2×C4⋊C4—532no—
619C2×C4⋊C4—534no—
620C2×C4⋊C4—5316no—
621C2×C4⋊C4—5316no—
622C2×C4⋊C4—5332no—
623C2×C4⋊C4—5332no—
624C2×C4⋊C4C22×D5311yescharacteristic
625C2×C4⋊C4C22×D5312yes—
626C2×C4⋊C4C22×D5314yes—
627C2×C4⋊C4C22×D5314yes—
628C2×C4⋊C4C22×D5312yes—
629C2×C4⋊C4C22×D5318yes—
630C2×C4⋊C4C22×D5311yescharacteristic
631C2×C4⋊C4C22×D5311yescharacteristic
632C2×C4⋊C4C22×D5311yescharacteristic
633C2×C4⋊C4C22×D5314yes—
634C2×C22⋊C4—532no—
635C2×C22⋊C4—534no—
636C2×C22⋊C4—532no—
637C2×C22⋊C4—532no—
638C2×C22⋊C4—534no—
639C2×C22⋊C4C22×D5312yes—
640C2×C22⋊C4C22×D5312yes—
641C2×C42—531no—
642C2×C42—534no—
643C2×C42—534no—
644C2×C42—532no—
645C2×C42—532no—
646C2×C42—532no—
647C2×C42—531no—
648C2×C42—531no—
649C2×C42—538no—
650C2×C42—531no—
651C2×C42—5316no—
652C2×C42C22×D5312yes—
653C2×C42C22×D5312yes—
654C24—532no—
655C24C23×D5311yescharacteristic
656#41—5364no—
657C2×Q8—48no—
658C2×Q8—538no—
659C2×Q8—534no—
660C2×Q8—538no—
661C2×Q8—5316no—
662C2×Q8—538no—
663C2×Q8—2124no—
664C2×Q8—2124no—
665C2×Q8—2128no—
666C2×Q8C23×D53116yes—
667C2×D4—5316no—
668C2×D4—538no—
669C2×D4—538no—
670C2×D4—534no—
671C22×C4—44no—
672C22×C4—532no—
673C22×C4—5316no—
674C22×C4—538no—
675C22×C4—531no—
676C22×C4—531no—
677C22×C4—532no—
678C22×C4—531no—
679C22×C4—531no—
680C22×C4—532no—
681C22×C4—534no—
682C22×C4—534no—
683C22×C4—534no—
684C22×C4—538no—
685C22×C4—538no—
686C22×C4—538no—
687C22×C4—5316no—
688C22×C4—5316no—
689C22×C4—2128no—
690C22×C4—2124no—
691C22×C4—2128no—
692C22×C4—2124no—
693C22×C4—2122no—
694C22×C4—2122no—
695C22×C4—2124no—
696C22×C4Q8×D5318yes—
697C22×C4C23×D5312yes—
698C22×C4C23×D5312yes—
699C22×C4C23×D5312yes—
700C22×C4C23×D5314yes—
701C22×C4C23×D5312yes—
702C22×C4C23×D5318yes—
703C22×C4C23×D5314yes—
704C22×C4C23×D5311yescharacteristic
705C22×C4C23×D5311yescharacteristic
706C4⋊C4—538no—
707C4⋊C4—534no—
708C4⋊C4—5316no—
709C4⋊C4—538no—
710C4⋊C4—5316no—
711C4⋊C4—538no—
712C4⋊C4—5316no—
713C4⋊C4—5316no—
714C4⋊C4—538no—
715C4⋊C4—5316no—
716C4⋊C4—5316no—
717C4⋊C4—5316no—
718C4⋊C4—5316no—
719C4⋊C4—534no—
720C4⋊C4—538no—
721C4⋊C4—538no—
722C4⋊C4—538no—
723C4⋊C4—538no—
724C4⋊C4—538no—
725C4⋊C4—538no—
726C4⋊C4—5316no—
727C4⋊C4C23×D5314yes—
728C4⋊C4C23×D5318yes—
729C4⋊C4C23×D53116yes—
730C4⋊C4C23×D53116yes—
731C4⋊C4C23×D5318yes—
732C4⋊C4C23×D5314yes—
733C4⋊C4C23×D5314yes—
734C4⋊C4C23×D5314yes—
735C4⋊C4C23×D53116yes—
736C22⋊C4—538no—
737C22⋊C4—5316no—
738C22⋊C4—538no—
739C22⋊C4—538no—
740C22⋊C4—5316no—
741C22⋊C4C23×D5318yes—
742C22⋊C4C23×D5318yes—
743C42—534no—
744C42—534no—
745C42—538no—
746C42—538no—
747C42—534no—
748C42—534no—
749C42—5316no—
750C42—5316no—
751C42—538no—
752C42C23×D5318yes—
753C42C23×D5318yes—
754C23—22no—
755C23—22no—
756C23—538no—
757C23—534no—
758C23—1064no—
759C23—1064no—
760C23C2×Q8×D5314yes—
761C23C24×D5312yes—
762C23C24×D5311yescharacteristic
763Q8—416no—
764Q8—5316no—
765Q8—2128no—
766Q8—2128no—
767Q8—21216no—
768D4—5332no—
769D4—5316no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—48no—
776C2×C4—538no—
777C2×C4—534no—
778C2×C4—5332no—
779C2×C4—532no—
780C2×C4—532no—
781C2×C4—534no—
782C2×C4—532no—
783C2×C4—532no—
784C2×C4—534no—
785C2×C4—538no—
786C2×C4—1062no—
787C2×C4—1064no—
788C2×C4—1062no—
789C2×C4—1062no—
790C2×C4—1068no—
791C2×C4—1062no—
792C2×C4—1064no—
793C2×C4—21216no—
794C2×C4—2128no—
795C2×C4—21216no—
796C2×C4—2128no—
797C2×C4—2124no—
798C2×C4—2124no—
799C2×C4—2128no—
800C2×C4C2×Q8×D5314yes—
801C2×C4C2×Q8×D5314yes—
802C2×C4C2×Q8×D53116yes—
803C2×C4C24×D5314yes—
804C2×C4C24×D5314yes—
805C2×C4C24×D5314yes—
806C2×C4C24×D5318yes—
807C2×C4C24×D5314yes—
808C2×C4C24×D5312yes—
809C2×C4C24×D5312yes—
810C22—28no—
811C22—22no—
812C22—22no—
813C22—538no—
814C22—10616no—
815C22—1064no—
816C22—1064no—
817C22C22×Q8×D5314yes—
818C22C22×Q8×D5312yes—
819C22#1681145812yes—
820C22#1681146012yes—
821C22C25×D5311yescharacteristic
822C4—28no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—538no—
828C4—1062no—
829C4—1064no—
830C4—1062no—
831C4—1062no—
832C4—1068no—
833C4—1062no—
834C4—1064no—
835C4C22×Q8×D5314yes—
836C4C22×Q8×D5314yes—
837C2—24no—
838C2—1068no—
839C2#2028853814yesdirect product factor
840C2C23×Q8×D5311yescharacteristic
841C2C2×#1681145811yescharacteristic
842C2C2×#1681146011yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#544C2
socleC23×C53C25
prime radicalC22×#11719945C22
hypercenterC2×#544D53
hypocenterC53C2×#3504
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #20288538C2direct (N × H)
2. C2×#16811350C2semidirect
3. C2×#16811348C2semidirect
4. C2×#16811334C2semidirect
5. C2×#16811331C2semidirect
6. C2×#16811329C2semidirect
7. C2×#16811327C2semidirect
8. C2×#16811253C2semidirect
9. C2×#16811251C2semidirect
10. C2×#16811250C2semidirect
11. C2×#16811178C2semidirect
12. C2×#16811176C2semidirect
13. C22×#13133208C2semidirect
14. C2×#125×D53C2semidirect
18. C2×C53×#544C2semidirect
20. #16811350C22semidirect
21. #16811348C22semidirect
22. #16811334C22semidirect
23. #16811331C22semidirect
24. #16811329C22semidirect
25. #16811327C22semidirect
26. #16811253C22semidirect
27. #16811251C22semidirect
28. #16811250C22semidirect
29. #16811178C22semidirect
30. #16811176C22semidirect
45. C2×#13133208C22semidirect
50. #125×D53C22semidirect
92. C53×#544C22semidirect
101. C2×#11719945Q8semidirect
263. #11719945C2×Q8semidirect
426. C2×#544D53semidirect
435. C2×C53#3504semidirect
450. #544C2×D53semidirect
522. C53C2×#3504semidirect
839. C2#20288538direct (N × H)

Maximal subgroups

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

subgroupindex
#202885382
C2×#168113502
C2×#168113482
C2×#168113342
C2×#168113312
C2×#168113292
C2×#168113272
C2×#168112532
C2×#168112512
C2×#168112502
C2×#168111782
C2×#168111762
C22×#131332082
C2×#125×D532
C2×#168111042
C2×#168111032
C2×#168110912
C2×C53×#5442
C2×#350453