Finite Group Databasebeta

← #28328929

Subgroups — #28328929

Order 13568.

3112 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811692C211yesmaximal, characteristic, complemented
2C22×Q8×#6157C211yesmaximal, characteristic, complemented
3#20291246C213yesmaximal, complemented
4#20291240C213yesmaximal, complemented
5#20291239C213yesmaximal, complemented
6Q8×C4⋊#6157C211yesmaximal, characteristic, complemented
7D4×C4⋊#6157C213yesmaximal, complemented
8#20291220C211yesmaximal, characteristic, complemented
9Q8×C22⋊#6157C211yesmaximal, characteristic, complemented
10#20291205C213yesmaximal, complemented
11#20291202C213yesmaximal, complemented
12#121×#6157C213yesmaximal, complemented
13#20291169C213yesmaximal, complemented
14#20291155C211yesmaximal, characteristic, complemented
15#548×D53C211yesmaximal, characteristic
16#16811692—28no—
17C2×Q8×#6157—28no—
18C2×Q8×#6157C2211yescharacteristic
19C2×Q8×#6157C2213yes—
20C2×Q8×#6157C2211yescharacteristic
21C2×Q8×#6157C2213yes—
22C2×Q8×#6157C2211yescharacteristic
23C2×Q8×#6157C2211yescharacteristic
24C2×D4×#6157C2213yes—
25C2×D4×#6157C2213yes—
26C2×D4×#6157C2216yes—
27C2×#13133296C2213yes—
28C22×C4⋊#6157C2213yes—
29C22×C4⋊#6157C2213yes—
30C22×C4×#6157C2213yes—
31(C2×#6157)⋊Q8C2213yes—
32(C2×#6157)⋊Q8C2213yes—
33#16811575C2213yes—
34#16811575C2213yes—
35#16811574C2213yes—
36#16811574C2216yes—
37#16811574C2213yes—
38#16811573C2213yes—
39#16811573C2213yes—
40#16811573C2216yes—
41#16811573C2216yes—
42#16811572C2213yes—
43#16811572C2213yes—
44#16811571C2213yes—
45#16811571C2213yes—
46#16811570C2211yescharacteristic
47#16811570C2213yes—
48#16811570C2216yes—
49#16811570C2216yes—
50#16811569C2213yes—
51#16811565C2213yes—
52#16811565C2213yes—
53C4⋊C4×#6157C2213yes—
54C4⋊C4×#6157C2213yes—
55C4×C4⋊#6157C2213yes—
56C4×C4⋊#6157C2213yes—
57C22⋊C4×#6157C2216yes—
58C4×C22⋊#6157C2213yes—
59C4×C22⋊#6157C2213yes—
60#16811559C2213yes—
61C2×#41×D53C2211yescharacteristic
62C22×Q8×D53C2211yescharacteristic
63#16811285C411yescharacteristic, complemented
64#16811284C411yescharacteristic, complemented
65#16811283C413yescomplemented
66#16811282C413yescomplemented
67#16811281C413yescomplemented
68#16811280C411yescharacteristic, complemented
69#16811279C413yescomplemented
70#124×D53C2213yes—
71C22⋊Q8×D53C2213yes—
72#121×D53C2213yes—
73C4×Q8×D53C2211yescharacteristic
74C4×D4×D53C2213yes—
75C53×#548C411yescharacteristic, complemented
76C23×#6157C2311yescharacteristic
77C23×#6157C2313yes—
78C23×#6157C2316yes—
79Q8×#6157—24no—
80Q8×#6157—24no—
81Q8×#6157—24no—
82Q8×#6157—212no—
83Q8×#6157—212no—
84Q8×#6157D418yescomplemented
85D4×#6157—212no—
86D4×#6157—212no—
87D4×#6157—412no—
88#13133296—212no—
89C2×C4⋊#6157—212no—
90C2×C4⋊#6157—212no—
91C2×C4⋊#6157C2311yescharacteristic
92C2×C4⋊#6157C2313yes—
93C2×C4⋊#6157C2313yes—
94C2×C4⋊#6157C2313yes—
95C2×C4⋊#6157C2316yes—
96C2×C4⋊#6157C2311yescharacteristic
97C2×C4⋊#6157C2313yes—
98C2×C4⋊#6157C2313yes—
99C2×C4⋊#6157C2316yes—
100C2×C4⋊#6157C2313yes—
101C2×C22⋊#6157C2311yescharacteristic
102C2×C22⋊#6157C2313yes—
103C2×C22⋊#6157C2313yes—
104C2×C22⋊#6157C2313yes—
105C2×C22⋊#6157C2313yes—
106C2×C22⋊#6157C2313yes—
107C2×C22⋊#6157C2316yes—
108C2×C4×#6157—212no—
109C2×C4×#6157C2313yes—
110C2×C4×#6157C2313yes—
111C2×C4×#6157C2313yes—
112C2×C4×#6157C2313yes—
113C2×C4×#6157C2313yes—
114C2×C4×#6157C2316yes—
115C2×C4×#6157C2313yes—
116(C2×#6157)⋊C4C2311yescharacteristic
117(C2×#6157)⋊C4C2313yes—
118(C2×#6157)⋊C4C2313yes—
119(C2×#6157)⋊C4C2313yes—
120(C2×#6157)⋊C4C2311yescharacteristic
121(C2×#6157)⋊C4C2313yes—
122(C2×#6157)⋊C4C2313yes—
123(C2×#6157)⋊C4C2313yes—
124(C2×#6157)⋊C4C2313yes—
125(C2×#6157)⋊C4C2316yes—
126(C2×#6157)⋊C4C2313yes—
127C2×#11719949C2×C411yescharacteristic, complemented
128C2×#11719945C2×C413yescomplemented
129C2×#11719947C2×C413yescomplemented
130#41×D53—24no—
131#41×D53—24no—
132C22×Dic106C2×C413yescomplemented
133C2×Q8×D53—24no—
134C2×Q8×D53—24no—
135C2×Q8×D53C2×C411yescharacteristic, complemented
136C2×Q8×D53C2×C413yescomplemented
137C2×Q8×D53C2313yes—
138C2×Q8×D53C2311yescharacteristic
139C2×D4×D53C2313yes—
140C2×D4×D53C2313yes—
141C22×C4×D53C2313yes—
142C22×C4×D53C2313yes—
143#13133206C2×C413yescomplemented
144#13133205C2×C413yescomplemented
145#13133204C2×C413yescomplemented
146#13133203C2×C416yescomplemented
147#13133203C2×C416yescomplemented
148#13133197C2×C413yescomplemented
149#13133196C2×C413yescomplemented
150#13133195C2×C416yescomplemented
151#13133194C2×C416yescomplemented
152#13133193C2×C413yescomplemented
153#13133192C2×C413yescomplemented
154#13133191C2×C413yescomplemented
155#13133190C2×C416yescomplemented
156#13133189C2×C416yescomplemented
157#13133188C2×C413yescomplemented
158Q8×Dic53C2×C411yescharacteristic, complemented
159C4×Dic106C2×C413yescomplemented
160#13133182C2×C413yescomplemented
161C4×D212C2×C413yescomplemented
162D4×Dic53C2×C413yescomplemented
163#13133179C2×C413yescomplemented
164C4×C22⋊D53C2×C413yescomplemented
165C4×C22⋊D53C2×C413yescomplemented
166#13133177C2×C413yescomplemented
167#13133177C2×C413yescomplemented
168C4⋊C4×D53C2313yes—
169C4⋊C4×D53C2313yes—
170C22⋊C4×D53C2316yes—
171C22⋊C4×D53C2311yescharacteristic
172C22⋊C4×D53C2313yes—
173C42×D53C2313yes—
174C2×#41×C53C2×C411yescharacteristic, complemented
175C22×Q8×C53C2×C411yescharacteristic, complemented
176#124×C53C2×C413yescomplemented
177C22⋊Q8×C53C2×C413yescomplemented
178#121×C53C2×C413yescomplemented
179C4×Q8×C53C2×C411yescharacteristic, complemented
180C4×D4×C53C2×C413yescomplemented
181C23×D53C2413yes—
182C23×D53C2411yescharacteristic
183C22×#6157—22no—
184C22×#6157—22no—
185C22×#6157—22no—
186C22×#6157—26no—
187C22×#6157—26no—
188C22×#6157—212no—
189C22×#6157—43no—
190C22×#6157—46no—
191C22×#6157—46no—
192C22×#6157C2411yescharacteristic
193C22×#6157C2411yescharacteristic
194C22×#6157C2413yes—
195C22×#6157C2413yes—
196C22×#6157C2413yes—
197C22×#6157C2411yescharacteristic
198C22×#6157C2413yes—
199C22×#6157C2411yescharacteristic
200#41×C53—24no—
201C2×Q8×C53—24no—
202C2×Q8×C53C22×C413yes—
203C2×Q8×C53C22×C411yescharacteristic
204C2×D4×C53C22×C413yes—
205C2×D4×C53C22×C413yes—
206C22×C4×C53C22×C413yes—
207C22×C4×C53C22×C413yes—
208C2×C22⋊D53C22×C413yes—
209C2×C22⋊D53C22×C413yes—
210C2×C22⋊D53C22×C416yes—
211C22×Dic53C22×C413yes—
212C22×Dic53C22×C413yes—
213#11719949—24no—
214Q8×D53—24no—
215Q8×D53—26no—
216Q8×D53—26no—
217Q8×D53—212no—
218Q8×D53C2×D414yes—
219Q8×D53#4114yes—
220#11719947—212no—
221D4×D53—26no—
222D4×D53—26no—
223D4×D53—26no—
224D4×D53—26no—
225#11719945—212no—
226C2×D212C22×C413yes—
227C2×D212C22×C413yes—
228C2×C4×D53—26no—
229C2×C4×D53—26no—
230C2×C4×D53—26no—
231C2×C4×D53—26no—
232C2×C4×D53C22×C413yes—
233C2×C4×D53C22×C413yes—
234C2×C4×D53C22×C413yes—
235C2×C4×D53C22×C413yes—
236C2×C4×D53C2411yescharacteristic
237C2×C4×D53C2413yes—
238C2×C4×D53C2413yes—
239C2×C4×D53C2411yescharacteristic
240C2×C4×D53C2413yes—
241C2×Dic106—212no—
242C2×Dic106C22×C416yes—
243C2×Dic106C22×C413yes—
244C2×Dic106C22×C413yes—
245C22⋊#6157—26no—
246C22⋊#6157—22no—
247C22⋊#6157—26no—
248C22⋊#6157—26no—
249C22⋊#6157—26no—
250C22⋊#6157—43no—
251C22⋊#6157—46no—
252C4⋊#6157—26no—
253C4⋊#6157—212no—
254C4⋊#6157—22no—
255C4⋊#6157—22no—
256C4⋊#6157—26no—
257C4⋊#6157—26no—
258C4⋊#6157—26no—
259C4⋊#6157—43no—
260C4⋊#6157—46no—
261C4⋊#6157C2×D4112yes—
262C4×#6157—26no—
263C4×#6157—26no—
264C4×#6157—26no—
265C4×#6157—26no—
266C4×#6157—26no—
267C4×#6157—46no—
268C4×#6157C2×D4112yes—
269C4⋊C4×C53C22×C413yes—
270C4⋊C4×C53C22×C413yes—
271C22⋊C4×C53C22×C411yescharacteristic
272C22⋊C4×C53C22×C413yes—
273C22⋊C4×C53C22×C416yes—
274C42×C53C22×C413yes—
275C22⋊Dic53C22×C411yescharacteristic
276C22⋊Dic53C22×C413yes—
277C22⋊Dic53C22×C416yes—
278#11719921C22×C411yescharacteristic
279#11719921C22×C413yes—
280#11719921C22×C411yescharacteristic
281#11719921C22×C413yes—
282#11719921C22×C416yes—
283#11719921C22×C416yes—
284C4⋊Dic53C22×C413yes—
285C4⋊Dic53C22×C413yes—
286#11719919C22×C413yes—
287#11719919C22×C413yes—
288#11719919C22×C416yes—
289C4×Dic53C22×C413yes—
290C4×Dic53C22×C413yes—
291C4×Dic53C22×C413yes—
292C23×C53C23×C413yes—
293C23×C53C23×C411yescharacteristic
294C22×D53—21no—
295C22×D53—21no—
296C22×D53—21no—
297C22×D53—21no—
298C22×D53—23no—
299C22×D53—23no—
300C22×D53—23no—
301C22×D53—23no—
302C22×D53—23no—
303C22×D53—23no—
304C22×D53C23×C413yes—
305C22×D53C23×C411yescharacteristic
306C22×D53H(5,𝔽2)12yes—
307C22×D532−1+412yes—
308C22×D53C2511yescharacteristic
309C2×#6157—28no—
310C2×#6157—21no—
311C2×#6157—23no—
312C2×#6157—21no—
313C2×#6157—21no—
314C2×#6157—21no—
315C2×#6157—23no—
316C2×#6157—21no—
317C2×#6157—23no—
318C2×#6157—23no—
319C2×#6157—21no—
320C2×#6157—23no—
321C2×#6157—23no—
322C2×#6157—23no—
323C2×#6157—23no—
324C2×#6157—21no—
325C2×#6157—21no—
326C2×#6157—21no—
327C2×#6157—23no—
328C2×#6157—23no—
329C2×#6157—23no—
330C2×#6157—21no—
331C2×#6157—412no—
332C2×#6157—812no—
333C2×#6157C22×D412yes—
334C2×#6157C22×D416yes—
335C2×#61572−1+412yes—
336Q8×C53—26no—
337Q8×C53C4×D414yescomplemented
338D4×C53—26no—
339D4×C53—26no—
340C2×C4×C53—26no—
341C2×C4×C53—26no—
342C2×C4×C53C23×C413yes—
343C2×C4×C53C23×C411yescharacteristic
344C2×C4×C53C23×C413yes—
345C2×C4×C53C23×C411yescharacteristic
346C2×C4×C53C23×C413yes—
347C22⋊D53—26no—
348C22⋊D53—26no—
349C22⋊D53—212no—
350C2×Dic53—26no—
351C2×Dic53—26no—
352C2×Dic53C23×C413yes—
353C2×Dic53C23×C411yescharacteristic
354C2×Dic53C23×C413yes—
355C2×Dic53C23×C411yescharacteristic
356C2×Dic53C23×C413yes—
357D212—26no—
358D212—26no—
359C4×D53—23no—
360C4×D53—21no—
361C4×D53—21no—
362C4×D53—23no—
363C4×D53—23no—
364C4×D53—21no—
365C4×D53—23no—
366C4×D53—21no—
367C4×D53—26no—
368C4×D53—26no—
369C4×D53—26no—
370C4×D53—26no—
371C4×D53C22×D416yes—
372C4×D53C2×#4116yes—
373Dic106—26no—
374Dic106—212no—
375Dic106C4×D4112yescomplemented
376#34294—531nomaximal, Sylow
377C22×C53—21no—
378C22×C53—21no—
379C22×C53—23no—
380C22×C53—23no—
381C22×C53—23no—
382C22×C53#52012yescomplemented
383C22×C53C24×C411yescharacteristic
384C2×D53—21no—
385C2×D53—21no—
386C2×D53—22no—
387C2×D53—22no—
388C2×D53—22no—
389C2×D53—22no—
390C2×D53—23no—
391C2×D53—23no—
392C2×D53—23no—
393C2×D53—43no—
394C2×D53—43no—
395C2×D53—43no—
396C2×D53—43no—
397C2×D53#52012yescomplemented
398C2×D53C23×D411yescharacteristic
399C2×D53C22×#4111yescharacteristic
400C2×D53C2×H(5,𝔽2)11yescharacteristic
401C2×D53C2×2−1+411yescharacteristic
402C2×D53C2×2−1+411yescharacteristic
403C2×D53#58511yescharacteristic
404#6157—22no—
405#6157—22no—
406#6157—26no—
407#6157—41no—
408#6157—43no—
409#6157—43no—
410#6157—41no—
411#6157—43no—
412C4×C53—23no—
413C4×C53—21no—
414C4×C53—23no—
415C4×C53—21no—
416C4×C53C2×C4×D416yes—
417Dic53—23no—
418Dic53—21no—
419Dic53—23no—
420Dic53—21no—
421Dic53C2×C4×D416yes—
422C2×#548—531no—
423C2×#520—531no—
424C22×C4×Q8—531no—
425#2367—533no—
426#2361—533no—
427#2360—533no—
428Q8×C4⋊C4—531no—
429D4×C4⋊C4—533no—
430#2341—531no—
431Q8×C22⋊C4—531no—
432#2326—533no—
433#2323—533no—
434C4×#121—533no—
435#2290—533no—
436#2276—531no—
437C2×C53—22no—
438C2×C53—43no—
439C2×C53C22×C4×D411yescharacteristic
440C2×C53C2×#52011yescharacteristic
441C2×C53C4×2−1+411yescharacteristic
442D53—22no—
443D53—43no—
444D53#348611yescharacteristic
445D53#348811yescharacteristic
446D53#351611yescharacteristic
447D53#352211yescharacteristic
448C22×#41—531no—
449C23×Q8—531no—
450#548—531no—
451#548—531no—
452#548—533no—
453#548—533no—
454#548—533no—
455#548—531no—
456#548—533no—
457#548#615711yescharacteristic, complemented
458C2×#124—533no—
459C2×C22⋊Q8—533no—
460C2×#121—533no—
461#520—1068no—
462C2×C4×Q8—531no—
463C2×C4×Q8—531no—
464C2×C4×Q8—533no—
465C2×C4×Q8—531no—
466C2×C4×Q8—531no—
467C2×C4×Q8—531no—
468C2×C4×Q8—533no—
469C2×C4×Q8—1068no—
470C2×C4×D4—533no—
471C2×C4×D4—533no—
472C2×C4×D4—533no—
473C2×C4×D4—536no—
474C2×#117—533no—
475C22×C4⋊C4—533no—
476C22×C4⋊C4—533no—
477C22×C42—533no—
478#391—533no—
479#391—533no—
480#390—533no—
481#390—533no—
482#389—536no—
483#389—533no—
484#389—533no—
485#388—536no—
486#388—536no—
487#388—533no—
488#388—533no—
489#387—533no—
490#387—533no—
491#386—533no—
492#386—533no—
493#385—536no—
494#385—536no—
495#385—533no—
496#385—531no—
497#384—533no—
498#380—533no—
499#380—533no—
500C4×C4⋊C4—533no—
501C4×C4⋊C4—533no—
502C4×C4⋊C4—533no—
503C4×C4⋊C4—533no—
504C4×C22⋊C4—533no—
505C4×C22⋊C4—533no—
506C4×C22⋊C4—536no—
507#376—533no—
508C53#3429411yescharacteristic, complemented, Sylow
509C2×#41—531no—
510C2×#41—533no—
511C2×#41—533no—
512C2×#41—1064no—
513C2×#41—1064no—
514C2×#41C2×#615711yescharacteristic, complemented
515C22×Q8—531no—
516C22×Q8—533no—
517C22×Q8—533no—
518C22×Q8—531no—
519C22×Q8—533no—
520C22×Q8—1064no—
521C22×Q8—1064no—
522C22×Q8C2×#615711yescharacteristic, complemented
523C22×D4—533no—
524C22×D4—533no—
525C23×C4—533no—
526C23×C4—533no—
527C23×C4—531no—
528C23×C4—533no—
529C23×C4—536no—
530#124—533no—
531#124—533no—
532#124—536no—
533#124—536no—
534#124—533no—
535#124C2×#615713yescomplemented
536C22⋊Q8—533no—
537C22⋊Q8—533no—
538C22⋊Q8—536no—
539C22⋊Q8—533no—
540C22⋊Q8—536no—
541C22⋊Q8C2×#615713yescomplemented
542#121—533no—
543#121—536no—
544#121—533no—
545#121—533no—
546#121—536no—
547#121C2×#615713yescomplemented
548C4×Q8—538no—
549C4×Q8—531no—
550C4×Q8—533no—
551C4×Q8—533no—
552C4×Q8—10612no—
553C4×Q8—10612no—
554C4×Q8—1064no—
555C4×Q8—1064no—
556C4×Q8—1064no—
557C4×Q8C2×#615711yescharacteristic, complemented
558C4×D4—533no—
559C4×D4—533no—
560C4×D4—533no—
561C4×D4—533no—
562C4×D4—533no—
563C4×D4—533no—
564C4×D4—533no—
565C4×D4—10612no—
566C4×D4—10612no—
567C4×D4—21212no—
568C4×D4C2×#615713yescomplemented
569#117—10612no—
570C2×C4⋊C4—533no—
571C2×C4⋊C4—533no—
572C2×C4⋊C4—533no—
573C2×C4⋊C4—533no—
574C2×C4⋊C4—533no—
575C2×C4⋊C4—533no—
576C2×C4⋊C4—536no—
577C2×C4⋊C4—531no—
578C2×C4⋊C4—533no—
579C2×C4⋊C4—531no—
580C2×C4⋊C4—536no—
581C2×C4⋊C4—533no—
582C2×C4⋊C4—10612no—
583C2×C4⋊C4—10612no—
584C2×C22⋊C4—531no—
585C2×C22⋊C4—533no—
586C2×C22⋊C4—536no—
587C2×C22⋊C4—533no—
588C2×C22⋊C4—533no—
589C2×C22⋊C4—533no—
590C2×C22⋊C4—531no—
591C2×C22⋊C4—533no—
592C2×C22⋊C4—536no—
593C2×C22⋊C4—533no—
594C2×C42—533no—
595C2×C42—533no—
596C2×C42—533no—
597C2×C42—533no—
598C2×C42—533no—
599C2×C42—533no—
600C2×C42—533no—
601C2×C42—536no—
602C2×C42—10612no—
603#95—531no—
604#95—533no—
605#95—533no—
606#95—533no—
607#95—531no—
608#95—533no—
609#95—533no—
610#95—536no—
611#95—533no—
612#95—533no—
613#95—533no—
614C24—531no—
615C24—533no—
616#41—24no—
617#41—10612no—
618#41—10612no—
619#41—1064no—
620C2×Q8—24no—
621C2×Q8—534no—
622C2×Q8—534no—
623C2×Q8—533no—
624C2×Q8—536no—
625C2×Q8—533no—
626C2×Q8—10612no—
627C2×Q8—1066no—
628C2×Q8—1066no—
629C2×Q8—10612no—
630C2×Q8—1064no—
631C2×Q8C22×#615713yes—
632C2×Q8C22×#615711yescharacteristic
633C2×D4—533no—
634C2×D4—533no—
635C2×D4—536no—
636C2×D4—533no—
637C2×D4—533no—
638C2×D4—1066no—
639C2×D4—1066no—
640C2×D4—1066no—
641C2×D4—1066no—
642C2×D4C22×#615713yes—
643C2×D4C22×#615713yes—
644C22×C4—533no—
645C22×C4—531no—
646C22×C4—531no—
647C22×C4—533no—
648C22×C4—533no—
649C22×C4—533no—
650C22×C4—533no—
651C22×C4—533no—
652C22×C4—533no—
653C22×C4—533no—
654C22×C4—531no—
655C22×C4—533no—
656C22×C4—533no—
657C22×C4—531no—
658C22×C4—531no—
659C22×C4—531no—
660C22×C4—533no—
661C22×C4—533no—
662C22×C4—533no—
663C22×C4—1066no—
664C22×C4—1066no—
665C22×C4—1066no—
666C22×C4—1066no—
667C22×C4—1062no—
668C22×C4—1062no—
669C22×C4—10612no—
670C22×C4—1066no—
671C22×C4—1062no—
672C22×C4—1066no—
673C22×C4—2126no—
674C22×C4—2126no—
675C22×C4—2123no—
676C22×C4C22×#615713yes—
677C22×C4C22×#615713yes—
678C4⋊C4—5312no—
679C4⋊C4—533no—
680C4⋊C4—533no—
681C4⋊C4—533no—
682C4⋊C4—536no—
683C4⋊C4—533no—
684C4⋊C4—1062no—
685C4⋊C4—1066no—
686C4⋊C4—1066no—
687C4⋊C4—1066no—
688C4⋊C4—10612no—
689C4⋊C4—1062no—
690C4⋊C4—1066no—
691C4⋊C4—2123no—
692C4⋊C4—2126no—
693C4⋊C4C22×#615713yes—
694C4⋊C4C22×#615713yes—
695C22⋊C4—531no—
696C22⋊C4—533no—
697C22⋊C4—536no—
698C22⋊C4—531no—
699C22⋊C4—531no—
700C22⋊C4—533no—
701C22⋊C4—533no—
702C22⋊C4—536no—
703C22⋊C4—536no—
704C22⋊C4—1066no—
705C22⋊C4—1066no—
706C22⋊C4—1066no—
707C22⋊C4—1062no—
708C22⋊C4—1066no—
709C22⋊C4—2123no—
710C22⋊C4—2126no—
711C22⋊C4C22×#615711yescharacteristic
712C22⋊C4C22×#615713yes—
713C22⋊C4C22×#615716yes—
714C42—5312no—
715C42—533no—
716C42—533no—
717C42—533no—
718C42—1066no—
719C42—1066no—
720C42—1066no—
721C42—1066no—
722C42—1066no—
723C42—2126no—
724C42C22×#615713yes—
725C23—531no—
726C23—532no—
727C23—532no—
728C23—531no—
729C23—533no—
730C23—1061no—
731C23—1061no—
732C23—1061no—
733C23—1061no—
734C23—1063no—
735C23—1063no—
736C23—1063no—
737C23—1063no—
738C23—1063no—
739C23—1063no—
740C23C23×#615713yes—
741C23C23×#615711yescharacteristic
742Q8—26no—
743Q8—5312no—
744Q8—10612no—
745Q8—1066no—
746Q8D4×#615714yescomplemented
747D4—26no—
748D4—26no—
749D4—1066no—
750D4—10612no—
751D4—1066no—
752D4—1066no—
753D4—1066no—
754C2×C4—26no—
755C2×C4—26no—
756C2×C4—533no—
757C2×C4—536no—
758C2×C4—536no—
759C2×C4—532no—
760C2×C4—536no—
761C2×C4—532no—
762C2×C4—531no—
763C2×C4—533no—
764C2×C4—533no—
765C2×C4—531no—
766C2×C4—1066no—
767C2×C4—1066no—
768C2×C4—1063no—
769C2×C4—1063no—
770C2×C4—1061no—
771C2×C4—1061no—
772C2×C4—1061no—
773C2×C4—1061no—
774C2×C4—1063no—
775C2×C4—1063no—
776C2×C4—1066no—
777C2×C4—1066no—
778C2×C4—1061no—
779C2×C4—1063no—
780C2×C4—1061no—
781C2×C4—1061no—
782C2×C4—1061no—
783C2×C4—1063no—
784C2×C4—1068no—
785C2×C4—1066no—
786C2×C4—1066no—
787C2×C4—1061no—
788C2×C4—1061no—
789C2×C4—1063no—
790C2×C4—1063no—
791C2×C4—1063no—
792C2×C4—1063no—
793C2×C4—1063no—
794C2×C4—1061no—
795C2×C4—1061no—
796C2×C4—1063no—
797C2×C4—1061no—
798C2×C4—1063no—
799C2×C4—1063no—
800C2×C4—1061no—
801C2×C4—1063no—
802C2×C4—42412no—
803C2×C4—21212no—
804C2×C4C23×#615711yescharacteristic
805C2×C4C23×#615713yes—
806C2×C4C23×#615713yes—
807C2×C4C23×#615711yescharacteristic
808C2×C4C23×#615713yes—
809C22—21no—
810C22—21no—
811C22—23no—
812C22—23no—
813C22—23no—
814C22—531no—
815C22—531no—
816C22—531no—
817C22—531no—
818C22—531no—
819C22—531no—
820C22—532no—
821C22—1062no—
822C22—1062no—
823C22—1062no—
824C22—1062no—
825C22—1061no—
826C22—1061no—
827C22—1063no—
828C22—1063no—
829C22—1063no—
830C22—2123no—
831C22—2123no—
832C22—2123no—
833C22—2123no—
834C22#1681169212yescomplemented
835C22C24×#615711yescharacteristic
836C4—21no—
837C4—23no—
838C4—23no—
839C4—21no—
840C4—536no—
841C4—1062no—
842C4—1062no—
843C4—1066no—
844C4—1061no—
845C4—1063no—
846C4—1063no—
847C4—1061no—
848C4—2123no—
849C4—2123no—
850C4—2121no—
851C4—2123no—
852C4—2121no—
853C4C2×D4×#615716yes—
854C2—22no—
855C2—43no—
856C2—531no—
857C2—531no—
858C2—531no—
859C2—531no—
860C2—1062no—
861C2—2123no—
862C2C22×D4×#615711yescharacteristic
863C2C2×#1681169211yescharacteristic
864C22−1+4×#615711yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6157
commutator, socleC22×C53C24×C4
FittingC53×#548C4
prime radical#548×D53C2
cosocleC22×D53C25
hypercenter#548#6157
hypocenterC53#34294
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#16811692C2semidirect
2. C22×Q8×#6157C2semidirect
3. #20291246C2semidirect
4. #20291240C2semidirect
5. #20291239C2semidirect
6. Q8×C4⋊#6157C2semidirect
7. D4×C4⋊#6157C2semidirect
8. #20291220C2semidirect
9. Q8×C22⋊#6157C2semidirect
10. #20291205C2semidirect
11. #20291202C2semidirect
12. #121×#6157C2semidirect
13. #20291169C2semidirect
14. #20291155C2semidirect
63. #16811285C4semidirect
64. #16811284C4semidirect
65. #16811283C4semidirect
66. #16811282C4semidirect
67. #16811281C4semidirect
68. #16811280C4semidirect
69. #16811279C4semidirect
75. C53×#548C4semidirect
84. Q8×#6157D4semidirect
127. C2×#11719949C2×C4semidirect
128. C2×#11719945C2×C4semidirect
129. C2×#11719947C2×C4semidirect
132. C22×Dic106C2×C4semidirect
135. C2×Q8×D53C2×C4semidirect
136. C2×Q8×D53C2×C4semidirect
143. #13133206C2×C4semidirect
144. #13133205C2×C4semidirect
145. #13133204C2×C4semidirect
146. #13133203C2×C4semidirect
147. #13133203C2×C4semidirect
148. #13133197C2×C4semidirect
149. #13133196C2×C4semidirect
150. #13133195C2×C4semidirect
151. #13133194C2×C4semidirect
152. #13133193C2×C4semidirect
153. #13133192C2×C4semidirect
154. #13133191C2×C4semidirect
155. #13133190C2×C4semidirect
156. #13133189C2×C4semidirect
157. #13133188C2×C4semidirect
158. Q8×Dic53C2×C4semidirect
159. C4×Dic106C2×C4semidirect
160. #13133182C2×C4semidirect
161. C4×D212C2×C4semidirect
162. D4×Dic53C2×C4semidirect
163. #13133179C2×C4semidirect
164. C4×C22⋊D53C2×C4semidirect
165. C4×C22⋊D53C2×C4semidirect
166. #13133177C2×C4semidirect
167. #13133177C2×C4semidirect
174. C2×#41×C53C2×C4semidirect
175. C22×Q8×C53C2×C4semidirect
176. #124×C53C2×C4semidirect
177. C22⋊Q8×C53C2×C4semidirect
178. #121×C53C2×C4semidirect
179. C4×Q8×C53C2×C4semidirect
180. C4×D4×C53C2×C4semidirect
337. Q8×C53C4×D4semidirect
375. Dic106C4×D4semidirect
382. C22×C53#520semidirect
397. C2×D53#520semidirect
457. #548#6157semidirect
508. C53#34294semidirect
514. C2×#41C2×#6157semidirect
522. C22×Q8C2×#6157semidirect
535. #124C2×#6157semidirect
541. C22⋊Q8C2×#6157semidirect
547. #121C2×#6157semidirect
557. C4×Q8C2×#6157semidirect
568. C4×D4C2×#6157semidirect
746. Q8D4×#6157semidirect
834. C22#16811692semidirect

Maximal subgroups

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

subgroupindex
C2×#168116922
C22×Q8×#61572
#202912462
#202912402
#202912392
Q8×C4⋊#61572
D4×C4⋊#61572
#202912202
Q8×C22⋊#61572
#202912052
#202912022
#121×#61572
#202911692
#202911552
#548×D532
#3429453