Finite Group Databasebeta

← #28328930

Subgroups — #28328930

Order 13568.

3200 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811692C211yesmaximal, characteristic, complemented
2C2×#41×#6157C211yesmaximal, characteristic, complemented
3#20291245C213yesmaximal, complemented
4#20291242C213yesmaximal, complemented
5#20291240C213yesmaximal, complemented
6#20291231C213yesmaximal, complemented
7#20291230C211yesmaximal, characteristic, complemented
8#20291220C211yesmaximal, characteristic, complemented
9#20291220C211yesmaximal, characteristic, complemented
10#20291207C213yesmaximal, complemented
11#20291203C213yesmaximal, complemented
12#121×#6157C213yesmaximal, complemented
13#20291169C213yesmaximal, complemented
14#20291155C211yesmaximal, characteristic, complemented
15#550×D53C211yesmaximal, characteristic
16#16811692—28no—
17#41×#6157—28no—
18C2×Q8×#6157C2211yescharacteristic
19C2×Q8×#6157C2211yescharacteristic
20C2×Q8×#6157C2211yescharacteristic
21C2×Q8×#6157C2211yescharacteristic
22C2×D4×#6157C2213yes—
23C2×D4×#6157C2213yes—
24C2×D4×#6157C2213yes—
25C2×D4×#6157C2213yes—
26C2×D4×#6157C2216yes—
27C2×#13133296C2213yes—
28C2×#13133296C2213yes—
29C22×C4⋊#6157C2213yes—
30C22×C4×#6157C2213yes—
31#16811575C2213yes—
32#16811575C2213yes—
33#16811575C2216yes—
34#16811575C2213yes—
35#16811575C2213yes—
36#16811574C2213yes—
37#16811574C2213yes—
38#16811573C2213yes—
39#16811573C2213yes—
40#16811573C2216yes—
41#16811572C2211yescharacteristic
42#16811572C2213yes—
43#16811571C2213yes—
44#16811571C2213yes—
45#16811571C2216yes—
46#16811571C2216yes—
47#16811571C2216yes—
48#16811570C2213yes—
49#16811570C2213yes—
50#16811567C2213yes—
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
62C2×#41×D53C2211yescharacteristic
63#16811295C411yescharacteristic, complemented
64#16811294C413yescomplemented
65#16811293C413yescomplemented
66#16811292C411yescharacteristic, complemented
67#16811292C411yescharacteristic, complemented
68#16811291C413yescomplemented
69#16811291C413yescomplemented
70#127×D53C2213yes—
71#121×D53C2213yes—
72#121×D53C2213yes—
73C4×Q8×D53C2211yescharacteristic
74C4×D4×D53C2213yes—
75C53×#550C411yescharacteristic, complemented
76C23×#6157C2313yes—
77C23×#6157C2316yes—
78C23×#6157C2313yes—
79Q8×#6157—24no—
80Q8×#6157—24no—
81Q8×#6157—24no—
82Q8×#6157D418yescomplemented
83D4×#6157—212no—
84D4×#6157—212no—
85D4×#6157—212no—
86D4×#6157—212no—
87D4×#6157—412no—
88#13133296—212no—
89#13133296—212no—
90C2×C4⋊#6157—212no—
91C2×C4⋊#6157C2313yes—
92C2×C4⋊#6157C2313yes—
93C2×C4⋊#6157C2313yes—
94C2×C4⋊#6157C2313yes—
95C2×C4⋊#6157C2311yescharacteristic
96C2×C4⋊#6157C2313yes—
97C2×C4⋊#6157C2313yes—
98C2×C4⋊#6157C2313yes—
99C2×C22⋊#6157C2313yes—
100C2×C22⋊#6157C2313yes—
101C2×C22⋊#6157C2316yes—
102C2×C22⋊#6157C2313yes—
103C2×C22⋊#6157C2313yes—
104C2×C22⋊#6157C2313yes—
105C2×C22⋊#6157C2313yes—
106C2×C22⋊#6157C2316yes—
107C2×C22⋊#6157C2316yes—
108C2×C4×#6157—212no—
109C2×C4×#6157C2313yes—
110C2×C4×#6157C2313yes—
111C2×C4×#6157C2313yes—
112C2×C4×#6157C2313yes—
113C2×C4×#6157C2311yescharacteristic
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)⋊C4C2311yescharacteristic
122(C2×#6157)⋊C4C2313yes—
123(C2×#6157)⋊C4C2313yes—
124(C2×#6157)⋊C4C2316yes—
125(C2×#6157)⋊C4C2311yescharacteristic
126(C2×#6157)⋊C4C2313yes—
127C2×#11719949C2×C411yescharacteristic, complemented
128C2×#11719949C2×C411yescharacteristic, complemented
129C2×#11719945C2×C413yescomplemented
130C2×#11719945C2×C413yescomplemented
131C2×#11719947C2×C413yescomplemented
132C2×#11719947C2×C413yescomplemented
133#41×D53—24no—
134#41×D53—24no—
135#41×D53—24no—
136#41×D53—24no—
137C2×Q8×D53C2311yescharacteristic
138C2×D4×D53C2313yes—
139C2×D4×D53C2313yes—
140C2×D4×D53C2313yes—
141C2×D4×D53C2316yes—
142C22×C4×D53C2313yes—
143C22×C4×D53C2313yes—
144#13133214C2×C413yescomplemented
145#13133213C2×C416yescomplemented
146#13133213C2×C413yescomplemented
147#13133213C2×C413yescomplemented
148#13133213C2×C416yescomplemented
149#13133192C2×C413yescomplemented
150#13133192C2×C413yescomplemented
151#13133191C2×C413yescomplemented
152#13133191C2×C413yescomplemented
153#13133190C2×C416yescomplemented
154#13133190C2×C416yescomplemented
155#13133189C2×C416yescomplemented
156#13133189C2×C416yescomplemented
157#13133188C2×C413yescomplemented
158#13133188C2×C413yescomplemented
159Q8×Dic53C2×C411yescharacteristic, complemented
160C4×Dic106C2×C413yescomplemented
161#13133182C2×C413yescomplemented
162C4×D212C2×C413yescomplemented
163D4×Dic53C2×C413yescomplemented
164#13133179C2×C413yescomplemented
165C4×C22⋊D53C2×C413yescomplemented
166C4×C22⋊D53C2×C413yescomplemented
167#13133177C2×C413yescomplemented
168#13133177C2×C413yescomplemented
169C4⋊C4×D53C2313yes—
170C4⋊C4×D53C2311yescharacteristic
171C22⋊C4×D53C2313yes—
172C22⋊C4×D53C2313yes—
173C42×D53C2313yes—
174C2×#41×C53C2×C411yescharacteristic, complemented
175C2×#41×C53C2×C411yescharacteristic, complemented
176#127×C53C2×C413yescomplemented
177#121×C53C2×C413yescomplemented
178#121×C53C2×C413yescomplemented
179C4×Q8×C53C2×C411yescharacteristic, complemented
180C4×D4×C53C2×C413yescomplemented
181C23×D53C2413yes—
182C23×D53C2413yes—
183C22×#6157—26no—
184C22×#6157—26no—
185C22×#6157—26no—
186C22×#6157—212no—
187C22×#6157—43no—
188C22×#6157—43no—
189C22×#6157—43no—
190C22×#6157—46no—
191C22×#6157—46no—
192C22×#6157C2411yescharacteristic
193C22×#6157C2413yes—
194C22×#6157C2413yes—
195C22×#6157C2413yes—
196C22×#6157C2411yescharacteristic
197C22×#6157C2411yescharacteristic
198C22×#6157C2413yes—
199C22×#6157C2411yescharacteristic
200#41×C53—24no—
201#41×C53—24no—
202C2×Q8×C53C22×C411yescharacteristic
203C2×D4×C53C22×C413yes—
204C2×D4×C53C22×C413yes—
205C2×D4×C53C22×C413yes—
206C2×D4×C53C22×C416yes—
207C22×C4×C53C22×C413yes—
208C22×C4×C53C22×C413yes—
209C2×C22⋊D53C22×C416yes—
210C2×C22⋊D53C22×C416yes—
211C2×C22⋊D53C22×C413yes—
212C2×C22⋊D53C22×C413yes—
213C2×C22⋊D53C22×C416yes—
214C2×C22⋊D53C22×C416yes—
215C22×Dic53C22×C413yes—
216C22×Dic53C22×C413yes—
217#11719949—24no—
218#11719949—24no—
219Q8×D53C2×D414yes—
220Q8×D53#4114yes—
221#11719947—212no—
222#11719947—212no—
223D4×D53—26no—
224D4×D53—26no—
225D4×D53—26no—
226D4×D53—26no—
227D4×D53—46no—
228D4×D53—43no—
229D4×D53—43no—
230D4×D53—46no—
231#11719945—212no—
232#11719945—212no—
233C2×D212C22×C413yes—
234C2×D212C22×C413yes—
235C2×D212C22×C413yes—
236C2×D212C22×C416yes—
237C2×C4×D53—26no—
238C2×C4×D53—26no—
239C2×C4×D53—26no—
240C2×C4×D53—26no—
241C2×C4×D53C22×C413yes—
242C2×C4×D53C22×C413yes—
243C2×C4×D53C22×C413yes—
244C2×C4×D53C22×C413yes—
245C2×C4×D53C2411yescharacteristic
246C2×C4×D53C2413yes—
247C2×C4×D53C2411yescharacteristic
248C2×C4×D53C2411yescharacteristic
249C2×C4×D53C2413yes—
250C2×Dic106C22×C413yes—
251C22⋊#6157—26no—
252C22⋊#6157—212no—
253C22⋊#6157—26no—
254C22⋊#6157—26no—
255C22⋊#6157—43no—
256C22⋊#6157—43no—
257C22⋊#6157—46no—
258C22⋊#6157—43no—
259C22⋊#6157—46no—
260C4⋊#6157—26no—
261C4⋊#6157—22no—
262C4⋊#6157—26no—
263C4⋊#6157—26no—
264C4⋊#6157—26no—
265C4⋊#6157—26no—
266C4⋊#6157—43no—
267C4⋊#6157C2×D4112yes—
268C4×#6157—22no—
269C4×#6157—26no—
270C4×#6157—26no—
271C4×#6157—26no—
272C4×#6157—26no—
273C4×#6157—46no—
274C4×#6157C2×D4112yes—
275C4⋊C4×C53C22×C411yescharacteristic
276C4⋊C4×C53C22×C413yes—
277C22⋊C4×C53C22×C413yes—
278C22⋊C4×C53C22×C413yes—
279C42×C53C22×C413yes—
280C22⋊Dic53C22×C413yes—
281C22⋊Dic53C22×C413yes—
282#11719921C22×C413yes—
283#11719921C22×C413yes—
284#11719921C22×C413yes—
285#11719921C22×C413yes—
286C4⋊Dic53C22×C411yescharacteristic
287C4⋊Dic53C22×C413yes—
288#11719919C22×C411yescharacteristic
289#11719919C22×C411yescharacteristic
290#11719919C22×C416yes—
291C4×Dic53C22×C413yes—
292C4×Dic53C22×C413yes—
293C4×Dic53C22×C413yes—
294C23×C53C23×C413yes—
295C23×C53C23×C413yes—
296C22×D53—23no—
297C22×D53—23no—
298C22×D53—23no—
299C22×D53—23no—
300C22×D53—23no—
301C22×D53—23no—
302C22×D53—23no—
303C22×D53—23no—
304C22×D53—23no—
305C22×D53—23no—
306C22×D53—23no—
307C22×D53—23no—
308C22×D53C23×C413yes—
309C22×D53C23×C413yes—
310C22×D53C2511yescharacteristic
311C2×#6157—21no—
312C2×#6157—23no—
313C2×#6157—21no—
314C2×#6157—21no—
315C2×#6157—21no—
316C2×#6157—23no—
317C2×#6157—21no—
318C2×#6157—23no—
319C2×#6157—23no—
320C2×#6157—21no—
321C2×#6157—23no—
322C2×#6157—23no—
323C2×#6157—23no—
324C2×#6157—21no—
325C2×#6157—23no—
326C2×#6157—21no—
327C2×#6157—23no—
328C2×#6157—21no—
329C2×#6157—21no—
330C2×#6157—23no—
331C2×#6157—23no—
332C2×#6157—412no—
333C2×#6157—412no—
334C2×#6157—812no—
335C2×#6157C22×D412yes—
336C2×#6157C22×D416yes—
337C2×#6157H(5,𝔽2)12yes—
338Q8×C53C4×D414yescomplemented
339D4×C53—26no—
340D4×C53—26no—
341D4×C53—43no—
342D4×C53—46no—
343C2×C4×C53—26no—
344C2×C4×C53—26no—
345C2×C4×C53C23×C411yescharacteristic
346C2×C4×C53C23×C411yescharacteristic
347C2×C4×C53C23×C411yescharacteristic
348C2×C4×C53C23×C413yes—
349C2×C4×C53C23×C413yes—
350C22⋊D53—212no—
351C22⋊D53—212no—
352C22⋊D53—43no—
353C22⋊D53—43no—
354C22⋊D53—46no—
355C22⋊D53—46no—
356C2×Dic53—26no—
357C2×Dic53—26no—
358C2×Dic53C23×C411yescharacteristic
359C2×Dic53C23×C411yescharacteristic
360C2×Dic53C23×C411yescharacteristic
361C2×Dic53C23×C413yes—
362C2×Dic53C23×C413yes—
363D212—26no—
364D212—26no—
365D212—43no—
366D212—46no—
367C4×D53—21no—
368C4×D53—21no—
369C4×D53—21no—
370C4×D53—21no—
371C4×D53—23no—
372C4×D53—23no—
373C4×D53—21no—
374C4×D53—21no—
375C4×D53—26no—
376C4×D53—26no—
377C4×D53—26no—
378C4×D53—26no—
379C4×D53C22×D416yes—
380C4×D53C2×#4116yes—
381Dic106C4×D4112yescomplemented
382#34295—531nomaximal, Sylow
383C22×C53—23no—
384C22×C53—23no—
385C22×C53—23no—
386C22×C53—23no—
387C22×C53—23no—
388C22×C53—23no—
389C22×C53C24×C411yescharacteristic
390C2×D53—23no—
391C2×D53—23no—
392C2×D53—23no—
393C2×D53—23no—
394C2×D53—23no—
395C2×D53—23no—
396C2×D53—43no—
397C2×D53—43no—
398C2×D53—43no—
399C2×D53—43no—
400C2×D53—43no—
401C2×D53—43no—
402C2×D53—43no—
403C2×D53—43no—
404C2×D53C23×D411yescharacteristic
405C2×D53C22×#4111yescharacteristic
406C2×D53C2×H(5,𝔽2)11yescharacteristic
407C2×D53#58511yescharacteristic
408C2×D53#58511yescharacteristic
409C2×D53#58511yescharacteristic
410#6157—22no—
411#6157—22no—
412#6157—26no—
413#6157—41no—
414#6157—43no—
415#6157—43no—
416#6157—43no—
417#6157—41no—
418C4×C53—21no—
419C4×C53—21no—
420C4×C53—21no—
421C4×C53—23no—
422C4×C53C2×C4×D416yes—
423Dic53—21no—
424Dic53—21no—
425Dic53—21no—
426Dic53—23no—
427Dic53C2×C4×D416yes—
428C2×#550—531no—
429C2×#520—531no—
430C2×C4×#41—531no—
431#2366—533no—
432#2363—533no—
433#2361—533no—
434#2352—533no—
435#2351—531no—
436#2341—531no—
437#2341—531no—
438#2328—533no—
439#2324—533no—
440C4×#121—533no—
441#2290—533no—
442#2276—531no—
443C2×C53—43no—
444C2×C53—43no—
445C2×C53C22×C4×D411yescharacteristic
446C2×C53#342811yescharacteristic
447C2×C53C4×H(5,𝔽2)11yescharacteristic
448D53—43no—
449D53—43no—
450D53#348711yescharacteristic
451D53#348811yescharacteristic
452D53#351711yescharacteristic
453D53#352411yescharacteristic
454C22×#41—531no—
455C22×#41—531no—
456#550—531no—
457#550—531no—
458#550—533no—
459#550—533no—
460#550—533no—
461#550—531no—
462#550—533no—
463#550#615711yescharacteristic, complemented
464C2×#127—533no—
465C2×#121—533no—
466C2×#121—533no—
467#520—1068no—
468C4×#41—1068no—
469C2×C4×Q8—531no—
470C2×C4×Q8—531no—
471C2×C4×Q8—531no—
472C2×C4×Q8—531no—
473C2×C4×Q8—531no—
474C2×C4×D4—533no—
475C2×C4×D4—533no—
476C2×C4×D4—533no—
477C2×C4×D4—533no—
478C2×C4×D4—533no—
479C2×C4×D4—536no—
480C2×#117—533no—
481C2×#117—533no—
482C22×C4⋊C4—533no—
483C22×C42—533no—
484#390—533no—
485#390—536no—
486#390—533no—
487#390—533no—
488#390—533no—
489#389—533no—
490#389—533no—
491#388—536no—
492#388—533no—
493#388—533no—
494#387—533no—
495#387—531no—
496#386—536no—
497#386—533no—
498#386—536no—
499#386—536no—
500#386—533no—
501#385—533no—
502#385—533no—
503#382—533no—
504#380—533no—
505#380—533no—
506C4×C4⋊C4—533no—
507C4×C4⋊C4—533no—
508C4×C4⋊C4—533no—
509C4×C4⋊C4—533no—
510C4×C22⋊C4—533no—
511C4×C22⋊C4—533no—
512C4×C22⋊C4—536no—
513#376—533no—
514C53#3429511yescharacteristic, complemented, Sylow
515C2×#41—531no—
516C2×#41—531no—
517C2×#41—533no—
518C2×#41—533no—
519C2×#41—533no—
520C2×#41—533no—
521C2×#41—1064no—
522C2×#41—1064no—
523C2×#41—1064no—
524C2×#41—1064no—
525C2×#41C2×#615711yescharacteristic, complemented
526C2×#41C2×#615711yescharacteristic, complemented
527C22×Q8—531no—
528C22×D4—533no—
529C22×D4—533no—
530C22×D4—536no—
531C22×D4—533no—
532C23×C4—533no—
533C23×C4—533no—
534C23×C4—533no—
535C23×C4—536no—
536C23×C4—533no—
537#127—536no—
538#127—536no—
539#127—533no—
540#127—533no—
541#127—533no—
542#127C2×#615713yescomplemented
543#121—533no—
544#121—533no—
545#121—536no—
546#121—536no—
547#121—533no—
548#121—533no—
549#121—533no—
550#121—533no—
551#121—536no—
552#121—536no—
553#121C2×#615713yescomplemented
554#121C2×#615713yescomplemented
555C4×Q8—538no—
556C4×Q8—531no—
557C4×Q8—533no—
558C4×Q8—533no—
559C4×Q8—1064no—
560C4×Q8—1064no—
561C4×Q8—1064no—
562C4×Q8C2×#615711yescharacteristic, complemented
563C4×D4—533no—
564C4×D4—533no—
565C4×D4—533no—
566C4×D4—533no—
567C4×D4—533no—
568C4×D4—533no—
569C4×D4—533no—
570C4×D4—10612no—
571C4×D4—10612no—
572C4×D4—10612no—
573C4×D4—10612no—
574C4×D4—21212no—
575C4×D4C2×#615713yescomplemented
576#117—10612no—
577#117—10612no—
578C2×C4⋊C4—533no—
579C2×C4⋊C4—531no—
580C2×C4⋊C4—533no—
581C2×C4⋊C4—533no—
582C2×C4⋊C4—533no—
583C2×C4⋊C4—531no—
584C2×C4⋊C4—533no—
585C2×C4⋊C4—533no—
586C2×C4⋊C4—533no—
587C2×C4⋊C4—533no—
588C2×C4⋊C4—10612no—
589C2×C22⋊C4—533no—
590C2×C22⋊C4—533no—
591C2×C22⋊C4—533no—
592C2×C22⋊C4—536no—
593C2×C22⋊C4—533no—
594C2×C22⋊C4—533no—
595C2×C22⋊C4—536no—
596C2×C22⋊C4—536no—
597C2×C22⋊C4—533no—
598C2×C22⋊C4—533no—
599C2×C22⋊C4—533no—
600C2×C42—533no—
601C2×C42—533no—
602C2×C42—533no—
603C2×C42—533no—
604C2×C42—533no—
605C2×C42—533no—
606C2×C42—531no—
607C2×C42—536no—
608C2×C42—10612no—
609#95—531no—
610#95—533no—
611#95—533no—
612#95—533no—
613#95—533no—
614#95—531no—
615#95—531no—
616#95—533no—
617#95—536no—
618#95—531no—
619#95—533no—
620C24—533no—
621C24—533no—
622#41—24no—
623#41—24no—
624#41—10612no—
625#41—10612no—
626#41—10612no—
627#41—10612no—
628#41—1064no—
629#41—1064no—
630C2×Q8—534no—
631C2×Q8—534no—
632C2×Q8—533no—
633C2×Q8C22×#615711yescharacteristic
634C2×D4—536no—
635C2×D4—536no—
636C2×D4—533no—
637C2×D4—533no—
638C2×D4—536no—
639C2×D4—536no—
640C2×D4—533no—
641C2×D4—533no—
642C2×D4—533no—
643C2×D4—536no—
644C2×D4—1066no—
645C2×D4—1066no—
646C2×D4—1066no—
647C2×D4—1066no—
648C2×D4—2126no—
649C2×D4—2126no—
650C2×D4—2123no—
651C2×D4—2123no—
652C2×D4C22×#615713yes—
653C2×D4C22×#615713yes—
654C2×D4C22×#615713yes—
655C2×D4C22×#615716yes—
656C22×C4—533no—
657C22×C4—531no—
658C22×C4—533no—
659C22×C4—531no—
660C22×C4—533no—
661C22×C4—533no—
662C22×C4—533no—
663C22×C4—533no—
664C22×C4—533no—
665C22×C4—533no—
666C22×C4—531no—
667C22×C4—531no—
668C22×C4—533no—
669C22×C4—531no—
670C22×C4—531no—
671C22×C4—533no—
672C22×C4—533no—
673C22×C4—533no—
674C22×C4—531no—
675C22×C4—1066no—
676C22×C4—1066no—
677C22×C4—1066no—
678C22×C4—1066no—
679C22×C4—10612no—
680C22×C4—1066no—
681C22×C4—1066no—
682C22×C4—1066no—
683C22×C4—2126no—
684C22×C4—2126no—
685C22×C4—2123no—
686C22×C4—2123no—
687C22×C4—2123no—
688C22×C4C22×#615713yes—
689C22×C4C22×#615713yes—
690C4⋊C4—5312no—
691C4⋊C4—531no—
692C4⋊C4—531no—
693C4⋊C4—531no—
694C4⋊C4—536no—
695C4⋊C4—533no—
696C4⋊C4—1066no—
697C4⋊C4—1066no—
698C4⋊C4—1062no—
699C4⋊C4—1066no—
700C4⋊C4—1066no—
701C4⋊C4—1066no—
702C4⋊C4—2123no—
703C4⋊C4C22×#615711yescharacteristic
704C4⋊C4C22×#615713yes—
705C22⋊C4—533no—
706C22⋊C4—533no—
707C22⋊C4—533no—
708C22⋊C4—533no—
709C22⋊C4—533no—
710C22⋊C4—533no—
711C22⋊C4—1066no—
712C22⋊C4—1066no—
713C22⋊C4—10612no—
714C22⋊C4—1066no—
715C22⋊C4—2123no—
716C22⋊C4—2126no—
717C22⋊C4—2123no—
718C22⋊C4—2123no—
719C22⋊C4—2126no—
720C22⋊C4C22×#615713yes—
721C22⋊C4C22×#615713yes—
722C42—5312no—
723C42—533no—
724C42—533no—
725C42—533no—
726C42—1062no—
727C42—1066no—
728C42—1066no—
729C42—1066no—
730C42—1066no—
731C42—2126no—
732C42C22×#615713yes—
733C23—531no—
734C23—533no—
735C23—533no—
736C23—1063no—
737C23—1063no—
738C23—1063no—
739C23—1063no—
740C23—1063no—
741C23—1063no—
742C23—1063no—
743C23—1063no—
744C23—1063no—
745C23—1063no—
746C23—1063no—
747C23—1063no—
748C23C23×#615713yes—
749C23C23×#615713yes—
750Q8—5312no—
751Q8D4×#615714yescomplemented
752D4—26no—
753D4—26no—
754D4—43no—
755D4—46no—
756D4—10612no—
757D4—10612no—
758D4—1066no—
759D4—1066no—
760D4—2123no—
761D4—2126no—
762D4—2123no—
763D4—2123no—
764D4—2126no—
765D4—2126no—
766C2×C4—26no—
767C2×C4—26no—
768C2×C4—533no—
769C2×C4—536no—
770C2×C4—536no—
771C2×C4—532no—
772C2×C4—536no—
773C2×C4—532no—
774C2×C4—531no—
775C2×C4—533no—
776C2×C4—531no—
777C2×C4—531no—
778C2×C4—1066no—
779C2×C4—1066no—
780C2×C4—1061no—
781C2×C4—1063no—
782C2×C4—1061no—
783C2×C4—1063no—
784C2×C4—1061no—
785C2×C4—1061no—
786C2×C4—1061no—
787C2×C4—1061no—
788C2×C4—1066no—
789C2×C4—1066no—
790C2×C4—1061no—
791C2×C4—1063no—
792C2×C4—1063no—
793C2×C4—1061no—
794C2×C4—1061no—
795C2×C4—1061no—
796C2×C4—1066no—
797C2×C4—1066no—
798C2×C4—1061no—
799C2×C4—1061no—
800C2×C4—1063no—
801C2×C4—1063no—
802C2×C4—1063no—
803C2×C4—1063no—
804C2×C4—1061no—
805C2×C4—1063no—
806C2×C4—1061no—
807C2×C4—1061no—
808C2×C4—1063no—
809C2×C4—1063no—
810C2×C4—1063no—
811C2×C4—1063no—
812C2×C4—1061no—
813C2×C4—42412no—
814C2×C4—21212no—
815C2×C4—21212no—
816C2×C4C23×#615711yescharacteristic
817C2×C4C23×#615713yes—
818C2×C4C23×#615711yescharacteristic
819C2×C4C23×#615711yescharacteristic
820C2×C4C23×#615713yes—
821C22—23no—
822C22—23no—
823C22—23no—
824C22—23no—
825C22—23no—
826C22—23no—
827C22—531no—
828C22—531no—
829C22—531no—
830C22—531no—
831C22—531no—
832C22—531no—
833C22—1063no—
834C22—1063no—
835C22—1063no—
836C22—1063no—
837C22—1063no—
838C22—1063no—
839C22—2123no—
840C22—2123no—
841C22—2123no—
842C22—2123no—
843C22—2123no—
844C22—2123no—
845C22—2123no—
846C22—2123no—
847C22C24×#615711yescharacteristic
848C4—21no—
849C4—21no—
850C4—21no—
851C4—23no—
852C4—536no—
853C4—1066no—
854C4—1062no—
855C4—1062no—
856C4—1061no—
857C4—1061no—
858C4—1061no—
859C4—1063no—
860C4—2123no—
861C4—2123no—
862C4—2121no—
863C4—2123no—
864C4—2121no—
865C4C2×D4×#615716yes—
866C2—43no—
867C2—43no—
868C2—531no—
869C2—531no—
870C2—531no—
871C2—531no—
872C2—2123no—
873C2—2123no—
874C2C22×D4×#615711yescharacteristic
875C2#2029169511yescharacteristic
876C2H(5,𝔽2)×#615711yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6157
commutator, socleC22×C53C24×C4
FittingC53×#550C4
prime radical#550×D53C2
cosocleC22×D53C25
hypercenter#550#6157
hypocenterC53#34295
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#16811692C2semidirect
2. C2×#41×#6157C2semidirect
3. #20291245C2semidirect
4. #20291242C2semidirect
5. #20291240C2semidirect
6. #20291231C2semidirect
7. #20291230C2semidirect
8. #20291220C2semidirect
9. #20291220C2semidirect
10. #20291207C2semidirect
11. #20291203C2semidirect
12. #121×#6157C2semidirect
13. #20291169C2semidirect
14. #20291155C2semidirect
63. #16811295C4semidirect
64. #16811294C4semidirect
65. #16811293C4semidirect
66. #16811292C4semidirect
67. #16811292C4semidirect
68. #16811291C4semidirect
69. #16811291C4semidirect
75. C53×#550C4semidirect
82. Q8×#6157D4semidirect
127. C2×#11719949C2×C4semidirect
128. C2×#11719949C2×C4semidirect
129. C2×#11719945C2×C4semidirect
130. C2×#11719945C2×C4semidirect
131. C2×#11719947C2×C4semidirect
132. C2×#11719947C2×C4semidirect
144. #13133214C2×C4semidirect
145. #13133213C2×C4semidirect
146. #13133213C2×C4semidirect
147. #13133213C2×C4semidirect
148. #13133213C2×C4semidirect
149. #13133192C2×C4semidirect
150. #13133192C2×C4semidirect
151. #13133191C2×C4semidirect
152. #13133191C2×C4semidirect
153. #13133190C2×C4semidirect
154. #13133190C2×C4semidirect
155. #13133189C2×C4semidirect
156. #13133189C2×C4semidirect
157. #13133188C2×C4semidirect
158. #13133188C2×C4semidirect
159. Q8×Dic53C2×C4semidirect
160. C4×Dic106C2×C4semidirect
161. #13133182C2×C4semidirect
162. C4×D212C2×C4semidirect
163. D4×Dic53C2×C4semidirect
164. #13133179C2×C4semidirect
165. C4×C22⋊D53C2×C4semidirect
166. C4×C22⋊D53C2×C4semidirect
167. #13133177C2×C4semidirect
168. #13133177C2×C4semidirect
174. C2×#41×C53C2×C4semidirect
175. C2×#41×C53C2×C4semidirect
176. #127×C53C2×C4semidirect
177. #121×C53C2×C4semidirect
178. #121×C53C2×C4semidirect
179. C4×Q8×C53C2×C4semidirect
180. C4×D4×C53C2×C4semidirect
338. Q8×C53C4×D4semidirect
381. Dic106C4×D4semidirect
463. #550#6157semidirect
514. C53#34295semidirect
525. C2×#41C2×#6157semidirect
526. C2×#41C2×#6157semidirect
542. #127C2×#6157semidirect
553. #121C2×#6157semidirect
554. #121C2×#6157semidirect
562. C4×Q8C2×#6157semidirect
575. C4×D4C2×#6157semidirect
751. Q8D4×#6157semidirect

Maximal subgroups

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

subgroupindex
C2×#168116922
C2×#41×#61572
#202912452
#202912422
#202912402
#202912312
#202912302
#202912202
#202912072
#202912032
#121×#61572
#202911692
#202911552
#550×D532
#3429553