Finite Group Databasebeta

← #548×#6157 #28328793

Subgroups — #548×#6157 #28328793

Order 13568.

3232 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×#41×#6157C211yesmaximal, characteristic, complemented
2C22×Q8×#6157C211yesmaximal, characteristic, complemented
3#20291246C213yesmaximal, complemented
4#20291241C213yesmaximal, complemented
5#20291240C213yesmaximal, complemented
6#20291231C213yesmaximal, complemented
7#20291230C211yesmaximal, characteristic, complemented
8#20291220C211yesmaximal, characteristic, complemented
9Q8×C22⋊#6157C211yesmaximal, characteristic, complemented
10#124×#6157C213yesmaximal, complemented
11C22⋊Q8×#6157C213yesmaximal, complemented
12#121×#6157C213yesmaximal, complemented
13C4×Q8×#6157C211yesmaximal, characteristic, complemented
14C4×D4×#6157C213yesmaximal, complemented
15#548×D53C211yesmaximal, characteristic
16#41×#6157—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×#6157C2213yes—
27C2×D4×#6157C2213yes—
28C2×#13133296C2213yes—
29C22×C4⋊#6157C2213yes—
30C22×C4×#6157C2213yes—
31C22×C4×#6157C2213yes—
32(C2×#6157)⋊Q8C2213yes—
33(C2×#6157)⋊Q8C2213yes—
34#16811575C2213yes—
35#16811575C2213yes—
36#16811574C2213yes—
37#16811574C2213yes—
38#16811573C2216yes—
39#16811573C2216yes—
40#16811573C2216yes—
41#16811572C2216yes—
42#16811571C2216yes—
43#16811570C2216yes—
44#16811567C2213yes—
45#16811565C2213yes—
46#16811565C2213yes—
47C4⋊C4×#6157C2213yes—
48C4⋊C4×#6157C2213yes—
49C4⋊C4×#6157C2213yes—
50C4⋊C4×#6157C2213yes—
51C4×C4⋊#6157C2213yes—
52C4×C4⋊#6157C2213yes—
53C22⋊C4×#6157C2211yescharacteristic
54C22⋊C4×#6157C2213yes—
55C22⋊C4×#6157C2213yes—
56C22⋊C4×#6157C2213yes—
57C22⋊C4×#6157C2216yes—
58C4×C22⋊#6157C2213yes—
59C4×C22⋊#6157C2213yes—
60C42×#6157C2213yes—
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×#6157C2313yes—
77C23×#6157C2313yes—
78C23×#6157C2313yes—
79C23×#6157C2311yescharacteristic
80Q8×#6157—24no—
81Q8×#6157—24no—
82Q8×#6157—24no—
83Q8×#6157—212no—
84Q8×#6157—212no—
85Q8×#6157D418yescomplemented
86D4×#6157—212no—
87D4×#6157—212no—
88D4×#6157—212no—
89D4×#6157—212no—
90#13133296—212no—
91C2×C4⋊#6157—212no—
92C2×C4⋊#6157C2313yes—
93C2×C4⋊#6157C2313yes—
94C2×C4⋊#6157C2313yes—
95C2×C4⋊#6157C2313yes—
96C2×C4⋊#6157C2313yes—
97C2×C4⋊#6157C2316yes—
98C2×C4⋊#6157C2313yes—
99C2×C22⋊#6157C2313yes—
100C2×C22⋊#6157C2313yes—
101C2×C22⋊#6157C2313yes—
102C2×C22⋊#6157C2316yes—
103C2×C22⋊#6157C2316yes—
104C2×C22⋊#6157C2311yescharacteristic
105C2×C4×#6157—212no—
106C2×C4×#6157—212no—
107C2×C4×#6157C2311yescharacteristic
108C2×C4×#6157C2313yes—
109C2×C4×#6157C2313yes—
110C2×C4×#6157C2313yes—
111C2×C4×#6157C2313yes—
112C2×C4×#6157C2313yes—
113C2×C4×#6157C2313yes—
114C2×C4×#6157C2311yescharacteristic
115C2×C4×#6157C2313yes—
116C2×C4×#6157C2313yes—
117C2×C4×#6157C2313yes—
118C2×C4×#6157C2313yes—
119(C2×#6157)⋊C4C2311yescharacteristic
120(C2×#6157)⋊C4C2313yes—
121(C2×#6157)⋊C4C2313yes—
122(C2×#6157)⋊C4C2313yes—
123(C2×#6157)⋊C4C2311yescharacteristic
124(C2×#6157)⋊C4C2313yes—
125(C2×#6157)⋊C4C2316yes—
126(C2×#6157)⋊C4C2316yes—
127(C2×#6157)⋊C4C2316yes—
128C2×#11719949C2×C411yescharacteristic, complemented
129C2×#11719945C2×C413yescomplemented
130C2×#11719947C2×C413yescomplemented
131#41×D53—24no—
132#41×D53—24no—
133C22×Dic106C2×C413yescomplemented
134C2×Q8×D53—24no—
135C2×Q8×D53—24no—
136C2×Q8×D53C2×C411yescharacteristic, complemented
137C2×Q8×D53C2×C413yescomplemented
138C2×Q8×D53C2313yes—
139C2×Q8×D53C2311yescharacteristic
140C2×D4×D53C2313yes—
141C2×D4×D53C2313yes—
142C22×C4×D53C2313yes—
143C22×C4×D53C2313yes—
144#13133206C2×C413yescomplemented
145#13133205C2×C413yescomplemented
146#13133204C2×C413yescomplemented
147#13133203C2×C416yescomplemented
148#13133203C2×C416yescomplemented
149#13133197C2×C413yescomplemented
150#13133196C2×C413yescomplemented
151#13133195C2×C416yescomplemented
152#13133194C2×C416yescomplemented
153#13133193C2×C413yescomplemented
154#13133192C2×C413yescomplemented
155#13133191C2×C413yescomplemented
156#13133190C2×C416yescomplemented
157#13133189C2×C416yescomplemented
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×D53C2313yes—
171C22⋊C4×D53C2311yescharacteristic
172C22⋊C4×D53C2313yes—
173C22⋊C4×D53C2316yes—
174C42×D53C2313yes—
175C2×#41×C53C2×C411yescharacteristic, complemented
176C22×Q8×C53C2×C411yescharacteristic, complemented
177#124×C53C2×C413yescomplemented
178C22⋊Q8×C53C2×C413yescomplemented
179#121×C53C2×C413yescomplemented
180C4×Q8×C53C2×C411yescharacteristic, complemented
181C4×D4×C53C2×C413yescomplemented
182C23×D53C2413yes—
183C23×D53C2411yescharacteristic
184C22×#6157—22no—
185C22×#6157—22no—
186C22×#6157—26no—
187C22×#6157—26no—
188C22×#6157—26no—
189C22×#6157—26no—
190C22×#6157—26no—
191C22×#6157—26no—
192C22×#6157—26no—
193C22×#6157—43no—
194C22×#6157—43no—
195C22×#6157#4114yescomplemented
196C22×#6157C2413yes—
197C22×#6157C2413yes—
198C22×#6157C2413yes—
199C22×#6157C2413yes—
200C22×#6157C2411yescharacteristic
201C22×#6157C2411yescharacteristic
202C22×#6157C2411yescharacteristic
203C22×#6157C2411yescharacteristic
204#41×C53—24no—
205C2×Q8×C53—24no—
206C2×Q8×C53C22×C413yes—
207C2×Q8×C53C22×C411yescharacteristic
208C2×D4×C53C22×C413yes—
209C2×D4×C53C22×C413yes—
210C22×C4×C53C22×C413yes—
211C22×C4×C53C22×C413yes—
212C2×C22⋊D53C22×C413yes—
213C2×C22⋊D53C22×C413yes—
214C2×C22⋊D53C22×C416yes—
215C22×Dic53C22×C413yes—
216C22×Dic53C22×C413yes—
217#11719949—24no—
218Q8×D53—24no—
219Q8×D53—26no—
220Q8×D53—26no—
221Q8×D53—212no—
222Q8×D53C2×D414yes—
223Q8×D53#4114yes—
224#11719947—212no—
225D4×D53—26no—
226D4×D53—26no—
227D4×D53—26no—
228D4×D53—26no—
229#11719945—212no—
230C2×D212C22×C413yes—
231C2×D212C22×C413yes—
232C2×C4×D53—26no—
233C2×C4×D53—26no—
234C2×C4×D53—26no—
235C2×C4×D53—26no—
236C2×C4×D53C22×C413yes—
237C2×C4×D53C22×C413yes—
238C2×C4×D53C22×C413yes—
239C2×C4×D53C22×C413yes—
240C2×C4×D53C2411yescharacteristic
241C2×C4×D53C2413yes—
242C2×C4×D53C2413yes—
243C2×C4×D53C2411yescharacteristic
244C2×C4×D53C2413yes—
245C2×Dic106—212no—
246C2×Dic106C22×C416yes—
247C2×Dic106C22×C413yes—
248C2×Dic106C22×C413yes—
249C22⋊#6157—26no—
250C22⋊#6157—212no—
251C22⋊#6157—26no—
252C22⋊#6157—26no—
253C22⋊#6157—46no—
254C22⋊#6157#4114yescomplemented
255C4⋊#6157—212no—
256C4⋊#6157—26no—
257C4⋊#6157—26no—
258C4⋊#6157—26no—
259C4⋊#6157—26no—
260C4⋊#6157—26no—
261C4⋊#6157C2×D4112yes—
262C4×#6157—22no—
263C4×#6157—26no—
264C4×#6157—26no—
265C4×#6157—26no—
266C4×#6157—26no—
267C4×#6157—26no—
268C4×#6157—22no—
269C4×#6157—26no—
270C4×#6157—26no—
271C4×#6157—26no—
272C4×#6157—43no—
273C4×#6157C2×D4112yes—
274C4⋊C4×C53C22×C413yes—
275C4⋊C4×C53C22×C413yes—
276C22⋊C4×C53C22×C411yescharacteristic
277C22⋊C4×C53C22×C413yes—
278C22⋊C4×C53C22×C416yes—
279C42×C53C22×C413yes—
280C22⋊Dic53C22×C411yescharacteristic
281C22⋊Dic53C22×C413yes—
282C22⋊Dic53C22×C416yes—
283#11719921C22×C411yescharacteristic
284#11719921C22×C413yes—
285#11719921C22×C411yescharacteristic
286#11719921C22×C413yes—
287#11719921C22×C416yes—
288#11719921C22×C416yes—
289C4⋊Dic53C22×C413yes—
290C4⋊Dic53C22×C413yes—
291#11719919C22×C413yes—
292#11719919C22×C413yes—
293#11719919C22×C416yes—
294C4×Dic53C22×C413yes—
295C4×Dic53C22×C413yes—
296C4×Dic53C22×C413yes—
297C23×C53C23×C413yes—
298C23×C53C23×C411yescharacteristic
299C22×D53—21no—
300C22×D53—21no—
301C22×D53—21no—
302C22×D53—21no—
303C22×D53—23no—
304C22×D53—23no—
305C22×D53—23no—
306C22×D53—23no—
307C22×D53—23no—
308C22×D53—23no—
309C22×D53C23×C413yes—
310C22×D53C23×C411yescharacteristic
311C22×D53C2×#4112yes—
312C22×D53C2×#4112yes—
313C22×D53C2511yescharacteristic
314C2×#6157—21no—
315C2×#6157—21no—
316C2×#6157—21no—
317C2×#6157—23no—
318C2×#6157—21no—
319C2×#6157—21no—
320C2×#6157—23no—
321C2×#6157—21no—
322C2×#6157—28no—
323C2×#6157—23no—
324C2×#6157—23no—
325C2×#6157—23no—
326C2×#6157—23no—
327C2×#6157—23no—
328C2×#6157—23no—
329C2×#6157—23no—
330C2×#6157—23no—
331C2×#6157—23no—
332C2×#6157—412no—
333C2×#6157—412no—
334C2×#6157—412no—
335C2×#6157C22×D416yes—
336C2×#6157C22×D412yes—
337C2×#6157C2×#4112yes—
338C2×#6157C2×#4112yes—
339C2×#6157C2×#4112yes—
340C2×#6157C2×#4112yes—
341C2×#61572−1+412yes—
342Q8×C53—26no—
343Q8×C53C4×D414yescomplemented
344D4×C53—26no—
345D4×C53—26no—
346C2×C4×C53—26no—
347C2×C4×C53—26no—
348C2×C4×C53C23×C413yes—
349C2×C4×C53C23×C411yescharacteristic
350C2×C4×C53C23×C413yes—
351C2×C4×C53C23×C411yescharacteristic
352C2×C4×C53C23×C413yes—
353C22⋊D53—26no—
354C22⋊D53—26no—
355C22⋊D53—212no—
356C2×Dic53—26no—
357C2×Dic53—26no—
358C2×Dic53C23×C413yes—
359C2×Dic53C23×C411yescharacteristic
360C2×Dic53C23×C413yes—
361C2×Dic53C23×C411yescharacteristic
362C2×Dic53C23×C413yes—
363D212—26no—
364D212—26no—
365C4×D53—21no—
366C4×D53—23no—
367C4×D53—23no—
368C4×D53—23no—
369C4×D53—21no—
370C4×D53—23no—
371C4×D53—21no—
372C4×D53—21no—
373C4×D53—26no—
374C4×D53—26no—
375C4×D53—26no—
376C4×D53—26no—
377C4×D53C22×D416yes—
378C4×D53C2×#4116yes—
379Dic106—26no—
380Dic106—212no—
381Dic106C4×D4112yescomplemented
382C4×#548—531nomaximal, Sylow
383C22×C53—21no—
384C22×C53—21no—
385C22×C53—23no—
386C22×C53—23no—
387C22×C53—23no—
388C22×C53C4×#4112yescomplemented
389C22×C53C24×C411yescharacteristic
390C2×D53—21no—
391C2×D53—21no—
392C2×D53—22no—
393C2×D53—22no—
394C2×D53—22no—
395C2×D53—22no—
396C2×D53—23no—
397C2×D53—23no—
398C2×D53—23no—
399C2×D53—43no—
400C2×D53—43no—
401C2×D53—43no—
402C2×D53—43no—
403C2×D53C4×#4112yescomplemented
404C2×D53C23×D411yescharacteristic
405C2×D53C22×#4111yescharacteristic
406C2×D53C22×#4111yescharacteristic
407C2×D53C22×#4111yescharacteristic
408C2×D53C2×2−1+411yescharacteristic
409C2×D53#58511yescharacteristic
410#6157—22no—
411#6157—22no—
412#6157—26no—
413#6157—22no—
414#6157—43no—
415#6157—43no—
416#6157—43no—
417#6157#54814yesdirect product factor
418C4×C53—23no—
419C4×C53—21no—
420C4×C53—23no—
421C4×C53—21no—
422C4×C53C2×C4×D416yes—
423Dic53—23no—
424Dic53—21no—
425Dic53—23no—
426Dic53—21no—
427Dic53C2×C4×D416yes—
428C2×#548—531no—
429C2×C4×#41—531no—
430C22×C4×Q8—531no—
431#2367—533no—
432#2362—533no—
433#2361—533no—
434#2352—533no—
435#2351—531no—
436#2341—531no—
437Q8×C22⋊C4—531no—
438C4×#124—533no—
439C4×C22⋊Q8—533no—
440C4×#121—533no—
441C42×Q8—531no—
442C42×D4—533no—
443C2×C53—22no—
444C2×C53—43no—
445C2×C53C22×C4×D411yescharacteristic
446C2×C53C2×C4×#4111yescharacteristic
447C2×C53C4×2−1+411yescharacteristic
448D53—22no—
449D53—43no—
450D53C2×#54811yescharacteristic
451D53D4×#4111yescharacteristic
452D53#348011yescharacteristic
453D53#348211yescharacteristic
454C22×#41—531no—
455C23×Q8—531no—
456#548—531no—
457#548—531no—
458#548—533no—
459#548—533no—
460#548—533no—
461#548—531no—
462#548—533no—
463#548#615711yescharacteristic, direct product factor
464C2×#124—533no—
465C2×C22⋊Q8—533no—
466C2×#121—533no—
467C4×#41—1068no—
468C2×C4×Q8—531no—
469C2×C4×Q8—531no—
470C2×C4×Q8—531no—
471C2×C4×Q8—531no—
472C2×C4×Q8—531no—
473C2×C4×Q8—533no—
474C2×C4×Q8—533no—
475C2×C4×Q8—1068no—
476C2×C4×D4—533no—
477C2×C4×D4—533no—
478C2×C4×D4—533no—
479C2×C4×D4—533no—
480C2×C4×D4—533no—
481C2×#117—533no—
482C22×C4⋊C4—533no—
483C22×C42—533no—
484C22×C42—533no—
485#391—533no—
486#391—533no—
487#390—533no—
488#390—533no—
489#389—533no—
490#389—533no—
491#388—536no—
492#388—536no—
493#388—536no—
494#387—536no—
495#386—536no—
496#385—536no—
497#382—533no—
498#380—533no—
499#380—533no—
500C4×C4⋊C4—533no—
501C4×C4⋊C4—533no—
502C4×C4⋊C4—533no—
503C4×C4⋊C4—533no—
504C4×C4⋊C4—533no—
505C4×C4⋊C4—533no—
506C4×C22⋊C4—533no—
507C4×C22⋊C4—533no—
508C4×C22⋊C4—533no—
509C4×C22⋊C4—533no—
510C4×C22⋊C4—531no—
511C4×C22⋊C4—533no—
512C4×C22⋊C4—536no—
513C43—533no—
514C53C4×#54811yescharacteristic, complemented, Sylow
515C2×#41—531no—
516C2×#41—533no—
517C2×#41—533no—
518C2×#41—1064no—
519C2×#41—1064no—
520C2×#41C2×#615711yescharacteristic, complemented
521C22×Q8—531no—
522C22×Q8—533no—
523C22×Q8—533no—
524C22×Q8—531no—
525C22×Q8—533no—
526C22×Q8—1064no—
527C22×Q8—1064no—
528C22×Q8C2×#615711yescharacteristic, complemented
529C22×D4—533no—
530C22×D4—533no—
531C23×C4—531no—
532C23×C4—533no—
533C23×C4—533no—
534C23×C4—533no—
535C23×C4—533no—
536C23×C4—533no—
537#124—533no—
538#124—533no—
539#124—536no—
540#124—536no—
541#124—533no—
542#124C2×#615713yescomplemented
543C22⋊Q8—533no—
544C22⋊Q8—533no—
545C22⋊Q8—536no—
546C22⋊Q8—533no—
547C22⋊Q8—536no—
548C22⋊Q8C2×#615713yescomplemented
549#121—533no—
550#121—536no—
551#121—533no—
552#121—533no—
553#121—536no—
554#121C2×#615713yescomplemented
555C4×Q8—538no—
556C4×Q8—531no—
557C4×Q8—533no—
558C4×Q8—533no—
559C4×Q8—10612no—
560C4×Q8—10612no—
561C4×Q8—1064no—
562C4×Q8—1064no—
563C4×Q8—1064no—
564C4×Q8C2×#615711yescharacteristic, complemented
565C4×D4—533no—
566C4×D4—533no—
567C4×D4—533no—
568C4×D4—533no—
569C4×D4—533no—
570C4×D4—533no—
571C4×D4—533no—
572C4×D4—10612no—
573C4×D4—10612no—
574C4×D4—10612no—
575C4×D4—10612no—
576C4×D4C2×#615713yescomplemented
577#117—10612no—
578C2×C4⋊C4—533no—
579C2×C4⋊C4—533no—
580C2×C4⋊C4—533no—
581C2×C4⋊C4—533no—
582C2×C4⋊C4—536no—
583C2×C4⋊C4—533no—
584C2×C4⋊C4—533no—
585C2×C4⋊C4—533no—
586C2×C4⋊C4—533no—
587C2×C4⋊C4—10612no—
588C2×C22⋊C4—531no—
589C2×C22⋊C4—531no—
590C2×C22⋊C4—533no—
591C2×C22⋊C4—536no—
592C2×C22⋊C4—536no—
593C2×C22⋊C4—533no—
594C2×C22⋊C4—533no—
595C2×C22⋊C4—533no—
596C2×C22⋊C4—536no—
597C2×C42—533no—
598C2×C42—533no—
599C2×C42—533no—
600C2×C42—533no—
601C2×C42—533no—
602C2×C42—533no—
603C2×C42—533no—
604C2×C42—533no—
605C2×C42—533no—
606C2×C42—533no—
607C2×C42—531no—
608C2×C42—531no—
609C2×C42—533no—
610C2×C42—10612no—
611C2×C42—10612no—
612#95—531no—
613#95—531no—
614#95—533no—
615#95—533no—
616#95—533no—
617#95—533no—
618#95—536no—
619#95—536no—
620#95—536no—
621C24—531no—
622C24—533no—
623#41—24no—
624#41—10612no—
625#41—10612no—
626#41—1064no—
627C2×Q8—24no—
628C2×Q8—534no—
629C2×Q8—534no—
630C2×Q8—533no—
631C2×Q8—536no—
632C2×Q8—533no—
633C2×Q8—10612no—
634C2×Q8—1066no—
635C2×Q8—1066no—
636C2×Q8—10612no—
637C2×Q8—1064no—
638C2×Q8C22×#615713yes—
639C2×Q8C22×#615711yescharacteristic
640C2×D4—533no—
641C2×D4—533no—
642C2×D4—536no—
643C2×D4—533no—
644C2×D4—533no—
645C2×D4—1066no—
646C2×D4—1066no—
647C2×D4—1066no—
648C2×D4—1066no—
649C2×D4C22×#615713yes—
650C2×D4C22×#615713yes—
651C22×C4—531no—
652C22×C4—533no—
653C22×C4—534no—
654C22×C4—531no—
655C22×C4—531no—
656C22×C4—531no—
657C22×C4—533no—
658C22×C4—533no—
659C22×C4—533no—
660C22×C4—533no—
661C22×C4—533no—
662C22×C4—533no—
663C22×C4—533no—
664C22×C4—531no—
665C22×C4—531no—
666C22×C4—533no—
667C22×C4—533no—
668C22×C4—533no—
669C22×C4—533no—
670C22×C4—533no—
671C22×C4—1066no—
672C22×C4—1066no—
673C22×C4—1066no—
674C22×C4—1066no—
675C22×C4—1062no—
676C22×C4—1062no—
677C22×C4—1066no—
678C22×C4—1066no—
679C22×C4—1066no—
680C22×C4—1066no—
681C22×C4—1066no—
682C22×C4—1066no—
683C22×C4—1066no—
684C22×C4—2123no—
685C22×C4—2123no—
686C22×C4C22×#615713yes—
687C22×C4C22×#615713yes—
688C4⋊C4—5312no—
689C4⋊C4—533no—
690C4⋊C4—533no—
691C4⋊C4—533no—
692C4⋊C4—536no—
693C4⋊C4—533no—
694C4⋊C4—1066no—
695C4⋊C4—10612no—
696C4⋊C4—1066no—
697C4⋊C4—1066no—
698C4⋊C4—1066no—
699C4⋊C4—1066no—
700C4⋊C4C22×#615713yes—
701C4⋊C4C22×#615713yes—
702C22⋊C4—534no—
703C22⋊C4—531no—
704C22⋊C4—533no—
705C22⋊C4—536no—
706C22⋊C4—531no—
707C22⋊C4—531no—
708C22⋊C4—533no—
709C22⋊C4—533no—
710C22⋊C4—536no—
711C22⋊C4—536no—
712C22⋊C4—10612no—
713C22⋊C4—1066no—
714C22⋊C4—1066no—
715C22⋊C4—1066no—
716C22⋊C4—2126no—
717C22⋊C4C22×#615711yescharacteristic
718C22⋊C4C22×#615713yes—
719C22⋊C4C22×#615716yes—
720C42—5312no—
721C42—533no—
722C42—533no—
723C42—533no—
724C42—1062no—
725C42—1062no—
726C42—1066no—
727C42—1066no—
728C42—1066no—
729C42—1066no—
730C42—1066no—
731C42—1066no—
732C42—1066no—
733C42—1066no—
734C42—2123no—
735C42C22×#615713yes—
736C23—531no—
737C23—532no—
738C23—532no—
739C23—531no—
740C23—533no—
741C23—1061no—
742C23—1061no—
743C23—1061no—
744C23—1061no—
745C23—1063no—
746C23—1063no—
747C23—1063no—
748C23—1063no—
749C23—1063no—
750C23—1063no—
751C23C23×#615713yes—
752C23C23×#615711yescharacteristic
753Q8—26no—
754Q8—5312no—
755Q8—10612no—
756Q8—1066no—
757Q8D4×#615714yescomplemented
758D4—26no—
759D4—26no—
760D4—1066no—
761D4—10612no—
762D4—1066no—
763D4—1066no—
764D4—1066no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—532no—
768C2×C4—532no—
769C2×C4—532no—
770C2×C4—533no—
771C2×C4—536no—
772C2×C4—536no—
773C2×C4—536no—
774C2×C4—532no—
775C2×C4—532no—
776C2×C4—532no—
777C2×C4—531no—
778C2×C4—533no—
779C2×C4—533no—
780C2×C4—531no—
781C2×C4—1066no—
782C2×C4—1066no—
783C2×C4—1061no—
784C2×C4—1063no—
785C2×C4—1063no—
786C2×C4—1063no—
787C2×C4—1061no—
788C2×C4—1061no—
789C2×C4—1061no—
790C2×C4—1063no—
791C2×C4—1066no—
792C2×C4—1066no—
793C2×C4—1068no—
794C2×C4—1061no—
795C2×C4—1061no—
796C2×C4—1061no—
797C2×C4—1061no—
798C2×C4—1063no—
799C2×C4—1063no—
800C2×C4—1061no—
801C2×C4—1061no—
802C2×C4—1066no—
803C2×C4—1066no—
804C2×C4—1063no—
805C2×C4—1063no—
806C2×C4—1063no—
807C2×C4—1063no—
808C2×C4—1063no—
809C2×C4—1063no—
810C2×C4—1063no—
811C2×C4—1063no—
812C2×C4—1063no—
813C2×C4—21212no—
814C2×C4—21212no—
815C2×C4—21212no—
816C2×C4C23×#615711yescharacteristic
817C2×C4C23×#615713yes—
818C2×C4C23×#615713yes—
819C2×C4C23×#615711yescharacteristic
820C2×C4C23×#615713yes—
821C22—21no—
822C22—21no—
823C22—23no—
824C22—23no—
825C22—23no—
826C22—531no—
827C22—531no—
828C22—531no—
829C22—531no—
830C22—531no—
831C22—531no—
832C22—532no—
833C22—1062no—
834C22—1062no—
835C22—1062no—
836C22—1062no—
837C22—1061no—
838C22—1061no—
839C22—1063no—
840C22—1063no—
841C22—1063no—
842C22—2123no—
843C22—2123no—
844C22—2123no—
845C22—2123no—
846C22#41×#615712yescomplemented
847C22C24×#615711yescharacteristic
848C4—21no—
849C4—23no—
850C4—23no—
851C4—21no—
852C4—534no—
853C4—536no—
854C4—1062no—
855C4—1062no—
856C4—1066no—
857C4—1062no—
858C4—1061no—
859C4—1063no—
860C4—1063no—
861C4—1061no—
862C4—2123no—
863C4—2123no—
864C4—2123no—
865C4C2×D4×#615716yes—
866C2—22no—
867C2—43no—
868C2—531no—
869C2—531no—
870C2—531no—
871C2—531no—
872C2—1062no—
873C2—2123no—
874C2C22×D4×#615711yescharacteristic
875C2C2×#41×#615711yescharacteristic
876C22−1+4×#615711yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6157
commutator, socleC22×C53C24×C4
FittingC53×#548C4
prime radical#548×D53C2
cosocleC22×D53C25
hypercenter#548#6157
hypocenterC53C4×#548
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×#6157C2semidirect
2. C22×Q8×#6157C2semidirect
3. #20291246C2semidirect
4. #20291241C2semidirect
5. #20291240C2semidirect
6. #20291231C2semidirect
7. #20291230C2semidirect
8. #20291220C2semidirect
9. Q8×C22⋊#6157C2semidirect
10. #124×#6157C2semidirect
11. C22⋊Q8×#6157C2semidirect
12. #121×#6157C2semidirect
13. C4×Q8×#6157C2semidirect
14. C4×D4×#6157C2semidirect
63. #16811285C4semidirect
64. #16811284C4semidirect
65. #16811283C4semidirect
66. #16811282C4semidirect
67. #16811281C4semidirect
68. #16811280C4semidirect
69. #16811279C4semidirect
75. C53×#548C4semidirect
85. Q8×#6157D4semidirect
128. C2×#11719949C2×C4semidirect
129. C2×#11719945C2×C4semidirect
130. C2×#11719947C2×C4semidirect
133. C22×Dic106C2×C4semidirect
136. C2×Q8×D53C2×C4semidirect
137. C2×Q8×D53C2×C4semidirect
144. #13133206C2×C4semidirect
145. #13133205C2×C4semidirect
146. #13133204C2×C4semidirect
147. #13133203C2×C4semidirect
148. #13133203C2×C4semidirect
149. #13133197C2×C4semidirect
150. #13133196C2×C4semidirect
151. #13133195C2×C4semidirect
152. #13133194C2×C4semidirect
153. #13133193C2×C4semidirect
154. #13133192C2×C4semidirect
155. #13133191C2×C4semidirect
156. #13133190C2×C4semidirect
157. #13133189C2×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
175. C2×#41×C53C2×C4semidirect
176. C22×Q8×C53C2×C4semidirect
177. #124×C53C2×C4semidirect
178. C22⋊Q8×C53C2×C4semidirect
179. #121×C53C2×C4semidirect
180. C4×Q8×C53C2×C4semidirect
181. C4×D4×C53C2×C4semidirect
195. C22×#6157#41semidirect
254. C22⋊#6157#41semidirect
343. Q8×C53C4×D4semidirect
381. Dic106C4×D4semidirect
388. C22×C53C4×#41semidirect
403. C2×D53C4×#41semidirect
417. #6157#548direct (N × H)
463. #548#6157direct (N × H)
514. C53C4×#548semidirect
520. C2×#41C2×#6157semidirect
528. C22×Q8C2×#6157semidirect
542. #124C2×#6157semidirect
548. C22⋊Q8C2×#6157semidirect
554. #121C2×#6157semidirect
564. C4×Q8C2×#6157semidirect
576. C4×D4C2×#6157semidirect
757. Q8D4×#6157semidirect
846. C22#41×#6157semidirect

Maximal subgroups

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

subgroupindex
C2×#41×#61572
C22×Q8×#61572
#202912462
#202912412
#202912402
#202912312
#202912302
#202912202
Q8×C22⋊#61572
#124×#61572
C22⋊Q8×#61572
#121×#61572
C4×Q8×#61572
C4×D4×#61572
#548×D532
C4×#54853