Finite Group Databasebeta

← C2×#41×C22⋊D53 #28291049

Subgroups — C2×#41×C22⋊D53 #28291049

Order 13568.

12314 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D53C211yesmaximal, characteristic, complemented
2#41×C22⋊D53C2132yesmaximal, direct product factor
3C2×#16811292C211yesmaximal, characteristic, complemented
4C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
5C2×#16811284C211yesmaximal, characteristic, complemented
6C2×#16811280C211yesmaximal, characteristic, complemented
7C2×#16811272C213yesmaximal, complemented
8C2×#16811267C213yesmaximal, complemented
9C2×#16811261C213yesmaximal, complemented
10C2×D4×C22⋊D53C213yesmaximal, complemented
11C2×#16811169C213yesmaximal, complemented
12C2×#16811134C213yesmaximal, complemented
13C2×#16811130C213yesmaximal, complemented
14C2×#41×Dic53C211yesmaximal, characteristic, complemented
15C22×C4×C22⋊D53C213yesmaximal, complemented
16C23×#41×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic, complemented
18C22×#11719945C2213yescomplemented
19C22×#11719947C2213yescomplemented
20C2×#41×D53—216no—
21C2×#41×D53C22116yescomplemented
22C22×Q8×D53C2211yescharacteristic, complemented
23C23×C22⋊D53C2213yes—
24C22×D4×D53C2213yescomplemented
25C23×C4×D53C2213yescomplemented
26#16811292C22116yescomplemented
27Q8×C22⋊D53C22116yescomplemented
28#16811284C22116yescomplemented
29#16811280C22116yescomplemented
30#16811272C22148yescomplemented
31#16811267C22148yescomplemented
32#16811261C22148yescomplemented
33D4×C22⋊D53C22148yescomplemented
34#16811169C22148yescomplemented
35C2×#13133215C2213yescomplemented
36C2×#13133213C2213yescomplemented
37C2×#13133206C2213yescomplemented
38C2×#13133204C2213yescomplemented
39#16811134C22148yescomplemented
40#16811130C22148yescomplemented
41C2×#13133200C2216yescomplemented
42C2×#13133198C2216yescomplemented
43C2×#13133196C2213yescomplemented
44C2×#13133196C2213yescomplemented
45C2×#13133193C2213yescomplemented
46C2×#13133193C2213yescomplemented
47C2×#13133191C2213yescomplemented
48C2×#13133191C2213yescomplemented
49C2×#13133189C2216yescomplemented
50C2×#13133189C2216yescomplemented
51C2×#13133188C2213yescomplemented
52C2×#13133188C2213yescomplemented
53C2×#13133186C2216yescomplemented
54C2×#13133185C2216yescomplemented
55#41×Dic53C22116yescomplemented
56C2×Q8×Dic53C2211yescharacteristic, complemented
57C2×Q8×Dic53C2211yescharacteristic, complemented
58C2×D4×Dic53C2213yescomplemented
59C2×D4×Dic53C2213yescomplemented
60C2×C4×C22⋊D53C2211yescharacteristic
61C2×C4×C22⋊D53C2213yes—
62C2×C4×C22⋊D53C2213yescomplemented
63C2×C4×C22⋊D53C2213yescomplemented
64C2×C4×C22⋊D53C2213yescomplemented
65C2×C4×C22⋊D53C2213yescomplemented
66C2×C4×C22⋊D53C2213yescomplemented
67C2×C4×C22⋊D53C2213yescomplemented
68C2×C4×C22⋊D53C2216yescomplemented
69C2×C4×C22⋊D53C22148yescomplemented
70C2×#13133176C2213yescomplemented
71C22×#11719919C2213yescomplemented
72C22×C22⋊Dic53C2213yescomplemented
73C22×#11719921C2213yescomplemented
74C22×C4×Dic53C2213yescomplemented
75C22×#41×C53—216no—
76C22×#41×C53C2211yescharacteristic
77C22×#41×C53C2213yescomplemented
78C22×#41×C53C2211yescharacteristic, complemented
79C22×#41×C53C2213yescomplemented
80C22×#41×C53C22116yescomplemented
81C23×Q8×C53C2211yescharacteristic, complemented
82C23×D4×C53C2213yescomplemented
83C24×C4×C53C2213yescomplemented
84C24×D53C2313yes—
85C2×#11719949—28no—
86C2×#11719949C2318yescomplemented
87C2×#11719945—224no—
88C2×#11719945C23124yescomplemented
89C2×#11719947—224no—
90C2×#11719947C23124yescomplemented
91#41×D53—2128no—
92C22×Dic106C2313yes—
93C2×Q8×D53—28no—
94C2×Q8×D53C2318yescomplemented
95C22×D212C2313yes—
96C22×C22⋊D53—224no—
97C22×C22⋊D53C2313yes—
98C22×C22⋊D53C2313yes—
99C22×C22⋊D53C2313yes—
100C22×C22⋊D53C23124yes—
101C22×C22⋊D53C2316yes—
102C22×C22⋊D53C2316yes—
103C22×C22⋊D53C2311yescharacteristic
104C2×D4×D53—224no—
105C2×D4×D53C23124yescomplemented
106C23×Dic53C2313yes—
107C23×Dic53C2313yes—
108C23×Dic53C2313yes—
109C22×C4×D53—224no—
110C22×C4×D53C2311yescharacteristic
111C22×C4×D53C2313yes—
112C22×C4×D53C2313yes—
113C22×C4×D53C2313yes—
114C22×C4×D53C23124yescomplemented
115#13133215C23124yescomplemented
116#13133213C23124yescomplemented
117#13133206C23124yescomplemented
118#13133204C23124yescomplemented
119#13133200C23148yescomplemented
120#13133198C23148yescomplemented
121#13133196C23124yescomplemented
122#13133196C23124yescomplemented
123#13133193C23124yescomplemented
124#13133193C23124yescomplemented
125#13133191C23124yescomplemented
126#13133191C23124yescomplemented
127#13133189C23148yescomplemented
128#13133189C23148yescomplemented
129#13133188C23124yescomplemented
130#13133188C23124yescomplemented
131#13133186C23148yescomplemented
132#13133185C23148yescomplemented
133Q8×Dic53C2318yescomplemented
134Q8×Dic53C2318yescomplemented
135D4×Dic53C23124yescomplemented
136D4×Dic53C23124yescomplemented
137C4×C22⋊D53C23124yes—
138C4×C22⋊D53C2318yes—
139C4×C22⋊D53C23124yescomplemented
140C4×C22⋊D53C23124yescomplemented
141C4×C22⋊D53C23124yescomplemented
142C4×C22⋊D53C23124yescomplemented
143C4×C22⋊D53C23124yescomplemented
144C4×C22⋊D53C23124yescomplemented
145C4×C22⋊D53C23148yescomplemented
146#13133176C23124yescomplemented
147C2×C4⋊Dic53C2313yes—
148C2×C4⋊Dic53C2313yes—
149C2×#11719919C2311yescharacteristic
150C2×#11719919C2313yes—
151C2×#11719919C2313yes—
152C2×#11719919C2313yes—
153C2×#11719919C2316yes—
154C2×#11719919C23124yescomplemented
155C2×C22⋊Dic53C2311yescharacteristic
156C2×C22⋊Dic53C2313yes—
157C2×C22⋊Dic53C2313yes—
158C2×C22⋊Dic53C2313yes—
159C2×C22⋊Dic53C2316yes—
160C2×C22⋊Dic53C2316yes—
161C2×C22⋊Dic53C23124yescomplemented
162C2×#11719921C2311yescharacteristic
163C2×#11719921C2313yes—
164C2×#11719921C2313yes—
165C2×#11719921C2313yes—
166C2×#11719921C2316yes—
167C2×#11719921C23124yescomplemented
168C2×C4×Dic53C2311yescharacteristic
169C2×C4×Dic53C2313yes—
170C2×C4×Dic53C2313yes—
171C2×C4×Dic53C2313yes—
172C2×C4×Dic53C23124yescomplemented
173C25×C53C2313yes—
174C2×#41×C53—2128no—
175C2×#41×C53—28no—
176C2×#41×C53—224no—
177C2×#41×C53—224no—
178C2×#41×C53D4116yescomplemented
179C2×#41×C53C2318yes—
180C2×#41×C53C23124yescomplemented
181C2×#41×C53C2318yescomplemented
182C2×#41×C53C23124yescomplemented
183C22×Q8×C53—28no—
184C22×Q8×C53C2313yes—
185C22×Q8×C53C2311yescharacteristic
186C22×Q8×C53C2318yescomplemented
187C22×D4×C53—224no—
188C22×D4×C53C2316yes—
189C22×D4×C53C2313yes—
190C22×D4×C53C2313yes—
191C22×D4×C53C23124yescomplemented
192C23×C4×C53—224no—
193C23×C4×C53C2313yes—
194C23×C4×C53C2311yescharacteristic
195C23×C4×C53C2313yes—
196C23×C4×C53C2313yes—
197C23×C4×C53C2313yes—
198C23×C4×C53C2313yes—
199C23×C4×C53C23124yescomplemented
200C24×C53—212no—
201C24×C53—212no—
202C24×C53—46no—
203C24×C53C2413yes—
204C24×C53C24112yes—
205C24×C53C2413yes—
206C24×C53C2411yescharacteristic
207C23×D53—212no—
208C23×D53—212no—
209C23×D53—46no—
210C23×D53C2413yes—
211C23×D53C24112yes—
212C23×D53C2411yescharacteristic
213#41×C53—232no—
214#41×C53—296no—
215#41×C53—296no—
216#41×C53C2×D4164yescomplemented
217C2×Q8×C53—232no—
218C2×Q8×C53—212no—
219C2×Q8×C53C2×D418yescomplemented
220C2×Q8×C53C24112yes—
221C2×Q8×C53C2414yes—
222C2×D4×C53—224no—
223C2×D4×C53—296no—
224C2×D4×C53—212no—
225C2×D4×C53C2×D4124yescomplemented
226C2×D4×C53C24124yes—
227C2×D4×C53C24112yes—
228C2×D4×C53C24112yes—
229C22×C4×C53—212no—
230C22×C4×C53—24no—
231C22×C4×C53—212no—
232C22×C4×C53—212no—
233C22×C4×C53—212no—
234C22×C4×C53—296no—
235C22×C4×C53C2×D4124yescomplemented
236C22×C4×C53C2411yescharacteristic
237C22×C4×C53C2413yes—
238C22×C4×C53C2414yes—
239C22×C4×C53C24112yes—
240C22×C4×C53C24112yes—
241C22×C4×C53C24112yes—
242C22×C4×C53C24112yes—
243C22×C4×C53C2413yes—
244C22×C4×C53C2411yescharacteristic
245C22×C4×C53C24112yes—
246C2×C22⋊D53—224no—
247C2×C22⋊D53—212no—
248C2×C22⋊D53—212no—
249C2×C22⋊D53—296no—
250C2×C22⋊D53—212no—
251C2×C22⋊D53—412no—
252C2×C22⋊D53#4118yesdirect product factor
253C2×C22⋊D53C24112yes—
254C2×C22⋊D53C24112yes—
255C2×C22⋊D53C24112yes—
256C2×C22⋊D53C24124yes—
257C2×C22⋊D53C24124yes—
258C2×C22⋊D53C2414yes—
259C22×Dic53—212no—
260C22×Dic53—212no—
261C22×Dic53—46no—
262C22×Dic53C2411yescharacteristic
263C22×Dic53C2413yes—
264C22×Dic53C2413yes—
265C22×Dic53C24112yes—
266C22×Dic53C2411yescharacteristic
267C22×Dic53C2413yes—
268C22×Dic53C24112yes—
269C22×Dic53C24112yes—
270C22×Dic53C2411yescharacteristic
271#11719949—232no—
272Q8×D53—232no—
273#11719947—296no—
274D4×D53—296no—
275#11719945—296no—
276C2×D212—212no—
277C2×D212C24112yes—
278C2×C4×D53—24no—
279C2×C4×D53—212no—
280C2×C4×D53—212no—
281C2×C4×D53—212no—
282C2×C4×D53—296no—
283C2×C4×D53C2414yes—
284C2×C4×D53C24112yes—
285C2×C4×D53C24112yes—
286C2×C4×D53C24112yes—
287C2×Dic106—212no—
288C2×Dic106C24112yes—
289C22⋊Dic53C2414yes—
290C22⋊Dic53C24112yes—
291C22⋊Dic53C24112yes—
292C22⋊Dic53C24112yes—
293C22⋊Dic53C24124yes—
294C22⋊Dic53C24124yes—
295#11719921C2414yes—
296#11719921C24112yes—
297#11719921C24112yes—
298#11719921C24112yes—
299#11719921C24124yes—
300C4⋊Dic53C24112yes—
301C4⋊Dic53C24112yes—
302#11719919C2414yes—
303#11719919C24112yes—
304#11719919C24112yes—
305#11719919C24112yes—
306#11719919C24124yes—
307C4×Dic53C2414yes—
308C4×Dic53C24112yes—
309C4×Dic53C24112yes—
310C4×Dic53C24112yes—
311C23×C53—22no—
312C23×C53—26no—
313C23×C53—26no—
314C23×C53—22no—
315C23×C53—224no—
316C23×C53—26no—
317C23×C53—26no—
318C23×C53—224no—
319C23×C53—26no—
320C23×C53—412no—
321C23×C53—448no—
322C23×C53C22×D4112yes—
323C23×C53C2×#4114yescomplemented
324C23×C53C2516yes—
325C23×C53C2516yes—
326C23×C53C2512yes—
327C23×C53C2511yescharacteristic
328C22×D53—22no—
329C22×D53—22no—
330C22×D53—26no—
331C22×D53—224no—
332C22×D53—26no—
333C22×D53—26no—
334C22×D53—224no—
335C22×D53—412no—
336C22×D53—448no—
337C22×D53C2×#4114yescomplemented
338C22×D53C2516yes—
339C22×D53C2512yes—
340Q8×C53—224no—
341Q8×C53C22×D4116yescomplemented
342D4×C53—248no—
343D4×C53—224no—
344D4×C53C22×D4148yescomplemented
345C2×C4×C53—22no—
346C2×C4×C53—26no—
347C2×C4×C53—224no—
348C2×C4×C53—28no—
349C2×C4×C53—224no—
350C2×C4×C53—224no—
351C2×C4×C53—224no—
352C2×C4×C53C22×D4112yes—
353C2×C4×C53C22×D414yes—
354C2×C4×C53C22×D4148yescomplemented
355C2×C4×C53C2512yes—
356C2×C4×C53C2516yes—
357C2×C4×C53C2516yes—
358C2×C4×C53C2512yes—
359C22⋊D53—248no—
360C22⋊D53—224no—
361C22⋊D53—224no—
362C22⋊D53—224no—
363C22⋊D53—424no—
364C22⋊D53C2×#41116yesdirect product factor
365C2×Dic53—26no—
366C2×Dic53—22no—
367C2×Dic53—224no—
368C2×Dic53—26no—
369C2×Dic53—22no—
370C2×Dic53—26no—
371C2×Dic53—224no—
372C2×Dic53—412no—
373C2×Dic53C2×#4114yescomplemented
374C2×Dic53C2516yes—
375C2×Dic53C2512yes—
376C2×Dic53C2512yes—
377C2×Dic53C2516yes—
378C2×Dic53C2516yes—
379C2×Dic53C2512yes—
380D212—224no—
381C4×D53—28no—
382C4×D53—224no—
383C4×D53—224no—
384C4×D53—224no—
385Dic106—224no—
386C2×D4×#41—531nomaximal, Sylow
387C22×C53—22no—
388C22×C53—26no—
389C22×C53—26no—
390C22×C53—22no—
391C22×C53—224no—
392C22×C53—28no—
393C22×C53—26no—
394C22×C53—26no—
395C22×C53—26no—
396C22×C53—448no—
397C22×C53—412no—
398C22×C53C23×D4112yes—
399C22×C53C23×D412yes—
400C22×C53C22×#4112yes—
401C22×C53C22×#4114yescomplemented
402C22×C53#58512yes—
403C22×C53C2611yescharacteristic
404C2×D53—22no—
405C2×D53—22no—
406C2×D53—28no—
407C2×D53—26no—
408C2×D53—26no—
409C2×D53—26no—
410C2×D53—448no—
411C2×D53—412no—
412C2×D53C22×#4114yescomplemented
413C4×C53—22no—
414C4×C53—26no—
415C4×C53C23×D4112yes—
416C4×C53C23×D414yes—
417Dic53—26no—
418Dic53—22no—
419Dic53—26no—
420Dic53—22no—
421Dic53—26no—
422Dic53C22×#4114yescomplemented
423C23×#41—531no—
424C23×#41D5311yescharacteristic, complemented
425D4×#41—5332no—
426C2×#550—531no—
427C2×D4×Q8—531no—
428C2×#548—531no—
429C2×#548—531no—
430C2×#547—533no—
431C2×#546—533no—
432C2×#546—533no—
433C2×D42—533no—
434C2×#532—533no—
435C2×#525—533no—
436C2×#525—533no—
437C2×C4×#41—531no—
438C22×C4×D4—533no—
439C2×C53—212no—
440C2×C53—24no—
441C2×C53—46no—
442C2×C53D4×#4114yescomplemented
443C2×C53C24×D411yescharacteristic
444C2×C53C23×#4111yescharacteristic
445C2×C53C2×#58511yescharacteristic
446D53—24no—
447D53—46no—
448C22×#41—216no—
449C22×#41—5316no—
450C22×#41—531no—
451C22×#41—533no—
452C22×#41—533no—
453C22×#41—10616no—
454C22×#41C2×D5311yescharacteristic
455C22×#41C2×D5313yescomplemented
456C22×#41C2×D5313yescomplemented
457C22×#41C2×D5311yescharacteristic, complemented
458C22×#41C2×D53116yescomplemented
459C23×Q8—531no—
460C23×Q8C2×D5311yescharacteristic, complemented
461C23×D4—533no—
462C23×D4—533no—
463C23×D4C2×D5313yescomplemented
464C24×C4—533no—
465C24×C4C2×D5313yescomplemented
466#550—5316no—
467D4×Q8—5316no—
468#548—5316no—
469#548—5316no—
470#547—5348no—
471#546—5348no—
472#546—5348no—
473D42—5348no—
474#532—5348no—
475C2×C4⋊Q8—533no—
476C2×#127—533no—
477C2×#124—533no—
478C2×#124—533no—
479#525—5348no—
480#525—5348no—
481C2×#123—536no—
482C2×#123—536no—
483C2×C22⋊Q8—533no—
484C2×C22⋊Q8—533no—
485C2×C22⋊Q8—533no—
486C2×C22⋊Q8—533no—
487C2×#121—533no—
488C2×#121—533no—
489C2×#121—536no—
490C2×#121—536no—
491C2×#121—533no—
492C2×#121—533no—
493C2×#120—536no—
494C2×#120—536no—
495C4×#41—5316no—
496C2×C4×Q8—531no—
497C2×C4×Q8—531no—
498C2×C4×D4—533no—
499C2×C4×D4—533no—
500C2×C4×D4—531no—
501C2×C4×D4—533no—
502C2×C4×D4—533no—
503C2×C4×D4—533no—
504C2×C4×D4—533no—
505C2×C4×D4—533no—
506C2×C4×D4—533no—
507C2×C4×D4—533no—
508C2×C4×D4—536no—
509C2×C4×D4—5348no—
510C2×#117—533no—
511C22×C4⋊C4—533no—
512C22×C22⋊C4—533no—
513C22×C22⋊C4—533no—
514C22×C42—533no—
515C53C2×D4×#4111yescharacteristic, complemented, Sylow
516C25—533no—
517C25C22×D5313yes—
518C2×#41—2128no—
519C2×#41—28no—
520C2×#41—224no—
521C2×#41—224no—
522C2×#41—538no—
523C2×#41—5324no—
524C2×#41—5324no—
525C2×#41—106128no—
526C2×#41—1068no—
527C2×#41—10624no—
528C2×#41—10624no—
529C2×#41C22⋊D53116yesdirect product factor
530C2×#41C22×D5318yes—
531C2×#41C22×D53124yescomplemented
532C2×#41C22×D53124yescomplemented
533C2×#41C22×D5318yescomplemented
534C22×Q8—28no—
535C22×Q8—538no—
536C22×Q8—533no—
537C22×Q8—1068no—
538C22×Q8C22×D5313yes—
539C22×Q8C22×D5311yescharacteristic
540C22×Q8C22×D5318yescomplemented
541C22×D4—224no—
542C22×D4—531no—
543C22×D4—533no—
544C22×D4—533no—
545C22×D4—533no—
546C22×D4—5324no—
547C22×D4—536no—
548C22×D4—536no—
549C22×D4—5324no—
550C22×D4—533no—
551C22×D4—10624no—
552C22×D4—10624no—
553C22×D4C22×D5316yes—
554C22×D4C22×D5313yes—
555C22×D4C22×D5313yes—
556C22×D4C22×D53124yescomplemented
557C23×C4—224no—
558C23×C4—533no—
559C23×C4—533no—
560C23×C4—533no—
561C23×C4—533no—
562C23×C4—533no—
563C23×C4—5324no—
564C23×C4—531no—
565C23×C4—533no—
566C23×C4—10624no—
567C23×C4C22×D5313yes—
568C23×C4C22×D5313yes—
569C23×C4C22×D5313yes—
570C23×C4C22×D5311yescharacteristic
571C23×C4C22×D5313yes—
572C23×C4C22×D5313yes—
573C23×C4C22×D53124yescomplemented
574C4⋊Q8—5324no—
575#127—5324no—
576#124—5324no—
577#124—5324no—
578#123—5348no—
579#123—5348no—
580C22⋊Q8—5324no—
581C22⋊Q8—5324no—
582C22⋊Q8—5324no—
583C22⋊Q8—5324no—
584#121—5324no—
585#121—5324no—
586#121—5348no—
587#121—5348no—
588#121—5324no—
589#121—5324no—
590#120—5348no—
591#120—5348no—
592C4×Q8—538no—
593C4×Q8—538no—
594C4×D4—5324no—
595C4×D4—5324no—
596C4×D4—538no—
597C4×D4—5324no—
598C4×D4—5324no—
599C4×D4—5324no—
600C4×D4—5324no—
601C4×D4—5324no—
602C4×D4—5324no—
603C4×D4—5324no—
604C4×D4—5348no—
605#117—5324no—
606C2×C4⋊C4—531no—
607C2×C4⋊C4—533no—
608C2×C4⋊C4—533no—
609C2×C4⋊C4—533no—
610C2×C4⋊C4—5324no—
611C2×C4⋊C4—533no—
612C2×C4⋊C4—533no—
613C2×C4⋊C4—536no—
614C2×C22⋊C4—531no—
615C2×C22⋊C4—533no—
616C2×C22⋊C4—533no—
617C2×C22⋊C4—533no—
618C2×C22⋊C4—5324no—
619C2×C22⋊C4—536no—
620C2×C22⋊C4—536no—
621C2×C22⋊C4—531no—
622C2×C22⋊C4—533no—
623C2×C22⋊C4—533no—
624C2×C22⋊C4—533no—
625C2×C22⋊C4—5324no—
626C2×C22⋊C4—536no—
627C2×C42—533no—
628C2×C42—533no—
629C2×C42—5324no—
630C2×C42—533no—
631C2×C42—531no—
632C24—212no—
633C24—212no—
634C24—46no—
635C24—531no—
636C24—533no—
637C24—5312no—
638C24—10612no—
639C24—10612no—
640C24—2126no—
641C24C23×D5313yes—
642C24C23×D53112yes—
643C24C23×D5313yes—
644C24C23×D5311yescharacteristic
645#41—232no—
646#41—296no—
647#41—296no—
648#41—10632no—
649#41—10696no—
650#41—10696no—
651#41C2×C22⋊D53164yesdirect product factor
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—5312no—
655C2×Q8—10632no—
656C2×Q8—10612no—
657C2×Q8C2×C22⋊D5318yescomplemented
658C2×Q8C23×D53112yes—
659C2×Q8C23×D5314yes—
660C2×D4—224no—
661C2×D4—296no—
662C2×D4—212no—
663C2×D4—538no—
664C2×D4—534no—
665C2×D4—5312no—
666C2×D4—5312no—
667C2×D4—5312no—
668C2×D4—5324no—
669C2×D4—5324no—
670C2×D4—5312no—
671C2×D4—10612no—
672C2×D4—10696no—
673C2×D4—10612no—
674C2×D4—10624no—
675C2×D4—10612no—
676C2×D4—10696no—
677C2×D4—10612no—
678C2×D4—21212no—
679C2×D4C2×C22⋊D53124yescomplemented
680C2×D4C23×D53124yes—
681C2×D4C23×D53112yes—
682C2×D4C23×D53112yes—
683C22×C4—212no—
684C22×C4—24no—
685C22×C4—212no—
686C22×C4—212no—
687C22×C4—212no—
688C22×C4—296no—
689C22×C4—531no—
690C22×C4—531no—
691C22×C4—533no—
692C22×C4—533no—
693C22×C4—5312no—
694C22×C4—531no—
695C22×C4—533no—
696C22×C4—5312no—
697C22×C4—5312no—
698C22×C4—534no—
699C22×C4—5312no—
700C22×C4—5312no—
701C22×C4—5312no—
702C22×C4—10612no—
703C22×C4—10612no—
704C22×C4—1064no—
705C22×C4—10612no—
706C22×C4—10612no—
707C22×C4—10612no—
708C22×C4—10696no—
709C22×C4—2126no—
710C22×C4C2×C22⋊D53124yescomplemented
711C22×C4C23×D5311yescharacteristic
712C22×C4C23×D5313yes—
713C22×C4C23×D53112yes—
714C22×C4C23×D5314yes—
715C22×C4C23×D53112yes—
716C22×C4C23×D53112yes—
717C22×C4C23×D53112yes—
718C22×C4C23×D5313yes—
719C22×C4C23×D53112yes—
720C22×C4C23×D5311yescharacteristic
721C4⋊C4—534no—
722C4⋊C4—5312no—
723C4⋊C4—5312no—
724C4⋊C4—5312no—
725C4⋊C4—5312no—
726C4⋊C4—5312no—
727C4⋊C4—5324no—
728C22⋊C4—534no—
729C22⋊C4—5312no—
730C22⋊C4—5312no—
731C22⋊C4—5312no—
732C22⋊C4—5324no—
733C22⋊C4—5324no—
734C22⋊C4—534no—
735C22⋊C4—5312no—
736C22⋊C4—5312no—
737C22⋊C4—5312no—
738C22⋊C4—5324no—
739C42—534no—
740C42—5312no—
741C42—5312no—
742C42—5312no—
743C23—22no—
744C23—26no—
745C23—26no—
746C23—22no—
747C23—224no—
748C23—26no—
749C23—26no—
750C23—224no—
751C23—26no—
752C23—412no—
753C23—448no—
754C23—534no—
755C23—532no—
756C23—536no—
757C23—10624no—
758C23—1062no—
759C23—1062no—
760C23—10624no—
761C23—1066no—
762C23—1066no—
763C23—1066no—
764C23—21212no—
765C23—21248no—
766C23C22×C22⋊D53112yes—
767C23#41×D5314yescomplemented
768C23C24×D5316yes—
769C23C24×D5316yes—
770C23C24×D5312yes—
771C23C24×D5311yescharacteristic
772Q8—224no—
773Q8—10624no—
774Q8C22×C22⋊D53116yescomplemented
775D4—248no—
776D4—224no—
777D4—5316no—
778D4—10624no—
779D4—10624no—
780D4—10648no—
781D4—10624no—
782D4—10624no—
783D4—21224no—
784D4C22×C22⋊D53148yescomplemented
785C2×C4—22no—
786C2×C4—26no—
787C2×C4—224no—
788C2×C4—28no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—224no—
792C2×C4—534no—
793C2×C4—532no—
794C2×C4—532no—
795C2×C4—536no—
796C2×C4—536no—
797C2×C4—532no—
798C2×C4—536no—
799C2×C4—10624no—
800C2×C4—1062no—
801C2×C4—1066no—
802C2×C4—10624no—
803C2×C4—1066no—
804C2×C4—1062no—
805C2×C4—1066no—
806C2×C4—1068no—
807C2×C4—10624no—
808C2×C4—10624no—
809C2×C4—10624no—
810C2×C4—21212no—
811C2×C4C22×C22⋊D5314yes—
812C2×C4C22×C22⋊D53112yes—
813C2×C4C22×C22⋊D53148yescomplemented
814C2×C4C24×D5312yes—
815C2×C4C24×D5316yes—
816C2×C4C24×D5312yes—
817C2×C4C24×D5316yes—
818C22—28no—
819C22—224no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—22no—
824C22—26no—
825C22—26no—
826C22—26no—
827C22—448no—
828C22—412no—
829C22—534no—
830C22—1068no—
831C22—1062no—
832C22—1062no—
833C22—1066no—
834C22—1066no—
835C22—1066no—
836C22—21248no—
837C22—21212no—
838C22C23×C22⋊D53112yes—
839C22C23×C22⋊D5312yes—
840C22C2×#41×D5312yes—
841C22C2×#41×D5314yescomplemented
842C22#1681145912yes—
843C22C25×D5311yescharacteristic
844C4—22no—
845C4—26no—
846C4—534no—
847C4—1062no—
848C4—1066no—
849C4—1066no—
850C4—1062no—
851C4—1066no—
852C4C23×C22⋊D5314yes—
853C4C23×C22⋊D53112yes—
854C2—24no—
855C2—212no—
856C2—46no—
857C2—1064no—
858C2—2126no—
859C2#41×C22⋊D5314yesdirect product factor
860C2C24×C22⋊D5311yescharacteristic
861C2C22×#41×D5311yescharacteristic
862C2C2×#1681145911yescharacteristic
subgroupG/H
centerC22×C4C23×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC23×#41×C53C2
socleC23×C53C25
hypercenterC23×#41D53
hypocenterC53C2×D4×#41
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C22×#41×D53C2semidirect
2. #41×C22⋊D53C2direct (N × H)
3. C2×#16811292C2semidirect
4. C2×Q8×C22⋊D53C2semidirect
5. C2×#16811284C2semidirect
6. C2×#16811280C2semidirect
7. C2×#16811272C2semidirect
8. C2×#16811267C2semidirect
9. C2×#16811261C2semidirect
10. C2×D4×C22⋊D53C2semidirect
11. C2×#16811169C2semidirect
12. C2×#16811134C2semidirect
13. C2×#16811130C2semidirect
14. C2×#41×Dic53C2semidirect
15. C22×C4×C22⋊D53C2semidirect
16. C23×#41×C53C2semidirect
17. C22×#11719949C22semidirect
18. C22×#11719945C22semidirect
19. C22×#11719947C22semidirect
21. C2×#41×D53C22semidirect
22. C22×Q8×D53C22semidirect
24. C22×D4×D53C22semidirect
25. C23×C4×D53C22semidirect
26. #16811292C22semidirect
27. Q8×C22⋊D53C22semidirect
28. #16811284C22semidirect
29. #16811280C22semidirect
30. #16811272C22semidirect
31. #16811267C22semidirect
32. #16811261C22semidirect
33. D4×C22⋊D53C22semidirect
34. #16811169C22semidirect
35. C2×#13133215C22semidirect
36. C2×#13133213C22semidirect
37. C2×#13133206C22semidirect
38. C2×#13133204C22semidirect
39. #16811134C22semidirect
40. #16811130C22semidirect
41. C2×#13133200C22semidirect
42. C2×#13133198C22semidirect
43. C2×#13133196C22semidirect
44. C2×#13133196C22semidirect
45. C2×#13133193C22semidirect
46. C2×#13133193C22semidirect
47. C2×#13133191C22semidirect
48. C2×#13133191C22semidirect
49. C2×#13133189C22semidirect
50. C2×#13133189C22semidirect
51. C2×#13133188C22semidirect
52. C2×#13133188C22semidirect
53. C2×#13133186C22semidirect
54. C2×#13133185C22semidirect
55. #41×Dic53C22semidirect
56. C2×Q8×Dic53C22semidirect
57. C2×Q8×Dic53C22semidirect
58. C2×D4×Dic53C22semidirect
59. C2×D4×Dic53C22semidirect
62. C2×C4×C22⋊D53C22semidirect
63. C2×C4×C22⋊D53C22semidirect
64. C2×C4×C22⋊D53C22semidirect
65. C2×C4×C22⋊D53C22semidirect
66. C2×C4×C22⋊D53C22semidirect
67. C2×C4×C22⋊D53C22semidirect
68. C2×C4×C22⋊D53C22semidirect
69. C2×C4×C22⋊D53C22semidirect
70. C2×#13133176C22semidirect
71. C22×#11719919C22semidirect
72. C22×C22⋊Dic53C22semidirect
73. C22×#11719921C22semidirect
74. C22×C4×Dic53C22semidirect
77. C22×#41×C53C22semidirect
78. C22×#41×C53C22semidirect
79. C22×#41×C53C22semidirect
80. C22×#41×C53C22semidirect
81. C23×Q8×C53C22semidirect
82. C23×D4×C53C22semidirect
83. C24×C4×C53C22semidirect
86. C2×#11719949C23semidirect
88. C2×#11719945C23semidirect
90. C2×#11719947C23semidirect
94. C2×Q8×D53C23semidirect
105. C2×D4×D53C23semidirect
114. C22×C4×D53C23semidirect
115. #13133215C23semidirect
116. #13133213C23semidirect
117. #13133206C23semidirect
118. #13133204C23semidirect
119. #13133200C23semidirect
120. #13133198C23semidirect
121. #13133196C23semidirect
122. #13133196C23semidirect
123. #13133193C23semidirect
124. #13133193C23semidirect
125. #13133191C23semidirect
126. #13133191C23semidirect
127. #13133189C23semidirect
128. #13133189C23semidirect
129. #13133188C23semidirect
130. #13133188C23semidirect
131. #13133186C23semidirect
132. #13133185C23semidirect
133. Q8×Dic53C23semidirect
134. Q8×Dic53C23semidirect
135. D4×Dic53C23semidirect
136. D4×Dic53C23semidirect
139. C4×C22⋊D53C23semidirect
140. C4×C22⋊D53C23semidirect
141. C4×C22⋊D53C23semidirect
142. C4×C22⋊D53C23semidirect
143. C4×C22⋊D53C23semidirect
144. C4×C22⋊D53C23semidirect
145. C4×C22⋊D53C23semidirect
146. #13133176C23semidirect
154. C2×#11719919C23semidirect
161. C2×C22⋊Dic53C23semidirect
167. C2×#11719921C23semidirect
172. C2×C4×Dic53C23semidirect
178. C2×#41×C53D4semidirect
180. C2×#41×C53C23semidirect
181. C2×#41×C53C23semidirect
182. C2×#41×C53C23semidirect
186. C22×Q8×C53C23semidirect
191. C22×D4×C53C23semidirect
199. C23×C4×C53C23semidirect
216. #41×C53C2×D4semidirect
219. C2×Q8×C53C2×D4semidirect
225. C2×D4×C53C2×D4semidirect
235. C22×C4×C53C2×D4semidirect
252. C2×C22⋊D53#41direct (N × H)
323. C23×C53C2×#41semidirect
337. C22×D53C2×#41semidirect
341. Q8×C53C22×D4semidirect
344. D4×C53C22×D4semidirect
354. C2×C4×C53C22×D4semidirect
364. C22⋊D53C2×#41direct (N × H)
373. C2×Dic53C2×#41semidirect
401. C22×C53C22×#41semidirect
412. C2×D53C22×#41semidirect
422. Dic53C22×#41semidirect
424. C23×#41D53semidirect
442. C2×C53D4×#41semidirect
455. C22×#41C2×D53semidirect
456. C22×#41C2×D53semidirect
457. C22×#41C2×D53semidirect
458. C22×#41C2×D53semidirect
460. C23×Q8C2×D53semidirect
463. C23×D4C2×D53semidirect
465. C24×C4C2×D53semidirect
515. C53C2×D4×#41semidirect
529. C2×#41C22⋊D53direct (N × H)
531. C2×#41C22×D53semidirect
532. C2×#41C22×D53semidirect
533. C2×#41C22×D53semidirect
540. C22×Q8C22×D53semidirect
556. C22×D4C22×D53semidirect
573. C23×C4C22×D53semidirect
651. #41C2×C22⋊D53direct (N × H)
657. C2×Q8C2×C22⋊D53semidirect
679. C2×D4C2×C22⋊D53semidirect
710. C22×C4C2×C22⋊D53semidirect
767. C23#41×D53semidirect
774. Q8C22×C22⋊D53semidirect
784. D4C22×C22⋊D53semidirect
813. C2×C4C22×C22⋊D53semidirect
841. C22C2×#41×D53semidirect
859. C2#41×C22⋊D53direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D532
#41×C22⋊D532
C2×#168112922
C2×Q8×C22⋊D532
C2×#168112842
C2×#168112802
C2×#168112722
C2×#168112672
C2×#168112612
C2×D4×C22⋊D532
C2×#168111692
C2×#168111342
C2×#168111302
C2×#41×Dic532
C22×C4×C22⋊D532
C23×#41×C532
C2×D4×#4153