Finite Group Databasebeta

← C2×#20288506 #28292560

Subgroups — C2×#20288506 #28292560

Order 13568.

11534 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
1C22×#13133265C211yesmaximal, characteristic, complemented
2C22×#13133263C211yesmaximal, characteristic, complemented
3#20288506C2132yesmaximal, direct product factor
4C2×#16811285C211yesmaximal, characteristic, complemented
5C2×#16811284C211yesmaximal, characteristic, complemented
6C2×#16811280C211yesmaximal, characteristic, complemented
7C2×#16811270C213yesmaximal, complemented
8C2×#16811269C213yesmaximal, complemented
9C2×#16811266C213yesmaximal, complemented
10C2×#16811264C213yesmaximal, complemented
11C2×#16811196C213yesmaximal, complemented
12C2×#16811189C213yesmaximal, complemented
13C2×#16811170C213yesmaximal, complemented
14C2×#124×D53C213yesmaximal, complemented
15C2×C4×#11719949C211yesmaximal, characteristic, complemented
16C2×C53×#548C211yesmaximal, characteristic, complemented
17C2×#13133265—216no—
18C2×#13133265C22116yescomplemented
19C2×#13133263—216no—
20C2×#13133263C22116yescomplemented
21C22×#11719949C2211yescharacteristic
22C22×#11719949C2211yescharacteristic
23C22×#11719949C2213yescomplemented
24C22×#11719945C2213yes—
25C22×#11719945C2213yescomplemented
26C22×#11719945C2213yescomplemented
27C22×Q8×D53C2213yescomplemented
28C22×Q8×D53C2211yescharacteristic, complemented
29C23×D212C2213yes—
30C22×D4×D53C2213yes—
31C22×D4×D53C2213yes—
32#16811285C22116yescomplemented
33#16811284C22116yescomplemented
34#16811280C22116yescomplemented
35#16811270C22148yescomplemented
36#16811269C22148yescomplemented
37#16811266C22148yescomplemented
38#16811264C22148yescomplemented
39#16811196C22148yescomplemented
40#16811189C22148yescomplemented
41#16811170C22148yescomplemented
42C2×#13133216C2213yescomplemented
43C2×#13133213C2213yescomplemented
44C2×#13133206C2213yescomplemented
45C2×#13133205C2213yescomplemented
46C2×#13133204C2213yescomplemented
47C2×#13133203C2216yescomplemented
48C2×#13133203C2213yescomplemented
49C2×#13133203C2211yescharacteristic, complemented
50#124×D53C22148yescomplemented
51C2×#13133202C2216yescomplemented
52C2×#13133199C2216yescomplemented
53C2×#13133197C2213yescomplemented
54C2×#13133196C2213yescomplemented
55C2×#13133193C2213yescomplemented
56C2×#13133192C2213yescomplemented
57C2×#13133192C2213yescomplemented
58C2×#13133191C2213yescomplemented
59C2×#13133190C2213yescomplemented
60C2×#13133190C2213yescomplemented
61C2×#13133188C2213yescomplemented
62C2×#13133188C2213yescomplemented
63C2×#13133187C2216yescomplemented
64C2×#13133185C2216yescomplemented
65C4×#11719949C22116yescomplemented
66C2×Q8×Dic53C2211yescharacteristic, complemented
67C2×C4×D212C2213yescomplemented
68C2×C4×D212C2213yescomplemented
69C2×#13133179C2213yescomplemented
70C2×C4×C22⋊D53C2213yescomplemented
71C2×C4×C22⋊D53C2213yescomplemented
72C2×#13133175C2213yescomplemented
73C2×C22⋊C4×D53C2216yescomplemented
74C2×C22⋊C4×D53C2216yescomplemented
75C2×C42×D53C2213yescomplemented
76C22×#41×C53C2211yescharacteristic
77C23×Q8×C53C2211yescharacteristic, complemented
78C53×#548C22116yescomplemented
79C2×#124×C53C2213yescomplemented
80C2×C22⋊Q8×C53C2213yescomplemented
81C2×#121×C53C2213yescomplemented
82C2×C4×Q8×C53C2211yescharacteristic, complemented
83C2×C4×D4×C53C2213yescomplemented
84C24×D53C2316yes—
85#13133265—2128no—
86#13133263—2128no—
87C2×#11719949—28no—
88C2×#11719949—224no—
89C2×#11719949D4116yescomplemented
90C2×#11719949C2318yes—
91C2×#11719949C2318yes—
92C2×#11719949C23124yescomplemented
93C2×#11719945—224no—
94C2×#11719945—224no—
95C2×#11719945—224no—
96C2×#11719945C23124yes—
97C2×#11719945C23124yescomplemented
98C2×#11719945C23124yescomplemented
99C22×Dic106C2313yes—
100C22×Dic106C2313yes—
101C22×Dic106C2311yescharacteristic
102C2×Q8×D53—28no—
103C2×Q8×D53—224no—
104C2×Q8×D53C2318yescomplemented
105C2×Q8×D53C23124yescomplemented
106C22×D212—224no—
107C22×D212C23124yes—
108C22×D212C2313yes—
109C22×D212C2313yes—
110C22×D212C2313yes—
111C22×D212C2313yes—
112C22×D212C2313yes—
113C22×C22⋊D53C2313yes—
114C22×C22⋊D53C2313yes—
115C22×C22⋊D53C2313yes—
116C22×C22⋊D53C2311yescharacteristic
117C22×C22⋊D53C2313yes—
118C22×C22⋊D53C2313yes—
119C2×D4×D53—224no—
120C2×D4×D53—224no—
121C2×D4×D53C23124yes—
122C2×D4×D53C23124yes—
123C22×C4×D53C2316yes—
124C22×C4×D53C2313yes—
125C22×C4×D53C2313yes—
126C22×C4×D53C2313yes—
127C22×C4×D53C2313yes—
128C22×C4×D53C2313yes—
129#13133216C23124yescomplemented
130#13133213C23124yescomplemented
131#13133206C23124yescomplemented
132#13133205C23124yescomplemented
133#13133204C23124yescomplemented
134#13133203C23124yescomplemented
135#13133203C23148yescomplemented
136#13133203C2318yescomplemented
137#13133202C23148yescomplemented
138#13133199C23148yescomplemented
139#13133197C23124yescomplemented
140#13133196C23124yescomplemented
141#13133193C23124yescomplemented
142#13133192C23124yescomplemented
143#13133192C23124yescomplemented
144#13133191C23124yescomplemented
145#13133190C23124yescomplemented
146#13133190C23124yescomplemented
147#13133188C23124yescomplemented
148#13133188C23124yescomplemented
149#13133187C23148yescomplemented
150#13133185C23148yescomplemented
151Q8×Dic53C2318yescomplemented
152C4×D212C23124yescomplemented
153C4×D212C23124yescomplemented
154#13133179C23124yescomplemented
155C4×C22⋊D53C23124yescomplemented
156C4×C22⋊D53C23124yescomplemented
157#13133175C23124yescomplemented
158C2×C4⋊Dic53C2313yes—
159C2×C4⋊Dic53C2313yes—
160C2×#11719919C2313yes—
161C2×#11719919C2313yes—
162C2×C22⋊Dic53C2313yes—
163C2×C22⋊Dic53C2316yes—
164C2×C22⋊Dic53C2311yescharacteristic
165C2×#11719921C2313yes—
166C2×#11719921C2313yes—
167C2×#11719921C2316yes—
168C2×#11719921C2316yes—
169C2×#11719921C2316yes—
170C2×#11719921C2311yescharacteristic
171C2×#11719921C2311yescharacteristic
172C22⋊C4×D53C23148yescomplemented
173C22⋊C4×D53C23148yescomplemented
174C2×C4×Dic53C2311yescharacteristic
175C2×C4×Dic53C2313yes—
176C2×C4×Dic53C2313yes—
177C42×D53C23124yescomplemented
178C2×#41×C53—28no—
179C2×#41×C53C2318yes—
180C22×Q8×C53—28no—
181C22×Q8×C53C2313yes—
182C22×Q8×C53C2311yescharacteristic
183C22×Q8×C53C2318yescomplemented
184C22×D4×C53C2313yes—
185C22×D4×C53C2313yes—
186C23×C4×C53C2313yes—
187C23×C4×C53C2313yes—
188#124×C53C23124yescomplemented
189C22⋊Q8×C53C23124yescomplemented
190#121×C53C23124yescomplemented
191C4×Q8×C53C2318yescomplemented
192C4×D4×C53C23124yescomplemented
193C2×C4⋊C4×C53C2313yes—
194C2×C4⋊C4×C53C2313yes—
195C2×C22⋊C4×C53C2311yescharacteristic
196C2×C22⋊C4×C53C2313yes—
197C2×C22⋊C4×C53C2316yes—
198C2×C42×C53C2313yes—
199C24×C53C2413yes—
200C24×C53C2411yescharacteristic
201C23×D53—224no—
202C23×D53—412no—
203C23×D53—412no—
204C23×D53C2413yes—
205C23×D53C2411yescharacteristic
206C23×D53C2413yes—
207C23×D53C24124yes—
208#41×C53—232no—
209C2×Q8×C53—232no—
210C2×Q8×C53—212no—
211C2×Q8×C53C2×D418yes—
212C2×Q8×C53C24112yes—
213C2×Q8×C53C2414yes—
214C2×D4×C53—212no—
215C2×D4×C53—46no—
216C2×D4×C53C24112yes—
217C2×D4×C53C24112yes—
218C22×C4×C53—212no—
219C22×C4×C53—212no—
220C22×C4×C53C2411yescharacteristic
221C22×C4×C53C2413yes—
222C22×C4×C53C2413yes—
223C22×C4×C53C2411yescharacteristic
224C22×C4×C53C24112yes—
225C22×C4×C53C24112yes—
226C22×C4×C53C2413yes—
227C2×C22⋊D53—212no—
228C2×C22⋊D53—212no—
229C2×C22⋊D53—212no—
230C2×C22⋊D53—24no—
231C2×C22⋊D53—46no—
232C2×C22⋊D53—46no—
233C2×C22⋊D53C24112yes—
234C2×C22⋊D53C24112yes—
235C2×C22⋊D53C24112yes—
236C2×C22⋊D53C2414yes—
237C2×C22⋊D53C24112yes—
238C2×C22⋊D53C24112yes—
239C22×Dic53C2411yescharacteristic
240C22×Dic53C2413yes—
241C22×Dic53C2413yes—
242C22×Dic53C2411yescharacteristic
243C22×Dic53C2411yescharacteristic
244#11719949—232no—
245#11719949—296no—
246#11719949C2×D4164yescomplemented
247Q8×D53—232no—
248Q8×D53—296no—
249D4×D53—296no—
250D4×D53—296no—
251#11719945—296no—
252#11719945—296no—
253#11719945—296no—
254C2×D212—212no—
255C2×D212—212no—
256C2×D212—212no—
257C2×D212—296no—
258C2×D212—46no—
259C2×D212C2×D4124yes—
260C2×D212C24112yes—
261C2×D212C24112yes—
262C2×D212C24112yes—
263C2×D212C24112yes—
264C2×D212C24112yes—
265C2×C4×D53—224no—
266C2×C4×D53—212no—
267C2×C4×D53—212no—
268C2×C4×D53—46no—
269C2×C4×D53—46no—
270C2×C4×D53C2×D4124yes—
271C2×C4×D53C24124yes—
272C2×C4×D53C24112yes—
273C2×C4×D53C24112yes—
274C2×C4×D53C24112yes—
275C2×C4×D53C24112yes—
276C2×C4×D53C24112yes—
277C2×Dic106—212no—
278C2×Dic106—212no—
279C2×Dic106—24no—
280C2×Dic106C24112yes—
281C2×Dic106C24112yes—
282C2×Dic106C2414yes—
283C4⋊C4×C53C24112yes—
284C4⋊C4×C53C24112yes—
285C22⋊C4×C53C2414yes—
286C22⋊C4×C53C24112yes—
287C22⋊C4×C53C24124yes—
288C42×C53C24112yes—
289C22⋊Dic53C24112yes—
290C22⋊Dic53C24124yes—
291C22⋊Dic53C2414yes—
292#11719921C24112yes—
293#11719921C24112yes—
294#11719921C24124yes—
295#11719921C24124yes—
296#11719921C24124yes—
297#11719921C2414yes—
298#11719921C2414yes—
299C4⋊Dic53C24112yes—
300C4⋊Dic53C24112yes—
301#11719919C24112yes—
302#11719919C24112yes—
303C4×Dic53C2414yes—
304C4×Dic53C24112yes—
305C4×Dic53C24112yes—
306C23×C53—22no—
307C23×C53—26no—
308C23×C53—22no—
309C23×C53—26no—
310C23×C53—22no—
311C23×C53—26no—
312C23×C53C2512yes—
313C23×C53C2516yes—
314C23×C53C2511yescharacteristic
315C22×D53—26no—
316C22×D53—26no—
317C22×D53—22no—
318C22×D53—26no—
319C22×D53—22no—
320C22×D53—26no—
321C22×D53—22no—
322C22×D53—26no—
323C22×D53—248no—
324C22×D53—424no—
325C22×D53—424no—
326C22×D53—848no—
327C22×D53C22×D4112yes—
328C22×D53C2512yes—
329C22×D53C2516yes—
330C22×D53C2516yes—
331Q8×C53—224no—
332Q8×C53C22×D4116yes—
333D4×C53—224no—
334D4×C53—412no—
335C2×C4×C53—26no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—26no—
339C2×C4×C53—224no—
340C2×C4×C53—224no—
341C2×C4×C53C22×D4112yes—
342C2×C4×C53C2516yes—
343C2×C4×C53C2512yes—
344C2×C4×C53C2512yes—
345C2×C4×C53C2516yes—
346C2×C4×C53C2516yes—
347C22⋊D53—224no—
348C22⋊D53—224no—
349C22⋊D53—28no—
350C22⋊D53—224no—
351C22⋊D53—412no—
352C22⋊D53—412no—
353C2×Dic53—26no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—26no—
357C2×Dic53C22×D414yes—
358C2×Dic53C2516yes—
359C2×Dic53C2512yes—
360C2×Dic53C2512yes—
361C2×Dic53C2516yes—
362C2×Dic53C2512yes—
363D212—224no—
364D212—224no—
365D212—224no—
366D212—412no—
367D212C22×D4148yes—
368C4×D53—248no—
369C4×D53—224no—
370C4×D53—224no—
371C4×D53—412no—
372C4×D53—412no—
373C4×D53C22×D4148yes—
374Dic106—224no—
375Dic106—28no—
376Dic106—224no—
377C2×#3500—531nomaximal, Sylow
378C22×C53—22no—
379C22×C53—26no—
380C22×C53—22no—
381C22×C53—26no—
382C22×C53—22no—
383C22×C53—26no—
384C22×C53—412no—
385C22×C53—44no—
386C22×C53C23×D412yes—
387C22×C53#58512yes—
388C22×C53#58512yes—
389C22×C53C2611yescharacteristic
390C2×D53—26no—
391C2×D53—26no—
392C2×D53—224no—
393C2×D53—22no—
394C2×D53—26no—
395C2×D53—22no—
396C2×D53—26no—
397C2×D53—22no—
398C2×D53—26no—
399C2×D53—44no—
400C2×D53—412no—
401C2×D53—848no—
402C2×D53C23×D4112yes—
403C4×C53—26no—
404C4×C53—22no—
405C4×C53—22no—
406C4×C53—26no—
407C4×C53C23×D4112yes—
408Dic53—26no—
409Dic53—22no—
410Dic53—22no—
411Dic53—26no—
412Dic53C23×D414yes—
413C22×2−1+4—531no—
414C22×H(5,𝔽2)—531no—
415#3500—5332no—
416C2×#548—531no—
417C2×#548—531no—
418C2×#548—531no—
419C2×#548D5311yescharacteristic, complemented
420C2×#546—533no—
421C2×#546—533no—
422C2×#546—533no—
423C2×#546—533no—
424C2×#536—533no—
425C2×#535—533no—
426C2×#532—533no—
427C22×#124—533no—
428C2×C4×#41—531no—
429C2×C53—46no—
430C2×C53—42no—
431C2×C53#350014yescomplemented
432C2×C53C24×D411yescharacteristic
433C2×C53C2×#58511yescharacteristic
434C2×C53C2×#58511yescharacteristic
435D53—212no—
436D53—42no—
437D53—46no—
438C2×2−1+4—5316no—
439C2×2−1+4—10616no—
440C2×H(5,𝔽2)—5316no—
441C2×H(5,𝔽2)—10616no—
442C22×#41—531no—
443C22×#41—531no—
444C22×#41—533no—
445C22×#41—533no—
446C22×#41—533no—
447C22×#41—533no—
448C22×#41C2×D5311yescharacteristic
449C23×Q8—533no—
450C23×Q8—531no—
451C23×Q8C2×D5311yescharacteristic, complemented
452C23×D4—533no—
453C23×D4—533no—
454C23×D4—533no—
455#548—5316no—
456#548—5316no—
457#548—5316no—
458#548C2×D53116yescomplemented
459#546—5348no—
460#546—5348no—
461#546—5348no—
462#546—5348no—
463#536—5348no—
464#535—5348no—
465#532—5348no—
466C2×C4⋊Q8—533no—
467C2×#127—533no—
468C2×#124—533no—
469C2×#124—533no—
470C2×#124—5348no—
471C2×#124—533no—
472C2×#124—536no—
473C2×#124—531no—
474C2×#124—533no—
475C2×#124C2×D5313yescomplemented
476C2×#123—536no—
477C2×#123—536no—
478C2×C22⋊Q8—533no—
479C2×C22⋊Q8—533no—
480C2×C22⋊Q8—533no—
481C2×C22⋊Q8C2×D5313yescomplemented
482C2×#121—533no—
483C2×#121—533no—
484C2×#121—533no—
485C2×#121—533no—
486C2×#121—533no—
487C2×#121—533no—
488C2×#121—533no—
489C2×#121C2×D5313yescomplemented
490C2×#120—536no—
491C2×#120—536no—
492C4×#41—5316no—
493C2×C4×Q8—531no—
494C2×C4×Q8C2×D5311yescharacteristic, complemented
495C2×C4×D4—533no—
496C2×C4×D4—533no—
497C2×C4×D4—533no—
498C2×C4×D4—533no—
499C2×C4×D4—533no—
500C2×C4×D4C2×D5313yescomplemented
501C2×#117—533no—
502C22×C22⋊C4—536no—
503C22×C22⋊C4—536no—
504C22×C42—533no—
505C53C2×#350011yescharacteristic, complemented, Sylow
506C25—536no—
5072−1+4—106128no—
508H(5,𝔽2)—106128no—
509C2×#41—28no—
510C2×#41—5316no—
511C2×#41—538no—
512C2×#41—5324no—
513C2×#41—538no—
514C2×#41—5324no—
515C2×#41—5324no—
516C2×#41—5324no—
517C2×#41—10624no—
518C2×#41—10624no—
519C2×#41—10624no—
520C2×#41—10624no—
521C2×#41—1068no—
522C2×#41C22×D5318yes—
523C22×Q8—28no—
524C22×Q8—5324no—
525C22×Q8—538no—
526C22×Q8—533no—
527C22×Q8—533no—
528C22×Q8—531no—
529C22×Q8—10624no—
530C22×Q8—1068no—
531C22×Q8C22×D5313yes—
532C22×Q8C22×D5311yescharacteristic
533C22×Q8C22×D5318yescomplemented
534C22×D4—533no—
535C22×D4—533no—
536C22×D4—533no—
537C22×D4—531no—
538C22×D4—533no—
539C22×D4—533no—
540C22×D4—5324no—
541C22×D4—5324no—
542C22×D4—533no—
543C22×D4—533no—
544C22×D4—533no—
545C22×D4—533no—
546C22×D4—5324no—
547C22×D4—533no—
548C22×D4—10624no—
549C22×D4—10624no—
550C22×D4—10624no—
551C22×D4C22×D5313yes—
552C22×D4C22×D5313yes—
553C23×C4—533no—
554C23×C4—536no—
555C23×C4—533no—
556C23×C4—533no—
557C23×C4—533no—
558C23×C4—533no—
559C23×C4C22×D5313yes—
560C23×C4C22×D5313yes—
561C4⋊Q8—5324no—
562#127—5324no—
563#124—5324no—
564#124—5324no—
565#124—5324no—
566#124—5348no—
567#124—538no—
568#124—5324no—
569#124C22×D53124yescomplemented
570#123—5348no—
571#123—5348no—
572C22⋊Q8—5324no—
573C22⋊Q8—5324no—
574C22⋊Q8—5324no—
575C22⋊Q8C22×D53124yescomplemented
576#121—5324no—
577#121—5324no—
578#121—5324no—
579#121—5324no—
580#121—5324no—
581#121—5324no—
582#121—5324no—
583#121C22×D53124yescomplemented
584#120—5348no—
585#120—5348no—
586C4×Q8—538no—
587C4×Q8C22×D5318yescomplemented
588C4×D4—5324no—
589C4×D4—5324no—
590C4×D4—5324no—
591C4×D4—5324no—
592C4×D4—5324no—
593C4×D4C22×D53124yescomplemented
594#117—5324no—
595C2×C4⋊C4—533no—
596C2×C4⋊C4—533no—
597C2×C4⋊C4—533no—
598C2×C4⋊C4—533no—
599C2×C4⋊C4C22×D5313yes—
600C2×C4⋊C4C22×D5313yes—
601C2×C22⋊C4—533no—
602C2×C22⋊C4—536no—
603C2×C22⋊C4—531no—
604C2×C22⋊C4—533no—
605C2×C22⋊C4—533no—
606C2×C22⋊C4—536no—
607C2×C22⋊C4—536no—
608C2×C22⋊C4—536no—
609C2×C22⋊C4—531no—
610C2×C22⋊C4—531no—
611C2×C22⋊C4—5348no—
612C2×C22⋊C4—5348no—
613C2×C22⋊C4C22×D5313yes—
614C2×C22⋊C4C22×D5316yes—
615C2×C22⋊C4C22×D5311yescharacteristic
616C2×C42—533no—
617C2×C42—533no—
618C2×C42—531no—
619C2×C42—5324no—
620C2×C42C22×D5313yes—
621C24—533no—
622C24—533no—
623C24—531no—
624C24—5324no—
625C24—10624no—
626C24—21212no—
627C24—21212no—
628C24C23×D5313yes—
629C24C23×D5311yescharacteristic
630#41—232no—
631#41—5364no—
632#41—10696no—
633#41—10696no—
634#41—10696no—
635#41—10696no—
636#41—10632no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—5312no—
640C2×Q8—5312no—
641C2×Q8—534no—
642C2×Q8—10612no—
643C2×Q8—1064no—
644C2×Q8—10696no—
645C2×Q8—10632no—
646C2×Q8—10612no—
647C2×Q8D4×D5318yes—
648C2×Q8C23×D53112yes—
649C2×Q8C23×D5314yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—5312no—
653C2×D4—5312no—
654C2×D4—5312no—
655C2×D4—534no—
656C2×D4—5312no—
657C2×D4—5312no—
658C2×D4—5324no—
659C2×D4—5312no—
660C2×D4—5312no—
661C2×D4—5312no—
662C2×D4—5312no—
663C2×D4—5312no—
664C2×D4—10696no—
665C2×D4—10612no—
666C2×D4—10612no—
667C2×D4—10696no—
668C2×D4—10612no—
669C2×D4—1064no—
670C2×D4—10696no—
671C2×D4—10612no—
672C2×D4—10612no—
673C2×D4—10612no—
674C2×D4—2126no—
675C2×D4—2126no—
676C2×D4—2126no—
677C2×D4C23×D53112yes—
678C2×D4C23×D53112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—531no—
682C22×C4—5324no—
683C22×C4—5312no—
684C22×C4—531no—
685C22×C4—533no—
686C22×C4—533no—
687C22×C4—531no—
688C22×C4—5324no—
689C22×C4—5312no—
690C22×C4—5312no—
691C22×C4—5312no—
692C22×C4—5312no—
693C22×C4—10624no—
694C22×C4—10612no—
695C22×C4—10612no—
696C22×C4—2126no—
697C22×C4—2126no—
698C22×C4C23×D53112yes—
699C22×C4C23×D53112yes—
700C22×C4C23×D5311yescharacteristic
701C22×C4C23×D5313yes—
702C22×C4C23×D5313yes—
703C22×C4C23×D5311yescharacteristic
704C22×C4C23×D5313yes—
705C4⋊C4—5312no—
706C4⋊C4—5312no—
707C4⋊C4—5312no—
708C4⋊C4—5312no—
709C4⋊C4C23×D53112yes—
710C4⋊C4C23×D53112yes—
711C22⋊C4—5312no—
712C22⋊C4—5324no—
713C22⋊C4—534no—
714C22⋊C4—5312no—
715C22⋊C4—5312no—
716C22⋊C4—5324no—
717C22⋊C4—5324no—
718C22⋊C4—5324no—
719C22⋊C4—534no—
720C22⋊C4—534no—
721C22⋊C4C23×D53112yes—
722C22⋊C4C23×D53124yes—
723C22⋊C4C23×D5314yes—
724C42—534no—
725C42—5312no—
726C42—5312no—
727C42C23×D53112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—5312no—
735C23—536no—
736C23—536no—
737C23—532no—
738C23—10648no—
739C23—1066no—
740C23—1066no—
741C23—1062no—
742C23—1066no—
743C23—1062no—
744C23—1066no—
745C23—1062no—
746C23—1066no—
747C23—42448no—
748C23—21224no—
749C23—21224no—
750C23C24×D5316yes—
751C23C24×D5312yes—
752C23C24×D5311yescharacteristic
753Q8—224no—
754Q8—10624no—
755Q8—1068no—
756Q8—10624no—
757Q8C2×D4×D53116yes—
758D4—224no—
759D4—412no—
760D4—5348no—
761D4—10624no—
762D4—10624no—
763D4—10624no—
764D4—1068no—
765D4—10624no—
766D4—10624no—
767D4—10624no—
768D4—21212no—
769D4—21212no—
770D4—21212no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—534no—
778C2×C4—532no—
779C2×C4—5348no—
780C2×C4—532no—
781C2×C4—536no—
782C2×C4—536no—
783C2×C4—532no—
784C2×C4—10648no—
785C2×C4—1062no—
786C2×C4—1066no—
787C2×C4—1062no—
788C2×C4—1066no—
789C2×C4—10624no—
790C2×C4—10624no—
791C2×C4—21212no—
792C2×C4—21212no—
793C2×C4C2×D4×D53112yes—
794C2×C4C24×D5312yes—
795C2×C4C24×D5316yes—
796C2×C4C24×D5316yes—
797C2×C4C24×D5312yes—
798C2×C4C24×D5316yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—5312no—
808C22—1066no—
809C22—1066no—
810C22—10624no—
811C22—1062no—
812C22—1066no—
813C22—1062no—
814C22—1066no—
815C22—1062no—
816C22—1066no—
817C22—42448no—
818C22—21212no—
819C22—2124no—
820C22C22×D4×D5312yes—
821C22#1681145912yes—
822C22#1681146012yes—
823C22C25×D5311yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—534no—
829C4—1062no—
830C4—1066no—
831C4—1062no—
832C4—1066no—
833C4C22×D4×D53112yes—
834C2—46no—
835C2—42no—
836C2—10612no—
837C2—2126no—
838C2—2122no—
839C2#2028850614yesdirect product factor
840C2C23×D4×D5311yescharacteristic
841C2C2×#1681145911yescharacteristic
842C2C2×#1681146011yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#548C2
socleC23×C53C25
hypercenterC2×#548D53
hypocenterC53C2×#3500
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13133265C2semidirect
2. C22×#13133263C2semidirect
3. #20288506C2direct (N × H)
4. C2×#16811285C2semidirect
5. C2×#16811284C2semidirect
6. C2×#16811280C2semidirect
7. C2×#16811270C2semidirect
8. C2×#16811269C2semidirect
9. C2×#16811266C2semidirect
10. C2×#16811264C2semidirect
11. C2×#16811196C2semidirect
12. C2×#16811189C2semidirect
13. C2×#16811170C2semidirect
14. C2×#124×D53C2semidirect
15. C2×C4×#11719949C2semidirect
16. C2×C53×#548C2semidirect
18. C2×#13133265C22semidirect
20. C2×#13133263C22semidirect
23. C22×#11719949C22semidirect
25. C22×#11719945C22semidirect
26. C22×#11719945C22semidirect
27. C22×Q8×D53C22semidirect
28. C22×Q8×D53C22semidirect
32. #16811285C22semidirect
33. #16811284C22semidirect
34. #16811280C22semidirect
35. #16811270C22semidirect
36. #16811269C22semidirect
37. #16811266C22semidirect
38. #16811264C22semidirect
39. #16811196C22semidirect
40. #16811189C22semidirect
41. #16811170C22semidirect
42. C2×#13133216C22semidirect
43. C2×#13133213C22semidirect
44. C2×#13133206C22semidirect
45. C2×#13133205C22semidirect
46. C2×#13133204C22semidirect
47. C2×#13133203C22semidirect
48. C2×#13133203C22semidirect
49. C2×#13133203C22semidirect
50. #124×D53C22semidirect
51. C2×#13133202C22semidirect
52. C2×#13133199C22semidirect
53. C2×#13133197C22semidirect
54. C2×#13133196C22semidirect
55. C2×#13133193C22semidirect
56. C2×#13133192C22semidirect
57. C2×#13133192C22semidirect
58. C2×#13133191C22semidirect
59. C2×#13133190C22semidirect
60. C2×#13133190C22semidirect
61. C2×#13133188C22semidirect
62. C2×#13133188C22semidirect
63. C2×#13133187C22semidirect
64. C2×#13133185C22semidirect
65. C4×#11719949C22semidirect
66. C2×Q8×Dic53C22semidirect
67. C2×C4×D212C22semidirect
68. C2×C4×D212C22semidirect
69. C2×#13133179C22semidirect
70. C2×C4×C22⋊D53C22semidirect
71. C2×C4×C22⋊D53C22semidirect
72. C2×#13133175C22semidirect
73. C2×C22⋊C4×D53C22semidirect
74. C2×C22⋊C4×D53C22semidirect
75. C2×C42×D53C22semidirect
77. C23×Q8×C53C22semidirect
78. C53×#548C22semidirect
79. C2×#124×C53C22semidirect
80. C2×C22⋊Q8×C53C22semidirect
81. C2×#121×C53C22semidirect
82. C2×C4×Q8×C53C22semidirect
83. C2×C4×D4×C53C22semidirect
89. C2×#11719949D4semidirect
92. C2×#11719949C23semidirect
97. C2×#11719945C23semidirect
98. C2×#11719945C23semidirect
104. C2×Q8×D53C23semidirect
105. C2×Q8×D53C23semidirect
129. #13133216C23semidirect
130. #13133213C23semidirect
131. #13133206C23semidirect
132. #13133205C23semidirect
133. #13133204C23semidirect
134. #13133203C23semidirect
135. #13133203C23semidirect
136. #13133203C23semidirect
137. #13133202C23semidirect
138. #13133199C23semidirect
139. #13133197C23semidirect
140. #13133196C23semidirect
141. #13133193C23semidirect
142. #13133192C23semidirect
143. #13133192C23semidirect
144. #13133191C23semidirect
145. #13133190C23semidirect
146. #13133190C23semidirect
147. #13133188C23semidirect
148. #13133188C23semidirect
149. #13133187C23semidirect
150. #13133185C23semidirect
151. Q8×Dic53C23semidirect
152. C4×D212C23semidirect
153. C4×D212C23semidirect
154. #13133179C23semidirect
155. C4×C22⋊D53C23semidirect
156. C4×C22⋊D53C23semidirect
157. #13133175C23semidirect
172. C22⋊C4×D53C23semidirect
173. C22⋊C4×D53C23semidirect
177. C42×D53C23semidirect
183. C22×Q8×C53C23semidirect
188. #124×C53C23semidirect
189. C22⋊Q8×C53C23semidirect
190. #121×C53C23semidirect
191. C4×Q8×C53C23semidirect
192. C4×D4×C53C23semidirect
246. #11719949C2×D4semidirect
419. C2×#548D53semidirect
431. C2×C53#3500semidirect
451. C23×Q8C2×D53semidirect
458. #548C2×D53semidirect
475. C2×#124C2×D53semidirect
481. C2×C22⋊Q8C2×D53semidirect
489. C2×#121C2×D53semidirect
494. C2×C4×Q8C2×D53semidirect
500. C2×C4×D4C2×D53semidirect
505. C53C2×#3500semidirect
533. C22×Q8C22×D53semidirect
569. #124C22×D53semidirect
575. C22⋊Q8C22×D53semidirect
583. #121C22×D53semidirect
587. C4×Q8C22×D53semidirect
593. C4×D4C22×D53semidirect
839. C2#20288506direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332652
C22×#131332632
#202885062
C2×#168112852
C2×#168112842
C2×#168112802
C2×#168112702
C2×#168112692
C2×#168112662
C2×#168112642
C2×#168111962
C2×#168111892
C2×#168111702
C2×#124×D532
C2×C4×#117199492
C2×C53×#5482
C2×#350053