Finite Group Databasebeta

← C2×#20286460 #28259362

Subgroups — C2×#20286460 #28259362

Order 13568.

2742 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11719925C211yesmaximal, characteristic, complemented
2C22×Q16×D53C211yesmaximal, characteristic, complemented
3C2×Q8×C22⋊D53C211yesmaximal, characteristic
4C2×#16811286C211yesmaximal, characteristic
5#20286460C2116yesmaximal, direct product factor
6C2×#16811001C211yesmaximal, characteristic, complemented
7C2×#16810863C211yesmaximal, characteristic, complemented
8C2×#16810862C211yesmaximal, characteristic, complemented
9C2×#16810832C211yesmaximal, characteristic, complemented
10C2×#16810831C211yesmaximal, characteristic, complemented
11C2×#16810781C211yesmaximal, characteristic, complemented
12C2×#16810780C211yesmaximal, characteristic, complemented
13C2×#16810777C211yesmaximal, characteristic, complemented
14C2×#16810715C211yesmaximal, characteristic, complemented
15C2×#16810686C211yesmaximal, characteristic
16C2×C53×#451C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic
20C22×Dic212C2211yescharacteristic
21C22×Dic212C2211yescharacteristic
22C22×#11719925—28no—
23C22×#11719925C2211yescharacteristic
24C22×#11719925C2211yescharacteristic
25C22×#11719925C2211yescharacteristic
26C22×#11719925C2211yescharacteristic
27C22×#11719925C2211yescharacteristic
28C22×#11719925C2218yescomplemented
29C2×Q16×D53—28no—
30C2×Q16×D53C2218yescomplemented
31C23×#88322C2211yescharacteristic
32C22×C8×D53C2211yescharacteristic
33Q8×C22⋊D53—24no—
34Q8×C22⋊D53C2218yes—
35#16811286—24no—
36#16811286C2218yes—
37C2×#13133216—21no—
38C2×#13133215—21no—
39C2×#13133215C2211yescharacteristic
40C2×#13133215C2211yescharacteristic
41C2×#13133197C2211yescharacteristic
42C2×#13133196—21no—
43C2×#13133196C2211yescharacteristic
44C2×#13133195—21no—
45C2×#13133194—21no—
46C2×#13133193—21no—
47C2×#13133193C2211yescharacteristic
48C2×Q8×Dic53C2211yescharacteristic
49C2×#13133182C2211yescharacteristic
50C2×C4×C22⋊D53—21no—
51C2×C4×C22⋊D53C2211yescharacteristic
52C2×#13133177—21no—
53#16811001C2218yescomplemented
54#16810863C2218yescomplemented
55#16810862C2218yescomplemented
56#16810832C2218yescomplemented
57#16810831C2218yescomplemented
58#16810781C2218yescomplemented
59#16810780C2218yescomplemented
60#16810777C2218yescomplemented
61#16810715C2218yescomplemented
62#16810686C2218yes—
63C2×#13133150C2211yescharacteristic
64C2×#13133146C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133142C2211yescharacteristic
67C2×#13133141C2211yescharacteristic
68C2×#13133140C2211yescharacteristic
69C2×#13133129C2211yescharacteristic
70C2×C8×Dic53C2211yescharacteristic
71C23×Q8×C53C2211yescharacteristic
72C22×Q16×C53C2211yescharacteristic
73C22×Q16×C53C2211yescharacteristic
74C2×C22⋊Q8×C53C2211yescharacteristic
75C53×#451C2218yescomplemented
76C2×#103×C53C2211yescharacteristic
77C2×#103×C53C2211yescharacteristic
78C2×C22⋊C8×C53C2211yescharacteristic
79C22×Dic106—24no—
80C22×Dic106—22no—
81C22×Dic106—21no—
82C22×Dic106—21no—
83C22×Dic106—21no—
84C22×Dic106—42no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2314yes—
88C22×Dic106C2311yescharacteristic
89C2×Q8×D53—22no—
90C2×Q8×D53—22no—
91C2×Q8×D53—24no—
92C2×Q8×D53—24no—
93C2×Q8×D53—42no—
94C2×Q8×D53—42no—
95C2×Q8×D53C2314yes—
96C2×Q8×D53C2314yes—
97C22×C22⋊D53D411yescharacteristic
98C23×Dic53—21no—
99C22×C4×D53—21no—
100C22×C4×D53—21no—
101C22×C4×D53C2311yescharacteristic
102C2×Dic212—24no—
103C2×Dic212—42no—
104C2×Dic212C2314yes—
105C2×Dic212C2314yes—
106C2×#11719925—232no—
107C2×#11719925—24no—
108C2×#11719925—24no—
109C2×#11719925—24no—
110C2×#11719925—24no—
111C2×#11719925D418yescomplemented
112C2×#11719925C2314yes—
113C2×#11719925C2314yes—
114C2×#11719925C2314yes—
115C2×#11719925C2314yes—
116C2×#11719925C2314yes—
117Q16×D53—232no—
118C22×#88322—24no—
119C22×#88322C2311yescharacteristic
120C22×#88322C2314yes—
121C22×#88322C2311yescharacteristic
122C2×C8×D53—24no—
123C2×C8×D53C2314yes—
124#13133216—28no—
125#13133215—28no—
126#13133215—22no—
127#13133215—22no—
128#13133215C2314yes—
129#13133215C2314yes—
130#13133197—22no—
131#13133197C2314yes—
132#13133196—28no—
133#13133196—22no—
134#13133196C2314yes—
135#13133195—28no—
136#13133194—28no—
137#13133193—28no—
138#13133193—22no—
139#13133193C2314yes—
140Q8×Dic53—22no—
141Q8×Dic53C2314yes—
142#13133182—22no—
143#13133182C2314yes—
144C4×C22⋊D53—28no—
145C4×C22⋊D53D414yes—
146C4×C22⋊D53C2314yes—
147#13133177—28no—
148C2×C4⋊Dic53—21no—
149C2×C4⋊Dic53—21no—
150C2×C4⋊Dic53C2311yescharacteristic
151C2×#11719919—21no—
152C2×#11719919—21no—
153C2×#11719919—21no—
154C2×#11719919—21no—
155C2×#11719919—21no—
156C2×#11719919—21no—
157C2×#11719919—21no—
158C2×#11719919D411yescharacteristic
159C2×C22⋊Dic53—21no—
160C2×C22⋊Dic53D411yescharacteristic
161C2×#11719921—21no—
162C2×#11719921—21no—
163C2×#11719921D411yescharacteristic
164C2×C4×Dic53—21no—
165C2×C4×Dic53—21no—
166C2×C4×Dic53C2311yescharacteristic
167#13133150C2314yes—
168#13133146C2314yes—
169#13133142C2314yes—
170#13133142C2314yes—
171#13133141C2314yes—
172#13133140C2314yes—
173#13133129C2314yes—
174C8×Dic53C2314yes—
175C22×Q8×C53—22no—
176C22×Q8×C53—21no—
177C22×Q8×C53—24no—
178C22×Q8×C53—42no—
179C22×Q8×C53C2311yescharacteristic
180C22×Q8×C53C2311yescharacteristic
181C22×Q8×C53C2314yes—
182C22×Q8×C53C2311yescharacteristic
183C23×C4×C53—21no—
184C23×C4×C53C2311yescharacteristic
185C2×Q16×C53—24no—
186C2×Q16×C53—42no—
187C2×Q16×C53C2314yes—
188C2×Q16×C53C2314yes—
189C22×C8×C53C2311yescharacteristic
190C22×C8×C53C2311yescharacteristic
191C22⋊Q8×C53—22no—
192C22⋊Q8×C53C2314yes—
193C2×C4⋊C4×C53—21no—
194C2×C4⋊C4×C53C2311yescharacteristic
195C2×C22⋊C4×C53—21no—
196#103×C53C2314yes—
197#103×C53C2314yes—
198C22⋊C8×C53C2314yes—
199C24×C53C2×D411yescharacteristic
200C23×D53C2×D411yescharacteristic
201C2×Q8×C53—21no—
202C2×Q8×C53—21no—
203C2×Q8×C53—24no—
204C2×Q8×C53—21no—
205C2×Q8×C53—22no—
206C2×Q8×C53—28no—
207C2×Q8×C53—22no—
208C2×Q8×C53—22no—
209C2×Q8×C53—22no—
210C2×Q8×C53—22no—
211C2×Q8×C53—44no—
212C2×Q8×C53—44no—
213C2×Q8×C53—48no—
214C2×Q8×C53C2×D414yes—
215C2×Q8×C53C2412yes—
216C2×Q8×C53C2412yes—
217C2×Q8×C53C2412yes—
218C22×C4×C53—21no—
219C22×C4×C53—22no—
220C22×C4×C53—22no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—24no—
225C22×C4×C53—44no—
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D412yes—
228C22×C4×C53C2412yes—
229C22×C4×C53C2411yescharacteristic
230C2×C22⋊D53Q1618yescomplemented
231C2×C22⋊D53C2×D414yes—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—24no—
237C22×Dic53—44no—
238C22×Dic53C2×D411yescharacteristic
239C22×Dic53C2×D411yescharacteristic
240C22×Dic53C2×D411yescharacteristic
241Q8×D53—28no—
242Q8×D53—28no—
243Q8×D53—44no—
244Q8×D53—44no—
245Q8×D53—48no—
246Q8×D53—48no—
247C2×C4×D53—22no—
248C2×C4×D53—22no—
249C2×C4×D53—24no—
250C2×C4×D53—24no—
251C2×C4×D53—44no—
252C2×C4×D53—44no—
253C2×C4×D53C2×D412yes—
254C2×C4×D53C2412yes—
255C2×Dic106—21no—
256C2×Dic106—22no—
257C2×Dic106—22no—
258C2×Dic106—22no—
259C2×Dic106—22no—
260C2×Dic106—22no—
261C2×Dic106—28no—
262C2×Dic106—24no—
263C2×Dic106—21no—
264C2×Dic106—21no—
265C2×Dic106—24no—
266C2×Dic106—24no—
267C2×Dic106—44no—
268C2×Dic106—48no—
269C2×Dic106—44no—
270C2×Dic106—44no—
271C2×Dic106—44no—
272C2×Dic106C2×D414yes—
273C2×Dic106C2412yes—
274C2×Dic106C2412yes—
275C2×Dic106C2412yes—
276Q16×C53—28no—
277Q16×C53—44no—
278C2×C8×C53—22no—
279C2×C8×C53—22no—
280C2×C8×C53C2412yes—
281C2×C8×C53C2412yes—
282C4⋊C4×C53—24no—
283C4⋊C4×C53—21no—
284C4⋊C4×C53C2412yes—
285C22⋊C4×C53—24no—
286C22⋊Dic53—24no—
287C22⋊Dic53C2×D414yes—
288#11719925—28no—
289#11719925—28no—
290#11719925—28no—
291#11719925—28no—
292#11719925C2×D4116yescomplemented
293#11719921—24no—
294#11719921—24no—
295#11719921C2×D414yes—
296C4⋊Dic53—21no—
297C4⋊Dic53—24no—
298C4⋊Dic53—24no—
299C4⋊Dic53C2412yes—
300#11719919—24no—
301#11719919—24no—
302#11719919—24no—
303#11719919—24no—
304#11719919—24no—
305#11719919—24no—
306#11719919—24no—
307#11719919C2×D414yes—
308C4×Dic53—24no—
309C4×Dic53—24no—
310C4×Dic53C2×D412yes—
311C4×Dic53C2412yes—
312C2×#88322—22no—
313C2×#88322—28no—
314C2×#88322C2×D414yes—
315C2×#88322C2412yes—
316C2×#88322C2412yes—
317Dic212—28no—
318Dic212—44no—
319C8×D53—28no—
320C23×C53—22no—
321C23×C53—22no—
322C23×C53C2×Q1614yescomplemented
323C23×C53C22×D412yes—
324C23×C53C22×D411yescharacteristic
325C22×D53—22no—
326C22×D53—22no—
327C22×D53C2×Q1614yescomplemented
328C22×D53C22×D412yes—
329Q8×C53—24no—
330Q8×C53—22no—
331Q8×C53—22no—
332Q8×C53—22no—
333Q8×C53—22no—
334Q8×C53—22no—
335Q8×C53—48no—
336Q8×C53—42no—
337Q8×C53—42no—
338Q8×C53C22×D414yes—
339C2×C4×C53—22no—
340C2×C4×C53—24no—
341C2×C4×C53—22no—
342C2×C4×C53—24no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—48no—
349C2×C4×C53—42no—
350C2×C4×C53—42no—
351C2×C4×C53—42no—
352C2×C4×C53C22×D412yes—
353C2×C4×C53C22×D411yescharacteristic
354C2×C4×C53C22×D412yes—
355C2×C4×C53H(5,𝔽2)12yes—
356C2×C4×C53C2511yescharacteristic
357C22⋊D53C2×Q16116yescomplemented
358C2×Dic53—24no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—22no—
363C2×Dic53—22no—
364C2×Dic53—22no—
365C2×Dic53—48no—
366C2×Dic53—42no—
367C2×Dic53—42no—
368C2×Dic53—42no—
369C2×Dic53C2×Q1614yescomplemented
370C2×Dic53C22×D412yes—
371C2×Dic53C22×D412yes—
372C2×Dic53C22×D412yes—
373C4×D53—24no—
374C4×D53—22no—
375C4×D53—22no—
376C4×D53—48no—
377C4×D53—48no—
378Dic106—24no—
379Dic106—22no—
380Dic106—22no—
381Dic106—22no—
382Dic106—22no—
383Dic106—22no—
384Dic106—48no—
385Dic106—48no—
386Dic106—48no—
387Dic106—42no—
388Dic106—42no—
389Dic106C22×D414yes—
390C8×C53—22no—
391C8×C53—22no—
392#88322—22no—
393#88322C22×D414yes—
394C2×D4×Q16—531nomaximal, Sylow
395C22×C53—22no—
396C22×C53—28no—
397C22×C53—22no—
398C22×C53D4212yes—
399C22×C53C22×Q1612yes—
400C22×C53C22×Q1614yescomplemented
401C22×C53#57812yes—
402C22×C53C23×D411yescharacteristic
403C2×D53—22no—
404C2×D53—28no—
405C2×D53—22no—
406C2×D53C22×Q1614yescomplemented
407C4×C53—22no—
408C4×C53—24no—
409C4×C53—42no—
410C4×C53—42no—
411C4×C53—42no—
412C4×C53D4212yes—
413C4×C53C23×D411yescharacteristic
414C4×C53C2×H(5,𝔽2)11yescharacteristic
415Dic53—24no—
416Dic53—22no—
417Dic53—22no—
418Dic53—42no—
419Dic53—42no—
420Dic53—42no—
421Dic53C22×Q1614yescomplemented
422C23×Q16—531no—
423C23×Q16—531no—
424C2×D4×Q8—531no—
425C2×D4×Q8—531no—
426D4×Q16—5316no—
427C2×#494—531no—
428C2×#467—531no—
429C2×#467—531no—
430C2×#462—531no—
431C2×#462—531no—
432C2×#451—531no—
433C2×#451—531no—
434C2×#451—531no—
435C2×#451D5311yescharacteristic, complemented
436C2×C4×Q16—531no—
437C2×C8×D4—531no—
438C2×C53—24no—
439C2×C53D4×Q1614yescomplemented
440C2×C53C2×D4211yescharacteristic
441C2×C53C23×Q1611yescharacteristic
442C2×C53C2×#57811yescharacteristic
443D53—24no—
444C23×Q8—531no—
445C23×Q8—531no—
446C23×Q8—531no—
447C23×Q8C2×D5311yescharacteristic
448C22×Q16—531no—
449C22×Q16—531no—
450C22×Q16—531no—
451C22×Q16—531no—
452C22×Q16—531no—
453C22×Q16—538no—
454C22×Q16—538no—
455C22×Q16—531no—
456C22×Q16—531no—
457C22×Q16—1068no—
458C22×Q16—1068no—
459C22×Q16C2×D5311yescharacteristic
460C22×Q16C2×D5311yescharacteristic
461C23×C8—531no—
462C23×C8—531no—
463D4×Q8—538no—
464D4×Q8—538no—
465D4×Q8—1064no—
466D4×Q8—1064no—
467C2×C4⋊Q8—531no—
468C2×C4⋊Q8—531no—
469C2×C4⋊Q8—1061no—
470C2×C4⋊Q8—1061no—
471C2×C22⋊Q8—531no—
472C2×C22⋊Q8—531no—
473C2×C22⋊Q8—531no—
474C2×C22⋊Q8—1061no—
475C2×C22⋊Q8—1061no—
476C2×C22⋊Q8—1061no—
477C2×C22⋊Q8—1061no—
478C2×C22⋊Q8C2×D5311yescharacteristic
479C2×C4×Q8—531no—
480C2×C4×Q8—531no—
481C2×C4×D4—531no—
482C2×C4×D4—1061no—
483C2×C4×D4—1061no—
484#494—538no—
485#467—538no—
486#467—538no—
487#462—538no—
488#462—538no—
489#451—538no—
490#451—538no—
491#451—538no—
492#451C2×D5318yescomplemented
493C4×Q16—538no—
494C8×D4—538no—
495C2×#107—531no—
496C2×C4⋊C8—531no—
497C2×#103—531no—
498C2×#103—531no—
499C2×#103—531no—
500C2×#103—531no—
501C2×#103C2×D5311yescharacteristic
502C2×#103C2×D5311yescharacteristic
503C2×C22⋊C8—531no—
504C2×C22⋊C8C2×D5311yescharacteristic
505C2×C4×C8—531no—
506C53C2×D4×Q1611yescharacteristic, complemented, Sylow
507C22×Q8—21no—
508C22×Q8—22no—
509C22×Q8—24no—
510C22×Q8—42no—
511C22×Q8—534no—
512C22×Q8—534no—
513C22×Q8—531no—
514C22×Q8—531no—
515C22×Q8—531no—
516C22×Q8—534no—
517C22×Q8—1061no—
518C22×Q8—1061no—
519C22×Q8—1064no—
520C22×Q8—1062no—
521C22×Q8—1062no—
522C22×Q8—1061no—
523C22×Q8—1062no—
524C22×Q8—1064no—
525C22×Q8—1064no—
526C22×Q8—2122no—
527C22×Q8—2122no—
528C22×Q8—2122no—
529C22×Q8C22×D5311yescharacteristic
530C22×Q8C22×D5311yescharacteristic
531C22×Q8C22×D5314yes—
532C22×Q8C22×D5311yescharacteristic
533C22×D4—531no—
534C23×C4—21no—
535C23×C4—531no—
536C23×C4—1061no—
537C23×C4—1061no—
538C23×C4—1061no—
539C23×C4C22×D5311yescharacteristic
540C2×Q16—24no—
541C2×Q16—42no—
542C2×Q16—538no—
543C2×Q16—534no—
544C2×Q16—534no—
545C2×Q16—534no—
546C2×Q16—534no—
547C2×Q16—534no—
548C2×Q16—534no—
549C2×Q16—534no—
550C2×Q16—1064no—
551C2×Q16—1064no—
552C2×Q16—1064no—
553C2×Q16—10632no—
554C2×Q16—10632no—
555C2×Q16—1064no—
556C2×Q16—1064no—
557C2×Q16—2122no—
558C2×Q16C22×D5314yes—
559C2×Q16C22×D5314yes—
560C22×C8—531no—
561C22×C8—531no—
562C22×C8—534no—
563C22×C8—534no—
564C22×C8—1064no—
565C22×C8—1064no—
566C22×C8C22×D5311yescharacteristic
567C22×C8C22×D5311yescharacteristic
568C4⋊Q8—534no—
569C4⋊Q8—534no—
570C4⋊Q8—1062no—
571C4⋊Q8—1062no—
572C4⋊Q8—1068no—
573C4⋊Q8—1068no—
574C22⋊Q8—22no—
575C22⋊Q8—534no—
576C22⋊Q8—534no—
577C22⋊Q8—534no—
578C22⋊Q8—1068no—
579C22⋊Q8—1068no—
580C22⋊Q8—1068no—
581C22⋊Q8—1068no—
582C22⋊Q8—1062no—
583C22⋊Q8—1062no—
584C22⋊Q8—1062no—
585C22⋊Q8C22×D5314yes—
586C4×Q8—534no—
587C4×Q8—534no—
588C4×Q8—1062no—
589C4×Q8—1062no—
590C4×D4—534no—
591C4×D4—534no—
592C4×D4—1068no—
593C4×D4—1068no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—531no—
596C2×C4⋊C4—531no—
597C2×C4⋊C4—1061no—
598C2×C4⋊C4—1061no—
599C2×C4⋊C4—1061no—
600C2×C4⋊C4—1061no—
601C2×C4⋊C4—1061no—
602C2×C4⋊C4—1061no—
603C2×C4⋊C4—1061no—
604C2×C4⋊C4—1061no—
605C2×C4⋊C4—1061no—
606C2×C4⋊C4C22×D5311yescharacteristic
607C2×C22⋊C4—21no—
608C2×C22⋊C4—531no—
609C2×C22⋊C4—531no—
610C2×C22⋊C4—1061no—
611C2×C22⋊C4—1061no—
612C2×C22⋊C4—1061no—
613C2×C42—531no—
614C2×C42—1061no—
615C2×C42—1061no—
616#107—534no—
617C4⋊C8—534no—
618#103—534no—
619#103—534no—
620#103—534no—
621#103—534no—
622#103C22×D5314yes—
623#103C22×D5314yes—
624C22⋊C8—534no—
625C22⋊C8C22×D5314yes—
626C4×C8—534no—
627C24—531no—
628C24D4×D5311yescharacteristic
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—24no—
632C2×Q8—21no—
633C2×Q8—22no—
634C2×Q8—28no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—44no—
640C2×Q8—44no—
641C2×Q8—48no—
642C2×Q8—534no—
643C2×Q8—532no—
644C2×Q8—532no—
645C2×Q8—532no—
646C2×Q8—1064no—
647C2×Q8—1064no—
648C2×Q8—1068no—
649C2×Q8—1061no—
650C2×Q8—1064no—
651C2×Q8—1061no—
652C2×Q8—1061no—
653C2×Q8—1062no—
654C2×Q8—1068no—
655C2×Q8—1068no—
656C2×Q8—1062no—
657C2×Q8—1062no—
658C2×Q8—1062no—
659C2×Q8—1062no—
660C2×Q8—2124no—
661C2×Q8—2124no—
662C2×Q8—2124no—
663C2×Q8—2128no—
664C2×Q8—2124no—
665C2×Q8—2124no—
666C2×Q8—2124no—
667C2×Q8—2128no—
668C2×Q8—2128no—
669C2×Q8D4×D5314yes—
670C2×Q8C23×D5312yes—
671C2×Q8C23×D5312yes—
672C2×Q8C23×D5312yes—
673C2×D4—538no—
674C2×D4—534no—
675C22×C4—21no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—24no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—44no—
683C22×C4—531no—
684C22×C4—531no—
685C22×C4—531no—
686C22×C4—532no—
687C22×C4—532no—
688C22×C4—1064no—
689C22×C4—1064no—
690C22×C4—1061no—
691C22×C4—1062no—
692C22×C4—1062no—
693C22×C4—1064no—
694C22×C4—1061no—
695C22×C4—1061no—
696C22×C4—1061no—
697C22×C4—2124no—
698C22×C4—2124no—
699C22×C4—2124no—
700C22×C4D4×D5312yes—
701C22×C4D4×D5311yescharacteristic
702C22×C4C23×D5312yes—
703C22×C4C23×D5311yescharacteristic
704Q16—28no—
705Q16—44no—
706Q16—5316no—
707Q16—1068no—
708Q16—1068no—
709Q16—1068no—
710Q16—1068no—
711Q16—1068no—
712Q16—2124no—
713C2×C8—22no—
714C2×C8—22no—
715C2×C8—534no—
716C2×C8—532no—
717C2×C8—532no—
718C2×C8—1068no—
719C2×C8—1068no—
720C2×C8—1062no—
721C2×C8C23×D5312yes—
722C2×C8C23×D5312yes—
723C4⋊C4—24no—
724C4⋊C4—21no—
725C4⋊C4—534no—
726C4⋊C4—532no—
727C4⋊C4—1064no—
728C4⋊C4—1064no—
729C4⋊C4—1064no—
730C4⋊C4—1064no—
731C4⋊C4—1064no—
732C4⋊C4—1064no—
733C4⋊C4—1064no—
734C4⋊C4—1064no—
735C4⋊C4—1061no—
736C4⋊C4—1064no—
737C4⋊C4C23×D5312yes—
738C22⋊C4—24no—
739C22⋊C4—534no—
740C22⋊C4—534no—
741C22⋊C4—1064no—
742C22⋊C4—1064no—
743C22⋊C4—1064no—
744C42—532no—
745C42—532no—
746C42—1064no—
747C42—1064no—
748C23—22no—
749C23—22no—
750C23—534no—
751C23—532no—
752C23—1062no—
753C23—1062no—
754C23Q16×D5314yescomplemented
755C23C2×D4×D5312yes—
756C23C2×D4×D5311yescharacteristic
757Q8—22no—
758Q8—24no—
759Q8—22no—
760Q8—22no—
761Q8—22no—
762Q8—22no—
763Q8—48no—
764Q8—42no—
765Q8—42no—
766Q8—534no—
767Q8—1062no—
768Q8—1064no—
769Q8—1062no—
770Q8—1062no—
771Q8—1062no—
772Q8—1062no—
773Q8—2128no—
774Q8—2128no—
775Q8—2128no—
776Q8—2122no—
777Q8—2122no—
778Q8C2×D4×D5314yes—
779D4—5316no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—48no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—534no—
794C2×C4—532no—
795C2×C4—532no—
796C2×C4—532no—
797C2×C4—1062no—
798C2×C4—1062no—
799C2×C4—1062no—
800C2×C4—1064no—
801C2×C4—1062no—
802C2×C4—1062no—
803C2×C4—1064no—
804C2×C4—1062no—
805C2×C4—1062no—
806C2×C4—1062no—
807C2×C4—2128no—
808C2×C4—2128no—
809C2×C4—2128no—
810C2×C4—2122no—
811C2×C4—2122no—
812C2×C4—2122no—
813C2×C4C2×D4×D5312yes—
814C2×C4C2×D4×D5312yes—
815C2×C4C2×D4×D5311yescharacteristic
816C2×C4#1313326212yes—
817C2×C4C24×D5311yescharacteristic
818C8—22no—
819C8—22no—
820C8—534no—
821C8—1062no—
822C22—22no—
823C22—22no—
824C22—28no—
825C22—534no—
826C22—1062no—
827C22—1062no—
828C22—1068no—
829C22#1681125512yes—
830C22C2×Q16×D5312yes—
831C22C2×Q16×D5314yescomplemented
832C22#1681143912yes—
833C22C22×D4×D5311yescharacteristic
834C4—22no—
835C4—24no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—534no—
840C4—1062no—
841C4—1064no—
842C4—1062no—
843C4—2122no—
844C4—2122no—
845C4—2122no—
846C4#1681125512yes—
847C4C22×D4×D5311yescharacteristic
848C4C2×#1313326211yescharacteristic
849C2—24no—
850C2—1064no—
851C2#2028646014yesdirect product factor
852C2C2×#1681125511yescharacteristic
853C2C22×Q16×D5311yescharacteristic
854C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#451C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC2×#451D53
hypocenterC53C2×D4×Q16
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C23×#11719925C2semidirect
2. C22×Q16×D53C2semidirect
5. #20286460C2direct (N × H)
6. C2×#16811001C2semidirect
7. C2×#16810863C2semidirect
8. C2×#16810862C2semidirect
9. C2×#16810832C2semidirect
10. C2×#16810831C2semidirect
11. C2×#16810781C2semidirect
12. C2×#16810780C2semidirect
13. C2×#16810777C2semidirect
14. C2×#16810715C2semidirect
16. C2×C53×#451C2semidirect
28. C22×#11719925C22semidirect
30. C2×Q16×D53C22semidirect
53. #16811001C22semidirect
54. #16810863C22semidirect
55. #16810862C22semidirect
56. #16810832C22semidirect
57. #16810831C22semidirect
58. #16810781C22semidirect
59. #16810780C22semidirect
60. #16810777C22semidirect
61. #16810715C22semidirect
75. C53×#451C22semidirect
111. C2×#11719925D4semidirect
230. C2×C22⋊D53Q16semidirect
292. #11719925C2×D4semidirect
322. C23×C53C2×Q16semidirect
327. C22×D53C2×Q16semidirect
357. C22⋊D53C2×Q16semidirect
369. C2×Dic53C2×Q16semidirect
400. C22×C53C22×Q16semidirect
406. C2×D53C22×Q16semidirect
421. Dic53C22×Q16semidirect
435. C2×#451D53semidirect
439. C2×C53D4×Q16semidirect
492. #451C2×D53semidirect
506. C53C2×D4×Q16semidirect
754. C23Q16×D53semidirect
831. C22C2×Q16×D53semidirect
851. C2#20286460direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117199252
C22×Q16×D532
C2×Q8×C22⋊D532
C2×#168112862
#202864602
C2×#168110012
C2×#168108632
C2×#168108622
C2×#168108322
C2×#168108312
C2×#168107812
C2×#168107802
C2×#168107772
C2×#168107152
C2×#168106862
C2×C53×#4512
C2×D4×Q1653