Finite Group Databasebeta

← C2×C4×#13133249 #28248167

Subgroups — C2×C4×#13133249 #28248167

Order 13568.

2810 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic
2C2×C4×#11719949C211yesmaximal, characteristic
3C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
4C4×#13133249C2116yesmaximal, direct product factor
5C2×#16810730C211yesmaximal, characteristic, complemented
6C2×#16810727C211yesmaximal, characteristic, complemented
7C2×#16810726C211yesmaximal, characteristic, complemented
8C2×#16810722C211yesmaximal, characteristic, complemented
9C2×C4×#11719925C211yesmaximal, characteristic, complemented
10C2×C4×#11719913C211yesmaximal, characteristic, complemented
11C2×C4×#11719924C211yesmaximal, characteristic, complemented
12C2×#16810664C211yesmaximal, characteristic, complemented
13C2×#16810623C211yesmaximal, characteristic
14C2×#16810630C211yesmaximal, characteristic, complemented
15C2×C4×#11719912C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C2×#13133249C4116yesdirect product factor
20C2×#13133249C2218yes—
21C22×#11719925C2211yescharacteristic
22C22×#11719913C2211yescharacteristic
23C22×#11719924C2211yescharacteristic
24C22×#11719912C2211yescharacteristic
25C22×#11719912C2211yescharacteristic
26C4×#11719949—24no—
27C4×#11719949C2218yes—
28C2×Q8×Dic53C2211yescharacteristic
29C2×Q8×Dic53C2211yescharacteristic
30C2×C4×Dic106—21no—
31C2×C4×Dic106C2211yescharacteristic
32C2×#13133182—21no—
33C2×#13133182C2211yescharacteristic
34C4×Q8×D53—24no—
35C4×Q8×D53C2218yescomplemented
36C2×C4×D212—21no—
37C2×C4×D212C2211yescharacteristic
38C2×#13133179—21no—
39C2×#13133179C2211yescharacteristic
40C2×#13133175—21no—
41C2×#13133175C2211yescharacteristic
42C2×C4⋊C4×D53—21no—
43C2×C4⋊C4×D53C2211yescharacteristic
44C2×C42×D53—21no—
45C2×C42×D53—21no—
46C2×C42×D53C2211yescharacteristic
47#16810730C2218yescomplemented
48#16810727C2218yescomplemented
49#16810726C2218yescomplemented
50#16810722C2218yescomplemented
51C4×#11719925C2218yescomplemented
52C4×#11719913C2218yescomplemented
53C4×#11719924C2218yescomplemented
54#16810664C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58#16810630C2218yescomplemented
59#16810623C2218yes—
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C4×#11719912C2218yescomplemented
67C2×#13133127C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C2×C4×#88322C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C2×C4×Q8×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C4×Q16×C53C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C2×C4×C8×C53C2211yescharacteristic
78C2×#11719949—22no—
79C2×#11719949—24no—
80C2×#11719949C2×C418yes—
81C2×#11719949C2314yes—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C2×Q8×D53—22no—
85C2×Q8×D53—24no—
86C2×Q8×D53C2×C418yescomplemented
87C2×Q8×D53C2314yes—
88C22×D212—21no—
89C22×D212C2311yescharacteristic
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53D411yescharacteristic
96C22×C4×D53D411yescharacteristic
97C22×C4×D53C2311yescharacteristic
98#13133249C2×C4164yesdirect product factor
99C2×#11719925C2×C418yescomplemented
100C2×#11719925C2314yes—
101C2×#11719913C2×C418yescomplemented
102C2×#11719913C2314yes—
103C2×#11719924C2×C418yescomplemented
104C2×#11719924C2314yes—
105C2×#11719912—24no—
106C2×#11719912C2×C418yescomplemented
107C2×#11719912C2314yes—
108C2×#11719912C2314yes—
109C22×#88322C2311yescharacteristic
110C22×#88322C2311yescharacteristic
111Q8×Dic53—22no—
112Q8×Dic53—22no—
113Q8×Dic53C2314yes—
114Q8×Dic53C2314yes—
115C4×Dic106—22no—
116C4×Dic106—28no—
117C4×Dic106C2314yes—
118#13133182—22no—
119#13133182—28no—
120#13133182C2314yes—
121C4×D212—22no—
122C4×D212—28no—
123C4×D212C2314yes—
124#13133179—22no—
125#13133179—28no—
126#13133179C2314yes—
127#13133175—28no—
128#13133175—22no—
129#13133175C2314yes—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C4⋊C4×D53—28no—
138C4⋊C4×D53—22no—
139C4⋊C4×D53C2314yes—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53D411yescharacteristic
149C2×C4×Dic53D411yescharacteristic
150C2×C4×Dic53C2311yescharacteristic
151C42×D53—28no—
152C42×D53—28no—
153C42×D53D414yes—
154C42×D53C2314yes—
155#13133150C2314yes—
156#13133149C2314yes—
157#13133148C2314yes—
158#13133142C2314yes—
159#13133141C2314yes—
160#13133141C2314yes—
161#13133140C2314yes—
162#13133139C2314yes—
163#13133137C2314yes—
164#13133127C2314yes—
165#13133127C2314yes—
166C4×#88322C2314yes—
167C22×Q8×C53C2311yescharacteristic
168C22×Q8×C53C2311yescharacteristic
169C2×Q16×C53C2×C418yescomplemented
170C2×Q16×C53C2314yes—
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C4×Q8×C53—22no—
174C4×Q8×C53—22no—
175C4×Q8×C53C2314yes—
176C4×Q8×C53C2314yes—
177C2×C4⋊C4×C53—21no—
178C2×C4⋊C4×C53—21no—
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C42×C53—21no—
182C2×C42×C53—21no—
183C2×C42×C53C2311yescharacteristic
184#107×C53C2314yes—
185#103×C53C2314yes—
186#103×C53C2314yes—
187C4×C8×C53C2314yes—
188C23×D53—21no—
189C23×D53C2×D411yescharacteristic
190C2×Q8×C53—21no—
191C2×Q8×C53—21no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53C22×C414yes—
195C2×Q8×C53C22×C414yes—
196C2×Q8×C53C2412yes—
197C2×Q8×C53C2412yes—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2411yescharacteristic
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53C2×D411yescharacteristic
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211#11719949—216no—
212#11719949—28no—
213#11719949C22×C4116yes—
214Q8×D53—216no—
215Q8×D53—28no—
216Q8×D53C22×C4116yescomplemented
217C2×D212—28no—
218C2×D212—24no—
219C2×D212—21no—
220C2×D212—22no—
221C2×D212C22×C414yes—
222C2×D212C2412yes—
223C2×C4×D53—28no—
224C2×C4×D53—24no—
225C2×C4×D53—24no—
226C2×C4×D53—28no—
227C2×C4×D53—24no—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—24no—
231C2×C4×D53—42no—
232C2×C4×D53—44no—
233C2×C4×D53—44no—
234C2×C4×D53—44no—
235C2×C4×D53C22×C414yes—
236C2×C4×D53C2×D414yes—
237C2×C4×D53C2×D414yes—
238C2×C4×D53C2×D412yes—
239C2×C4×D53#4114yes—
240C2×C4×D53C2412yes—
241C2×Dic106—21no—
242C2×Dic106—22no—
243C2×Dic106—28no—
244C2×Dic106—24no—
245C2×Dic106C22×C414yes—
246C2×Dic106C2412yes—
247Q16×C53C22×C4116yescomplemented
248C2×C8×C53—22no—
249C2×C8×C53C22×C414yes—
250C2×C8×C53C2412yes—
251C2×C8×C53C2412yes—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—24no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C42×C53—24no—
259C42×C53—24no—
260C42×C53C2×D412yes—
261C42×C53C2412yes—
262#11719925C22×C4116yescomplemented
263#11719924C22×C4116yescomplemented
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267C4⋊Dic53—21no—
268C4⋊Dic53—21no—
269C4⋊Dic53—24no—
270C4⋊Dic53—24no—
271C4⋊Dic53C2412yes—
272C4⋊Dic53C2412yes—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276C4×Dic53—24no—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C4×Dic53—24no—
280C4×Dic53—24no—
281C4×Dic53C2×D414yes—
282C4×Dic53C2×D412yes—
283C4×Dic53C2×D414yes—
284C4×Dic53C2412yes—
285C2×#88322—22no—
286C2×#88322C22×C414yes—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289#11719913C22×C4116yescomplemented
290#11719912—28no—
291#11719912C22×C4116yescomplemented
292C23×C53C22×D411yescharacteristic
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—24no—
296C22×D53—22no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53C4×D414yes—
300C22×D53C22×D412yes—
301Q8×C53—24no—
302Q8×C53—24no—
303Q8×C53—22no—
304Q8×C53—22no—
305Q8×C53C23×C414yes—
306Q8×C53C23×C414yes—
307C2×C4×C53—24no—
308C2×C4×C53—24no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53#13714yescomplemented
317C2×C4×C53C23×C412yes—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53C22×D412yes—
321C2×C4×C53C2×#4112yes—
322C2×C4×C53C2511yescharacteristic
323C2×Dic53—24no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53C4×D414yes—
332C2×Dic53C22×D412yes—
333C2×Dic53C22×D412yes—
334C2×Dic53C22×D412yes—
335D212—216no—
336D212—24no—
337D212—22no—
338D212C23×C414yes—
339C4×D53—216no—
340C4×D53—28no—
341C4×D53—216no—
342C4×D53—44no—
343C4×D53—48no—
344C4×D53—48no—
345C4×D53—48no—
346C4×D53C4×D418yes—
347C4×D53C23×C414yes—
348C4×D53C2×#4114yes—
349Dic106—24no—
350Dic106—22no—
351Dic106—216no—
352Dic106C23×C414yes—
353C8×C53—22no—
354C8×C53C23×C414yes—
355#88322—22no—
356#88322C23×C414yes—
357C2×C4×#137—531nomaximal, Sylow
358C22×C53C2×C4×D412yes—
359C22×C53C2×#13712yes—
360C22×C53#57512yes—
361C22×C53C23×D411yescharacteristic
362C2×D53—28no—
363C2×D53—22no—
364C2×D53—22no—
365C2×D53—24no—
366C2×D53—48no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53C2×C4×D414yes—
370C4×C53—24no—
371C4×C53—24no—
372C4×C53—22no—
373C4×C53—42no—
374C4×C53—42no—
375C4×C53C2×C4×D412yes—
376C4×C53C2×#13714yescomplemented
377C4×C53C24×C411yescharacteristic
378C4×C53C22×#4111yescharacteristic
379Dic53—24no—
380Dic53—22no—
381Dic53—22no—
382Dic53—42no—
383Dic53—42no—
384Dic53C2×C4×D414yes—
385C22×#137—531no—
386C2×C4×#41—531no—
387C22×C4×Q8—531no—
388C4×#137—5316no—
389C2×#441—531no—
390C2×#441—531no—
391C2×#440—531no—
392C2×#440—531no—
393C2×C4×Q16—531no—
394C2×C4×Q16D5311yescharacteristic, complemented
395C2×C4×SD16—531no—
396C2×C4×SD16—531no—
397C2×#428—531no—
398C2×#417—531no—
399C2×#419—531no—
400C2×C4×M16—531no—
401C2×C53C4×#13714yescomplemented
402C2×C53C22×C4×D411yescharacteristic
403C2×C53C22×#13711yescharacteristic
404C2×C53C2×#57511yescharacteristic
405D53—24no—
406D53—44no—
407C22×#41—531no—
408C23×Q8—531no—
409C2×#137—5316no—
410C2×#137—538no—
411C22×Q16—531no—
412C22×Q16C2×D5311yescharacteristic
413C22×SD16—531no—
414C22×SD16—531no—
415C22×M16—531no—
416C22×M16—531no—
417C4×#41—538no—
418C4×#41—1064no—
419C2×C4×Q8—531no—
420C2×C4×Q8—531no—
421C2×C4×Q8—538no—
422C2×C4×Q8—531no—
423C2×C4×Q8—531no—
424C2×C4×Q8—1061no—
425C2×C4×Q8—1061no—
426C2×C4×Q8—1064no—
427C2×C4×Q8C2×D5311yescharacteristic
428C2×C4×Q8C2×D5311yescharacteristic
429C2×C4×D4—531no—
430C2×C4×D4—531no—
431C2×C4×D4—1061no—
432C2×C4×D4—1061no—
433C2×#117—531no—
434C2×#117—1061no—
435C22×C4⋊C4—531no—
436C22×C4⋊C4—1061no—
437C22×C42—531no—
438C22×C42—1061no—
439C22×C42—1061no—
440#441—538no—
441#441—538no—
442#440—538no—
443#440—538no—
444C4×Q16—538no—
445C4×Q16C2×D5318yescomplemented
446C4×SD16—538no—
447C4×SD16—538no—
448#428—538no—
449C2×#107—531no—
450C2×#107C2×D5311yescharacteristic
451C2×#106—531no—
452C2×#106—531no—
453#419—538no—
454#417—538no—
455C2×#103—531no—
456C2×#103—531no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103C2×D5311yescharacteristic
460C2×#103C2×D5311yescharacteristic
461C2×#102—531no—
462C2×#102—531no—
463C4×M16—538no—
464C2×#97—531no—
465C2×#97—531no—
466C2×C4×C8—531no—
467C2×C4×C8C2×D5311yescharacteristic
468C53C2×C4×#13711yescharacteristic, complemented, Sylow
469C2×#41—538no—
470C2×#41—534no—
471C2×#41—1062no—
472C2×#41—1064no—
473C22×Q8—538no—
474C22×Q8—534no—
475C22×Q8—531no—
476C22×Q8—1061no—
477C22×Q8—1062no—
478C22×Q8—1064no—
479C22×Q8C22×D5311yescharacteristic
480C22×Q8C22×D5311yescharacteristic
481C22×D4—531no—
482C22×D4—1061no—
483C23×C4—531no—
484C23×C4—531no—
485C23×C4—531no—
486C23×C4—1061no—
487C23×C4—1061no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4—1061no—
491#137—5364no—
492C2×Q16—538no—
493C2×Q16—534no—
494C2×Q16C4×D5318yescomplemented
495C2×Q16C22×D5314yes—
496C2×SD16—538no—
497C2×SD16—534no—
498C2×SD16—538no—
499C2×SD16—534no—
500C2×M16—538no—
501C2×M16—534no—
502C2×M16—534no—
503C2×M16—1064no—
504C22×C8—531no—
505C22×C8—531no—
506C22×C8C22×D5311yescharacteristic
507C22×C8C22×D5311yescharacteristic
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—534no—
511C4×Q8—534no—
512C4×Q8—534no—
513C4×Q8—534no—
514C4×Q8—1068no—
515C4×Q8—1068no—
516C4×Q8—1062no—
517C4×Q8—1062no—
518C4×Q8—1062no—
519C4×Q8—1062no—
520C4×Q8C22×D5314yes—
521C4×Q8C22×D5314yes—
522C4×D4—534no—
523C4×D4—534no—
524C4×D4—1068no—
525C4×D4—1062no—
526C4×D4—1068no—
527C4×D4—1062no—
528#117—534no—
529#117—1068no—
530#117—1062no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—531no—
535C2×C4⋊C4—534no—
536C2×C4⋊C4—1062no—
537C2×C4⋊C4—1068no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4C22×D5311yescharacteristic
544C2×C4⋊C4C22×D5311yescharacteristic
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C42—21no—
549C2×C42—21no—
550C2×C42—531no—
551C2×C42—531no—
552C2×C42—531no—
553C2×C42—534no—
554C2×C42—534no—
555C2×C42—1068no—
556C2×C42—1068no—
557C2×C42—1061no—
558C2×C42—1061no—
559C2×C42—1061no—
560C2×C42—1061no—
561C2×C42—1061no—
562C2×C42C22×D5311yescharacteristic
563#107—534no—
564#107C22×D5314yes—
565#106—534no—
566#106—534no—
567#103—534no—
568#103—534no—
569#103—534no—
570#103—534no—
571#103C22×D5314yes—
572#103C22×D5314yes—
573#102—534no—
574#102—534no—
575#97—534no—
576#97—534no—
577C4×C8—534no—
578C4×C8C22×D5314yes—
579C24—531no—
580C24—1061no—
581#41—5316no—
582#41—10616no—
583#41—1068no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—5316no—
589C2×Q8—534no—
590C2×Q8—532no—
591C2×Q8—1064no—
592C2×Q8—1068no—
593C2×Q8—10616no—
594C2×Q8—1068no—
595C2×Q8—1061no—
596C2×Q8—1062no—
597C2×Q8C2×C4×D5314yes—
598C2×Q8C2×C4×D5314yes—
599C2×Q8C23×D5312yes—
600C2×Q8C23×D5312yes—
601C2×D4—534no—
602C2×D4—532no—
603C2×D4—1064no—
604C2×D4—1068no—
605C2×D4—1061no—
606C2×D4—1062no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—531no—
612C22×C4—534no—
613C22×C4—532no—
614C22×C4—534no—
615C22×C4—532no—
616C22×C4—531no—
617C22×C4—531no—
618C22×C4—534no—
619C22×C4—534no—
620C22×C4—1064no—
621C22×C4—1068no—
622C22×C4—1064no—
623C22×C4—1064no—
624C22×C4—1068no—
625C22×C4—1064no—
626C22×C4—1061no—
627C22×C4—1064no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1064no—
631C22×C4—2122no—
632C22×C4—2124no—
633C22×C4—2124no—
634C22×C4—2124no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638Q16—5316no—
639Q16C2×C4×D53116yescomplemented
640SD16—5316no—
641SD16—5316no—
642M16—5316no—
643M16—1068no—
644C2×C8—22no—
645C2×C8—534no—
646C2×C8—532no—
647C2×C8—532no—
648C2×C8—1062no—
649C2×C8C2×C4×D5314yes—
650C2×C8C23×D5312yes—
651C2×C8C23×D5312yes—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—532no—
657C4⋊C4—532no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1061no—
663C4⋊C4—1061no—
664C4⋊C4—1064no—
665C4⋊C4C23×D5312yes—
666C4⋊C4C23×D5312yes—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C42—24no—
671C42—24no—
672C42—534no—
673C42—534no—
674C42—532no—
675C42—532no—
676C42—1064no—
677C42—1064no—
678C42—1064no—
679C42—1064no—
680C42—1064no—
681C42D4×D5312yes—
682C42C23×D5312yes—
683C23—534no—
684C23—532no—
685C23—1062no—
686C23—1062no—
687C23—1064no—
688C23—1062no—
689C23—2122no—
690C23—2122no—
691C23C2×D4×D5311yescharacteristic
692Q8—24no—
693Q8—24no—
694Q8—22no—
695Q8—22no—
696Q8—534no—
697Q8—10616no—
698Q8—1064no—
699Q8—1062no—
700Q8C22×C4×D5314yes—
701Q8C22×C4×D5314yes—
702D4—534no—
703D4—10616no—
704D4—1064no—
705D4—1062no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—534no—
716C2×C4—532no—
717C2×C4—538no—
718C2×C4—534no—
719C2×C4—534no—
720C2×C4—532no—
721C2×C4—532no—
722C2×C4—10616no—
723C2×C4—10616no—
724C2×C4—1064no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1068no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—2124no—
732C2×C4—2128no—
733C2×C4—2128no—
734C2×C4—2122no—
735C2×C4—2122no—
736C2×C4—2128no—
737C2×C4#1313324914yesdirect product factor
738C2×C4C22×C4×D5312yes—
739C2×C4C2×D4×D5312yes—
740C2×C4C2×D4×D5311yescharacteristic
741C2×C4C2×D4×D5312yes—
742C2×C4#41×D5312yes—
743C2×C4C24×D5311yescharacteristic
744C8—22no—
745C8—534no—
746C8—1062no—
747C8C22×C4×D5314yes—
748C22—534no—
749C22—1068no—
750C22—1062no—
751C22—1062no—
752C22—1064no—
753C22—2128no—
754C22—2122no—
755C22—2122no—
756C22C4×D4×D5312yes—
757C22C2×#1313324912yes—
758C22#1681142012yes—
759C22C22×D4×D5311yescharacteristic
760C4—24no—
761C4—24no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—534no—
766C4—1064no—
767C4—1062no—
768C4—1062no—
769C4—2122no—
770C4—2122no—
771C4C4×D4×D5312yes—
772C4C2×#1313324914yesdirect product factor
773C4C23×C4×D5311yescharacteristic
774C4C2×#41×D5311yescharacteristic
775C2—1064no—
776C2—2124no—
777C2C4×#1313324914yesdirect product factor
778C2C2×C4×D4×D5311yescharacteristic
779C2C22×#1313324911yescharacteristic
780C2C2×#1681142011yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC2×C4×Q16×C53C2
socleC23×C53C22×D4
prime radicalC22×#11719949C22
cosocleC2×C4×C53C25
hypercenterC2×C4×Q16D53
hypocenterC53C2×C4×#137
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q8×D53C2semidirect
4. C4×#13133249C2direct (N × H)
5. C2×#16810730C2semidirect
6. C2×#16810727C2semidirect
7. C2×#16810726C2semidirect
8. C2×#16810722C2semidirect
9. C2×C4×#11719925C2semidirect
10. C2×C4×#11719913C2semidirect
11. C2×C4×#11719924C2semidirect
12. C2×#16810664C2semidirect
14. C2×#16810630C2semidirect
15. C2×C4×#11719912C2semidirect
16. C2×C4×Q16×C53C2semidirect
19. C2×#13133249C4direct (N × H)
35. C4×Q8×D53C22semidirect
47. #16810730C22semidirect
48. #16810727C22semidirect
49. #16810726C22semidirect
50. #16810722C22semidirect
51. C4×#11719925C22semidirect
52. C4×#11719913C22semidirect
53. C4×#11719924C22semidirect
54. #16810664C22semidirect
58. #16810630C22semidirect
66. C4×#11719912C22semidirect
73. C4×Q16×C53C22semidirect
86. C2×Q8×D53C2×C4semidirect
98. #13133249C2×C4direct (N × H)
99. C2×#11719925C2×C4semidirect
101. C2×#11719913C2×C4semidirect
103. C2×#11719924C2×C4semidirect
106. C2×#11719912C2×C4semidirect
169. C2×Q16×C53C2×C4semidirect
216. Q8×D53C22×C4semidirect
247. Q16×C53C22×C4semidirect
262. #11719925C22×C4semidirect
263. #11719924C22×C4semidirect
289. #11719913C22×C4semidirect
291. #11719912C22×C4semidirect
316. C2×C4×C53#137semidirect
376. C4×C53C2×#137semidirect
394. C2×C4×Q16D53semidirect
401. C2×C53C4×#137semidirect
445. C4×Q16C2×D53semidirect
468. C53C2×C4×#137semidirect
494. C2×Q16C4×D53semidirect
639. Q16C2×C4×D53semidirect
737. C2×C4#13133249direct (N × H)
772. C4C2×#13133249direct (N × H)
777. C2C4×#13133249direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332492
C2×C4×#117199492
C2×C4×Q8×D532
C4×#131332492
C2×#168107302
C2×#168107272
C2×#168107262
C2×#168107222
C2×C4×#117199252
C2×C4×#117199132
C2×C4×#117199242
C2×#168106642
C2×#168106232
C2×#168106302
C2×C4×#117199122
C2×C4×Q16×C532
C2×C4×#13753