Finite Group Databasebeta

← C2×C4×#13133246 #28248161

Subgroups — C2×C4×#13133246 #28248161

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×#13133246C211yesmaximal, characteristic
2C2×C4×#11719947C211yesmaximal, characteristic
3C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
4C4×#13133246C2116yesmaximal, direct product factor
5C2×#16810729C211yesmaximal, characteristic, complemented
6C2×#16810727C211yesmaximal, characteristic, complemented
7C2×#16810724C211yesmaximal, characteristic, complemented
8C2×#16810720C211yesmaximal, characteristic, complemented
9C2×C4×Dic212C211yesmaximal, characteristic, complemented
10C2×C4×#11719925C211yesmaximal, characteristic, complemented
11C2×C4×#11719923C211yesmaximal, characteristic, complemented
12C2×#16810662C211yesmaximal, characteristic, complemented
13C2×#16810621C211yesmaximal, characteristic
14C2×#16810630C211yesmaximal, characteristic, complemented
15C2×C4×#11719912C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C53C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C2×#13133246C4116yesdirect product factor
20C2×#13133246C2218yes—
21C22×Dic212C2211yescharacteristic
22C22×#11719925C2211yescharacteristic
23C22×#11719923C2211yescharacteristic
24C22×#11719912C2211yescharacteristic
25C22×#11719912C2211yescharacteristic
26C4×#11719947—24no—
27C4×#11719947C2218yes—
28C2×Q8×Dic53C2211yescharacteristic
29C2×C4×Dic106—21no—
30C2×C4×Dic106C2211yescharacteristic
31C2×C4×Dic106C2211yescharacteristic
32C2×#13133182—21no—
33C2×#13133182C2211yescharacteristic
34C2×#13133182C2211yescharacteristic
35C4×Q8×D53—24no—
36C4×Q8×D53C2218yescomplemented
37C2×D4×Dic53C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×#13133177—21no—
40C2×#13133175C2211yescharacteristic
41C2×#13133173—21no—
42C2×C4⋊C4×D53—21no—
43C2×C4⋊C4×D53C2211yescharacteristic
44C22×C4×Dic53—21no—
45C2×C42×D53—21no—
46C2×C42×D53C2211yescharacteristic
47#16810729C2218yescomplemented
48#16810727C2218yescomplemented
49#16810724C2218yescomplemented
50#16810720C2218yescomplemented
51C4×Dic212C2218yescomplemented
52C4×#11719925C2218yescomplemented
53C4×#11719923C2218yescomplemented
54#16810662C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58#16810630C2218yescomplemented
59#16810621C2218yes—
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C4×#11719912C2218yescomplemented
67C2×#13133127C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C2×C4×#88322C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C2×C4×Q8×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C4×SD16×C53C2218yescomplemented
74C2×#106×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×C4×C8×C53C2211yescharacteristic
78C2×#11719947—22no—
79C2×#11719947—24no—
80C2×#11719947C2×C418yes—
81C2×#11719947C2314yes—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C22×Dic106C2311yescharacteristic
85C2×Q8×D53—22no—
86C2×Q8×D53—24no—
87C2×Q8×D53C2×C418yescomplemented
88C2×Q8×D53C2314yes—
89C22×C22⋊D53—21no—
90C23×Dic53—21no—
91C23×Dic53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53D411yescharacteristic
95C22×C4×D53D411yescharacteristic
96C22×C4×D53C2311yescharacteristic
97#13133246C2×C4164yesdirect product factor
98C2×Dic212C2×C418yescomplemented
99C2×Dic212C2314yes—
100C2×#11719925C2×C418yescomplemented
101C2×#11719925C2314yes—
102C2×#11719923C2×C418yescomplemented
103C2×#11719923C2314yes—
104C2×#11719912—24no—
105C2×#11719912C2×C418yescomplemented
106C2×#11719912C2314yes—
107C2×#11719912C2314yes—
108C22×#88322C2311yescharacteristic
109C22×#88322C2311yescharacteristic
110Q8×Dic53—22no—
111Q8×Dic53C2314yes—
112C4×Dic106—22no—
113C4×Dic106—22no—
114C4×Dic106—28no—
115C4×Dic106C2314yes—
116C4×Dic106C2314yes—
117#13133182—22no—
118#13133182—28no—
119#13133182—22no—
120#13133182C2314yes—
121#13133182C2314yes—
122D4×Dic53—22no—
123D4×Dic53C2314yes—
124C4×C22⋊D53—28no—
125#13133177—28no—
126#13133175—22no—
127#13133175C2314yes—
128#13133173—28no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C4⋊C4×D53—28no—
138C4⋊C4×D53—22no—
139C4⋊C4×D53C2314yes—
140C2×C22⋊Dic53—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—28no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147C2×C4×Dic53—21no—
148C2×C4×Dic53—21no—
149C2×C4×Dic53D411yescharacteristic
150C2×C4×Dic53D411yescharacteristic
151C2×C4×Dic53C2311yescharacteristic
152C42×D53—28no—
153C42×D53D414yes—
154C42×D53C2314yes—
155#13133151C2314yes—
156#13133150C2314yes—
157#13133148C2314yes—
158#13133142C2314yes—
159#13133142C2314yes—
160#13133141C2314yes—
161#13133140C2314yes—
162#13133140C2314yes—
163#13133138C2314yes—
164#13133127C2314yes—
165#13133127C2314yes—
166C4×#88322C2314yes—
167C22×Q8×C53C2311yescharacteristic
168C22×D4×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C2×SD16×C53C2×C418yescomplemented
171C2×SD16×C53C2314yes—
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C4×Q8×C53—22no—
175C4×Q8×C53C2314yes—
176C4×D4×C53—22no—
177C4×D4×C53C2314yes—
178C2×C4⋊C4×C53—21no—
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182C2×C42×C53—21no—
183C2×C42×C53C2311yescharacteristic
184#106×C53C2314yes—
185#103×C53C2314yes—
186#102×C53C2314yes—
187C4×C8×C53C2314yes—
188C24×C53—21no—
189C23×D53C2×D411yescharacteristic
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53C22×C414yes—
193C2×Q8×C53C2412yes—
194C2×D4×C53—21no—
195C2×D4×C53—22no—
196C2×D4×C53C22×C414yes—
197C2×D4×C53C2412yes—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—44no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—28no—
207C2×C22⋊D53—24no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—28no—
211C22×Dic53—24no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—44no—
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C22×Dic53C2×D411yescharacteristic
219Q8×D53—216no—
220Q8×D53—28no—
221Q8×D53C22×C4116yescomplemented
222#11719947—216no—
223#11719947—28no—
224#11719947C22×C4116yes—
225C2×C4×D53—28no—
226C2×C4×D53—24no—
227C2×C4×D53—24no—
228C2×C4×D53—24no—
229C2×C4×D53—42no—
230C2×C4×D53—44no—
231C2×C4×D53C22×C414yes—
232C2×C4×D53C2×D414yes—
233C2×C4×D53C2×D414yes—
234C2×C4×D53C2×D412yes—
235C2×C4×D53#4114yes—
236C2×C4×D53C2412yes—
237C2×Dic106—21no—
238C2×Dic106—21no—
239C2×Dic106—22no—
240C2×Dic106—22no—
241C2×Dic106—28no—
242C2×Dic106—24no—
243C2×Dic106C22×C414yes—
244C2×Dic106C22×C414yes—
245C2×Dic106C2412yes—
246C2×Dic106C2412yes—
247SD16×C53C22×C4116yescomplemented
248C2×C8×C53—22no—
249C2×C8×C53C22×C414yes—
250C2×C8×C53C2412yes—
251C2×C8×C53C2412yes—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53C2412yes—
256C4⋊C4×C53C2412yes—
257C22⋊C4×C53—24no—
258C42×C53—24no—
259C42×C53C2×D412yes—
260C42×C53C2412yes—
261C22⋊Dic53—24no—
262#11719925C22×C4116yescomplemented
263#11719923C22×C4116yescomplemented
264#11719921—24no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53C2412yes—
269C4⋊Dic53C2412yes—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275C4×Dic53—24no—
276C4×Dic53—24no—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C4×Dic53—24no—
280C4×Dic53—24no—
281C4×Dic53C2×D412yes—
282C4×Dic53C2×D414yes—
283C4×Dic53C2×D414yes—
284C4×Dic53C2412yes—
285C2×#88322—22no—
286C2×#88322C22×C414yes—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289Dic212C22×C4116yescomplemented
290#11719912—28no—
291#11719912C22×C4116yescomplemented
292C23×C53—24no—
293C23×C53—22no—
294C23×C53—42no—
295C23×C53—42no—
296C23×C53C22×D411yescharacteristic
297C22×D53—22no—
298C22×D53—22no—
299C22×D53C4×D414yes—
300C22×D53C22×D412yes—
301Q8×C53—24no—
302Q8×C53—22no—
303Q8×C53C23×C414yes—
304D4×C53—24no—
305D4×C53—22no—
306D4×C53C23×C414yes—
307C2×C4×C53—24no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—48no—
315C2×C4×C53#13714yescomplemented
316C2×C4×C53C23×C412yes—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D411yescharacteristic
319C2×C4×C53C22×D412yes—
320C2×C4×C53C2×#4112yes—
321C2×C4×C53C2511yescharacteristic
322C22⋊D53—216no—
323C2×Dic53—24no—
324C2×Dic53—24no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—216no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—48no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53C4×D414yes—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338C2×Dic53C22×D412yes—
339C4×D53—216no—
340C4×D53—28no—
341C4×D53—44no—
342C4×D53—48no—
343C4×D53C4×D418yes—
344C4×D53C23×C414yes—
345C4×D53C2×#4114yes—
346Dic106—24no—
347Dic106—24no—
348Dic106—22no—
349Dic106—22no—
350Dic106—216no—
351Dic106C23×C414yes—
352Dic106C23×C414yes—
353C8×C53—22no—
354C8×C53C23×C414yes—
355#88322—22no—
356#88322C23×C414yes—
357C2×C4×#137—531nomaximal, Sylow
358C22×C53—24no—
359C22×C53—48no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53C2×C4×D412yes—
363C22×C53C2×#13712yes—
364C22×C53#57512yes—
365C22×C53C23×D411yescharacteristic
366C2×D53—28no—
367C2×D53—22no—
368C2×D53—22no—
369C2×D53C2×C4×D414yes—
370C4×C53—24no—
371C4×C53—22no—
372C4×C53—42no—
373C4×C53—42no—
374C4×C53C2×C4×D412yes—
375C4×C53C2×#13714yescomplemented
376C4×C53C24×C411yescharacteristic
377C4×C53C22×#4111yescharacteristic
378Dic53—24no—
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×Q16—531no—
395C2×C4×SD16—531no—
396C2×C4×SD16D5311yescharacteristic, complemented
397C2×#428—531no—
398C2×#417—531no—
399C2×#419—531no—
400C2×C4×M16—531no—
401C2×C53—44no—
402C2×C53C4×#13714yescomplemented
403C2×C53C22×C4×D411yescharacteristic
404C2×C53C22×#13711yescharacteristic
405C2×C53C2×#57511yescharacteristic
406D53—24no—
407C22×#41—531no—
408C23×Q8—531no—
409C2×#137—5316no—
410C2×#137—538no—
411C22×Q16—531no—
412C22×Q16—531no—
413C22×SD16—531no—
414C22×SD16C2×D5311yescharacteristic
415C22×M16—531no—
416C22×M16—531no—
417C4×#41—538no—
418C4×#41—1064no—
419C2×C4×Q8—531no—
420C2×C4×Q8—538no—
421C2×C4×Q8—531no—
422C2×C4×Q8—531no—
423C2×C4×Q8—531no—
424C2×C4×Q8—531no—
425C2×C4×Q8—1061no—
426C2×C4×Q8—1061no—
427C2×C4×Q8—1064no—
428C2×C4×Q8C2×D5311yescharacteristic
429C2×C4×D4—531no—
430C2×C4×D4—1061no—
431C2×C4×D4—1061no—
432C2×C4×D4C2×D5311yescharacteristic
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×Q16—538no—
446C4×SD16—538no—
447C4×SD16C2×D5318yescomplemented
448#428—538no—
449C2×#107—531no—
450C2×#107—531no—
451C2×#106—531no—
452C2×#106C2×D5311yescharacteristic
453#419—538no—
454#417—538no—
455C2×#103—531no—
456C2×#103—531no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103C2×D5311yescharacteristic
461C2×#102—531no—
462C2×#102C2×D5311yescharacteristic
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—531no—
477C22×Q8—1061no—
478C22×Q8—1062no—
479C22×Q8—1064no—
480C22×Q8C22×D5311yescharacteristic
481C22×D4—1061no—
482C22×D4C22×D5311yescharacteristic
483C23×C4—21no—
484C23×C4—531no—
485C23×C4—531no—
486C23×C4—531no—
487C23×C4—1061no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4—1061no—
491#137—5364no—
492C2×Q16—538no—
493C2×Q16—534no—
494C2×Q16—538no—
495C2×Q16—534no—
496C2×SD16—538no—
497C2×SD16—534no—
498C2×SD16C4×D5318yescomplemented
499C2×SD16C22×D5314yes—
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—534no—
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×Q8—1062no—
521C4×Q8C22×D5314yes—
522C4×D4—22no—
523C4×D4—534no—
524C4×D4—1062no—
525C4×D4—1068no—
526C4×D4—1068no—
527C4×D4C22×D5314yes—
528#117—534no—
529#117—1068no—
530#117—1062no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—531no—
534C2×C4⋊C4—534no—
535C2×C4⋊C4—1062no—
536C2×C4⋊C4—1068no—
537C2×C4⋊C4—1061no—
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—21no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C42—21no—
549C2×C42—531no—
550C2×C42—531no—
551C2×C42—531no—
552C2×C42—534no—
553C2×C42—534no—
554C2×C42—1068no—
555C2×C42—1068no—
556C2×C42—1061no—
557C2×C42—1061no—
558C2×C42—1061no—
559C2×C42—1061no—
560C2×C42—1061no—
561C2×C42—1061no—
562C2×C42C22×D5311yescharacteristic
563#107—534no—
564#107—534no—
565#106—534no—
566#106C22×D5314yes—
567#103—534no—
568#103—534no—
569#103—534no—
570#103—534no—
571#103—534no—
572#103C22×D5314yes—
573#102—534no—
574#102C22×D5314yes—
575#97—534no—
576#97—534no—
577C4×C8—534no—
578C4×C8C22×D5314yes—
579C24—21no—
580C24—531no—
581#41—5316no—
582#41—10616no—
583#41—1068no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—5316no—
587C2×Q8—534no—
588C2×Q8—534no—
589C2×Q8—532no—
590C2×Q8—532no—
591C2×Q8—1064no—
592C2×Q8—1068no—
593C2×Q8—10616no—
594C2×Q8—1068no—
595C2×Q8—1061no—
596C2×Q8—1061no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8C2×C4×D5314yes—
600C2×Q8C23×D5312yes—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—1064no—
604C2×D4—1068no—
605C2×D4C2×C4×D5314yes—
606C2×D4C23×D5312yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—44no—
612C22×C4—531no—
613C22×C4—534no—
614C22×C4—532no—
615C22×C4—534no—
616C22×C4—532no—
617C22×C4—531no—
618C22×C4—531no—
619C22×C4—534no—
620C22×C4—534no—
621C22×C4—1064no—
622C22×C4—1068no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1068no—
626C22×C4—1064no—
627C22×C4—1061no—
628C22×C4—1061no—
629C22×C4—1064no—
630C22×C4—1061no—
631C22×C4—1061no—
632C22×C4—2122no—
633C22×C4—2124no—
634C22×C4—2124no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638Q16—5316no—
639Q16—5316no—
640SD16—5316no—
641SD16C2×C4×D53116yescomplemented
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—21no—
654C4⋊C4—21no—
655C4⋊C4—532no—
656C4⋊C4—532no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1061no—
662C4⋊C4—1061no—
663C4⋊C4—1064no—
664C4⋊C4—1064no—
665C4⋊C4C23×D5312yes—
666C4⋊C4C23×D5312yes—
667C22⋊C4—24no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C42—24no—
671C42—534no—
672C42—534no—
673C42—532no—
674C42—532no—
675C42—1064no—
676C42—1064no—
677C42—1064no—
678C42—1064no—
679C42—1064no—
680C42—1064no—
681C42D4×D5312yes—
682C42C23×D5312yes—
683C23—24no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—534no—
688C23—532no—
689C23—1062no—
690C23—1062no—
691C23C2×D4×D5311yescharacteristic
692Q8—24no—
693Q8—22no—
694Q8—534no—
695Q8—534no—
696Q8—10616no—
697Q8—1064no—
698Q8—1064no—
699Q8—1062no—
700Q8—1062no—
701Q8C22×C4×D5314yes—
702D4—24no—
703D4—22no—
704D4—10616no—
705D4C22×C4×D5314yes—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—48no—
714C2×C4—534no—
715C2×C4—532no—
716C2×C4—538no—
717C2×C4—534no—
718C2×C4—534no—
719C2×C4—532no—
720C2×C4—532no—
721C2×C4—10616no—
722C2×C4—10616no—
723C2×C4—1064no—
724C2×C4—1064no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1068no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—2124no—
733C2×C4—2128no—
734C2×C4—2128no—
735C2×C4—2122no—
736C2×C4—2122no—
737C2×C4#1313324614yesdirect 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—24no—
749C22—48no—
750C22—42no—
751C22—42no—
752C22—534no—
753C22—1068no—
754C22—1062no—
755C22—1062no—
756C22C4×D4×D5312yes—
757C22C2×#1313324612yes—
758C22#1681142012yes—
759C22C22×D4×D5311yescharacteristic
760C4—24no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—534no—
765C4—1064no—
766C4—1064no—
767C4—1062no—
768C4—1062no—
769C4—2122no—
770C4—2122no—
771C4C4×D4×D5312yes—
772C4C2×#1313324614yesdirect product factor
773C4C23×C4×D5311yescharacteristic
774C4C2×#41×D5311yescharacteristic
775C2—44no—
776C2—1064no—
777C2C4×#1313324614yesdirect product factor
778C2C2×C4×D4×D5311yescharacteristic
779C2C22×#1313324611yescharacteristic
780C2C2×#1681142011yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC2×C4×SD16×C53C2
socleC23×C53C22×D4
prime radicalC22×#11719947C22
cosocleC2×C4×C53C25
hypercenterC2×C4×SD16D53
hypocenterC53C2×C4×#137
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q8×D53C2semidirect
4. C4×#13133246C2direct (N × H)
5. C2×#16810729C2semidirect
6. C2×#16810727C2semidirect
7. C2×#16810724C2semidirect
8. C2×#16810720C2semidirect
9. C2×C4×Dic212C2semidirect
10. C2×C4×#11719925C2semidirect
11. C2×C4×#11719923C2semidirect
12. C2×#16810662C2semidirect
14. C2×#16810630C2semidirect
15. C2×C4×#11719912C2semidirect
16. C2×C4×SD16×C53C2semidirect
19. C2×#13133246C4direct (N × H)
36. C4×Q8×D53C22semidirect
47. #16810729C22semidirect
48. #16810727C22semidirect
49. #16810724C22semidirect
50. #16810720C22semidirect
51. C4×Dic212C22semidirect
52. C4×#11719925C22semidirect
53. C4×#11719923C22semidirect
54. #16810662C22semidirect
58. #16810630C22semidirect
66. C4×#11719912C22semidirect
73. C4×SD16×C53C22semidirect
87. C2×Q8×D53C2×C4semidirect
97. #13133246C2×C4direct (N × H)
98. C2×Dic212C2×C4semidirect
100. C2×#11719925C2×C4semidirect
102. C2×#11719923C2×C4semidirect
105. C2×#11719912C2×C4semidirect
170. C2×SD16×C53C2×C4semidirect
221. Q8×D53C22×C4semidirect
247. SD16×C53C22×C4semidirect
262. #11719925C22×C4semidirect
263. #11719923C22×C4semidirect
289. Dic212C22×C4semidirect
291. #11719912C22×C4semidirect
315. C2×C4×C53#137semidirect
375. C4×C53C2×#137semidirect
396. C2×C4×SD16D53semidirect
402. C2×C53C4×#137semidirect
447. C4×SD16C2×D53semidirect
468. C53C2×C4×#137semidirect
498. C2×SD16C4×D53semidirect
641. SD16C2×C4×D53semidirect
737. C2×C4#13133246direct (N × H)
772. C4C2×#13133246direct (N × H)
777. C2C4×#13133246direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332462
C2×C4×#117199472
C2×C4×Q8×D532
C4×#131332462
C2×#168107292
C2×#168107272
C2×#168107242
C2×#168107202
C2×C4×Dic2122
C2×C4×#117199252
C2×C4×#117199232
C2×#168106622
C2×#168106212
C2×#168106302
C2×C4×#117199122
C2×C4×SD16×C532
C2×C4×#13753