Finite Group Databasebeta

← C2×#20283587 #28248243

Subgroups — C2×#20283587 #28248243

Order 13568.

2806 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133238C211yesmaximal, characteristic
2C2×#16811105C211yesmaximal, characteristic, complemented
3C2×#16811102C211yesmaximal, characteristic, complemented
4#20283587C2116yesmaximal, direct product factor
5C2×#16810725C211yesmaximal, characteristic, complemented
6C2×#16810724C211yesmaximal, characteristic, complemented
7C2×#16810722C211yesmaximal, characteristic, complemented
8C2×C4×#11719925C211yesmaximal, characteristic, complemented
9C2×#16810715C211yesmaximal, characteristic, complemented
10C2×C4×#11719922C211yesmaximal, characteristic, complemented
11C2×#16810703C211yesmaximal, characteristic, complemented
12C2×#107×D53C211yesmaximal, characteristic, complemented
13C2×#16810623C211yesmaximal, characteristic, complemented
14C2×#16810621C211yesmaximal, characteristic, complemented
15C2×#16810580C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C2×#13133238C4116yescomplemented
20C2×#13133238C2218yes—
21C22×#11719925C2211yescharacteristic
22C22×#11719913C2211yescharacteristic
23C22×#11719922C2211yescharacteristic
24C22×#11719912C2211yescharacteristic
25C22×C8×D53C2211yescharacteristic
26#16811105—24no—
27#16811105C2218yescomplemented
28#16811102—24no—
29#16811102C2218yescomplemented
30C2×Q8×Dic53C2211yescharacteristic
31C2×C4×Dic106C2211yescharacteristic
32C2×#13133182C2211yescharacteristic
33C2×C4×D212—21no—
34C2×C4×D212C2211yescharacteristic
35C2×D4×Dic53C2211yescharacteristic
36C2×#13133179—21no—
37C2×#13133179C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×#13133177—21no—
40C2×#13133174—21no—
41C2×#13133174C2211yescharacteristic
42C2×#13133173—21no—
43C22×#11719919—21no—
44C2×C4⋊C4×D53—21no—
45C2×C4⋊C4×D53C2211yescharacteristic
46C2×C4⋊C4×D53C2211yescharacteristic
47#16810725C2218yescomplemented
48#16810724C2218yescomplemented
49#16810722C2218yescomplemented
50C4×#11719925C2218yescomplemented
51#16810715C2218yescomplemented
52C4×#11719922C2218yescomplemented
53#16810703C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57#107×D53C2218yescomplemented
58#16810623C2218yescomplemented
59#16810621C2218yescomplemented
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66#16810580C2218yescomplemented
67C2×#13133127C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic
69C2×C8×Dic53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C2×C4×Q8×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C53×#440C2218yescomplemented
74C2×#107×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#97×C53C2211yescharacteristic
78C2×#11719949—22no—
79C2×#11719949—24no—
80C2×#11719949C2×C418yescomplemented
81C2×#11719949C2314yes—
82C2×#11719947—22no—
83C2×#11719947—24no—
84C2×#11719947C2×C418yescomplemented
85C2×#11719947C2314yes—
86C22×Dic106C2311yescharacteristic
87C22×D212—21no—
88C22×D212C2311yescharacteristic
89C22×C22⋊D53—21no—
90C23×Dic53—21no—
91C23×Dic53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53C2311yescharacteristic
98#13133238C2×C4164yescomplemented
99C2×#11719925C2×C418yescomplemented
100C2×#11719925C2314yes—
101C2×#11719913C2×C418yescomplemented
102C2×#11719913C2314yes—
103C2×#11719922C2×C418yescomplemented
104C2×#11719922C2314yes—
105C2×#11719912—24no—
106C2×#11719912C2314yes—
107C22×#88322C2311yescharacteristic
108C22×#88322C2311yescharacteristic
109C2×C8×D53C2×C418yescomplemented
110C2×C8×D53C2314yes—
111Q8×Dic53—22no—
112Q8×Dic53C2314yes—
113C4×Dic106—22no—
114C4×Dic106C2314yes—
115#13133182—22no—
116#13133182C2314yes—
117C4×D212—22no—
118C4×D212—28no—
119C4×D212C2314yes—
120D4×Dic53—22no—
121D4×Dic53C2314yes—
122#13133179—28no—
123#13133179—22no—
124#13133179C2314yes—
125C4×C22⋊D53—28no—
126#13133177—28no—
127#13133174—28no—
128#13133174D414yes—
129#13133174C2314yes—
130#13133173—28no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—28no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C2×#11719919D411yescharacteristic
141C4⋊C4×D53—28no—
142C4⋊C4×D53—22no—
143C4⋊C4×D53—22no—
144C4⋊C4×D53C2314yes—
145C4⋊C4×D53C2314yes—
146C2×C22⋊Dic53—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921D411yescharacteristic
150C2×#11719921D411yescharacteristic
151C2×C4×Dic53—21no—
152C2×C4×Dic53—21no—
153C2×C4×Dic53—21no—
154C2×C4×Dic53C2311yescharacteristic
155#13133151C2314yes—
156#13133150C2314yes—
157#13133150C2314yes—
158#13133142C2314yes—
159#13133141C2314yes—
160#13133140C2314yes—
161#13133139C2314yes—
162#13133138C2314yes—
163#13133137C2314yes—
164#13133127C2314yes—
165C4×#88322C2314yes—
166C8×Dic53C2314yes—
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#107×C53C2314yes—
185#103×C53C2314yes—
186#102×C53C2314yes—
187#97×C53C2314yes—
188C24×C53—21no—
189C23×D53—21no—
190C23×D53C2×D411yescharacteristic
191C2×Q8×C53—21no—
192C2×Q8×C53—22no—
193C2×Q8×C53C22×C414yes—
194C2×Q8×C53C2412yes—
195C2×D4×C53—21no—
196C2×D4×C53—22no—
197C2×D4×C53C22×C414yes—
198C2×D4×C53C2412yes—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—24no—
203C22×C4×C53—82no—
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2411yescharacteristic
207C2×C22⋊D53—28no—
208C2×C22⋊D53—24no—
209C22×Dic53—21no—
210C22×Dic53—28no—
211C22×Dic53—24no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—24no—
215C22×Dic53—82no—
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218C22×Dic53C2×D411yescharacteristic
219#11719949—216no—
220#11719949—28no—
221#11719949C22×C4116yescomplemented
222#11719947—216no—
223#11719947—28no—
224#11719947C22×C4116yescomplemented
225C2×D212—28no—
226C2×D212—24no—
227C2×D212—21no—
228C2×D212—22no—
229C2×D212C22×C414yes—
230C2×D212C2412yes—
231C2×C4×D53—28no—
232C2×C4×D53—24no—
233C2×C4×D53—24no—
234C2×C4×D53—24no—
235C2×C4×D53—24no—
236C2×C4×D53—24no—
237C2×C4×D53—82no—
238C2×C4×D53—82no—
239C2×C4×D53—82no—
240C2×C4×D53—82no—
241C2×C4×D53C22×C414yes—
242C2×C4×D53C2×D412yes—
243C2×C4×D53#4114yes—
244C2×C4×D53C2412yes—
245C2×Dic106—21no—
246C2×Dic106—22no—
247C2×Dic106C22×C414yes—
248C2×Dic106C2412yes—
249SD16×C53C22×C4116yescomplemented
250C2×C8×C53—22no—
251C2×C8×C53C22×C414yes—
252C2×C8×C53C2412yes—
253C2×C8×C53C2412yes—
254C4⋊C4×C53—24no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53C2412yes—
258C4⋊C4×C53C2412yes—
259C22⋊C4×C53—24no—
260C42×C53—24no—
261C42×C53C2×D412yes—
262C42×C53C2412yes—
263C22⋊Dic53—24no—
264#11719925C22×C4116yescomplemented
265#11719922C22×C4116yescomplemented
266#11719921—24no—
267#11719921—24no—
268#11719921C2×D414yes—
269#11719921C2×D414yes—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—24no—
273C4⋊Dic53C2412yes—
274C4⋊Dic53C2412yes—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919C2×D414yes—
280#11719919C2×D414yes—
281C4×Dic53—24no—
282C4×Dic53—24no—
283C4×Dic53—24no—
284C4×Dic53C2×D412yes—
285C4×Dic53C2412yes—
286C2×#88322—22no—
287C2×#88322C22×C414yes—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290#11719913C22×C4116yescomplemented
291#11719912—28no—
292C8×D53C22×C4116yescomplemented
293C23×C53—24no—
294C23×C53—22no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53C22×D411yescharacteristic
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—24no—
301C22×D53—22no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53C4×D414yes—
305C22×D53C22×D412yes—
306Q8×C53—24no—
307Q8×C53—22no—
308Q8×C53C23×C414yes—
309D4×C53—24no—
310D4×C53—22no—
311D4×C53C23×C414yes—
312C2×C4×C53—24no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—84no—
321C2×C4×C53C23×C412yes—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C2×#4112yes—
326C2×C4×C53C2511yescharacteristic
327C22⋊D53—216no—
328C2×Dic53—24no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—216no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—84no—
338C2×Dic53C4×D414yes—
339C2×Dic53C22×D412yes—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342D212—216no—
343D212—24no—
344D212—22no—
345D212C23×C414yes—
346C4×D53—216no—
347C4×D53—84no—
348C4×D53—84no—
349C4×D53—84no—
350C4×D53—84no—
351C4×D53C4×D418yes—
352C4×D53C23×C414yes—
353C4×D53C2×#4114yes—
354Dic106—24no—
355Dic106—22no—
356Dic106C23×C414yes—
357C8×C53—22no—
358C8×C53C23×C414yes—
359#88322—22no—
360#88322C23×C414yes—
361C2×#2951—531nomaximal, Sylow
362C22×C53—24no—
363C22×C53—48no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53C2×C4×D412yes—
367C22×C53#57612yes—
368C22×C53#57812yes—
369C22×C53C23×D411yescharacteristic
370C2×D53—28no—
371C2×D53—22no—
372C2×D53—22no—
373C2×D53—24no—
374C2×D53—48no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53C2×C4×D414yes—
378C4×C53—24no—
379C4×C53—22no—
380C4×C53—22no—
381C4×C53—42no—
382C4×C53—42no—
383C4×C53C2×C4×D412yes—
384C4×C53C24×C411yescharacteristic
385C4×C53C22×#4111yescharacteristic
386Dic53—24no—
387Dic53—22no—
388Dic53—22no—
389Dic53—42no—
390Dic53—42no—
391Dic53C2×C4×D414yes—
392C22×#135—531no—
393C2×#520—531no—
394C2×#520—531no—
395#2951—5316no—
396C2×#440—531no—
397C2×#440—531no—
398C2×#440—531no—
399C2×#440D5311yescharacteristic, complemented
400C2×C4×Q16—531no—
401C2×C4×Q16—531no—
402C2×C4×D8—531no—
403C2×C4×D8—531no—
404C22×#107—531no—
405C2×#417—531no—
406C2×#417—531no—
407C2×#405—531no—
408C2×C53—44no—
409C2×C53#295114yescomplemented
410C2×C53C22×C4×D411yescharacteristic
411C2×C53C2×#57611yescharacteristic
412C2×C53C2×#57811yescharacteristic
413D53—24no—
414D53—44no—
415C22×#41—531no—
416C22×#41—531no—
417C2×#135—5316no—
418C2×#135—538no—
419C22×Q16—531no—
420C22×SD16—531no—
421C22×SD16C2×D5311yescharacteristic
422C22×D8—531no—
423C22×M16—531no—
424C23×C8—531no—
425#520—538no—
426#520—538no—
427#520—1064no—
428#520—1064no—
429C2×C4×Q8—531no—
430C2×C4×Q8—531no—
431C2×C4×Q8—531no—
432C2×C4×Q8C2×D5311yescharacteristic
433C2×C4×D4—531no—
434C2×C4×D4—531no—
435C2×C4×D4—531no—
436C2×C4×D4—1061no—
437C2×C4×D4—1061no—
438C2×C4×D4—1061no—
439C2×C4×D4—1061no—
440C2×C4×D4C2×D5311yescharacteristic
441C2×#117—531no—
442C2×#117—1061no—
443C2×#117—1061no—
444C22×C4⋊C4—531no—
445C22×C4⋊C4—531no—
446C22×C4⋊C4—1061no—
447C22×C4⋊C4—1061no—
448#440—538no—
449#440—538no—
450#440—538no—
451#440C2×D5318yescomplemented
452C4×Q16—538no—
453C4×Q16—538no—
454C4×D8—538no—
455C4×D8—538no—
456C2×#107—531no—
457C2×#107—531no—
458C2×#107—531no—
459C2×#107—538no—
460C2×#107C2×D5311yescharacteristic
461#417—538no—
462#417—538no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#103—531no—
466C2×#103C2×D5311yescharacteristic
467C2×#102—531no—
468C2×#102—531no—
469C2×#102—531no—
470C2×#102C2×D5311yescharacteristic
471#405—538no—
472C2×#97—531no—
473C2×#97C2×D5311yescharacteristic
474C2×C4×C8—531no—
475C2×C4×C8—531no—
476C53C2×#295111yescharacteristic, complemented, Sylow
477C2×#41—538no—
478C2×#41—534no—
479C2×#41—538no—
480C2×#41—534no—
481C2×#41—1062no—
482C2×#41—1064no—
483C2×#41—1062no—
484C2×#41—1064no—
485C22×Q8—531no—
486C22×Q8C22×D5311yescharacteristic
487C22×D4—531no—
488C22×D4—1061no—
489C22×D4—1061no—
490C22×D4C22×D5311yescharacteristic
491C23×C4—21no—
492C23×C4—531no—
493C23×C4—1061no—
494C23×C4—1061no—
495C23×C4—1061no—
496C23×C4—1061no—
497C23×C4—1061no—
498C23×C4—1061no—
499C23×C4—1061no—
500#135—5364no—
501C2×Q16—538no—
502C2×Q16—534no—
503C2×SD16—538no—
504C2×SD16—534no—
505C2×SD16C4×D5318yescomplemented
506C2×SD16C22×D5314yes—
507C2×D8—538no—
508C2×D8—534no—
509C2×M16—534no—
510C2×M16—1064no—
511C22×C8—531no—
512C22×C8—538no—
513C22×C8—534no—
514C22×C8—531no—
515C22×C8C22×D5311yescharacteristic
516C22×C8C22×D5311yescharacteristic
517C4×Q8—22no—
518C4×Q8—534no—
519C4×Q8—534no—
520C4×Q8—534no—
521C4×Q8—1062no—
522C4×Q8—1062no—
523C4×Q8—1062no—
524C4×Q8C22×D5314yes—
525C4×D4—22no—
526C4×D4—534no—
527C4×D4—534no—
528C4×D4—534no—
529C4×D4—1068no—
530C4×D4—1062no—
531C4×D4—1062no—
532C4×D4—1068no—
533C4×D4—1068no—
534C4×D4—1068no—
535C4×D4—1062no—
536C4×D4C22×D5314yes—
537#117—534no—
538#117—534no—
539#117—1068no—
540#117—1068no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—531no—
543C2×C4⋊C4—531no—
544C2×C4⋊C4—531no—
545C2×C4⋊C4—531no—
546C2×C4⋊C4—534no—
547C2×C4⋊C4—534no—
548C2×C4⋊C4—1068no—
549C2×C4⋊C4—1062no—
550C2×C4⋊C4—1062no—
551C2×C4⋊C4—1068no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4—1061no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4C22×D5311yescharacteristic
558C2×C4⋊C4C22×D5311yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—531no—
561C2×C22⋊C4—531no—
562C2×C22⋊C4—1061no—
563C2×C22⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C42—21no—
566C2×C42—531no—
567C2×C42—1061no—
568C2×C42—1061no—
569C2×C42—1061no—
570C2×C42C22×D5311yescharacteristic
571#107—534no—
572#107—534no—
573#107—534no—
574#107C22×D5314yes—
575#103—534no—
576#103—534no—
577#103—534no—
578#103C22×D5314yes—
579#102—534no—
580#102—534no—
581#102—534no—
582#102C22×D5314yes—
583#97—534no—
584#97C22×D5314yes—
585C4×C8—534no—
586C4×C8—534no—
587C24—21no—
588C24—531no—
589C24—1061no—
590#41—5316no—
591#41—5316no—
592#41—10616no—
593#41—1068no—
594#41—10616no—
595#41—1068no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—534no—
599C2×Q8—532no—
600C2×Q8—1061no—
601C2×Q8—1062no—
602C2×Q8C2×C4×D5314yes—
603C2×Q8C23×D5312yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—534no—
607C2×D4—532no—
608C2×D4—1064no—
609C2×D4—1068no—
610C2×D4—1064no—
611C2×D4—1068no—
612C2×D4—1061no—
613C2×D4—1062no—
614C2×D4C2×C4×D5314yes—
615C2×D4C23×D5312yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—531no—
622C22×C4—534no—
623C22×C4—532no—
624C22×C4—534no—
625C22×C4—532no—
626C22×C4—531no—
627C22×C4—531no—
628C22×C4—1064no—
629C22×C4—1068no—
630C22×C4—1064no—
631C22×C4—1064no—
632C22×C4—1064no—
633C22×C4—1064no—
634C22×C4—1068no—
635C22×C4—1064no—
636C22×C4—1061no—
637C22×C4—1061no—
638C22×C4—1061no—
639C22×C4—1064no—
640C22×C4—4242no—
641C22×C4—4242no—
642C22×C4—4242no—
643C22×C4—4242no—
644C22×C4—4242no—
645C22×C4D4×D5311yescharacteristic
646C22×C4D4×D5311yescharacteristic
647C22×C4C23×D5311yescharacteristic
648Q16—5316no—
649SD16—5316no—
650SD16C2×C4×D53116yescomplemented
651D8—5316no—
652M16—1068no—
653C2×C8—22no—
654C2×C8—534no—
655C2×C8—532no—
656C2×C8—5316no—
657C2×C8—532no—
658C2×C8—1062no—
659C2×C8C2×C4×D5314yes—
660C2×C8C23×D5312yes—
661C2×C8C23×D5312yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—534no—
666C4⋊C4—534no—
667C4⋊C4—532no—
668C4⋊C4—532no—
669C4⋊C4—1064no—
670C4⋊C4—1064no—
671C4⋊C4—1064no—
672C4⋊C4—1064no—
673C4⋊C4—1061no—
674C4⋊C4—1061no—
675C4⋊C4—1064no—
676C4⋊C4C23×D5312yes—
677C4⋊C4C23×D5312yes—
678C22⋊C4—24no—
679C22⋊C4—534no—
680C22⋊C4—534no—
681C22⋊C4—1064no—
682C22⋊C4—1064no—
683C22⋊C4—1064no—
684C42—24no—
685C42—532no—
686C42—532no—
687C42—1064no—
688C42—1064no—
689C42—1064no—
690C42D4×D5312yes—
691C42C23×D5312yes—
692C23—24no—
693C23—22no—
694C23—42no—
695C23—42no—
696C23—534no—
697C23—532no—
698C23—1062no—
699C23—1062no—
700C23—1064no—
701C23—1062no—
702C23—2122no—
703C23—2122no—
704C23C2×D4×D5311yescharacteristic
705Q8—24no—
706Q8—22no—
707Q8—534no—
708Q8—1064no—
709Q8—1062no—
710Q8C22×C4×D5314yes—
711D4—24no—
712D4—22no—
713D4—534no—
714D4—10616no—
715D4—10616no—
716D4—1064no—
717D4—1062no—
718D4C22×C4×D5314yes—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—84no—
728C2×C4—534no—
729C2×C4—532no—
730C2×C4—538no—
731C2×C4—534no—
732C2×C4—534no—
733C2×C4—532no—
734C2×C4—532no—
735C2×C4—10616no—
736C2×C4—10616no—
737C2×C4—1064no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—4244no—
744C2×C4—4244no—
745C2×C4—4244no—
746C2×C4—4244no—
747C2×C4—4244no—
748C2×C4—2122no—
749C2×C4—2122no—
750C2×C4C22×C4×D5312yes—
751C2×C4C2×D4×D5312yes—
752C2×C4C2×D4×D5312yes—
753C2×C4C2×D4×D5311yescharacteristic
754C2×C4#41×D5312yes—
755C2×C4C24×D5311yescharacteristic
756C8—22no—
757C8—534no—
758C8—1062no—
759C8C22×C4×D5314yes—
760C22—24no—
761C22—42no—
762C22—48no—
763C22—42no—
764C22—534no—
765C22—1062no—
766C22—1068no—
767C22—1062no—
768C22—1064no—
769C22—2122no—
770C22—2128no—
771C22—2122no—
772C22C4×D4×D5312yes—
773C22#1681142712yes—
774C22#1681143912yes—
775C22C22×D4×D5311yescharacteristic
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—534no—
782C4—1064no—
783C4—1062no—
784C4—1062no—
785C4—2122no—
786C4—2122no—
787C4C4×D4×D5312yes—
788C4C23×C4×D5311yescharacteristic
789C4C2×#41×D5311yescharacteristic
790C2—44no—
791C2—1064no—
792C2—2124no—
793C2#2028358714yesdirect product factor
794C2C2×C4×D4×D5311yescharacteristic
795C2C2×#1681142711yescharacteristic
796C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
prime radicalC22×#13133238C2
cosocleC2×C4×C53C25
hypercenterC2×#440D53
hypocenterC53C2×#2951
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#16811105C2semidirect
3. C2×#16811102C2semidirect
4. #20283587C2direct (N × H)
5. C2×#16810725C2semidirect
6. C2×#16810724C2semidirect
7. C2×#16810722C2semidirect
8. C2×C4×#11719925C2semidirect
9. C2×#16810715C2semidirect
10. C2×C4×#11719922C2semidirect
11. C2×#16810703C2semidirect
12. C2×#107×D53C2semidirect
13. C2×#16810623C2semidirect
14. C2×#16810621C2semidirect
15. C2×#16810580C2semidirect
16. C2×C53×#440C2semidirect
19. C2×#13133238C4semidirect
27. #16811105C22semidirect
29. #16811102C22semidirect
47. #16810725C22semidirect
48. #16810724C22semidirect
49. #16810722C22semidirect
50. C4×#11719925C22semidirect
51. #16810715C22semidirect
52. C4×#11719922C22semidirect
53. #16810703C22semidirect
57. #107×D53C22semidirect
58. #16810623C22semidirect
59. #16810621C22semidirect
66. #16810580C22semidirect
73. C53×#440C22semidirect
80. C2×#11719949C2×C4semidirect
84. C2×#11719947C2×C4semidirect
98. #13133238C2×C4semidirect
99. C2×#11719925C2×C4semidirect
101. C2×#11719913C2×C4semidirect
103. C2×#11719922C2×C4semidirect
109. C2×C8×D53C2×C4semidirect
170. C2×SD16×C53C2×C4semidirect
221. #11719949C22×C4semidirect
224. #11719947C22×C4semidirect
249. SD16×C53C22×C4semidirect
264. #11719925C22×C4semidirect
265. #11719922C22×C4semidirect
290. #11719913C22×C4semidirect
292. C8×D53C22×C4semidirect
399. C2×#440D53semidirect
409. C2×C53#2951semidirect
451. #440C2×D53semidirect
476. C53C2×#2951semidirect
505. C2×SD16C4×D53semidirect
650. SD16C2×C4×D53semidirect
793. C2#20283587direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332382
C2×#168111052
C2×#168111022
#202835872
C2×#168107252
C2×#168107242
C2×#168107222
C2×C4×#117199252
C2×#168107152
C2×C4×#117199222
C2×#168107032
C2×#107×D532
C2×#168106232
C2×#168106212
C2×#168105802
C2×C53×#4402
C2×#295153