Finite Group Databasebeta

← C2×#20283569 #28248223

Subgroups — C2×#20283569 #28248223

Order 13568.

2870 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D53C211yesmaximal, characteristic
2C2×#16811099C211yesmaximal, characteristic, complemented
3C2×#16811095C211yesmaximal, characteristic
4#20283569C2116yesmaximal, direct product factor
5C2×#16810726C211yesmaximal, characteristic, complemented
6C2×#16810723C211yesmaximal, characteristic, complemented
7C2×#16810721C211yesmaximal, characteristic, complemented
8C2×#16810720C211yesmaximal, characteristic, complemented
9C2×C4×#11719913C211yesmaximal, characteristic, complemented
10C2×SD16×Dic53C211yesmaximal, characteristic, complemented
11C2×#16810710C211yesmaximal, characteristic, complemented
12C2×#16810658C211yesmaximal, characteristic, complemented
13C2×#16810630C211yesmaximal, characteristic, complemented
14C2×#16810626C211yesmaximal, characteristic
15C2×#16810577C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C53C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×D4×D53C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C2×SD16×D53C4116yescomplemented
23C2×SD16×D53C2218yes—
24C22×#11719912C2211yescharacteristic
25C22×C8×D53C2211yescharacteristic
26#16811099—24no—
27#16811099C2218yescomplemented
28#16811095—24no—
29#16811095C2218yes—
30C2×Q8×Dic53C2211yescharacteristic, complemented
31C2×C4×Dic106—21no—
32C2×C4×Dic106C2211yescharacteristic, complemented
33C2×#13133182—21no—
34C2×#13133182C2211yescharacteristic, complemented
35C2×C4×D212C2211yescharacteristic
36C2×D4×Dic53C2211yescharacteristic
37C2×#13133179C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×#13133177—21no—
40C2×#13133175—21no—
41C2×#13133175C2211yescharacteristic
42C2×#13133175C2211yescharacteristic
43C2×#13133174—21no—
44C2×#13133174C2211yescharacteristic
45C22×#11719921—21no—
46C2×C22⋊C4×D53—21no—
47#16810726C2218yescomplemented
48#16810723C2218yescomplemented
49#16810721C2218yescomplemented
50#16810720C2218yescomplemented
51C4×#11719913C2218yescomplemented
52SD16×Dic53C2218yescomplemented
53#16810710C2218yescomplemented
54#16810658C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133149C2211yescharacteristic, complemented
58#16810630C2218yescomplemented
59#16810626C2218yes—
60C2×#13133142C2211yescharacteristic, complemented
61C2×#13133141C2211yescharacteristic, complemented
62C2×#13133140C2211yescharacteristic, complemented
63C2×#13133139C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66#16810577C2218yescomplemented
67C2×#13133128C2211yescharacteristic, complemented
68C2×#13133127C2211yescharacteristic, complemented
69C2×C8×Dic53C2211yescharacteristic, complemented
70C22×SD16×C53C2211yescharacteristic
71C2×C4×Q8×C53C2211yescharacteristic, complemented
72C2×C4×D4×C53C2211yescharacteristic
73C4×SD16×C53C2218yescomplemented
74C2×#106×C53C2211yescharacteristic, complemented
75C2×#103×C53C2211yescharacteristic, complemented
76C2×#102×C53C2211yescharacteristic
77C2×C4×C8×C53C2211yescharacteristic, complemented
78C24×D53—21no—
79C22×Dic106—21no—
80C22×Dic106C2311yescharacteristic
81C2×Q8×D53—22no—
82C2×Q8×D53—24no—
83C2×Q8×D53C2×C418yescomplemented
84C2×Q8×D53C2314yes—
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C2×D4×D53—22no—
88C2×D4×D53—24no—
89C2×D4×D53C2×C418yes—
90C2×D4×D53C2314yes—
91C23×Dic53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53—21no—
95C22×C4×D53C2311yescharacteristic
96C2×#11719913C2×C418yescomplemented
97C2×#11719913C2314yes—
98C2×#11719923C2×C418yescomplemented
99C2×#11719923C2314yes—
100C2×#11719924C2×C418yescomplemented
101C2×#11719924C2314yes—
102SD16×D53C2×C4164yescomplemented
103C2×#11719912—24no—
104C2×#11719912C2314yes—
105C22×#88322C2311yescharacteristic
106C22×#88322C2311yescharacteristic
107C2×C8×D53C2×C418yescomplemented
108C2×C8×D53C2314yes—
109Q8×Dic53—22no—
110Q8×Dic53C2314yescomplemented
111C4×Dic106—22no—
112C4×Dic106—28no—
113C4×Dic106C2314yescomplemented
114#13133182—28no—
115#13133182—22no—
116#13133182C2314yescomplemented
117C4×D212—22no—
118C4×D212C2314yes—
119D4×Dic53—22no—
120D4×Dic53C2314yes—
121#13133179—22no—
122#13133179C2314yes—
123C4×C22⋊D53—28no—
124#13133177—28no—
125#13133175—28no—
126#13133175—22no—
127#13133175—22no—
128#13133175C2314yes—
129#13133175C2314yes—
130#13133174—28no—
131#13133174D414yes—
132#13133174C2314yes—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53C2311yescharacteristic
135C2×C4⋊Dic53C2311yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919D411yescharacteristic
139C2×#11719919D411yescharacteristic
140C2×C22⋊Dic53—21no—
141C2×#11719921—28no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921D411yescharacteristic
147C2×#11719921D411yescharacteristic
148C22⋊C4×D53—28no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53—21no—
153C2×C4×Dic53—21no—
154C2×C4×Dic53C2311yescharacteristic
155#13133150C2314yescomplemented
156#13133150C2314yescomplemented
157#13133149C2314yescomplemented
158#13133142C2314yescomplemented
159#13133141C2314yescomplemented
160#13133140C2314yescomplemented
161#13133139C2314yes—
162#13133138C2314yes—
163#13133137C2314yes—
164#13133128C2314yescomplemented
165#13133127C2314yescomplemented
166C8×Dic53C2314yescomplemented
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×C53C2314yescomplemented
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×C53C2314yescomplemented
185#103×C53C2314yescomplemented
186#102×C53C2314yes—
187C4×C8×C53C2314yescomplemented
188C24×C53—21no—
189C23×D53—21no—
190C23×D53—28no—
191C23×D53—24no—
192C23×D53—82no—
193C23×D53—82no—
194C23×D53C2×D411yescharacteristic
195C2×Q8×C53—21no—
196C2×Q8×C53—22no—
197C2×Q8×C53C22×C414yes—
198C2×Q8×C53C2412yes—
199C2×D4×C53—21no—
200C2×D4×C53—22no—
201C2×D4×C53C22×C414yes—
202C2×D4×C53C2412yes—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—24no—
207C22×C4×C53—82no—
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2411yescharacteristic
211C2×C22⋊D53—28no—
212C2×C22⋊D53—24no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—24no—
217C22×Dic53—82no—
218C22×Dic53C2×D411yescharacteristic
219C22×Dic53C2×D411yescharacteristic
220C22×Dic53C2×D411yescharacteristic
221Q8×D53—216no—
222Q8×D53—28no—
223Q8×D53C22×C4116yescomplemented
224D4×D53—216no—
225D4×D53—28no—
226D4×D53C22×C4116yes—
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—82no—
236C2×C4×D53—82no—
237C2×C4×D53C22×C414yes—
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—
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#11719924C22×C4116yescomplemented
263#11719923C22×C4116yescomplemented
264#11719921—24no—
265#11719921—24no—
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#11719919C2×D414yes—
278#11719919C2×D414yes—
279C4×Dic53—24no—
280C4×Dic53—24no—
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—216no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—816no—
306C22×D53—84no—
307C22×D53—84no—
308C22×D53C4×D414yes—
309C22×D53C22×D412yes—
310Q8×C53—24no—
311Q8×C53—22no—
312Q8×C53C23×C414yes—
313D4×C53—24no—
314D4×C53—22no—
315D4×C53C23×C414yes—
316C2×C4×C53—24no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53—84no—
325C2×C4×C53C23×C412yes—
326C2×C4×C53C22×D412yes—
327C2×C4×C53C22×D412yes—
328C2×C4×C53C22×D411yescharacteristic
329C2×C4×C53C2×#4112yes—
330C2×C4×C53C2511yescharacteristic
331C22⋊D53—216no—
332C2×Dic53—24no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—84no—
341C2×Dic53C4×D414yes—
342C2×Dic53C22×D412yes—
343C2×Dic53C22×D412yes—
344C2×Dic53C22×D412yes—
345D212—24no—
346D212—22no—
347D212C23×C414yes—
348C4×D53—216no—
349C4×D53—84no—
350C4×D53—84no—
351C4×D53C4×D418yes—
352C4×D53C23×C414yes—
353C4×D53C2×#4114yes—
354Dic106—24no—
355Dic106—22no—
356Dic106—216no—
357Dic106C23×C414yes—
358C8×C53—22no—
359C8×C53C23×C414yes—
360#88322—22no—
361#88322C23×C414yes—
362C2×#2949—531nomaximal, Sylow
363C22×C53—24no—
364C22×C53—48no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53C2×C4×D412yes—
368C22×C53#57712yes—
369C22×C53#57712yes—
370C22×C53C23×D411yescharacteristic
371C2×D53—28no—
372C2×D53—22no—
373C2×D53—22no—
374C2×D53—24no—
375C2×D53—48no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—816no—
379C2×D53C2×C4×D414yes—
380C4×C53—24no—
381C4×C53—22no—
382C4×C53—22no—
383C4×C53—42no—
384C4×C53—42no—
385C4×C53C2×C4×D412yes—
386C4×C53C24×C411yescharacteristic
387C4×C53C22×#4111yescharacteristic
388Dic53—24no—
389Dic53—22no—
390Dic53—22no—
391Dic53—42no—
392Dic53—42no—
393Dic53C2×C4×D414yes—
394C23×SD16—531no—
395C2×#519—531no—
396C2×#518—531no—
397#2949—5316no—
398C2×#440—531no—
399C2×#440—531no—
400C2×#440—531no—
401C2×#440—531no—
402C2×C4×SD16—531no—
403C2×C4×SD16—531no—
404C2×C4×SD16—531no—
405C2×C4×SD16D5311yescharacteristic, complemented
406C2×#427—531no—
407C2×#419—531no—
408C2×#418—531no—
409C2×#405—531no—
410C2×C53—44no—
411C2×C53#294914yescomplemented
412C2×C53C22×C4×D411yescharacteristic
413C2×C53C2×#57711yescharacteristic
414C2×C53C2×#57711yescharacteristic
415D53—24no—
416D53—44no—
417C23×Q8—531no—
418C23×D4—531no—
419C22×SD16—531no—
420C22×SD16—531no—
421C22×SD16—5316no—
422C22×SD16—538no—
423C22×SD16—531no—
424C22×SD16C2×D5311yescharacteristic
425C22×M16—531no—
426C23×C8—531no—
427#519—538no—
428#519—1064no—
429#518—538no—
430#518—1064no—
431C2×C4×Q8—531no—
432C2×C4×Q8—531no—
433C2×C4×Q8—531no—
434C2×C4×Q8—1061no—
435C2×C4×Q8—1061no—
436C2×C4×Q8C2×D5311yescharacteristic, complemented
437C2×C4×D4—531no—
438C2×C4×D4—531no—
439C2×C4×D4—531no—
440C2×C4×D4—1061no—
441C2×C4×D4—1061no—
442C2×C4×D4C2×D5311yescharacteristic
443C2×#117—531no—
444C2×#117—531no—
445C2×#117—531no—
446C2×#117—1061no—
447C2×#117—1061no—
448C22×C22⋊C4—1061no—
449C22×C22⋊C4—1061no—
450#440—538no—
451#440—538no—
452#440—538no—
453#440—538no—
454C4×SD16—538no—
455C4×SD16—538no—
456C4×SD16—538no—
457C4×SD16C2×D5318yescomplemented
458#427—538no—
459C2×#107—531no—
460C2×#107—531no—
461C2×#106—531no—
462C2×#106C2×D5311yescharacteristic, complemented
463#419—538no—
464#418—538no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#103C2×D5311yescharacteristic, complemented
469C2×#102—531no—
470C2×#102—531no—
471C2×#102—531no—
472C2×#102C2×D5311yescharacteristic
473#405—538no—
474C2×#97—531no—
475C2×#97—531no—
476C2×C4×C8—531no—
477C2×C4×C8C2×D5311yescharacteristic, complemented
478C53C2×#294911yescharacteristic, complemented, Sylow
479C25—1061no—
480C22×Q8—538no—
481C22×Q8—534no—
482C22×Q8—531no—
483C22×Q8—1061no—
484C22×Q8—1062no—
485C22×Q8—1064no—
486C22×Q8C22×D5311yescharacteristic
487C22×D4—538no—
488C22×D4—534no—
489C22×D4—531no—
490C22×D4—1062no—
491C22×D4—1064no—
492C22×D4—1061no—
493C22×D4C22×D5311yescharacteristic
494C23×C4—21no—
495C23×C4—531no—
496C23×C4—1061no—
497C23×C4—1061no—
498C23×C4—1061no—
499C23×C4—1061no—
500C2×SD16—538no—
501C2×SD16—534no—
502C2×SD16—538no—
503C2×SD16—534no—
504C2×SD16—5364no—
505C2×SD16—538no—
506C2×SD16—534no—
507C2×SD16C4×D5318yescomplemented
508C2×SD16C22×D5314yes—
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—1068no—
522C4×Q8—1062no—
523C4×Q8—1062no—
524C4×Q8—1068no—
525C4×Q8—1062no—
526C4×Q8C22×D5314yescomplemented
527C4×D4—22no—
528C4×D4—534no—
529C4×D4—534no—
530C4×D4—534no—
531C4×D4—1062no—
532C4×D4—1062no—
533C4×D4—1068no—
534C4×D4—1068no—
535C4×D4—1062no—
536C4×D4C22×D5314yes—
537#117—534no—
538#117—534no—
539#117—534no—
540#117—534no—
541#117—1068no—
542#117—1068no—
543#117—1062no—
544#117—1062no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—531no—
547C2×C4⋊C4—531no—
548C2×C4⋊C4—531no—
549C2×C4⋊C4—531no—
550C2×C4⋊C4—1061no—
551C2×C4⋊C4—1061no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4C22×D5311yescharacteristic
554C2×C4⋊C4C22×D5311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—531no—
557C2×C22⋊C4—531no—
558C2×C22⋊C4—1068no—
559C2×C22⋊C4—1068no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4—1061no—
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×C42—1061no—
571C2×C42—1061no—
572C2×C42C22×D5311yescharacteristic
573#107—534no—
574#107—534no—
575#106—534no—
576#106C22×D5314yescomplemented
577#103—534no—
578#103—534no—
579#103—534no—
580#103C22×D5314yescomplemented
581#102—534no—
582#102—534no—
583#102—534no—
584#102C22×D5314yes—
585#97—534no—
586#97—534no—
587C4×C8—534no—
588C4×C8C22×D5314yescomplemented
589C24—21no—
590C24—531no—
591C24—1064no—
592C24—1068no—
593C24—1061no—
594C24—4242no—
595C24—4242no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—5316no—
599C2×Q8—534no—
600C2×Q8—532no—
601C2×Q8—1064no—
602C2×Q8—1068no—
603C2×Q8—10616no—
604C2×Q8—1068no—
605C2×Q8—1061no—
606C2×Q8—1062no—
607C2×Q8C2×C4×D5314yes—
608C2×Q8C23×D5312yes—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—5316no—
612C2×D4—534no—
613C2×D4—532no—
614C2×D4—10616no—
615C2×D4—1068no—
616C2×D4—1064no—
617C2×D4—1068no—
618C2×D4—1061no—
619C2×D4—1062no—
620C2×D4C2×C4×D5314yes—
621C2×D4C23×D5312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—82no—
627C22×C4—531no—
628C22×C4—534no—
629C22×C4—532no—
630C22×C4—534no—
631C22×C4—532no—
632C22×C4—531no—
633C22×C4—531no—
634C22×C4—1064no—
635C22×C4—1064no—
636C22×C4—1068no—
637C22×C4—1064no—
638C22×C4—1061no—
639C22×C4—1061no—
640C22×C4—1061no—
641C22×C4—1064no—
642C22×C4—4242no—
643C22×C4—4242no—
644C22×C4—4242no—
645C22×C4D4×D5311yescharacteristic
646C22×C4D4×D5311yescharacteristic
647C22×C4C23×D5311yescharacteristic
648SD16—5316no—
649SD16—5316no—
650SD16—5316no—
651SD16C2×C4×D53116yescomplemented
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—1061no—
672C4⋊C4—1061no—
673C4⋊C4—1064no—
674C4⋊C4C23×D5312yes—
675C4⋊C4C23×D5312yes—
676C22⋊C4—24no—
677C22⋊C4—534no—
678C22⋊C4—534no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C22⋊C4—1064no—
683C22⋊C4—1064no—
684C42—24no—
685C42—532no—
686C42—532no—
687C42—1064no—
688C42—1064no—
689C42—1064no—
690C42—1064no—
691C42—1064no—
692C42D4×D5312yes—
693C42C23×D5312yes—
694C23—24no—
695C23—22no—
696C23—42no—
697C23—42no—
698C23—534no—
699C23—532no—
700C23—10616no—
701C23—1062no—
702C23—1062no—
703C23—1064no—
704C23—1062no—
705C23—42416no—
706C23—4244no—
707C23—4244no—
708C23—2122no—
709C23—2122no—
710C23C2×D4×D5311yescharacteristic
711Q8—24no—
712Q8—22no—
713Q8—534no—
714Q8—10616no—
715Q8—1064no—
716Q8—1062no—
717Q8C22×C4×D5314yes—
718D4—24no—
719D4—22no—
720D4—534no—
721D4—10616no—
722D4—1064no—
723D4—1062no—
724D4C22×C4×D5314yes—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—84no—
734C2×C4—534no—
735C2×C4—532no—
736C2×C4—538no—
737C2×C4—534no—
738C2×C4—534no—
739C2×C4—532no—
740C2×C4—532no—
741C2×C4—10616no—
742C2×C4—1064no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—4244no—
749C2×C4—4244no—
750C2×C4—4244no—
751C2×C4—2122no—
752C2×C4—2122no—
753C2×C4C22×C4×D5312yes—
754C2×C4C2×D4×D5312yes—
755C2×C4C2×D4×D5312yes—
756C2×C4C2×D4×D5311yescharacteristic
757C2×C4#41×D5312yes—
758C2×C4C24×D5311yescharacteristic
759C8—22no—
760C8—534no—
761C8—1062no—
762C8C22×C4×D5314yes—
763C22—24no—
764C22—48no—
765C22—42no—
766C22—42no—
767C22—534no—
768C22—1068no—
769C22—1062no—
770C22—1062no—
771C22—1064no—
772C22—42416no—
773C22—2128no—
774C22—2122no—
775C22—2122no—
776C22C4×D4×D5312yes—
777C22#1681142912yes—
778C22#1681143012yes—
779C22C22×D4×D5311yescharacteristic
780C4—24no—
781C4—22no—
782C4—22no—
783C4—42no—
784C4—42no—
785C4—534no—
786C4—1064no—
787C4—1062no—
788C4—1062no—
789C4—2122no—
790C4—2122no—
791C4C4×D4×D5312yes—
792C4C23×C4×D5311yescharacteristic
793C4C2×#41×D5311yescharacteristic
794C2—44no—
795C2—1064no—
796C2—2124no—
797C2#2028356914yesdirect product factor
798C2C2×C4×D4×D5311yescharacteristic
799C2C2×#1681142911yescharacteristic
800C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC2×C4×SD16×C53C2
socleC23×C53C22×D4
prime radicalC22×D4×D53C22
cosocleC2×C4×C53C25
hypercenterC2×C4×SD16D53
hypocenterC53C2×#2949
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#16811099C2semidirect
4. #20283569C2direct (N × H)
5. C2×#16810726C2semidirect
6. C2×#16810723C2semidirect
7. C2×#16810721C2semidirect
8. C2×#16810720C2semidirect
9. C2×C4×#11719913C2semidirect
10. C2×SD16×Dic53C2semidirect
11. C2×#16810710C2semidirect
12. C2×#16810658C2semidirect
13. C2×#16810630C2semidirect
15. C2×#16810577C2semidirect
16. C2×C4×SD16×C53C2semidirect
22. C2×SD16×D53C4semidirect
27. #16811099C22semidirect
30. C2×Q8×Dic53C22semidirect
32. C2×C4×Dic106C22semidirect
34. C2×#13133182C22semidirect
47. #16810726C22semidirect
48. #16810723C22semidirect
49. #16810721C22semidirect
50. #16810720C22semidirect
51. C4×#11719913C22semidirect
52. SD16×Dic53C22semidirect
53. #16810710C22semidirect
54. #16810658C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133149C22semidirect
58. #16810630C22semidirect
60. C2×#13133142C22semidirect
61. C2×#13133141C22semidirect
62. C2×#13133140C22semidirect
66. #16810577C22semidirect
67. C2×#13133128C22semidirect
68. C2×#13133127C22semidirect
69. C2×C8×Dic53C22semidirect
71. C2×C4×Q8×C53C22semidirect
73. C4×SD16×C53C22semidirect
74. C2×#106×C53C22semidirect
75. C2×#103×C53C22semidirect
77. C2×C4×C8×C53C22semidirect
83. C2×Q8×D53C2×C4semidirect
96. C2×#11719913C2×C4semidirect
98. C2×#11719923C2×C4semidirect
100. C2×#11719924C2×C4semidirect
102. SD16×D53C2×C4semidirect
107. C2×C8×D53C2×C4semidirect
110. Q8×Dic53C23semidirect
113. C4×Dic106C23semidirect
116. #13133182C23semidirect
155. #13133150C23semidirect
156. #13133150C23semidirect
157. #13133149C23semidirect
158. #13133142C23semidirect
159. #13133141C23semidirect
160. #13133140C23semidirect
164. #13133128C23semidirect
165. #13133127C23semidirect
166. C8×Dic53C23semidirect
170. C2×SD16×C53C2×C4semidirect
175. C4×Q8×C53C23semidirect
184. #106×C53C23semidirect
185. #103×C53C23semidirect
187. C4×C8×C53C23semidirect
223. Q8×D53C22×C4semidirect
247. SD16×C53C22×C4semidirect
262. #11719924C22×C4semidirect
263. #11719923C22×C4semidirect
290. #11719913C22×C4semidirect
292. C8×D53C22×C4semidirect
405. C2×C4×SD16D53semidirect
411. C2×C53#2949semidirect
436. C2×C4×Q8C2×D53semidirect
457. C4×SD16C2×D53semidirect
462. C2×#106C2×D53semidirect
468. C2×#103C2×D53semidirect
477. C2×C4×C8C2×D53semidirect
478. C53C2×#2949semidirect
507. C2×SD16C4×D53semidirect
526. C4×Q8C22×D53semidirect
576. #106C22×D53semidirect
580. #103C22×D53semidirect
588. C4×C8C22×D53semidirect
651. SD16C2×C4×D53semidirect
797. C2#20283569direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD16×D532
C2×#168110992
C2×#168110952
#202835692
C2×#168107262
C2×#168107232
C2×#168107212
C2×#168107202
C2×C4×#117199132
C2×SD16×Dic532
C2×#168107102
C2×#168106582
C2×#168106302
C2×#168106262
C2×#168105772
C2×C4×SD16×C532
C2×#294953