Finite Group Databasebeta

← C2×#20286578 #28260473

Subgroups — C2×#20286578 #28260473

Order 13568.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811286C211yesmaximal, characteristic, complemented
2C2×#16811274C211yesmaximal, characteristic
3#20286578C2116yesmaximal, direct product factor
4C2×#16810972C211yesmaximal, characteristic, complemented
5C2×#16810955C211yesmaximal, characteristic, complemented
6C2×#16810907C211yesmaximal, characteristic, complemented
7C2×#16810854C211yesmaximal, characteristic, complemented
8C2×#16810853C211yesmaximal, characteristic, complemented
9C2×#16810827C211yesmaximal, characteristic, complemented
10C2×#16810764C211yesmaximal, characteristic, complemented
11C2×#16810763C211yesmaximal, characteristic, complemented
12C2×#16810710C211yesmaximal, characteristic, complemented
13C2×#16810686C211yesmaximal, characteristic, complemented
14C22×#13133140C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#483C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C23×Dic106C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719924C2211yescharacteristic
23C23×#88322C2211yescharacteristic
24C22×C8×D53C2211yescharacteristic
25#16811286—24no—
26#16811286C2218yescomplemented
27#16811274—24no—
28#16811274C2218yes—
29C2×#13133216—21no—
30C2×#13133216C2211yescharacteristic
31C2×#13133215C2211yescharacteristic
32C2×#13133202—21no—
33C2×#13133200—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133195—21no—
36C2×#13133195—21no—
37C2×#13133194—21no—
38C2×#13133192C2211yescharacteristic
39C2×#13133191C2211yescharacteristic
40C2×#13133182C2211yescharacteristic
41C2×#13133179C2211yescharacteristic
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×#13133177—21no—
44C2×C4⋊C4×D53C2211yescharacteristic
45#16810972C2218yescomplemented
46#16810955C2218yescomplemented
47#16810907C2218yescomplemented
48#16810854C2218yescomplemented
49#16810853C2218yescomplemented
50#16810827C2218yescomplemented
51#16810764C2218yescomplemented
52#16810763C2218yescomplemented
53#16810710C2218yescomplemented
54#16810686C2218yescomplemented
55C2×#13133148C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57C2×#13133142C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2218yescomplemented
65#103×D53C2218yescomplemented
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#483C2218yescomplemented
72C2×#106×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—24no—
80C22×Dic106—22no—
81C22×Dic106—21no—
82C22×Dic106—21no—
83C22×Dic106—21no—
84C22×Dic106—42no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2314yes—
87C22×Dic106C2311yescharacteristic
88C2×Q8×D53—22no—
89C2×Q8×D53—24no—
90C2×Q8×D53—42no—
91C2×Q8×D53C2314yes—
92C22×D212—21no—
93C22×D212C2311yescharacteristic
94C22×C22⋊D53—21no—
95C22×C22⋊D53D411yescharacteristic
96C23×Dic53—21no—
97C22×C4×D53—21no—
98C22×C4×D53—21no—
99C22×C4×D53—21no—
100C22×C4×D53C2311yescharacteristic
101C2×#11719913—24no—
102C2×#11719913—42no—
103C2×#11719913C2314yes—
104C2×#11719913C2314yes—
105C2×#11719924—42no—
106C2×#11719924C2314yes—
107C22×#88322—42no—
108C22×#88322C2311yescharacteristic
109C22×#88322C2311yescharacteristic
110C22×#88322C2314yes—
111C2×C8×D53—42no—
112C2×C8×D53C2314yes—
113#13133216—28no—
114#13133216—22no—
115#13133216C2314yes—
116#13133215—22no—
117#13133215C2314yes—
118#13133202—28no—
119#13133200—28no—
120#13133197—22no—
121#13133197C2314yes—
122#13133195—28no—
123#13133195—28no—
124#13133194—28no—
125#13133192—22no—
126#13133192C2314yes—
127#13133191—22no—
128#13133191C2314yes—
129#13133182—22no—
130#13133182C2314yes—
131#13133179—22no—
132#13133179C2314yes—
133C4×C22⋊D53D414yes—
134C4×C22⋊D53C2314yes—
135#13133177—28no—
136C2×C4⋊Dic53—21no—
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×#11719919D411yescharacteristic
144C4⋊C4×D53—22no—
145C4⋊C4×D53C2314yes—
146C2×C22⋊Dic53D411yescharacteristic
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921D411yescharacteristic
152C2×C4×Dic53—21no—
153C2×C4×Dic53C2311yescharacteristic
154#13133148C2314yes—
155#13133146C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133141C2314yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133140C2314yes—
162#13133140C2314yes—
163#13133137C2314yes—
164#13133129C2314yes—
165C8×Dic53C2314yes—
166C22×Q8×C53C2311yescharacteristic
167C23×C4×C53—21no—
168C23×C4×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C22⋊Q8×C53—22no—
172C22⋊Q8×C53C2314yes—
173C2×C4⋊C4×C53—22no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2314yes—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C22⋊C4×C53—21no—
181#106×C53C2314yes—
182#106×C53C2314yes—
183#103×C53C2314yes—
184#103×C53C2314yes—
185C22⋊C8×C53C2314yes—
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—24no—
200C22×C4×C53—44no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2412yes—
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53—24no—
206C2×C22⋊D53—44no—
207C2×C22⋊D53SD1618yescomplemented
208C2×C22⋊D53C2×D414yes—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—24no—
213C22×Dic53—44no—
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217Q8×D53—28no—
218Q8×D53—44no—
219Q8×D53—48no—
220#11719945—432no—
221C2×D212—22no—
222C2×D212—22no—
223C2×D212—24no—
224C2×D212—21no—
225C2×D212—44no—
226C2×D212C2412yes—
227C2×C4×D53—22no—
228C2×C4×D53—22no—
229C2×C4×D53—24no—
230C2×C4×D53—24no—
231C2×C4×D53—24no—
232C2×C4×D53—44no—
233C2×C4×D53—44no—
234C2×C4×D53—44no—
235C2×C4×D53C2×D412yes—
236C2×C4×D53C2412yes—
237C2×Dic106—21no—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—22no—
241C2×Dic106—28no—
242C2×Dic106—24no—
243C2×Dic106—21no—
244C2×Dic106—24no—
245C2×Dic106—24no—
246C2×Dic106—44no—
247C2×Dic106—48no—
248C2×Dic106—44no—
249C2×Dic106—44no—
250C2×Dic106—44no—
251C2×Dic106#4114yescomplemented
252C2×Dic106C2412yes—
253C2×Dic106C2412yes—
254C2×C8×C53—22no—
255C2×C8×C53—22no—
256C2×C8×C53C2412yes—
257C2×C8×C53C2412yes—
258C4⋊C4×C53—21no—
259C4⋊C4×C53—21no—
260C4⋊C4×C53—24no—
261C4⋊C4×C53—24no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53C2412yes—
264C4⋊C4×C53C2412yes—
265C4⋊C4×C53C2412yes—
266C22⋊C4×C53—24no—
267C22⋊Dic53C2×D414yes—
268#11719924—44no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921C2×D414yes—
274C4⋊Dic53—21no—
275C4⋊Dic53—24no—
276C4⋊Dic53C2412yes—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281#11719919—24no—
282#11719919C2×D414yes—
283C4×Dic53—24no—
284C4×Dic53C2×D412yes—
285C4×Dic53C2412yes—
286C2×#88322—22no—
287C2×#88322—22no—
288C2×#88322—44no—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291#11719913—28no—
292#11719913—44no—
293C8×D53—44no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53C2×SD1614yes—
297C23×C53C22×D412yes—
298C23×C53C22×D411yescharacteristic
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53C2×SD1614yes—
306C22×D53C22×D412yes—
307Q8×C53—22no—
308Q8×C53—22no—
309Q8×C53—42no—
310C2×C4×C53—22no—
311C2×C4×C53—24no—
312C2×C4×C53—22no—
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—42no—
321C2×C4×C53—48no—
322C2×C4×C53—42no—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C2×#4112yes—
326C2×C4×C53H(5,𝔽2)12yes—
327C2×C4×C53C2511yescharacteristic
328C22⋊D53—48no—
329C22⋊D53C2×SD16116yescomplemented
330C2×Dic53—24no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—48no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53C2×SD1614yes—
340C2×Dic53C22×D412yes—
341C2×Dic53C22×D412yes—
342C2×Dic53C22×D412yes—
343D212—22no—
344D212—22no—
345D212—48no—
346D212—42no—
347C4×D53—24no—
348C4×D53—22no—
349C4×D53—22no—
350C4×D53—48no—
351C4×D53—48no—
352C4×D53—48no—
353Dic106—24no—
354Dic106—22no—
355Dic106—22no—
356Dic106—22no—
357Dic106—48no—
358Dic106—48no—
359Dic106—42no—
360Dic106—48no—
361Dic106C2×#4114yescomplemented
362C8×C53—22no—
363C8×C53—22no—
364#88322—22no—
365#88322—22no—
366C2×#3298—531nomaximal, Sylow
367C22×C53—22no—
368C22×C53—28no—
369C22×C53—22no—
370C22×C53#54612yes—
371C22×C53C22×SD1614yes—
372C22×C53C22×SD1612yes—
373C22×C53#57812yes—
374C22×C53C23×D411yescharacteristic
375C2×D53—22no—
376C2×D53—28no—
377C2×D53—22no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—84no—
382C2×D53C22×SD1614yes—
383C4×C53—22no—
384C4×C53—42no—
385C4×C53—42no—
386C4×C53—42no—
387C4×C53—42no—
388C4×C53#54612yes—
389C4×C53C22×#4111yescharacteristic
390C4×C53C2×H(5,𝔽2)11yescharacteristic
391Dic53—24no—
392Dic53—22no—
393Dic53—22no—
394Dic53—42no—
395Dic53—42no—
396Dic53C22×SD1614yes—
397C2×D4×Q8—531no—
398C2×#547—531no—
399#3298—5316no—
400C2×#487—531no—
401C2×#483—531no—
402C2×#483D5311yescharacteristic, complemented
403C2×#475—531no—
404C2×#465—531no—
405C2×#465—531no—
406C2×#461—531no—
407C2×#448—531no—
408C2×#448—531no—
409C2×C4×SD16—531no—
410C2×C8×D4—531no—
411C22×#103—531no—
412C22×#103—531no—
413C2×C53—24no—
414C2×C53#329814yescomplemented
415C2×C53C2×#54611yescharacteristic
416C2×C53C23×SD1611yescharacteristic
417C2×C53C2×#57811yescharacteristic
418D53—24no—
419D53—82no—
420C22×#41—1061no—
421C23×Q8—531no—
422C23×Q8—531no—
423C22×SD16—531no—
424C22×SD16—531no—
425C22×SD16—531no—
426C23×C8—531no—
427C23×C8—531no—
428D4×Q8—538no—
429D4×Q8—1064no—
430#547—538no—
431#547—1064no—
432C2×C4⋊Q8—531no—
433C2×C4⋊Q8—531no—
434C2×C4⋊Q8—1061no—
435C2×#123—1061no—
436C2×#123—1061no—
437C2×C22⋊Q8—531no—
438C2×C22⋊Q8—1061no—
439C2×C22⋊Q8—1061no—
440C2×C22⋊Q8—1061no—
441C2×C22⋊Q8C2×D5311yescharacteristic
442C2×#121—531no—
443C2×#121—531no—
444C2×C4×Q8—531no—
445C2×C4×D4—531no—
446C2×C4×D4—531no—
447C2×C4×D4—1061no—
448C22×C4⋊C4—531no—
449C22×C4⋊C4C2×D5311yescharacteristic
450#487—538no—
451#483—538no—
452#483C2×D5318yescomplemented
453#475—538no—
454#465—538no—
455#465—538no—
456#461—538no—
457#448—538no—
458#448—538no—
459C4×SD16—538no—
460C8×D4—538no—
461C2×#106—531no—
462C2×#106C2×D5311yescharacteristic
463C2×#106C2×D5311yescharacteristic
464C2×C4⋊C8—531no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#103—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—538no—
473C2×#103—538no—
474C2×#103C2×D5311yescharacteristic
475C2×#103C2×D5311yescharacteristic
476C2×#102—531no—
477C2×C22⋊C8—531no—
478C2×C22⋊C8C2×D5311yescharacteristic
479C2×C4×C8—531no—
480C53C2×#329811yescharacteristic, complemented, Sylow
481C2×#41—1068no—
482C2×#41—2128no—
483C22×Q8—534no—
484C22×Q8—531no—
485C22×Q8—531no—
486C22×Q8—534no—
487C22×Q8—1061no—
488C22×Q8—1061no—
489C22×Q8—1064no—
490C22×Q8—1062no—
491C22×Q8—1061no—
492C22×Q8—1062no—
493C22×Q8—1064no—
494C22×Q8—2122no—
495C22×Q8—2122no—
496C22×Q8C22×D5311yescharacteristic
497C22×D4—531no—
498C22×D4—531no—
499C22×D4—1061no—
500C22×D4—1061no—
501C23×C4—21no—
502C23×C4—531no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4—1061no—
507C23×C4C22×D5311yescharacteristic
508C2×SD16—534no—
509C2×SD16—534no—
510C2×SD16—534no—
511C2×SD16—1064no—
512C2×SD16—2122no—
513C2×SD16—2122no—
514C22×C8—531no—
515C22×C8—531no—
516C22×C8—534no—
517C22×C8—534no—
518C22×C8—2122no—
519C22×C8—2122no—
520C22×C8C22×D5311yescharacteristic
521C22×C8C22×D5311yescharacteristic
522C4⋊Q8—534no—
523C4⋊Q8—534no—
524C4⋊Q8—1062no—
525C4⋊Q8—1062no—
526C4⋊Q8—1068no—
527#123—1068no—
528#123—1068no—
529C22⋊Q8—22no—
530C22⋊Q8—534no—
531C22⋊Q8—1068no—
532C22⋊Q8—1068no—
533C22⋊Q8—1068no—
534C22⋊Q8—1062no—
535C22⋊Q8C22×D5314yes—
536#121—534no—
537#121—534no—
538#121—1062no—
539#121—1062no—
540C4×Q8—534no—
541C4×Q8—1062no—
542C4×D4—534no—
543C4×D4—534no—
544C4×D4—534no—
545C4×D4—1062no—
546C4×D4—1068no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—534no—
553C2×C4⋊C4—1062no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4C22×D5311yescharacteristic
561C2×C4⋊C4C22×D5311yescharacteristic
562C2×C4⋊C4C22×D5314yes—
563C2×C4⋊C4C22×D5311yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—531no—
566C2×C22⋊C4—531no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C42—531no—
572C2×C42—1061no—
573#106—534no—
574#106C22×D5314yes—
575#106C22×D5314yes—
576C4⋊C8—534no—
577#103—534no—
578#103—534no—
579#103—534no—
580#103—534no—
581#103—534no—
582#103—534no—
583#103—534no—
584#103C22×D5314yes—
585#103C22×D5314yes—
586#102—534no—
587C22⋊C8—534no—
588C22⋊C8C22×D5314yes—
589C4×C8—534no—
590C24—531no—
591C24—1061no—
592C24D4×D5311yescharacteristic
593#41—21232no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—534no—
598C2×Q8—532no—
599C2×Q8—532no—
600C2×Q8—1064no—
601C2×Q8—1064no—
602C2×Q8—1068no—
603C2×Q8—1061no—
604C2×Q8—1064no—
605C2×Q8—1061no—
606C2×Q8—1062no—
607C2×Q8—1068no—
608C2×Q8—1062no—
609C2×Q8—1062no—
610C2×Q8—2124no—
611C2×Q8—2124no—
612C2×Q8—2128no—
613C2×Q8—2124no—
614C2×Q8—2124no—
615C2×Q8—2124no—
616C2×Q8—2128no—
617C2×Q8C23×D5312yes—
618C2×D4—538no—
619C2×D4—534no—
620C2×D4—532no—
621C2×D4—1064no—
622C2×D4—1064no—
623C2×D4—1061no—
624C2×D4—1062no—
625C2×D4—1062no—
626C2×D4—2124no—
627C2×D4—2124no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—44no—
636C22×C4—531no—
637C22×C4—531no—
638C22×C4—531no—
639C22×C4—532no—
640C22×C4—532no—
641C22×C4—1064no—
642C22×C4—1064no—
643C22×C4—1064no—
644C22×C4—1061no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—1064no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—2124no—
651C22×C4—2124no—
652C22×C4—2124no—
653C22×C4—2124no—
654C22×C4D4×D5312yes—
655C22×C4D4×D5311yescharacteristic
656C22×C4C23×D5312yes—
657C22×C4C23×D5311yescharacteristic
658SD16—1068no—
659SD16—2124no—
660SD16—2124no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—532no—
664C2×C8—532no—
665C2×C8—1062no—
666C2×C8—1062no—
667C2×C8—2124no—
668C2×C8—2124no—
669C2×C8C23×D5312yes—
670C2×C8C23×D5312yes—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—534no—
677C4⋊C4—532no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4—1064no—
683C4⋊C4—1064no—
684C4⋊C4—1061no—
685C4⋊C4C23×D5312yes—
686C4⋊C4C23×D5312yes—
687C4⋊C4C23×D5312yes—
688C22⋊C4—24no—
689C22⋊C4—534no—
690C22⋊C4—534no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4—1064no—
694C22⋊C4—1064no—
695C42—532no—
696C42—532no—
697C42—1064no—
698C23—22no—
699C23—22no—
700C23—534no—
701C23—532no—
702C23—1062no—
703C23—1062no—
704C23—1062no—
705C23—2122no—
706C23—2122no—
707C23—2122no—
708C23SD16×D5314yes—
709C23C2×D4×D5312yes—
710C23C2×D4×D5311yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—42no—
714Q8—534no—
715Q8—1064no—
716Q8—1062no—
717Q8—1062no—
718Q8—1062no—
719Q8—2128no—
720Q8—2128no—
721Q8—2128no—
722Q8—2122no—
723D4—5316no—
724D4—1062no—
725D4—1062no—
726D4—2128no—
727D4—2128no—
728D4—2122no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—48no—
741C2×C4—42no—
742C2×C4—534no—
743C2×C4—532no—
744C2×C4—532no—
745C2×C4—532no—
746C2×C4—1062no—
747C2×C4—1064no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1064no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—2128no—
756C2×C4—2128no—
757C2×C4—2128no—
758C2×C4—2128no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4C2×D4×D5312yes—
762C2×C4C2×D4×D5311yescharacteristic
763C2×C4#41×D5312yes—
764C2×C4#1313326312yes—
765C2×C4C24×D5311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1062no—
769C8—1062no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—534no—
774C22—1068no—
775C22—1062no—
776C22—1062no—
777C22—4244no—
778C22—2122no—
779C22—2122no—
780C22—2122no—
781C22#1681126512yes—
782C22C2×SD16×D5314yes—
783C22C2×SD16×D5312yes—
784C22#1681143912yes—
785C22C22×D4×D5311yescharacteristic
786C4—22no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—534no—
792C4—1062no—
793C4—1064no—
794C4—1062no—
795C4—2122no—
796C4—2122no—
797C4#1681126512yes—
798C4C2×#41×D5311yescharacteristic
799C4C2×#1313326311yescharacteristic
800C2—24no—
801C2—1064no—
802C2—4242no—
803C2#2028657814yesdirect product factor
804C2C2×#1681126511yescharacteristic
805C2C22×SD16×D5311yescharacteristic
806C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#483C2
socleC23×C53C22×D4
prime radicalC2×#16811274C2
hypercenterC2×#483D53
hypocenterC53C2×#3298
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#16811286C2semidirect
3. #20286578C2direct (N × H)
4. C2×#16810972C2semidirect
5. C2×#16810955C2semidirect
6. C2×#16810907C2semidirect
7. C2×#16810854C2semidirect
8. C2×#16810853C2semidirect
9. C2×#16810827C2semidirect
10. C2×#16810764C2semidirect
11. C2×#16810763C2semidirect
12. C2×#16810710C2semidirect
13. C2×#16810686C2semidirect
14. C22×#13133140C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#483C2semidirect
26. #16811286C22semidirect
45. #16810972C22semidirect
46. #16810955C22semidirect
47. #16810907C22semidirect
48. #16810854C22semidirect
49. #16810853C22semidirect
50. #16810827C22semidirect
51. #16810764C22semidirect
52. #16810763C22semidirect
53. #16810710C22semidirect
54. #16810686C22semidirect
64. C2×#13133140C22semidirect
65. #103×D53C22semidirect
71. C53×#483C22semidirect
207. C2×C22⋊D53SD16semidirect
251. C2×Dic106#41semidirect
329. C22⋊D53C2×SD16semidirect
361. Dic106C2×#41semidirect
402. C2×#483D53semidirect
414. C2×C53#3298semidirect
452. #483C2×D53semidirect
480. C53C2×#3298semidirect
803. C2#20286578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112862
C2×#168112742
#202865782
C2×#168109722
C2×#168109552
C2×#168109072
C2×#168108542
C2×#168108532
C2×#168108272
C2×#168107642
C2×#168107632
C2×#168107102
C2×#168106862
C22×#131331402
C2×#103×D532
C2×C53×#4832
C2×#329853