Finite Group Databasebeta

← C2×#20287468 #28263841

Subgroups — C2×#20287468 #28263841

Order 13568.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811358C211yesmaximal, characteristic, complemented
2#20287468C2116yesmaximal, direct product factor
3C2×#16810989C211yesmaximal, characteristic, complemented
4C2×#16810985C211yesmaximal, characteristic, complemented
5C2×#16810980C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810920C211yesmaximal, characteristic, complemented
8C2×#16810900C211yesmaximal, characteristic, complemented
9C2×#16810838C211yesmaximal, characteristic, complemented
10C2×#16810838C211yesmaximal, characteristic, complemented
11C2×#16810818C211yesmaximal, characteristic
12C2×#16810754C211yesmaximal, characteristic, complemented
13C2×#16810733C211yesmaximal, characteristic, complemented
14C2×#16810723C211yesmaximal, characteristic, complemented
15C2×C4×#11719922C211yesmaximal, characteristic, complemented
16C2×C53×#554C211yesmaximal, characteristic, complemented
17C22×#11719923C2211yescharacteristic
18C22×#11719922C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20#16811358—24no—
21#16811358C2218yescomplemented
22C2×#13133214C2211yescharacteristic
23C2×#13133206—21no—
24C2×#13133205C2211yescharacteristic
25C2×#13133205C2211yescharacteristic
26C2×#13133202—21no—
27C2×#13133202—21no—
28C2×C4×Dic106C2211yescharacteristic
29C2×C4×D212C2211yescharacteristic
30C2×C4×D212C2211yescharacteristic
31C2×#13133179—21no—
32#16810989C2218yescomplemented
33#16810985C2218yescomplemented
34#16810980C2218yescomplemented
35#16810927C2218yescomplemented
36#16810920C2218yescomplemented
37#16810900C2218yescomplemented
38#16810838C2218yescomplemented
39#16810838C2218yescomplemented
40#16810818C2218yes—
41#16810754C2218yescomplemented
42#16810733C2218yescomplemented
43#16810723C2218yescomplemented
44C4×#11719922C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49C2×C4⋊#88322C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×#13133140C2211yescharacteristic
52C2×#13133140C2211yescharacteristic
53C2×#13133140C2211yescharacteristic
54C2×#13133138C2211yescharacteristic
55C2×#13133137C2211yescharacteristic
56C2×#13133137C2211yescharacteristic
57C2×#13133137C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×#13133128C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#554—24no—
65C53×#554C2218yescomplemented
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#125×C53C2211yescharacteristic
68C2×#125×C53C2211yescharacteristic
69C2×C22⋊Q8×C53—21no—
70C2×C22⋊Q8×C53—21no—
71C2×C22⋊Q8×C53—21no—
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×D4×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C22×C4⋊C4×C53—21no—
77C22×Dic106C2311yescharacteristic
78C22×D212—21no—
79C22×D212—21no—
80C22×D212C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C2×#11719923—24no—
85C2×#11719923C2314yes—
86C2×#11719922—24no—
87C2×#11719922—24no—
88C2×#11719922C2314yes—
89C2×#11719922C2314yes—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94#13133214—22no—
95#13133214C2314yes—
96#13133206—28no—
97#13133205—22no—
98#13133205—22no—
99#13133205C2314yes—
100#13133205C2314yes—
101#13133202—28no—
102#13133202—28no—
103C4×Dic106—22no—
104C4×Dic106C2314yes—
105C4×D212—22no—
106C4×D212—22no—
107C4×D212C2314yes—
108C4×D212C2314yes—
109#13133179—28no—
110C2×C4⋊Dic53C2311yescharacteristic
111C2×#11719919—21no—
112C2×#11719921—21no—
113C2×#11719921—21no—
114C2×#11719921—21no—
115C2×#11719921—21no—
116C2×#11719921—21no—
117C2×#11719921—21no—
118C2×C4×Dic53—21no—
119#13133150C2314yes—
120#13133150C2314yes—
121#13133148C2314yes—
122C4⋊#88322C2314yes—
123C4⋊#88322C2314yes—
124C4⋊#88322C2314yes—
125#13133140C2314yes—
126#13133140C2314yes—
127#13133140C2314yes—
128#13133138C2314yes—
129#13133137C2314yes—
130#13133137C2314yes—
131#13133137C2314yes—
132#13133137C2314yes—
133#13133137C2314yes—
134#13133137C2314yes—
135#13133128C2314yes—
136#13133128C2314yes—
137C4×#88322C2314yes—
138C22×Q8×C53—21no—
139C22×Q8×C53D411yescharacteristic
140C22×D4×C53C2311yescharacteristic
141C23×C4×C53—21no—
142C23×C4×C53—21no—
143C23×C4×C53—21no—
144C4⋊Q8×C53—22no—
145C4⋊Q8×C53C2314yes—
146#125×C53—22no—
147#125×C53—22no—
148#125×C53C2314yes—
149#125×C53C2314yes—
150C22⋊Q8×C53—28no—
151C22⋊Q8×C53—28no—
152C22⋊Q8×C53—28no—
153C4×Q8×C53D414yes—
154C4×Q8×C53C2314yes—
155C4×D4×C53—22no—
156C4×D4×C53—22no—
157C4×D4×C53—22no—
158C4×D4×C53C2314yes—
159C4×D4×C53C2314yes—
160C4×D4×C53C2314yes—
161C2×C4⋊C4×C53—28no—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53—21no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53D411yescharacteristic
168C2×C4⋊C4×C53D411yescharacteristic
169C2×C4⋊C4×C53D411yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C42×C53C2311yescharacteristic
177C2×C42×C53C2311yescharacteristic
178C2×C42×C53C2311yescharacteristic
179C24×C53—21no—
180C23×D53—21no—
181C23×D53—21no—
182C2×Q8×C53—24no—
183C2×Q8×C53—42no—
184C2×Q8×C53—82no—
185C2×Q8×C53C2×D414yes—
186C2×D4×C53—21no—
187C2×D4×C53—22no—
188C2×D4×C53#4114yes—
189C2×D4×C53C2412yes—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—24no—
194C22×C4×C53—24no—
195C22×C4×C53—24no—
196C22×C4×C53—44no—
197C22×C4×C53—82no—
198C22×C4×C53—82no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2411yescharacteristic
206C22×Dic53—21no—
207C22×Dic53—21no—
208C2×D212—22no—
209C2×D212—22no—
210C2×D212—22no—
211C2×D212—22no—
212C2×D212—24no—
213C2×D212—21no—
214C2×D212—21no—
215C2×D212—24no—
216C2×D212—44no—
217C2×D212—82no—
218C2×D212C2412yes—
219C2×D212C2412yes—
220C2×C4×D53—24no—
221C2×C4×D53—24no—
222C2×C4×D53—82no—
223C2×C4×D53—82no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—21no—
227C2×Dic106C2412yes—
228C4⋊C4×C53—24no—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53C2×D414yes—
237C4⋊C4×C53C2×D414yes—
238C4⋊C4×C53C2×D414yes—
239C4⋊C4×C53C2412yes—
240C4⋊C4×C53C2412yes—
241C4⋊C4×C53C2412yes—
242C22⋊C4×C53—24no—
243C22⋊C4×C53—24no—
244C22⋊C4×C53—24no—
245C42×C53C2×D412yes—
246C42×C53C2×D412yes—
247C42×C53C2×D412yes—
248C42×C53C2412yes—
249C42×C53C2412yes—
250C42×C53C2412yes—
251#11719923—28no—
252#11719922—28no—
253#11719922—28no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259#11719921—24no—
260C4⋊Dic53—21no—
261C4⋊Dic53C2412yes—
262#11719919—24no—
263C4×Dic53—24no—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322—22no—
267C2×#88322—22no—
268C2×#88322C2412yes—
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271C2×#88322C2412yes—
272C23×C53—24no—
273C23×C53—22no—
274C23×C53—42no—
275C23×C53—42no—
276C23×C53C22×D411yescharacteristic
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53—42no—
284C22×D53—42no—
285Q8×C53—44no—
286Q8×C53—84no—
287D4×C53—24no—
288D4×C53—22no—
289D4×C53C2×#4114yes—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—48no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—84no—
304C2×C4×C53—84no—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D411yescharacteristic
312C2×C4×C53C2×#4112yes—
313C2×C4×C532−1+412yes—
314C2×C4×C53C2511yescharacteristic
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319D212—22no—
320D212—22no—
321D212—22no—
322D212—22no—
323D212—48no—
324D212—42no—
325D212—42no—
326D212—84no—
327C4×D53—84no—
328C4×D53—84no—
329Dic106—22no—
330Dic106—22no—
331Dic106—42no—
332#88322—22no—
333#88322—22no—
334#88322—22no—
335#88322—22no—
336C2×#3370—531nomaximal, Sylow
337C22×C53—24no—
338C22×C53—48no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53#54812yes—
342C22×C53#57512yes—
343C22×C53#57612yes—
344C22×C53C23×D411yescharacteristic
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—42no—
348C2×D53—42no—
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—84no—
352C2×D53—84no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—22no—
356C4×C53—22no—
357C4×C53—22no—
358C4×C53—22no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53—42no—
362C4×C53#54812yes—
363C4×C53C22×#4111yescharacteristic
364C4×C53C2×2−1+411yescharacteristic
365Dic53—42no—
366Dic53—42no—
367C2×#559—531no—
368C2×#554D5311yescharacteristic, complemented
369#3370—5316no—
370C2×#490—531no—
371C2×#489—531no—
372C2×#488—531no—
373C2×#479—531no—
374C2×#478—531no—
375C2×#474—531no—
376C2×#463—531no—
377C2×#463—531no—
378C2×#459—531no—
379C2×#446—531no—
380C2×#442—531no—
381C2×#440—531no—
382C2×C4×D8—531no—
383C2×C53—44no—
384C2×C53#337014yescomplemented
385C2×C53C2×#54811yescharacteristic
386C2×C53C2×#57511yescharacteristic
387C2×C53C2×#57611yescharacteristic
388D53—82no—
389D53—82no—
390C22×SD16—531no—
391C22×D8—531no—
392C22×D8—531no—
393#559—538no—
394#559—1064no—
395#554—24no—
396#554C2×D5318yescomplemented
397C2×C4⋊Q8C2×D5311yescharacteristic
398C2×#127—531no—
399C2×#125C2×D5311yescharacteristic
400C2×#125C2×D5311yescharacteristic
401C2×#124—531no—
402C2×#124—531no—
403C2×#124—1061no—
404C2×#123—1061no—
405C2×#123—1061no—
406C2×C22⋊Q8—21no—
407C2×C22⋊Q8—21no—
408C2×C22⋊Q8—21no—
409C2×C4×Q8—531no—
410C2×C4×Q8C2×D5311yescharacteristic
411C2×C4×D4—531no—
412C2×C4×D4—531no—
413C2×C4×D4—1061no—
414C2×C4×D4C2×D5311yescharacteristic
415C2×C4×D4C2×D5311yescharacteristic
416C2×C4×D4C2×D5311yescharacteristic
417C22×C4⋊C4—21no—
418#490—538no—
419#489—538no—
420#488—538no—
421#479—538no—
422#478—538no—
423#474—538no—
424#463—538no—
425#463—538no—
426#459—538no—
427#446—538no—
428#442—538no—
429#440—538no—
430C4×D8—538no—
431C2×#107—531no—
432C2×#107—531no—
433C2×#106—531no—
434C2×C4⋊C8—531no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×#103—531no—
438C2×#103—531no—
439C2×#103—531no—
440C2×#102—531no—
441C2×#102—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—531no—
445C2×#102—531no—
446C2×#102—531no—
447C2×#97—531no—
448C2×#97—531no—
449C2×C4×C8—531no—
450C53C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—21no—
452C22×Q8—531no—
453C22×Q8C22⋊D5311yescharacteristic
454C22×D4—531no—
455C22×D4—531no—
456C22×D4—1061no—
457C22×D4—1061no—
458C22×D4C22×D5311yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—1061no—
463C23×C4—1061no—
464C2×SD16—534no—
465C2×SD16—1064no—
466C2×D8—534no—
467C2×D8—534no—
468C2×D8—1064no—
469C2×D8—1064no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8—531no—
474C4⋊Q8—22no—
475C4⋊Q8C22×D5314yes—
476#127—534no—
477#127—1062no—
478#125—22no—
479#125—22no—
480#125C22×D5314yes—
481#125C22×D5314yes—
482#124—534no—
483#124—534no—
484#124—1068no—
485#124—1062no—
486#124—1062no—
487#123—1068no—
488#123—1068no—
489C22⋊Q8—28no—
490C22⋊Q8—28no—
491C22⋊Q8—28no—
492C4×Q8—534no—
493C4×Q8—1062no—
494C4×Q8C22⋊D5314yes—
495C4×Q8C22×D5314yes—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—534no—
500C4×D4—534no—
501C4×D4—1068no—
502C4×D4—1062no—
503C4×D4—1062no—
504C4×D4C22×D5314yes—
505C4×D4C22×D5314yes—
506C4×D4C22×D5314yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—28no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4C22⋊D5311yescharacteristic
516C2×C4⋊C4C22⋊D5311yescharacteristic
517C2×C4⋊C4C22⋊D5311yescharacteristic
518C2×C4⋊C4C22×D5311yescharacteristic
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C42—1061no—
531C2×C42C22×D5311yescharacteristic
532C2×C42C22×D5311yescharacteristic
533C2×C42C22×D5311yescharacteristic
534#107—534no—
535#107—534no—
536#106—534no—
537C4⋊C8—534no—
538C4⋊C8—534no—
539C4⋊C8—534no—
540#103—534no—
541#103—534no—
542#103—534no—
543#102—534no—
544#102—534no—
545#102—534no—
546#102—534no—
547#102—534no—
548#102—534no—
549#102—534no—
550#97—534no—
551#97—534no—
552C4×C8—534no—
553C24—21no—
554C24—1061no—
555C24—1061no—
556C2×Q8—24no—
557C2×Q8—42no—
558C2×Q8—82no—
559C2×Q8—532no—
560C2×Q8—1061no—
561C2×Q8—1062no—
562C2×Q8—1062no—
563C2×Q8C2×C22⋊D5314yes—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—532no—
567C2×D4—532no—
568C2×D4—1064no—
569C2×D4—1064no—
570C2×D4—1061no—
571C2×D4—1061no—
572C2×D4—1062no—
573C2×D4—1062no—
574C2×D4—1062no—
575C2×D4—1062no—
576C2×D4—4242no—
577C2×D4—2124no—
578C2×D4#1171994914yes—
579C2×D4C23×D5312yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—44no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1064no—
592C22×C4—1064no—
593C22×C4—4242no—
594C22×C4—4242no—
595C22×C4C2×C22⋊D5311yescharacteristic
596C22×C4C2×C22⋊D5311yescharacteristic
597C22×C4C2×C22⋊D5311yescharacteristic
598C22×C4C2×C22⋊D5311yescharacteristic
599C22×C4C2×C22⋊D5311yescharacteristic
600C22×C4C2×C22⋊D5311yescharacteristic
601C22×C4C23×D5311yescharacteristic
602SD16—1068no—
603D8—1068no—
604D8—1068no—
605C2×C8—532no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—532no—
609C2×C8—1062no—
610C2×C8—1062no—
611C2×C8—1062no—
612C2×C8—1062no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—532no—
622C4⋊C4—1061no—
623C4⋊C4—1064no—
624C4⋊C4C2×C22⋊D5314yes—
625C4⋊C4C2×C22⋊D5314yes—
626C4⋊C4C2×C22⋊D5314yes—
627C4⋊C4C23×D5312yes—
628C4⋊C4C23×D5312yes—
629C4⋊C4C23×D5312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1064no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—1064no—
638C22⋊C4—1064no—
639C42—1064no—
640C42C2×C22⋊D5312yes—
641C42C2×C22⋊D5312yes—
642C42C2×C22⋊D5312yes—
643C42C23×D5312yes—
644C42C23×D5312yes—
645C42C23×D5312yes—
646C23—24no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—1062no—
651C23—1062no—
652C23—2122no—
653C23—2122no—
654C23—2122no—
655C23—2122no—
656C23—2122no—
657C23—2122no—
658C23C22×C22⋊D5311yescharacteristic
659Q8—44no—
660Q8—84no—
661Q8—1062no—
662Q8—1062no—
663Q8—2122no—
664D4—24no—
665D4—22no—
666D4—1062no—
667D4—1062no—
668D4—1062no—
669D4—1062no—
670D4—4244no—
671D4—2128no—
672D4—2122no—
673D4—2122no—
674D4C2×#1171994914yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—4244no—
693C2×C4—4244no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4C22×C22⋊D5312yes—
697C2×C4C22×C22⋊D5312yes—
698C2×C4C22×C22⋊D5312yes—
699C2×C4C22×C22⋊D5312yes—
700C2×C4C22×C22⋊D5312yes—
701C2×C4C22×C22⋊D5312yes—
702C2×C4C22×C22⋊D5311yescharacteristic
703C2×C4C2×#1171994912yes—
704C2×C4#1313326512yes—
705C2×C4C24×D5311yescharacteristic
706C8—1062no—
707C8—1062no—
708C8—1062no—
709C8—1062no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—4244no—
715C22—4244no—
716C22—2122no—
717C22—2122no—
718C22—2122no—
719C22—2122no—
720C22—2122no—
721C22—2122no—
722C22#1681128412yes—
723C22#1681142112yes—
724C22#1681142612yes—
725C22C23×C22⋊D5311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—2122no—
736C4—2122no—
737C4#1681128412yes—
738C4C22×#1171994911yescharacteristic
739C4C2×#1313326511yescharacteristic
740C2—44no—
741C2—4242no—
742C2—4242no—
743C2#2028746814yesdirect product factor
744C2C2×#1681128411yescharacteristic
745C2C2×#1681142111yescharacteristic
746C2C2×#1681142611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#554C2
socleC23×C53C22×D4
prime radicalC2×#16810818C2
hypercenterC2×#554D53
hypocenterC53C2×#3370
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16811358C2semidirect
2. #20287468C2direct (N × H)
3. C2×#16810989C2semidirect
4. C2×#16810985C2semidirect
5. C2×#16810980C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810920C2semidirect
8. C2×#16810900C2semidirect
9. C2×#16810838C2semidirect
10. C2×#16810838C2semidirect
12. C2×#16810754C2semidirect
13. C2×#16810733C2semidirect
14. C2×#16810723C2semidirect
15. C2×C4×#11719922C2semidirect
16. C2×C53×#554C2semidirect
21. #16811358C22semidirect
32. #16810989C22semidirect
33. #16810985C22semidirect
34. #16810980C22semidirect
35. #16810927C22semidirect
36. #16810920C22semidirect
37. #16810900C22semidirect
38. #16810838C22semidirect
39. #16810838C22semidirect
41. #16810754C22semidirect
42. #16810733C22semidirect
43. #16810723C22semidirect
44. C4×#11719922C22semidirect
65. C53×#554C22semidirect
368. C2×#554D53semidirect
384. C2×C53#3370semidirect
396. #554C2×D53semidirect
450. C53C2×#3370semidirect
743. C2#20287468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113582
#202874682
C2×#168109892
C2×#168109852
C2×#168109802
C2×#168109272
C2×#168109202
C2×#168109002
C2×#168108382
C2×#168108182
C2×#168107542
C2×#168107332
C2×#168107232
C2×C4×#117199222
C2×C53×#5542
C2×#337053