Finite Group Databasebeta

← C2×#20278774 #27552184

Subgroups — C2×#20278774 #27552184

Order 13568.

3006 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133210C211yesmaximal, characteristic, complemented
2C22×D4×Dic53C211yesmaximal, characteristic
3#20278774C2116yesmaximal, direct product factor
4C2×#16810556C211yesmaximal, characteristic, complemented
5C2×#16810555C211yesmaximal, characteristic, complemented
6C2×#16810537C211yesmaximal, characteristic
7C2×#16810516C211yesmaximal, characteristic, complemented
8C2×#16810511C211yesmaximal, characteristic, complemented
9C2×#16810511C211yesmaximal, characteristic, complemented
10C2×#16810505C211yesmaximal, characteristic, complemented
11C2×#16810498C211yesmaximal, characteristic, complemented
12C2×#16810498C211yesmaximal, characteristic, complemented
13C2×#16810484C211yesmaximal, characteristic, complemented
14C2×#16810481C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
16C2×C53×#394C211yesmaximal, characteristic
17C24×Dic53C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C2×#13133210—28no—
20C2×#13133210C2218yescomplemented
21C2×D4×Dic53—28no—
22C2×D4×Dic53C2218yes—
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C4⋊Dic53C2211yescharacteristic
25C22×C4⋊Dic53C2211yescharacteristic
26C22×C4⋊Dic53C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×C22⋊Dic53C2211yescharacteristic
32C22×C22⋊Dic53C2211yescharacteristic
33C22×C22⋊Dic53C2211yescharacteristic
34C22×C22⋊Dic53C2211yescharacteristic
35C22×C22⋊Dic53C2211yescharacteristic
36C22×C22⋊Dic53C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39C22×C4×Dic53C2211yescharacteristic
40#16810556C2218yescomplemented
41#16810555C2218yescomplemented
42#16810537C2218yes—
43#16810516C2218yescomplemented
44#16810511C2218yescomplemented
45#16810511C2218yescomplemented
46#16810505C2218yescomplemented
47#16810498C2218yescomplemented
48#16810498C2218yescomplemented
49#16810484C2218yescomplemented
50#16810481C2218yescomplemented
51C4⋊C4×Dic53C2218yescomplemented
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C23×D4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C22⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C22⋊C4×C53C2211yescharacteristic
66C22×C22⋊C4×C53C2211yescharacteristic
67C53×#394C2218yes—
68C2×#95×C53C2211yescharacteristic
69C23×Dic53—24no—
70C23×Dic53—24no—
71C23×Dic53—24no—
72C23×Dic53—24no—
73C23×Dic53—42no—
74C23×Dic53—42no—
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2314yes—
81C23×Dic53C2314yes—
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85#13133210—232no—
86D4×Dic53—232no—
87C2×C4⋊Dic53—24no—
88C2×C4⋊Dic53—24no—
89C2×C4⋊Dic53—24no—
90C2×C4⋊Dic53—42no—
91C2×C4⋊Dic53C2314yes—
92C2×C4⋊Dic53C2314yes—
93C2×C4⋊Dic53C2314yes—
94C2×C4⋊Dic53C2314yes—
95C2×#11719919—24no—
96C2×#11719919—24no—
97C2×#11719919—24no—
98C2×#11719919—42no—
99C2×#11719919C2314yes—
100C2×#11719919C2314yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×C22⋊Dic53—24no—
104C2×C22⋊Dic53—24no—
105C2×C22⋊Dic53—24no—
106C2×C22⋊Dic53—42no—
107C2×C22⋊Dic53—42no—
108C2×C22⋊Dic53D418yes—
109C2×C22⋊Dic53C2314yes—
110C2×C22⋊Dic53C2314yes—
111C2×C22⋊Dic53C2314yes—
112C2×C22⋊Dic53C2314yes—
113C2×C22⋊Dic53C2314yes—
114C2×C22⋊Dic53C2314yes—
115C2×C4×Dic53—24no—
116C2×C4×Dic53—24no—
117C2×C4×Dic53—24no—
118C2×C4×Dic53C2314yes—
119C2×C4×Dic53C2314yes—
120C2×C4×Dic53C2314yes—
121#13133124C2314yes—
122#13133124C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130C25×C53C2311yescharacteristic
131C25×C53C2311yescharacteristic
132C22×D4×C53—24no—
133C22×D4×C53—24no—
134C22×D4×C53—24no—
135C22×D4×C53C2314yes—
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C2×C4⋊C4×C53—24no—
142C2×C4⋊C4×C53C2314yes—
143C2×C22⋊C4×C53—24no—
144C2×C22⋊C4×C53—24no—
145C2×C22⋊C4×C53—24no—
146C2×C22⋊C4×C53—24no—
147C2×C22⋊C4×C53C2314yes—
148C2×C22⋊C4×C53C2314yes—
149C2×C22⋊C4×C53C2314yes—
150C2×C22⋊C4×C53C2314yes—
151#95×C53C2314yes—
152C24×C53—22no—
153C24×C53—22no—
154C24×C53—22no—
155C24×C53—22no—
156C24×C53—22no—
157C24×C53—22no—
158C24×C53—22no—
159C24×C53—22no—
160C24×C53—22no—
161C24×C53—22no—
162C24×C53—22no—
163C24×C53—22no—
164C24×C53C2×D414yes—
165C24×C53#4114yes—
166C24×C53C2412yes—
167C24×C53C2412yes—
168C24×C53C2411yescharacteristic
169C2×D4×C53—232no—
170C2×D4×C53—28no—
171C2×D4×C53—28no—
172C2×D4×C53—28no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—22no—
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53#4114yes—
187C22×C4×C53#4114yes—
188C22×C4×C53C2412yes—
189C22×C4×C53C2412yes—
190C22×C4×C53C2412yes—
191C22×C4×C53C2412yes—
192C22×C4×C53C2412yes—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—28no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53—22no—
214C22×Dic53—22no—
215C22×Dic53—28no—
216C22×Dic53—28no—
217C22×Dic53—28no—
218C22×Dic53—44no—
219C22×Dic53—44no—
220C22×Dic53—416no—
221C22×Dic53—416no—
222C22×Dic53C2×D414yes—
223C22×Dic53C2×D414yes—
224C22×Dic53#4114yes—
225C22×Dic53C2412yes—
226C22×Dic53C2412yes—
227C22×Dic53C2412yes—
228C22×Dic53C2412yes—
229C22×Dic53C2412yes—
230C22×Dic53C2412yes—
231C22×Dic53C2412yes—
232C22×Dic53C2412yes—
233C4⋊C4×C53—28no—
234C22⋊C4×C53—28no—
235C22⋊C4×C53—28no—
236C22⋊C4×C53—28no—
237C22⋊C4×C53—28no—
238C22⋊Dic53—28no—
239C22⋊Dic53—28no—
240C22⋊Dic53—28no—
241C22⋊Dic53—44no—
242C22⋊Dic53—44no—
243C22⋊Dic53C2×D4116yes—
244C4⋊Dic53—28no—
245C4⋊Dic53—28no—
246C4⋊Dic53—28no—
247C4⋊Dic53—44no—
248#11719919—28no—
249#11719919—28no—
250#11719919—28no—
251#11719919—44no—
252C4×Dic53—28no—
253C4×Dic53—28no—
254C4×Dic53—28no—
255C23×C53—28no—
256C23×C53—28no—
257C23×C53—28no—
258C23×C53—28no—
259C23×C53—28no—
260C23×C53—28no—
261C23×C53—22no—
262C23×C53—22no—
263C23×C53—22no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—44no—
274C23×C53—44no—
275C23×C53—44no—
276C23×C53—44no—
277C23×C53—44no—
278C23×C53—44no—
279C23×C53—44no—
280C23×C53—44no—
281C23×C53C22×D414yes—
282C23×C53C22×D412yes—
283C23×C53C2×#4112yes—
284C23×C53C2×#4114yes—
285C23×C53C2×#4112yes—
286C23×C53C2×#4112yes—
287C23×C53C2×#4112yes—
288C23×C53H(5,𝔽2)12yes—
289C23×C532−1+412yes—
290C23×C53C2511yescharacteristic
291D4×C53—232no—
292C2×C4×C53—28no—
293C2×C4×C53—28no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—44no—
308C2×C4×C53—44no—
309C2×C4×C53—44no—
310C2×C4×C53C2×#4114yes—
311C2×C4×C53C2×#4114yes—
312C2×Dic53—28no—
313C2×Dic53—28no—
314C2×Dic53—28no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—416no—
337C2×Dic53—416no—
338C2×Dic53—44no—
339C2×Dic53—44no—
340C2×Dic53—44no—
341C2×Dic53—44no—
342C2×Dic53—44no—
343C2×Dic53C22×D414yes—
344C2×Dic53C22×D414yes—
345C2×Dic53C2×#4114yes—
346C2×#2468—531nomaximal, Sylow
347C22×C53—24no—
348C22×C53—24no—
349C22×C53—24no—
350C22×C53—24no—
351C22×C53—24no—
352C22×C53—24no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53—416no—
362C22×C53—416no—
363C22×C53#52514yes—
364C22×C53#52914yes—
365C22×C53#54214yes—
366C22×C53#54614yes—
367C22×C53#54714yes—
368C22×C53#55214yes—
369C22×C53#55314yes—
370C22×C53C23×D411yescharacteristic
371C22×C53C22×#4111yescharacteristic
372C22×C53C22×#4111yescharacteristic
373C22×C53C22×#4111yescharacteristic
374C22×C53C22×#4111yescharacteristic
375C22×C53C2×H(5,𝔽2)11yescharacteristic
376C22×C53C2×2−1+411yescharacteristic
377C4×C53—24no—
378C4×C53—24no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53—42no—
382Dic53—24no—
383Dic53—24no—
384Dic53—24no—
385Dic53—42no—
386Dic53—42no—
387Dic53—42no—
388Dic53—42no—
389Dic53—42no—
390C22×#126—531no—
391C22×C4×D4—531no—
392#2468—5316no—
393C2×#398—531no—
394C2×#398—531no—
395C2×#394—531no—
396C2×#394D5311yescharacteristic
397C2×#388—531no—
398C2×#388—531no—
399C2×#388—531no—
400C2×#387—531no—
401C2×#385—531no—
402C2×#385—531no—
403C2×#381—531no—
404C2×#380—531no—
405C2×C4×C4⋊C4—531no—
406C2×C53—44no—
407C2×C53—44no—
408C2×C53#246818yescomplemented
409C2×C53C2×#52511yescharacteristic
410C2×C53C2×#52911yescharacteristic
411C2×C53C2×#54211yescharacteristic
412C2×C53C2×#54611yescharacteristic
413C2×C53C2×#54711yescharacteristic
414C2×C53C2×#55211yescharacteristic
415C2×C53C2×#55311yescharacteristic
416C23×D4C2×D5311yescharacteristic
417C24×C4—531no—
418C24×C4—531no—
419C2×#126—538no—
420C2×#126—1068no—
421C2×C4×D4—538no—
422C2×C4×D4—1068no—
423C22×C4⋊C4—531no—
424C22×C4⋊C4—531no—
425C22×C4⋊C4—531no—
426C22×C4⋊C4—531no—
427C22×C4⋊C4—531no—
428C22×C4⋊C4—531no—
429C22×C4⋊C4—531no—
430C22×C4⋊C4—531no—
431C22×C4⋊C4C2×D5311yescharacteristic
432C22×C22⋊C4—531no—
433C22×C22⋊C4—531no—
434C22×C22⋊C4—531no—
435C22×C22⋊C4—531no—
436C22×C22⋊C4—531no—
437C22×C22⋊C4—531no—
438C22×C22⋊C4C2×D5311yescharacteristic
439C22×C22⋊C4C2×D5311yescharacteristic
440C22×C22⋊C4C2×D5311yescharacteristic
441C22×C22⋊C4C2×D5311yescharacteristic
442C22×C42—531no—
443C22×C42—531no—
444C22×C42—531no—
445#398—538no—
446#398—538no—
447#394—538no—
448#394C2×D5318yes—
449#388—538no—
450#388—538no—
451#388—538no—
452#387—538no—
453#385—538no—
454#385—538no—
455#381—538no—
456#380—538no—
457C4×C4⋊C4—538no—
458C2×#95—531no—
459C2×#95—531no—
460C2×#95—531no—
461C2×#95—531no—
462C2×#95—531no—
463C2×#95—531no—
464C2×#95—531no—
465C2×#95—531no—
466C2×#95—531no—
467C2×#95C2×D5311yescharacteristic
468C53C2×#246811yescharacteristic, complemented, Sylow
469C25C22×D5311yescharacteristic
470C25C22×D5311yescharacteristic
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4C22×D5314yes—
475C23×C4—531no—
476C23×C4—531no—
477C23×C4—531no—
478C23×C4—531no—
479C23×C4—531no—
480C23×C4—531no—
481C23×C4—531no—
482C23×C4—531no—
483C23×C4—534no—
484C23×C4—534no—
485C23×C4—1064no—
486C23×C4—1064no—
487C23×C4—1064no—
488C23×C4—1064no—
489C23×C4—2122no—
490C23×C4—2122no—
491C23×C4C22×D5311yescharacteristic
492C23×C4C22×D5311yescharacteristic
493C23×C4C22×D5311yescharacteristic
494C23×C4C22×D5311yescharacteristic
495C23×C4C22×D5311yescharacteristic
496#126—10632no—
497C4×D4—10632no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—534no—
500C2×C4⋊C4—534no—
501C2×C4⋊C4—534no—
502C2×C4⋊C4—534no—
503C2×C4⋊C4—534no—
504C2×C4⋊C4—534no—
505C2×C4⋊C4—534no—
506C2×C4⋊C4—534no—
507C2×C4⋊C4—1064no—
508C2×C4⋊C4—1064no—
509C2×C4⋊C4—1064no—
510C2×C4⋊C4—1064no—
511C2×C4⋊C4—1064no—
512C2×C4⋊C4—1064no—
513C2×C4⋊C4—2122no—
514C2×C4⋊C4—2122no—
515C2×C4⋊C4C22×D5314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—538no—
521C2×C22⋊C4—534no—
522C2×C22⋊C4—534no—
523C2×C22⋊C4—534no—
524C2×C22⋊C4—534no—
525C2×C22⋊C4—534no—
526C2×C22⋊C4—534no—
527C2×C22⋊C4—1064no—
528C2×C22⋊C4—1064no—
529C2×C22⋊C4—1064no—
530C2×C22⋊C4—2122no—
531C2×C22⋊C4—2122no—
532C2×C22⋊C4C22×D5314yes—
533C2×C22⋊C4C22×D5314yes—
534C2×C22⋊C4C22×D5314yes—
535C2×C22⋊C4C22×D5314yes—
536C2×C42—534no—
537C2×C42—534no—
538C2×C42—534no—
539C2×C42—1064no—
540C2×C42—1064no—
541C2×C42—1064no—
542#95—534no—
543#95—534no—
544#95—534no—
545#95—534no—
546#95—534no—
547#95—534no—
548#95—534no—
549#95—534no—
550#95—534no—
551#95C22×D5314yes—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24D4×D5314yes—
565C24#1171994714yes—
566C24C23×D5312yes—
567C24C23×D5312yes—
568C24C23×D5311yescharacteristic
569C2×D4—232no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—534no—
587C22×C4—534no—
588C22×C4—534no—
589C22×C4—532no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—532no—
593C22×C4—532no—
594C22×C4—532no—
595C22×C4—532no—
596C22×C4—532no—
597C22×C4—1068no—
598C22×C4—1068no—
599C22×C4—1068no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1068no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—2124no—
623C22×C4—2124no—
624C22×C4—21216no—
625C22×C4—21216no—
626C22×C4#1171994714yes—
627C22×C4#1171994714yes—
628C22×C4C23×D5312yes—
629C22×C4C23×D5312yes—
630C22×C4C23×D5312yes—
631C22×C4C23×D5312yes—
632C22×C4C23×D5312yes—
633C4⋊C4—28no—
634C4⋊C4—1068no—
635C4⋊C4—1068no—
636C4⋊C4—1068no—
637C4⋊C4—1068no—
638C4⋊C4—1068no—
639C4⋊C4—1068no—
640C4⋊C4—2124no—
641C4⋊C4—2124no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—28no—
645C22⋊C4—28no—
646C22⋊C4—5316no—
647C22⋊C4—1068no—
648C22⋊C4—1068no—
649C22⋊C4—1068no—
650C22⋊C4—2124no—
651C22⋊C4—2124no—
652C42—1068no—
653C42—1068no—
654C42—1068no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23C2×D4×D5314yes—
682C23C2×D4×D5312yes—
683C23#41×D5312yes—
684C23C2×#1171994714yes—
685C23C2×#1171994712yes—
686C23C2×#1171994712yes—
687C23C2×#1171994712yes—
688C23#1313326312yes—
689C23#1313326412yes—
690C23C24×D5311yescharacteristic
691D4—232no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—534no—
711C2×C4—534no—
712C2×C4—534no—
713C2×C4—1068no—
714C2×C4—1068no—
715C2×C4—1068no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1062no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—21216no—
738C2×C4—21216no—
739C2×C4—2124no—
740C2×C4—2124no—
741C2×C4—2124no—
742C2×C4—2124no—
743C2×C4—2124no—
744C2×C4C2×#1171994714yes—
745C2×C4C2×#1171994714yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—416no—
761C22—416no—
762C22#1681112914yes—
763C22#1681115414yes—
764C22#1681124214yes—
765C22#1681126514yes—
766C22#1681127314yes—
767C22#1681131014yes—
768C22#1681132514yes—
769C22C22×D4×D5311yescharacteristic
770C22C2×#41×D5311yescharacteristic
771C22C22×#1171994711yescharacteristic
772C22C22×#1171994711yescharacteristic
773C22C22×#1171994711yescharacteristic
774C22C2×#1313326311yescharacteristic
775C22C2×#1313326411yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—1064no—
782C4—1064no—
783C4—1064no—
784C4—2122no—
785C4—2122no—
786C4—2122no—
787C4—2122no—
788C4—2122no—
789C2—44no—
790C2—44no—
791C2#2027877418yesdirect product factor
792C2C2×#1681112911yescharacteristic
793C2C2×#1681115411yescharacteristic
794C2C2×#1681124211yescharacteristic
795C2C2×#1681126511yescharacteristic
796C2C2×#1681127311yescharacteristic
797C2C2×#1681131011yescharacteristic
798C2C2×#1681132511yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#394C2
socleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#394D53
hypocenterC53C2×#2468
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#13133210C2semidirect
3. #20278774C2direct (N × H)
4. C2×#16810556C2semidirect
5. C2×#16810555C2semidirect
7. C2×#16810516C2semidirect
8. C2×#16810511C2semidirect
9. C2×#16810511C2semidirect
10. C2×#16810505C2semidirect
11. C2×#16810498C2semidirect
12. C2×#16810498C2semidirect
13. C2×#16810484C2semidirect
14. C2×#16810481C2semidirect
15. C2×C4⋊C4×Dic53C2semidirect
20. C2×#13133210C22semidirect
40. #16810556C22semidirect
41. #16810555C22semidirect
43. #16810516C22semidirect
44. #16810511C22semidirect
45. #16810511C22semidirect
46. #16810505C22semidirect
47. #16810498C22semidirect
48. #16810498C22semidirect
49. #16810484C22semidirect
50. #16810481C22semidirect
51. C4⋊C4×Dic53C22semidirect
408. C2×C53#2468semidirect
468. C53C2×#2468semidirect
791. C2#20278774direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332102
C22×D4×Dic532
#202787742
C2×#168105562
C2×#168105552
C2×#168105372
C2×#168105162
C2×#168105112
C2×#168105052
C2×#168104982
C2×#168104842
C2×#168104812
C2×C4⋊C4×Dic532
C2×C53×#3942
C2×#246853