Finite Group Databasebeta

← C2×#20279728 #27554134

Subgroups — C2×#20279728 #27554134

Order 13568.

3094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133196C211yesmaximal, characteristic
2C22×#13133194C211yesmaximal, characteristic
3#20279728C2116yesmaximal, direct product factor
4C2×#16810557C211yesmaximal, characteristic, complemented
5C2×#16810556C211yesmaximal, characteristic, complemented
6C2×#16810544C211yesmaximal, characteristic, complemented
7C2×#16810543C211yesmaximal, characteristic, complemented
8C2×#16810527C211yesmaximal, characteristic, complemented
9C2×#16810527C211yesmaximal, characteristic, complemented
10C2×#16810522C211yesmaximal, characteristic, complemented
11C2×#16810519C211yesmaximal, characteristic, complemented
12C2×#16810498C211yesmaximal, characteristic
13C2×#16810481C211yesmaximal, characteristic
14C2×C22⋊C4×Dic53C211yesmaximal, characteristic
15C22×#13133124C211yesmaximal, characteristic
16C2×C53×#385C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C24×Dic53C2211yescharacteristic
20C24×Dic53C2211yescharacteristic
21C2×#13133196—28no—
22C2×#13133196C2218yes—
23C2×#13133194—28no—
24C2×#13133194C2218yes—
25C22×C4⋊Dic53C2211yescharacteristic
26C22×C4⋊Dic53C2211yescharacteristic
27C22×C4⋊Dic53C2211yescharacteristic
28C22×C4⋊Dic53C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×#11719919C2211yescharacteristic
33C22×#11719919C2211yescharacteristic
34C22×#11719919C2211yescharacteristic
35C22×C22⋊Dic53C2211yescharacteristic
36C22×C22⋊Dic53C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39#16810557C2218yescomplemented
40#16810556C2218yescomplemented
41#16810544C2218yescomplemented
42#16810543C2218yescomplemented
43#16810527C2218yescomplemented
44#16810527C2218yescomplemented
45#16810522C2218yescomplemented
46#16810519C2218yescomplemented
47#16810498C2218yes—
48#16810481C2218yes—
49C22⋊C4×Dic53C2218yes—
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2218yes—
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C24×C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C22⋊C4×C53C2211yescharacteristic
66C53×#385C2218yes—
67C2×#95×C53C2211yescharacteristic
68C2×#95×C53C2211yescharacteristic
69C22×Dic106—24no—
70C22×Dic106—24no—
71C22×Dic106—24no—
72C22×Dic106—24no—
73C22×Dic106—42no—
74C22×Dic106—42no—
75C22×Dic106C2314yes—
76C22×Dic106C2314yes—
77C23×Dic53—24no—
78C23×Dic53—24no—
79C23×Dic53—42no—
80C23×Dic53—42no—
81C23×Dic53—42no—
82C23×Dic53Q818yescomplemented
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C23×Dic53C2311yescharacteristic
86C23×Dic53C2314yes—
87C23×Dic53C2311yescharacteristic
88C23×Dic53C2311yescharacteristic
89C23×Dic53C2311yescharacteristic
90C23×Dic53C2311yescharacteristic
91C23×Dic53C2311yescharacteristic
92C23×Dic53C2314yes—
93#13133196—232no—
94#13133194—232no—
95C2×C4⋊Dic53—24no—
96C2×C4⋊Dic53—24no—
97C2×C4⋊Dic53—24no—
98C2×C4⋊Dic53—42no—
99C2×C4⋊Dic53C2314yes—
100C2×C4⋊Dic53C2314yes—
101C2×C4⋊Dic53C2314yes—
102C2×C4⋊Dic53C2314yes—
103C2×#11719919—24no—
104C2×#11719919—24no—
105C2×#11719919—24no—
106C2×#11719919—24no—
107C2×#11719919—42no—
108C2×#11719919—42no—
109C2×#11719919C2314yes—
110C2×#11719919C2314yes—
111C2×#11719919C2314yes—
112C2×#11719919C2314yes—
113C2×#11719919C2314yes—
114C2×#11719919C2314yes—
115C2×C22⋊Dic53—24no—
116C2×C22⋊Dic53D418yes—
117C2×C22⋊Dic53C2314yes—
118C2×C22⋊Dic53C2314yes—
119C2×C4×Dic53—42no—
120C2×C4×Dic53—42no—
121C2×C4×Dic53C2314yes—
122C2×C4×Dic53C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130#13133124C2314yes—
131#13133124C2314yes—
132#13133124C2314yes—
133C25×C53C2311yescharacteristic
134C23×C4×C53—24no—
135C23×C4×C53—24no—
136C23×C4×C53—42no—
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2314yes—
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C2×C4⋊C4×C53—24no—
145C2×C4⋊C4×C53—42no—
146C2×C4⋊C4×C53C2314yes—
147C2×C4⋊C4×C53C2314yes—
148C2×C22⋊C4×C53—24no—
149C2×C22⋊C4×C53Q818yescomplemented
150C2×C22⋊C4×C53C2314yes—
151C2×C22⋊C4×C53C2314yes—
152#95×C53C2314yes—
153#95×C53C2314yes—
154C24×C53—22no—
155C24×C53—22no—
156C24×C53—22no—
157C24×C53—22no—
158C24×C53C2×D414yes—
159C24×C53C2×Q814yes—
160C24×C53C2×Q814yes—
161C24×C53C2412yes—
162C24×C53C2411yescharacteristic
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—22no—
172C22×C4×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—28no—
180C22×C4×C53—44no—
181C22×C4×C53—416no—
182C22×C4×C53C2×Q814yes—
183C22×C4×C53C2×Q814yes—
184C22×C4×C53#4114yes—
185C22×C4×C53C2412yes—
186C22×C4×C53C2412yes—
187C22×C4×C53C2412yes—
188C22×C4×C53C2412yes—
189C22×C4×C53C2412yes—
190C22×C4×C53C2412yes—
191C22×Dic53—22no—
192C22×Dic53—22no—
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—22no—
203C22×Dic53—22no—
204C22×Dic53—28no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—28no—
212C22×Dic53—416no—
213C22×Dic53—44no—
214C22×Dic53—44no—
215C22×Dic53—44no—
216C22×Dic53—416no—
217C22×Dic53C2×D414yes—
218C22×Dic53C2×D414yes—
219C22×Dic53C2×Q814yes—
220C22×Dic53C2×Q814yes—
221C22×Dic53C2×Q8116yescomplemented
222C22×Dic53#4114yes—
223C22×Dic53C2412yes—
224C22×Dic53C2412yes—
225C22×Dic53C2412yes—
226C22×Dic53C2412yes—
227C22×Dic53C2412yes—
228C22×Dic53C2412yes—
229C22×Dic53C2412yes—
230C22×Dic53C2412yes—
231C2×Dic106—28no—
232C2×Dic106—28no—
233C2×Dic106—28no—
234C2×Dic106—28no—
235C2×Dic106—44no—
236C2×Dic106—44no—
237C2×Dic106—416no—
238C2×Dic106—416no—
239C4⋊C4×C53—28no—
240C4⋊C4×C53—44no—
241C22⋊C4×C53—28no—
242C22⋊C4×C53C2×Q8116yescomplemented
243C22⋊Dic53—28no—
244C22⋊Dic53C2×D4116yes—
245C4⋊Dic53—28no—
246C4⋊Dic53—28no—
247C4⋊Dic53—28no—
248C4⋊Dic53—44no—
249#11719919—28no—
250#11719919—28no—
251#11719919—28no—
252#11719919—28no—
253#11719919—44no—
254#11719919—44no—
255C4×Dic53—44no—
256C4×Dic53—44no—
257C23×C53—28no—
258C23×C53—28no—
259C23×C53—28no—
260C23×C53—28no—
261C23×C53—28no—
262C23×C53—28no—
263C23×C53—22no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53C4⋊Q8116yes—
268C23×C53C22×D414yes—
269C23×C53C22×D412yes—
270C23×C53C22×Q814yes—
271C23×C53C22×Q812yes—
272C23×C53C22×Q814yes—
273C23×C53C22×Q812yes—
274C23×C53C2×#4112yes—
275C23×C53C2×#4112yes—
276C23×C53H(5,𝔽2)12yes—
277C23×C53H(5,𝔽2)12yes—
278C23×C53C2511yescharacteristic
279C2×C4×C53—28no—
280C2×C4×C53—28no—
281C2×C4×C53—28no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
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—416no—
298C2×C4×C53—44no—
299C2×C4×C53—44no—
300C2×C4×C53—44no—
301C2×C4×C53C22×Q814yes—
302C2×C4×C53C22×Q814yes—
303C2×C4×C53C2×#4114yes—
304C2×Dic53—28no—
305C2×Dic53—28no—
306C2×Dic53—28no—
307C2×Dic53—28no—
308C2×Dic53—28no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
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—416no—
329C2×Dic53—416no—
330C2×Dic53—44no—
331C2×Dic53—44no—
332C2×Dic53—44no—
333C2×Dic53C22×D414yes—
334C2×Dic53C22×D414yes—
335C2×Dic53C22×Q814yes—
336C2×Dic53C22×Q814yes—
337C2×Dic53C2×#4114yes—
338Dic106—416no—
339Dic106—416no—
340C2×#2549—531nomaximal, Sylow
341C22×C53—24no—
342C22×C53—24no—
343C22×C53—24no—
344C22×C53—24no—
345C22×C53—24no—
346C22×C53—24no—
347C22×C53—232no—
348C22×C53C2×C4⋊Q818yes—
349C22×C53C2×C4⋊Q814yes—
350C22×C53#53314yes—
351C22×C53#54314yes—
352C22×C53#54614yes—
353C22×C53#54614yes—
354C22×C53#55414yes—
355C22×C53#55414yes—
356C22×C53C23×D411yescharacteristic
357C22×C53C23×Q811yescharacteristic
358C22×C53C23×Q811yescharacteristic
359C22×C53C22×#4111yescharacteristic
360C22×C53C22×#4111yescharacteristic
361C22×C53C2×H(5,𝔽2)11yescharacteristic
362C22×C53C2×H(5,𝔽2)11yescharacteristic
363C4×C53—24no—
364C4×C53—24no—
365C4×C53—24no—
366C4×C53—42no—
367C4×C53—42no—
368C4×C53—42no—
369Dic53—24no—
370Dic53—24no—
371Dic53—24no—
372Dic53—24no—
373Dic53—24no—
374Dic53—42no—
375Dic53—42no—
376Dic53—42no—
377C22×C22⋊Q8—531no—
378C22×C22⋊Q8—531no—
379#2549—5316no—
380C2×#398—531no—
381C2×#398—531no—
382C2×#395—531no—
383C2×#395—531no—
384C2×#391—531no—
385C2×#391—531no—
386C2×#389—531no—
387C2×#389—531no—
388C2×#385—531no—
389C2×#385D5311yescharacteristic
390C2×#380—531no—
391C2×C4×C22⋊C4—531no—
392C22×#95—531no—
393C2×C53—28no—
394C2×C53#254918yescomplemented
395C2×C53C22×C4⋊Q811yescharacteristic
396C2×C53C2×#53311yescharacteristic
397C2×C53C2×#54311yescharacteristic
398C2×C53C2×#54611yescharacteristic
399C2×C53C2×#54611yescharacteristic
400C2×C53C2×#55411yescharacteristic
401C2×C53C2×#55411yescharacteristic
402C23×Q8—531no—
403C23×Q8—531no—
404C24×C4—531no—
405C24×C4—531no—
406C24×C4C2×D5311yescharacteristic
407C2×C22⋊Q8—538no—
408C2×C22⋊Q8—538no—
409C2×C22⋊Q8—1068no—
410C2×C22⋊Q8—1068no—
411C22×C4⋊C4—531no—
412C22×C4⋊C4—531no—
413C22×C4⋊C4—531no—
414C22×C4⋊C4—531no—
415C22×C4⋊C4—531no—
416C22×C4⋊C4—531no—
417C22×C4⋊C4—531no—
418C22×C4⋊C4—531no—
419C22×C4⋊C4—531no—
420C22×C4⋊C4—531no—
421C22×C4⋊C4C2×D5311yescharacteristic
422C22×C4⋊C4C2×D5311yescharacteristic
423C22×C22⋊C4—531no—
424C22×C22⋊C4—531no—
425C22×C22⋊C4C2×D5311yescharacteristic
426C22×C22⋊C4C2×D5311yescharacteristic
427C22×C42—531no—
428C22×C42—531no—
429#398—538no—
430#398—538no—
431#395—538no—
432#395—538no—
433#391—538no—
434#391—538no—
435#389—538no—
436#389—538no—
437#385—538no—
438#385C2×D5318yes—
439#380—538no—
440C4×C22⋊C4—538no—
441C2×#95—531no—
442C2×#95—531no—
443C2×#95—531no—
444C2×#95—531no—
445C2×#95—531no—
446C2×#95—531no—
447C2×#95—531no—
448C2×#95—531no—
449C2×#95—538no—
450C2×#95—531no—
451C2×#95—531no—
452C2×#95C2×D5311yescharacteristic
453C2×#95C2×D5311yescharacteristic
454C53C2×#254911yescharacteristic, complemented, Sylow
455C25C22×D5311yescharacteristic
456C22×Q8—534no—
457C22×Q8—534no—
458C22×Q8—1064no—
459C22×Q8—1064no—
460C22×Q8—1064no—
461C22×Q8—1064no—
462C22×Q8—2122no—
463C22×Q8—2122no—
464C23×C4—24no—
465C23×C4—24no—
466C23×C4—42no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—531no—
470C23×C4—531no—
471C23×C4—531no—
472C23×C4—538no—
473C23×C4—534no—
474C23×C4—531no—
475C23×C4—531no—
476C23×C4—531no—
477C23×C4—534no—
478C23×C4—1064no—
479C23×C4—1064no—
480C23×C4—2122no—
481C23×C4—2122no—
482C23×C4—2122no—
483C23×C4C22×D5311yescharacteristic
484C23×C4C22×D5311yescharacteristic
485C23×C4C22×D5311yescharacteristic
486C23×C4C22×D5314yes—
487C23×C4C22×D5311yescharacteristic
488C23×C4C22×D5311yescharacteristic
489C23×C4C22×D5311yescharacteristic
490C22⋊Q8—10632no—
491C22⋊Q8—10632no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—534no—
495C2×C4⋊C4—534no—
496C2×C4⋊C4—534no—
497C2×C4⋊C4—534no—
498C2×C4⋊C4—534no—
499C2×C4⋊C4—534no—
500C2×C4⋊C4—534no—
501C2×C4⋊C4—534no—
502C2×C4⋊C4—534no—
503C2×C4⋊C4—534no—
504C2×C4⋊C4—1064no—
505C2×C4⋊C4—1064no—
506C2×C4⋊C4—1064no—
507C2×C4⋊C4—1064no—
508C2×C4⋊C4—1064no—
509C2×C4⋊C4—1064no—
510C2×C4⋊C4—1064no—
511C2×C4⋊C4—2122no—
512C2×C4⋊C4—2122no—
513C2×C4⋊C4—2122no—
514C2×C4⋊C4C22×D5314yes—
515C2×C4⋊C4C22×D5314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—538no—
518C2×C22⋊C4—534no—
519C2×C22⋊C4—534no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4Dic10618yescomplemented
522C2×C22⋊C4C22×D5314yes—
523C2×C22⋊C4C22×D5314yes—
524C2×C42—534no—
525C2×C42—534no—
526C2×C42—2122no—
527C2×C42—2122no—
528#95—534no—
529#95—534no—
530#95—534no—
531#95—534no—
532#95—534no—
533#95—534no—
534#95—534no—
535#95—534no—
536#95—534no—
537#95—534no—
538#95C22×D5314yes—
539#95C22×D5314yes—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24C2×Dic10614yes—
545C24D4×D5314yes—
546C24Q8×D5314yes—
547C24C23×D5312yes—
548C24C23×D5311yescharacteristic
549C2×Q8—1068no—
550C2×Q8—1068no—
551C2×Q8—1068no—
552C2×Q8—1068no—
553C2×Q8—2124no—
554C2×Q8—2124no—
555C2×Q8—21216no—
556C2×Q8—21216no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—44no—
575C22×C4—416no—
576C22×C4—534no—
577C22×C4—534no—
578C22×C4—534no—
579C22×C4—534no—
580C22×C4—534no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—532no—
586C22×C4—5316no—
587C22×C4—532no—
588C22×C4—532no—
589C22×C4—532no—
590C22×C4—1068no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1068no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—2124no—
612C22×C4—2124no—
613C22×C4—2124no—
614C22×C4—21216no—
615C22×C4—21216no—
616C22×C4C2×Dic10614yes—
617C22×C4C2×Dic10614yes—
618C22×C4#1171994714yes—
619C22×C4C23×D5312yes—
620C22×C4C23×D5312yes—
621C22×C4C23×D5312yes—
622C22×C4C23×D5312yes—
623C22×C4C23×D5312yes—
624C22×C4C23×D5312yes—
625C4⋊C4—28no—
626C4⋊C4—44no—
627C4⋊C4—1068no—
628C4⋊C4—1068no—
629C4⋊C4—1068no—
630C4⋊C4—1068no—
631C4⋊C4—1068no—
632C4⋊C4—1068no—
633C4⋊C4—1068no—
634C4⋊C4—2124no—
635C4⋊C4—2124no—
636C4⋊C4—2124no—
637C22⋊C4—28no—
638C22⋊C4—5316no—
639C22⋊C4—1068no—
640C22⋊C4C2×Dic106116yescomplemented
641C42—2124no—
642C42—2124no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—28no—
652C23—28no—
653C23#13133216116yes—
654C23C2×D4×D5314yes—
655C23C2×D4×D5312yes—
656C23C2×Q8×D5314yes—
657C23C2×Q8×D5312yes—
658C23C22×Dic10614yes—
659C23C22×Dic10612yes—
660C23#41×D5312yes—
661C23C2×#1171994712yes—
662C23#1313326212yes—
663C23#1313326312yes—
664C23C24×D5311yescharacteristic
665Q8—21216no—
666Q8—21216no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—28no—
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—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—534no—
690C2×C4—534no—
691C2×C4—534no—
692C2×C4—534no—
693C2×C4—534no—
694C2×C4—1068no—
695C2×C4—1068no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1068no—
707C2×C4—1068no—
708C2×C4—1068no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—21216no—
719C2×C4—21216no—
720C2×C4—2124no—
721C2×C4—2124no—
722C2×C4—2124no—
723C2×C4C22×Dic10614yes—
724C2×C4C22×Dic10614yes—
725C2×C4C2×#1171994714yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—232no—
731C22—24no—
732C22—24no—
733C22C2×#1313321618yes—
734C22C2×#1313321614yes—
735C22#1681117514yes—
736C22#1681124814yes—
737C22#1681126014yes—
738C22#1681126514yes—
739C22#1681133014yes—
740C22#1681133214yes—
741C22C22×D4×D5311yescharacteristic
742C22C22×Q8×D5311yescharacteristic
743C22C23×Dic10611yescharacteristic
744C22C2×#41×D5311yescharacteristic
745C22C22×#1171994711yescharacteristic
746C22C2×#1313326211yescharacteristic
747C22C2×#1313326311yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—1064no—
755C4—1064no—
756C4—1064no—
757C4—1064no—
758C4—1064no—
759C4—2122no—
760C4—2122no—
761C4—2122no—
762C2—28no—
763C2#2027972818yesdirect product factor
764C2C22×#1313321611yescharacteristic
765C2C2×#1681117511yescharacteristic
766C2C2×#1681124811yescharacteristic
767C2C2×#1681126011yescharacteristic
768C2C2×#1681126511yescharacteristic
769C2C2×#1681133011yescharacteristic
770C2C2×#1681133211yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#385D53
hypocenterC53C2×#2549
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. #20279728C2direct (N × H)
4. C2×#16810557C2semidirect
5. C2×#16810556C2semidirect
6. C2×#16810544C2semidirect
7. C2×#16810543C2semidirect
8. C2×#16810527C2semidirect
9. C2×#16810527C2semidirect
10. C2×#16810522C2semidirect
11. C2×#16810519C2semidirect
39. #16810557C22semidirect
40. #16810556C22semidirect
41. #16810544C22semidirect
42. #16810543C22semidirect
43. #16810527C22semidirect
44. #16810527C22semidirect
45. #16810522C22semidirect
46. #16810519C22semidirect
82. C23×Dic53Q8semidirect
149. C2×C22⋊C4×C53Q8semidirect
221. C22×Dic53C2×Q8semidirect
242. C22⋊C4×C53C2×Q8semidirect
394. C2×C53#2549semidirect
454. C53C2×#2549semidirect
521. C2×C22⋊C4Dic106semidirect
640. C22⋊C4C2×Dic106semidirect
763. C2#20279728direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331962
C22×#131331942
#202797282
C2×#168105572
C2×#168105562
C2×#168105442
C2×#168105432
C2×#168105272
C2×#168105222
C2×#168105192
C2×#168104982
C2×#168104812
C2×C22⋊C4×Dic532
C22×#131331242
C2×C53×#3852
C2×#254953