Finite Group Databasebeta

← C2×#20279798 #27554196

Subgroups — C2×#20279798 #27554196

Order 13568.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133208C211yesmaximal, characteristic, complemented
2C22×#13133194C211yesmaximal, characteristic
3#20279798C2116yesmaximal, direct product factor
4C2×#16810559C211yesmaximal, characteristic
5C2×#16810556C211yesmaximal, characteristic, complemented
6C2×#16810546C211yesmaximal, characteristic
7C2×#16810544C211yesmaximal, characteristic, complemented
8C2×#16810527C211yesmaximal, characteristic, complemented
9C2×#16810521C211yesmaximal, characteristic, complemented
10C2×#16810520C211yesmaximal, characteristic, complemented
11C2×#16810516C211yesmaximal, characteristic
12C2×#16810506C211yesmaximal, characteristic, complemented
13C2×#16810498C211yesmaximal, characteristic
14C2×C4×C4⋊Dic53C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic53C211yesmaximal, characteristic
16C2×C53×#388C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C2×#13133208—28no—
20C2×#13133208C2218yescomplemented
21C2×#13133194—28no—
22C2×#13133194C2218yes—
23C22×C4⋊Dic53C2211yescharacteristic
24C22×C4⋊Dic53C2211yescharacteristic
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×C22⋊Dic53C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39C22×C4×Dic53C2211yescharacteristic
40C22×C4×Dic53C2211yescharacteristic
41#16810559C2218yes—
42#16810556C2218yescomplemented
43#16810546C2218yes—
44#16810544C2218yescomplemented
45#16810527C2218yescomplemented
46#16810521C2218yescomplemented
47#16810520C2218yescomplemented
48#16810516C2218yes—
49#16810506C2218yescomplemented
50#16810498C2218yes—
51C4×C4⋊Dic53C2218yescomplemented
52C22⋊C4×Dic53C2218yes—
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C22⋊C4×C53C2211yescharacteristic
63C22×C22⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C42×C53C2211yescharacteristic
66C53×#388C2218yes—
67C2×#95×C53C2211yescharacteristic
68C2×#95×C53C2211yescharacteristic
69C22×Dic106—24no—
70C22×Dic106—24no—
71C22×Dic106—42no—
72C22×Dic106C2314yes—
73C23×Dic53—24no—
74C23×Dic53—24no—
75C23×Dic53—42no—
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2314yes—
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85#13133208—232no—
86#13133194—232no—
87C2×C4⋊Dic53—24no—
88C2×C4⋊Dic53—24no—
89C2×C4⋊Dic53—24no—
90C2×C4⋊Dic53—24no—
91C2×C4⋊Dic53—24no—
92C2×C4⋊Dic53D418yes—
93C2×C4⋊Dic53C2314yes—
94C2×C4⋊Dic53C2314yes—
95C2×C4⋊Dic53C2314yes—
96C2×C4⋊Dic53C2314yes—
97C2×C4⋊Dic53C2314yes—
98C2×C4⋊Dic53C2314yes—
99C2×#11719919—24no—
100C2×#11719919—24no—
101C2×#11719919—24no—
102C2×#11719919—24no—
103C2×#11719919—24no—
104C2×#11719919—42no—
105C2×#11719919C2314yes—
106C2×#11719919C2314yes—
107C2×#11719919C2314yes—
108C2×#11719919C2314yes—
109C2×#11719919C2314yes—
110C2×#11719919C2314yes—
111C2×C22⋊Dic53—24no—
112C2×C22⋊Dic53—24no—
113C2×C22⋊Dic53—42no—
114C2×C22⋊Dic53C2314yes—
115C2×C22⋊Dic53C2314yes—
116C2×C22⋊Dic53C2314yes—
117C2×C4×Dic53—24no—
118C2×C4×Dic53—42no—
119C2×C4×Dic53—42no—
120C2×C4×Dic53C2314yes—
121C2×C4×Dic53C2314yes—
122C2×C4×Dic53C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130#13133124C2314yes—
131C25×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C2×C4⋊C4×C53—24no—
139C2×C4⋊C4×C53C2314yes—
140C2×C22⋊C4×C53—24no—
141C2×C22⋊C4×C53—24no—
142C2×C22⋊C4×C53Q818yescomplemented
143C2×C22⋊C4×C53C2314yes—
144C2×C22⋊C4×C53C2314yes—
145C2×C22⋊C4×C53C2314yes—
146C2×C42×C53—24no—
147C2×C42×C53C2314yes—
148#95×C53C2314yes—
149#95×C53C2314yes—
150C24×C53—22no—
151C24×C53—22no—
152C24×C53—22no—
153C24×C53—22no—
154C24×C53—22no—
155C24×C53—22no—
156C24×C53C2×Q814yes—
157C24×C53C2412yes—
158C24×C53C2411yescharacteristic
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
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—22no—
173C22×C4×C53C2×D414yes—
174C22×C4×C53C2×Q814yes—
175C22×C4×C53C2×Q814yes—
176C22×C4×C53#4114yes—
177C22×C4×C53C2412yes—
178C22×C4×C53C2412yes—
179C22×C4×C53C2412yes—
180C22×C4×C53C2412yes—
181C22×C4×C53C2412yes—
182C22×C4×C53C2412yes—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
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—28no—
204C22×Dic53—28no—
205C22×Dic53—44no—
206C22×Dic53—416no—
207C22×Dic53C2×D414yes—
208C22×Dic53C2×D414yes—
209C22×Dic53#4114yes—
210C22×Dic53#4114yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C22×Dic53C2412yes—
214C22×Dic53C2412yes—
215C22×Dic53C2412yes—
216C22×Dic53C2412yes—
217C22×Dic53C2412yes—
218C22×Dic53C2412yes—
219C2×Dic106—28no—
220C2×Dic106—28no—
221C2×Dic106—44no—
222C2×Dic106—416no—
223C4⋊C4×C53—28no—
224C22⋊C4×C53—28no—
225C22⋊C4×C53—28no—
226C22⋊C4×C53C2×Q8116yescomplemented
227C42×C53—28no—
228C22⋊Dic53—28no—
229C22⋊Dic53—28no—
230C22⋊Dic53—44no—
231C4⋊Dic53—28no—
232C4⋊Dic53—28no—
233C4⋊Dic53—28no—
234C4⋊Dic53—28no—
235C4⋊Dic53—28no—
236C4⋊Dic53C2×D4116yes—
237#11719919—28no—
238#11719919—28no—
239#11719919—28no—
240#11719919—28no—
241#11719919—28no—
242#11719919—44no—
243C4×Dic53—28no—
244C4×Dic53—44no—
245C4×Dic53—44no—
246C23×C53—28no—
247C23×C53—28no—
248C23×C53—28no—
249C23×C53—22no—
250C23×C53—22no—
251C23×C53—22no—
252C23×C53—22no—
253C23×C53—22no—
254C23×C53—22no—
255C23×C53—44no—
256C23×C53—44no—
257C23×C53—44no—
258C23×C53—44no—
259C23×C53C22×D412yes—
260C23×C53C22×Q814yes—
261C23×C53C22×Q812yes—
262C23×C53C2×#4112yes—
263C23×C53C2×#4112yes—
264C23×C53C2×#4112yes—
265C23×C53H(5,𝔽2)12yes—
266C23×C532−1+412yes—
267C23×C53C2511yescharacteristic
268C2×C4×C53—28no—
269C2×C4×C53—28no—
270C2×C4×C53—28no—
271C2×C4×C53—28no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—44no—
287C2×C4×C53—44no—
288C2×C4×C53C22×D414yes—
289C2×C4×C53C22×Q814yes—
290C2×C4×C53C22×Q814yes—
291C2×C4×C53C2×#4114yes—
292C2×Dic53—28no—
293C2×Dic53—28no—
294C2×Dic53—28no—
295C2×Dic53—28no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—416no—
317C2×Dic53—44no—
318C2×Dic53—44no—
319C2×Dic53—44no—
320C2×Dic53—44no—
321C2×Dic53C22×D414yes—
322C2×Dic53C22×D414yes—
323C2×Dic53C2×#4114yes—
324C2×Dic53C2×#4114yes—
325Dic106—416no—
326C2×#2556—531nomaximal, Sylow
327C22×C53—24no—
328C22×C53—24no—
329C22×C53—24no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53—42no—
334C22×C53—416no—
335C22×C53#53214yes—
336C22×C53#53314yes—
337C22×C53#53914yes—
338C22×C53#54614yes—
339C22×C53D4×Q814yes—
340C22×C53#55214yes—
341C22×C53#55414yes—
342C22×C53C23×D411yescharacteristic
343C22×C53C23×Q811yescharacteristic
344C22×C53C22×#4111yescharacteristic
345C22×C53C22×#4111yescharacteristic
346C22×C53C22×#4111yescharacteristic
347C22×C53C2×H(5,𝔽2)11yescharacteristic
348C22×C53C2×2−1+411yescharacteristic
349C4×C53—24no—
350C4×C53—24no—
351C4×C53—24no—
352C4×C53—24no—
353C4×C53—42no—
354C4×C53—42no—
355Dic53—24no—
356Dic53—24no—
357Dic53—24no—
358Dic53—24no—
359Dic53—42no—
360Dic53—42no—
361Dic53—42no—
362Dic53—42no—
363C22×#125—531no—
364C22×C22⋊Q8—531no—
365#2556—5316no—
366C2×#399—531no—
367C2×#398—531no—
368C2×#396—531no—
369C2×#395—531no—
370C2×#391—531no—
371C2×#389—531no—
372C2×#389—531no—
373C2×#388—531no—
374C2×#388D5311yescharacteristic
375C2×#387—531no—
376C2×#385—531no—
377C2×C4×C4⋊C4—531no—
378C2×C4×C22⋊C4—531no—
379C2×C53—44no—
380C2×C53#255618yescomplemented
381C2×C53C2×#53211yescharacteristic
382C2×C53C2×#53311yescharacteristic
383C2×C53C2×#53911yescharacteristic
384C2×C53C2×#54611yescharacteristic
385C2×C53C2×D4×Q811yescharacteristic
386C2×C53C2×#55211yescharacteristic
387C2×C53C2×#55411yescharacteristic
388C23×Q8—531no—
389C24×C4—531no—
390C2×#125—538no—
391C2×#125—1068no—
392C2×C22⋊Q8—538no—
393C2×C22⋊Q8—1068no—
394C22×C4⋊C4—531no—
395C22×C4⋊C4—531no—
396C22×C4⋊C4—531no—
397C22×C4⋊C4—531no—
398C22×C4⋊C4—531no—
399C22×C4⋊C4—531no—
400C22×C4⋊C4—531no—
401C22×C4⋊C4—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4—531no—
404C22×C4⋊C4—531no—
405C22×C4⋊C4—531no—
406C22×C4⋊C4C2×D5311yescharacteristic
407C22×C22⋊C4—531no—
408C22×C22⋊C4—531no—
409C22×C22⋊C4—531no—
410C22×C22⋊C4C2×D5311yescharacteristic
411C22×C22⋊C4C2×D5311yescharacteristic
412C22×C22⋊C4C2×D5311yescharacteristic
413C22×C42—531no—
414C22×C42—531no—
415C22×C42—531no—
416C22×C42C2×D5311yescharacteristic
417#399—538no—
418#398—538no—
419#396—538no—
420#395—538no—
421#391—538no—
422#389—538no—
423#389—538no—
424#388—538no—
425#388C2×D5318yes—
426#387—538no—
427#385—538no—
428C4×C4⋊C4—538no—
429C4×C22⋊C4—538no—
430C2×#95—531no—
431C2×#95—531no—
432C2×#95—531no—
433C2×#95—531no—
434C2×#95—531no—
435C2×#95—531no—
436C2×#95—531no—
437C2×#95—531no—
438C2×#95C2×D5311yescharacteristic
439C2×#95C2×D5311yescharacteristic
440C53C2×#255611yescharacteristic, complemented, Sylow
441C25C22×D5311yescharacteristic
442C22×Q8—534no—
443C22×Q8—1064no—
444C22×Q8—1064no—
445C22×Q8—2122no—
446C23×C4—531no—
447C23×C4—531no—
448C23×C4—531no—
449C23×C4—531no—
450C23×C4—531no—
451C23×C4—531no—
452C23×C4—531no—
453C23×C4—531no—
454C23×C4—534no—
455C23×C4—1064no—
456C23×C4—1064no—
457C23×C4—2122no—
458C23×C4C22×D5311yescharacteristic
459C23×C4C22×D5311yescharacteristic
460C23×C4C22×D5311yescharacteristic
461C23×C4C22×D5311yescharacteristic
462C23×C4C22×D5311yescharacteristic
463C23×C4C22×D5311yescharacteristic
464#125—10632no—
465C22⋊Q8—10632no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—538no—
468C2×C4⋊C4—534no—
469C2×C4⋊C4—534no—
470C2×C4⋊C4—534no—
471C2×C4⋊C4—534no—
472C2×C4⋊C4—534no—
473C2×C4⋊C4—534no—
474C2×C4⋊C4—534no—
475C2×C4⋊C4—534no—
476C2×C4⋊C4—534no—
477C2×C4⋊C4—534no—
478C2×C4⋊C4—534no—
479C2×C4⋊C4—534no—
480C2×C4⋊C4—1064no—
481C2×C4⋊C4—1064no—
482C2×C4⋊C4—1064no—
483C2×C4⋊C4—1064no—
484C2×C4⋊C4—1064no—
485C2×C4⋊C4—1064no—
486C2×C4⋊C4—1064no—
487C2×C4⋊C4—1064no—
488C2×C4⋊C4—1064no—
489C2×C4⋊C4—1064no—
490C2×C4⋊C4—2122no—
491C2×C4⋊C4C22×D5314yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—534no—
495C2×C22⋊C4—534no—
496C2×C22⋊C4—534no—
497C2×C22⋊C4—1064no—
498C2×C22⋊C4—1064no—
499C2×C22⋊C4—2122no—
500C2×C22⋊C4Dic10618yescomplemented
501C2×C22⋊C4C22×D5314yes—
502C2×C22⋊C4C22×D5314yes—
503C2×C22⋊C4C22×D5314yes—
504C2×C42—24no—
505C2×C42—534no—
506C2×C42—534no—
507C2×C42—534no—
508C2×C42—1064no—
509C2×C42—2122no—
510C2×C42—2122no—
511C2×C42C22×D5314yes—
512#95—534no—
513#95—534no—
514#95—534no—
515#95—534no—
516#95—534no—
517#95—534no—
518#95—534no—
519#95—534no—
520#95C22×D5314yes—
521#95C22×D5314yes—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24C2×Dic10614yes—
529C24C23×D5312yes—
530C24C23×D5311yescharacteristic
531C2×Q8—1068no—
532C2×Q8—1068no—
533C2×Q8—2124no—
534C2×Q8—21216no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—534no—
550C22×C4—534no—
551C22×C4—534no—
552C22×C4—534no—
553C22×C4—532no—
554C22×C4—532no—
555C22×C4—532no—
556C22×C4—532no—
557C22×C4—532no—
558C22×C4—532no—
559C22×C4—532no—
560C22×C4—532no—
561C22×C4—1068no—
562C22×C4—1068no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1062no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—2124no—
584C22×C4—21216no—
585C22×C4C2×Dic10614yes—
586C22×C4C2×Dic10614yes—
587C22×C4D4×D5314yes—
588C22×C4#1171994714yes—
589C22×C4C23×D5312yes—
590C22×C4C23×D5312yes—
591C22×C4C23×D5312yes—
592C22×C4C23×D5312yes—
593C22×C4C23×D5312yes—
594C22×C4C23×D5312yes—
595C4⋊C4—28no—
596C4⋊C4—5316no—
597C4⋊C4—1068no—
598C4⋊C4—1068no—
599C4⋊C4—1068no—
600C4⋊C4—1068no—
601C4⋊C4—1068no—
602C4⋊C4—1068no—
603C4⋊C4—1068no—
604C4⋊C4—1068no—
605C4⋊C4—1068no—
606C4⋊C4—1068no—
607C4⋊C4—2124no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—1068no—
611C22⋊C4—1068no—
612C22⋊C4—2124no—
613C22⋊C4C2×Dic106116yescomplemented
614C42—28no—
615C42—1068no—
616C42—2124no—
617C42—2124no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23C2×D4×D5312yes—
632C23C22×Dic10614yes—
633C23C22×Dic10612yes—
634C23#41×D5312yes—
635C23#41×D5312yes—
636C23C2×#1171994712yes—
637C23#1313326312yes—
638C23#1313326412yes—
639C23C24×D5311yescharacteristic
640Q8—21216no—
641C2×C4—28no—
642C2×C4—28no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—534no—
662C2×C4—534no—
663C2×C4—534no—
664C2×C4—534no—
665C2×C4—1068no—
666C2×C4—1068no—
667C2×C4—1068no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1068no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—21216no—
690C2×C4—2124no—
691C2×C4—2124no—
692C2×C4—2124no—
693C2×C4—2124no—
694C2×C4C2×D4×D5314yes—
695C2×C4C22×Dic10614yes—
696C2×C4C22×Dic10614yes—
697C2×C4C2×#1171994714yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—416no—
705C22—42no—
706C22#1681116814yes—
707C22#1681117614yes—
708C22#1681121414yes—
709C22#1681126614yes—
710C22D4×Dic10614yes—
711C22#1681131014yes—
712C22#1681133014yes—
713C22C22×D4×D5311yescharacteristic
714C22C23×Dic10611yescharacteristic
715C22C2×#41×D5311yescharacteristic
716C22C2×#41×D5311yescharacteristic
717C22C22×#1171994711yescharacteristic
718C22C2×#1313326311yescharacteristic
719C22C2×#1313326411yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—1064no—
727C4—1064no—
728C4—1064no—
729C4—1064no—
730C4—2122no—
731C4—2122no—
732C4—2122no—
733C4—2122no—
734C2—44no—
735C2#2027979818yesdirect product factor
736C2C2×#1681116811yescharacteristic
737C2C2×#1681117611yescharacteristic
738C2C2×#1681121411yescharacteristic
739C2C2×#1681126611yescharacteristic
740C2C2×D4×Dic10611yescharacteristic
741C2C2×#1681131011yescharacteristic
742C2C2×#1681133011yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#388C2
socleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#388D53
hypocenterC53C2×#2556
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#13133208C2semidirect
3. #20279798C2direct (N × H)
5. C2×#16810556C2semidirect
7. C2×#16810544C2semidirect
8. C2×#16810527C2semidirect
9. C2×#16810521C2semidirect
10. C2×#16810520C2semidirect
12. C2×#16810506C2semidirect
14. C2×C4×C4⋊Dic53C2semidirect
20. C2×#13133208C22semidirect
42. #16810556C22semidirect
44. #16810544C22semidirect
45. #16810527C22semidirect
46. #16810521C22semidirect
47. #16810520C22semidirect
49. #16810506C22semidirect
51. C4×C4⋊Dic53C22semidirect
142. C2×C22⋊C4×C53Q8semidirect
226. C22⋊C4×C53C2×Q8semidirect
380. C2×C53#2556semidirect
440. C53C2×#2556semidirect
500. C2×C22⋊C4Dic106semidirect
613. C22⋊C4C2×Dic106semidirect
735. C2#20279798direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332082
C22×#131331942
#202797982
C2×#168105592
C2×#168105562
C2×#168105462
C2×#168105442
C2×#168105272
C2×#168105212
C2×#168105202
C2×#168105162
C2×#168105062
C2×#168104982
C2×C4×C4⋊Dic532
C2×C22⋊C4×Dic532
C2×C53×#3882
C2×#255653