Finite Group Databasebeta

← C2×#20279665 #27555870

Subgroups — C2×#20279665 #27555870

Order 13568.

4006 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133215C211yesmaximal, characteristic, complemented
2C22×#13133197C211yesmaximal, characteristic, complemented
3C22×#13133196C211yesmaximal, characteristic, complemented
4C22×#13133193C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊D53C211yesmaximal, characteristic
6#20279665C2116yesmaximal, direct product factor
7C2×#16810559C212yesmaximal, complemented
8C2×#16810558C212yesmaximal, complemented
9C2×#16810523C212yesmaximal
10C2×#16810492C212yesmaximal, complemented
11C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
12C22×C22⋊Q8×C53C211yesmaximal, characteristic, complemented
13C23×Dic106C2211yescharacteristic
14C23×C22⋊D53C2211yescharacteristic
15C23×C4×D53C2211yescharacteristic
16C2×#13133215—28no—
17C2×#13133215C2218yescomplemented
18C2×#13133197—28no—
19C2×#13133197C2218yescomplemented
20C2×#13133196—28no—
21C2×#13133196C2218yescomplemented
22C2×#13133193—28no—
23C2×#13133193C2218yescomplemented
24C2×C4×C22⋊D53—28no—
25C2×C4×C22⋊D53C2218yes—
26C22×C4⋊Dic53C2212yes—
27C22×C4⋊Dic53C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2212yes—
30C22×#11719919C2212yes—
31C22×#11719919C2212yes—
32C22×#11719919C2212yes—
33C22×C22⋊Dic53C2211yescharacteristic
34C22×C22⋊Dic53C2212yes—
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2212yes—
37C22×#11719921C2212yes—
38C22×C4×Dic53C2212yes—
39C22×C4×Dic53C2211yescharacteristic
40#16810559C22116yescomplemented
41#16810558C22116yescomplemented
42#16810523C22116yes—
43#16810492C22116yescomplemented
44C4⋊C4×Dic53C2218yescomplemented
45C2×#13133124C2212yes—
46C23×Q8×C53C2211yescharacteristic
47C24×C4×C53C2211yescharacteristic
48C2×C22⋊Q8×C53—28no—
49C2×C22⋊Q8×C53C2218yescomplemented
50C22×C4⋊C4×C53C2212yes—
51C22×C4⋊C4×C53C2211yescharacteristic
52C22×C22⋊C4×C53C2212yes—
53C24×D53C2311yescharacteristic
54C22×Dic106—24no—
55C22×Dic106—24no—
56C22×Dic106—24no—
57C22×Dic106C2314yes—
58C22×C22⋊D53—24no—
59C22×C22⋊D53—24no—
60C22×C22⋊D53Q818yescomplemented
61C22×C22⋊D53C2314yes—
62C23×Dic53C2312yes—
63C23×Dic53C2311yescharacteristic
64C23×Dic53C2312yes—
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C22×C4×D53—24no—
68C22×C4×D53—24no—
69C22×C4×D53—24no—
70C22×C4×D53C2314yes—
71#13133215—232no—
72#13133197—232no—
73#13133196—232no—
74#13133193—232no—
75C4×C22⋊D53—232no—
76C2×C4⋊Dic53—28no—
77C2×C4⋊Dic53D418yescomplemented
78C2×C4⋊Dic53C2318yes—
79C2×C4⋊Dic53C2314yes—
80C2×#11719919—24no—
81C2×#11719919—28no—
82C2×#11719919—28no—
83C2×#11719919—28no—
84C2×#11719919—28no—
85C2×#11719919C2318yes—
86C2×#11719919C2318yes—
87C2×#11719919C2318yes—
88C2×#11719919C2318yes—
89C2×#11719919C2314yes—
90C2×C22⋊Dic53—24no—
91C2×C22⋊Dic53—28no—
92C2×C22⋊Dic53C2318yes—
93C2×C22⋊Dic53C2314yes—
94C2×#11719921—28no—
95C2×#11719921—24no—
96C2×#11719921—28no—
97C2×#11719921C2318yes—
98C2×#11719921C2318yes—
99C2×#11719921C2314yes—
100C2×C4×Dic53—28no—
101C2×C4×Dic53D418yes—
102C2×C4×Dic53C2318yes—
103C2×C4×Dic53C2314yes—
104#13133124C2318yes—
105C25×C53C2311yescharacteristic
106C22×Q8×C53—24no—
107C22×Q8×C53—24no—
108C22×Q8×C53—24no—
109C22×Q8×C53C2314yes—
110C23×C4×C53—24no—
111C23×C4×C53—24no—
112C23×C4×C53—24no—
113C23×C4×C53C2312yes—
114C23×C4×C53C2311yescharacteristic
115C23×C4×C53C2314yes—
116C23×C4×C53C2312yes—
117C23×C4×C53C2311yescharacteristic
118C22⋊Q8×C53—232no—
119C2×C4⋊C4×C53—28no—
120C2×C4⋊C4×C53D418yescomplemented
121C2×C4⋊C4×C53C2318yes—
122C2×C4⋊C4×C53C2314yes—
123C2×C22⋊C4×C53—28no—
124C2×C22⋊C4×C53C2318yes—
125C24×C53—22no—
126C24×C53—22no—
127C24×C53—22no—
128C24×C53—22no—
129C24×C53—22no—
130C24×C53—22no—
131C24×C53C2×Q814yes—
132C24×C53C2412yes—
133C24×C53C2411yescharacteristic
134C23×D53—22no—
135C23×D53—22no—
136C23×D53—22no—
137C23×D53—22no—
138C23×D53—22no—
139C23×D53—22no—
140C23×D53C2×Q814yes—
141C23×D53C2412yes—
142C2×Q8×C53—28no—
143C2×Q8×C53—28no—
144C2×Q8×C53—28no—
145C2×Q8×C53—416no—
146C22×C4×C53—24no—
147C22×C4×C53—24no—
148C22×C4×C53—24no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—24no—
153C22×C4×C53—24no—
154C22×C4×C53—28no—
155C22×C4×C53—28no—
156C22×C4×C53—28no—
157C22×C4×C53—416no—
158C22×C4×C53C2×D418yes—
159C22×C4×C53C2×D414yes—
160C22×C4×C53C2×D414yes—
161C22×C4×C53C2×D414yes—
162C22×C4×C53C2414yes—
163C22×C4×C53C2412yes—
164C22×C4×C53C2414yes—
165C22×C4×C53C2412yes—
166C2×C22⋊D53—232no—
167C2×C22⋊D53—28no—
168C2×C22⋊D53—28no—
169C2×C22⋊D53C2×Q8116yescomplemented
170C22×Dic53—24no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—24no—
174C22×Dic53—24no—
175C22×Dic53—22no—
176C22×Dic53—24no—
177C22×Dic53—22no—
178C22×Dic53—24no—
179C22×Dic53—22no—
180C22×Dic53C2×D414yes—
181C22×Dic53C2×D418yes—
182C22×Dic53C2×D414yes—
183C22×Dic53C2×Q814yes—
184C22×Dic53#4114yes—
185C22×Dic53C2414yes—
186C22×Dic53C2412yes—
187C22×Dic53C2412yes—
188C22×Dic53C2414yes—
189C22×Dic53C2412yes—
190C2×C4×D53—28no—
191C2×C4×D53—28no—
192C2×C4×D53—28no—
193C2×C4×D53—416no—
194C2×Dic106—28no—
195C2×Dic106—28no—
196C2×Dic106—28no—
197C2×Dic106—416no—
198C4⋊C4×C53—216no—
199C4⋊C4×C53C2×D4116yescomplemented
200C22⋊C4×C53—216no—
201C22⋊Dic53—28no—
202C22⋊Dic53—216no—
203#11719921—216no—
204#11719921—28no—
205#11719921—216no—
206C4⋊Dic53—216no—
207C4⋊Dic53C2×D4116yescomplemented
208#11719919—28no—
209#11719919—216no—
210#11719919—216no—
211#11719919—216no—
212#11719919—216no—
213C4×Dic53—216no—
214C4×Dic53C2×D4116yes—
215C23×C53—28no—
216C23×C53—28no—
217C23×C53—28no—
218C23×C53—22no—
219C23×C53—22no—
220C23×C53—22no—
221C23×C53—22no—
222C23×C53—22no—
223C23×C53—22no—
224C23×C53—44no—
225C23×C53—44no—
226C23×C53—44no—
227C23×C53—44no—
228C23×C53C22×D412yes—
229C23×C53C22×D412yes—
230C23×C53C22×D412yes—
231C23×C53C22×Q814yes—
232C23×C53C22×Q812yes—
233C23×C53C2×#4112yes—
234C23×C532−1+412yes—
235C23×C532−1+412yes—
236C23×C53C2511yescharacteristic
237C22×D53—28no—
238C22×D53—28no—
239C22×D53—28no—
240C22×D53—22no—
241C22×D53—22no—
242C22×D53—22no—
243C22×D53—22no—
244C22×D53—22no—
245C22×D53—22no—
246C22×D53—44no—
247C22×D53—44no—
248C22×D53—44no—
249C22×D53—44no—
250C22×D53C22×Q814yes—
251Q8×C53—416no—
252C2×C4×C53—216no—
253C2×C4×C53—24no—
254C2×C4×C53—24no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—24no—
259C2×C4×C53—24no—
260C2×C4×C53—24no—
261C2×C4×C53—44no—
262C2×C4×C53—48no—
263C2×C4×C53—416no—
264C2×C4×C53#127116yes—
265C2×C4×C53C22×D414yes—
266C2×C4×C53C22×D414yes—
267C2×C4×C53C22×D418yes—
268C2×C4×C53C22×D414yes—
269C22⋊D53—232no—
270C2×Dic53—28no—
271C2×Dic53—216no—
272C2×Dic53—24no—
273C2×Dic53—22no—
274C2×Dic53—22no—
275C2×Dic53—24no—
276C2×Dic53—24no—
277C2×Dic53—24no—
278C2×Dic53—24no—
279C2×Dic53—22no—
280C2×Dic53—22no—
281C2×Dic53—22no—
282C2×Dic53—48no—
283C2×Dic53—44no—
284C2×Dic53C22⋊Q8116yescomplemented
285C2×Dic53C22×D414yes—
286C2×Dic53C22×D418yes—
287C2×Dic53C22×D414yes—
288C2×Dic53C22×Q814yes—
289C2×Dic53C2×#4114yes—
290C4×D53—416no—
291Dic106—416no—
292C2×#2542—531nomaximal, Sylow
293C22×C53—24no—
294C22×C53—24no—
295C22×C53—24no—
296C22×C53—42no—
297C22×C53—42no—
298C22×C53—42no—
299C22×C53—42no—
300C22×C53—416no—
301C22×C53C2×C22⋊Q814yes—
302C22×C53C2×#12714yes—
303C22×C53#53614yes—
304C22×C53#54714yes—
305C22×C53#54714yes—
306C22×C53D4×Q814yes—
307C22×C53D4×Q814yes—
308C22×C53C23×D411yescharacteristic
309C22×C53C23×D411yescharacteristic
310C22×C53C23×D411yescharacteristic
311C22×C53C23×Q811yescharacteristic
312C22×C53C22×#4111yescharacteristic
313C22×C53C2×2−1+411yescharacteristic
314C22×C53C2×2−1+411yescharacteristic
315C2×D53—24no—
316C2×D53—24no—
317C2×D53—24no—
318C2×D53—42no—
319C2×D53—42no—
320C2×D53—42no—
321C2×D53—42no—
322C2×D53—416no—
323C4×C53—28no—
324C4×C53—42no—
325C4×C53—44no—
326C4×C53C2×#12718yes—
327Dic53—24no—
328Dic53—28no—
329Dic53—44no—
330Dic53—42no—
331Dic53C2×C22⋊Q818yescomplemented
332C22×C4⋊Q8—531no—
333C22×C22⋊Q8—531no—
334C22×C22⋊Q8—531no—
335C22×C22⋊Q8—531no—
336C22×C22⋊Q8D5311yescharacteristic, complemented
337C22×C4×D4—531no—
338#2542—5316no—
339C2×#399—532no—
340C2×#399—532no—
341C2×#390—532no—
342C2×#384—532no—
343C2×C4×C4⋊C4—531no—
344C2×C53—44no—
345C2×C53#254218yescomplemented
346C2×C53C22×C22⋊Q811yescharacteristic
347C2×C53C22×#12711yescharacteristic
348C2×C53C2×#53611yescharacteristic
349C2×C53C2×#54711yescharacteristic
350C2×C53C2×#54711yescharacteristic
351C2×C53C2×D4×Q811yescharacteristic
352C2×C53C2×D4×Q811yescharacteristic
353D53—44no—
354C23×Q8—531no—
355C23×Q8C2×D5311yescharacteristic
356C23×D4—531no—
357C24×C4—531no—
358C24×C4C2×D5311yescharacteristic
359C2×C4⋊Q8—538no—
360C2×C4⋊Q8—1068no—
361C2×C22⋊Q8—28no—
362C2×C22⋊Q8—538no—
363C2×C22⋊Q8—538no—
364C2×C22⋊Q8—538no—
365C2×C22⋊Q8—1068no—
366C2×C22⋊Q8—1068no—
367C2×C22⋊Q8—1068no—
368C2×C22⋊Q8C2×D5318yescomplemented
369C2×C4×D4—538no—
370C2×C4×D4—1068no—
371C22×C4⋊C4—531no—
372C22×C4⋊C4—532no—
373C22×C4⋊C4—532no—
374C22×C4⋊C4—532no—
375C22×C4⋊C4—531no—
376C22×C4⋊C4—532no—
377C22×C4⋊C4—532no—
378C22×C4⋊C4C2×D5312yes—
379C22×C4⋊C4C2×D5311yescharacteristic
380C22×C22⋊C4—531no—
381C22×C22⋊C4—532no—
382C22×C22⋊C4—531no—
383C22×C22⋊C4—532no—
384C22×C22⋊C4—532no—
385C22×C22⋊C4C2×D5312yes—
386C22×C42—531no—
387C22×C42—532no—
388#399—5316no—
389#399—5316no—
390#390—5316no—
391#384—5316no—
392C4×C4⋊C4—538no—
393C2×#95—532no—
394C53C2×#254211yescharacteristic, complemented, Sylow
395C25—531no—
396C25C22×D5311yescharacteristic
397C22×Q8—24no—
398C22×Q8—24no—
399C22×Q8—24no—
400C22×Q8—534no—
401C22×Q8—1064no—
402C22×Q8—1064no—
403C22×Q8—1064no—
404C22×Q8C22×D5314yes—
405C22×D4—538no—
406C22×D4—534no—
407C22×D4—1064no—
408C22×D4—1064no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—24no—
412C23×C4—531no—
413C23×C4—532no—
414C23×C4—531no—
415C23×C4—532no—
416C23×C4—531no—
417C23×C4—534no—
418C23×C4—1064no—
419C23×C4—1064no—
420C23×C4—1064no—
421C23×C4C22×D5314yes—
422C23×C4C22×D5312yes—
423C23×C4C22×D5311yescharacteristic
424C23×C4C22×D5312yes—
425C23×C4C22×D5311yescharacteristic
426C4⋊Q8—10632no—
427C22⋊Q8—232no—
428C22⋊Q8—10632no—
429C22⋊Q8—10632no—
430C22⋊Q8—10632no—
431C4×D4—10632no—
432C2×C4⋊C4—28no—
433C2×C4⋊C4—538no—
434C2×C4⋊C4—534no—
435C2×C4⋊C4—534no—
436C2×C4⋊C4—538no—
437C2×C4⋊C4—538no—
438C2×C4⋊C4—538no—
439C2×C4⋊C4—538no—
440C2×C4⋊C4—538no—
441C2×C4⋊C4—1064no—
442C2×C4⋊C4—1068no—
443C2×C4⋊C4—1068no—
444C2×C4⋊C4—1068no—
445C2×C4⋊C4—1068no—
446C2×C4⋊C4—1068no—
447C2×C4⋊C4C22⋊D5318yescomplemented
448C2×C4⋊C4C22×D5318yes—
449C2×C4⋊C4C22×D5314yes—
450C2×C22⋊C4—28no—
451C2×C22⋊C4—534no—
452C2×C22⋊C4—538no—
453C2×C22⋊C4—534no—
454C2×C22⋊C4—538no—
455C2×C22⋊C4—538no—
456C2×C22⋊C4—1064no—
457C2×C22⋊C4—1068no—
458C2×C22⋊C4—1064no—
459C2×C22⋊C4—1068no—
460C2×C22⋊C4—1068no—
461C2×C22⋊C4C22×D5318yes—
462C2×C42—538no—
463C2×C42—534no—
464C2×C42—538no—
465C2×C42—1068no—
466#95—538no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—534no—
474C24—532no—
475C24—1062no—
476C24—1062no—
477C24—1062no—
478C24—1062no—
479C24—1062no—
480C24—1062no—
481C24Q8×D5314yes—
482C24C23×D5312yes—
483C24C23×D5311yescharacteristic
484C2×Q8—28no—
485C2×Q8—28no—
486C2×Q8—28no—
487C2×Q8—416no—
488C2×Q8—1068no—
489C2×Q8—1068no—
490C2×Q8—1068no—
491C2×Q8—21216no—
492C2×D4—5316no—
493C2×D4—1068no—
494C2×D4—10632no—
495C2×D4—1068no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—416no—
508C22×C4—534no—
509C22×C4—534no—
510C22×C4—534no—
511C22×C4—532no—
512C22×C4—534no—
513C22×C4—538no—
514C22×C4—532no—
515C22×C4—534no—
516C22×C4—534no—
517C22×C4—532no—
518C22×C4—1064no—
519C22×C4—1062no—
520C22×C4—1064no—
521C22×C4—1062no—
522C22×C4—1062no—
523C22×C4—1064no—
524C22×C4—1062no—
525C22×C4—1064no—
526C22×C4—1064no—
527C22×C4—1062no—
528C22×C4—1068no—
529C22×C4—1068no—
530C22×C4—1068no—
531C22×C4—21216no—
532C22×C4D4×D5314yes—
533C22×C4D4×D5314yes—
534C22×C4C2×C22⋊D5318yes—
535C22×C4C2×C22⋊D5314yes—
536C22×C4C23×D5314yes—
537C22×C4C23×D5312yes—
538C22×C4C23×D5314yes—
539C22×C4C23×D5312yes—
540C4⋊C4—216no—
541C4⋊C4—5316no—
542C4⋊C4—1068no—
543C4⋊C4—10616no—
544C4⋊C4—10616no—
545C4⋊C4—10616no—
546C4⋊C4—10616no—
547C4⋊C4—10616no—
548C4⋊C4C2×C22⋊D53116yescomplemented
549C22⋊C4—216no—
550C22⋊C4—1068no—
551C22⋊C4—10616no—
552C22⋊C4—1068no—
553C22⋊C4—10616no—
554C22⋊C4—10616no—
555C42—5316no—
556C42—10616no—
557C23—28no—
558C23—28no—
559C23—28no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—534no—
571C23—1068no—
572C23—1068no—
573C23—1068no—
574C23—1062no—
575C23—1062no—
576C23—1062no—
577C23—1062no—
578C23—1062no—
579C23—1062no—
580C23—2124no—
581C23—2124no—
582C23—2124no—
583C23—2124no—
584C23C2×D4×D5312yes—
585C23C2×D4×D5312yes—
586C23C22×C22⋊D5312yes—
587C23C2×Q8×D5314yes—
588C23C2×Q8×D5312yes—
589C23#41×D5312yes—
590C23#1313326412yes—
591C23#1313326512yes—
592C23C24×D5311yescharacteristic
593Q8—416no—
594Q8—21216no—
595D4—10632no—
596C2×C4—216no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—44no—
606C2×C4—48no—
607C2×C4—416no—
608C2×C4—5316no—
609C2×C4—534no—
610C2×C4—534no—
611C2×C4—534no—
612C2×C4—534no—
613C2×C4—538no—
614C2×C4—10616no—
615C2×C4—1064no—
616C2×C4—1068no—
617C2×C4—1062no—
618C2×C4—1062no—
619C2×C4—1064no—
620C2×C4—1062no—
621C2×C4—1064no—
622C2×C4—1062no—
623C2×C4—1064no—
624C2×C4—1064no—
625C2×C4—1062no—
626C2×C4—2124no—
627C2×C4—2128no—
628C2×C4—21216no—
629C2×C4#13133213116yes—
630C2×C4C2×D4×D5314yes—
631C2×C4C2×D4×D5314yes—
632C2×C4C22×C22⋊D5318yes—
633C2×C4C22×C22⋊D5314yes—
634C22—24no—
635C22—24no—
636C22—24no—
637C22—42no—
638C22—416no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—1064no—
643C22—1064no—
644C22—1064no—
645C22—2122no—
646C22—21216no—
647C22—2122no—
648C22—2122no—
649C22—2122no—
650C22C22⋊Q8×D5314yes—
651C22C2×#1313321314yes—
652C22#1681119614yes—
653C22#1681127214yes—
654C22#1681127514yes—
655C22#1681128614yes—
656C22Q8×C22⋊D5314yes—
657C22C22×D4×D5311yescharacteristic
658C22C22×D4×D5311yescharacteristic
659C22C23×C22⋊D5311yescharacteristic
660C22C22×Q8×D5311yescharacteristic
661C22C2×#41×D5311yescharacteristic
662C22C2×#1313326411yescharacteristic
663C22C2×#1313326511yescharacteristic
664C4—28no—
665C4—42no—
666C4—44no—
667C4—538no—
668C4—1064no—
669C4—1068no—
670C4—2122no—
671C4—2124no—
672C4C2×#1313321318yes—
673C2—44no—
674C2—2124no—
675C2#2027966518yesdirect product factor
676C2C2×C22⋊Q8×D5311yescharacteristic
677C2C22×#1313321311yescharacteristic
678C2C2×#1681119611yescharacteristic
679C2C2×#1681127211yescharacteristic
680C2C2×#1681127511yescharacteristic
681C2C2×#1681128611yescharacteristic
682C2C2×Q8×C22⋊D5311yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC22×C22⋊Q8×C53C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC22×C22⋊Q8D53
hypocenterC53C2×#2542
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13133215C2semidirect
2. C22×#13133197C2semidirect
3. C22×#13133196C2semidirect
4. C22×#13133193C2semidirect
6. #20279665C2direct (N × H)
7. C2×#16810559C2semidirect
8. C2×#16810558C2semidirect
10. C2×#16810492C2semidirect
11. C2×C4⋊C4×Dic53C2semidirect
12. C22×C22⋊Q8×C53C2semidirect
17. C2×#13133215C22semidirect
19. C2×#13133197C22semidirect
21. C2×#13133196C22semidirect
23. C2×#13133193C22semidirect
40. #16810559C22semidirect
41. #16810558C22semidirect
43. #16810492C22semidirect
44. C4⋊C4×Dic53C22semidirect
49. C2×C22⋊Q8×C53C22semidirect
60. C22×C22⋊D53Q8semidirect
77. C2×C4⋊Dic53D4semidirect
120. C2×C4⋊C4×C53D4semidirect
169. C2×C22⋊D53C2×Q8semidirect
199. C4⋊C4×C53C2×D4semidirect
207. C4⋊Dic53C2×D4semidirect
284. C2×Dic53C22⋊Q8semidirect
331. Dic53C2×C22⋊Q8semidirect
336. C22×C22⋊Q8D53semidirect
345. C2×C53#2542semidirect
368. C2×C22⋊Q8C2×D53semidirect
394. C53C2×#2542semidirect
447. C2×C4⋊C4C22⋊D53semidirect
548. C4⋊C4C2×C22⋊D53semidirect
675. C2#20279665direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332152
C22×#131331972
C22×#131331962
C22×#131331932
C22×C4×C22⋊D532
#202796652
C2×#168105592
C2×#168105582
C2×#168105232
C2×#168104922
C2×C4⋊C4×Dic532
C22×C22⋊Q8×C532
C2×#254253