Finite Group Databasebeta

← C2×#20277640 #27543415

Subgroups — C2×#20277640 #27543415

Order 13568.

3894 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D53C211yesmaximal, characteristic
2C22×#13133175C211yesmaximal, characteristic, complemented
3#20277640C2116yesmaximal, direct product factor
4C2×#16810513C212yesmaximal, complemented
5C2×#16810504C212yesmaximal, complemented
6C2×#16810502C212yesmaximal
7C2×#16810488C211yesmaximal, characteristic, complemented
8C2×#16810483C211yesmaximal, characteristic, complemented
9C2×#16810480C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic53C212yesmaximal, complemented
12C23×C4⋊C4×C53C211yesmaximal, characteristic, complemented
13C23×C22⋊D53C2211yescharacteristic
14C23×C4×D53C2211yescharacteristic
15C2×C4×C22⋊D53C4116yescomplemented
16C2×C4×C22⋊D53C2218yes—
17C2×#13133175—28no—
18C2×#13133175C2218yescomplemented
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×C22⋊Dic53C2212yes—
23C22×C22⋊Dic53C2211yescharacteristic
24C22×#11719921C2212yes—
25C22×#11719921C2212yes—
26C22×#11719921C2211yescharacteristic
27C22×C4×Dic53C2212yes—
28C22×C4×Dic53C2212yes—
29C22×C4×Dic53C2211yescharacteristic
30#16810513C22116yescomplemented
31#16810504C22116yescomplemented
32#16810502C22116yes—
33#16810488C2218yescomplemented
34#16810483C2218yescomplemented
35#16810480C2218yescomplemented
36C4⋊C4×Dic53C2218yescomplemented
37C4×C22⋊Dic53C22116yescomplemented
38C2×#13133124C2212yes—
39C2×#13133124C2212yes—
40C2×#13133124C2212yes—
41C2×#13133124C2212yes—
42C2×#13133124C2212yes—
43C24×C4×C53C2212yes—
44C24×C4×C53C2211yescharacteristic
45C22×C4⋊C4×C53—28no—
46C22×C4⋊C4×C53C2211yescharacteristic
47C22×C4⋊C4×C53C2212yes—
48C22×C4⋊C4×C53C2211yescharacteristic
49C22×C4⋊C4×C53C2218yescomplemented
50C24×D53C2311yescharacteristic
51C22×C22⋊D53—24no—
52C22×C22⋊D53—24no—
53C22×C22⋊D53C2×C418yes—
54C22×C22⋊D53C2314yes—
55C23×Dic53C2312yes—
56C23×Dic53C2312yes—
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C22×C4×D53—24no—
61C22×C4×D53—24no—
62C22×C4×D53C2×C418yescomplemented
63C22×C4×D53C2314yes—
64C4×C22⋊D53C2×C4164yescomplemented
65#13133175—232no—
66C2×C4⋊Dic53—24no—
67C2×C4⋊Dic53—24no—
68C2×C4⋊Dic53C2314yes—
69C2×C4⋊Dic53C2314yes—
70C2×#11719919C2×C418yescomplemented
71C2×#11719919C2314yes—
72C2×C22⋊Dic53—28no—
73C2×C22⋊Dic53C2×C418yes—
74C2×C22⋊Dic53C2318yes—
75C2×C22⋊Dic53C2314yes—
76C2×#11719921—28no—
77C2×#11719921—44no—
78C2×#11719921C2×C418yescomplemented
79C2×#11719921C2318yes—
80C2×#11719921C2318yes—
81C2×#11719921C2314yes—
82C2×C4×Dic53—28no—
83C2×C4×Dic53—44no—
84C2×C4×Dic53C2×C418yescomplemented
85C2×C4×Dic53C2318yes—
86C2×C4×Dic53C2318yes—
87C2×C4×Dic53C2314yes—
88#13133124C2318yes—
89#13133124C2318yes—
90#13133124C2318yes—
91#13133124C2318yes—
92#13133124C2318yes—
93C25×C53C2311yescharacteristic
94C23×C4×C53—24no—
95C23×C4×C53—24no—
96C23×C4×C53—28no—
97C23×C4×C53—28no—
98C23×C4×C53—44no—
99C23×C4×C53C2×C418yes—
100C23×C4×C53C2312yes—
101C23×C4×C53C2318yes—
102C23×C4×C53C2311yescharacteristic
103C23×C4×C53C2314yes—
104C23×C4×C53C2312yes—
105C23×C4×C53C2311yescharacteristic
106C2×C4⋊C4×C53—232no—
107C2×C4⋊C4×C53—28no—
108C2×C4⋊C4×C53—24no—
109C2×C4⋊C4×C53D418yescomplemented
110C2×C4⋊C4×C53C2318yes—
111C2×C4⋊C4×C53C2314yes—
112C2×C4⋊C4×C53C2314yes—
113C24×C53—22no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53C22×C414yes—
118C24×C53#4114yes—
119C24×C53#4114yes—
120C24×C53C2412yes—
121C24×C53C2411yescharacteristic
122C23×D53—22no—
123C23×D53—22no—
124C23×D53—22no—
125C23×D53—22no—
126C23×D53—22no—
127C23×D53—22no—
128C23×D53C22×C414yes—
129C23×D53C2412yes—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—24no—
133C22×C4×C53—24no—
134C22×C4×C53—232no—
135C22×C4×C53—28no—
136C22×C4×C53—28no—
137C22×C4×C53—24no—
138C22×C4×C53—216no—
139C22×C4×C53—24no—
140C22×C4×C53—24no—
141C22×C4×C53—216no—
142C22×C4×C53—48no—
143C22×C4×C53—432no—
144C22×C4×C53C22×C414yes—
145C22×C4×C53C22×C4116yes—
146C22×C4×C53C22×C414yes—
147C22×C4×C53C2×D418yes—
148C22×C4×C53C2×D414yes—
149C22×C4×C53#4114yes—
150C22×C4×C53C2414yes—
151C22×C4×C53C2412yes—
152C22×C4×C53C2414yes—
153C22×C4×C53C2412yes—
154C2×C22⋊D53—232no—
155C2×C22⋊D53—28no—
156C2×C22⋊D53—28no—
157C2×C22⋊D53C22×C4116yes—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—24no—
165C22×Dic53—24no—
166C22×Dic53—24no—
167C22×Dic53—24no—
168C22×Dic53—24no—
169C22×Dic53—24no—
170C22×Dic53C22×C414yes—
171C22×Dic53C22×C414yes—
172C22×Dic53C22×C414yes—
173C22×Dic53C2414yes—
174C22×Dic53C2414yes—
175C22×Dic53C2412yes—
176C22×Dic53C2412yes—
177C22×Dic53C2412yes—
178C2×C4×D53—232no—
179C2×C4×D53—28no—
180C2×C4×D53—28no—
181C2×C4×D53C22×C4116yescomplemented
182C4⋊C4×C53—216no—
183C4⋊C4×C53—28no—
184C4⋊C4×C53C2×D4116yescomplemented
185C22⋊Dic53—216no—
186C22⋊Dic53C22×C4116yes—
187#11719921—216no—
188#11719921—48no—
189#11719921C22×C4116yescomplemented
190C4⋊Dic53—28no—
191C4⋊Dic53—28no—
192#11719919C22×C4116yescomplemented
193C4×Dic53—216no—
194C4×Dic53—48no—
195C4×Dic53C22×C4116yescomplemented
196C23×C53—28no—
197C23×C53—28no—
198C23×C53—28no—
199C23×C53—28no—
200C23×C53—28no—
201C23×C53—28no—
202C23×C53—22no—
203C23×C53—22no—
204C23×C53—22no—
205C23×C53—22no—
206C23×C53#117116yescomplemented
207C23×C53C23×C414yes—
208C23×C53C23×C412yes—
209C23×C53C22×D412yes—
210C23×C53C2×#4114yes—
211C23×C53C2×#4112yes—
212C23×C53C2×#4112yes—
213C23×C53C2×#4114yes—
214C23×C53C2×#4112yes—
215C23×C53H(5,𝔽2)12yes—
216C23×C532−1+412yes—
217C23×C53C2511yescharacteristic
218C22×D53—28no—
219C22×D53—28no—
220C22×D53—28no—
221C22×D53—22no—
222C22×D53—22no—
223C22×D53—22no—
224C22×D53—22no—
225C22×D53—22no—
226C22×D53—22no—
227C22×D53—44no—
228C22×D53—44no—
229C22×D53—44no—
230C22×D53—44no—
231C22×D53C23×C414yes—
232C2×C4×C53—28no—
233C2×C4×C53—216no—
234C2×C4×C53—22no—
235C2×C4×C53—24no—
236C2×C4×C53—22no—
237C2×C4×C53—24no—
238C2×C4×C53—232no—
239C2×C4×C53—24no—
240C2×C4×C53—24no—
241C2×C4×C53—24no—
242C2×C4×C53—432no—
243C2×C4×C53—48no—
244C2×C4×C53C4×D4116yes—
245C2×C4×C53C23×C414yes—
246C2×C4×C53C23×C414yes—
247C2×C4×C53C22×D418yes—
248C2×C4×C53C22×D414yes—
249C2×C4×C53C2×#4114yes—
250C22⋊D53—232no—
251C2×Dic53—28no—
252C2×Dic53—28no—
253C2×Dic53—28no—
254C2×Dic53—22no—
255C2×Dic53—22no—
256C2×Dic53—22no—
257C2×Dic53—22no—
258C2×Dic53—22no—
259C2×Dic53—22no—
260C2×Dic53—24no—
261C2×Dic53—24no—
262C2×Dic53—24no—
263C2×Dic53—24no—
264C2×Dic53—24no—
265C2×Dic53—24no—
266C2×Dic53—48no—
267C2×Dic53—48no—
268C2×Dic53C23×C414yes—
269C2×Dic53C23×C414yes—
270C2×Dic53C23×C414yes—
271C4×D53—232no—
272C2×#2352—531nomaximal, Sylow
273C22×C53—232no—
274C22×C53—24no—
275C22×C53—24no—
276C22×C53—24no—
277C22×C53—24no—
278C22×C53—24no—
279C22×C53—24no—
280C22×C53C2×#11714yes—
281C22×C53C2×#11718yescomplemented
282C22×C53C2×C4×D414yes—
283C22×C53#52014yes—
284C22×C53#54614yes—
285C22×C53#54814yes—
286C22×C53#55214yes—
287C22×C53#55314yes—
288C22×C53C24×C411yescharacteristic
289C22×C53C23×D411yescharacteristic
290C22×C53C22×#4111yescharacteristic
291C22×C53C22×#4111yescharacteristic
292C22×C53C22×#4111yescharacteristic
293C22×C53C2×H(5,𝔽2)11yescharacteristic
294C22×C53C2×2−1+411yescharacteristic
295C2×D53—24no—
296C2×D53—24no—
297C2×D53—24no—
298C2×D53—416no—
299C2×D53—42no—
300C2×D53—42no—
301C2×D53—42no—
302C2×D53—42no—
303C4×C53—24no—
304C4×C53—28no—
305C4×C53—44no—
306C4×C53C2×C4×D418yes—
307Dic53—24no—
308Dic53—24no—
309Dic53—24no—
310Dic53—44no—
311Dic53—44no—
312C22×C4×D4—531no—
313C22×#117—531no—
314C23×C4⋊C4D5311yescharacteristic, complemented
315#2352—5316no—
316C2×#388—532no—
317C2×#387—532no—
318C2×#386—532no—
319C2×#382—531no—
320C2×#380—531no—
321C2×#380—531no—
322C2×C4×C4⋊C4—531no—
323C2×C4×C22⋊C4—532no—
324C2×C53—28no—
325C2×C53#235218yescomplemented
326C2×C53C22×#11711yescharacteristic
327C2×C53C22×C4×D411yescharacteristic
328C2×C53C2×#52011yescharacteristic
329C2×C53C2×#54611yescharacteristic
330C2×C53C2×#54811yescharacteristic
331C2×C53C2×#55211yescharacteristic
332C2×C53C2×#55311yescharacteristic
333D53—44no—
334C23×D4—531no—
335C24×C4—531no—
336C24×C4C2×D5312yes—
337C24×C4C2×D5311yescharacteristic
338C2×C4×D4—5316no—
339C2×C4×D4—538no—
340C2×#117—538no—
341C2×#117—1068no—
342C22×C4⋊C4—28no—
343C22×C4⋊C4—531no—
344C22×C4⋊C4—531no—
345C22×C4⋊C4—531no—
346C22×C4⋊C4C2×D5311yescharacteristic
347C22×C4⋊C4C2×D5312yes—
348C22×C4⋊C4C2×D5311yescharacteristic
349C22×C4⋊C4C2×D5318yescomplemented
350C22×C22⋊C4—531no—
351C22×C22⋊C4—531no—
352C22×C22⋊C4—532no—
353C22×C22⋊C4—532no—
354C22×C22⋊C4—532no—
355C22×C42—531no—
356C22×C42—532no—
357C22×C42—532no—
358#388—5316no—
359#387—5316no—
360#386—5316no—
361#382—538no—
362#380—538no—
363#380—538no—
364C4×C4⋊C4—538no—
365C4×C22⋊C4—5316no—
366C2×#95—532no—
367C2×#95—532no—
368C2×#95—532no—
369C2×#95—532no—
370C2×#95—532no—
371C53C2×#235211yescharacteristic, complemented, Sylow
372C25—531no—
373C25C22×D5311yescharacteristic
374C22×D4—538no—
375C22×D4—534no—
376C22×D4—1064no—
377C22×D4—1064no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—28no—
381C23×C4—28no—
382C23×C4—44no—
383C23×C4—531no—
384C23×C4—531no—
385C23×C4—531no—
386C23×C4—538no—
387C23×C4—534no—
388C23×C4—532no—
389C23×C4—532no—
390C23×C4—1064no—
391C23×C4—1064no—
392C23×C4C4×D5318yes—
393C23×C4C22×D5312yes—
394C23×C4C22×D5318yes—
395C23×C4C22×D5314yes—
396C23×C4C22×D5311yescharacteristic
397C23×C4C22×D5312yes—
398C23×C4C22×D5311yescharacteristic
399C4×D4—5364no—
400#117—10632no—
401C2×C4⋊C4—28no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—232no—
404C2×C4⋊C4—538no—
405C2×C4⋊C4—534no—
406C2×C4⋊C4—534no—
407C2×C4⋊C4—534no—
408C2×C4⋊C4—1064no—
409C2×C4⋊C4—1064no—
410C2×C4⋊C4C22⋊D5318yescomplemented
411C2×C4⋊C4C22×D5314yes—
412C2×C4⋊C4C22×D5318yes—
413C2×C4⋊C4C22×D5314yes—
414C2×C22⋊C4—538no—
415C2×C22⋊C4—534no—
416C2×C22⋊C4—538no—
417C2×C22⋊C4—534no—
418C2×C22⋊C4—538no—
419C2×C22⋊C4—538no—
420C2×C22⋊C4—538no—
421C2×C22⋊C4—1068no—
422C2×C22⋊C4—1068no—
423C2×C22⋊C4—2124no—
424C2×C42—538no—
425C2×C42—534no—
426C2×C42—538no—
427C2×C42—538no—
428C2×C42—1068no—
429C2×C42—2124no—
430#95—538no—
431#95—538no—
432#95—538no—
433#95—538no—
434#95—538no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—534no—
440C24—532no—
441C24—1062no—
442C24—1062no—
443C24—1062no—
444C24—1062no—
445C24—1062no—
446C24—1062no—
447C24C2×C4×D5314yes—
448C24#1171994714yes—
449C24#1171994914yes—
450C24C23×D5312yes—
451C24C23×D5311yescharacteristic
452C2×D4—5316no—
453C2×D4—10632no—
454C2×D4—1068no—
455C2×D4—1068no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—232no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—24no—
464C22×C4—216no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—216no—
468C22×C4—48no—
469C22×C4—432no—
470C22×C4—534no—
471C22×C4—534no—
472C22×C4—534no—
473C22×C4—532no—
474C22×C4—532no—
475C22×C4—532no—
476C22×C4—5316no—
477C22×C4—534no—
478C22×C4—534no—
479C22×C4—1062no—
480C22×C4—1062no—
481C22×C4—1062no—
482C22×C4—1062no—
483C22×C4—1062no—
484C22×C4—1062no—
485C22×C4—10632no—
486C22×C4—1068no—
487C22×C4—1068no—
488C22×C4—1064no—
489C22×C4—1064no—
490C22×C4—1064no—
491C22×C4—1064no—
492C22×C4—1064no—
493C22×C4—1064no—
494C22×C4C2×C4×D5314yes—
495C22×C4C2×C4×D53116yes—
496C22×C4C2×C4×D5314yes—
497C22×C4#1171994514yes—
498C22×C4C2×C22⋊D5318yes—
499C22×C4C2×C22⋊D5314yes—
500C22×C4C23×D5314yes—
501C22×C4C23×D5312yes—
502C22×C4C23×D5314yes—
503C22×C4C23×D5312yes—
504C4⋊C4—216no—
505C4⋊C4—28no—
506C4⋊C4—5316no—
507C4⋊C4—1068no—
508C4⋊C4—1068no—
509C4⋊C4C2×C22⋊D53116yescomplemented
510C22⋊C4—5316no—
511C22⋊C4—5316no—
512C22⋊C4—10616no—
513C22⋊C4—10616no—
514C22⋊C4—2128no—
515C42—5316no—
516C42—10616no—
517C42—2128no—
518C23—28no—
519C23—28no—
520C23—28no—
521C23—28no—
522C23—28no—
523C23—28no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—22no—
528C23—534no—
529C23—1068no—
530C23—1068no—
531C23—1068no—
532C23—1062no—
533C23—1062no—
534C23—1062no—
535C23—1062no—
536C23—1062no—
537C23—1062no—
538C23—2124no—
539C23—2124no—
540C23—2124no—
541C23—2124no—
542C23#13133175116yescomplemented
543C23C22×C4×D5314yes—
544C23C22×C4×D5312yes—
545C23C22×C22⋊D5312yes—
546C23C2×#1171994714yes—
547C23C2×#1171994712yes—
548C23C2×#1171994512yes—
549C23C2×#1171994914yes—
550C23C2×#1171994912yes—
551C23#1313326212yes—
552C23#1313326512yes—
553C23C24×D5311yescharacteristic
554D4—10632no—
555C2×C4—216no—
556C2×C4—28no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—232no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—432no—
566C2×C4—48no—
567C2×C4—534no—
568C2×C4—534no—
569C2×C4—534no—
570C2×C4—1068no—
571C2×C4—1068no—
572C2×C4—1068no—
573C2×C4—1062no—
574C2×C4—1062no—
575C2×C4—1062no—
576C2×C4—1062no—
577C2×C4—1062no—
578C2×C4—1062no—
579C2×C4—10632no—
580C2×C4—1064no—
581C2×C4—1064no—
582C2×C4—1064no—
583C2×C4—1064no—
584C2×C4—1064no—
585C2×C4—1064no—
586C2×C4—2128no—
587C2×C4—2128no—
588C2×C4C4×C22⋊D53116yes—
589C2×C4C22×C4×D5314yes—
590C2×C4C22×C4×D5314yes—
591C2×C4C22×C22⋊D5318yes—
592C2×C4C22×C22⋊D5314yes—
593C2×C4C2×#1171994514yes—
594C22—232no—
595C22—24no—
596C22—24no—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—24no—
601C22—1064no—
602C22—1064no—
603C22—1064no—
604C22—21216no—
605C22—2122no—
606C22—2122no—
607C22—2122no—
608C22—2122no—
609C22C2×#1313317514yes—
610C22C2×#1313317518yescomplemented
611C22C2×C4×C22⋊D5314yes—
612C22#1681110414yes—
613C22#1681126714yes—
614C22#1681128414yes—
615C22#1681130814yes—
616C22#1681132114yes—
617C22C23×C4×D5311yescharacteristic
618C22C23×C22⋊D5311yescharacteristic
619C22C22×#1171994711yescharacteristic
620C22C22×#1171994511yescharacteristic
621C22C22×#1171994911yescharacteristic
622C22C2×#1313326211yescharacteristic
623C22C2×#1313326511yescharacteristic
624C4—24no—
625C4—28no—
626C4—44no—
627C4—1064no—
628C4—1064no—
629C4—1064no—
630C4—2124no—
631C4—2124no—
632C4C2×C4×C22⋊D5318yes—
633C2—28no—
634C2—2124no—
635C2#2027764018yesdirect product factor
636C2C22×#1313317511yescharacteristic
637C2C22×C4×C22⋊D5311yescharacteristic
638C2C2×#1681110411yescharacteristic
639C2C2×#1681126711yescharacteristic
640C2C2×#1681128411yescharacteristic
641C2C2×#1681130811yescharacteristic
642C2C2×#1681132111yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC23×C4⋊C4×C53C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
cosocleC23×C53C25
hypercenterC23×C4⋊C4D53
hypocenterC53C2×#2352
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#13133175C2semidirect
3. #20277640C2direct (N × H)
4. C2×#16810513C2semidirect
5. C2×#16810504C2semidirect
7. C2×#16810488C2semidirect
8. C2×#16810483C2semidirect
9. C2×#16810480C2semidirect
10. C2×C4⋊C4×Dic53C2semidirect
11. C2×C4×C22⋊Dic53C2semidirect
12. C23×C4⋊C4×C53C2semidirect
15. C2×C4×C22⋊D53C4semidirect
18. C2×#13133175C22semidirect
30. #16810513C22semidirect
31. #16810504C22semidirect
33. #16810488C22semidirect
34. #16810483C22semidirect
35. #16810480C22semidirect
36. C4⋊C4×Dic53C22semidirect
37. C4×C22⋊Dic53C22semidirect
49. C22×C4⋊C4×C53C22semidirect
62. C22×C4×D53C2×C4semidirect
64. C4×C22⋊D53C2×C4semidirect
70. C2×#11719919C2×C4semidirect
78. C2×#11719921C2×C4semidirect
84. C2×C4×Dic53C2×C4semidirect
109. C2×C4⋊C4×C53D4semidirect
181. C2×C4×D53C22×C4semidirect
184. C4⋊C4×C53C2×D4semidirect
189. #11719921C22×C4semidirect
192. #11719919C22×C4semidirect
195. C4×Dic53C22×C4semidirect
206. C23×C53#117semidirect
281. C22×C53C2×#117semidirect
314. C23×C4⋊C4D53semidirect
325. C2×C53#2352semidirect
349. C22×C4⋊C4C2×D53semidirect
371. C53C2×#2352semidirect
410. C2×C4⋊C4C22⋊D53semidirect
509. C4⋊C4C2×C22⋊D53semidirect
542. C23#13133175semidirect
610. C22C2×#13133175semidirect
635. C2#20277640direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D532
C22×#131331752
#202776402
C2×#168105132
C2×#168105042
C2×#168105022
C2×#168104882
C2×#168104832
C2×#168104802
C2×C4⋊C4×Dic532
C2×C4×C22⋊Dic532
C23×C4⋊C4×C532
C2×#235253