Finite Group Databasebeta

← C2×#20274813 #27383918

Subgroups — C2×#20274813 #27383918

Order 13568.

1606 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D53C211yesmaximal, characteristic
2C2×#16810586C211yesmaximal, characteristic
3C2×C4×#11719921C211yesmaximal, characteristic
4#20274813C218yesmaximal, direct product factor
5C2×#16810384C211yesmaximal, characteristic, complemented
6C2×#16810383C211yesmaximal, characteristic, complemented
7C2×#16810382C211yesmaximal, characteristic, complemented
8C2×C53×#339C211yesmaximal, characteristic, complemented
9C23×C4×D53C2211yescharacteristic
10C22×#11719917C2211yescharacteristic
11C2×#13133176C2211yescharacteristic
12C2×#13133175C411yescharacteristic, complemented
13C2×#13133175C411yescharacteristic, complemented
14C2×#13133174—21no—
15C2×#13133173—21no—
16#117×D53—22no—
17#117×D53—22no—
18#117×D53C414yescomplemented
19#117×D53C2214yes—
20C2×C4⋊C4×D53C411yescharacteristic, complemented
21C2×C4⋊C4×D53C411yescharacteristic, complemented
22C22×#11719921—21no—
23C2×C22⋊C4×D53—21no—
24C22×C4×Dic53C2211yescharacteristic
25C2×C42×D53—21no—
26#16810586—22no—
27#16810586C2214yes—
28C2×#13133129—21no—
29C2×#13133129—21no—
30C4×#11719921—22no—
31C4×#11719921C2214yes—
32C2×#13133124—21no—
33#16810384C2214yescomplemented
34#16810383C2214yescomplemented
35#16810382C2214yescomplemented
36C22×M16×C53C2211yescharacteristic
37C2×#117×C53C2211yescharacteristic
38C22×C42×C53C2211yescharacteristic
39C53×#339C2214yescomplemented
40C24×D53D411yescharacteristic
41C23×Dic53—21no—
42C23×Dic53D411yescharacteristic
43C22×C4×D53—22no—
44C22×C4×D53—22no—
45C22×C4×D53—22no—
46C22×C4×D53—22no—
47C22×C4×D53—21no—
48C22×C4×D53—21no—
49C22×C4×D53C2×C411yescharacteristic
50C22×C4×D53C2×C412yes—
51C22×C4×D53C2×C411yescharacteristic
52C22×C4×D53D412yes—
53C22×C4×D53D411yescharacteristic
54C22×C4×D53D412yes—
55C22×C4×D53D411yescharacteristic
56C22×C4×D53C2312yes—
57C2×#11719917—21no—
58C2×#11719917—22no—
59C2×#11719917—22no—
60C2×#11719917C2312yes—
61C22×#88322—21no—
62#13133176—21no—
63#13133176—21no—
64#13133176C2×C412yes—
65#13133176C2312yes—
66#13133175—22no—
67#13133175—22no—
68#13133175C2×C414yescomplemented
69#13133175C2×C414yescomplemented
70#13133174—24no—
71#13133174—24no—
72#13133173—24no—
73#13133173—24no—
74C2×C4⋊Dic53C2×C411yescharacteristic
75C2×C4⋊Dic53C2×C411yescharacteristic
76C2×#11719919—21no—
77C2×#11719919—21no—
78C4⋊C4×D53—22no—
79C4⋊C4×D53—22no—
80C4⋊C4×D53C2×C414yescomplemented
81C4⋊C4×D53C2×C414yescomplemented
82C2×C22⋊Dic53—21no—
83C2×#11719921—28no—
84C2×#11719921—21no—
85C2×#11719921—21no—
86C2×#11719921—24no—
87C22⋊C4×D53—24no—
88C22⋊C4×D53—24no—
89C2×C4×Dic53—21no—
90C2×C4×Dic53—21no—
91C2×C4×Dic53—21no—
92C2×C4×Dic53—21no—
93C2×C4×Dic53—22no—
94C2×C4×Dic53—22no—
95C2×C4×Dic53C2312yes—
96C42×D53—24no—
97C42×D53—24no—
98#13133129—24no—
99#13133129—24no—
100#13133124—24no—
101C23×C4×C53—21no—
102C23×C4×C53C2311yescharacteristic
103C2×M16×C53—21no—
104C2×M16×C53—22no—
105C2×M16×C53—22no—
106C2×M16×C53C2312yes—
107C22×C8×C53—21no—
108#117×C53—21no—
109#117×C53—21no—
110#117×C53C2×C412yes—
111#117×C53C2312yes—
112C2×C4⋊C4×C53C2×C411yescharacteristic
113C2×C4⋊C4×C53C2×C411yescharacteristic
114C2×C22⋊C4×C53—21no—
115C2×C42×C53—21no—
116C2×C42×C53—21no—
117C2×C42×C53—22no—
118C2×C42×C53—22no—
119C2×C42×C53C2312yes—
120C24×C53C2×D411yescharacteristic
121C23×D53—22no—
122C23×D53—22no—
123C23×D53—24no—
124C23×D53—42no—
125C23×D53C22⋊C411yescharacteristic
126C23×D53C22⋊C412yes—
127C23×D53C22⋊C411yescharacteristic
128C23×D53C2×D412yes—
129C22×C4×C53—24no—
130C22×C4×C53—21no—
131C22×C4×C53—21no—
132C22×C4×C53—22no—
133C22×C4×C53—42no—
134C22×C4×C53—42no—
135C22×C4×C53C22×C411yescharacteristic
136C22×C4×C53C22×C411yescharacteristic
137C22×C4×C53C2×D411yescharacteristic
138C22×C4×C53C2×D411yescharacteristic
139C22×C4×C53C2×D411yescharacteristic
140C22×C4×C53#4112yes—
141C22×C4×C53#4112yes—
142C22×C4×C53#4112yes—
143C22×C4×C53#4112yes—
144C22×C4×C53C2411yescharacteristic
145C22×Dic53—22no—
146C22×Dic53—22no—
147C22×Dic53—24no—
148C22×Dic53—21no—
149C22×Dic53—21no—
150C22×Dic53—22no—
151C22×Dic53—42no—
152C22×Dic53—42no—
153C22×Dic53C22⋊C411yescharacteristic
154C22×Dic53C22⋊C411yescharacteristic
155C22×Dic53C22⋊C412yes—
156C22×Dic53C2×D412yes—
157C2×C4×D53—22no—
158C2×C4×D53—24no—
159C2×C4×D53—22no—
160C2×C4×D53—22no—
161C2×C4×D53—24no—
162C2×C4×D53—22no—
163C2×C4×D53—22no—
164C2×C4×D53—22no—
165C2×C4×D53—24no—
166C2×C4×D53—22no—
167C2×C4×D53—22no—
168C2×C4×D53—24no—
169C2×C4×D53—24no—
170C2×C4×D53—24no—
171C2×C4×D53—22no—
172C2×C4×D53—22no—
173C2×C4×D53—22no—
174C2×C4×D53—22no—
175C2×C4×D53—24no—
176C2×C4×D53—24no—
177C2×C4×D53—44no—
178C2×C4×D53—44no—
179C2×C4×D53C22⋊C412yes—
180C2×C4×D53C22⋊C412yes—
181C2×C4×D53C22⋊C412yes—
182C2×C4×D53C22⋊C412yes—
183C2×C4×D53C22×C412yes—
184C2×C4×D53C22×C412yes—
185C2×C4×D53C2×D412yes—
186C2×C4×D53C2×D412yes—
187M16×C53—22no—
188M16×C53—22no—
189M16×C53—42no—
190C2×C8×C53—22no—
191C2×C8×C53—42no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53C22×C412yes—
195C4⋊C4×C53C22×C412yes—
196C22⋊C4×C53—22no—
197C22⋊C4×C53—22no—
198C42×C53—22no—
199C42×C53—22no—
200C42×C53—22no—
201C42×C53—22no—
202C42×C53—42no—
203C22⋊Dic53—22no—
204C22⋊Dic53—22no—
205#11719921—216no—
206#11719921—24no—
207#11719921—24no—
208C4⋊Dic53—21no—
209C4⋊Dic53—21no—
210C4⋊Dic53C22×C412yes—
211C4⋊Dic53C22×C412yes—
212#11719919—24no—
213#11719919—24no—
214C4×Dic53—22no—
215C4×Dic53—22no—
216C4×Dic53—24no—
217C4×Dic53—24no—
218C4×Dic53—22no—
219C4×Dic53—22no—
220C4×Dic53—42no—
221#11719917—22no—
222#11719917—22no—
223#11719917—42no—
224C2×#88322—22no—
225C2×#88322—42no—
226C23×C53—22no—
227C23×C53—22no—
228C23×C53C2×C22⋊C411yescharacteristic
229C23×C53C2×C22⋊C411yescharacteristic
230C23×C53#12312yes—
231C23×C53#12312yes—
232C23×C53C22×D411yescharacteristic
233C22×D53—22no—
234C22×D53—22no—
235C22×D53—22no—
236C22×D53—22no—
237C22×D53—24no—
238C22×D53—22no—
239C22×D53—22no—
240C22×D53—22no—
241C22×D53—24no—
242C22×D53—24no—
243C22×D53—42no—
244C22×D53—42no—
245C22×D53—48no—
246C22×D53—48no—
247C22×D53#10414yes—
248C22×D53C2×C22⋊C412yes—
249C22×D53C2×C22⋊C412yes—
250C2×C4×C53—24no—
251C2×C4×C53—22no—
252C2×C4×C53—22no—
253C2×C4×C53—48no—
254C2×C4×C53—42no—
255C2×C4×C53—42no—
256C2×C4×C53—42no—
257C2×C4×C53—42no—
258C2×C4×C53C2×C22⋊C411yescharacteristic
259C2×C4×C53C2×C22⋊C411yescharacteristic
260C2×C4×C53#11712yes—
261C2×C4×C53#11712yes—
262C2×C4×C53#11712yes—
263C2×C4×C53#11712yes—
264C2×C4×C53#12312yes—
265C2×C4×C53#12312yes—
266C2×C4×C53#12312yes—
267C2×C4×C53#12312yes—
268C2×C4×C53#12312yes—
269C2×C4×C53#12312yes—
270C2×C4×C53C23×C411yescharacteristic
271C2×C4×C53C22×D411yescharacteristic
272C2×C4×C53C2×#4111yescharacteristic
273C2×C4×C53C2×#4111yescharacteristic
274C2×C4×C53C2×#4111yescharacteristic
275C2×C4×C53C2×#4111yescharacteristic
276C2×Dic53—22no—
277C2×Dic53—22no—
278C2×Dic53—24no—
279C2×Dic53—22no—
280C2×Dic53—22no—
281C2×Dic53—24no—
282C2×Dic53—22no—
283C2×Dic53—22no—
284C2×Dic53—48no—
285C2×Dic53—42no—
286C2×Dic53—42no—
287C2×Dic53—42no—
288C2×Dic53—42no—
289C2×Dic53C2×C22⋊C412yes—
290C2×Dic53C2×C22⋊C412yes—
291C4×D53—22no—
292C4×D53—22no—
293C4×D53—22no—
294C4×D53—22no—
295C4×D53—22no—
296C4×D53—22no—
297C4×D53—22no—
298C4×D53—22no—
299C4×D53—24no—
300C4×D53—24no—
301C4×D53—24no—
302C4×D53—24no—
303C4×D53—48no—
304C4×D53—48no—
305C8×C53—42no—
306#88322—42no—
307C2×#1826—531nomaximal, Sylow
308C22×C53—24no—
309C22×C53—24no—
310C22×C53—21no—
311C22×C53—21no—
312C22×C53—21no—
313C22×C53—21no—
314C22×C53#38112yes—
315C22×C53#38112yes—
316C22×C53C2×#10412yes—
317C22×C53#42112yes—
318C22×C53C22×C22⋊C411yescharacteristic
319C22×C53C2×#12311yescharacteristic
320C22×C53C2×#12311yescharacteristic
321C2×D53—28no—
322C2×D53—22no—
323C2×D53—22no—
324C2×D53—22no—
325C2×D53—22no—
326C2×D53—22no—
327C2×D53—44no—
328C2×D53—44no—
329C2×D53—48no—
330C2×D53—44no—
331C2×D53C2×#10414yes—
332C4×C53—44no—
333C4×C53—42no—
334C4×C53—42no—
335C4×C53#38112yes—
336C4×C53#38112yes—
337C4×C53C2×#11711yescharacteristic
338C4×C53C2×#11711yescharacteristic
339C4×C53C2×#12311yescharacteristic
340C4×C53C2×#12311yescharacteristic
341Dic53—22no—
342Dic53—22no—
343Dic53—44no—
344Dic53—42no—
345Dic53—42no—
346C22×#117—531no—
347C2×#407—531no—
348C2×C4×C22⋊C4—531no—
349#1826—538no—
350C2×#339—531no—
351C2×#339—531no—
352C2×#339—531no—
353C2×#339D5311yescharacteristic, complemented
354C2×C53—21no—
355C2×C53—21no—
356C2×C53—22no—
357C2×C53#182614yescomplemented
358C2×C53C2×#38111yescharacteristic
359C2×C53C22×#10411yescharacteristic
360C2×C53C2×#42111yescharacteristic
361D53—24no—
362D53—42no—
363C24×C4—531no—
364C22×M16—531no—
365C22×M16C2×D5311yescharacteristic
366C2×#117—531no—
367C2×#117—534no—
368C2×#117—534no—
369C2×#117—531no—
370C2×#117—531no—
371C2×#117—1061no—
372C2×#117—1061no—
373C2×#117—1062no—
374C2×#117—1062no—
375C2×#117C2×D5311yescharacteristic
376C22×C4⋊C4—531no—
377C22×C4⋊C4—531no—
378C22×C22⋊C4—1061no—
379C22×C22⋊C4—1061no—
380C22×C42—531no—
381C22×C42—1061no—
382C22×C42C2×D5311yescharacteristic
383#407—534no—
384#407—1062no—
385C2×C22⋊C8—1061no—
386C2×C22⋊C8—1061no—
387C4×C22⋊C4—534no—
388C4×C22⋊C4—1062no—
389C2×#95—1061no—
390#339—534no—
391#339—534no—
392#339—534no—
393#339C2×D5314yescomplemented
394C53C2×#182611yescharacteristic, complemented, Sylow
395C25—531no—
396C23×C4—21no—
397C23×C4—531no—
398C23×C4—531no—
399C23×C4—531no—
400C23×C4—532no—
401C23×C4—532no—
402C23×C4—532no—
403C23×C4—531no—
404C23×C4—531no—
405C23×C4—532no—
406C23×C4—1061no—
407C23×C4—1061no—
408C23×C4—1062no—
409C23×C4—1062no—
410C23×C4—1062no—
411C23×C4—1062no—
412C23×C4—1061no—
413C23×C4C22×D5311yescharacteristic
414C2×M16—21no—
415C2×M16—22no—
416C2×M16—22no—
417C2×M16—532no—
418C2×M16—1061no—
419C2×M16—1062no—
420C2×M16—1062no—
421C2×M16C22×D5312yes—
422C22×C8—21no—
423C22×C8—1061no—
424#117—21no—
425#117—21no—
426#117—532no—
427#117—532no—
428#117—534no—
429#117—534no—
430#117—1064no—
431#117—1064no—
432#117—1064no—
433#117—1064no—
434#117—1062no—
435#117—1062no—
436#117—1061no—
437#117—1061no—
438#117C4×D5312yes—
439#117C22×D5312yes—
440C2×C4⋊C4—531no—
441C2×C4⋊C4—531no—
442C2×C4⋊C4—534no—
443C2×C4⋊C4—534no—
444C2×C4⋊C4—1062no—
445C2×C4⋊C4—1062no—
446C2×C4⋊C4—1061no—
447C2×C4⋊C4—1061no—
448C2×C4⋊C4C4×D5311yescharacteristic
449C2×C4⋊C4C4×D5311yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—1064no—
452C2×C22⋊C4—1064no—
453C2×C22⋊C4—1061no—
454C2×C22⋊C4—1061no—
455C2×C22⋊C4—1064no—
456C2×C22⋊C4—1068no—
457C2×C22⋊C4—1061no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—21no—
462C2×C42—532no—
463C2×C42—1064no—
464C2×C42—1064no—
465C2×C42—1061no—
466C2×C42—1061no—
467C2×C42—1061no—
468C2×C42—1062no—
469C2×C42—1062no—
470C2×C42—1061no—
471C2×C42C22×D5312yes—
472C22⋊C8—1064no—
473C22⋊C8—1064no—
474#95—1064no—
475C24—531no—
476C24—531no—
477C24—532no—
478C24—532no—
479C24—1064no—
480C24—1062no—
481C24—1062no—
482C24—2122no—
483C24D4×D5311yescharacteristic
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—531no—
491C22×C4—531no—
492C22×C4—532no—
493C22×C4—532no—
494C22×C4—532no—
495C22×C4—532no—
496C22×C4—532no—
497C22×C4—532no—
498C22×C4—532no—
499C22×C4—532no—
500C22×C4—532no—
501C22×C4—532no—
502C22×C4—1064no—
503C22×C4—1064no—
504C22×C4—1062no—
505C22×C4—1062no—
506C22×C4—1062no—
507C22×C4—1064no—
508C22×C4—1062no—
509C22×C4—1062no—
510C22×C4—1064no—
511C22×C4—1062no—
512C22×C4—1064no—
513C22×C4—1062no—
514C22×C4—1062no—
515C22×C4—1064no—
516C22×C4—1064no—
517C22×C4—1062no—
518C22×C4—1062no—
519C22×C4—1064no—
520C22×C4—1062no—
521C22×C4—1062no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—1064no—
525C22×C4—1061no—
526C22×C4—1061no—
527C22×C4—1062no—
528C22×C4—2124no—
529C22×C4—2124no—
530C22×C4—2122no—
531C22×C4—2122no—
532C22×C4C2×C4×D5311yescharacteristic
533C22×C4C2×C4×D5311yescharacteristic
534C22×C4#1171994512yes—
535C22×C4#1171994512yes—
536C22×C4D4×D5311yescharacteristic
537C22×C4D4×D5311yescharacteristic
538C22×C4D4×D5311yescharacteristic
539C22×C4#1171994712yes—
540C22×C4#1171994912yes—
541C22×C4C23×D5311yescharacteristic
542M16—22no—
543M16—22no—
544M16—42no—
545M16—1062no—
546M16—1062no—
547M16—2122no—
548C2×C8—22no—
549C2×C8—42no—
550C2×C8—1062no—
551C2×C8—2122no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—532no—
555C4⋊C4—532no—
556C4⋊C4—1064no—
557C4⋊C4—1064no—
558C4⋊C4—1061no—
559C4⋊C4—1061no—
560C4⋊C4C2×C4×D5312yes—
561C4⋊C4C2×C4×D5312yes—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—1064no—
565C22⋊C4—1064no—
566C22⋊C4—10616no—
567C22⋊C4—1062no—
568C22⋊C4—1062no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—42no—
574C42—1064no—
575C42—1064no—
576C42—1062no—
577C42—1062no—
578C42—1062no—
579C42—1062no—
580C42—2122no—
581C23—22no—
582C23—22no—
583C23—532no—
584C23—534no—
585C23—532no—
586C23—1064no—
587C23—1064no—
588C23—1062no—
589C23—1062no—
590C23—1062no—
591C23—1062no—
592C23—1062no—
593C23—1062no—
594C23—1064no—
595C23—1062no—
596C23—2122no—
597C23—2122no—
598C23—2128no—
599C23—2128no—
600C23C22⋊C4×D5311yescharacteristic
601C23C22⋊C4×D5311yescharacteristic
602C23#1313319912yes—
603C23#1313320212yes—
604C23C2×D4×D5311yescharacteristic
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—42no—
609C2×C4—48no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—532no—
614C2×C4—532no—
615C2×C4—1062no—
616C2×C4—1062no—
617C2×C4—1064no—
618C2×C4—1062no—
619C2×C4—1062no—
620C2×C4—1062no—
621C2×C4—1062no—
622C2×C4—1062no—
623C2×C4—1062no—
624C2×C4—1062no—
625C2×C4—1062no—
626C2×C4—1062no—
627C2×C4—1062no—
628C2×C4—1064no—
629C2×C4—1064no—
630C2×C4—1064no—
631C2×C4—1064no—
632C2×C4—1064no—
633C2×C4—1062no—
634C2×C4—1062no—
635C2×C4—2128no—
636C2×C4—2128no—
637C2×C4—2122no—
638C2×C4—2128no—
639C2×C4—2122no—
640C2×C4—2122no—
641C2×C4—2122no—
642C2×C4C22⋊C4×D5311yescharacteristic
643C2×C4C22⋊C4×D5311yescharacteristic
644C2×C4#1313317412yes—
645C2×C4#1313317412yes—
646C2×C4#1313317512yes—
647C2×C4#1313317512yes—
648C2×C4#1313319912yes—
649C2×C4#1313319912yes—
650C2×C4#1313319912yes—
651C2×C4#1313320212yes—
652C2×C4#1313320212yes—
653C2×C4#1313320212yes—
654C2×C4C22×C4×D5311yescharacteristic
655C2×C4C2×D4×D5311yescharacteristic
656C2×C4C2×#1171994711yescharacteristic
657C2×C4C2×#1171994511yescharacteristic
658C2×C4C2×#1171994511yescharacteristic
659C2×C4C2×#1171994911yescharacteristic
660C8—42no—
661C8—2122no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—24no—
667C22—24no—
668C22—534no—
669C22—1062no—
670C22—1062no—
671C22—1068no—
672C22—1062no—
673C22—1062no—
674C22—1062no—
675C22—2124no—
676C22—2124no—
677C22—2128no—
678C22—2124no—
679C22#1681048512yes—
680C22#1681048512yes—
681C22#104×D5312yes—
682C22#1681063812yes—
683C22C2×C22⋊C4×D5311yescharacteristic
684C22C2×#1313319911yescharacteristic
685C22C2×#1313320211yescharacteristic
686C4—44no—
687C4—42no—
688C4—42no—
689C4—1062no—
690C4—1062no—
691C4—2124no—
692C4—2122no—
693C4—2122no—
694C4#1681048512yes—
695C4#1681048512yes—
696C4C2×#1313317411yescharacteristic
697C4C2×#1313317511yescharacteristic
698C4C2×#1313319911yescharacteristic
699C4C2×#1313320211yescharacteristic
700C2—21no—
701C2—21no—
702C2—22no—
703C2—1064no—
704C2—2122no—
705C2#2027481314yesdirect product factor
706C2C2×#1681048511yescharacteristic
707C2C2×#104×D5311yescharacteristic
708C2C2×#1681063811yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#339C2
socleC23×C53C2×C22⋊C4
prime radicalC24×D53D4
cosocleC22×C4×C53C24
hypercenterC2×#339D53
hypocenterC53C2×#1826
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. #20274813C2direct (N × H)
5. C2×#16810384C2semidirect
6. C2×#16810383C2semidirect
7. C2×#16810382C2semidirect
8. C2×C53×#339C2semidirect
12. C2×#13133175C4semidirect
13. C2×#13133175C4semidirect
18. #117×D53C4semidirect
20. C2×C4⋊C4×D53C4semidirect
21. C2×C4⋊C4×D53C4semidirect
33. #16810384C22semidirect
34. #16810383C22semidirect
35. #16810382C22semidirect
39. C53×#339C22semidirect
68. #13133175C2×C4semidirect
69. #13133175C2×C4semidirect
80. C4⋊C4×D53C2×C4semidirect
81. C4⋊C4×D53C2×C4semidirect
353. C2×#339D53semidirect
357. C2×C53#1826semidirect
393. #339C2×D53semidirect
394. C53C2×#1826semidirect
705. C2#20274813direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117×D532
C2×#168105862
C2×C4×#117199212
#202748132
C2×#168103842
C2×#168103832
C2×#168103822
C2×C53×#3392
C2×#182653