Finite Group Databasebeta

← #27351870

Subgroups — #27351870

Order 13568.

1074 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283744C211yesmaximal, characteristic, complemented
2#20277625C211yesmaximal, characteristic, complemented
3#20273287C211yesmaximal, characteristic, complemented
4#20273283C211yesmaximal, characteristic, complemented
5#20273258C212yesmaximal, complemented
6#20273253C212yesmaximal, complemented
7#20273240C212yesmaximal, complemented
8#20273219C212yesmaximal, complemented
9C2×#16810360C211yesmaximal, characteristic, complemented
10C2×#16810357C211yesmaximal, characteristic, complemented
11C53×#3505C211yesmaximal, characteristic
12C2×D4×Dic53—21no—
13#16810695—22no—
14#16810695—22no—
15#16810680C2212yescomplemented
16#16810587C2212yescomplemented
17C2×C22⋊#88322C2211yescharacteristic
18C2×C22⋊#88322C2211yescharacteristic
19#16810522—21no—
20#16810498—21no—
21#16810498—21no—
22#16810489C2211yescharacteristic, complemented
23#16810483C2211yescharacteristic
24#16810483C2211yescharacteristic, complemented
25C4×C4⋊Dic53C2211yescharacteristic, complemented
26C2×#13133124C2211yescharacteristic
27C2×#13133124C2211yescharacteristic, complemented
28#16810360C2212yescomplemented
29#16810360C2212yescomplemented
30#16810360C2212yescomplemented
31#16810360C2212yescomplemented
32#16810357C2212yes—
33#16810357C2212yes—
34#16810357C2212yes—
35#16810357C2212yes—
36C53×#553—22no—
37C53×#553C412yescomplemented
38C53×#552C412yescomplemented
39C53×#551—22no—
40C53×#548C412yescomplemented
41C53×#546C412yescomplemented
42C53×#539—21no—
43C53×#538—21no—
44C53×#534—21no—
45C53×#529C2212yes—
46C53×#525C2212yes—
47C2×C22⋊Q8×C53C2211yescharacteristic
48C2×#121×C53C2211yescharacteristic
49C53×#518—21no—
50C2×C4×D4×C53C2211yescharacteristic
51C23×Dic53—21no—
52C23×Dic53—21no—
53C2×#11719917—22no—
54C22×#88322—21no—
55C22×#88322—21no—
56D4×Dic53—44no—
57C2×C4⋊Dic53—21no—
58C2×C4⋊Dic53—21no—
59C2×C4⋊Dic53—21no—
60C2×C4⋊Dic53—21no—
61C2×C22⋊Dic53—21no—
62C2×C22⋊Dic53—21no—
63C2×C4×Dic53—21no—
64C4⋊#88322—22no—
65C22⋊#88322—21no—
66C22⋊#88322—21no—
67C22⋊#88322—22no—
68C22⋊#88322C2312yes—
69C22⋊#88322C2312yes—
70#13133128—22no—
71#13133124—21no—
72#13133124—21no—
73#13133124—21no—
74#13133124C2311yescharacteristic
75#13133124C2311yescharacteristic
76#13133124C2311yescharacteristic
77#13133124C2311yescharacteristic
78C2×#41×C53C2×C412yescomplemented
79C22×Q8×C53C2×C411yescharacteristic, complemented
80C22×D4×C53—21no—
81C22×D4×C53C2×C411yescharacteristic, complemented
82C22×D4×C53D411yescharacteristic
83C23×C4×C53C2311yescharacteristic
84C23×C4×C53C2311yescharacteristic
85#126×C53—22no—
86#126×C53—22no—
87#126×C53—22no—
88#125×C53—22no—
89#125×C53C2×C412yescomplemented
90#124×C53—22no—
91#124×C53C2×C412yescomplemented
92#123×C53—22no—
93#123×C53—22no—
94#123×C53—22no—
95#123×C53—22no—
96#123×C53—22no—
97C22⋊Q8×C53—22no—
98C22⋊Q8×C53—21no—
99C22⋊Q8×C53—21no—
100C22⋊Q8×C53C2×C412yescomplemented
101C22⋊Q8×C53C2×C412yescomplemented
102C22⋊Q8×C53C2312yes—
103#121×C53—22no—
104#121×C53—22no—
105#121×C53—22no—
106#121×C53—21no—
107#121×C53—21no—
108#121×C53C2×C412yescomplemented
109#121×C53C2×C412yescomplemented
110#121×C53C2312yes—
111#120×C53—22no—
112#120×C53—22no—
113C4×Q8×C53C2×C412yescomplemented
114C4×D4×C53—22no—
115C4×D4×C53—22no—
116C4×D4×C53—22no—
117C4×D4×C53—22no—
118C4×D4×C53—22no—
119C4×D4×C53C2×C412yes—
120C4×D4×C53C2×C412yes—
121C4×D4×C53C2×C412yescomplemented
122C4×D4×C53D412yes—
123C4×D4×C53D412yes—
124#117×C53—22no—
125#117×C53—22no—
126#117×C53C2×C412yescomplemented
127C2×C4⋊C4×C53—21no—
128C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
129C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C53D411yescharacteristic
131C2×C22⋊C4×C53—22no—
132C2×C22⋊C4×C53—21no—
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53D411yescharacteristic
135C2×C22⋊C4×C53D411yescharacteristic
136C2×C42×C53C2311yescharacteristic
137C24×C53—21no—
138C24×C53C2×D411yescharacteristic
139C24×C53C2×D411yescharacteristic
140#41×C53—82no—
141C2×Q8×C53—21no—
142C2×Q8×C53—81no—
143C2×Q8×C53C22×C412yes—
144C2×D4×C53—22no—
145C2×D4×C53—22no—
146C2×D4×C53—22no—
147C2×D4×C53—22no—
148C2×D4×C53—22no—
149C2×D4×C53—22no—
150C2×D4×C53—21no—
151C2×D4×C53—42no—
152C2×D4×C53—42no—
153C2×D4×C53—81no—
154C2×D4×C53C22⋊C412yes—
155C2×D4×C53C22⋊C412yes—
156C2×D4×C53C22×C412yes—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—22no—
161C22×C4×C53—22no—
162C22×C4×C53—81no—
163C22×C4×C53—81no—
164C22×C4×C53C22×C411yescharacteristic
165C22×C4×C53C22×C411yescharacteristic
166C22×C4×C53C22×C412yes—
167C22×C4×C53C2×D411yescharacteristic
168C22×C4×C53C2×D411yescharacteristic
169C22×C4×C53C2×D411yescharacteristic
170C22×C4×C53C2×D411yescharacteristic
171C22×C4×C53C2×D411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D412yes—
174C22×C4×C53C2411yescharacteristic
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—42no—
180C22×Dic53—42no—
181C22×Dic53—42no—
182C22×Dic53—42no—
183C22×Dic53—81no—
184C22×Dic53—81no—
185C4⋊C4×C53—22no—
186C4⋊C4×C53—21no—
187C4⋊C4×C53—21no—
188C4⋊C4×C53—22no—
189C4⋊C4×C53—22no—
190C4⋊C4×C53—22no—
191C4⋊C4×C53—22no—
192C4⋊C4×C53—22no—
193C4⋊C4×C53C22⋊C412yes—
194C4⋊C4×C53C22⋊C412yes—
195C4⋊C4×C53C22×C412yes—
196C4⋊C4×C53C22×C412yes—
197C22⋊C4×C53—22no—
198C22⋊C4×C53—22no—
199C22⋊C4×C53—22no—
200C22⋊C4×C53—22no—
201C22⋊C4×C53—22no—
202C22⋊C4×C53—22no—
203C22⋊C4×C53—22no—
204C22⋊C4×C53—22no—
205C22⋊C4×C53—22no—
206C22⋊C4×C53—22no—
207C22⋊C4×C53C22⋊C412yes—
208C22⋊C4×C53C22⋊C412yes—
209C22⋊C4×C53C22⋊C412yes—
210C22⋊C4×C53C22⋊C412yes—
211C42×C53—22no—
212C42×C53—22no—
213C42×C53C22×C412yes—
214C42×C53C2×D412yes—
215C22⋊Dic53—42no—
216C22⋊Dic53—42no—
217C4⋊Dic53—42no—
218C4⋊Dic53—42no—
219C4⋊Dic53—81no—
220C4⋊Dic53—81no—
221C4×Dic53—42no—
222#11719917—82no—
223C2×#88322—22no—
224C2×#88322—22no—
225C2×#88322—81no—
226C2×#88322—81no—
227C23×C53—21no—
228C23×C53—21no—
229C23×C53—22no—
230C23×C53—41no—
231C23×C53—41no—
232C23×C53—41no—
233C23×C53—41no—
234C23×C53—42no—
235C23×C53—81no—
236C23×C53—81no—
237C23×C53C2×C22⋊C412yes—
238C23×C53C2×C22⋊C411yescharacteristic
239C23×C53C2×C22⋊C411yescharacteristic
240C23×C53AGL(1,ℤ/8)12yes—
241C23×C53#13712yes—
242C23×C53C22×D411yescharacteristic
243Q8×C53—42no—
244Q8×C53—81no—
245D4×C53—24no—
246D4×C53—24no—
247D4×C53—42no—
248D4×C53—42no—
249D4×C53—42no—
250D4×C53—44no—
251D4×C53—81no—
252D4×C53—82no—
253D4×C53—82no—
254C2×C4×C53—21no—
255C2×C4×C53—21no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—41no—
260C2×C4×C53—41no—
261C2×C4×C53—41no—
262C2×C4×C53—42no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—42no—
266C2×C4×C53—41no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—42no—
270C2×C4×C53—82no—
271C2×C4×C53—82no—
272C2×C4×C53—81no—
273C2×C4×C53—81no—
274C2×C4×C53C2×C22⋊C412yes—
275C2×C4×C53C2×C22⋊C412yes—
276C2×C4×C53C2×C22⋊C411yescharacteristic
277C2×C4×C53C2×C22⋊C411yescharacteristic
278C2×C4×C53C2×C22⋊C412yes—
279C2×C4×C53C23×C411yescharacteristic
280C2×C4×C53C22×D411yescharacteristic
281C2×Dic53—22no—
282C2×Dic53—41no—
283C2×Dic53—41no—
284C2×Dic53—41no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—84no—
294C2×Dic53—84no—
295#88322—42no—
296#88322—42no—
297#17622—531nomaximal, Sylow
298C22×C53—21no—
299C22×C53—21no—
300C22×C53—21no—
301C22×C53—21no—
302C22×C53—21no—
303C22×C53—21no—
304C22×C53—22no—
305C22×C53—22no—
306C22×C53—22no—
307C22×C53—42no—
308C22×C53—42no—
309C22×C53—42no—
310C22×C53—42no—
311C22×C53—42no—
312C22×C53—42no—
313C22×C53—42no—
314C22×C53—162no—
315C22×C53#41712yes—
316C22×C53#41712yes—
317C22×C53C22×C22⋊C411yescharacteristic
318C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C53C2×#13711yescharacteristic
320C4×C53—21no—
321C4×C53—21no—
322C4×C53—22no—
323C4×C53—21no—
324C4×C53—21no—
325C4×C53—22no—
326C4×C53—22no—
327C4×C53—42no—
328C4×C53—42no—
329C4×C53—42no—
330Dic53—42no—
331Dic53—81no—
332Dic53—81no—
333Dic53—81no—
334#3505D5311yescharacteristic
335#2973—531no—
336#2349—531no—
337#1520—531no—
338#1519—531no—
339#1513—532no—
340#1512—532no—
341#1509—532no—
342#1504—532no—
343C2×#328—531no—
344C2×#327—531no—
345C2×C53—21no—
346C2×C53—21no—
347C2×C53—22no—
348C2×C53—22no—
349C2×C53—42no—
350C2×C53—82no—
351C2×C53#288311yescharacteristic
352C2×C53C2×#41711yescharacteristic
353C2×C53#290111yescharacteristic
354#553—22no—
355#553Dic5312yescomplemented
356#552Dic5312yescomplemented
357#551—22no—
358#548Dic5312yescomplemented
359#546Dic5312yescomplemented
360#539—21no—
361#538—21no—
362#534—21no—
363#529C2×D5312yes—
364#525C2×D5312yes—
365C2×C22⋊Q8C2×D5311yescharacteristic
366C2×#121C2×D5311yescharacteristic
367#518—21no—
368C2×C4×D4—1061no—
369C2×C4×D4C2×D5311yescharacteristic
370#435—1062no—
371#435—1062no—
372#432—532no—
373#407—532no—
374C2×C22⋊C8—531no—
375C2×C22⋊C8—531no—
376#389—1061no—
377#385—1061no—
378#385—1061no—
379#382—531no—
380#380—531no—
381#380—531no—
382C4×C4⋊C4—531no—
383C2×#95—531no—
384C2×#95—531no—
385#328—532no—
386#328—532no—
387#328—532no—
388#328—532no—
389#327—532no—
390#327—532no—
391#327—532no—
392#327—532no—
393C53#1762211yescharacteristic, complemented, Sylow
394C2×#41C2×Dic5312yescomplemented
395C22×Q8C2×Dic5311yescharacteristic, complemented
396C22×D4—21no—
397C22×D4C2×Dic5311yescharacteristic, complemented
398C22×D4C22⋊D5311yescharacteristic
399C23×C4—1061no—
400C23×C4—1061no—
401C23×C4C22×D5311yescharacteristic
402C23×C4C22×D5311yescharacteristic
403C2×M16—1062no—
404C22×C8—1061no—
405C22×C8—1061no—
406#126—22no—
407#126—22no—
408#126—22no—
409#125—22no—
410#125C2×Dic5312yescomplemented
411#124—22no—
412#124C2×Dic5312yescomplemented
413#123—22no—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—22no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8C2×Dic5312yescomplemented
422C22⋊Q8C2×Dic5312yescomplemented
423C22⋊Q8C22×D5312yes—
424#121—22no—
425#121—22no—
426#121—21no—
427#121—21no—
428#121—22no—
429#121C2×Dic5312yescomplemented
430#121C2×Dic5312yescomplemented
431#121C22×D5312yes—
432#120—22no—
433#120—22no—
434C4×Q8C2×Dic5312yescomplemented
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—2124no—
441C4×D4C2×Dic5312yes—
442C4×D4C2×Dic5312yes—
443C4×D4C2×Dic5312yescomplemented
444C4×D4C22⋊D5312yes—
445C4×D4C22⋊D5312yes—
446#117—22no—
447#117—22no—
448#117C2×Dic5312yescomplemented
449C2×C4⋊C4—21no—
450C2×C4⋊C4—1061no—
451C2×C4⋊C4—1061no—
452C2×C4⋊C4—1061no—
453C2×C4⋊C4—1061no—
454C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
455C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
456C2×C4⋊C4C22⋊D5311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—1061no—
461C2×C22⋊C4—1061no—
462C2×C22⋊C4C22⋊D5311yescharacteristic
463C2×C22⋊C4C22⋊D5311yescharacteristic
464C2×C42—1061no—
465C2×C42C22×D5311yescharacteristic
466C4⋊C8—1062no—
467C22⋊C8—532no—
468C22⋊C8—532no—
469C22⋊C8—1061no—
470C22⋊C8—1061no—
471C22⋊C8—1062no—
472#97—1062no—
473#95—531no—
474#95—531no—
475#95—531no—
476#95—531no—
477#95—1061no—
478#95—1061no—
479#95—1061no—
480C24—21no—
481C24C2×C22⋊D5311yescharacteristic
482C24C2×C22⋊D5311yescharacteristic
483#41—82no—
484C2×Q8—21no—
485C2×Q8—81no—
486C2×Q8C22×Dic5312yes—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C2×D4C22⋊Dic5312yes—
498C2×D4C22⋊Dic5312yes—
499C2×D4C22×Dic5312yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—1061no—
508C22×C4—1061no—
509C22×C4—1061no—
510C22×C4—1061no—
511C22×C4—4241no—
512C22×C4—4241no—
513C22×C4—2122no—
514C22×C4—2122no—
515C22×C4—2122no—
516C22×C4—2122no—
517C22×C4C22×Dic5311yescharacteristic
518C22×C4C22×Dic5311yescharacteristic
519C22×C4C22×Dic5312yes—
520C22×C4C2×C22⋊D5311yescharacteristic
521C22×C4C2×C22⋊D5311yescharacteristic
522C22×C4C2×C22⋊D5311yescharacteristic
523C22×C4C2×C22⋊D5311yescharacteristic
524C22×C4C2×C22⋊D5311yescharacteristic
525C22×C4C2×C22⋊D5311yescharacteristic
526C22×C4C2×C22⋊D5312yes—
527C22×C4C23×D5311yescharacteristic
528M16—4242no—
529C2×C8—1062no—
530C2×C8—1062no—
531C2×C8—4241no—
532C2×C8—4241no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—4241no—
542C4⋊C4—4241no—
543C4⋊C4—2122no—
544C4⋊C4—2122no—
545C4⋊C4C22⋊Dic5312yes—
546C4⋊C4C22⋊Dic5312yes—
547C4⋊C4C22×Dic5312yes—
548C4⋊C4C22×Dic5312yes—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—2122no—
560C22⋊C4—2122no—
561C22⋊C4C22⋊Dic5312yes—
562C22⋊C4C22⋊Dic5312yes—
563C22⋊C4C22⋊Dic5312yes—
564C22⋊C4C22⋊Dic5312yes—
565C42—22no—
566C42—22no—
567C42—2122no—
568C42C22×Dic5312yes—
569C42C2×C22⋊D5312yes—
570C23—21no—
571C23—21no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—42no—
578C23—81no—
579C23—81no—
580C23C2×C22⋊Dic5312yes—
581C23C2×C22⋊Dic5311yescharacteristic
582C23C2×C22⋊Dic5311yescharacteristic
583C23#1313324212yes—
584C23#1313324712yes—
585C23C22×C22⋊D5311yescharacteristic
586Q8—42no—
587Q8—81no—
588D4—24no—
589D4—24no—
590D4—42no—
591D4—44no—
592D4—42no—
593D4—42no—
594D4—81no—
595D4—82no—
596D4—82no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—82no—
614C2×C4—82no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—1062no—
618C2×C4—4244no—
619C2×C4—4244no—
620C2×C4—2121no—
621C2×C4—2121no—
622C2×C4—2121no—
623C2×C4—2121no—
624C2×C4—2121no—
625C2×C4—2121no—
626C2×C4—2121no—
627C2×C4—2121no—
628C2×C4—2121no—
629C2×C4—2121no—
630C2×C4—2121no—
631C2×C4C2×C22⋊Dic5312yes—
632C2×C4C2×C22⋊Dic5312yes—
633C2×C4C2×C22⋊Dic5312yes—
634C2×C4C2×C22⋊Dic5311yescharacteristic
635C2×C4C2×C22⋊Dic5311yescharacteristic
636C2×C4C23×Dic5311yescharacteristic
637C2×C4C22×C22⋊D5311yescharacteristic
638C8—2122no—
639C8—2122no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—162no—
657C22#1681062412yes—
658C22#1681062412yes—
659C22C22×C22⋊Dic5311yescharacteristic
660C22C2×#1313324211yescharacteristic
661C22C2×#1313324711yescharacteristic
662C4—21no—
663C4—21no—
664C4—22no—
665C4—21no—
666C4—21no—
667C4—22no—
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—4241no—
673C4—4241no—
674C4—4241no—
675C4—2122no—
676C2—21no—
677C2—21no—
678C2—22no—
679C2—22no—
680C2—42no—
681C2—82no—
682C2#2028317611yescharacteristic
683C2C2×#1681062411yescharacteristic
684C2#2028326211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC53×#3505C2
socleC22×C53C22×C22⋊C4
cosocleC22×C4×C53C24
hypercenter#3505D53
hypocenterC53#17622
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. #20283744C2semidirect
2. #20277625C2semidirect
3. #20273287C2semidirect
4. #20273283C2semidirect
5. #20273258C2semidirect
6. #20273253C2semidirect
7. #20273240C2semidirect
8. #20273219C2semidirect
9. C2×#16810360C2semidirect
10. C2×#16810357C2semidirect
15. #16810680C22semidirect
16. #16810587C22semidirect
22. #16810489C22semidirect
24. #16810483C22semidirect
25. C4×C4⋊Dic53C22semidirect
27. C2×#13133124C22semidirect
28. #16810360C22semidirect
29. #16810360C22semidirect
30. #16810360C22semidirect
31. #16810360C22semidirect
37. C53×#553C4semidirect
38. C53×#552C4semidirect
40. C53×#548C4semidirect
41. C53×#546C4semidirect
78. C2×#41×C53C2×C4semidirect
79. C22×Q8×C53C2×C4semidirect
81. C22×D4×C53C2×C4semidirect
89. #125×C53C2×C4semidirect
91. #124×C53C2×C4semidirect
100. C22⋊Q8×C53C2×C4semidirect
101. C22⋊Q8×C53C2×C4semidirect
108. #121×C53C2×C4semidirect
109. #121×C53C2×C4semidirect
113. C4×Q8×C53C2×C4semidirect
121. C4×D4×C53C2×C4semidirect
126. #117×C53C2×C4semidirect
128. C2×C4⋊C4×C53C2×C4semidirect
129. C2×C4⋊C4×C53C2×C4semidirect
355. #553Dic53semidirect
356. #552Dic53semidirect
358. #548Dic53semidirect
359. #546Dic53semidirect
393. C53#17622semidirect
394. C2×#41C2×Dic53semidirect
395. C22×Q8C2×Dic53semidirect
397. C22×D4C2×Dic53semidirect
410. #125C2×Dic53semidirect
412. #124C2×Dic53semidirect
421. C22⋊Q8C2×Dic53semidirect
422. C22⋊Q8C2×Dic53semidirect
429. #121C2×Dic53semidirect
430. #121C2×Dic53semidirect
434. C4×Q8C2×Dic53semidirect
443. C4×D4C2×Dic53semidirect
448. #117C2×Dic53semidirect
454. C2×C4⋊C4C2×Dic53semidirect
455. C2×C4⋊C4C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
#202837442
#202776252
#202732872
#202732832
#202732582
#202732532
#202732402
#202732192
C2×#168103602
C2×#168103572
C53×#35052
#1762253