Finite Group Databasebeta

← #27391116

Subgroups — #27391116

Order 13568.

924 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810702C211yesmaximal, characteristic
2C2×C4×#11719912C211yesmaximal, characteristic, complemented
3C4×#13133202C211yesmaximal, characteristic
4#20275327C211yesmaximal, characteristic, complemented
5#20275319C211yesmaximal, characteristic, complemented
6#20275282C211yesmaximal, characteristic, complemented
7#20275274C211yesmaximal, characteristic, complemented
8#20275011C211yesmaximal, characteristic
9#20274896C211yesmaximal, characteristic, complemented
10#20274782C211yesmaximal, characteristic, complemented
11#20274589C211yesmaximal, characteristic, complemented
12#20274498C211yesmaximal, characteristic, complemented
13#20274498C211yesmaximal, characteristic, complemented
14#20274498C211yesmaximal, characteristic, complemented
15C8×C4⋊C4×C53C211yesmaximal, characteristic, complemented
16C22×#11719912C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×#11719912C2211yescharacteristic
19C2×#13133202C411yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×C42×D53C2211yescharacteristic
22#16810702—24no—
23C2×C4⋊#88322C2211yescharacteristic
24C2×#13133146C2211yescharacteristic
25C2×#13133129C2211yescharacteristic
26C2×#13133129C2211yescharacteristic
27C2×#13133129C2211yescharacteristic
28C2×#13133129C2211yescharacteristic
29C2×#13133129C2211yescharacteristic
30C4×#11719912—24no—
31C2×#13133127C2211yescharacteristic
32C2×#13133127C2211yescharacteristic
33C2×#13133127C2211yescharacteristic
34C2×C4×#88322C2211yescharacteristic
35#16810513C411yescharacteristic
36#16810512C411yescharacteristic
37#16810510C411yescharacteristic
38#16810509C411yescharacteristic
39#16810501C411yescharacteristic
40#16810494C411yescharacteristic
41#16810485C411yescharacteristic
42C4×#11719919C2211yescharacteristic
43C4×#11719921C2211yescharacteristic
44C4×#11719921C2211yescharacteristic
45C4×#11719921C2211yescharacteristic
46#16810378C2211yescharacteristic
47#16810378C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C2×C4⋊C8×C53C2211yescharacteristic
55C2×C4×C8×C53C2211yescharacteristic
56C2×C4×C8×C53C2211yescharacteristic
57C2×C4×C8×C53C2211yescharacteristic
58C4×C4⋊C4×C53C2211yescharacteristic
59C53×#336C2211yescharacteristic
60C53×#336C2211yescharacteristic
61C22×D212C2×C411yescharacteristic
62C22×C4×D53C2×C411yescharacteristic
63C22×C4×D53C2×C411yescharacteristic
64C22×C4×D53C2311yescharacteristic
65C22×C4×D53C2311yescharacteristic
66C2×#11719912—22no—
67C2×#11719912—22no—
68C2×#11719912—22no—
69C2×#11719912—22no—
70C2×#11719912—22no—
71C2×#11719912—22no—
72C2×#11719912—22no—
73C2×#11719912—22no—
74C2×#11719912D414yes—
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C22×#88322C2311yescharacteristic
79#13133202—24no—
80C4×D212—22no—
81C4×D212—22no—
82C2×C4⋊Dic53C2×C411yescharacteristic
83C2×#11719919C2×C411yescharacteristic
84C2×#11719919C2×C411yescharacteristic
85C2×#11719921C2×C411yescharacteristic
86C2×#11719921C2×C411yescharacteristic
87C2×#11719921C2×C411yescharacteristic
88C2×#11719921C2×C411yescharacteristic
89C2×#11719921C2×C411yescharacteristic
90C2×#11719921C2×C411yescharacteristic
91C2×#11719921C2×C411yescharacteristic
92C2×#11719921C2×C411yescharacteristic
93C2×C4×Dic53C2×C411yescharacteristic
94C2×C4×Dic53C2×C411yescharacteristic
95C2×C4×Dic53C2311yescharacteristic
96C2×C4×Dic53C2311yescharacteristic
97C42×D53—22no—
98C42×D53—22no—
99C4⋊#88322—22no—
100#13133146—22no—
101#13133129—22no—
102#13133129—22no—
103#13133129—22no—
104#13133129—22no—
105#13133129—22no—
106#13133127—22no—
107#13133127—22no—
108#13133127—22no—
109C4×#88322—22no—
110#13133124C2×C411yescharacteristic
111#13133124C2×C411yescharacteristic
112#13133124C2×C411yescharacteristic
113#13133124C2×C411yescharacteristic
114#13133124C2×C411yescharacteristic
115#13133124C2×C411yescharacteristic
116#13133124C2×C411yescharacteristic
117#13133124C2×C411yescharacteristic
118C22×C8×C53C2311yescharacteristic
119C22×C8×C53C2311yescharacteristic
120C22×C8×C53C2311yescharacteristic
121C22×C8×C53C2311yescharacteristic
122C2×C4⋊C4×C53C2×C411yescharacteristic
123C2×C4⋊C4×C53C2×C411yescharacteristic
124C2×C42×C53C2311yescharacteristic
125C2×C42×C53C2311yescharacteristic
126C2×C42×C53C2311yescharacteristic
127C4⋊C8×C53—22no—
128C4×C8×C53—22no—
129C4×C8×C53—22no—
130C4×C8×C53—22no—
131#95×C53C2×C411yescharacteristic
132#95×C53C2×C411yescharacteristic
133C23×D53C22×C411yescharacteristic
134C23×D53C22×C411yescharacteristic
135C22×C4×C53C22×C411yescharacteristic
136C22×C4×C53C22×C411yescharacteristic
137C22×C4×C53C22×C411yescharacteristic
138C22×C4×C53C22×C411yescharacteristic
139C22×C4×C53C22×C411yescharacteristic
140C22×C4×C53C22×C411yescharacteristic
141C22×C4×C53C2411yescharacteristic
142C22×Dic53C22×C411yescharacteristic
143C22×Dic53C22×C411yescharacteristic
144C22×Dic53C22×C411yescharacteristic
145C22×Dic53C22×C411yescharacteristic
146C22×Dic53C22×C411yescharacteristic
147C22×Dic53C22×C411yescharacteristic
148C2×D212—22no—
149C2×D212—22no—
150C2×D212—41no—
151C2×C4×D53—21no—
152C2×C4×D53—21no—
153C2×C4×D53—21no—
154C2×C4×D53—21no—
155C2×C4×D53—22no—
156C2×C4×D53—22no—
157C2×C4×D53—22no—
158C2×C4×D53—22no—
159C2×C4×D53—21no—
160C2×C4×D53—21no—
161C2×C4×D53—21no—
162C2×C4×D53—21no—
163C2×C4×D53—21no—
164C2×C4×D53—21no—
165C2×C4×D53—41no—
166C2×C4×D53—41no—
167C2×C4×D53C2×D412yes—
168C2×C4×D53#4112yes—
169C2×C8×C53—21no—
170C2×C8×C53—21no—
171C2×C8×C53—21no—
172C2×C8×C53—21no—
173C2×C8×C53—21no—
174C2×C8×C53—21no—
175C2×C8×C53—21no—
176C2×C8×C53—21no—
177C2×C8×C53C2×D412yes—
178C2×C8×C53#4112yes—
179C2×C8×C53#4112yes—
180C2×C8×C53#4112yes—
181C4⋊C4×C53—22no—
182C4⋊C4×C53M1614yescomplemented
183C42×C53—21no—
184C42×C53—21no—
185C42×C53—21no—
186C42×C53—21no—
187C42×C53—21no—
188C42×C53—21no—
189#11719921—22no—
190#11719921—22no—
191#11719921—22no—
192#11719921—22no—
193#11719921—22no—
194#11719921—22no—
195#11719921—41no—
196#11719921—41no—
197C4⋊Dic53—22no—
198#11719919—22no—
199#11719919—41no—
200C4×Dic53—21no—
201C4×Dic53—21no—
202C4×Dic53—21no—
203C4×Dic53—21no—
204C4×Dic53—22no—
205C4×Dic53—22no—
206C2×#88322—21no—
207C2×#88322—21no—
208C2×#88322—21no—
209C2×#88322—21no—
210C2×#88322—21no—
211C2×#88322—21no—
212C2×#88322—21no—
213C2×#88322—21no—
214C2×#88322—21no—
215C2×#88322—21no—
216C2×#88322C2×D412yes—
217C2×#88322#4112yes—
218#11719912—28no—
219#11719912—28no—
220#11719912—44no—
221C23×C53C23×C411yescharacteristic
222C22×D53—21no—
223C22×D53—21no—
224C22×D53—21no—
225C22×D53—21no—
226C22×D53—21no—
227C22×D53—21no—
228C22×D53—21no—
229C22×D53—21no—
230C22×D53—21no—
231C22×D53—21no—
232C22×D53—21no—
233C22×D53—21no—
234C22×D53—21no—
235C22×D53C4×D412yes—
236C2×C4×C53—21no—
237C2×C4×C53—21no—
238C2×C4×C53—21no—
239C2×C4×C53—21no—
240C2×C4×C53—21no—
241C2×C4×C53—21no—
242C2×C4×C53—21no—
243C2×C4×C53—21no—
244C2×C4×C53—21no—
245C2×C4×C53—21no—
246C2×C4×C53—21no—
247C2×C4×C53—21no—
248C2×C4×C53—21no—
249C2×C4×C53—21no—
250C2×C4×C53C2×M1612yes—
251C2×C4×C53C2×M1612yes—
252C2×C4×C53C2×M1612yes—
253C2×C4×C53#13112yes—
254C2×C4×C53C22×D411yescharacteristic
255C2×C4×C53C2×#4111yescharacteristic
256C2×C4×C53C2×#4111yescharacteristic
257C2×C4×C53C2×#4111yescharacteristic
258C2×C4×C53C2×#4111yescharacteristic
259C2×C4×C53C2×#4111yescharacteristic
260C2×Dic53—21no—
261C2×Dic53—21no—
262C2×Dic53—21no—
263C2×Dic53—21no—
264C2×Dic53—21no—
265C2×Dic53—21no—
266C2×Dic53—21no—
267C2×Dic53—21no—
268C2×Dic53—21no—
269C2×Dic53—21no—
270C2×Dic53—21no—
271C2×Dic53—21no—
272C2×Dic53—21no—
273C2×Dic53—21no—
274C2×Dic53—21no—
275C2×Dic53—21no—
276C2×Dic53—21no—
277C2×Dic53C4×D412yes—
278D212—44no—
279C4×D53—22no—
280C4×D53—22no—
281C4×D53—22no—
282C4×D53—22no—
283C4×D53—44no—
284C4×D53—44no—
285C4×D53—41no—
286C4×D53—41no—
287C4×D53—41no—
288C4×D53—41no—
289C8×C53—22no—
290C8×C53—41no—
291C8×C53—41no—
292C8×C53#12314yescomplemented
293#88322—22no—
294#88322—22no—
295#88322—41no—
296#88322—41no—
297#21565—531nomaximal, Sylow
298C22×C53C2×C4×D411yescharacteristic
299C22×C53C4×#4111yescharacteristic
300C22×C53C4×#4111yescharacteristic
301C22×C53C22×M1611yescharacteristic
302C22×C53C2×#13111yescharacteristic
303C22×C53#56811yescharacteristic
304C22×C53#56811yescharacteristic
305C2×D53—22no—
306C2×D53—22no—
307C2×D53—22no—
308C2×D53—41no—
309C2×D53—41no—
310C2×D53—41no—
311C2×D53—41no—
312C2×D53—41no—
313C2×D53—41no—
314C2×D53—41no—
315C2×D53—41no—
316C2×D53—41no—
317C2×D53—41no—
318C2×D53—41no—
319C4×C53—22no—
320C4×C53—22no—
321C4×C53—22no—
322C4×C53—22no—
323C4×C53—41no—
324C4×C53—41no—
325C4×C53C2×#12311yescharacteristic
326C4×C53#52511yescharacteristic
327C4×C53#52911yescharacteristic
328C4×C53#52911yescharacteristic
329Dic53—22no—
330Dic53—41no—
331Dic53—41no—
332Dic53—41no—
333Dic53—41no—
334Dic53—41no—
335C2×#436—531no—
336C2×C4×M16—531no—
337C4×#123—531no—
338#1924—531no—
339#1923—531no—
340#1917—531no—
341#1916—531no—
342#1870—531no—
343#1851—531no—
344#1817—531no—
345#1771—531no—
346C8×C4⋊C4D5311yescharacteristic, complemented
347#1753—531no—
348#1753—531no—
349#1753—531no—
350C2×C53C4×#12311yescharacteristic
351C2×C53#293311yescharacteristic
352C2×C53D4×M1611yescharacteristic
353C2×C53#296511yescharacteristic
354C2×C53#296711yescharacteristic
355C2×C53#296911yescharacteristic
356C2×C53#297111yescharacteristic
357D53—42no—
358D53—81no—
359C22×M16—531no—
360C22×M16—531no—
361C22×M16—531no—
362C2×#123—531no—
363C2×C4×D4—531no—
364C22×C42—531no—
365#436—1064no—
366C2×C4⋊C8—531no—
367C2×C4⋊C8—531no—
368C2×C4⋊C8C2×D5311yescharacteristic
369C2×C22⋊C8—531no—
370C2×C22⋊C8—531no—
371C2×C22⋊C8—531no—
372C2×C22⋊C8—531no—
373C2×C22⋊C8—531no—
374C4×M16—1064no—
375C2×#97—531no—
376C2×#97—531no—
377C2×#97—531no—
378C2×C4×C8—531no—
379C2×C4×C8C2×D5311yescharacteristic
380C2×C4×C8C2×D5311yescharacteristic
381C2×C4×C8C2×D5311yescharacteristic
382#388—531no—
383#388—531no—
384#387—531no—
385#387—531no—
386#386—531no—
387#385—531no—
388#381—531no—
389C4×C4⋊C4—531no—
390C4×C4⋊C4C2×D5311yescharacteristic
391C4×C22⋊C4—531no—
392C4×C22⋊C4—531no—
393C4×C22⋊C4—531no—
394#336—531no—
395#336—531no—
396#336—531no—
397#336—531no—
398#336—531no—
399#336—531no—
400#336—531no—
401#336—531no—
402#336C2×D5311yescharacteristic
403#336C2×D5311yescharacteristic
404C53#2156511yescharacteristic, complemented, Sylow
405C22×D4—531no—
406C23×C4—531no—
407C23×C4—531no—
408C23×C4—531no—
409C23×C4—531no—
410C2×M16—534no—
411C2×M16—1062no—
412C2×M16—1062no—
413C2×M16—1062no—
414C2×M16—1062no—
415C2×M16—1062no—
416C2×M16—1062no—
417C2×M16—1062no—
418C2×M16—1062no—
419C22×C8—531no—
420C22×C8—531no—
421C22×C8—531no—
422C22×C8—531no—
423C22×C8C22×D5311yescharacteristic
424C22×C8C22×D5311yescharacteristic
425C22×C8C22×D5311yescharacteristic
426C22×C8C22×D5311yescharacteristic
427#123—1064no—
428C4×D4—1062no—
429C4×D4—1062no—
430C2×C4⋊C4—531no—
431C2×C4⋊C4—531no—
432C2×C4⋊C4—531no—
433C2×C4⋊C4C4×D5311yescharacteristic
434C2×C4⋊C4C4×D5311yescharacteristic
435C2×C22⋊C4—531no—
436C2×C22⋊C4—531no—
437C2×C22⋊C4—531no—
438C2×C22⋊C4—531no—
439C2×C22⋊C4—531no—
440C2×C22⋊C4—531no—
441C2×C22⋊C4—531no—
442C2×C22⋊C4—531no—
443C2×C42—531no—
444C2×C42—531no—
445C2×C42—531no—
446C2×C42—531no—
447C2×C42—1062no—
448C2×C42—1062no—
449C2×C42C22×D5311yescharacteristic
450C2×C42C22×D5311yescharacteristic
451C2×C42C22×D5311yescharacteristic
452C4⋊C8—22no—
453C4⋊C8—1062no—
454C4⋊C8—1062no—
455C22⋊C8—1062no—
456C22⋊C8—1062no—
457C22⋊C8—1062no—
458C22⋊C8—1062no—
459C22⋊C8—1062no—
460#97—1062no—
461#97—1062no—
462#97—1062no—
463C4×C8—22no—
464C4×C8—22no—
465C4×C8—22no—
466C4×C8—1062no—
467#95—531no—
468#95—531no—
469#95—531no—
470#95—531no—
471#95—531no—
472#95—531no—
473#95—531no—
474#95—531no—
475#95C4×D5311yescharacteristic
476#95C4×D5311yescharacteristic
477C24—531no—
478C24—531no—
479C2×D4—1062no—
480C2×D4—1062no—
481C2×D4—2121no—
482C22×C4—531no—
483C22×C4—532no—
484C22×C4—532no—
485C22×C4—531no—
486C22×C4—531no—
487C22×C4—531no—
488C22×C4—531no—
489C22×C4—531no—
490C22×C4—1062no—
491C22×C4—1062no—
492C22×C4—1061no—
493C22×C4—1061no—
494C22×C4—1061no—
495C22×C4—1061no—
496C22×C4—1062no—
497C22×C4—1062no—
498C22×C4—1061no—
499C22×C4—1061no—
500C22×C4—1061no—
501C22×C4—1061no—
502C22×C4—1061no—
503C22×C4—1061no—
504C22×C4—2121no—
505C22×C4—2121no—
506C22×C4C2×C4×D5311yescharacteristic
507C22×C4C2×C4×D5311yescharacteristic
508C22×C4C2×C4×D5311yescharacteristic
509C22×C4C2×C4×D5311yescharacteristic
510C22×C4C2×C4×D5311yescharacteristic
511C22×C4C2×C4×D5311yescharacteristic
512C22×C4C23×D5311yescharacteristic
513M16—1068no—
514M16—1068no—
515M16—2124no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—532no—
525C2×C8—532no—
526C2×C8—1061no—
527C2×C8—1061no—
528C2×C8—1061no—
529C2×C8—1061no—
530C2×C8—1061no—
531C2×C8—1061no—
532C2×C8—1061no—
533C2×C8—1061no—
534C2×C8—1061no—
535C2×C8—1061no—
536C2×C8#1171994512yes—
537C2×C8#1171994512yes—
538C2×C8D4×D5312yes—
539C2×C8#1171994912yes—
540C4⋊C4—22no—
541C4⋊C4—1062no—
542C4⋊C4—1062no—
543C4⋊C4—2121no—
544C4⋊C4#1171991214yescomplemented
545C22⋊C4—1062no—
546C22⋊C4—1062no—
547C22⋊C4—1062no—
548C22⋊C4—1062no—
549C22⋊C4—1062no—
550C22⋊C4—1062no—
551C22⋊C4—2121no—
552C22⋊C4—2121no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—1062no—
560C42—1062no—
561C42—1061no—
562C42—1061no—
563C42—1061no—
564C42—1061no—
565C23—532no—
566C23—1061no—
567C23—1061no—
568C23—1061no—
569C23—1061no—
570C23—1061no—
571C23—1061no—
572C23—1061no—
573C23—1061no—
574C23—1061no—
575C23—1061no—
576C23—1061no—
577C23—1061no—
578C23—1061no—
579C23C22×C4×D5311yescharacteristic
580D4—2124no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—532no—
596C2×C4—1061no—
597C2×C4—1061no—
598C2×C4—1062no—
599C2×C4—1062no—
600C2×C4—1062no—
601C2×C4—1062no—
602C2×C4—1061no—
603C2×C4—1061no—
604C2×C4—1061no—
605C2×C4—1061no—
606C2×C4—1061no—
607C2×C4—1061no—
608C2×C4—1061no—
609C2×C4—1061no—
610C2×C4—1061no—
611C2×C4—1061no—
612C2×C4—1061no—
613C2×C4—1061no—
614C2×C4—1061no—
615C2×C4—1061no—
616C2×C4—1061no—
617C2×C4—2124no—
618C2×C4—2124no—
619C2×C4—2121no—
620C2×C4—2121no—
621C2×C4—2121no—
622C2×C4—2121no—
623C2×C4C2×#1171991212yes—
624C2×C4C2×#1171991212yes—
625C2×C4C2×#1171991212yes—
626C2×C4#1313322312yes—
627C2×C4C2×D4×D5311yescharacteristic
628C2×C4#41×D5311yescharacteristic
629C2×C4#41×D5311yescharacteristic
630C2×C4C2×#1171994511yescharacteristic
631C2×C4C2×#1171994511yescharacteristic
632C2×C4C2×#1171994911yescharacteristic
633C8—22no—
634C8—41no—
635C8—41no—
636C8—1062no—
637C8—1062no—
638C8—2121no—
639C8—2121no—
640C8#1313320214yescomplemented
641C22—1062no—
642C22—1062no—
643C22—1062no—
644C22—2121no—
645C22—2121no—
646C22—2121no—
647C22—2121no—
648C22—2121no—
649C22—2121no—
650C22—2121no—
651C22—2121no—
652C22—2121no—
653C22—2121no—
654C22—2121no—
655C22C4×D4×D5311yescharacteristic
656C22C4×#1171994511yescharacteristic
657C22C4×#1171994911yescharacteristic
658C22C22×#1171991211yescharacteristic
659C22C2×#1313322311yescharacteristic
660C22#1681138811yescharacteristic
661C22#1681138811yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—1062no—
669C4—2121no—
670C4—2121no—
671C4—2121no—
672C4—2121no—
673C4—2121no—
674C4C2×#1313320211yescharacteristic
675C4#1681113211yescharacteristic
676C4#1681115111yescharacteristic
677C4#1681116011yescharacteristic
678C2—4241no—
679C2—2122no—
680C2C4×#1313320211yescharacteristic
681C2#2028343511yescharacteristic
682C2D4×#1171991211yescharacteristic
683C2#2028368111yescharacteristic
684C2#2028369611yescharacteristic
685C2#2028371811yescharacteristic
686C2#2028373411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC8×C4⋊C4×C53C2
prime radicalC22×D212C2×C4
cosocleC22×C4×C53C24
hypercenterC8×C4⋊C4D53
hypocenterC53#21565
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719912C2semidirect
4. #20275327C2semidirect
5. #20275319C2semidirect
6. #20275282C2semidirect
7. #20275274C2semidirect
9. #20274896C2semidirect
10. #20274782C2semidirect
11. #20274589C2semidirect
12. #20274498C2semidirect
13. #20274498C2semidirect
14. #20274498C2semidirect
15. C8×C4⋊C4×C53C2semidirect
182. C4⋊C4×C53M16semidirect
292. C8×C53#123semidirect
346. C8×C4⋊C4D53semidirect
404. C53#21565semidirect
544. C4⋊C4#11719912semidirect
640. C8#13133202semidirect

Maximal subgroups

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

subgroupindex
C2×#168107022
C2×C4×#117199122
C4×#131332022
#202753272
#202753192
#202752822
#202752742
#202750112
#202748962
#202747822
#202745892
#202744982
C8×C4⋊C4×C532
#2156553