Finite Group Databasebeta

← #27432301

Subgroups — #27432301

Order 13568.

940 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810953C211yesmaximal, characteristic, complemented
2C2×#16810850C211yesmaximal, characteristic
3#20277718C211yesmaximal, characteristic, complemented
4#20276192C211yesmaximal, characteristic, complemented
5#20276124C211yesmaximal, characteristic, complemented
6#20276089C211yesmaximal, characteristic, complemented
7#20276032C211yesmaximal, characteristic, complemented
8#20275476C211yesmaximal, characteristic, complemented
9#20275339C211yesmaximal, characteristic, complemented
10#20275073C211yesmaximal, characteristic, complemented
11#20275033C211yesmaximal, characteristic
12#20274895C211yesmaximal, characteristic, complemented
13#20274717C211yesmaximal, characteristic, complemented
14C2×#16810385C211yesmaximal, characteristic, complemented
15C53×#2501C211yesmaximal, characteristic
16C22×#11719923C2211yescharacteristic
17C23×#88322C2211yescharacteristic
18C2×#13133196C2211yescharacteristic
19C2×C4×Dic106C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21#16810953—24no—
22#16810850—24no—
23C2×#13133148C2211yescharacteristic
24C2×#13133148C2211yescharacteristic
25C2×#13133148C2211yescharacteristic
26C2×C4⋊#88322C2211yescharacteristic
27C2×C4⋊#88322C2211yescharacteristic
28C2×#13133140C2211yescharacteristic
29C2×#13133140C2211yescharacteristic
30C2×#13133140C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133138C2211yescharacteristic
33C2×#13133138C2211yescharacteristic
34C2×C22⋊#88322C2211yescharacteristic
35#16810529C2211yescharacteristic
36#16810521C2211yescharacteristic
37#16810520—21no—
38#16810510—21no—
39#16810495—21no—
40C4×C4⋊Dic53C2211yescharacteristic
41C22⋊C4×Dic53—21no—
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810385C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810378C2211yescharacteristic
49#16810378C2211yescharacteristic
50C2×#123×C53—21no—
51C2×#123×C53—21no—
52C2×#121×C53C2211yescharacteristic
53C22×C4⋊C4×C53C2211yescharacteristic
54C53×#399—21no—
55C53×#399—21no—
56C53×#390C2211yescharacteristic
57C53×#390C2211yescharacteristic
58C53×#384C2211yescharacteristic
59C53×#384C2211yescharacteristic
60C4×C22⋊C4×C53C2211yescharacteristic
61C22×Dic106C2311yescharacteristic
62C23×Dic53—21no—
63C2×#11719923—22no—
64C2×#11719923—22no—
65C2×#11719923—41no—
66C22×#88322—22no—
67C22×#88322—22no—
68C22×#88322—41no—
69C22×#88322C2311yescharacteristic
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73#13133196—22no—
74#13133196D414yes—
75C4×Dic106—22no—
76C4×Dic106—41no—
77C2×C4⋊Dic53—21no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—41no—
80C2×C4⋊Dic53C2311yescharacteristic
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×#11719919—21no—
84C2×#11719919—21no—
85C2×#11719919—21no—
86C2×C22⋊Dic53—21no—
87C2×C4×Dic53—21no—
88C2×C4×Dic53—21no—
89#13133148—22no—
90#13133148—22no—
91#13133148—22no—
92C4⋊#88322—22no—
93C4⋊#88322—41no—
94#13133140—22no—
95#13133140—22no—
96#13133140—22no—
97#13133138—22no—
98#13133138—22no—
99#13133138—41no—
100C22⋊#88322—22no—
101#13133124—21no—
102#13133124—21no—
103#13133124—21no—
104#13133124—21no—
105C22×D4×C53—21no—
106C22×D4×C53C2311yescharacteristic
107C23×C4×C53—21no—
108C23×C4×C53C2311yescharacteristic
109#123×C53—44no—
110#123×C53—44no—
111#121×C53—22no—
112#121×C53—22no—
113C2×C4⋊C4×C53—21no—
114C2×C4⋊C4×C53—21no—
115C2×C4⋊C4×C53—21no—
116C2×C4⋊C4×C53—21no—
117C2×C4⋊C4×C53—21no—
118C2×C4⋊C4×C53—22no—
119C2×C4⋊C4×C53—22no—
120C2×C4⋊C4×C53C2311yescharacteristic
121C2×C4⋊C4×C53C2311yescharacteristic
122C2×C4⋊C4×C53C2311yescharacteristic
123C2×C22⋊C4×C53—21no—
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53D411yescharacteristic
129C2×C22⋊C4×C53D411yescharacteristic
130C2×C42×C53C2311yescharacteristic
131C2×C42×C53C2311yescharacteristic
132#95×C53D411yescharacteristic
133#95×C53D411yescharacteristic
134C24×C53—21no—
135C24×C53C2×D411yescharacteristic
136C2×D4×C53—21no—
137C2×D4×C53—21no—
138C2×D4×C53—21no—
139C2×D4×C53—21no—
140C2×D4×C53—21no—
141C2×D4×C53—21no—
142C2×D4×C53—42no—
143C2×D4×C53—42no—
144C2×D4×C53—42no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—42no—
153C22×C4×C53—42no—
154C22×C4×C53—42no—
155C22×C4×C53C2×D411yescharacteristic
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×D411yescharacteristic
158C22×C4×C53C2×D412yes—
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D411yescharacteristic
161C22×C4×C53#4112yes—
162C22×C4×C53C2411yescharacteristic
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—42no—
168C22×Dic53—42no—
169C22×Dic53—81no—
170C2×Dic106—21no—
171C2×Dic106—21no—
172C2×Dic106—21no—
173C2×Dic106—21no—
174C2×Dic106—21no—
175C2×Dic106C2×D412yes—
176C4⋊C4×C53—21no—
177C4⋊C4×C53—21no—
178C4⋊C4×C53—21no—
179C4⋊C4×C53—21no—
180C4⋊C4×C53—21no—
181C4⋊C4×C53—21no—
182C4⋊C4×C53—42no—
183C4⋊C4×C53—42no—
184C4⋊C4×C53—42no—
185C4⋊C4×C53—42no—
186C4⋊C4×C53—42no—
187C22⋊C4×C53—22no—
188C22⋊C4×C53—42no—
189C22⋊C4×C53—42no—
190C22⋊C4×C53—42no—
191C22⋊C4×C53—42no—
192C22⋊C4×C53—42no—
193C22⋊C4×C53SD1614yescomplemented
194C42×C53—21no—
195C42×C53—21no—
196C42×C53—21no—
197C42×C53—21no—
198C22⋊Dic53—24no—
199#11719923—44no—
200C4⋊Dic53—21no—
201C4⋊Dic53—21no—
202C4⋊Dic53—21no—
203C4⋊Dic53—21no—
204C4⋊Dic53—42no—
205C4⋊Dic53C2×D412yes—
206C4⋊Dic53#4112yes—
207#11719919—24no—
208#11719919—42no—
209#11719919—81no—
210C4×Dic53—42no—
211C4×Dic53—81no—
212C2×#88322—21no—
213C2×#88322—21no—
214C2×#88322—21no—
215C2×#88322—21no—
216C2×#88322—21no—
217C2×#88322—21no—
218C2×#88322—21no—
219C2×#88322—21no—
220C2×#88322—21no—
221C2×#88322—21no—
222C2×#88322—21no—
223C2×#88322—44no—
224C2×#88322#4112yes—
225C23×C53—21no—
226C23×C53—21no—
227C23×C53—21no—
228C23×C53—21no—
229C23×C53—41no—
230C23×C53—41no—
231C23×C53—41no—
232C23×C53—41no—
233C23×C53—41no—
234C23×C53—41no—
235C23×C53—41no—
236C23×C53#12112yes—
237C23×C53C2×SD1612yes—
238C23×C53AGL(1,ℤ/8)12yes—
239C23×C53C22×D411yescharacteristic
240D4×C53—41no—
241D4×C53—41no—
242D4×C53—41no—
243D4×C53—41no—
244D4×C53—84no—
245C2×C4×C53—21no—
246C2×C4×C53—21no—
247C2×C4×C53—21no—
248C2×C4×C53—21no—
249C2×C4×C53—21no—
250C2×C4×C53—21no—
251C2×C4×C53—22no—
252C2×C4×C53—22no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—21no—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—41no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—41no—
267C2×C4×C53—41no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—84no—
271C2×C4×C53#12112yes—
272C2×C4×C53C2×SD1612yes—
273C2×C4×C53C2×SD1612yes—
274C2×C4×C53C22×D411yescharacteristic
275C2×C4×C53C2×#4111yescharacteristic
276C2×C4×C53C2×#4111yescharacteristic
277C2×C4×C53C2×#4111yescharacteristic
278C2×C4×C53H(5,𝔽2)11yescharacteristic
279C2×C4×C532−1+411yescharacteristic
280C2×Dic53—22no—
281C2×Dic53—22no—
282C2×Dic53—22no—
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—84no—
293Dic106—22no—
294Dic106—22no—
295Dic106—41no—
296Dic106—41no—
297#88322—22no—
298#88322—41no—
299#88322—41no—
300#88322—41no—
301#25204—531nomaximal, Sylow
302C22×C53—22no—
303C22×C53—22no—
304C22×C53—22no—
305C22×C53—22no—
306C22×C53—22no—
307C22×C53—22no—
308C22×C53—81no—
309C22×C53—81no—
310C22×C53—81no—
311C22×C53—81no—
312C22×C53—81no—
313C22×C53—81no—
314C22×C53—81no—
315C22×C53#46014yes—
316C22×C53C2×#12111yescharacteristic
317C22×C53#54611yescharacteristic
318C22×C53#54711yescharacteristic
319C22×C53C22×SD1611yescharacteristic
320C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C53#57711yescharacteristic
322C22×C53#57811yescharacteristic
323C4×C53—22no—
324C4×C53—22no—
325C4×C53—22no—
326C4×C53—41no—
327C4×C53—41no—
328C4×C53—81no—
329C4×C53—81no—
330C4×C53—81no—
331C4×C53#52911yescharacteristic
332C4×C53#53911yescharacteristic
333C4×C53#54611yescharacteristic
334C4×C53#54711yescharacteristic
335Dic53—42no—
336Dic53—42no—
337Dic53—42no—
338Dic53—81no—
339C2×#483—531no—
340C2×#465—531no—
341#2501D5311yescharacteristic
342#2360—531no—
343#2084—531no—
344#2072—531no—
345#2065—531no—
346#2055—531no—
347#1948—531no—
348#1926—531no—
349#1880—531no—
350#1874—531no—
351#1850—531no—
352#1803—531no—
353C2×#340—531no—
354C2×C53—24no—
355C2×C53—161no—
356C2×C53#242511yescharacteristic
357C2×C53C2×#46011yescharacteristic
358C2×C53#304611yescharacteristic
359C2×C53#329811yescharacteristic
360C2×C53#330611yescharacteristic
361C2×C53#333511yescharacteristic
362C2×C53#334311yescharacteristic
363C22×SD16—531no—
364C23×C8—531no—
365C2×#123—21no—
366C2×#123—21no—
367C2×C22⋊Q8—531no—
368C2×#121C2×D5311yescharacteristic
369C2×C4×Q8—531no—
370C22×C4⋊C4—531no—
371C22×C4⋊C4C2×D5311yescharacteristic
372#483—1064no—
373#465—1064no—
374C2×#106—531no—
375C2×#106—531no—
376C2×#106—531no—
377C2×C4⋊C8—531no—
378C2×C4⋊C8—531no—
379C2×#103—531no—
380C2×#103—531no—
381C2×#103—531no—
382C2×#102—531no—
383C2×#102—531no—
384C2×#102—531no—
385C2×C22⋊C8—531no—
386#399—21no—
387#399—21no—
388#391—531no—
389#390C2×D5311yescharacteristic
390#390C2×D5311yescharacteristic
391#389—531no—
392#389—1061no—
393#387—1061no—
394#385—1061no—
395#384C2×D5311yescharacteristic
396#384C2×D5311yescharacteristic
397C4×C4⋊C4—531no—
398C4×C22⋊C4—1061no—
399C4×C22⋊C4C2×D5311yescharacteristic
400#340—531no—
401#340—531no—
402#340—531no—
403#340—531no—
404#340—531no—
405#340—531no—
406#336—531no—
407#336—531no—
408C53#2520411yescharacteristic, complemented, Sylow
409C22×Q8—531no—
410C22×D4—21no—
411C22×D4C22×D5311yescharacteristic
412C23×C4—21no—
413C23×C4—1061no—
414C23×C4C22×D5311yescharacteristic
415C2×SD16—1062no—
416C2×SD16—1062no—
417C2×SD16—2121no—
418C22×C8—531no—
419C22×C8—531no—
420C22×C8—531no—
421C22×C8—531no—
422C22×C8—1062no—
423C22×C8—1062no—
424C22×C8—2121no—
425#123—44no—
426#123—44no—
427C22⋊Q8—534no—
428C22⋊Q8—1062no—
429#121—22no—
430#121—22no—
431C4×Q8—1062no—
432C4×Q8—2121no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—531no—
441C2×C4⋊C4—531no—
442C2×C4⋊C4—531no—
443C2×C4⋊C4—1062no—
444C2×C4⋊C4—1061no—
445C2×C4⋊C4—1061no—
446C2×C4⋊C4—1061no—
447C2×C4⋊C4—1061no—
448C2×C4⋊C4—2121no—
449C2×C4⋊C4C22×D5311yescharacteristic
450C2×C4⋊C4C22×D5311yescharacteristic
451C2×C4⋊C4C22×D5311yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—1061no—
458C2×C22⋊C4C22⋊D5311yescharacteristic
459C2×C22⋊C4C22⋊D5311yescharacteristic
460C2×C42—1061no—
461C2×C42—1061no—
462C2×C42C22×D5311yescharacteristic
463C2×C42C22×D5311yescharacteristic
464#106—1062no—
465#106—1062no—
466#106—1062no—
467C4⋊C8—1062no—
468C4⋊C8—2121no—
469#103—1062no—
470#103—1062no—
471#103—1062no—
472#102—1062no—
473#102—1062no—
474#102—2121no—
475C22⋊C8—1062no—
476#95—1061no—
477#95—1061no—
478#95—1061no—
479#95—1061no—
480#95C22⋊D5311yescharacteristic
481#95C22⋊D5311yescharacteristic
482C24—21no—
483C24C2×C22⋊D5311yescharacteristic
484C2×Q8—532no—
485C2×Q8—1061no—
486C2×Q8—1061no—
487C2×Q8—1061no—
488C2×Q8—1061no—
489C2×Q8—1061no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—1061no—
510C22×C4—1061no—
511C22×C4—1061no—
512C22×C4—1061no—
513C22×C4—4241no—
514C22×C4—2122no—
515C22×C4—2122no—
516C22×C4D4×D5312yes—
517C22×C4#1171994712yes—
518C22×C4C2×C22⋊D5311yescharacteristic
519C22×C4C2×C22⋊D5311yescharacteristic
520C22×C4C2×C22⋊D5311yescharacteristic
521C22×C4C2×C22⋊D5311yescharacteristic
522C22×C4C2×C22⋊D5311yescharacteristic
523C22×C4C23×D5311yescharacteristic
524SD16—2124no—
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—1061no—
537C2×C8—2124no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—532no—
550C4⋊C4—532no—
551C4⋊C4—1064no—
552C4⋊C4—1061no—
553C4⋊C4—1061no—
554C4⋊C4—1061no—
555C4⋊C4—1061no—
556C4⋊C4—4241no—
557C4⋊C4—2122no—
558C4⋊C4—2122no—
559C22⋊C4—22no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—1064no—
566C22⋊C4#1171992314yescomplemented
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—4241no—
572C42—2122no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23#1313318812yes—
585C23C2×#1171992312yes—
586C23#1313324312yes—
587C23C22×C22⋊D5311yescharacteristic
588Q8—1062no—
589Q8—1062no—
590Q8—2121no—
591Q8—2121no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—84no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—84no—
623C2×C4—1062no—
624C2×C4—1062no—
625C2×C4—1062no—
626C2×C4—4244no—
627C2×C4—2121no—
628C2×C4—2121no—
629C2×C4—2121no—
630C2×C4—2121no—
631C2×C4—2121no—
632C2×C4—2121no—
633C2×C4—2121no—
634C2×C4—2121no—
635C2×C4—2121no—
636C2×C4#1313318812yes—
637C2×C4C2×#1171992312yes—
638C2×C4C2×#1171992312yes—
639C2×C4C2×D4×D5311yescharacteristic
640C2×C4#41×D5311yescharacteristic
641C2×C4#41×D5311yescharacteristic
642C2×C4C2×#1171994711yescharacteristic
643C2×C4#1313326311yescharacteristic
644C2×C4#1313326411yescharacteristic
645C8—1062no—
646C8—2121no—
647C8—2121no—
648C8—2121no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22#1681082014yes—
663C22C2×#1313318811yescharacteristic
664C22#1681126111yescharacteristic
665C22#1681127211yescharacteristic
666C22C22×#1171992311yescharacteristic
667C22C2×#1313324311yescharacteristic
668C22#1681143111yescharacteristic
669C22#1681143811yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—41no—
675C4—81no—
676C4—81no—
677C4—81no—
678C4—4241no—
679C4—2122no—
680C4—2122no—
681C4—2122no—
682C4#1681115011yescharacteristic
683C4#1681121711yescharacteristic
684C4#1681126511yescharacteristic
685C4#1681127111yescharacteristic
686C2—24no—
687C2—161no—
688C2#2027826211yescharacteristic
689C2C2×#1681082011yescharacteristic
690C2#2028426111yescharacteristic
691C2#2028657411yescharacteristic
692C2#2028667011yescharacteristic
693C2#2028707211yescharacteristic
694C2#2028714911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC53×#2501C2
socleC23×C53C22×D4
prime radicalC2×#121×C53C22
hypercenter#2501D53
hypocenterC53#25204
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
1. C2×#16810953C2semidirect
3. #20277718C2semidirect
4. #20276192C2semidirect
5. #20276124C2semidirect
6. #20276089C2semidirect
7. #20276032C2semidirect
8. #20275476C2semidirect
9. #20275339C2semidirect
10. #20275073C2semidirect
12. #20274895C2semidirect
13. #20274717C2semidirect
14. C2×#16810385C2semidirect
193. C22⋊C4×C53SD16semidirect
408. C53#25204semidirect
566. C22⋊C4#11719923semidirect

Maximal subgroups

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

subgroupindex
C2×#168109532
C2×#168108502
#202777182
#202761922
#202761242
#202760892
#202760322
#202754762
#202753392
#202750732
#202750332
#202748952
#202747172
C2×#168103852
C53×#25012
#2520453