Finite Group Databasebeta

← #27350121

Subgroups — #27350121

Order 13568.

984 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811220C211yesmaximal, characteristic
2#20283741C211yesmaximal, characteristic, complemented
3#20283737C211yesmaximal, characteristic, complemented
4#20273083C212yesmaximal, complemented
5#20273077C212yesmaximal, complemented
6#20273069C212yesmaximal, complemented
7#20273062C212yesmaximal, complemented
8#20273031C211yesmaximal, characteristic, complemented
9#20273031C211yesmaximal, characteristic, complemented
10C2×#16810349C211yesmaximal, characteristic, complemented
11C2×C53×#324C211yesmaximal, characteristic, complemented
12#16811220—22no—
13#16811220—22no—
14#16811220—22no—
15#16811220—22no—
16C2×#13133212C411yescharacteristic
17C2×#13133212C2211yescharacteristic
18C2×#13133207C411yescharacteristic
19C2×#13133207C2211yescharacteristic
20C2×#13133202C411yescharacteristic
21C2×#13133202C2211yescharacteristic
22C2×#13133200C411yescharacteristic
23C2×#13133200C411yescharacteristic
24C2×#13133196C411yescharacteristic
25C2×#13133195C411yescharacteristic
26C2×#13133195C2211yescharacteristic
27C2×#13133191C411yescharacteristic
28C2×C4×C22⋊D53C2211yescharacteristic
29C2×C4×C22⋊D53C2211yescharacteristic
30#16810694—22no—
31#16810691—22no—
32C8×C22⋊D53—22no—
33#16810686—22no—
34#16810677C2212yes—
35#16810673C2212yes—
36#16810585C2212yes—
37C2×C22⋊#88322C2211yescharacteristic
38C2×C22⋊#88322C2211yescharacteristic
39C22⋊C8×D53C2212yes—
40#16810349C2212yes—
41#16810349C2212yes—
42#16810348C2212yes—
43#16810348C2212yes—
44#16810346C2212yes—
45#16810346C2212yes—
46C22×C4⋊C4×C53C2211yescharacteristic
47C2×C22⋊C8×C53C2211yescharacteristic
48C2×C22⋊C8×C53C2211yescharacteristic
49C53×#324C2212yes—
50C53×#324C2212yes—
51C22×Dic106C2×C411yescharacteristic
52C22×D212C2×C411yescharacteristic
53C22×C22⋊D53C2×C411yescharacteristic
54C22×C22⋊D53C2×C411yescharacteristic
55C22×C4×D53C2×C411yescharacteristic
56C22×C4×D53C2311yescharacteristic
57C2×#11719912—22no—
58C22×#88322—21no—
59C22×#88322—21no—
60C2×C8×D53—22no—
61#13133212—22no—
62#13133212—22no—
63#13133212—22no—
64#13133212—22no—
65#13133207—22no—
66#13133207—22no—
67#13133207—22no—
68#13133207—22no—
69#13133202—22no—
70#13133202—22no—
71#13133202—22no—
72#13133202—22no—
73#13133200—22no—
74#13133200—22no—
75#13133200—22no—
76#13133200—22no—
77#13133196—22no—
78#13133196—22no—
79#13133195—22no—
80#13133195—22no—
81#13133195—22no—
82#13133195—22no—
83#13133191—22no—
84#13133191—22no—
85C4×C22⋊D53—21no—
86C4×C22⋊D53—21no—
87C4×C22⋊D53—21no—
88C4×C22⋊D53—21no—
89C4×C22⋊D53D412yes—
90C4×C22⋊D53D412yes—
91C4×C22⋊D53D412yes—
92C4×C22⋊D53D412yes—
93C2×C4⋊Dic53C2×C411yescharacteristic
94C2×C4⋊Dic53C2×C411yescharacteristic
95C2×#11719919C2×C411yescharacteristic
96C2×#11719919C2×C411yescharacteristic
97C2×#11719919C2×C411yescharacteristic
98C2×#11719919C2×C411yescharacteristic
99C2×#11719919C2×C411yescharacteristic
100C2×#11719919C2×C411yescharacteristic
101C2×#11719919C2×C411yescharacteristic
102C2×#11719919C2311yescharacteristic
103C2×C22⋊Dic53C2×C411yescharacteristic
104C2×C22⋊Dic53C2×C411yescharacteristic
105C2×#11719921C2×C411yescharacteristic
106C2×#11719921C2×C411yescharacteristic
107C2×#11719921C2×C411yescharacteristic
108C2×#11719921C2×C411yescharacteristic
109C2×#11719921C2×C411yescharacteristic
110C2×#11719921C2×C411yescharacteristic
111C2×#11719921C2×C411yescharacteristic
112C2×#11719921C2311yescharacteristic
113C2×C4×Dic53C2×C411yescharacteristic
114C2×C4×Dic53C2311yescharacteristic
115#13133146—22no—
116#13133146—22no—
117C22⋊#88322—21no—
118C22⋊#88322—21no—
119C22⋊#88322C2312yes—
120C22⋊#88322C2312yes—
121#13133129—22no—
122#13133129—22no—
123#13133127—22no—
124C8×Dic53—22no—
125C23×C4×C53C2×C411yescharacteristic
126C23×C4×C53C2×C411yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C22×C8×C53—21no—
129C22×C8×C53—21no—
130C2×C4⋊C4×C53—21no—
131C2×C4⋊C4×C53—21no—
132C2×C4⋊C4×C53—21no—
133C2×C4⋊C4×C53—21no—
134C2×C4⋊C4×C53C2×C411yescharacteristic
135C2×C4⋊C4×C53C2×C411yescharacteristic
136C2×C4⋊C4×C53C2311yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C22⋊C8×C53—21no—
139C22⋊C8×C53—21no—
140C22⋊C8×C53C2312yes—
141C22⋊C8×C53C2312yes—
142C24×C53C22×C411yescharacteristic
143C23×D53C22×C411yescharacteristic
144C23×D53C22×C411yescharacteristic
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—81no—
152C22×C4×C53—81no—
153C22×C4×C53C22×C411yescharacteristic
154C22×C4×C53C22×C411yescharacteristic
155C22×C4×C53C22×C411yescharacteristic
156C22×C4×C53C22×C411yescharacteristic
157C22×C4×C53C22×C411yescharacteristic
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D411yescharacteristic
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53C2411yescharacteristic
163C2×C22⋊D53—22no—
164C2×C22⋊D53—22no—
165C2×C22⋊D53—21no—
166C2×C22⋊D53—21no—
167C2×C22⋊D53—22no—
168C2×C22⋊D53—22no—
169C2×C22⋊D53C22⋊C412yes—
170C2×C22⋊D53C22⋊C412yes—
171C22×Dic53C22×C411yescharacteristic
172C22×Dic53C22×C411yescharacteristic
173C22×Dic53C22×C411yescharacteristic
174C22×Dic53C22×C411yescharacteristic
175C22×Dic53C22×C411yescharacteristic
176C22×Dic53C22×C411yescharacteristic
177C2×D212—22no—
178C2×D212—81no—
179C2×C4×D53—21no—
180C2×C4×D53—21no—
181C2×C4×D53—81no—
182C2×C4×D53—81no—
183C2×C4×D53C2×D412yes—
184C2×C4×D53C2×D412yes—
185C2×Dic106—22no—
186C2×Dic106—81no—
187C2×C8×C53—22no—
188C2×C8×C53—22no—
189C2×C8×C53—81no—
190C2×C8×C53—81no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—21no—
195C4⋊C4×C53—21no—
196C4⋊C4×C53—21no—
197C4⋊C4×C53—21no—
198C4⋊C4×C53—21no—
199C22⋊Dic53—21no—
200C22⋊Dic53—21no—
201C22⋊Dic53C22⋊C412yes—
202C22⋊Dic53C22⋊C412yes—
203#11719921—22no—
204#11719921—22no—
205#11719921—22no—
206#11719921—21no—
207#11719921—21no—
208#11719921—22no—
209#11719921—22no—
210#11719921—22no—
211#11719921C22⋊C412yes—
212#11719921C22⋊C412yes—
213C4⋊Dic53—22no—
214C4⋊Dic53—22no—
215#11719919—21no—
216#11719919—21no—
217#11719919—22no—
218#11719919—22no—
219#11719919—22no—
220#11719919—22no—
221#11719919—22no—
222#11719919—22no—
223#11719919C22⋊C412yes—
224#11719919C22⋊C412yes—
225C4×Dic53—21no—
226C4×Dic53—21no—
227C4×Dic53C2×D412yes—
228C4×Dic53C2×D412yes—
229C2×#88322—22no—
230C2×#88322—22no—
231C2×#88322—81no—
232C2×#88322—81no—
233#11719912—82no—
234C8×D53—82no—
235C23×C53—41no—
236C23×C53—41no—
237C23×C53C2×C22⋊C411yescharacteristic
238C23×C53C2×C22⋊C411yescharacteristic
239C23×C53#13112yes—
240C23×C53#13112yes—
241C23×C53C23×C411yescharacteristic
242C22×D53—21no—
243C22×D53—21no—
244C22×D53—21no—
245C22×D53—21no—
246C22×D53—21no—
247C22×D53—41no—
248C22×D53—41no—
249C22×D53—41no—
250C22×D53—41no—
251C22×D53C2×C22⋊C412yes—
252C2×C4×C53—21no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—21no—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—41no—
261C2×C4×C53—41no—
262C2×C4×C53—41no—
263C2×C4×C53—41no—
264C2×C4×C53—41no—
265C2×C4×C53—41no—
266C2×C4×C53—42no—
267C2×C4×C53—42no—
268C2×C4×C53—41no—
269C2×C4×C53—41no—
270C2×C4×C53—81no—
271C2×C4×C53—81no—
272C2×C4×C53C2×C22⋊C411yescharacteristic
273C2×C4×C53C2×C22⋊C411yescharacteristic
274C2×C4×C53C22×D411yescharacteristic
275C2×C4×C53C22×D411yescharacteristic
276C22⋊D53—24no—
277C22⋊D53—24no—
278C22⋊D53—42no—
279C22⋊D53—42no—
280C2×Dic53—21no—
281C2×Dic53—21no—
282C2×Dic53—21no—
283C2×Dic53—21no—
284C2×Dic53—21no—
285C2×Dic53—21no—
286C2×Dic53—21no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53C2×C22⋊C412yes—
292C2×Dic53C2×C22⋊C412yes—
293C2×Dic53C2×C22⋊C412yes—
294D212—82no—
295C4×D53—42no—
296C4×D53—42no—
297C4×D53—81no—
298C4×D53—81no—
299Dic106—82no—
300C8×C53—42no—
301C8×C53—42no—
302#88322—42no—
303#88322—42no—
304#17387—531nomaximal, Sylow
305C22×C53—21no—
306C22×C53—21no—
307C22×C53—21no—
308C22×C53—21no—
309C22×C53—21no—
310C22×C53—21no—
311C22×C53—42no—
312C22×C53—42no—
313C22×C53#40812yes—
314C22×C53#40812yes—
315C22×C53C22×C22⋊C411yescharacteristic
316C22×C53C2×#13111yescharacteristic
317C22×C53C2×#13111yescharacteristic
318C2×D53—22no—
319C2×D53—22no—
320C2×D53—22no—
321C2×D53—41no—
322C2×D53—41no—
323C2×D53—41no—
324C2×D53—81no—
325C2×D53—81no—
326C2×D53—81no—
327C2×D53—81no—
328C4×C53—21no—
329C4×C53—21no—
330C4×C53—21no—
331C4×C53—21no—
332C4×C53—41no—
333C4×C53—41no—
334C4×C53—41no—
335C4×C53—41no—
336Dic53—22no—
337Dic53—22no—
338Dic53—22no—
339Dic53—41no—
340Dic53—41no—
341Dic53—41no—
342C2×#539—531no—
343#2973—531no—
344#2972—531no—
345#1473—532no—
346#1472—532no—
347#1470—532no—
348#1468—532no—
349#1459—531no—
350#1459—531no—
351C2×#324—531no—
352C2×#324D5311yescharacteristic, complemented
353C2×C53—21no—
354C2×C53—21no—
355C2×C53—22no—
356C2×C53—22no—
357C2×C53C2×#40811yescharacteristic
358C2×C53#288311yescharacteristic
359C2×C53#288911yescharacteristic
360D53—42no—
361D53—81no—
362#539—1062no—
363#539—1062no—
364#539—1062no—
365#539—1062no—
366C2×#126—531no—
367C2×#126—531no—
368C2×#125—531no—
369C2×#125—531no—
370C2×#123—531no—
371C2×#123—531no—
372C2×#123—531no—
373C2×#123—531no—
374C2×C22⋊Q8—531no—
375C2×C22⋊Q8—531no—
376C2×C22⋊Q8—531no—
377C2×#121—531no—
378C2×C4×D4—531no—
379C2×C4×D4—531no—
380C22×C4⋊C4C2×D5311yescharacteristic
381#435—1062no—
382#435—1062no—
383C8×D4—1062no—
384C8×D4—1062no—
385#432—532no—
386#431—532no—
387#407—532no—
388C2×C22⋊C8—531no—
389C2×C22⋊C8—531no—
390C2×C22⋊C8—532no—
391C2×C22⋊C8C2×D5311yescharacteristic
392C2×C22⋊C8C2×D5311yescharacteristic
393#324—532no—
394#324—532no—
395#324—532no—
396#324—532no—
397#324C2×D5312yes—
398#324C2×D5312yes—
399#323—532no—
400#323—532no—
401C53#1738711yescharacteristic, complemented, Sylow
402C22×Q8—531no—
403C22×D4—531no—
404C22×D4—531no—
405C22×D4—531no—
406C23×C4—531no—
407C23×C4—531no—
408C23×C4C4×D5311yescharacteristic
409C23×C4C4×D5311yescharacteristic
410C23×C4C22×D5311yescharacteristic
411C2×M16—1062no—
412C22×C8—21no—
413C22×C8—21no—
414C22×C8—1062no—
415C22×C8—1061no—
416C22×C8—1061no—
417#126—1062no—
418#126—1062no—
419#126—1062no—
420#126—1062no—
421#125—1062no—
422#125—1062no—
423#125—1062no—
424#125—1062no—
425#123—1062no—
426#123—1062no—
427#123—1062no—
428#123—1062no—
429#123—1062no—
430#123—1062no—
431#123—1062no—
432#123—1062no—
433C22⋊Q8—1062no—
434C22⋊Q8—1062no—
435C22⋊Q8—1062no—
436C22⋊Q8—1062no—
437C22⋊Q8—1062no—
438C22⋊Q8—1062no—
439#121—1062no—
440#121—1062no—
441C4×D4—532no—
442C4×D4—532no—
443C4×D4—532no—
444C4×D4—532no—
445C4×D4—1061no—
446C4×D4—1061no—
447C4×D4—1061no—
448C4×D4—1061no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—531no—
454C2×C4⋊C4—531no—
455C2×C4⋊C4—531no—
456C2×C4⋊C4—531no—
457C2×C4⋊C4—531no—
458C2×C4⋊C4—531no—
459C2×C4⋊C4—531no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4C4×D5311yescharacteristic
464C2×C4⋊C4C4×D5311yescharacteristic
465C2×C4⋊C4C22×D5311yescharacteristic
466C2×C4⋊C4C22×D5311yescharacteristic
467C2×C22⋊C4—531no—
468C2×C22⋊C4—531no—
469C2×C22⋊C4—531no—
470C2×C22⋊C4—531no—
471C2×C22⋊C4—531no—
472C2×C22⋊C4—531no—
473C2×C22⋊C4—531no—
474C2×C22⋊C4—531no—
475C2×C22⋊C4—531no—
476C2×C22⋊C4—531no—
477C2×C42—531no—
478C2×C42—531no—
479C4⋊C8—1062no—
480C4⋊C8—1062no—
481C22⋊C8—21no—
482C22⋊C8—21no—
483C22⋊C8—532no—
484C22⋊C8—532no—
485C22⋊C8—1062no—
486C22⋊C8—1062no—
487C22⋊C8—1061no—
488C22⋊C8—1061no—
489C22⋊C8C22×D5312yes—
490C22⋊C8C22×D5312yes—
491#97—1062no—
492C4×C8—1062no—
493C24—531no—
494C24—531no—
495C24C2×C4×D5311yescharacteristic
496C2×Q8—1062no—
497C2×Q8—4241no—
498C2×D4—532no—
499C2×D4—532no—
500C2×D4—1062no—
501C2×D4—1062no—
502C2×D4—1062no—
503C2×D4—1061no—
504C2×D4—1061no—
505C2×D4—1062no—
506C2×D4—1062no—
507C2×D4—4241no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—81no—
515C22×C4—81no—
516C22×C4—531no—
517C22×C4—531no—
518C22×C4—531no—
519C22×C4—532no—
520C22×C4—532no—
521C22×C4—531no—
522C22×C4—531no—
523C22×C4—531no—
524C22×C4—1061no—
525C22×C4—1061no—
526C22×C4—4241no—
527C22×C4—4241no—
528C22×C4C2×C4×D5311yescharacteristic
529C22×C4C2×C4×D5311yescharacteristic
530C22×C4C2×C4×D5311yescharacteristic
531C22×C4C2×C4×D5311yescharacteristic
532C22×C4C2×C4×D5311yescharacteristic
533C22×C4D4×D5311yescharacteristic
534C22×C4D4×D5311yescharacteristic
535C22×C4D4×D5311yescharacteristic
536C22×C4D4×D5311yescharacteristic
537C22×C4C23×D5311yescharacteristic
538M16—4242no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—81no—
542C2×C8—81no—
543C2×C8—1062no—
544C2×C8—1062no—
545C2×C8—4242no—
546C2×C8—4241no—
547C2×C8—4241no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—532no—
557C4⋊C4—532no—
558C4⋊C4—1062no—
559C4⋊C4—1062no—
560C4⋊C4—1062no—
561C4⋊C4—1062no—
562C4⋊C4—1062no—
563C4⋊C4—1062no—
564C4⋊C4—1062no—
565C4⋊C4—1062no—
566C4⋊C4—1061no—
567C4⋊C4—1061no—
568C22⋊C4—532no—
569C22⋊C4—532no—
570C22⋊C4—532no—
571C22⋊C4—532no—
572C22⋊C4—1062no—
573C22⋊C4—1062no—
574C22⋊C4—1062no—
575C22⋊C4—1062no—
576C22⋊C4—1062no—
577C22⋊C4—1062no—
578C22⋊C4—1061no—
579C22⋊C4—1061no—
580C22⋊C4—1061no—
581C22⋊C4—1061no—
582C42—532no—
583C42—532no—
584C42—1061no—
585C42—1061no—
586C23—41no—
587C23—41no—
588C23—532no—
589C23—1061no—
590C23—1061no—
591C23—1061no—
592C23—1061no—
593C23—1061no—
594C23—2121no—
595C23—2121no—
596C23—2121no—
597C23—2121no—
598C23C22⋊C4×D5311yescharacteristic
599C23C22⋊C4×D5311yescharacteristic
600C23#1313322312yes—
601C23#1313322512yes—
602C23C22×C4×D5311yescharacteristic
603Q8—4242no—
604D4—1064no—
605D4—1064no—
606D4—4242no—
607D4—2122no—
608D4—2122no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—532no—
630C2×C4—532no—
631C2×C4—532no—
632C2×C4—1061no—
633C2×C4—1061no—
634C2×C4—1061no—
635C2×C4—1061no—
636C2×C4—1061no—
637C2×C4—1061no—
638C2×C4—1061no—
639C2×C4—4241no—
640C2×C4—4241no—
641C2×C4—2122no—
642C2×C4—2122no—
643C2×C4—2121no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4C22⋊C4×D5311yescharacteristic
648C2×C4C22⋊C4×D5311yescharacteristic
649C2×C4C2×D4×D5311yescharacteristic
650C2×C4C2×D4×D5311yescharacteristic
651C8—42no—
652C8—42no—
653C8—2122no—
654C8—2122no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—42no—
662C22—42no—
663C22—1062no—
664C22—1062no—
665C22—1062no—
666C22—4241no—
667C22—4241no—
668C22—4241no—
669C22—4241no—
670C22—2121no—
671C22—2121no—
672C22—2121no—
673C22#1681058812yes—
674C22#1681058812yes—
675C22C2×C22⋊C4×D5311yescharacteristic
676C22C2×#1313322311yescharacteristic
677C22C2×#1313322511yescharacteristic
678C4—21no—
679C4—21no—
680C4—21no—
681C4—21no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—1062no—
687C4—1062no—
688C4—1062no—
689C4—2121no—
690C4—2121no—
691C4—2121no—
692C2—21no—
693C2—21no—
694C2—22no—
695C2—22no—
696C2—4241no—
697C2—2122no—
698C2C2×#1681058811yescharacteristic
699C2#2028317311yescharacteristic
700C2#2028319511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D53
commutatorC23×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#324C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#13133191C4
cosocleC22×C4×C53C24
hypercenterC2×#324D53
hypocenterC53#17387
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #20283741C2semidirect
3. #20283737C2semidirect
4. #20273083C2semidirect
5. #20273077C2semidirect
6. #20273069C2semidirect
7. #20273062C2semidirect
8. #20273031C2semidirect
9. #20273031C2semidirect
10. C2×#16810349C2semidirect
11. C2×C53×#324C2semidirect
352. C2×#324D53semidirect
401. C53#17387semidirect

Maximal subgroups

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

subgroupindex
C2×#168112202
#202837412
#202837372
#202730832
#202730772
#202730692
#202730622
#202730312
C2×#168103492
C2×C53×#3242
#1738753