Finite Group Databasebeta

← #10973008

Subgroups — #10973008

Order 768.

3398 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5525C211yesmaximal, characteristic, complemented
2C2×#5525C211yesmaximal, characteristic, complemented
3C2×#5522C211yesmaximal, characteristic, complemented
4C2×#5510C211yesmaximal, characteristic, complemented
5C3×#2317C211yesmaximal, characteristic, complemented
6#82228C211yesmaximal, characteristic, complemented
7C2×#4988C211yesmaximal, characteristic, complemented
8#76220C214yesmaximal, complemented
9#76218C214yesmaximal, complemented
10#74605C218yesmaximal, complemented
11#74375C212yesmaximal, complemented
12#74370C212yesmaximal, complemented
13#74256C212yesmaximal, complemented
14#74244C212yesmaximal, complemented
15#35256—31nomaximal, Sylow
16C22×#235C2211yescharacteristic
17C22×#235C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C2×C3×#117C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C2×#930C2214yes—
23C22×(C2×D3)⋊C4C2214yes—
24C22×C4×Dic3C2211yescharacteristic
25#5525—28no—
26#5525—28no—
27#5522—28no—
28#5510—28no—
29C2×#897C2212yescomplemented
30C2×#897C2212yescomplemented
31C2×#895C2212yes—
32C2×#895C2212yes—
33C2×#895C2214yes—
34C2×#895C2212yescomplemented
35C2×#895C2212yescomplemented
36C2×#895C2218yescomplemented
37C2×#893C2212yescomplemented
38C2×#887C2212yescomplemented
39C2×#882C2214yes—
40C2×#882C2214yes—
41C2×#67⋊C4C2214yes—
42C2×#875C2212yes—
43C2×#875C2212yes—
44C2×#874C2212yes—
45C2×#874C2212yes—
46C2×#872C2212yescomplemented
47C2×C42×D3C2212yescomplemented
48C3×#389C2214yescomplemented
49C3×#385C2214yes—
50C3×#384C2212yescomplemented
51C3×#382C2212yescomplemented
52#4994C2218yescomplemented
53#4991C2218yescomplemented
54#4988C2212yes—
55#4988C2212yes—
56#4988C2214yes—
57#4988C2211yescharacteristic, complemented
58#4988C2211yescharacteristic, complemented
59#4988C2218yescomplemented
60#4973C2211yescharacteristic, complemented
61#4973C2211yescharacteristic, complemented
62#4958C2214yes—
63C4×(C2×D3)⋊C4C2214yescomplemented
64#4672C2218yescomplemented
65#4671C2218yescomplemented
66#4670C2218yescomplemented
67#4665C2218yescomplemented
68C2×#537—31no—
69C2×#535—31no—
70C2×#535—31no—
71C2×C4×#41—31no—
72#2856—32no—
73#2850—32no—
74#2620—32no—
75#2619—32no—
76#2428—34no—
77#2426—34no—
78#2424—38no—
79#2317D311yescharacteristic, complemented
80#2297—31no—
81C2×#390—31no—
82C24×D3C2312yes—
83C23×C3×C4C2312yes—
84C23×C3×C4C2311yescharacteristic
85C22×#67C2312yes—
86C22×#67C2312yes—
87C23×Dic3C2312yes—
88C2×#235—24no—
89C2×#235—24no—
90C2×#235—24no—
91C2×#235—24no—
92C2×#235—24no—
93C2×#235D418yescomplemented
94C22×D12—24no—
95C22×D12—24no—
96C22×D12—24no—
97C22×D12C2312yes—
98C22×D12C2312yes—
99C22×D12C2311yescharacteristic
100C22×D12C2311yescharacteristic
101C22×D12C2314yes—
102C22×D12C2314yes—
103C22×D12C2318yes—
104C22×D12C2314yes—
105C22×C4×D3C2312yes—
106C22×C4×D3C2314yes—
107C22×C4×D3C2312yes—
108C22×Dic6C2311yescharacteristic
109C22×Dic6C2311yescharacteristic
110C3×#117—24no—
111C3×#117D418yescomplemented
112C2×C3×C4⋊C4—24no—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2312yes—
116C2×C3×C4⋊C4C2312yes—
117C2×C3×C4⋊C4C2318yes—
118C2×C3×C4⋊C4C2312yes—
119C2×C3×C22⋊C4C2312yes—
120C2×C3×C22⋊C4C2312yes—
121C2×C3×C42C2312yes—
122C2×C3×C42C2312yes—
123#930—216no—
124C2×(C2×D3)⋊C4—48no—
125C2×(C2×D3)⋊C4C2314yes—
126C2×(C2×D3)⋊C4C2318yes—
127C2×(C2×D3)⋊C4C2318yes—
128C2×(C2×D3)⋊C4C2314yes—
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2314yes—
131C2×(C2×D3)⋊C4C2314yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2318yes—
135C2×C4⋊Dic3C2314yes—
136C2×Dic3⋊C4C2314yes—
137C2×C4×Dic3—24no—
138C2×C4×Dic3C2314yes—
139C2×C4×Dic3C2312yes—
140C2×C4×Dic3C2311yescharacteristic
141C2×C4×Dic3C2311yescharacteristic
142#897—28no—
143#897—28no—
144#895—28no—
145#895—28no—
146#895—28no—
147#895—28no—
148#895—216no—
149#895—416no—
150#893—28no—
151#887—28no—
152#882—216no—
153#882—216no—
154#67⋊C4—216no—
155#875—28no—
156#875—28no—
157#874—28no—
158#874—28no—
159#872—28no—
160C42×D3—28no—
161C3×#95C2318yes—
162C3⋊#95C2314yes—
163C3⋊#95C2314yes—
164C22×#41—31no—
165C22×#41—31no—
166C23×D4—31no—
167#537—68no—
168#535—68no—
169#535—68no—
170C2×#127—32no—
171C2×#127—32no—
172C2×#124—32no—
173C2×#124—32no—
174C2×C22⋊Q8—32no—
175C2×C22⋊Q8—32no—
176C2×#121—34no—
177C2×#121—32no—
178C2×#121—32no—
179C2×#121—32no—
180C2×#121—34no—
181C2×#121—32no—
182C2×#121—38no—
183C2×#120—34no—
184C2×#120—34no—
185C4×#41—68no—
186C2×C4×Q8—32no—
187C2×C4×D4—32no—
188C2×C4×D4—34no—
189C2×#117—32no—
190C2×#117C2×D311yescharacteristic
191C2×#117C2×D311yescharacteristic
192C22×C4⋊C4C2×D311yescharacteristic
193C22×C22⋊C4—34no—
194C22×C42—31no—
195C22×C42—32no—
196#396—38no—
197#394—38no—
198#394—38no—
199#392—38no—
200#391—31no—
201#391—31no—
202#390—32no—
203#390—31no—
204#390—38no—
205#390—31no—
206#390—32no—
207#390—34no—
208#389C2×D314yescomplemented
209#388—38no—
210#386—34no—
211#386—38no—
212#385C2×D314yes—
213#384C2×D312yescomplemented
214#382C2×D312yescomplemented
215C4×C22⋊C4—34no—
216C24×C3C2411yescharacteristic
217C23×D3—24no—
218C23×D3—24no—
219C23×D3—24no—
220C23×D3—44no—
221C23×D3—44no—
222C23×D3C2414yes—
223C23×D3C2412yes—
224C23×D3C2412yes—
225C22×C3×C4—24no—
226C22×C3×C4—44no—
227C22×C3×C4C2×D414yes—
228C22×C3×C4C2×D414yes—
229C22×C3×C4#4114yes—
230C22×C3×C4C2412yes—
231C22×C3×C4C2412yes—
232C22×C3×C4C2414yes—
233C22×C3×C4C2414yes—
234C22×C3×C4C2411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C2×#67—24no—
237C2×#67—24no—
238C2×#67—24no—
239C2×#67—24no—
240C2×#67—24no—
241C2×#67C2×D418yes—
242C22×Dic3—24no—
243C22×Dic3—24no—
244C22×Dic3—42no—
245C22×Dic3C2412yes—
246C22×Dic3C2412yes—
247C22×Dic3C2412yes—
248C22×Dic3C2412yes—
249#235—232no—
250#235—416no—
251C2×D12—22no—
252C2×D12—22no—
253C2×D12—22no—
254C2×D12—24no—
255C2×D12—24no—
256C2×D12—24no—
257C2×D12—24no—
258C2×D12—22no—
259C2×D12—24no—
260C2×D12—24no—
261C2×D12—22no—
262C2×D12—28no—
263C2×D12—28no—
264C2×D12—28no—
265C2×D12—216no—
266C2×D12—416no—
267C2×D12—48no—
268C2×D12—48no—
269C2×D12—48no—
270C2×D12—48no—
271C2×D12—48no—
272C2×D12C2×D414yes—
273C2×C4×D3—24no—
274C2×C4×D3—24no—
275C2×C4×D3—28no—
276C2×C4×D3—24no—
277C2×C4×D3—24no—
278C2×C4×D3—24no—
279C2×C4×D3—28no—
280C2×C4×D3—44no—
281C2×C4×D3C2×D418yes—
282C2×Dic6—22no—
283C2×Dic6—22no—
284C2×Dic6—22no—
285C2×Dic6—22no—
286C2×Dic6—22no—
287C2×Dic6C2×D414yes—
288C3×C4⋊C4—22no—
289C3×C4⋊C4—22no—
290C3×C4⋊C4—24no—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—48no—
293C3×C4⋊C4C2×D418yes—
294C3×C22⋊C4—24no—
295C3×C22⋊C4C2×D418yes—
296C3×C42—24no—
297C3×C42C2×D418yes—
298(C2×D3)⋊C4—28no—
299(C2×D3)⋊C4—28no—
300(C2×D3)⋊C4—216no—
301(C2×D3)⋊C4—28no—
302(C2×D3)⋊C4—28no—
303(C2×D3)⋊C4—28no—
304(C2×D3)⋊C4—28no—
305(C2×D3)⋊C4—216no—
306(C2×D3)⋊C4—48no—
307(C2×D3)⋊C4—44no—
308C4⋊Dic3—28no—
309Dic3⋊C4—28no—
310C4×Dic3—22no—
311C4×Dic3—28no—
312C4×Dic3—22no—
313C4×Dic3—24no—
314C25—32no—
315C2×#41—38no—
316C2×#41—64no—
317C2×#41—64no—
318C2×#41—64no—
319C2×#41—64no—
320C2×#41—64no—
321C22×Q8—31no—
322C22×Q8—31no—
323C22×D4—32no—
324C22×D4—32no—
325C22×D4—31no—
326C22×D4—32no—
327C22×D4—32no—
328C22×D4—31no—
329C22×D4—34no—
330C22×D4—38no—
331C22×D4—34no—
332C22×D4—34no—
333C22×D4—64no—
334C22×D4—64no—
335C22×D4—64no—
336C23×C4—32no—
337C23×C4—32no—
338C23×C4—32no—
339C23×C4—34no—
340C23×C4C22×D312yes—
341C23×C4C22×D311yescharacteristic
342#127—68no—
343#127—68no—
344#124—68no—
345#124—68no—
346C22⋊Q8—68no—
347C22⋊Q8—68no—
348#121—68no—
349#121—68no—
350#121—68no—
351#121—68no—
352#121—616no—
353#121—616no—
354#121—1216no—
355#120—616no—
356#120—616no—
357C4×Q8—68no—
358C4×D4—68no—
359C4×D4—616no—
360#117—24no—
361#117—68no—
362#117D1218yescomplemented
363C2×C4⋊C4—24no—
364C2×C4⋊C4—34no—
365C2×C4⋊C4—34no—
366C2×C4⋊C4C22×D312yes—
367C2×C4⋊C4C22×D312yes—
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D318yes—
371C2×C4⋊C4C22×D312yes—
372C2×C22⋊C4—38no—
373C2×C22⋊C4—34no—
374C2×C22⋊C4—38no—
375C2×C22⋊C4—34no—
376C2×C22⋊C4—34no—
377C2×C22⋊C4—34no—
378C2×C22⋊C4—34no—
379C2×C22⋊C4—34no—
380C2×C22⋊C4—38no—
381C2×C22⋊C4—34no—
382C2×C22⋊C4—128no—
383C2×C22⋊C4C22×D312yes—
384C2×C22⋊C4C22×D312yes—
385C2×C42—31no—
386C2×C42—32no—
387C2×C42—34no—
388C2×C42—31no—
389C2×C42—64no—
390C2×C42—68no—
391C2×C42C22×D312yes—
392C2×C42C22×D312yes—
393#95—34no—
394#95—34no—
395#95C22×D318yes—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3C22×D412yes—
399C23×C3C22×D412yes—
400C23×C3C2×#4112yes—
401C23×C3C2511yescharacteristic
402C22×D3—22no—
403C22×D3—22no—
404C22×D3—24no—
405C22×D3—24no—
406C22×D3—22no—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3—24no—
412C22×D3—28no—
413C22×D3—24no—
414C22×D3—24no—
415C22×D3—28no—
416C22×D3—416no—
417C22×D3—48no—
418C22×D3—88no—
419C22×D3—84no—
420C22×D3—84no—
421C22×D3C22×D414yes—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—28no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—84no—
431C2×C3×C4#121116yescomplemented
432C2×C3×C4C22×D418yes—
433C2×C3×C4C22×D412yes—
434C2×C3×C4C22×D412yes—
435C2×C3×C4C22×D412yes—
436C2×C3×C4C22×D412yes—
437C2×C3×C4C2×#4112yes—
438C2×C3×C4C2×#4112yes—
439#67—216no—
440#67—48no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—48no—
452C2×Dic3C22×D414yes—
453C2×Dic3H(5,𝔽2)14yes—
454D12—28no—
455D12—48no—
456D12—48no—
457D12—44no—
458D12—816no—
459D12—88no—
460D12—88no—
461D12—88no—
462C4×D3—216no—
463C4×D3—416no—
464C4×D3—48no—
465Dic6—28no—
466Dic6—44no—
467C24—32no—
468C24—34no—
469C24—32no—
470C24—64no—
471C24—64no—
472C24—64no—
473C24—124no—
474C24—124no—
475C24C23×D311yescharacteristic
476#41—632no—
477#41—1216no—
478C2×Q8—34no—
479C2×Q8—62no—
480C2×Q8—62no—
481C2×Q8—62no—
482C2×Q8—62no—
483C2×Q8—62no—
484C2×D4—38no—
485C2×D4—34no—
486C2×D4—68no—
487C2×D4—68no—
488C2×D4—68no—
489C2×D4—64no—
490C2×D4—64no—
491C2×D4—64no—
492C2×D4—64no—
493C2×D4—64no—
494C2×D4—62no—
495C2×D4—64no—
496C2×D4—64no—
497C2×D4—62no—
498C2×D4—616no—
499C2×D4—64no—
500C2×D4—62no—
501C2×D4—64no—
502C2×D4—62no—
503C2×D4—64no—
504C2×D4—64no—
505C2×D4—62no—
506C2×D4—128no—
507C2×D4—128no—
508C2×D4—128no—
509C2×D4—128no—
510C2×D4—128no—
511C2×D4—1216no—
512C22×C4—24no—
513C22×C4—32no—
514C22×C4—32no—
515C22×C4—38no—
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—44no—
519C22×C4—68no—
520C22×C4—64no—
521C22×C4—64no—
522C22×C4—64no—
523C22×C4—64no—
524C22×C4—68no—
525C22×C4—64no—
526C22×C4—64no—
527C22×C4—64no—
528C22×C4—124no—
529C22×C4—122no—
530C22×C4C2×D1214yes—
531C22×C4D3×D414yes—
532C22×C4#23914yes—
533C22×C4C23×D312yes—
534C22×C4C23×D312yes—
535C22×C4C23×D314yes—
536C22×C4C23×D314yes—
537C22×C4C23×D311yescharacteristic
538C22×C4C23×D311yescharacteristic
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—48no—
544C4⋊C4—68no—
545C4⋊C4—68no—
546C4⋊C4C2×D1218yes—
547C22⋊C4—24no—
548C22⋊C4—616no—
549C22⋊C4—68no—
550C22⋊C4—68no—
551C22⋊C4—68no—
552C22⋊C4—68no—
553C22⋊C4—68no—
554C22⋊C4—68no—
555C22⋊C4—616no—
556C22⋊C4—128no—
557C22⋊C4—124no—
558C22⋊C4C2×D1218yes—
559C42—24no—
560C42—62no—
561C42—62no—
562C42—68no—
563C42—64no—
564C42C2×D1218yes—
565C22×C3—24no—
566C22×C3—24no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3C2×#12114yes—
570C22×C3C23×D411yescharacteristic
571C22×C3C23×D411yescharacteristic
572C22×C3C22×#4111yescharacteristic
573C22×C3C2×H(5,𝔽2)12yes—
574C22×C3#58512yes—
575C2×D3—24no—
576C2×D3—24no—
577C2×D3—24no—
578C2×D3—44no—
579C2×D3—44no—
580C2×D3—42no—
581C2×D3—44no—
582C2×D3—44no—
583C2×D3—48no—
584C2×D3—44no—
585C2×D3—48no—
586C2×D3—42no—
587C2×D3—44no—
588C2×D3—44no—
589C2×D3—42no—
590C2×D3—816no—
591C3×C4—28no—
592C3×C4—42no—
593C3×C4—44no—
594C3×C4—42no—
595C3×C4C2×#12114yes—
596C3×C4C2×#12114yes—
597Dic3—24no—
598Dic3—24no—
599Dic3—42no—
600Dic3—42no—
601C23—22no—
602C23—22no—
603C23—34no—
604C23—62no—
605C23—62no—
606C23—64no—
607C23—64no—
608C23—64no—
609C23—62no—
610C23—62no—
611C23—64no—
612C23—62no—
613C23—64no—
614C23—68no—
615C23—64no—
616C23—64no—
617C23—68no—
618C23—1216no—
619C23—128no—
620C23—244no—
621C23—244no—
622C23—248no—
623C23C22×D1212yes—
624C23C2×D3×D412yes—
625C23C2×#23912yes—
626C23C24×D311yescharacteristic
627Q8—68no—
628Q8—124no—
629D4—616no—
630D4—68no—
631D4—128no—
632D4—128no—
633D4—128no—
634D4—124no—
635D4—2416no—
636D4—248no—
637D4—248no—
638D4—248no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—28no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—34no—
648C2×C4—34no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—616no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—84no—
661C2×C4—1216no—
662C2×C4—128no—
663C2×C4—128no—
664C2×C4#895116yescomplemented
665C2×C4C22×D1218yes—
666C2×C4C22×D1212yes—
667C2×C4C22×D1212yes—
668C2×C4C2×D3×D412yes—
669C2×C4C2×D3×D412yes—
670C2×C4C2×#23912yes—
671C2×C4C2×#23912yes—
672C2×C3—24no—
673C2×C3C22×#12111yescharacteristic
674C2×C3#346012yes—
675C2×C3#348812yes—
676C2×C3#349811yescharacteristic
677C2×C3#350011yescharacteristic
678D3—44no—
679D3—82no—
680D3—84no—
681C22—22no—
682C22—24no—
683C22—22no—
684C22—24no—
685C22—64no—
686C22—64no—
687C22—64no—
688C22—124no—
689C22—124no—
690C22—122no—
691C22—124no—
692C22—128no—
693C22—124no—
694C22—124no—
695C22—122no—
696C22—124no—
697C22—128no—
698C22—122no—
699C22—124no—
700C22—2416no—
701C22C2×#89514yes—
702C22C23×D1211yescharacteristic
703C22C22×D3×D411yescharacteristic
704C22C22×#23911yescharacteristic
705C22D3×H(5,𝔽2)12yes—
706C22#596812yes—
707C4—28no—
708C4—44no—
709C4—42no—
710C4—42no—
711C4—64no—
712C4—64no—
713C4—122no—
714C4—122no—
715C4C2×#89514yes—
716C4C2×#89514yes—
717C3#3525611yescharacteristic, complemented, Sylow
718C2—24no—
719C2—124no—
720C2—244no—
721C2—242no—
722C2C22×#89511yescharacteristic
723C2#8590012yes—
724C2#8631611yescharacteristic
725C2#8634111yescharacteristic
726C2#8658212yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2317C2
hypercenter#2317D3
hypocenterC3#35256
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
1. C2×#5525C2semidirect
2. C2×#5525C2semidirect
3. C2×#5522C2semidirect
4. C2×#5510C2semidirect
5. C3×#2317C2semidirect
6. #82228C2semidirect
7. C2×#4988C2semidirect
8. #76220C2semidirect
9. #76218C2semidirect
10. #74605C2semidirect
11. #74375C2semidirect
12. #74370C2semidirect
13. #74256C2semidirect
14. #74244C2semidirect
29. C2×#897C22semidirect
30. C2×#897C22semidirect
34. C2×#895C22semidirect
35. C2×#895C22semidirect
36. C2×#895C22semidirect
37. C2×#893C22semidirect
38. C2×#887C22semidirect
46. C2×#872C22semidirect
47. C2×C42×D3C22semidirect
48. C3×#389C22semidirect
50. C3×#384C22semidirect
51. C3×#382C22semidirect
52. #4994C22semidirect
53. #4991C22semidirect
57. #4988C22semidirect
58. #4988C22semidirect
59. #4988C22semidirect
60. #4973C22semidirect
61. #4973C22semidirect
63. C4×(C2×D3)⋊C4C22semidirect
64. #4672C22semidirect
65. #4671C22semidirect
66. #4670C22semidirect
67. #4665C22semidirect
79. #2317D3semidirect
93. C2×#235D4semidirect
111. C3×#117D4semidirect
208. #389C2×D3semidirect
213. #384C2×D3semidirect
214. #382C2×D3semidirect
362. #117D12semidirect
431. C2×C3×C4#121semidirect
664. C2×C4#895semidirect
717. C3#35256semidirect

Maximal subgroups

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

subgroupindex
C2×#55252
C2×#55222
C2×#55102
C3×#23172
#822282
C2×#49882
#762202
#762182
#746052
#743752
#743702
#742562
#742442
#352563