Finite Group Databasebeta

← #10728719

Subgroups — #10728719

Order 768.

2086 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#887C211yesmaximal, characteristic, complemented
2C2×#4959C212yesmaximal
3C2×#4947C211yesmaximal, characteristic, complemented
4C2×#4957C211yesmaximal, characteristic
5C2×#4673C211yesmaximal, characteristic, complemented
6C3×#1439C211yesmaximal, characteristic, complemented
7#71570C211yesmaximal, characteristic, complemented
8#71545C212yesmaximal, complemented
9#69409C212yesmaximal, complemented
10#69408C212yesmaximal, complemented
11#69403C211yesmaximal, characteristic, complemented
12#14883—31nomaximal, Sylow
13C23×#67C2211yescharacteristic
14C23×Dic6C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×#217C2211yescharacteristic
19C22×#217C2212yes—
20C22×(C2×D3)⋊C4C2211yescharacteristic
21C22×(C2×D3)⋊C4C2212yes—
22C22×(C2×D3)⋊C4C2211yescharacteristic
23C22×(C2×D3)⋊C4C2212yes—
24C22×Dic3⋊C4C2212yes—
25C22×Dic3⋊C4C2211yescharacteristic
26C22×C4×Dic3C2212yes—
27C22×C4×Dic3C2211yescharacteristic
28C2×#887—28no—
29C2×#887—24no—
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2211yescharacteristic
35C2×C3⋊#95C2212yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38#4959—28no—
39#4957—24no—
40#4947—24no—
41#4673—24no—
42C22×C4×Q8—31no—
43C2×#394—32no—
44C2×#393—31no—
45C2×#393—31no—
46C2×#390—31no—
47#1441—32no—
48#1439—31no—
49#1439D311yescharacteristic, complemented
50#1437—32no—
51#1437—32no—
52#1434—31no—
53C25×C3C2311yescharacteristic
54C24×D3C2311yescharacteristic
55C23×C3×C4C2312yes—
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C22×#67—22no—
60C22×#67—22no—
61C22×#67—22no—
62C22×#67—24no—
63C22×#67—42no—
64C23×Dic3C2312yes—
65C23×Dic3C2311yescharacteristic
66C23×Dic3C2311yescharacteristic
67C23×Dic3C2312yes—
68C23×Dic3C2311yescharacteristic
69C22×Dic6—22no—
70C22×Dic6—22no—
71C22×Dic6—24no—
72C22×Dic6—24no—
73C22×Dic6D414yescomplemented
74C2×C3×C4⋊C4—24no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C22⋊C4—24no—
77C2×C3×C22⋊C4—22no—
78C2×C3×C22⋊C4—22no—
79C2×C3×C22⋊C4—24no—
80C2×C3×C22⋊C4—22no—
81C2×C3×C22⋊C4—42no—
82C2×#217—24no—
83C2×#217—22no—
84C2×#217—24no—
85C2×#217—24no—
86C2×#217—24no—
87C2×(C2×D3)⋊C4—24no—
88C2×(C2×D3)⋊C4—22no—
89C2×(C2×D3)⋊C4—22no—
90C2×(C2×D3)⋊C4—24no—
91C2×(C2×D3)⋊C4—22no—
92C2×(C2×D3)⋊C4—24no—
93C2×(C2×D3)⋊C4—22no—
94C2×(C2×D3)⋊C4—24no—
95C2×(C2×D3)⋊C4—24no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—42no—
98C2×Dic3⋊C4—24no—
99C2×Dic3⋊C4—24no—
100C2×Dic3⋊C4—22no—
101C2×Dic3⋊C4—42no—
102C2×Dic3⋊C4D418yes—
103C2×C4×Dic3—24no—
104C2×C4×Dic3—24no—
105C2×C4×Dic3—24no—
106C2×C4×Dic3—24no—
107C2×C4×Dic3D414yes—
108#887—232no—
109C3×#95—22no—
110C3×#95—42no—
111C3⋊#95—22no—
112C3⋊#95—24no—
113C3⋊#95—24no—
114C3⋊#95—24no—
115C3⋊#95—24no—
116C3⋊#95—42no—
117C23×Q8—31no—
118C23×D4—31no—
119C2×C4×Q8—64no—
120C2×C4×Q8—68no—
121C22×C4⋊C4—32no—
122C22×C4⋊C4—31no—
123C22×C4⋊C4C2×D311yescharacteristic
124C22×C22⋊C4—32no—
125C22×C22⋊C4—31no—
126C22×C22⋊C4—32no—
127C22×C22⋊C4—31no—
128C22×C22⋊C4—31no—
129C22×C22⋊C4—32no—
130C22×C22⋊C4C2×D311yescharacteristic
131C22×C22⋊C4C2×D312yes—
132C22×C42—31no—
133C22×C42—32no—
134#394—68no—
135#393—64no—
136#393—64no—
137#390—64no—
138C2×#95—31no—
139C2×#95—32no—
140C2×#95—32no—
141C2×#95—32no—
142C2×#95—32no—
143C2×#95—32no—
144C2×#95C2×D311yescharacteristic
145C2×#95C2×D312yes—
146C24×C3—21no—
147C24×C3—21no—
148C24×C3—22no—
149C24×C3—22no—
150C24×C3—22no—
151C24×C3—21no—
152C24×C3—21no—
153C24×C3—22no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3#4112yes—
157C24×C3C2411yescharacteristic
158C23×D3—21no—
159C23×D3—21no—
160C23×D3—22no—
161C23×D3—21no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—21no—
165C23×D3—22no—
166C23×D3—21no—
167C23×D3—21no—
168C23×D3#4112yes—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4C2×D414yes—
190C22×C3×C4C2×D412yes—
191C22×C3×C4C2×D412yes—
192C22×C3×C4#4112yes—
193C2×#67—28no—
194C2×#67—48no—
195C2×#67—48no—
196C2×#67—44no—
197C2×#67—44no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—22no—
201C22×Dic3—22no—
202C22×Dic3—22no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—22no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—21no—
212C22×Dic3—22no—
213C22×Dic3—21no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3C2×D414yes—
221C22×Dic3C2×D412yes—
222C22×Dic3C2×D414yes—
223C22×Dic3C2×D414yes—
224C22×Dic3C2×D412yes—
225C22×Dic3#4114yes—
226C22×Dic3#4114yes—
227C2×Dic6—28no—
228C2×Dic6—216no—
229C2×Dic6—28no—
230C2×Dic6—28no—
231C2×Dic6—216no—
232C3×C4⋊C4—28no—
233C3×C22⋊C4—48no—
234C3×C22⋊C4—44no—
235#217—48no—
236#217—44no—
237(C2×D3)⋊C4—48no—
238(C2×D3)⋊C4—44no—
239(C2×D3)⋊C4—48no—
240(C2×D3)⋊C4—44no—
241Dic3⋊C4—216no—
242Dic3⋊C4—44no—
243C4×Dic3—216no—
244C4×Dic3—28no—
245C25—31no—
246C25C22×D311yescharacteristic
247C22×Q8—34no—
248C22×Q8—64no—
249C22×Q8—64no—
250C22×Q8—62no—
251C22×Q8—62no—
252C22×D4—62no—
253C22×D4—64no—
254C22×D4—62no—
255C22×D4—62no—
256C22×D4—122no—
257C23×C4—32no—
258C23×C4—31no—
259C23×C4—31no—
260C23×C4—31no—
261C23×C4—32no—
262C23×C4C22×D311yescharacteristic
263C23×C4C22×D312yes—
264C23×C4C22×D312yes—
265C23×C4C22×D311yescharacteristic
266C4×Q8—632no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—38no—
270C2×C4⋊C4—64no—
271C2×C4⋊C4—64no—
272C2×C4⋊C4—62no—
273C2×C4⋊C4—122no—
274C2×C22⋊C4—24no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—42no—
280C2×C22⋊C4—62no—
281C2×C22⋊C4—64no—
282C2×C22⋊C4—64no—
283C2×C22⋊C4—64no—
284C2×C22⋊C4—64no—
285C2×C22⋊C4—64no—
286C2×C22⋊C4—62no—
287C2×C22⋊C4—64no—
288C2×C22⋊C4—64no—
289C2×C22⋊C4—64no—
290C2×C22⋊C4—64no—
291C2×C22⋊C4—62no—
292C2×C22⋊C4—62no—
293C2×C22⋊C4—62no—
294C2×C22⋊C4—64no—
295C2×C22⋊C4—122no—
296C2×C42—34no—
297C2×C42—64no—
298C2×C42—64no—
299C2×C42—64no—
300C2×C42—64no—
301#95—22no—
302#95—42no—
303#95—64no—
304#95—64no—
305#95—64no—
306#95—64no—
307#95—62no—
308#95—122no—
309C23×C3—22no—
310C23×C3—24no—
311C23×C3—24no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—41no—
315C23×C3—42no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—42no—
319C23×C3—41no—
320C23×C3—42no—
321C23×C3—41no—
322C23×C3—41no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—41no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—41no—
331C23×C3—42no—
332C23×C3C22×D411yescharacteristic
333C23×C3C22×D412yes—
334C23×C3C22×D411yescharacteristic
335C23×C3C2×#4111yescharacteristic
336C23×C3C2×#4111yescharacteristic
337C23×C3C2×#4112yes—
338C23×C3C2×#4111yescharacteristic
339C23×C3C2×#4112yes—
340C23×C3H(5,𝔽2)12yes—
341C23×C32−1+411yescharacteristic
342C23×C32−1+411yescharacteristic
343C22×D3—22no—
344C22×D3—24no—
345C22×D3—24no—
346C22×D3—22no—
347C22×D3—22no—
348C22×D3—41no—
349C22×D3—41no—
350C22×D3—42no—
351C22×D3—41no—
352C22×D3—42no—
353C22×D3—41no—
354C22×D3—42no—
355C22×D3—41no—
356C22×D3—41no—
357C22×D3—42no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—41no—
363C22×D3—42no—
364C22×D3—41no—
365C22×D3—42no—
366C2×C3×C4—22no—
367C2×C3×C4—24no—
368C2×C3×C4—22no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—42no—
381C2×C3×C4—41no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4#12114yes—
390#67—416no—
391C2×Dic3—22no—
392C2×Dic3—24no—
393C2×Dic3—24no—
394C2×Dic3—24no—
395C2×Dic3—24no—
396C2×Dic3—24no—
397C2×Dic3—24no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—24no—
402C2×Dic3—24no—
403C2×Dic3—24no—
404C2×Dic3—24no—
405C2×Dic3—41no—
406C2×Dic3—42no—
407C2×Dic3—41no—
408C2×Dic3—42no—
409C2×Dic3—41no—
410C2×Dic3—42no—
411C2×Dic3—42no—
412C2×Dic3—42no—
413C2×Dic3—42no—
414C2×Dic3—42no—
415C2×Dic3—42no—
416C2×Dic3—42no—
417C2×Dic3#12014yes—
418C2×Dic3#12118yes—
419C2×Dic3#12414yes—
420Dic6—232no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—21no—
425C24—22no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24—21no—
430C24—21no—
431C24—32no—
432C24—61no—
433C24—61no—
434C24—61no—
435C24—62no—
436C24—61no—
437C24—62no—
438C24—61no—
439C24—62no—
440C24—62no—
441C24—61no—
442C24#23712yes—
443C24C23×D311yescharacteristic
444C2×Q8—616no—
445C2×Q8—68no—
446C2×Q8—68no—
447C2×Q8—616no—
448C2×Q8—68no—
449C2×D4—68no—
450C2×D4—124no—
451C2×D4—128no—
452C2×D4—128no—
453C2×D4—124no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—34no—
475C22×C4—34no—
476C22×C4—32no—
477C22×C4—32no—
478C22×C4—34no—
479C22×C4—34no—
480C22×C4—34no—
481C22×C4—62no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—62no—
485C22×C4—61no—
486C22×C4—62no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—62no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—62no—
493C22×C4—61no—
494C22×C4—62no—
495C22×C4—61no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4#23512yes—
504C22×C4D3×D414yes—
505C22×C4D3×D412yes—
506C22×C4D3×D412yes—
507C4⋊C4—28no—
508C4⋊C4—616no—
509C4⋊C4—124no—
510C22⋊C4—48no—
511C22⋊C4—44no—
512C22⋊C4—128no—
513C22⋊C4—124no—
514C22⋊C4—128no—
515C22⋊C4—124no—
516C22⋊C4—128no—
517C22⋊C4—124no—
518C42—68no—
519C42—616no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—42no—
525C22×C3—81no—
526C22×C3—81no—
527C22×C3—82no—
528C22×C3—81no—
529C22×C3—82no—
530C22×C3—81no—
531C22×C3C2×#12011yescharacteristic
532C22×C3C2×#12111yescharacteristic
533C22×C3C2×#12112yes—
534C22×C3#52511yescharacteristic
535C22×C3#52512yes—
536C22×C3#52511yescharacteristic
537C22×C3C2×#12411yescharacteristic
538C22×C3#52912yes—
539C22×C3#52912yes—
540C22×C3#53511yescharacteristic
541C22×C3#53611yescharacteristic
542C22×C3#54212yes—
543C22×C3#54212yes—
544C22×C3#54612yes—
545C22×C3#54612yes—
546C22×C3#54811yescharacteristic
547C22×C3#54812yes—
548C22×C3#54812yes—
549C22×C3#54811yescharacteristic
550C22×C3#55012yes—
551C22×C3#55211yescharacteristic
552C22×C3#55211yescharacteristic
553C22×C3#55912yes—
554C2×D3—42no—
555C2×D3—42no—
556C2×D3—44no—
557C2×D3—44no—
558C2×D3—42no—
559C2×D3—81no—
560C2×D3—81no—
561C2×D3—82no—
562C2×D3—81no—
563C2×D3—82no—
564C2×D3—81no—
565C3×C4—24no—
566C3×C4—44no—
567C3×C4—82no—
568C3×C4—81no—
569Dic3—28no—
570Dic3—24no—
571Dic3—24no—
572Dic3—82no—
573Dic3—81no—
574C23—24no—
575C23—22no—
576C23—24no—
577C23—22no—
578C23—22no—
579C23—42no—
580C23—41no—
581C23—42no—
582C23—41no—
583C23—42no—
584C23—41no—
585C23—42no—
586C23—42no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—42no—
591C23—42no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—41no—
597C23—62no—
598C23—64no—
599C23—62no—
600C23—62no—
601C23—64no—
602C23—122no—
603C23—122no—
604C23—122no—
605C23—121no—
606C23—122no—
607C23—121no—
608C23—122no—
609C23—121no—
610C23—121no—
611C23—121no—
612C23—122no—
613C23—122no—
614C23—121no—
615C23—122no—
616C23—121no—
617C23—122no—
618C23—122no—
619C23—121no—
620C23C2×#23511yescharacteristic
621C23C2×D3×D412yes—
622C23C2×D3×D411yescharacteristic
623C23C2×D3×D411yescharacteristic
624C23C2×#23711yescharacteristic
625C23#100412yes—
626C23#100711yescharacteristic
627C23D3×#4112yes—
628C23D3×#4111yescharacteristic
629C23D3×#4112yes—
630C23#101011yescharacteristic
631Q8—632no—
632D4—1216no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—34no—
641C2×C4—34no—
642C2×C4—38no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—64no—
660C2×C4—64no—
661C2×C4—64no—
662C2×C4—62no—
663C2×C4—64no—
664C2×C4—64no—
665C2×C4—64no—
666C2×C4—62no—
667C2×C4—64no—
668C2×C4—64no—
669C2×C4—64no—
670C2×C4—62no—
671C2×C4—64no—
672C2×C4—62no—
673C2×C4—122no—
674C2×C4—122no—
675C2×C4—122no—
676C2×C4—121no—
677C2×C4—122no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—122no—
681C2×C4—122no—
682C2×C4—122no—
683C2×C4—122no—
684C2×C4—122no—
685C2×C4#88414yes—
686C2×C3—82no—
687C2×C3#239811yescharacteristic
688C2×C3#240411yescharacteristic
689C2×C3#242612yes—
690C2×C3#242612yes—
691C2×C3#243611yescharacteristic
692C2×C3#245812yes—
693C2×C3#245812yes—
694C2×C3#253611yescharacteristic
695C2×C3#254811yescharacteristic
696C2×C3#263211yescharacteristic
697C2×C3#284711yescharacteristic
698D3—82no—
699C22—44no—
700C22—42no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—82no—
706C22—81no—
707C22—81no—
708C22—82no—
709C22—81no—
710C22—124no—
711C22—122no—
712C22—122no—
713C22—122no—
714C22—124no—
715C22—241no—
716C22—242no—
717C22—241no—
718C22—242no—
719C22—241no—
720C22—241no—
721C22C2×#88411yescharacteristic
722C22#551311yescharacteristic
723C22#552911yescharacteristic
724C22#554712yes—
725C22#555912yes—
726C22D3×#12011yescharacteristic
727C22#559112yes—
728C22#559811yescharacteristic
729C22#559912yes—
730C22D3×#12112yes—
731C22#560611yescharacteristic
732C22#561012yes—
733C22#562811yescharacteristic
734C22#563312yes—
735C22#563311yescharacteristic
736C22#564012yes—
737C22#564912yes—
738C22#565611yescharacteristic
739C22#566212yes—
740C22D3×#12411yescharacteristic
741C22#567712yes—
742C22#570612yes—
743C22#571511yescharacteristic
744C4—24no—
745C4—44no—
746C4—68no—
747C4—64no—
748C4—64no—
749C4—81no—
750C4—82no—
751C4—241no—
752C4—242no—
753C3#1488311yescharacteristic, complemented, Sylow
754C2—82no—
755C2—242no—
756C2#7393411yescharacteristic
757C2#7442812yes—
758C2#7493511yescharacteristic
759C2#7585412yes—
760C2#7635211yescharacteristic
761C2#7675411yescharacteristic
762C2#7678111yescharacteristic
763C2#7690112yes—
764C2#7728612yes—
765C2#7746011yescharacteristic
766C2#7805011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC3×#1439C2
prime radicalC23×#67C22
hypercenter#1439D3
hypocenterC3#14883
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×#887C2semidirect
3. C2×#4947C2semidirect
5. C2×#4673C2semidirect
6. C3×#1439C2semidirect
7. #71570C2semidirect
8. #71545C2semidirect
9. #69409C2semidirect
10. #69408C2semidirect
11. #69403C2semidirect
49. #1439D3semidirect
73. C22×Dic6D4semidirect
753. C3#14883semidirect

Maximal subgroups

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

subgroupindex
C22×#8872
C2×#49592
C2×#49472
C2×#49572
C2×#46732
C3×#14392
#715702
#715452
#694092
#694082
#694032
#148833