Finite Group Databasebeta

← #6439718

Subgroups — #6439718

Order 512.

2244 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3082C211yesmaximal, characteristic, complemented
2C2×#2949C211yesmaximal, characteristic
3#35529C211yesmaximal, characteristic
4#34209C211yesmaximal, characteristic, complemented
5#26919C214yesmaximal, complemented
6#26918C214yesmaximal, complemented
7#26903C214yesmaximal, complemented
8#26902C214yesmaximal, complemented
9#23541C211yesmaximal, characteristic
10#23507C211yesmaximal, characteristic, complemented
11#23457C211yesmaximal, characteristic, complemented
12C2×#2013C211yesmaximal, characteristic
13#21090C211yesmaximal, characteristic, complemented
14#21060C211yesmaximal, characteristic
15#21032C211yesmaximal, characteristic, complemented
16#21025C211yesmaximal, characteristic, complemented
17#20936C211yesmaximal, characteristic
18#20933C211yesmaximal, characteristic
19#20877C211yesmaximal, characteristic, complemented
20C23×SD16C2211yescharacteristic
21C23×SD16C2211yescharacteristic
22C2×#544C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C2×#519C2211yescharacteristic
25C2×#519C2211yescharacteristic
26C2×#518C2211yescharacteristic
27#3082—28no—
28C2×#479C2212yescomplemented
29C2×#479C2212yescomplemented
30C2×#477C2212yescomplemented
31C2×#475C2212yescomplemented
32#2949—28no—
33C2×#440C2212yes—
34C2×#440C2212yes—
35C2×C4×SD16C2212yes—
36C2×C4×SD16C2212yes—
37C2×#428C2211yescharacteristic
38C2×#427C2211yescharacteristic
39C2×#424C2211yescharacteristic
40C2×#419C2211yescharacteristic
41C2×#419C2211yescharacteristic
42C2×#419C2211yescharacteristic
43C2×#419C2211yescharacteristic
44C2×#418C2211yescharacteristic
45C2×#418C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C2×#405C2211yescharacteristic
49#2566—21no—
50#2566—21no—
51#2563—21no—
52#2542—21no—
53#2454C2214yes—
54#2452C2214yes—
55#2437—24no—
56#2365C2214yescomplemented
57#2365C2214yescomplemented
58#2344—24no—
59#2327—21no—
60#2327—21no—
61#2317C2211yescharacteristic
62#2310C2211yescharacteristic
63#2310C2211yescharacteristic
64#2309C2211yescharacteristic
65C4×C4⋊Q8—21no—
66C4×C4⋊Q8—21no—
67#2296C2211yescharacteristic
68C2×#390C2211yescharacteristic
69#2285C2211yescharacteristic
70C4×#117C2211yescharacteristic
71#2055C2214yes—
72#2055C2214yes—
73#2043C2214yescomplemented
74#2043C2214yescomplemented
75#2026C2214yescomplemented
76#2024C2214yescomplemented
77#2013C2214yes—
78#2013C2214yes—
79#1935C2214yescomplemented
80#1933C2214yescomplemented
81#1926C2214yes—
82#1925C2214yes—
83#1921C2212yescomplemented
84#1920C2212yescomplemented
85#1919C2212yescomplemented
86#1918C2212yescomplemented
87#1917C2214yescomplemented
88#1916C2214yescomplemented
89#1880C2214yes—
90#1880C2214yes—
91#1877C2214yes—
92#1877C2214yes—
93#1865C2214yescomplemented
94#1863C2214yescomplemented
95#1736C2211yescharacteristic
96#1735C2211yescharacteristic
97#1735C2211yescharacteristic
98#1735C2211yescharacteristic
99#1729C2211yescharacteristic
100#1729C2211yescharacteristic
101#1728C2211yescharacteristic
102C2×#336C2211yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×D4C2311yescharacteristic
106C22×SD16—24no—
107C22×SD16—24no—
108C22×SD16—24no—
109C22×SD16—24no—
110C22×SD16—24no—
111C22×SD16—42no—
112C22×SD16C2312yes—
113C22×SD16C2312yes—
114C22×SD16C2314yes—
115C22×M16C2311yescharacteristic
116C22×M16C2311yescharacteristic
117C23×C8C2311yescharacteristic
118C23×C8C2311yescharacteristic
119#544—24no—
120#544—42no—
121C2×C4⋊Q8—24no—
122C2×C4⋊Q8—24no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—21no—
125C2×C4⋊Q8—21no—
126C2×C4⋊Q8C2314yes—
127C2×C4⋊Q8C2312yes—
128C2×#125—21no—
129C2×#125C2312yes—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—22no—
132#519—24no—
133#519—24no—
134#519—42no—
135#519—42no—
136#518—24no—
137#518—42no—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8C2312yes—
143C2×C4×Q8C2312yes—
144C2×C4×Q8C2312yes—
145C2×C4×Q8C2312yes—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4C2312yes—
149C2×C4×D4C2312yes—
150C2×#117—22no—
151C2×#117—22no—
152C2×#117C2311yescharacteristic
153C2×#117C2311yescharacteristic
154C2×#117C2311yescharacteristic
155C2×#117C2311yescharacteristic
156C2×#117C2311yescharacteristic
157C2×#117C2311yescharacteristic
158C22×C4⋊C4—22no—
159C22×C4⋊C4C2311yescharacteristic
160C22×C22⋊C4—22no—
161C22×C22⋊C4—22no—
162C22×C42C2311yescharacteristic
163#479—28no—
164#479—28no—
165#477—28no—
166#475—28no—
167#440—28no—
168#440—28no—
169C4×SD16—28no—
170C4×SD16—28no—
171#428—24no—
172#427D418yes—
173C2×#107C2312yes—
174C2×#107C2311yescharacteristic
175C2×#107C2311yescharacteristic
176C2×#106C2312yes—
177C2×#106C2311yescharacteristic
178C2×#106C2311yescharacteristic
179#424—24no—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182#419—24no—
183#419—24no—
184#419—24no—
185#419—24no—
186#418—24no—
187#418—24no—
188C2×#103—24no—
189C2×#103—42no—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2314yes—
195C2×#103C2314yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2314yes—
199C2×#102C2314yes—
200C2×#102C2312yes—
201C2×#102C2312yes—
202#405—24no—
203C2×#97C2312yes—
204C2×C4×C8C2312yes—
205#399—24no—
206#396—24no—
207#396—24no—
208#393—24no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391C2314yes—
214#391C2314yes—
215#390—21no—
216#390—21no—
217#390—21no—
218#390—21no—
219#390C2314yes—
220#390C2314yes—
221#389—24no—
222#389—24no—
223#389C2314yes—
224#389C2312yes—
225#389C2312yes—
226#387—24no—
227#387—24no—
228#387—24no—
229#387—24no—
230#385—22no—
231#385—24no—
232#385—22no—
233#385—24no—
234#384—21no—
235#384D411yescharacteristic
236#384D411yescharacteristic
237#382—21no—
238#382D411yescharacteristic
239#382D411yescharacteristic
240#381—22no—
241#381—22no—
242#380—24no—
243#380D414yes—
244#379—22no—
245C4×C4⋊C4—24no—
246C4×C4⋊C4—24no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4C2312yes—
250C4×C4⋊C4C2312yes—
251C4×C4⋊C4C2314yes—
252C4×C22⋊C4—22no—
253#376—21no—
254C43—21no—
255#340C2312yes—
256#340C2312yes—
257#340C2312yes—
258#340C2312yes—
259#340C2312yes—
260#340C2312yes—
261#340C2314yes—
262#336C2314yes—
263#336C2314yes—
264#336C2312yes—
265#336C2314yes—
266#336C2312yes—
267C25—21no—
268C22×Q8—21no—
269C22×Q8—21no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8#4114yes—
282C22×Q8#4114yes—
283C22×Q8C2412yes—
284C22×Q8C2412yes—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4#4114yes—
292C22×D4C2412yes—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4C2×D412yes—
299C23×C4C2411yescharacteristic
300C2×SD16—232no—
301C2×SD16—24no—
302C2×SD16—24no—
303C2×SD16—24no—
304C2×SD16—24no—
305C2×SD16—28no—
306C2×SD16—28no—
307C2×SD16—24no—
308C2×SD16—24no—
309C2×SD16—44no—
310C2×SD16—416no—
311C2×M16—22no—
312C2×M16—22no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
316C2×M16—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8C2×D414yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2411yescharacteristic
327C22×C8C2411yescharacteristic
328C4⋊Q8—28no—
329C4⋊Q8—28no—
330C4⋊Q8—28no—
331C4⋊Q8—28no—
332C4⋊Q8—24no—
333C4⋊Q8—42no—
334C4⋊Q8—44no—
335#125—24no—
336#125—42no—
337#125—44no—
338C22⋊Q8—48no—
339C22⋊Q8—88no—
340C4×Q8—24no—
341C4×Q8—24no—
342C4×Q8—24no—
343C4×Q8—24no—
344C4×Q8—42no—
345C4×Q8—42no—
346C4×Q8—42no—
347C4×Q8—42no—
348C4×Q8—44no—
349C4×Q8—44no—
350C4×Q8—44no—
351C4×Q8—44no—
352C4×D4—24no—
353C4×D4—24no—
354C4×D4—42no—
355C4×D4—42no—
356C4×D4—44no—
357C4×D4—44no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—22no—
362#117—22no—
363#117—22no—
364#117—22no—
365#117—22no—
366#117—22no—
367#117—22no—
368#117—48no—
369#117—48no—
370#117C2×D414yes—
371#117C2×D414yes—
372C2×C4⋊C4—216no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2×D414yes—
393C2×C4⋊C4C2×D414yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2411yescharacteristic
398C2×C4⋊C4C2411yescharacteristic
399C2×C4⋊C4C2411yescharacteristic
400C2×C4⋊C4C2411yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—48no—
412C2×C22⋊C4—84no—
413C2×C22⋊C4C2×D412yes—
414C2×C22⋊C4C2×D412yes—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2412yes—
430C2×C42C2412yes—
431C2×C42C2412yes—
432#107—24no—
433#107C2×D414yes—
434#107C2×D414yes—
435#106—24no—
436#106C2×D414yes—
437#106C2×D414yes—
438C4⋊C8—24no—
439C4⋊C8—24no—
440#103—28no—
441#103—28no—
442#103—24no—
443#103—24no—
444#103—24no—
445#103—24no—
446#103—24no—
447#103—24no—
448#103—44no—
449#102—28no—
450#102—24no—
451#102—24no—
452#97—24no—
453C4×C8—24no—
454#95—22no—
455#95—22no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—22no—
461#95—22no—
462#95—24no—
463#95C2×D414yes—
464#95C2×D414yes—
465C24—22no—
466C24—24no—
467C24—42no—
468C24—42no—
469C24—82no—
470C24—82no—
471C24C22×D411yescharacteristic
472C2×Q8—24no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—28no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—84no—
498C2×Q8C2×#4114yes—
499C2×Q8C2×#4114yes—
500C2×D4—28no—
501C2×D4—24no—
502C2×D4—28no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—42no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—44no—
512C2×D4C2×#4114yes—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—42no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—84no—
535C22×C4—84no—
536C22×C4—82no—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D412yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4H(5,𝔽2)12yes—
549C22×C42−1+412yes—
550C22×C4C2511yescharacteristic
551SD16—216no—
552SD16—216no—
553SD16—416no—
554M16—44no—
555M16—44no—
556C2×C8—28no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—44no—
571C2×C8C22×D412yes—
572C2×C8C22×D412yes—
573C4⋊C4—216no—
574C4⋊C4—216no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—28no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—44no—
600C4⋊C4—82no—
601C4⋊C4—84no—
602C4⋊C4C22×D412yes—
603C4⋊C4C22×D412yes—
604C4⋊C4C22×D412yes—
605C4⋊C4C22×D412yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—48no—
615C22⋊C4—84no—
616C22⋊C4—84no—
617C22⋊C4—84no—
618C42—22no—
619C42—22no—
620C42—24no—
621C42—24no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—44no—
629C42—44no—
630C42—44no—
631C42—44no—
632C42—44no—
633C42—42no—
634C42—42no—
635C42—44no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—44no—
640C23—42no—
641C23—42no—
642C23—44no—
643C23—48no—
644C23—88no—
645C23—162no—
646C23—162no—
647C23—164no—
648C23#52512yes—
649C23D4212yes—
650C23#54812yes—
651C23C23×D411yescharacteristic
652Q8—24no—
653Q8—24no—
654Q8—24no—
655Q8—24no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—48no—
661Q8—48no—
662Q8—164no—
663D4—24no—
664D4—24no—
665D4—42no—
666D4—42no—
667D4—48no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—48no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—164no—
707C2×C4—164no—
708C2×C4—162no—
709C2×C4#52514yes—
710C2×C4#52512yes—
711C2×C4#53914yes—
712C2×C4D4212yes—
713C2×C4#54814yes—
714C2×C4#54812yes—
715C2×C4#55114yes—
716C2×C4#57714yes—
717C2×C4C23×D411yescharacteristic
718C2×C4C22×#4111yescharacteristic
719C2×C4C22×#4111yescharacteristic
720C2×C4C22×#4111yescharacteristic
721C2×C4C2×H(5,𝔽2)11yescharacteristic
722C2×C4C2×2−1+411yescharacteristic
723C8—22no—
724C8—22no—
725C8—42no—
726C8—42no—
727C8—42no—
728C22—22no—
729C22—24no—
730C22—22no—
731C22—24no—
732C22—44no—
733C22—48no—
734C22—82no—
735C22—82no—
736C22—84no—
737C22—168no—
738C22#246314yes—
739C22C2×#52511yescharacteristic
740C22C2×D4211yescharacteristic
741C22C2×#54811yescharacteristic
742C22C2×#57712yes—
743C22#358612yes—
744C4—24no—
745C4—44no—
746C4—44no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—82no—
757C4—82no—
758C4—82no—
759C4#246314yes—
760C4C2×#52511yescharacteristic
761C4C2×#53911yescharacteristic
762C4C2×#54811yescharacteristic
763C4C2×#55111yescharacteristic
764C2—24no—
765C2—84no—
766C2C2×#246311yescharacteristic
767C2#6058212yes—
768C2#6108311yescharacteristic
769C2#6108711yescharacteristic
770C2#6134012yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2285 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3082C2semidirect
4. #34209C2semidirect
5. #26919C2semidirect
6. #26918C2semidirect
7. #26903C2semidirect
8. #26902C2semidirect
10. #23507C2semidirect
11. #23457C2semidirect
13. #21090C2semidirect
15. #21032C2semidirect
16. #21025C2semidirect
19. #20877C2semidirect
28. C2×#479C22semidirect
29. C2×#479C22semidirect
30. C2×#477C22semidirect
31. C2×#475C22semidirect
56. #2365C22semidirect
57. #2365C22semidirect
73. #2043C22semidirect
74. #2043C22semidirect
75. #2026C22semidirect
76. #2024C22semidirect
79. #1935C22semidirect
80. #1933C22semidirect
83. #1921C22semidirect
84. #1920C22semidirect
85. #1919C22semidirect
86. #1918C22semidirect
87. #1917C22semidirect
88. #1916C22semidirect
93. #1865C22semidirect
94. #1863C22semidirect

Maximal subgroups

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

subgroupindex
C2×#30822
C2×#29492
#355292
#342092
#269192
#269182
#269032
#269022
#235412
#235072
#234572
C2×#20132
#210902
#210602
#210322
#210252
#209362
#209332
#208772