Finite Group Databasebeta

← #396573

Subgroups — #396573

Order 512.

1286 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1878C211yesmaximal, characteristic
2C2×#1878C211yesmaximal, characteristic
3C2×#1878C211yesmaximal, characteristic
4C2×#1805C211yesmaximal, characteristic
5#15241C211yesmaximal, characteristic
6Q8×#95C211yesmaximal, characteristic
7#11372C211yesmaximal, characteristic
8#11316C211yesmaximal, characteristic
9#11315C211yesmaximal, characteristic
10#11255C211yesmaximal, characteristic
11#11190C211yesmaximal, characteristic
12#11190C211yesmaximal, characteristic
13#11077C211yesmaximal, characteristic
14#10789C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C23×Q16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#382C2211yescharacteristic
31#1878—24no—
32#1878—24no—
33#1878—24no—
34#1805—24no—
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49#1443—21no—
50#1443—21no—
51#1443—21no—
52#1443—21no—
53C4⋊#95—21no—
54C4⋊#95—21no—
55C4⋊#95—21no—
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4×#95—21no—
62C4×#95C2211yescharacteristic
63C23×Q8C2311yescharacteristic
64C23×Q8C2311yescharacteristic
65C22×Q16—22no—
66C22×Q16—22no—
67C22×Q16—22no—
68C22×Q16—22no—
69C22×Q16—22no—
70C22×Q16—22no—
71C22×Q16D414yes—
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8—22no—
83C2×C4×Q8—22no—
84C2×C4×Q8—22no—
85C2×C4×Q8—22no—
86C2×C4×Q8—22no—
87C2×C4×Q8—41no—
88C2×C4×Q8—41no—
89C2×C4×Q8—41no—
90C2×C4×Q8—41no—
91C2×C4×Q8—41no—
92C2×C4×Q8—41no—
93C2×C4×Q8D414yes—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4—21no—
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C42—21no—
104C22×C42—21no—
105C22×C42—21no—
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C2×C4⋊C8—22no—
110C2×C4⋊C8—41no—
111C2×C4⋊C8—41no—
112C2×#103—22no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103—22no—
124C2×#103—22no—
125C2×#103—22no—
126C2×#103—41no—
127C2×#103—41no—
128C2×#103—41no—
129C2×#103—41no—
130#391—22no—
131#391—22no—
132#391—22no—
133#391—22no—
134#391—41no—
135#391—41no—
136#382—22no—
137#382—22no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95D411yescharacteristic
157C2×#95D411yescharacteristic
158C2×#95D411yescharacteristic
159C2×#95D411yescharacteristic
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—41no—
168#340—41no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—41no—
173#336—41no—
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8C2×D412yes—
195C22×Q8C2×D412yes—
196C22×Q8C2×D412yes—
197C22×Q8#4112yes—
198C22×Q8#4112yes—
199C22×Q8#4112yes—
200C22×Q8#4112yes—
201C22×Q8#4112yes—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2411yescharacteristic
217C2×Q16—28no—
218C2×Q16—28no—
219C2×Q16—28no—
220C2×Q16—44no—
221C2×Q16—44no—
222C2×Q16—44no—
223C2×Q16—44no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8C2×D412yes—
252C4×Q8—28no—
253C4×Q8—44no—
254C4×Q8—44no—
255C4×Q8—44no—
256C4×Q8—44no—
257C4×Q8—44no—
258C4×Q8—44no—
259C4×Q8—44no—
260C4×Q8—44no—
261C4×Q8—44no—
262C4×Q8—44no—
263C4×Q8—44no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4C2×D412yes—
307C2×C4⋊C4#4112yes—
308C2×C4⋊C4#4112yes—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—24no—
314C2×C42—24no—
315C2×C42—24no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42—42no—
333C2×C42—42no—
334C2×C42C2×D412yes—
335C2×C42#4112yes—
336C4⋊C8—44no—
337#103—44no—
338#103—44no—
339#103—44no—
340#103—44no—
341#103—44no—
342#103—44no—
343#95—22no—
344#95—22no—
345#95—41no—
346#95—41no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—81no—
363#95—81no—
364#95—81no—
365C24C22×D411yescharacteristic
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8#12114yes—
416C2×Q8#12314yes—
417C2×Q8#12314yes—
418C2×Q8#12314yes—
419C2×Q8#12414yes—
420C2×Q8#12614yes—
421C2×Q8#12614yes—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4#12112yes—
517C22×C4#12112yes—
518C22×C4#13512yes—
519C22×C4#13712yes—
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4C2×#4111yescharacteristic
525C22×C4C2×#4111yescharacteristic
526C22×C4C2×#4111yescharacteristic
527C22×C4C2×#4111yescharacteristic
528C22×C4C2×#4111yescharacteristic
529C22×C4C2×#4111yescharacteristic
530C22×C4H(5,𝔽2)11yescharacteristic
531C22×C4H(5,𝔽2)11yescharacteristic
532C22×C4H(5,𝔽2)11yescharacteristic
533C22×C42−1+411yescharacteristic
534Q16—416no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—48no—
570C4⋊C4—48no—
571C4⋊C4—48no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—22no—
594C42—48no—
595C42—48no—
596C42—48no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C23C2×#12111yescharacteristic
606C23#52511yescharacteristic
607C23#52511yescharacteristic
608C23D4211yescharacteristic
609C23#54611yescharacteristic
610C23#54611yescharacteristic
611C23#54811yescharacteristic
612C23C2×#13511yescharacteristic
613C23C2×#13711yescharacteristic
614C23#57511yescharacteristic
615C23#57511yescharacteristic
616C23#57711yescharacteristic
617C23#57811yescharacteristic
618C23#57811yescharacteristic
619C23#57811yescharacteristic
620Q8—24no—
621Q8—24no—
622Q8—24no—
623Q8—24no—
624Q8—24no—
625Q8—24no—
626Q8—24no—
627Q8—42no—
628Q8—42no—
629Q8—42no—
630Q8—42no—
631Q8—81no—
632Q8—81no—
633Q8—81no—
634Q8—81no—
635Q8#39718yes—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4C2×#12111yescharacteristic
735C2×C4C2×#12311yescharacteristic
736C2×C4C2×#12311yescharacteristic
737C2×C4C2×#12311yescharacteristic
738C2×C4C2×#12411yescharacteristic
739C2×C4C2×#12611yescharacteristic
740C2×C4C2×#12611yescharacteristic
741C2×C4#52911yescharacteristic
742C2×C4#52911yescharacteristic
743C2×C4#53211yescharacteristic
744C2×C4#53411yescharacteristic
745C2×C4#53711yescharacteristic
746C2×C4#53811yescharacteristic
747C2×C4#53811yescharacteristic
748C2×C4#53911yescharacteristic
749C2×C4#53911yescharacteristic
750C2×C4#54611yescharacteristic
751C2×C4#54611yescharacteristic
752C2×C4#54711yescharacteristic
753C2×C4#55111yescharacteristic
754C2×C4#55111yescharacteristic
755C2×C4#55111yescharacteristic
756C2×C4#55111yescharacteristic
757C2×C4#55211yescharacteristic
758C2×C4#55211yescharacteristic
759C2×C4#55311yescharacteristic
760C2×C4#55311yescharacteristic
761C2×C4#55311yescharacteristic
762C8—42no—
763C8—81no—
764C8—81no—
765C8—81no—
766C22#241211yescharacteristic
767C22#241611yescharacteristic
768C22#241811yescharacteristic
769C22#241811yescharacteristic
770C22#248111yescharacteristic
771C22#248111yescharacteristic
772C22#285011yescharacteristic
773C22#303511yescharacteristic
774C22#303711yescharacteristic
775C22#304411yescharacteristic
776C22#304611yescharacteristic
777C22#310211yescharacteristic
778C22#310811yescharacteristic
779C22#311111yescharacteristic
780C22#311711yescharacteristic
781C22#312011yescharacteristic
782C22#312011yescharacteristic
783C22#312711yescharacteristic
784C22#312711yescharacteristic
785C22#327011yescharacteristic
786C22#327111yescharacteristic
787C22#327711yescharacteristic
788C22#328511yescharacteristic
789C22#330011yescharacteristic
790C22#330411yescharacteristic
791C22#331211yescharacteristic
792C22#331311yescharacteristic
793C22#331311yescharacteristic
794C22#331711yescharacteristic
795C22#332711yescharacteristic
796C22#332811yescharacteristic
797C22#336411yescharacteristic
798C22#336911yescharacteristic
799C22#337711yescharacteristic
800C22#337711yescharacteristic
801C4—28no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—82no—
808C4—81no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—161no—
813C4—161no—
814C4—161no—
815C4C2×#39711yescharacteristic
816C4#241911yescharacteristic
817C4#241911yescharacteristic
818C4#249811yescharacteristic
819C4#251011yescharacteristic
820C4#251011yescharacteristic
821C4#254311yescharacteristic
822C4#263911yescharacteristic
823C2#1473511yescharacteristic
824C2#2453411yescharacteristic
825C2#2454011yescharacteristic
826C2#2473611yescharacteristic
827C2#2474111yescharacteristic
828C2#2490211yescharacteristic
829C2#2490811yescharacteristic
830C2#2492011yescharacteristic
831C2#2492211yescharacteristic
832C2#2755111yescharacteristic
833C2#2756211yescharacteristic
834C2#2757011yescharacteristic
835C2#2757511yescharacteristic
836C2#3302911yescharacteristic
837C2#3304111yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#18782
C2×#18052
#152412
Q8×#952
#113722
#113162
#113152
#112552
#111902
#110772
#107892