Finite Group Databasebeta

← #384348

Subgroups — #384348

Order 512.

1272 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1968C211yesmaximal, characteristic
2C2×#1880C211yesmaximal, characteristic
3C2×#1835C211yesmaximal, characteristic, complemented
4#14002C211yesmaximal, characteristic
5#13978C211yesmaximal, characteristic, complemented
6#11220C211yesmaximal, characteristic, complemented
7#11189C211yesmaximal, characteristic
8#11066C211yesmaximal, characteristic
9#11052C211yesmaximal, characteristic, complemented
10#11051C211yesmaximal, characteristic
11#11023C211yesmaximal, characteristic
12#10932C211yesmaximal, characteristic, complemented
13#10908C211yesmaximal, characteristic, complemented
14#10797C211yesmaximal, characteristic, complemented
15#10789C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C2×#391C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#390C2211yescharacteristic
29C2×#390C2211yescharacteristic
30C2×#390C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#382C2211yescharacteristic
33C2×#382C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35#1968C418yescomplemented
36#1880—24no—
37#1835—24no—
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51#1442—21no—
52#1442—21no—
53#1440—21no—
54#1440—21no—
55#1437—21no—
56#1437—21no—
57#1436—21no—
58#1436—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4×#95C2211yescharacteristic
62C23×Q8C2311yescharacteristic
63C23×D4C2311yescharacteristic
64C22×SD16—22no—
65C22×SD16—22no—
66C22×SD16—22no—
67C22×SD16—22no—
68C22×SD16—41no—
69C22×SD16—41no—
70C22×SD16C2×C414yes—
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C2×C4×Q8—22no—
76C2×C4×Q8—22no—
77C2×C4×Q8—41no—
78C2×C4×Q8—41no—
79C2×C4×Q8—41no—
80C2×C4×Q8—41no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C22⋊C4—21no—
90C22×C22⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C42—21no—
96C22×C42—21no—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100C2×#106—41no—
101C2×#106—41no—
102C2×#106C2×C414yes—
103C2×#103—22no—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—41no—
107C2×#103—41no—
108C2×#103—41no—
109C2×#103—41no—
110C2×#103—41no—
111C2×#103C2×C414yes—
112C2×#102—22no—
113C2×#102—41no—
114C2×#102—41no—
115C2×#102—41no—
116C2×#102—41no—
117C2×#102—41no—
118C2×#102—41no—
119C2×#102—41no—
120C2×#102C2×C414yes—
121C2×C4×C8—22no—
122C2×C4×C8—22no—
123C2×C4×C8C2×C414yes—
124#391—22no—
125#391—22no—
126#391—41no—
127#391C2×C414yes—
128#390—22no—
129#390—22no—
130#390—41no—
131#390—41no—
132#390—41no—
133#390C2×C414yes—
134#389—41no—
135#389—41no—
136#382—22no—
137#382—22no—
138#382—41no—
139#382—41no—
140C4×C4⋊C4—41no—
141C4×C4⋊C4—41no—
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—41no—
164#340—41no—
165#340—41no—
166#340—41no—
167#340D414yes—
168#336—22no—
169#336—22no—
170#336—22no—
171#336—41no—
172#336—41no—
173C25—21no—
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×Q8C22×C412yes—
186C22×Q8#4112yes—
187C22×Q8#4112yes—
188C22×D4—21no—
189C22×D4—21no—
190C22×D4—21no—
191C22×D4—21no—
192C22×D4—21no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4C22×C412yes—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2411yescharacteristic
216C2×SD16—28no—
217C2×SD16—28no—
218C2×SD16—44no—
219C2×SD16—44no—
220C2×SD16—44no—
221C2×SD16—44no—
222C2×SD16—44no—
223C22×C8—21no—
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×C8C22×C412yes—
248C22×C8C22×C412yes—
249C22×C8C2×D412yes—
250C22×C8#4112yes—
251C4×Q8—44no—
252C4×Q8—44no—
253C4×Q8—44no—
254C4×Q8—44no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
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—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
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—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4C22×C412yes—
294C2×C4⋊C4C22×C412yes—
295C2×C4⋊C4C2×D412yes—
296C2×C4⋊C4C2×D412yes—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—81no—
308C2×C22⋊C4—81no—
309C2×C22⋊C4—81no—
310C2×C22⋊C4—81no—
311C2×C22⋊C4—81no—
312C2×C22⋊C4—81no—
313C2×C22⋊C4—81no—
314C2×C22⋊C4—81no—
315C2×C42—21no—
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—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—42no—
332C2×C42—42no—
333C2×C42—42no—
334C2×C42—42no—
335C2×C42—81no—
336C2×C42—81no—
337C2×C42C22×C412yes—
338C2×C42#4112yes—
339#106—44no—
340#103—44no—
341#103—44no—
342#103—44no—
343#102—44no—
344#102—44no—
345#102—44no—
346C4×C8—28no—
347#95—24no—
348#95—24no—
349#95—22no—
350#95—22no—
351#95—41no—
352#95—41no—
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—42no—
363#95—81no—
364#95—81no—
365C24—22no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24C22×D411yescharacteristic
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—22no—
394C2×Q8—22no—
395C2×Q8—22no—
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#11714yes—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
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—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4C4×D412yes—
525C22×C4C4×D412yes—
526C22×C4#13512yes—
527C22×C4#13512yes—
528C22×C4C23×C411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C2×#4111yescharacteristic
531C22×C4C2×#4111yescharacteristic
532C22×C4C2×#4111yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4H(5,𝔽2)11yescharacteristic
535C22×C4H(5,𝔽2)11yescharacteristic
536C22×C4H(5,𝔽2)11yescharacteristic
537C22×C4H(5,𝔽2)11yescharacteristic
538C22×C4H(5,𝔽2)11yescharacteristic
539C22×C4H(5,𝔽2)11yescharacteristic
540C22×C42−1+411yescharacteristic
541C22×C42−1+411yescharacteristic
542SD16—416no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
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—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8C4×D414yes—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—48no—
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—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4—84no—
597C22⋊C4—84no—
598C22⋊C4—84no—
599C22⋊C4—84no—
600C22⋊C4—84no—
601C22⋊C4—84no—
602C22⋊C4—84no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—48no—
608C42—41no—
609C42—41no—
610C42—41no—
611C42—41no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—41no—
616C42—84no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23—81no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23—81no—
647C23—81no—
648C23—81no—
649C23—81no—
650C23—81no—
651C23—81no—
652C23C2×C4×D411yescharacteristic
653C23#53511yescharacteristic
654C23#53511yescharacteristic
655C23D4211yescharacteristic
656C23#54611yescharacteristic
657C23#54711yescharacteristic
658C23#54811yescharacteristic
659C23C2×#13511yescharacteristic
660C23C2×#13511yescharacteristic
661C23#57511yescharacteristic
662C23#57511yescharacteristic
663C23#57711yescharacteristic
664C23#57711yescharacteristic
665C23#57711yescharacteristic
666C23#57711yescharacteristic
667Q8—24no—
668Q8—24no—
669Q8—42no—
670Q8—42no—
671Q8—42no—
672Q8—42no—
673Q8—42no—
674Q8—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—81no—
680D4—81no—
681D4—81no—
682D4—81no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4C2×#11711yescharacteristic
775C2×C4C2×C4×D411yescharacteristic
776C2×C4#51811yescharacteristic
777C2×C4#51811yescharacteristic
778C2×C4#52011yescharacteristic
779C2×C4#52011yescharacteristic
780C2×C4#53511yescharacteristic
781C2×C4#53711yescharacteristic
782C2×C4#53811yescharacteristic
783C2×C4#53811yescharacteristic
784C2×C4#53911yescharacteristic
785C2×C4#53911yescharacteristic
786C2×C4#54011yescharacteristic
787C2×C4#54011yescharacteristic
788C2×C4#54011yescharacteristic
789C2×C4#54211yescharacteristic
790C2×C4#54611yescharacteristic
791C2×C4#54611yescharacteristic
792C2×C4#54811yescharacteristic
793C2×C4#55111yescharacteristic
794C2×C4#55111yescharacteristic
795C2×C4#55211yescharacteristic
796C2×C4#55311yescharacteristic
797C2×C4#55311yescharacteristic
798C2×C4H(3,𝔽4)11yescharacteristic
799C2×C4#56211yescharacteristic
800C2×C4#56211yescharacteristic
801C2×C4#56311yescharacteristic
802C8—24no—
803C8—42no—
804C8—81no—
805C8—81no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—161no—
814C22—161no—
815C22—161no—
816C22—161no—
817C22—161no—
818C22—161no—
819C22—161no—
820C22—161no—
821C22#232811yescharacteristic
822C22#235211yescharacteristic
823C22#236111yescharacteristic
824C22#267011yescharacteristic
825C22#267611yescharacteristic
826C22#270611yescharacteristic
827C22#272311yescharacteristic
828C22C4×#13511yescharacteristic
829C22#294311yescharacteristic
830C22#294911yescharacteristic
831C22#294911yescharacteristic
832C22#321111yescharacteristic
833C22#321111yescharacteristic
834C22#321211yescharacteristic
835C22#321211yescharacteristic
836C22#322111yescharacteristic
837C22#322111yescharacteristic
838C22#322211yescharacteristic
839C22#322211yescharacteristic
840C22#326711yescharacteristic
841C22#327111yescharacteristic
842C22#328211yescharacteristic
843C22#328411yescharacteristic
844C22#330111yescharacteristic
845C22#330111yescharacteristic
846C22#332611yescharacteristic
847C22#332611yescharacteristic
848C22#333711yescharacteristic
849C22#334011yescharacteristic
850C22#334811yescharacteristic
851C22#335011yescharacteristic
852C22#336511yescharacteristic
853C22#336511yescharacteristic
854C22#337111yescharacteristic
855C22#337111yescharacteristic
856C4—44no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—82no—
862C4—81no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—82no—
867C4—161no—
868C4—161no—
869C4#231811yescharacteristic
870C4#232411yescharacteristic
871C4#234211yescharacteristic
872C4#237911yescharacteristic
873C4#270711yescharacteristic
874C4#271111yescharacteristic
875C4#275311yescharacteristic
876C4#276111yescharacteristic
877C2—162no—
878C2#1437711yescharacteristic
879C2#2227111yescharacteristic
880C2#2227511yescharacteristic
881C2#2276511yescharacteristic
882C2#2277311yescharacteristic
883C2#2302311yescharacteristic
884C2#2303311yescharacteristic
885C2#3052611yescharacteristic
886C2#3053311yescharacteristic
887C2#3088411yescharacteristic
888C2#3088911yescharacteristic
889C2#3194311yescharacteristic
890C2#3194411yescharacteristic
891C2#3243611yescharacteristic
892C2#3244111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1835C2semidirect
5. #13978C2semidirect
6. #11220C2semidirect
9. #11052C2semidirect
12. #10932C2semidirect
13. #10908C2semidirect
14. #10797C2semidirect
15. #10789C2semidirect
35. #1968C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19682
C2×#18802
C2×#18352
#140022
#139782
#112202
#111892
#110662
#110522
#110512
#110232
#109322
#109082
#107972
#107892