Finite Group Databasebeta

← #385264

Subgroups — #385264

Order 512.

1308 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1936C211yesmaximal, characteristic
2C2×#1925C211yesmaximal, characteristic
3C2×#1864C211yesmaximal, characteristic
4#13977C211yesmaximal, characteristic
5#13918C211yesmaximal, characteristic, complemented
6#11327C211yesmaximal, characteristic, complemented
7#11323C211yesmaximal, characteristic, complemented
8#11293C211yesmaximal, characteristic, complemented
9#11219C211yesmaximal, characteristic, complemented
10#11121C211yesmaximal, characteristic
11#11076C211yesmaximal, characteristic
12#10877C211yesmaximal, characteristic, complemented
13#10863C211yesmaximal, characteristic, complemented
14#10849C211yesmaximal, characteristic, complemented
15#10788C211yesmaximal, characteristic
16C22×C4×D4C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#390C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#385—21no—
32C2×#385—21no—
33C2×#384C2211yescharacteristic
34C2×#382—21no—
35C2×C4×C4⋊C4C2211yescharacteristic
36#1936—24no—
37#1925C418yescomplemented
38#1864—24no—
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52#1442—21no—
53#1442—21no—
54#1439—21no—
55#1439—21no—
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60#1434—21no—
61C4×#95C2211yescharacteristic
62C23×D4C2311yescharacteristic
63C24×C4—21no—
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×C4×D4—22no—
69C2×C4×D4—22no—
70C2×C4×D4—41no—
71C2×C4×D4—41no—
72C2×C4×D4—41no—
73C2×C4×D4—41no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C22⋊C4—21no—
87C22×C22⋊C4—21no—
88C22×C22⋊C4—21no—
89C22×C22⋊C4—21no—
90C22×C22⋊C4—21no—
91C22×C42—21no—
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C2×#107—41no—
96C2×#107—41no—
97C2×#107C2×C414yescomplemented
98C2×#106—22no—
99C2×#106—22no—
100C2×#106—41no—
101C2×#106—41no—
102C2×#106—41no—
103C2×#106—41no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—41no—
107C2×#102—22no—
108C2×#102—22no—
109C2×#102—22no—
110C2×#102—41no—
111C2×#102—41no—
112C2×#102—41no—
113C2×#102—41no—
114C2×#102—41no—
115C2×#102C2×C414yes—
116C2×#102C2×C414yes—
117C2×#102D414yes—
118C2×#102Q814yes—
119C2×#97—22no—
120C2×#97—22no—
121C2×#97—41no—
122#390—22no—
123#390—22no—
124#390—41no—
125#390C2×C414yes—
126#389—22no—
127#389—22no—
128#389—41no—
129#389—41no—
130#389—41no—
131#389—41no—
132#385—44no—
133#385—44no—
134#384—22no—
135#384—41no—
136#382—44no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4C2×C414yescomplemented
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×#95D411yescharacteristic
152C2×#95D411yescharacteristic
153C2×#95D411yescharacteristic
154C2×#95D411yescharacteristic
155#340—22no—
156#340—22no—
157#340—22no—
158#340—41no—
159#340—41no—
160#340—41no—
161#340—41no—
162#340—41no—
163#340C2×C414yescomplemented
164#336—22no—
165#336—41no—
166#336—41no—
167#336C2×C414yescomplemented
168C25—21no—
169C22×D4—21no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4—21no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4C22×C412yes—
181C22×D4C2×D412yes—
182C22×D4C2×Q812yes—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—42no—
191C23×C4—42no—
192C23×C4—42no—
193C23×C4—42no—
194C23×C4—42no—
195C23×C4—81no—
196C23×C4—81no—
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2×D411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4C2411yescharacteristic
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8C22×C412yes—
228C22×C8C22×C412yes—
229C22×C8C2×D412yes—
230C22×C8C2×Q812yes—
231C22×C8#4112yes—
232C4×D4—44no—
233C4×D4—44no—
234C4×D4—44no—
235C4×D4—44no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
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—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—81no—
284C2×C4⋊C4—81no—
285C2×C4⋊C4—81no—
286C2×C4⋊C4—81no—
287C2×C4⋊C4C22×C412yes—
288C2×C4⋊C4C22×C412yes—
289C2×C4⋊C4C22×C412yes—
290C2×C4⋊C4C2×D412yes—
291C2×C4⋊C4C2×Q812yes—
292C2×C4⋊C4#4112yes—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
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—81no—
307C2×C22⋊C4—81no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—24no—
313C2×C42—21no—
314C2×C42—21no—
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—42no—
326C2×C42—42no—
327C2×C42C22×C412yes—
328C2×C42#4112yes—
329#107—44no—
330#106—44no—
331#106—44no—
332C4⋊C8—44no—
333#102—44no—
334#102—44no—
335#102—44no—
336#102C4⋊C4116yescomplemented
337#97—44no—
338#95—24no—
339#95—22no—
340#95—22no—
341#95—22no—
342#95—41no—
343#95—42no—
344#95—42no—
345#95—42no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—81no—
354C24—22no—
355C24—22no—
356C24—22no—
357C24—41no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—41no—
363C24—41no—
364C24—41no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24C22×D411yescharacteristic
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4C2×C4⋊C414yes—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
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—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—48no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
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—84no—
486C22×C4—84no—
487C22×C4—84no—
488C22×C4—84no—
489C22×C4—84no—
490C22×C4—84no—
491C22×C4C4×D412yes—
492C22×C4C4×D412yes—
493C22×C4AGL(1,ℤ/8)12yes—
494C22×C4AGL(1,ℤ/8)12yes—
495C22×C4AGL(1,ℤ/8)12yes—
496C22×C4C23×C411yescharacteristic
497C22×C4C22×D411yescharacteristic
498C22×C4C22×Q811yescharacteristic
499C22×C4C2×#4111yescharacteristic
500C22×C4C2×#4111yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4H(5,𝔽2)11yescharacteristic
503C22×C4H(5,𝔽2)11yescharacteristic
504C22×C4H(5,𝔽2)11yescharacteristic
505C22×C4H(5,𝔽2)11yescharacteristic
506C22×C4H(5,𝔽2)11yescharacteristic
507C22×C42−1+411yescharacteristic
508C22×C42−1+411yescharacteristic
509C22×C42−1+411yescharacteristic
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8C2×C4⋊C414yes—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—84no—
566C4⋊C4—84no—
567C4⋊C4—84no—
568C4⋊C4—84no—
569C4⋊C4—84no—
570C4⋊C4C2×C4⋊C414yes—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—84no—
575C22⋊C4—84no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—48no—
589C23—24no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23—81no—
616C23—81no—
617C23—81no—
618C23—81no—
619C23—81no—
620C23—81no—
621C23—81no—
622C23—81no—
623C23—81no—
624C23C2×C4×D411yescharacteristic
625C23#53511yescharacteristic
626C23#53711yescharacteristic
627C23D4211yescharacteristic
628C23#54611yescharacteristic
629C23#54711yescharacteristic
630C23D4×Q811yescharacteristic
631C23C2×AGL(1,ℤ/8)11yescharacteristic
632C23C2×AGL(1,ℤ/8)11yescharacteristic
633C23C2×AGL(1,ℤ/8)11yescharacteristic
634C23#57511yescharacteristic
635C23#57711yescharacteristic
636C23#57711yescharacteristic
637C23#57711yescharacteristic
638C23#57811yescharacteristic
639D4—24no—
640D4—24no—
641D4—42no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
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—816no—
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×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4#44214yes—
739C2×C4C22×C4⋊C411yescharacteristic
740C2×C4C4×#4111yescharacteristic
741C2×C4#51811yescharacteristic
742C2×C4#52011yescharacteristic
743C2×C4#52011yescharacteristic
744C2×C4#52011yescharacteristic
745C2×C4#53511yescharacteristic
746C2×C4#53611yescharacteristic
747C2×C4#53811yescharacteristic
748C2×C4#53911yescharacteristic
749C2×C4#54011yescharacteristic
750C2×C4#54111yescharacteristic
751C2×C4#54211yescharacteristic
752C2×C4#54211yescharacteristic
753C2×C4#54411yescharacteristic
754C2×C4#54411yescharacteristic
755C2×C4#54611yescharacteristic
756C2×C4#54611yescharacteristic
757C2×C4#54711yescharacteristic
758C2×C4#55111yescharacteristic
759C2×C4#55211yescharacteristic
760C2×C4#55411yescharacteristic
761C2×C4#55411yescharacteristic
762C2×C4#55411yescharacteristic
763C2×C4H(3,𝔽4)11yescharacteristic
764C2×C4#56211yescharacteristic
765C2×C4#56211yescharacteristic
766C2×C4#56311yescharacteristic
767C8—24no—
768C8—42no—
769C8—42no—
770C8—81no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22#232411yescharacteristic
787C22D4×C4⋊C411yescharacteristic
788C22#235911yescharacteristic
789C22#267011yescharacteristic
790C22#267211yescharacteristic
791C22#270411yescharacteristic
792C22#272011yescharacteristic
793C22C2×#44211yescharacteristic
794C22C4×AGL(1,ℤ/8)11yescharacteristic
795C22#294711yescharacteristic
796C22#295211yescharacteristic
797C22#321411yescharacteristic
798C22#321711yescharacteristic
799C22#322211yescharacteristic
800C22#322511yescharacteristic
801C22#325111yescharacteristic
802C22#325311yescharacteristic
803C22#325811yescharacteristic
804C22#326311yescharacteristic
805C22#326511yescharacteristic
806C22#326911yescharacteristic
807C22#327211yescharacteristic
808C22#327211yescharacteristic
809C22#330811yescharacteristic
810C22#331011yescharacteristic
811C22#331011yescharacteristic
812C22#332111yescharacteristic
813C22#334311yescharacteristic
814C22#334511yescharacteristic
815C22#335111yescharacteristic
816C22#335411yescharacteristic
817C22#338411yescharacteristic
818C22#338411yescharacteristic
819C22#338611yescharacteristic
820C22#338811yescharacteristic
821C4—24no—
822C4—42no—
823C4—42no—
824C4—44no—
825C4—81no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—81no—
830C4—81no—
831C4—161no—
832C4—161no—
833C4—161no—
834C4#231711yescharacteristic
835C4#233411yescharacteristic
836C4#234911yescharacteristic
837C4#237911yescharacteristic
838C4#269811yescharacteristic
839C4#270611yescharacteristic
840C4#276311yescharacteristic
841C4#276811yescharacteristic
842C2—84no—
843C2#1440311yescharacteristic
844C2#2215111yescharacteristic
845C2#2215911yescharacteristic
846C2#2267011yescharacteristic
847C2#2267711yescharacteristic
848C2#2292411yescharacteristic
849C2#2293811yescharacteristic
850C2#3054511yescharacteristic
851C2#3054711yescharacteristic
852C2#3068711yescharacteristic
853C2#3068911yescharacteristic
854C2#3188611yescharacteristic
855C2#3189511yescharacteristic
856C2#3236411yescharacteristic
857C2#3236811yescharacteristic
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
5. #13918C2semidirect
6. #11327C2semidirect
7. #11323C2semidirect
8. #11293C2semidirect
9. #11219C2semidirect
12. #10877C2semidirect
13. #10863C2semidirect
14. #10849C2semidirect
37. #1925C4semidirect
97. C2×#107C2×C4semidirect
138. C4×C4⋊C4C2×C4semidirect
163. #340C2×C4semidirect
167. #336C2×C4semidirect
336. #102C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19362
C2×#19252
C2×#18642
#139772
#139182
#113272
#113232
#112932
#112192
#111212
#110762
#108772
#108632
#108492
#107882