Finite Group Databasebeta

← #355735

Subgroups — #355735

Order 512.

1342 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1934C211yesmaximal, characteristic
2C2×#1926C211yesmaximal, characteristic
3C2×#1864C211yesmaximal, characteristic
4#13785C211yesmaximal, characteristic
5#13783C211yesmaximal, characteristic, complemented
6#10931C211yesmaximal, characteristic
7#10927C211yesmaximal, characteristic
8#10908C211yesmaximal, characteristic, complemented
9#10908C211yesmaximal, characteristic, complemented
10#10884C211yesmaximal, characteristic, complemented
11#10881C211yesmaximal, characteristic, complemented
12#10861C211yesmaximal, characteristic, complemented
13#10806C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic
15#10694C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#97C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25C2×#390C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32C2×#376C2211yescharacteristic
33#1934C418yescomplemented
34#1926C418yescomplemented
35#1864C418yescomplemented
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50#1437—21no—
51#1437—21no—
52#1436—21no—
53#1436—21no—
54C4⋊#95—21no—
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59#1434—21no—
60C22⋊#95—21no—
61C22⋊#95—21no—
62C23×D4C2311yescharacteristic
63C24×C4—21no—
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C2×C4×D4—22no—
69C2×C4×D4—41no—
70C2×C4×D4—41no—
71C2×C4×D4—41no—
72C2×C4×D4—41no—
73C2×C4×D4C2×C414yes—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C22⋊C4—21no—
84C22×C22⋊C4—21no—
85C22×C22⋊C4—21no—
86C22×C22⋊C4—21no—
87C22×C22⋊C4—21no—
88C22×C42—21no—
89C22×C42—21no—
90C22×C42—21no—
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C2×#106—41no—
95C2×#106—41no—
96C2×#106—41no—
97C2×#106—41no—
98C2×#106C2×C414yes—
99C2×#106C2×C414yescomplemented
100C2×#102—41no—
101C2×#102—41no—
102C2×#102—41no—
103C2×#102—41no—
104C2×#102—41no—
105C2×#102—41no—
106C2×#102C2×C414yes—
107C2×#102C2×C414yes—
108C2×#102C2×C414yes—
109C2×#102C2×C414yes—
110C2×#102C2×C414yes—
111C2×#102C2×C414yes—
112C2×#97—22no—
113C2×#97—41no—
114C2×#97—41no—
115C2×C4×C8—41no—
116C2×C4×C8—41no—
117C2×C4×C8C2×C414yescomplemented
118#390—22no—
119#390—22no—
120#390C2×C414yes—
121#390C2×C414yes—
122#389—22no—
123#389—22no—
124#389C2×C414yes—
125#389C2×C414yescomplemented
126C4×C4⋊C4—22no—
127C4×C4⋊C4—41no—
128C4×C4⋊C4—41no—
129C4×C4⋊C4—41no—
130C4×C4⋊C4—41no—
131C4×C4⋊C4C2×C414yescomplemented
132#376—41no—
133#376—41no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
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×#95D411yescharacteristic
148C2×#95D411yescharacteristic
149C2×#95D411yescharacteristic
150C2×#95D411yescharacteristic
151#340—41no—
152#340—41no—
153#340—41no—
154#340—41no—
155#340—41no—
156#340—41no—
157#340C2×C414yes—
158#340C2×C414yescomplemented
159#340C2×C414yescomplemented
160#340C2×C414yescomplemented
161#336—22no—
162#336—22no—
163#336C2×C414yes—
164#336C2×C414yescomplemented
165C25—21no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4—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×D4C22×C412yes—
178C22×D4C22×C412yes—
179C22×D4C22×C412yes—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—24no—
188C23×C4—42no—
189C23×C4—42no—
190C23×C4—81no—
191C23×C4—81no—
192C23×C4—81no—
193C23×C4—81no—
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D411yescharacteristic
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2411yescharacteristic
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
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×C8C22×C412yes—
224C22×C8C22×C412yes—
225C22×C8C22×C412yes—
226C22×C8C22×C412yes—
227C22×C8C22×C412yes—
228C22×C8C22×C412yes—
229C4×D4—44no—
230C4×D4—44no—
231C4×D4—44no—
232C4×D4—44no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
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—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—81no—
269C2×C4⋊C4—81no—
270C2×C4⋊C4—81no—
271C2×C4⋊C4—81no—
272C2×C4⋊C4C22×C412yes—
273C2×C4⋊C4C22×C412yes—
274C2×C4⋊C4C22×C412yes—
275C2×C4⋊C4C22×C412yes—
276C2×C4⋊C4C22×C412yes—
277C2×C4⋊C4C22×C412yes—
278C2×C4⋊C4C22×C412yes—
279C2×C4⋊C4C22×C412yes—
280C2×C4⋊C4C22×C412yes—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—42no—
287C2×C22⋊C4—42no—
288C2×C22⋊C4—81no—
289C2×C22⋊C4—81no—
290C2×C22⋊C4—81no—
291C2×C22⋊C4—81no—
292C2×C22⋊C4—81no—
293C2×C22⋊C4—81no—
294C2×C22⋊C4—81no—
295C2×C22⋊C4—81no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—24no—
309C2×C42—42no—
310C2×C42—42no—
311C2×C42—81no—
312C2×C42—81no—
313C2×C42—81no—
314C2×C42—81no—
315C2×C42—81no—
316C2×C42—81no—
317C2×C42C22×C412yes—
318C2×C42C22×C412yes—
319C2×C42C22×C412yes—
320C2×C42#4112yes—
321C2×C42#4112yes—
322C2×C42#4112yes—
323#106—44no—
324#106—44no—
325#102—44no—
326#102—44no—
327#102—44no—
328#102C42116yescomplemented
329#97—44no—
330C4×C8—44no—
331#95—24no—
332#95—24no—
333#95—24no—
334#95—41no—
335#95—41no—
336#95—41no—
337#95—41no—
338#95—42no—
339#95—42no—
340#95—81no—
341#95—81no—
342#95—81no—
343#95—81no—
344#95—81no—
345#95—81no—
346#95—81no—
347#95—81no—
348C24—22no—
349C24—22no—
350C24—22no—
351C24—41no—
352C24—41no—
353C24—41no—
354C24—41no—
355C24—41no—
356C24—41no—
357C24—41no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—41no—
363C24C22×D411yescharacteristic
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
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—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4C2×C4214yes—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—48no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
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—84no—
479C22×C4—84no—
480C22×C4—84no—
481C22×C4—84no—
482C22×C4—84no—
483C22×C4—84no—
484C22×C4C4×D412yes—
485C22×C4C4×D412yes—
486C22×C4C4×D412yes—
487C22×C4C4×D412yes—
488C22×C4C4×D412yes—
489C22×C4C4×D412yes—
490C22×C4C23×C411yescharacteristic
491C22×C4C23×C411yescharacteristic
492C22×C4C23×C411yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4H(5,𝔽2)11yescharacteristic
497C22×C4H(5,𝔽2)11yescharacteristic
498C22×C4H(5,𝔽2)11yescharacteristic
499C22×C4H(5,𝔽2)11yescharacteristic
500C22×C4H(5,𝔽2)11yescharacteristic
501C22×C42−1+411yescharacteristic
502C22×C42−1+411yescharacteristic
503C22×C42−1+411yescharacteristic
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
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—41no—
520C2×C8—41no—
521C2×C8—41no—
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×C8C2×C4214yes—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
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—84no—
560C4⋊C4—84no—
561C4⋊C4C2×C4214yes—
562C22⋊C4—48no—
563C22⋊C4—84no—
564C22⋊C4—84no—
565C22⋊C4—84no—
566C22⋊C4—84no—
567C42—22no—
568C42—22no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—84no—
580C42—84no—
581C42—84no—
582C23—24no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—81no—
602C23—81no—
603C23—81no—
604C23—81no—
605C23—81no—
606C23—81no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23—81no—
616C23—81no—
617C23C2×C4×D411yescharacteristic
618C23C2×C4×D411yescharacteristic
619C23C2×C4×D411yescharacteristic
620C23#53411yescharacteristic
621C23#53511yescharacteristic
622C23#53611yescharacteristic
623C23#53711yescharacteristic
624C23#57611yescharacteristic
625C23#57611yescharacteristic
626C23#57711yescharacteristic
627C23#57711yescharacteristic
628C23#57711yescharacteristic
629C23#57711yescharacteristic
630C23#57711yescharacteristic
631C23#57711yescharacteristic
632D4—24no—
633D4—24no—
634D4—42no—
635D4—42no—
636D4—42no—
637D4—42no—
638D4—42no—
639D4—42no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
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—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
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—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
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—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—816no—
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×C4C22×C4211yescharacteristic
733C2×C4C4×#4111yescharacteristic
734C2×C4C4×#4111yescharacteristic
735C2×C4C4×#4111yescharacteristic
736C2×C4#51811yescharacteristic
737C2×C4#51811yescharacteristic
738C2×C4#51811yescharacteristic
739C2×C4#51811yescharacteristic
740C2×C4#51911yescharacteristic
741C2×C4#52011yescharacteristic
742C2×C4#52011yescharacteristic
743C2×C4#52011yescharacteristic
744C2×C4#52011yescharacteristic
745C2×C4#52011yescharacteristic
746C2×C4#52011yescharacteristic
747C2×C4#52011yescharacteristic
748C2×C4#53811yescharacteristic
749C2×C4#53811yescharacteristic
750C2×C4#53811yescharacteristic
751C2×C4#53911yescharacteristic
752C2×C4#53911yescharacteristic
753C2×C4#53911yescharacteristic
754C2×C4#54011yescharacteristic
755C2×C4#54111yescharacteristic
756C2×C4#54211yescharacteristic
757C2×C4#54211yescharacteristic
758C2×C4#54211yescharacteristic
759C2×C4#54211yescharacteristic
760C8—24no—
761C8—42no—
762C8—42no—
763C8—42no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22C42×D411yescharacteristic
780C22#232111yescharacteristic
781C22#232211yescharacteristic
782C22#232311yescharacteristic
783C22#232411yescharacteristic
784C22#232511yescharacteristic
785C22#232611yescharacteristic
786C22#294611yescharacteristic
787C22#294611yescharacteristic
788C22#294611yescharacteristic
789C22#294611yescharacteristic
790C22#294811yescharacteristic
791C22#294911yescharacteristic
792C22#294911yescharacteristic
793C22#294911yescharacteristic
794C22#295211yescharacteristic
795C22#295211yescharacteristic
796C22#295211yescharacteristic
797C22#295211yescharacteristic
798C22#319811yescharacteristic
799C22#319811yescharacteristic
800C22#320011yescharacteristic
801C22#320411yescharacteristic
802C22#322111yescharacteristic
803C22#322211yescharacteristic
804C22#322411yescharacteristic
805C22#322411yescharacteristic
806C22#324111yescharacteristic
807C22#324111yescharacteristic
808C22#324411yescharacteristic
809C22#324411yescharacteristic
810C22#325711yescharacteristic
811C22#325711yescharacteristic
812C22#326011yescharacteristic
813C22#326311yescharacteristic
814C4—44no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4#227411yescharacteristic
828C4#227511yescharacteristic
829C4#233211yescharacteristic
830C4#233411yescharacteristic
831C4#233411yescharacteristic
832C4#233511yescharacteristic
833C4#233511yescharacteristic
834C4#233711yescharacteristic
835C2—84no—
836C2#1378911yescharacteristic
837C2#2050311yescharacteristic
838C2#2050611yescharacteristic
839C2#2205211yescharacteristic
840C2#2205311yescharacteristic
841C2#2209011yescharacteristic
842C2#2209111yescharacteristic
843C2#2212211yescharacteristic
844C2#2212311yescharacteristic
845C2#2216011yescharacteristic
846C2#2216111yescharacteristic
847C2#2219311yescharacteristic
848C2#2219511yescharacteristic
849C2#2222711yescharacteristic
850C2#2223011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #13783C2semidirect
8. #10908C2semidirect
9. #10908C2semidirect
10. #10884C2semidirect
11. #10881C2semidirect
12. #10861C2semidirect
13. #10806C2semidirect
15. #10694C2semidirect
33. #1934C4semidirect
34. #1926C4semidirect
35. #1864C4semidirect
99. C2×#106C2×C4semidirect
117. C2×C4×C8C2×C4semidirect
125. #389C2×C4semidirect
131. C4×C4⋊C4C2×C4semidirect
158. #340C2×C4semidirect
159. #340C2×C4semidirect
160. #340C2×C4semidirect
164. #336C2×C4semidirect
328. #102C42semidirect

Maximal subgroups

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

subgroupindex
C2×#19342
C2×#19262
C2×#18642
#137852
#137832
#109312
#109272
#109082
#108842
#108812
#108612
#108062
#107882
#106942