Finite Group Databasebeta

← #377939

Subgroups — #377939

Order 512.

1398 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2067C211yesmaximal, characteristic
2C2×#1949C211yesmaximal, characteristic, complemented
3C2×#1864C211yesmaximal, characteristic
4C2×#1862C211yesmaximal, characteristic
5C2×C4×#107C211yesmaximal, characteristic, complemented
6#14006C211yesmaximal, characteristic, complemented
7#13820C211yesmaximal, characteristic
8#11293C211yesmaximal, characteristic, complemented
9#11219C211yesmaximal, characteristic, complemented
10#11051C211yesmaximal, characteristic
11#10931C211yesmaximal, characteristic
12#10925C211yesmaximal, characteristic
13#10908C211yesmaximal, characteristic, complemented
14#10885C211yesmaximal, characteristic, complemented
15#10876C211yesmaximal, characteristic, complemented
16C22×C4×D4C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#390C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#382C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C22⋊C4—21no—
36#2067C418yescomplemented
37#1949—24no—
38#1864—24no—
39#1862—24no—
40C4×#107—24no—
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54#1442—21no—
55#1441—21no—
56#1437—21no—
57#1437—21no—
58#1436—21no—
59C4⋊#95—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C22⋊#95—21no—
63C4×#95C2211yescharacteristic
64C23×D4C2311yescharacteristic
65C24×C4—21no—
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×C4×D4—22no—
71C2×C4×D4—22no—
72C2×C4×D4—22no—
73C2×C4×D4—22no—
74C2×C4×D4—41no—
75C2×C4×D4—41no—
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×C42—21no—
93C22×C42—21no—
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C2×#107—22no—
98C2×#107—22no—
99C2×#107—22no—
100C2×#107—22no—
101C2×#107C2×C414yescomplemented
102C2×#107D414yes—
103C2×#106—22no—
104C2×#106—22no—
105C2×#106—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×C4⋊C8C2×C414yescomplemented
109C2×#102—22no—
110C2×#102—22no—
111C2×#102—22no—
112C2×#102—22no—
113C2×#102—22no—
114C2×#102—22no—
115C2×#102—22no—
116C2×#102—22no—
117C2×#102—41no—
118C2×#102—41no—
119C2×#102C2×C414yes—
120C2×#102C2×C414yes—
121C2×C4×C8—22no—
122C2×C4×C8—22no—
123C2×C4×C8—22no—
124#390—22no—
125#390—22no—
126#390C2×C414yes—
127#390Q814yes—
128#389—22no—
129#389—22no—
130#389—22no—
131#389—41no—
132#389—41no—
133#389C2×C414yescomplemented
134#382—22no—
135#382—41no—
136C4×C4⋊C4—22no—
137C4×C4⋊C4—22no—
138C4×C4⋊C4—22no—
139C4×C4⋊C4—41no—
140C4×C4⋊C4—41no—
141C4×C4⋊C4—41no—
142C4×C22⋊C4—44no—
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×#95D411yescharacteristic
156C2×#95D411yescharacteristic
157C2×#95D411yescharacteristic
158C2×#95D411yescharacteristic
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—41no—
165#340—41no—
166#340C2×C414yescomplemented
167#340D414yes—
168#336—22no—
169#336—22no—
170#336—22no—
171#336—22no—
172C25—21no—
173C22×D4—21no—
174C22×D4—21no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4C22×C412yes—
185C22×D4C2×Q812yes—
186C22×D4#4112yes—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—24no—
194C23×C4—21no—
195C23×C4—42no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—81no—
200C23×C4—81no—
201C23×C4C2×D411yescharacteristic
202C23×C4C2×D411yescharacteristic
203C23×C4C2×D411yescharacteristic
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2411yescharacteristic
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×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8C22×C412yes—
232C22×C8C22×C412yes—
233C22×C8C2×D412yes—
234C22×C8C2×D412yes—
235C22×C8#4112yes—
236C4×D4—44no—
237C4×D4—44no—
238C4×D4—44no—
239C4×D4—44no—
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—24no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—81no—
278C2×C4⋊C4—81no—
279C2×C4⋊C4—81no—
280C2×C4⋊C4—81no—
281C2×C4⋊C4C22×C412yes—
282C2×C4⋊C4C22×C412yes—
283C2×C4⋊C4C22×C412yes—
284C2×C4⋊C4C2×D412yes—
285C2×C4⋊C4C2×D412yes—
286C2×C4⋊C4C2×D412yes—
287C2×C4⋊C4C2×D412yes—
288C2×C4⋊C4C2×Q812yes—
289C2×C4⋊C4#4112yes—
290C2×C4⋊C4#4112yes—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
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—81no—
303C2×C22⋊C4—81no—
304C2×C22⋊C4—81no—
305C2×C22⋊C4—81no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—42no—
321C2×C42—42no—
322C2×C42—42no—
323C2×C42—42no—
324C2×C42—42no—
325C2×C42—42no—
326C2×C42—81no—
327C2×C42—81no—
328C2×C42—81no—
329C2×C42C22×C412yes—
330C2×C42C2×Q812yes—
331C2×C42#4112yes—
332C2×C42#4112yes—
333#107—28no—
334#107—28no—
335#106—44no—
336C4⋊C8—28no—
337#102—28no—
338#102—28no—
339#102—44no—
340#102—44no—
341C4×C8—28no—
342#95—24no—
343#95—22no—
344#95—22no—
345#95—22no—
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—81no—
357#95—81no—
358C24—22no—
359C24—22no—
360C24—22no—
361C24—41no—
362C24—41no—
363C24—41no—
364C24—41no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24C22×D411yescharacteristic
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—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
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×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4C4×Q814yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
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—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—48no—
448C22×C4—48no—
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—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—84no—
489C22×C4—84no—
490C22×C4—84no—
491C22×C4—84no—
492C22×C4—84no—
493C22×C4C4×D412yes—
494C22×C4C4×D412yes—
495C22×C4C22⋊Q812yes—
496C22×C4C22⋊Q812yes—
497C22×C4#13512yes—
498C22×C4#13512yes—
499C22×C4AGL(1,ℤ/8)12yes—
500C22×C4C23×C411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×D411yescharacteristic
503C22×C4C22×Q811yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4C2×#4111yescharacteristic
508C22×C4C2×#4111yescharacteristic
509C22×C4C2×#4111yescharacteristic
510C22×C4H(5,𝔽2)11yescharacteristic
511C22×C4H(5,𝔽2)11yescharacteristic
512C22×C42−1+411yescharacteristic
513C22×C42−1+411yescharacteristic
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—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
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×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8C4×D414yes—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
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—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—84no—
569C4⋊C4—84no—
570C4⋊C4—84no—
571C4⋊C4C4×D414yes—
572C4⋊C4#12114yes—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—84no—
577C22⋊C4—84no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—84no—
591C42—84no—
592C42—84no—
593C23—24no—
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—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23—81no—
616C23—81no—
617C23—81no—
618C23—81no—
619C23—81no—
620C23—81no—
621C23—81no—
622C23—81no—
623C23—81no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23—81no—
628C23C2×C4×D411yescharacteristic
629C23C2×C22⋊Q811yescharacteristic
630C23#52511yescharacteristic
631C23D4211yescharacteristic
632C23D4211yescharacteristic
633C23#54711yescharacteristic
634C23#54811yescharacteristic
635C23C2×#13511yescharacteristic
636C23C2×#13511yescharacteristic
637C23C2×AGL(1,ℤ/8)11yescharacteristic
638C23#57511yescharacteristic
639C23#57611yescharacteristic
640C23#57611yescharacteristic
641C23#57711yescharacteristic
642C23#57811yescharacteristic
643D4—24no—
644D4—24no—
645D4—42no—
646D4—42no—
647D4—42no—
648D4—42no—
649D4—42no—
650D4—42no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—816no—
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—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4#47814yes—
743C2×C4C2×C4×D411yescharacteristic
744C2×C4C2×C4×D411yescharacteristic
745C2×C4C2×C4×Q811yescharacteristic
746C2×C4C4×#4111yescharacteristic
747C2×C4#52011yescharacteristic
748C2×C4#52011yescharacteristic
749C2×C4C2×#12111yescharacteristic
750C2×C4#52511yescharacteristic
751C2×C4#52911yescharacteristic
752C2×C4#52911yescharacteristic
753C2×C4#53211yescharacteristic
754C2×C4#53311yescharacteristic
755C2×C4#53811yescharacteristic
756C2×C4#53911yescharacteristic
757C2×C4#54111yescharacteristic
758C2×C4#54211yescharacteristic
759C2×C4#54611yescharacteristic
760C2×C4#54611yescharacteristic
761C2×C4#54711yescharacteristic
762C2×C4#54811yescharacteristic
763C2×C4D4×Q811yescharacteristic
764C2×C4D4×Q811yescharacteristic
765C2×C4#55211yescharacteristic
766C2×C4#55211yescharacteristic
767C2×C4#55311yescharacteristic
768C2×C4#55311yescharacteristic
769C2×C4#55411yescharacteristic
770C2×C4#55411yescharacteristic
771C8—24no—
772C8—42no—
773C8—42no—
774C8—81no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22C4×C22⋊Q811yescharacteristic
791C22#236111yescharacteristic
792C22#236111yescharacteristic
793C22#242411yescharacteristic
794C22#244911yescharacteristic
795C22#245211yescharacteristic
796C22#247511yescharacteristic
797C22C4×#13511yescharacteristic
798C22C4×AGL(1,ℤ/8)11yescharacteristic
799C22#294711yescharacteristic
800C22#294811yescharacteristic
801C22C2×#47811yescharacteristic
802C22#307611yescharacteristic
803C22#308111yescharacteristic
804C22#308311yescharacteristic
805C22#310211yescharacteristic
806C22#310511yescharacteristic
807C22#311811yescharacteristic
808C22#312411yescharacteristic
809C22#326411yescharacteristic
810C22#326811yescharacteristic
811C22#327211yescharacteristic
812C22#327711yescharacteristic
813C22#328011yescharacteristic
814C22#328211yescharacteristic
815C22#328511yescharacteristic
816C22#328711yescharacteristic
817C22#333911yescharacteristic
818C22#334111yescharacteristic
819C22#334311yescharacteristic
820C22#335011yescharacteristic
821C22#336411yescharacteristic
822C22#336511yescharacteristic
823C22#336611yescharacteristic
824C22#337011yescharacteristic
825C4—24no—
826C4—42no—
827C4—42no—
828C4—44no—
829C4—44no—
830C4—42no—
831C4—42no—
832C4—82no—
833C4—81no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—161no—
838C4C4×#12111yescharacteristic
839C4#233411yescharacteristic
840C4#236011yescharacteristic
841C4#236011yescharacteristic
842C4#242911yescharacteristic
843C4#247011yescharacteristic
844C4#255811yescharacteristic
845C4#258711yescharacteristic
846C2—84no—
847C2#1420411yescharacteristic
848C2C4×#47811yescharacteristic
849C2#2162411yescharacteristic
850C2#2300011yescharacteristic
851C2#2300811yescharacteristic
852C2#2302711yescharacteristic
853C2#2304011yescharacteristic
854C2#2516011yescharacteristic
855C2#2516311yescharacteristic
856C2#2634311yescharacteristic
857C2#2635011yescharacteristic
858C2#2646711yescharacteristic
859C2#2647111yescharacteristic
860C2#2736311yescharacteristic
861C2#2737211yescharacteristic
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
2. C2×#1949C2semidirect
5. C2×C4×#107C2semidirect
6. #14006C2semidirect
8. #11293C2semidirect
9. #11219C2semidirect
13. #10908C2semidirect
14. #10885C2semidirect
15. #10876C2semidirect
36. #2067C4semidirect
101. C2×#107C2×C4semidirect
108. C2×C4⋊C8C2×C4semidirect
133. #389C2×C4semidirect
166. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#20672
C2×#19492
C2×#18642
C2×#18622
C2×C4×#1072
#140062
#138202
#112932
#112192
#110512
#109312
#109252
#109082
#108852
#108762