Finite Group Databasebeta

← #359244

Subgroups — #359244

Order 512.

1238 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2077C211yesmaximal, characteristic
2C2×C4×#106C211yesmaximal, characteristic, complemented
3C2×#1750C211yesmaximal, characteristic
4#13777C211yesmaximal, characteristic
5#13777C211yesmaximal, characteristic
6#11378C211yesmaximal, characteristic, complemented
7#11316C211yesmaximal, characteristic, complemented
8#11315C211yesmaximal, characteristic, complemented
9#11257C211yesmaximal, characteristic, complemented
10#11200C211yesmaximal, characteristic
11#11199C211yesmaximal, characteristic
12#11095C211yesmaximal, characteristic
13#10703C211yesmaximal, characteristic, complemented
14#10703C211yesmaximal, characteristic, complemented
15C4×#340C211yesmaximal, characteristic, complemented
16C22×#117C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×#97C2211yescharacteristic
22C22×C4×C8C2211yescharacteristic
23C2×#380C2211yescharacteristic
24C2×#380C2211yescharacteristic
25C2×#380C2211yescharacteristic
26C2×#380C2211yescharacteristic
27C2×C4×C4⋊C4C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31#2077C418yescomplemented
32C4×#106—24no—
33#1750—24no—
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50#1437—21no—
51#1437—21no—
52#1437—21no—
53#1437—21no—
54#1436—21no—
55#1436—21no—
56#1436—21no—
57#1436—21no—
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C24×C4C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C2×#117—22no—
68C2×#117—22no—
69C2×#117—22no—
70C2×#117—22no—
71C2×#117—22no—
72C2×#117—22no—
73C22×C4⋊C4D411yescharacteristic
74C22×C4⋊C4D411yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
88C22×C22⋊C4D411yescharacteristic
89C22×C42—21no—
90C22×C42—21no—
91C22×C42—21no—
92C22×C42—21no—
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C2×#106—22no—
96C2×#106—22no—
97C2×#106—22no—
98C2×#106—22no—
99C2×#106—22no—
100C2×#106C2×C414yes—
101C2×C22⋊C8—22no—
102C2×C22⋊C8—22no—
103C2×C22⋊C8—22no—
104C2×C22⋊C8—22no—
105C2×C22⋊C8—22no—
106C2×C22⋊C8C2×C414yes—
107C2×#97—22no—
108C2×#97—22no—
109C2×#97—22no—
110C2×C4×C8—22no—
111C2×C4×C8—22no—
112C2×C4×C8D414yes—
113#380—22no—
114#380—22no—
115#380—22no—
116#380—22no—
117#380—22no—
118#380—22no—
119#380C2×C414yes—
120#380C2×C414yes—
121C4×C4⋊C4—22no—
122C4×C4⋊C4—22no—
123C4×C4⋊C4—22no—
124C4×C4⋊C4—22no—
125C4×C4⋊C4—22no—
126C4×C4⋊C4—22no—
127C4×C4⋊C4—22no—
128C4×C4⋊C4—22no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
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—
145#340—22no—
146#340—22no—
147#340—22no—
148#340—22no—
149#340—22no—
150#340—22no—
151#340—22no—
152#340—22no—
153#340—22no—
154#340—22no—
155#340—22no—
156#340C2×C414yes—
157#340C2×C414yes—
158#340C2×C414yes—
159#336—22no—
160#336—22no—
161C25C2×D411yescharacteristic
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4C22×C412yes—
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4#4112yes—
189C23×C4C2411yescharacteristic
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
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×C8C22×C412yes—
213C22×C8C22×C412yes—
214C22×C8C2×D412yes—
215C22×C8C2×D412yes—
216C22×C8#4112yes—
217C22×C8#4112yes—
218#117—44no—
219#117—44no—
220#117—44no—
221#117—44no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
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—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
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⋊C4C22×C412yes—
269C2×C4⋊C4C22×C412yes—
270C2×C4⋊C4C22×C412yes—
271C2×C4⋊C4C22×C412yes—
272C2×C4⋊C4#4112yes—
273C2×C4⋊C4#4112yes—
274C2×C4⋊C4#4112yes—
275C2×C4⋊C4#4112yes—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—81no—
287C2×C22⋊C4—81no—
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×C42—21no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—42no—
301C2×C42—42no—
302C2×C42—42no—
303C2×C42—42no—
304C2×C42—81no—
305C2×C42—81no—
306C2×C42—81no—
307C2×C42—81no—
308C2×C42—81no—
309C2×C42—81no—
310C2×C42—81no—
311C2×C42—81no—
312C2×C42C2×D412yes—
313C2×C42#4112yes—
314C2×C42#4112yes—
315C2×C42#4112yes—
316C2×C42#4112yes—
317C2×C42#4112yes—
318#106—28no—
319#106—28no—
320C22⋊C8—28no—
321C22⋊C8—28no—
322#97—44no—
323C4×C8—28no—
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—42no—
329#95—42no—
330#95—42no—
331#95—42no—
332#95—81no—
333#95—81no—
334#95—81no—
335#95—81no—
336#95—81no—
337#95—81no—
338#95—81no—
339#95—81no—
340C24—21no—
341C24—21no—
342C24—21no—
343C24—21no—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—21no—
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24C4×D412yes—
355C24C22×D411yescharacteristic
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
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—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
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×C4C4×D412yes—
469C22×C4#12112yes—
470C22×C4#12112yes—
471C22×C4#12312yes—
472C22×C4#12312yes—
473C22×C4#12312yes—
474C22×C4#12312yes—
475C22×C4C23×C411yescharacteristic
476C22×C4C22×D411yescharacteristic
477C22×C4C2×#4111yescharacteristic
478C22×C4C2×#4111yescharacteristic
479C22×C4C2×#4111yescharacteristic
480C22×C4C2×#4111yescharacteristic
481C22×C4C2×#4111yescharacteristic
482C22×C4C2×#4111yescharacteristic
483C22×C4C2×#4111yescharacteristic
484C22×C4C2×#4111yescharacteristic
485C22×C4C2×#4111yescharacteristic
486C22×C4C2×#4111yescharacteristic
487C22×C4C2×#4111yescharacteristic
488C22×C4C2×#4111yescharacteristic
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8C4×D414yes—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—44no—
550C4⋊C4—44no—
551C22⋊C4—44no—
552C22⋊C4—44no—
553C22⋊C4—84no—
554C22⋊C4—84no—
555C22⋊C4—84no—
556C22⋊C4—84no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42—41no—
561C42—84no—
562C42—84no—
563C42—84no—
564C42—84no—
565C42#12314yes—
566C42#12414yes—
567C42#12614yes—
568C42#12614yes—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C2×C4×D411yescharacteristic
605C23C2×#12111yescharacteristic
606C23C2×#12311yescharacteristic
607C23C2×#12311yescharacteristic
608C23#52511yescharacteristic
609C23#52511yescharacteristic
610C23#53211yescharacteristic
611C23#57611yescharacteristic
612C23#57711yescharacteristic
613C23#57711yescharacteristic
614C23#57711yescharacteristic
615C23#57711yescharacteristic
616C23#57711yescharacteristic
617C23#57711yescharacteristic
618C23#57811yescharacteristic
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
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#39714yes—
717C2×C4#39714yes—
718C2×C4C2×C4×D411yescharacteristic
719C2×C4C4×#4111yescharacteristic
720C2×C4C4×#4111yescharacteristic
721C2×C4C4×#4111yescharacteristic
722C2×C4C4×#4111yescharacteristic
723C2×C4C4×#4111yescharacteristic
724C2×C4C2×#12311yescharacteristic
725C2×C4#52511yescharacteristic
726C2×C4#52511yescharacteristic
727C2×C4C2×#12411yescharacteristic
728C2×C4C2×#12611yescharacteristic
729C2×C4C2×#12611yescharacteristic
730C2×C4#52911yescharacteristic
731C2×C4#52911yescharacteristic
732C2×C4#52911yescharacteristic
733C2×C4#52911yescharacteristic
734C2×C4#52911yescharacteristic
735C2×C4#52911yescharacteristic
736C2×C4#52911yescharacteristic
737C2×C4#52911yescharacteristic
738C2×C4#52911yescharacteristic
739C2×C4#52911yescharacteristic
740C2×C4#52911yescharacteristic
741C2×C4#52911yescharacteristic
742C2×C4#52911yescharacteristic
743C2×C4#52911yescharacteristic
744C2×C4#52911yescharacteristic
745C2×C4#53211yescharacteristic
746C8—24no—
747C8—42no—
748C8—42no—
749C8—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22C4×#12111yescharacteristic
766C22C4×#12311yescharacteristic
767C22C4×#12311yescharacteristic
768C22C2×#39711yescharacteristic
769C22#239211yescharacteristic
770C22#239511yescharacteristic
771C22#239511yescharacteristic
772C22#294611yescharacteristic
773C22#294711yescharacteristic
774C22#294911yescharacteristic
775C22#295211yescharacteristic
776C22#305711yescharacteristic
777C22#305711yescharacteristic
778C22#306011yescharacteristic
779C22#306111yescharacteristic
780C22#309611yescharacteristic
781C22#309611yescharacteristic
782C22#309711yescharacteristic
783C22#309711yescharacteristic
784C22#309911yescharacteristic
785C22#309911yescharacteristic
786C22#309911yescharacteristic
787C22#309911yescharacteristic
788C22#311811yescharacteristic
789C22#311911yescharacteristic
790C22#312011yescharacteristic
791C22#312111yescharacteristic
792C22#312311yescharacteristic
793C22#312511yescharacteristic
794C22#312511yescharacteristic
795C22#312611yescharacteristic
796C22#317311yescharacteristic
797C22#317411yescharacteristic
798C22#317811yescharacteristic
799C22#317911yescharacteristic
800C4—24no—
801C4—24no—
802C4—42no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4—81no—
808C4—81no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4C4×#12311yescharacteristic
814C4C4×#12411yescharacteristic
815C4C4×#12611yescharacteristic
816C4C4×#12611yescharacteristic
817C4#239511yescharacteristic
818C4#239811yescharacteristic
819C4#240111yescharacteristic
820C4#240111yescharacteristic
821C2—82no—
822C2C4×#39711yescharacteristic
823C2#2152311yescharacteristic
824C2#2153511yescharacteristic
825C2#2158411yescharacteristic
826C2#2158711yescharacteristic
827C2#2158811yescharacteristic
828C2#2159111yescharacteristic
829C2#2364011yescharacteristic
830C2#2364111yescharacteristic
831C2#2370611yescharacteristic
832C2#2370711yescharacteristic
833C2#2376611yescharacteristic
834C2#2376911yescharacteristic
835C2#2377111yescharacteristic
836C2#2377211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×#106C2semidirect
6. #11378C2semidirect
7. #11316C2semidirect
8. #11315C2semidirect
9. #11257C2semidirect
13. #10703C2semidirect
14. #10703C2semidirect
15. C4×#340C2semidirect
31. #2077C4semidirect

Maximal subgroups

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

subgroupindex
C2×#20772
C2×C4×#1062
C2×#17502
#137772
#113782
#113162
#113152
#112572
#112002
#111992
#110952
#107032
C4×#3402