Finite Group Databasebeta

← #367114

Subgroups — #367114

Order 512.

1580 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#462C211yesmaximal, characteristic
2C2×#1971C211yesmaximal, characteristic
3C2×#1969C211yesmaximal, characteristic
4C2×#1960C211yesmaximal, characteristic
5C2×#1949C211yesmaximal, characteristic
6C2×#1771C211yesmaximal, characteristic
7C2×#1763C211yesmaximal, characteristic
8#14155C211yesmaximal, characteristic
9#13942C211yesmaximal, characteristic
10#11124C211yesmaximal, characteristic
11#11122C211yesmaximal, characteristic
12#11024C211yesmaximal, characteristic
13#11024C211yesmaximal, characteristic
14#10928C211yesmaximal, characteristic
15#10926C211yesmaximal, characteristic
16C23×Q16C2211yescharacteristic
17C23×Q16C2211yescharacteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C2×#462—24no—
21C2×#462—24no—
22C2×#462C418yescomplemented
23C22×#107C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×C4⋊C8C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#103C2211yescharacteristic
29C22×#103C2211yescharacteristic
30C22×#103C2211yescharacteristic
31C22×#103C2211yescharacteristic
32C22×#103C2211yescharacteristic
33C22×#103C2211yescharacteristic
34C22×#97C2211yescharacteristic
35C22×#97C2211yescharacteristic
36C22×C4×C8C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#382C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46#1971—24no—
47#1969—24no—
48#1960—24no—
49#1949—24no—
50#1771—24no—
51#1763—24no—
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1445—22no—
59#1441—22no—
60C4⋊#95—22no—
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63#1434—22no—
64C23×Q8C2311yescharacteristic
65C23×Q8C2311yescharacteristic
66C23×Q8C2311yescharacteristic
67C22×Q16—22no—
68C22×Q16—22no—
69C22×Q16—22no—
70C22×Q16—22no—
71C22×Q16—22no—
72C22×Q16—22no—
73C22×Q16—22no—
74C22×Q16—22no—
75C22×Q16—41no—
76C22×Q16—41no—
77C22×Q16—41no—
78C22×Q16—41no—
79C22×Q16C2×C414yes—
80C22×Q16C2×C414yes—
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C2×C4⋊Q8—22no—
86C2×C4⋊Q8—22no—
87C2×C4⋊Q8—22no—
88C2×C4⋊Q8—22no—
89C2×C4⋊Q8—22no—
90C2×C4⋊Q8C2×C414yes—
91C2×C4×Q8—22no—
92C2×C4×Q8—22no—
93C2×C4×Q8—22no—
94C2×C4×Q8—22no—
95C2×C4×Q8—22no—
96C2×C4×Q8C2×C414yes—
97C22×C4⋊C4—21no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4—21no—
100C22×C4⋊C4D412yes—
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C42—21no—
107C22×C42—21no—
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111#462—232no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—41no—
115C2×#106—22no—
116C2×#106—22no—
117C2×#106—41no—
118C2×C4⋊C8C2×C414yes—
119C2×C4⋊C8D414yes—
120C2×C4⋊C8D414yes—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103—22no—
124C2×#103—22no—
125C2×#103—22no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103—22no—
132C2×#103—22no—
133C2×#103—22no—
134C2×#103—22no—
135C2×#103—22no—
136C2×#103—22no—
137C2×#103—22no—
138C2×#103—41no—
139C2×#103—41no—
140C2×#103—41no—
141C2×#103—41no—
142C2×#103C2×C414yes—
143C2×#103C2×C414yes—
144C2×#103D414yes—
145C2×#97—22no—
146C2×#97—22no—
147C2×#97—22no—
148C2×#97—22no—
149C2×#97—41no—
150C2×#97D414yes—
151C2×C4×C8—22no—
152C2×C4×C8—22no—
153C2×C4×C8—41no—
154#391—22no—
155#391—22no—
156#391—22no—
157#391—22no—
158#391—22no—
159#391—22no—
160#391—41no—
161#391—41no—
162#391—41no—
163#391—41no—
164#391—41no—
165#391—41no—
166#382—22no—
167#382—22no—
168C4×C4⋊C4—22no—
169C4×C4⋊C4—22no—
170C4×C4⋊C4—22no—
171C4×C4⋊C4—22no—
172C2×#95—21no—
173C2×#95—22no—
174C2×#95—22no—
175C2×#95—22no—
176C2×#95—22no—
177C2×#95—22no—
178C2×#95—22no—
179C2×#95—22no—
180C2×#95—22no—
181C2×#95—21no—
182C2×#95—21no—
183C2×#95D412yes—
184#340—22no—
185#340—22no—
186#340—22no—
187#340—22no—
188#336—22no—
189#336—22no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—21no—
210C22×Q8—21no—
211C22×Q8—21no—
212C22×Q8—21no—
213C22×Q8—21no—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—21no—
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—21no—
220C22×Q8—21no—
221C22×Q8—21no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8—21no—
225C22×Q8—21no—
226C22×Q8—21no—
227C22×Q8C22×C412yes—
228C22×Q8C22×C412yes—
229C22×Q8C22×C412yes—
230C22×Q8C2×D412yes—
231C22×Q8#4112yes—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4C2×D412yes—
241C23×C4C2×D412yes—
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2411yescharacteristic
245C2×Q16—28no—
246C2×Q16—28no—
247C2×Q16—28no—
248C2×Q16—28no—
249C2×Q16—44no—
250C2×Q16—44no—
251C2×Q16—44no—
252C2×Q16—44no—
253C2×Q16—44no—
254C2×Q16—44no—
255C2×Q16—44no—
256C2×Q16—44no—
257C2×Q16—44no—
258C2×Q16—44no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8C22×C412yes—
278C22×C8C22×C412yes—
279C22×C8C2×D412yes—
280C22×C8C2×D412yes—
281C22×C8C2×D412yes—
282C22×C8C2×D412yes—
283C22×C8C2×D412yes—
284C22×C8C2×D412yes—
285C22×C8C2×D412yes—
286C22×C8#4112yes—
287C4⋊Q8—28no—
288C4⋊Q8—28no—
289C4⋊Q8—44no—
290C4⋊Q8—44no—
291C4×Q8—28no—
292C4×Q8—28no—
293C4×Q8—44no—
294C4×Q8—44no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4C22×C412yes—
335C2×C4⋊C4C2×D412yes—
336C2×C4⋊C4#4112yes—
337C2×C42—24no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—42no—
351C2×C42—42no—
352C2×C42—44no—
353C2×C42—42no—
354C2×C42C22×C412yes—
355C2×C42C2×D412yes—
356C2×C42C2×D412yes—
357C2×C42C2×D412yes—
358C2×C42#4112yes—
359C2×C42#4112yes—
360#107—44no—
361#106—44no—
362C4⋊C8C22⋊C4116yes—
363#103—28no—
364#103—28no—
365#103—28no—
366#103—28no—
367#103—44no—
368#103—44no—
369#103—44no—
370#103—44no—
371#97—28no—
372#97—44no—
373C4×C8—44no—
374#95—24no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—42no—
383#95—42no—
384#95—42no—
385#95—44no—
386C24C22×D411yescharacteristic
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—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—41no—
439C2×Q8—41no—
440C2×Q8—41no—
441C2×Q8—41no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—41no—
448C2×Q8—41no—
449C2×Q8—41no—
450C2×Q8—41no—
451C2×Q8—41no—
452C2×Q8—41no—
453C2×Q8—41no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×Q8—41no—
461C2×Q8—41no—
462C2×Q8—41no—
463C2×Q8—41no—
464C2×Q8—41no—
465C2×Q8—41no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×Q8—41no—
469C2×Q8—41no—
470C2×Q8C4×D414yes—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
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—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4C4×D412yes—
535C22×C4C4×D412yes—
536C22×C4#12112yes—
537C22×C4#12112yes—
538C22×C4#12712yes—
539C22×C4#12712yes—
540C22×C4#13714yes—
541C22×C4C23×C411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C2×#4111yescharacteristic
547C22×C4C2×#4111yescharacteristic
548C22×C4C2×#4111yescharacteristic
549C22×C4C2×#4111yescharacteristic
550C22×C4C2×#4111yescharacteristic
551C22×C4H(5,𝔽2)11yescharacteristic
552C22×C4H(5,𝔽2)11yescharacteristic
553C22×C4H(5,𝔽2)11yescharacteristic
554C22×C42−1+411yescharacteristic
555Q16—416no—
556Q16—416no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8C2×C22⋊C414yes—
583C2×C8C2×C22⋊C414yes—
584C2×C8#12114yes—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—48no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—48no—
599C4⋊C4—48no—
600C4⋊C4—48no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C42—41no—
610C42—41no—
611C42—41no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—48no—
618C42—84no—
619C42C2×C22⋊C414yes—
620C42C4×D414yes—
621C42#12114yes—
622C42#12414yes—
623C23C2×C4×D411yescharacteristic
624C23C2×#12111yescharacteristic
625C23C2×#12711yescharacteristic
626C23D4211yescharacteristic
627C23#54611yescharacteristic
628C23#54811yescharacteristic
629C23#55011yescharacteristic
630C23C2×#13712yes—
631C23#57512yes—
632C23#57812yes—
633C23#57812yes—
634Q8—24no—
635Q8—24no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—42no—
641Q8—42no—
642Q8—42no—
643Q8—42no—
644Q8—42no—
645Q8—42no—
646Q8—42no—
647Q8—42no—
648Q8—42no—
649Q8—42no—
650Q8—81no—
651Q8—81no—
652Q8—81no—
653Q8—81no—
654Q8—81no—
655Q8—81no—
656Q8—81no—
657Q8—81no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—82no—
700C2×C4—82no—
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—82no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—82no—
723C2×C4—82no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4#39014yes—
727C2×C4#39014yes—
728C2×C4C22×C22⋊C411yescharacteristic
729C2×C4C2×C4×D411yescharacteristic
730C2×C4C2×C4×D411yescharacteristic
731C2×C4C4×#4111yescharacteristic
732C2×C4#51811yescharacteristic
733C2×C4#52011yescharacteristic
734C2×C4C2×#12111yescharacteristic
735C2×C4C2×#12111yescharacteristic
736C2×C4#52511yescharacteristic
737C2×C4C2×#12411yescharacteristic
738C2×C4#52911yescharacteristic
739C2×C4#53211yescharacteristic
740C2×C4#53511yescharacteristic
741C2×C4#53711yescharacteristic
742C2×C4#54011yescharacteristic
743C2×C4#54211yescharacteristic
744C2×C4D4211yescharacteristic
745C2×C4D4211yescharacteristic
746C2×C4#54611yescharacteristic
747C2×C4#54611yescharacteristic
748C2×C4#54711yescharacteristic
749C2×C4#54811yescharacteristic
750C2×C4#54811yescharacteristic
751C2×C4#55011yescharacteristic
752C2×C4#55011yescharacteristic
753C2×C4#55311yescharacteristic
754C2×C4#55311yescharacteristic
755C2×C4#55511yescharacteristic
756C8—24no—
757C8—24no—
758C8—24no—
759C8—42no—
760C22C2×#39011yescharacteristic
761C22#236111yescharacteristic
762C22#236311yescharacteristic
763C22#242611yescharacteristic
764C22#242811yescharacteristic
765C22#254011yescharacteristic
766C22#254111yescharacteristic
767C22C4×#13712yes—
768C22#295012yes—
769C22#305612yes—
770C22#305912yes—
771C22#315211yescharacteristic
772C22#315311yescharacteristic
773C22#315611yescharacteristic
774C22#315611yescharacteristic
775C22#326912yes—
776C22#327012yes—
777C22#331212yes—
778C22#331512yes—
779C22#337412yes—
780C22#337712yes—
781C22#339812yes—
782C22#340212yes—
783C4—24no—
784C4—24no—
785C4—44no—
786C4—44no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—161no—
794C4—161no—
795C4C4×#12111yescharacteristic
796C4#232411yescharacteristic
797C4D4×C22⋊C411yescharacteristic
798C4#234111yescharacteristic
799C4#241411yescharacteristic
800C4#241611yescharacteristic
801C4#249011yescharacteristic
802C4#249111yescharacteristic
803C2#1399811yescharacteristic
804C2#2123211yescharacteristic
805C2#2123711yescharacteristic
806C2#2301412yes—
807C2#2311012yes—
808C2#2530612yes—
809C2#2539812yes—
810C2#2842311yescharacteristic
811C2#2842711yescharacteristic
812C2#2847611yescharacteristic
813C2#2847711yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
22. C2×#462C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4622
C2×#19712
C2×#19692
C2×#19602
C2×#19492
C2×#17712
C2×#17632
#141552
#139422
#111242
#111222
#110242
#109282
#109262