Finite Group Databasebeta

← #354594

Subgroups — #354594

Order 512.

1850 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#440C211yesmaximal, characteristic
2C2×#1973C211yesmaximal, characteristic
3C2×#1968C211yesmaximal, characteristic
4C2×#1776C211yesmaximal, characteristic, complemented
5C2×C4×#103C211yesmaximal, characteristic, complemented
6C2×C4×#102C211yesmaximal, characteristic
7C2×#1726C211yesmaximal, characteristic, complemented
8#13786C211yesmaximal, characteristic, complemented
9#13785C211yesmaximal, characteristic
10#10928C211yesmaximal, characteristic, complemented
11#10927C211yesmaximal, characteristic
12#10926C211yesmaximal, characteristic, complemented
13#10925C211yesmaximal, characteristic
14#10863C211yesmaximal, characteristic, complemented
15#10862C211yesmaximal, characteristic, complemented
16C23×SD16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C2×#440—24no—
20C2×#440—24no—
21C2×#440C418yescomplemented
22C22×#107C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#106C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C22×#97C2211yescharacteristic
33C22×#97C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35C22×C4×C8C2211yescharacteristic
36C22×C4×C8C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×#376C2211yescharacteristic
44#1973C418yescomplemented
45#1968C418yescomplemented
46#1776—24no—
47C4×#103—24no—
48C4×#102—24no—
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55#1726—24no—
56#1437—22no—
57#1436—22no—
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62#1434—22no—
63C22⋊#95—22no—
64C23×Q8C2311yescharacteristic
65C23×D4C2311yescharacteristic
66C24×C4—21no—
67C22×SD16—22no—
68C22×SD16—22no—
69C22×SD16—22no—
70C22×SD16—22no—
71C22×SD16C2×C414yes—
72C22×SD16C2×C414yes—
73C22×SD16C2×C414yes—
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—22no—
81C2×C4×Q8—22no—
82C2×C4×Q8—22no—
83C2×C4×Q8C2×C414yes—
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—22no—
88C2×C4×D4—22no—
89C2×C4×D4C2×C414yes—
90C22×C4⋊C4—21no—
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C22⋊C4—21no—
98C22×C22⋊C4—22no—
99C22×C22⋊C4—22no—
100C22×C42—21no—
101C22×C42—21no—
102C22×C42—21no—
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106#440—232no—
107C2×#107—22no—
108C2×#107—22no—
109C2×#107—22no—
110C2×#107—22no—
111C2×#107C2×C414yes—
112C2×#107C2×C414yescomplemented
113C2×#106—22no—
114C2×#106—22no—
115C2×#106C2×C414yescomplemented
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—22no—
121C2×#103—22no—
122C2×#103C2×C414yes—
123C2×#103C2×C414yescomplemented
124C2×#103C2×C414yescomplemented
125C2×#102—22no—
126C2×#102—22no—
127C2×#102—22no—
128C2×#102—22no—
129C2×#102—22no—
130C2×#102—22no—
131C2×#102C2×C414yes—
132C2×#102C2×C414yes—
133C2×#102C2×C414yes—
134C2×#97—22no—
135C2×#97—22no—
136C2×#97—22no—
137C2×#97—22no—
138C2×#97—22no—
139C2×#97C2×C414yes—
140C2×#97C2×C414yescomplemented
141C2×#97D414yes—
142C2×#97D414yes—
143C2×C4×C8—22no—
144C2×C4×C8—22no—
145C2×C4×C8—22no—
146C2×C4×C8—22no—
147C2×C4×C8—22no—
148C2×C4×C8—22no—
149C2×C4×C8—22no—
150C2×C4×C8C2×C414yescomplemented
151C2×C4×C8D414yes—
152#391—22no—
153#391—22no—
154#391C2×C414yescomplemented
155#391C2×C414yescomplemented
156#390—22no—
157#390—22no—
158#390C2×C414yes—
159#390C2×C414yes—
160C4×C4⋊C4—22no—
161C4×C4⋊C4—22no—
162C4×C4⋊C4—22no—
163C4×C4⋊C4—22no—
164#376—22no—
165#376—22no—
166C2×#95—22no—
167C2×#95—22no—
168C2×#95—21no—
169C2×#95—21no—
170C2×#95—22no—
171C2×#95—22no—
172C2×#95—22no—
173C2×#95—22no—
174C2×#95D412yes—
175C2×#95D412yes—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—22no—
180#340—22no—
181#340—22no—
182C25—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8C22×C412yes—
195C22×Q8C22×C412yes—
196C22×Q8C22×C412yes—
197C22×D4—21no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4C22×C412yes—
209C22×D4C22×C412yes—
210C22×D4C22×C412yes—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—24no—
219C23×C4—42no—
220C23×C4—42no—
221C23×C4—82no—
222C23×C4—82no—
223C23×C4C2×D412yes—
224C23×C4C2×D412yes—
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D411yescharacteristic
227C23×C4C2411yescharacteristic
228C2×SD16—28no—
229C2×SD16—28no—
230C2×SD16—28no—
231C2×SD16—28no—
232C2×SD16—28no—
233C2×SD16—28no—
234C2×SD16C42116yescomplemented
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8C22×C412yes—
248C22×C8C22×C412yes—
249C22×C8C22×C412yes—
250C22×C8C22×C412yes—
251C22×C8C22×C412yes—
252C22×C8C22×C412yes—
253C22×C8C2×D412yes—
254C22×C8C2×D412yes—
255C22×C8C2×D412yes—
256C22×C8C2×D412yes—
257C22×C8C2×D412yes—
258C22×C8C2×D412yes—
259C22×C8#4112yes—
260C22×C8#4112yes—
261C22×C8#4112yes—
262C22×C8#4112yes—
263C4×Q8—28no—
264C4×Q8—28no—
265C4×Q8—44no—
266C4×Q8—44no—
267C4×D4—28no—
268C4×D4—28no—
269C4×D4—44no—
270C4×D4—44no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—24no—
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—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4C22×C412yes—
305C2×C4⋊C4C22×C412yes—
306C2×C4⋊C4C22×C412yes—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4C22×C412yes—
309C2×C4⋊C4C22×C412yes—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—82no—
316C2×C22⋊C4—82no—
317C2×C22⋊C4—82no—
318C2×C22⋊C4—82no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—24no—
328C2×C42—42no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42—42no—
332C2×C42—82no—
333C2×C42—82no—
334C2×C42C22×C412yes—
335C2×C42C22×C412yes—
336C2×C42C22×C412yes—
337C2×C42C2×D412yes—
338C2×C42C2×D412yes—
339C2×C42C2×D412yes—
340C2×C42#4112yes—
341C2×C42#4112yes—
342C2×C42#4112yes—
343C2×C42#4112yes—
344#107—28no—
345#107—28no—
346#106—28no—
347#103—28no—
348#103—28no—
349#103—28no—
350#102—28no—
351#102—28no—
352#102—28no—
353#97—28no—
354#97—28no—
355#97C22⋊C4116yescomplemented
356C4×C8—28no—
357C4×C8—28no—
358C4×C8—28no—
359#95—28no—
360#95—28no—
361#95—24no—
362#95—24no—
363#95—42no—
364#95—42no—
365#95—82no—
366#95—82no—
367#95—82no—
368#95—82no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—42no—
377C24—42no—
378C24—42no—
379C24—42no—
380C24C22×D411yescharacteristic
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
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—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8C2×C4214yes—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4C2×C4214yes—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
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—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—48no—
491C22×C4—88no—
492C22×C4—84no—
493C22×C4—84no—
494C22×C4—88no—
495C22×C4C4×D414yes—
496C22×C4C4×D414yes—
497C22×C4C4×D412yes—
498C22×C4C4×D412yes—
499C22×C4#12112yes—
500C22×C4#12112yes—
501C22×C4#12712yes—
502C22×C4#12712yes—
503C22×C4C23×C411yescharacteristic
504C22×C4C23×C411yescharacteristic
505C22×C4C23×C411yescharacteristic
506C22×C4C22×D411yescharacteristic
507C22×C4C22×D411yescharacteristic
508C22×C4C22×D411yescharacteristic
509C22×C4C2×#4111yescharacteristic
510C22×C4C2×#4111yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517SD16—232no—
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—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8C2×C4214yes—
537C2×C8C2×C22⋊C414yes—
538C2×C8C2×C22⋊C414yes—
539C2×C8#11714yes—
540C2×C8C4×D414yes—
541C2×C8C4×D414yes—
542C2×C8C4×D414yes—
543C2×C8C4×D414yes—
544C2×C8C4×D414yes—
545C2×C8C4×D414yes—
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—22no—
557C4⋊C4—22no—
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—41no—
569C4⋊C4—41no—
570C4⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—88no—
573C22⋊C4—88no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—48no—
583C42—84no—
584C42—84no—
585C42C2×C22⋊C414yes—
586C42C4×D414yes—
587C42#12114yes—
588C42#12414yes—
589C23—24no—
590C23—42no—
591C23—42no—
592C23—44no—
593C23—44no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23—44no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—81no—
603C23—81no—
604C23—81no—
605C23—81no—
606C23—82no—
607C23—82no—
608C23—82no—
609C23—82no—
610C23—82no—
611C23—82no—
612C23C2×C4×D411yescharacteristic
613C23C2×C4×D411yescharacteristic
614C23C2×C4×D411yescharacteristic
615C23C2×#12111yescharacteristic
616C23C2×#12711yescharacteristic
617C23#53211yescharacteristic
618C23#53211yescharacteristic
619C23#57612yes—
620C23#57712yes—
621C23#57712yes—
622C23#57812yes—
623Q8—24no—
624Q8—24no—
625Q8—42no—
626Q8—42no—
627Q8—42no—
628Q8—42no—
629Q8—42no—
630Q8—42no—
631D4—24no—
632D4—24no—
633D4—42no—
634D4—42no—
635D4—42no—
636D4—42no—
637D4—42no—
638D4—42no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
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—42no—
663C2×C4—42no—
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—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—816no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
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—82no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4—82no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4#39014yes—
700C2×C4#39014yes—
701C2×C4C22×C4211yescharacteristic
702C2×C4C22×C22⋊C411yescharacteristic
703C2×C4C2×#11711yescharacteristic
704C2×C4C2×C4×D411yescharacteristic
705C2×C4C2×C4×D411yescharacteristic
706C2×C4C2×C4×D411yescharacteristic
707C2×C4C2×C4×D411yescharacteristic
708C2×C4C2×C4×D411yescharacteristic
709C2×C4C2×C4×D411yescharacteristic
710C2×C4C2×C4×D411yescharacteristic
711C2×C4C4×#4111yescharacteristic
712C2×C4C4×#4111yescharacteristic
713C2×C4C4×#4111yescharacteristic
714C2×C4C4×#4111yescharacteristic
715C2×C4C4×#4111yescharacteristic
716C2×C4C4×#4111yescharacteristic
717C2×C4C2×#12111yescharacteristic
718C2×C4#52511yescharacteristic
719C2×C4#52511yescharacteristic
720C2×C4C2×#12411yescharacteristic
721C2×C4#52911yescharacteristic
722C2×C4#52911yescharacteristic
723C2×C4#52911yescharacteristic
724C2×C4#52911yescharacteristic
725C2×C4#53211yescharacteristic
726C2×C4#53211yescharacteristic
727C2×C4#53211yescharacteristic
728C2×C4#53211yescharacteristic
729C8—24no—
730C8—24no—
731C8—24no—
732C8C4×C22⋊C418yes—
733C22—48no—
734C22—44no—
735C22—84no—
736C22—84no—
737C22—84no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22C42×D411yescharacteristic
745C22C2×#39011yescharacteristic
746C22#229311yescharacteristic
747C22C4×#12111yescharacteristic
748C22C4×#12111yescharacteristic
749C22C4×#12711yescharacteristic
750C22C4×#12711yescharacteristic
751C22#294612yes—
752C22#294612yes—
753C22#294712yes—
754C22#294712yes—
755C22#294912yes—
756C22#295112yes—
757C22#306212yes—
758C22#306312yes—
759C22#315411yescharacteristic
760C22#315411yescharacteristic
761C22#315511yescharacteristic
762C22#315611yescharacteristic
763C22#317412yes—
764C22#317512yes—
765C22#317812yes—
766C22#317912yes—
767C4—24no—
768C4—24no—
769C4—44no—
770C4—44no—
771C4—44no—
772C4—82no—
773C4—82no—
774C4—82no—
775C4—82no—
776C4—82no—
777C4—82no—
778C4C2×C4×C22⋊C411yescharacteristic
779C4C42×D411yescharacteristic
780C4#229311yescharacteristic
781C4#229711yescharacteristic
782C4C4×#12111yescharacteristic
783C4C4×#12111yescharacteristic
784C4C4×#12411yescharacteristic
785C4C4×#12411yescharacteristic
786C2—84no—
787C2C4×#39011yescharacteristic
788C2#2050412yes—
789C2#2123411yescharacteristic
790C2#2123511yescharacteristic
791C2#2129112yes—
792C2#2153112yes—
793C2#2154312yes—
794C2#2169511yescharacteristic
795C2#2169611yescharacteristic
796C2#2170311yescharacteristic
797C2#2170411yescharacteristic
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
4. C2×#1776C2semidirect
5. C2×C4×#103C2semidirect
7. C2×#1726C2semidirect
8. #13786C2semidirect
10. #10928C2semidirect
12. #10926C2semidirect
14. #10863C2semidirect
15. #10862C2semidirect
21. C2×#440C4semidirect
44. #1973C4semidirect
45. #1968C4semidirect
112. C2×#107C2×C4semidirect
115. C2×#106C2×C4semidirect
123. C2×#103C2×C4semidirect
124. C2×#103C2×C4semidirect
140. C2×#97C2×C4semidirect
150. C2×C4×C8C2×C4semidirect
154. #391C2×C4semidirect
155. #391C2×C4semidirect
234. C2×SD16C42semidirect
355. #97C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#4402
C2×#19732
C2×#19682
C2×#17762
C2×C4×#1032
C2×C4×#1022
C2×#17262
#137862
#137852
#109282
#109272
#109262
#109252
#108632
#108622