Finite Group Databasebeta

← #354501

Subgroups — #354501

Order 512.

1344 conjugacy classes of subgroups.

The subgroup lattice has 745 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1919C211yesmaximal, characteristic
2C2×#1920C211yesmaximal, characteristic
3C2×#1776C211yesmaximal, characteristic
4C4×#389C211yesmaximal, characteristic
5C42×C4⋊C4C211yesmaximal, characteristic
6#10907C211yesmaximal, characteristic
7#10907C211yesmaximal, characteristic
8#10885C211yesmaximal, characteristic
9#10884C211yesmaximal, characteristic
10#10807C211yesmaximal, characteristic
11#10806C211yesmaximal, characteristic
12#10703C211yesmaximal, characteristic
13#10703C211yesmaximal, characteristic
14#10703C211yesmaximal, characteristic
15#10693C211yesmaximal, characteristic
16C22×#107C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×#97C2211yescharacteristic
19C22×#97C2211yescharacteristic
20C2×#389C2211yescharacteristic
21C2×#389C2211yescharacteristic
22C2×C4×C4⋊C4—21no—
23C2×C4×C4⋊C4C2211yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×C4×C4⋊C4C2211yescharacteristic
26C2×C4×C4⋊C4C2211yescharacteristic
27C2×C4×C4⋊C4C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C43—21no—
32C2×C43C2211yescharacteristic
33#1920C418yescomplemented
34#1919C418yescomplemented
35#1776C418yescomplemented
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×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54#1436—21no—
55#1436—21no—
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4×#95—21no—
59C4×#95—21no—
60C4×#95—21no—
61C4×#95—21no—
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C22×C4⋊C4—21no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4C2311yescharacteristic
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C42—21no—
77C22×C42—21no—
78C22×C42—21no—
79C22×C42—21no—
80C22×C42—21no—
81C22×C42—21no—
82C22×C42—21no—
83C22×C42—21no—
84C22×C42D411yescharacteristic
85C22×C42D411yescharacteristic
86C22×C42D411yescharacteristic
87C22×C42D411yescharacteristic
88C22×C42C2311yescharacteristic
89C22×C42C2311yescharacteristic
90C22×C42C2311yescharacteristic
91C2×#107—22no—
92C2×#107—22no—
93C2×#107C2×C414yes—
94C2×#106C2×C414yes—
95C2×#106C2×C414yes—
96C2×#106C2×C414yes—
97C2×#97—22no—
98C2×#97—22no—
99C2×#97—22no—
100C2×#97—22no—
101C2×#97—22no—
102C2×#97C2×C414yes—
103#389—22no—
104#389—22no—
105#389C2×C414yes—
106#389C2×C414yes—
107C4×C4⋊C4—22no—
108C4×C4⋊C4—22no—
109C4×C4⋊C4—22no—
110C4×C4⋊C4—22no—
111C4×C4⋊C4—22no—
112C4×C4⋊C4—22no—
113C4×C4⋊C4—22no—
114C4×C4⋊C4—22no—
115C4×C4⋊C4—22no—
116C4×C4⋊C4—22no—
117C4×C4⋊C4—22no—
118C4×C4⋊C4—44no—
119C4×C4⋊C4C2×C414yes—
120C4×C4⋊C4C2×C414yes—
121C4×C4⋊C4C2×C414yes—
122C4×C4⋊C4C2×C414yes—
123C4×C4⋊C4Q814yes—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95—21no—
127C2×#95—21no—
128C2×#95—21no—
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—
138C43—22no—
139C43—22no—
140C43—44no—
141#340—22no—
142#340—22no—
143#340—22no—
144#340—22no—
145#340—22no—
146#340—22no—
147#340C2×C414yes—
148#340C2×C414yes—
149#340C2×C414yes—
150#340C2×C414yes—
151#340C2×C414yes—
152#340C2×C414yes—
153#340C2×C414yes—
154#340C2×C414yes—
155#336—22no—
156#336—22no—
157#336C2×C414yes—
158#336C2×C414yes—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—21no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4C2×D411yescharacteristic
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D411yescharacteristic
173C23×C4C2411yescharacteristic
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—21no—
177C22×C8—21no—
178C22×C8—21no—
179C22×C8—21no—
180C22×C8—21no—
181C22×C8—21no—
182C22×C8—21no—
183C22×C8—21no—
184C22×C8—21no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8C22×C412yes—
197C22×C8C22×C412yes—
198C22×C8C22×C412yes—
199C22×C8C22×C412yes—
200C22×C8C22×C412yes—
201C22×C8C22×C412yes—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
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—24no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4—42no—
236C2×C4⋊C4—42no—
237C2×C4⋊C4—42no—
238C2×C4⋊C4C22×C412yes—
239C2×C4⋊C4C22×C412yes—
240C2×C4⋊C4C22×C412yes—
241C2×C4⋊C4C22×C412yes—
242C2×C4⋊C4C22×C412yes—
243C2×C4⋊C4C22×C412yes—
244C2×C4⋊C4C22×C412yes—
245C2×C4⋊C4C22×C412yes—
246C2×C4⋊C4C22×C412yes—
247C2×C4⋊C4C22×C412yes—
248C2×C4⋊C4C22×C412yes—
249C2×C4⋊C4C22×C412yes—
250C2×C4⋊C4C2×Q812yes—
251C2×C4⋊C4C2×Q812yes—
252C2×C4⋊C4#4112yes—
253C2×C4⋊C4#4112yes—
254C2×C4⋊C4#4112yes—
255C2×C4⋊C4#4112yes—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42—22no—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42—21no—
262C2×C42—21no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42—21no—
266C2×C42—21no—
267C2×C42—24no—
268C2×C42—24no—
269C2×C42—24no—
270C2×C42—24no—
271C2×C42—24no—
272C2×C42—24no—
273C2×C42—24no—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42—22no—
278C2×C42—22no—
279C2×C42—41no—
280C2×C42—41no—
281C2×C42—41no—
282C2×C42—41no—
283C2×C42—42no—
284C2×C42—42no—
285C2×C42—42no—
286C2×C42—42no—
287C2×C42—42no—
288C2×C42—42no—
289C2×C42—42no—
290C2×C42—42no—
291C2×C42—42no—
292C2×C42—42no—
293C2×C42—42no—
294C2×C42—42no—
295C2×C42—42no—
296C2×C42—42no—
297C2×C42—42no—
298C2×C42—42no—
299C2×C42—42no—
300C2×C42C22×C412yes—
301C2×C42C22×C412yes—
302C2×C42C22×C412yes—
303C2×C42C2×Q812yes—
304C2×C42#4112yes—
305C2×C42#4112yes—
306C2×C42#4112yes—
307C2×C42#4112yes—
308C2×C42#4112yes—
309C2×C42#4112yes—
310#107—28no—
311#106C42116yescomplemented
312#97—28no—
313#97—44no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—24no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327#95—42no—
328C24C22×D411yescharacteristic
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
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×C4C4×D412yes—
414C22×C4C4×D412yes—
415C22×C4C4×D412yes—
416C22×C4C4×D412yes—
417C22×C4C4×D412yes—
418C22×C4C4×D412yes—
419C22×C4C22⋊Q812yes—
420C22×C4C22⋊Q812yes—
421C22×C4#12312yes—
422C22×C4#12312yes—
423C22×C4AGL(1,ℤ/8)12yes—
424C22×C4AGL(1,ℤ/8)12yes—
425C22×C4#13712yes—
426C22×C4#13712yes—
427C22×C4C23×C411yescharacteristic
428C22×C4C23×C411yescharacteristic
429C22×C4C23×C411yescharacteristic
430C22×C4C22×Q811yescharacteristic
431C22×C4C2×#4111yescharacteristic
432C22×C4C2×#4111yescharacteristic
433C22×C4C2×#4111yescharacteristic
434C22×C4C2×#4111yescharacteristic
435C22×C4C2×#4111yescharacteristic
436C22×C4C2×#4111yescharacteristic
437C22×C4C2×#4111yescharacteristic
438C22×C4C2×#4111yescharacteristic
439C22×C4C2×#4111yescharacteristic
440C22×C4C2×#4111yescharacteristic
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—41no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8C2×C4214yes—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—48no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—48no—
498C4⋊C4C2×C4214yes—
499C4⋊C4C2×C4214yes—
500C4⋊C4#11714yes—
501C4⋊C4C4×Q814yes—
502C4⋊C4C4×Q814yes—
503C42—28no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—22no—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—44no—
513C42—44no—
514C42—48no—
515C42—44no—
516C42—48no—
517C42—48no—
518C42—48no—
519C42—48no—
520C42—48no—
521C42—48no—
522C42—84no—
523C42#11714yes—
524C42C4×Q814yes—
525C42#12514yes—
526C42#12614yes—
527C23C2×C4×D411yescharacteristic
528C23C2×C4×D411yescharacteristic
529C23C2×C4×D411yescharacteristic
530C23C2×C22⋊Q811yescharacteristic
531C23C2×#12311yescharacteristic
532C23#52511yescharacteristic
533C23#52511yescharacteristic
534C23C2×AGL(1,ℤ/8)11yescharacteristic
535C23C2×AGL(1,ℤ/8)11yescharacteristic
536C23C2×#13711yescharacteristic
537C23C2×#13711yescharacteristic
538C23#57511yescharacteristic
539C23#57511yescharacteristic
540C23#57511yescharacteristic
541C23#57511yescharacteristic
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—81no—
625C2×C4—81no—
626C2×C4—81no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—81no—
636C2×C4#38714yes—
637C2×C4#38714yes—
638C2×C4#44014yes—
639C2×C4#44014yes—
640C2×C4C22×C4211yescharacteristic
641C2×C4C2×#11711yescharacteristic
642C2×C4C2×#11711yescharacteristic
643C2×C4C2×C4×Q811yescharacteristic
644C2×C4C2×C4×Q811yescharacteristic
645C2×C4C2×C4×Q811yescharacteristic
646C2×C4C4×#4111yescharacteristic
647C2×C4C4×#4111yescharacteristic
648C2×C4C4×#4111yescharacteristic
649C2×C4C4×#4111yescharacteristic
650C2×C4C4×#4111yescharacteristic
651C2×C4C4×#4111yescharacteristic
652C2×C4C4×#4111yescharacteristic
653C2×C4C4×#4111yescharacteristic
654C2×C4C4×#4111yescharacteristic
655C2×C4C4×#4111yescharacteristic
656C2×C4C2×#12511yescharacteristic
657C2×C4C2×#12611yescharacteristic
658C2×C4#52911yescharacteristic
659C2×C4#52911yescharacteristic
660C2×C4#52911yescharacteristic
661C2×C4#52911yescharacteristic
662C2×C4#52911yescharacteristic
663C2×C4#52911yescharacteristic
664C2×C4#52911yescharacteristic
665C2×C4#52911yescharacteristic
666C2×C4#53311yescharacteristic
667C2×C4#53311yescharacteristic
668C8—24no—
669C8—42no—
670C8—42no—
671C8—42no—
672C22C42×D411yescharacteristic
673C22C2×#38711yescharacteristic
674C22#229011yescharacteristic
675C22C4×#12311yescharacteristic
676C22C4×#12311yescharacteristic
677C22C4×C22⋊Q811yescharacteristic
678C22C4×C22⋊Q811yescharacteristic
679C22C2×#44011yescharacteristic
680C22C2×#44011yescharacteristic
681C22#294311yescharacteristic
682C22#294311yescharacteristic
683C22C4×AGL(1,ℤ/8)11yescharacteristic
684C22C4×AGL(1,ℤ/8)11yescharacteristic
685C22C4×AGL(1,ℤ/8)11yescharacteristic
686C22C4×AGL(1,ℤ/8)11yescharacteristic
687C22C4×#13711yescharacteristic
688C22C4×#13711yescharacteristic
689C22C4×#13711yescharacteristic
690C22C4×#13711yescharacteristic
691C22#307711yescharacteristic
692C22#307811yescharacteristic
693C22#307911yescharacteristic
694C22#308011yescharacteristic
695C22#309211yescharacteristic
696C22#309311yescharacteristic
697C22#309411yescharacteristic
698C22#309511yescharacteristic
699C22#310911yescharacteristic
700C22#311111yescharacteristic
701C22#311111yescharacteristic
702C22#311311yescharacteristic
703C22#311411yescharacteristic
704C22#311511yescharacteristic
705C22#311611yescharacteristic
706C22#311711yescharacteristic
707C4—24no—
708C4—24no—
709C4—24no—
710C4—24no—
711C4—44no—
712C4—44no—
713C4—42no—
714C4—42no—
715C4—44no—
716C4—44no—
717C4—44no—
718C4—82no—
719C4—82no—
720C4—82no—
721C4C4×#11711yescharacteristic
722C4C42×Q811yescharacteristic
723C4#229511yescharacteristic
724C4#229811yescharacteristic
725C4C4×#12611yescharacteristic
726C4C4×#12611yescharacteristic
727C4C4×#12511yescharacteristic
728C4C4×#12511yescharacteristic
729C2C4×#38711yescharacteristic
730C2C4×#44011yescharacteristic
731C2C4×#44011yescharacteristic
732C2#2103311yescharacteristic
733C2#2103411yescharacteristic
734C2#2112211yescharacteristic
735C2#2112311yescharacteristic
736C2#2157911yescharacteristic
737C2#2158011yescharacteristic
738C2#2158211yescharacteristic
739C2#2158311yescharacteristic
740C2#2161411yescharacteristic
741C2#2161511yescharacteristic
742C2#2161711yescharacteristic
743C2#2161811yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
33. #1920C4semidirect
34. #1919C4semidirect
35. #1776C4semidirect
311. #106C42semidirect

Maximal subgroups

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

subgroupindex
C2×#19192
C2×#19202
C2×#17762
C4×#3892
C42×C4⋊C42
#109072
#108852
#108842
#108072
#108062
#107032
#106932