Finite Group Databasebeta

← #355829

Subgroups — #355829

Order 512.

1624 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1870C211yesmaximal, characteristic
2C2×#1869C211yesmaximal, characteristic
3C2×#1752C211yesmaximal, characteristic, complemented
4C2×#1753C211yesmaximal, characteristic, complemented
5C4×#390C211yesmaximal, characteristic
6#10922C211yesmaximal, characteristic, complemented
7#10922C211yesmaximal, characteristic, complemented
8#10922C211yesmaximal, characteristic, complemented
9#10921C211yesmaximal, characteristic, complemented
10#10875C211yesmaximal, characteristic, complemented
11#10874C211yesmaximal, characteristic, complemented
12#10795C211yesmaximal, characteristic, complemented
13#10715C211yesmaximal, characteristic, complemented
14#10714C211yesmaximal, characteristic, complemented
15#10693C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×#97C2211yescharacteristic
26C22×#97C2211yescharacteristic
27C22×#97C2211yescharacteristic
28C22×C4×C8C2211yescharacteristic
29C2×#390C412yes—
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32C2×C4×C22⋊C4C2211yescharacteristic
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2211yescharacteristic
35C2×C43C2211yescharacteristic
36#1870C418yescomplemented
37#1869C418yescomplemented
38#1753—24no—
39#1752—24no—
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56#1437C412yes—
57#1437C412yes—
58C4⋊#95C412yes—
59C23×D4C2×C411yescharacteristic
60C24×C4C2311yescharacteristic
61C24×C4C2311yescharacteristic
62C22×M16—22no—
63C22×M16—22no—
64C22×M16—41no—
65C22×M16—41no—
66C22×M16—41no—
67C22×M16—41no—
68C22×M16C2×C414yes—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—41no—
72C23×C8—41no—
73C23×C8—41no—
74C23×C8—41no—
75C23×C8C2×C414yes—
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C2×C4×D4—41no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C2×C4×D4—41no—
88C2×C4×D4C2×C414yes—
89C2×C4×D4C2×C414yes—
90C22×C4⋊C4C2×C412yes—
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2×C412yes—
93C22×C22⋊C4C2×C412yes—
94C22×C22⋊C4C2×C412yes—
95C22×C22⋊C4C2×C411yescharacteristic
96C22×C22⋊C4C2×C411yescharacteristic
97C22×C22⋊C4C2×C412yes—
98C22×C42C2×C412yes—
99C22×C42C2×C412yes—
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C2×C22⋊C8—22no—
106C2×C22⋊C8—22no—
107C2×C22⋊C8—22no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—41no—
110C2×C22⋊C8—41no—
111C2×C22⋊C8—41no—
112C2×C22⋊C8—41no—
113C2×C22⋊C8—41no—
114C2×C22⋊C8—41no—
115C2×C22⋊C8—41no—
116C2×C22⋊C8—41no—
117C2×C22⋊C8C2×C414yes—
118C2×C22⋊C8C2×C414yes—
119C2×C22⋊C8C2×C414yes—
120C2×C22⋊C8C2×C414yes—
121C2×C22⋊C8C2×C414yes—
122C2×C22⋊C8C2×C414yes—
123C2×#97—22no—
124C2×#97—22no—
125C2×#97—41no—
126C2×#97—41no—
127C2×#97—41no—
128C2×#97—41no—
129C2×#97—41no—
130C2×#97—41no—
131C2×#97D414yescomplemented
132C2×C4×C8—22no—
133C2×C4×C8—41no—
134C2×C4×C8—41no—
135#390—28no—
136C4×C4⋊C4—41no—
137C4×C4⋊C4—41no—
138C4×C22⋊C4—22no—
139C4×C22⋊C4—22no—
140C4×C22⋊C4—22no—
141C4×C22⋊C4—22no—
142C4×C22⋊C4—41no—
143C4×C22⋊C4—41no—
144C4×C22⋊C4—41no—
145C4×C22⋊C4—41no—
146C2×#95C2×C412yes—
147C2×#95C2×C412yes—
148C2×#95C2×C412yes—
149C2×#95C2×C412yes—
150C2×#95C2×C412yes—
151C43—41no—
152C43—41no—
153#336—22no—
154#336—22no—
155#336—22no—
156#336—22no—
157#336—22no—
158#336—22no—
159#336—41no—
160#336—41no—
161#336—41no—
162#336—41no—
163#336—41no—
164#336—41no—
165#336C2×C414yes—
166#336C2×C414yes—
167#336C2×C414yes—
168#336C2×C414yes—
169C25C22×C411yescharacteristic
170C25C22×C411yescharacteristic
171C22×D4—24no—
172C22×D4—24no—
173C22×D4—41no—
174C22×D4—41no—
175C22×D4C4214yes—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4C22×C412yes—
201C23×C4C22×C411yescharacteristic
202C23×C4C22×C411yescharacteristic
203C23×C4C22×C411yescharacteristic
204C23×C4C22×C412yes—
205C23×C4C22×C412yes—
206C23×C4C22×C412yes—
207C23×C4C22×C412yes—
208C23×C4C22×C412yes—
209C23×C4C22×C412yes—
210C23×C4C22×C412yes—
211C23×C4C22×C411yescharacteristic
212C23×C4C2411yescharacteristic
213C2×M16—28no—
214C2×M16—44no—
215C2×M16—44no—
216C2×M16—44no—
217C2×M16—44no—
218C2×M16—44no—
219C2×M16—44no—
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×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
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×C8—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—28no—
265C22×C8—44no—
266C22×C8—44no—
267C22×C8—44no—
268C22×C8—44no—
269C22×C8—44no—
270C22×C8—44no—
271C22×C8C22×C412yes—
272C22×C8C22×C412yes—
273C22×C8C22×C412yes—
274C22×C8C22×C412yes—
275C22×C8C22×C412yes—
276C22×C8C22×C412yes—
277C22×C8C22×C412yes—
278C22×C8C22×C412yes—
279C22×C8C2×D412yes—
280C22×C8C2×D412yes—
281C22×C8#4112yes—
282C22×C8#4112yes—
283C4×D4—44no—
284C4×D4—44no—
285C4×D4—44no—
286C4×D4—44no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4C4214yes—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—41no—
303C2×C22⋊C4—41no—
304C2×C22⋊C4—41no—
305C2×C22⋊C4—41no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4C4214yes—
309C2×C22⋊C4C4214yes—
310C2×C22⋊C4M1618yescomplemented
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—24no—
320C2×C42—24no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42C22×C412yes—
344C2×C42C22×C412yes—
345C2×C42C2×D412yes—
346C2×C42#4112yes—
347C22⋊C8—28no—
348C22⋊C8—28no—
349C22⋊C8—44no—
350C22⋊C8—44no—
351C22⋊C8—44no—
352C22⋊C8—44no—
353#97—44no—
354#97—44no—
355#97—44no—
356C4×C8—44no—
357#95—24no—
358#95—24no—
359#95—42no—
360#95—42no—
361#95—42no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24C2×C4212yes—
382C24C2×C4212yes—
383C24C2×M1614yes—
384C24C23×C411yescharacteristic
385C2×D4—28no—
386C2×D4—28no—
387C2×D4—44no—
388C2×D4—48no—
389C2×D4—48no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
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—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—41no—
489C22×C4—41no—
490C22×C4C2×C4212yes—
491C22×C4C2×C4212yes—
492C22×C4C2×C4212yes—
493C22×C4C2×C4212yes—
494C22×C4C4×D414yes—
495C22×C4C2×M1614yes—
496C22×C4C2×M1614yes—
497C22×C4#13114yes—
498C22×C4C23×C411yescharacteristic
499C22×C4C23×C411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4C2×#4111yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4H(5,𝔽2)11yescharacteristic
505C22×C4H(5,𝔽2)11yescharacteristic
506C22×C4H(5,𝔽2)11yescharacteristic
507C22×C4H(5,𝔽2)11yescharacteristic
508C22×C4H(5,𝔽2)11yescharacteristic
509C22×C4H(5,𝔽2)11yescharacteristic
510C22×C4H(5,𝔽2)11yescharacteristic
511C22×C42−1+411yescharacteristic
512M16—416no—
513C2×C8—22no—
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—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×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—416no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8C4×D414yes—
569C2×C8C4×D414yes—
570C4⋊C4—44no—
571C4⋊C4—48no—
572C22⋊C4—44no—
573C22⋊C4—44no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—48no—
587C42—48no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23C4×M1614yes—
646C23C22×C4211yescharacteristic
647C23C2×C4×D411yescharacteristic
648C23C4×#4111yescharacteristic
649C23#51811yescharacteristic
650C23#51811yescharacteristic
651C23#51811yescharacteristic
652C23#52011yescharacteristic
653C23C22×M1612yes—
654C23C2×#13112yes—
655C23#56812yes—
656C23#56812yes—
657D4—416no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4#40514yes—
726C2×C4C2×C4×D411yescharacteristic
727C2×C4C2×C4×D411yescharacteristic
728C2×C4C4×#4111yescharacteristic
729C2×C4C4×#4111yescharacteristic
730C2×C4#51811yescharacteristic
731C2×C4#51811yescharacteristic
732C2×C4#51811yescharacteristic
733C2×C4#51811yescharacteristic
734C2×C4#51811yescharacteristic
735C2×C4#51811yescharacteristic
736C2×C4#52011yescharacteristic
737C2×C4#52011yescharacteristic
738C2×C4#53411yescharacteristic
739C2×C4#53511yescharacteristic
740C2×C4#53511yescharacteristic
741C2×C4#53711yescharacteristic
742C2×C4#53811yescharacteristic
743C2×C4#53811yescharacteristic
744C2×C4#53811yescharacteristic
745C2×C4#53811yescharacteristic
746C2×C4#53811yescharacteristic
747C2×C4#53911yescharacteristic
748C2×C4#54011yescharacteristic
749C2×C4#54011yescharacteristic
750C2×C4#54011yescharacteristic
751C2×C4#54011yescharacteristic
752C2×C4#54211yescharacteristic
753C2×C4#54211yescharacteristic
754C8—24no—
755C8—24no—
756C8—42no—
757C8—42no—
758C8—42no—
759C8—42no—
760C8—42no—
761C8—42no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—42no—
766C22—42no—
767C22—44no—
768C22—42no—
769C22—44no—
770C22—44no—
771C22—42no—
772C22—44no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22C42×D411yescharacteristic
785C22#227311yescharacteristic
786C22#227511yescharacteristic
787C22#232511yescharacteristic
788C22#232811yescharacteristic
789C22#233311yescharacteristic
790C22#233711yescharacteristic
791C22C2×C4×M1611yescharacteristic
792C22C2×#40511yescharacteristic
793C22#287511yescharacteristic
794C22#287511yescharacteristic
795C22D4×M1612yes—
796C22#293512yes—
797C22#296912yes—
798C22#297012yes—
799C22#297312yes—
800C22#297412yes—
801C22#297412yes—
802C22#297812yes—
803C22#298012yes—
804C22#298112yes—
805C22#298912yes—
806C22#299312yes—
807C4—24no—
808C4—42no—
809C4—44no—
810C4—44no—
811C4—42no—
812C4—42no—
813C4—44no—
814C4—82no—
815C4#232111yescharacteristic
816C4#232111yescharacteristic
817C4#232411yescharacteristic
818C4#232411yescharacteristic
819C4#233311yescharacteristic
820C4#233311yescharacteristic
821C4#233511yescharacteristic
822C4#233511yescharacteristic
823C2—44no—
824C2—82no—
825C2#1379111yescharacteristic
826C2#2049111yescharacteristic
827C2#2049511yescharacteristic
828C2#2052511yescharacteristic
829C2#2053211yescharacteristic
830C2#2055611yescharacteristic
831C2#2056511yescharacteristic
832C2#2217412yes—
833C2#2226612yes—
834C2#2233512yes—
835C2#2239112yes—
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutatorC23C22×C42
socleC24C23×C4
prime radicalC23×D4C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1752C2semidirect
4. C2×#1753C2semidirect
6. #10922C2semidirect
7. #10922C2semidirect
8. #10922C2semidirect
9. #10921C2semidirect
10. #10875C2semidirect
11. #10874C2semidirect
12. #10795C2semidirect
13. #10715C2semidirect
14. #10714C2semidirect
15. #10693C2semidirect
36. #1870C4semidirect
37. #1869C4semidirect
131. C2×#97D4semidirect
310. C2×C22⋊C4M16semidirect

Maximal subgroups

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

subgroupindex
C2×#18702
C2×#18692
C2×#17522
C2×#17532
C4×#3902
#109222
#109212
#108752
#108742
#107952
#107152
#107142
#106932