Finite Group Databasebeta

← #354192

Subgroups — #354192

Order 512.

2254 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#405C211yesmaximal, characteristic, complemented
2C2×#2290C211yesmaximal, characteristic
3C2×#1870C211yesmaximal, characteristic
4C2×#1869C211yesmaximal, characteristic
5C2×#1749C211yesmaximal, characteristic, complemented
6C2×#1750C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
8#10922C211yesmaximal, characteristic, complemented
9#10921C211yesmaximal, characteristic, complemented
10#10875C211yesmaximal, characteristic, complemented
11#10874C211yesmaximal, characteristic, complemented
12#10715C211yesmaximal, characteristic, complemented
13#10714C211yesmaximal, characteristic, complemented
14#10694C211yesmaximal, characteristic, complemented
15#10694C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C2×#405—24no—
28C2×#405—24no—
29C2×#405—24no—
30C22×#97C2211yescharacteristic
31C22×#97C2211yescharacteristic
32C22×#97C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35C22×C4×C8C2211yescharacteristic
36#2290—24no—
37#2290—24no—
38C2×#388C412yes—
39C2×#387C412yes—
40C2×#386C412yes—
41C2×#385C412yes—
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2211yescharacteristic
44C2×C4×C22⋊C4C2211yescharacteristic
45C2×#376C2211yescharacteristic
46#1870C418yescomplemented
47#1869C418yescomplemented
48#1750—24no—
49#1749—24no—
50C4×C22⋊C8—24no—
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60C2×#336C2211yescharacteristic
61C2×#336C2211yescharacteristic
62C2×#336C2211yescharacteristic
63C2×#336C2211yescharacteristic
64C2×#336C2211yescharacteristic
65C23×D4C2×C411yescharacteristic
66C24×C4C2×C412yes—
67C24×C4C2311yescharacteristic
68C24×C4C2311yescharacteristic
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16C2×C414yescomplemented
76C23×C8—22no—
77C23×C8—22no—
78C23×C8—22no—
79C23×C8—22no—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8C2×C414yescomplemented
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88C23×C8C2311yescharacteristic
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C2×C4×D4—22no—
92C2×C4×D4—22no—
93C2×C4×D4—22no—
94C2×C4×D4—22no—
95C2×C4×D4C2×C414yes—
96C2×C4×D4C2×C414yes—
97C2×#117—22no—
98C2×#117—22no—
99C2×#117—22no—
100C2×#117—22no—
101C2×#117D414yes—
102C2×#117D414yes—
103C22×C4⋊C4C2×C412yes—
104C22×C4⋊C4C2×C411yescharacteristic
105C22×C4⋊C4C2×C412yes—
106C22×C22⋊C4C2×C412yes—
107C22×C22⋊C4C2×C412yes—
108C22×C22⋊C4C2×C411yescharacteristic
109C22×C22⋊C4C2×C411yescharacteristic
110C22×C22⋊C4C2×C412yes—
111C22×C42—22no—
112C22×C42—22no—
113C22×C42—22no—
114C22×C42—22no—
115C22×C42—22no—
116C22×C42—22no—
117C22×C42C2×C412yes—
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—22no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—22no—
129C2×C22⋊C8—22no—
130C2×C22⋊C8—22no—
131C2×C22⋊C8—22no—
132C2×C22⋊C8—22no—
133C2×C22⋊C8—22no—
134C2×C22⋊C8—22no—
135C2×C22⋊C8C2×C414yes—
136C2×C22⋊C8C2×C414yes—
137C2×C22⋊C8C2×C414yes—
138C2×C22⋊C8C2×C414yes—
139C2×C22⋊C8C2×C414yescomplemented
140C2×C22⋊C8C2×C414yescomplemented
141#405—232no—
142C2×#97—22no—
143C2×#97—22no—
144C2×#97—22no—
145C2×#97—22no—
146C2×#97—22no—
147C2×#97—22no—
148C2×#97—22no—
149C2×#97—22no—
150C2×#97D414yescomplemented
151C2×C4×C8—22no—
152C2×C4×C8—22no—
153C2×C4×C8—22no—
154C2×C4×C8—22no—
155C2×C4×C8—22no—
156C2×C4×C8—22no—
157C2×C4×C8—22no—
158C2×C4×C8—22no—
159C2×C4×C8D414yescomplemented
160#388—28no—
161#387—28no—
162#386—28no—
163#385—28no—
164C4×C4⋊C4—22no—
165C4×C4⋊C4—22no—
166C4×C22⋊C4—22no—
167C4×C22⋊C4—22no—
168C4×C22⋊C4—22no—
169C4×C22⋊C4—22no—
170#376—22no—
171#376—22no—
172C2×#95C2×C412yes—
173C2×#95C2×C412yes—
174C2×#95C2×C412yes—
175C2×#95C2×C412yes—
176C2×#95C2×C412yes—
177#336—22no—
178#336—22no—
179#336—22no—
180#336—22no—
181#336—22no—
182#336—22no—
183#336—22no—
184#336—22no—
185#336—22no—
186#336—22no—
187#336C2×C414yescomplemented
188#336C2×C414yescomplemented
189#336C2×C414yescomplemented
190#336C2×C414yescomplemented
191C25C22×C411yescharacteristic
192C25C22×C411yescharacteristic
193C22×D4—22no—
194C22×D4—22no—
195C22×D4—24no—
196C22×D4—42no—
197C22×D4C4214yes—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—24no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—42no—
224C23×C4—42no—
225C23×C4C22×C412yes—
226C23×C4C22×C411yescharacteristic
227C23×C4C22×C411yescharacteristic
228C23×C4C22×C411yescharacteristic
229C23×C4C22×C412yes—
230C23×C4C22×C412yes—
231C23×C4C22×C412yes—
232C23×C4C22×C412yes—
233C23×C4C22×C411yescharacteristic
234C23×C4C22×C412yes—
235C23×C4C22×C412yes—
236C23×C4C22×C412yes—
237C23×C4C2×D412yes—
238C23×C4C2×D412yes—
239C23×C4#4112yes—
240C23×C4#4112yes—
241C23×C4C2411yescharacteristic
242C2×M16—28no—
243C2×M16—28no—
244C2×M16—28no—
245C2×M16—28no—
246C2×M16—28no—
247C2×M16—28no—
248C2×M16—28no—
249C22×C8—28no—
250C22×C8—28no—
251C22×C8—28no—
252C22×C8—28no—
253C22×C8—28no—
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—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—28no—
271C22×C8—28no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8C22×C412yes—
297C22×C8C22×C412yes—
298C22×C8C22×C412yes—
299C22×C8C22×C412yes—
300C22×C8C22×C412yes—
301C22×C8C22×C412yes—
302C22×C8C22×C412yes—
303C22×C8C22×C412yes—
304C22×C8C2×D412yes—
305C22×C8C2×D412yes—
306C22×C8C2×D412yes—
307C22×C8C2×D412yes—
308C22×C8#4112yes—
309C22×C8#4112yes—
310C22×C8#4112yes—
311C22×C8#4112yes—
312C4×D4—28no—
313C4×D4—28no—
314C4×D4—28no—
315C4×D4—28no—
316#117—28no—
317#117—28no—
318#117—28no—
319#117—28no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4C4214yes—
328C2×C4⋊C4C22⋊C418yes—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4C4214yes—
342C2×C22⋊C4C4214yes—
343C2×C22⋊C4C22⋊C418yes—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—44no—
368C2×C42—44no—
369C2×C42—44no—
370C2×C42—44no—
371C2×C42C22×C412yes—
372C2×C42C22×C412yes—
373C2×C42C2×D412yes—
374C2×C42C2×D412yes—
375C2×C42C2×D412yes—
376C2×C42C2×D412yes—
377C2×C42C2×D412yes—
378C2×C42C2×D412yes—
379C2×C42#4112yes—
380C2×C42#4112yes—
381C22⋊C8—28no—
382C22⋊C8—28no—
383C22⋊C8—28no—
384C22⋊C8—28no—
385C22⋊C8—28no—
386C22⋊C8—28no—
387#97—28no—
388#97—28no—
389#97—44no—
390C4×C8—28no—
391C4×C8—28no—
392C4×C8—44no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24C2×C4212yes—
416C24C2×C4212yes—
417C24C2×C22⋊C412yes—
418C24#11712yes—
419C24#13114yes—
420C24C23×C411yescharacteristic
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—44no—
424C2×D4—48no—
425C2×D4—48no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
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—216no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
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—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—48no—
505C22×C4—48no—
506C22×C4—48no—
507C22×C4—48no—
508C22×C4—48no—
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—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—48no—
526C22×C4C2×C4212yes—
527C22×C4C2×C4212yes—
528C22×C4C2×C4212yes—
529C22×C4C2×C4212yes—
530C22×C4C2×C22⋊C414yes—
531C22×C4C2×C22⋊C412yes—
532C22×C4C2×C22⋊C414yes—
533C22×C4#11712yes—
534C22×C4C4×D414yes—
535C22×C4C4×D414yes—
536C22×C4C4×D414yes—
537C22×C4C4×D414yes—
538C22×C4C4×D414yes—
539C22×C4C4×D414yes—
540C22×C4#13114yes—
541C22×C4C23×C411yescharacteristic
542C22×C4C23×C411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C2×#4111yescharacteristic
548C22×C4C2×#4111yescharacteristic
549C22×C4C2×#4111yescharacteristic
550C22×C4C2×#4111yescharacteristic
551C22×C4C2×#4111yescharacteristic
552C22×C4C2×#4111yescharacteristic
553C22×C4C2×#4111yescharacteristic
554C22×C4C2×#4111yescharacteristic
555M16—232no—
556C2×C8—232no—
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—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—41no—
602C2×C8—41no—
603C2×C8—41no—
604C2×C8—41no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8C4×D414yes—
610C2×C8C4×D414yes—
611C2×C8C4×D414yes—
612C2×C8C4×D414yes—
613C4⋊C4—28no—
614C4⋊C4—216no—
615C4⋊C4—48no—
616C22⋊C4—28no—
617C22⋊C4—28no—
618C22⋊C4—216no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—48no—
638C42#12014yes—
639C42#12114yes—
640C42#12114yes—
641C42#12314yes—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23C4×C22⋊C414yes—
687C23#40514yescomplemented
688C23C22×C4211yescharacteristic
689C23C22×C22⋊C411yescharacteristic
690C23C2×#11711yescharacteristic
691C23C2×C4×D411yescharacteristic
692C23C2×C4×D411yescharacteristic
693C23C4×#4111yescharacteristic
694C23C4×#4111yescharacteristic
695C23C2×#13112yes—
696C23C2×#13112yes—
697C23#56812yes—
698C23#56812yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—432no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4C4×C22⋊C414yes—
768C2×C4#38618yes—
769C2×C4C2×C4×D411yescharacteristic
770C2×C4C2×C4×D411yescharacteristic
771C2×C4C2×C4×D411yescharacteristic
772C2×C4C2×C4×D411yescharacteristic
773C2×C4C2×C4×D411yescharacteristic
774C2×C4C2×C4×D411yescharacteristic
775C2×C4C2×C4×D411yescharacteristic
776C2×C4C2×C4×D411yescharacteristic
777C2×C4C4×#4111yescharacteristic
778C2×C4C4×#4111yescharacteristic
779C2×C4C4×#4111yescharacteristic
780C2×C4C4×#4111yescharacteristic
781C2×C4C2×#12011yescharacteristic
782C2×C4C2×#12111yescharacteristic
783C2×C4C2×#12111yescharacteristic
784C2×C4C2×#12311yescharacteristic
785C2×C4#52511yescharacteristic
786C2×C4#52511yescharacteristic
787C2×C4#52511yescharacteristic
788C2×C4#52511yescharacteristic
789C2×C4#52511yescharacteristic
790C2×C4#52511yescharacteristic
791C2×C4#52911yescharacteristic
792C2×C4#52911yescharacteristic
793C2×C4#52911yescharacteristic
794C2×C4#52911yescharacteristic
795C2×C4#53211yescharacteristic
796C2×C4#53211yescharacteristic
797C8—24no—
798C8—24no—
799C8—24no—
800C8—24no—
801C8—42no—
802C8—42no—
803C8—42no—
804C8—42no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—24no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22C2×C4×C22⋊C411yescharacteristic
828C22C42×D411yescharacteristic
829C22C42×D411yescharacteristic
830C22C2×#38611yescharacteristic
831C22#229011yescharacteristic
832C22#229011yescharacteristic
833C22#229711yescharacteristic
834C22C2×#40511yescharacteristic
835C22#287311yescharacteristic
836C22C4×#13111yescharacteristic
837C22#287511yescharacteristic
838C22#288012yes—
839C22#288012yes—
840C22#292412yes—
841C22#292512yes—
842C22#292912yes—
843C22#293012yes—
844C22#293312yes—
845C22#293312yes—
846C22#296612yes—
847C22#296712yes—
848C22#296812yes—
849C22#296912yes—
850C4—28no—
851C4—24no—
852C4—42no—
853C4—42no—
854C4—44no—
855C4—44no—
856C4—42no—
857C4—82no—
858C4C4×#12011yescharacteristic
859C4C4×#12011yescharacteristic
860C4C4×#12111yescharacteristic
861C4C4×#12111yescharacteristic
862C4C4×#12111yescharacteristic
863C4C4×#12111yescharacteristic
864C4C4×#12311yescharacteristic
865C4C4×#12311yescharacteristic
866C2—44no—
867C2—44no—
868C2C4×#38611yescharacteristic
869C2#2037811yescharacteristic
870C2#2037911yescharacteristic
871C2#2048411yescharacteristic
872C2#2048711yescharacteristic
873C2#2049011yescharacteristic
874C2#2049311yescharacteristic
875C2#2089912yes—
876C2#2110912yes—
877C2#2111212yes—
878C2#2138112yes—
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
1. C22×#405C2semidirect
5. C2×#1749C2semidirect
6. C2×#1750C2semidirect
7. C2×C4×C22⋊C8C2semidirect
8. #10922C2semidirect
9. #10921C2semidirect
10. #10875C2semidirect
11. #10874C2semidirect
12. #10715C2semidirect
13. #10714C2semidirect
14. #10694C2semidirect
15. #10694C2semidirect
46. #1870C4semidirect
47. #1869C4semidirect
75. C22×M16C2×C4semidirect
82. C23×C8C2×C4semidirect
139. C2×C22⋊C8C2×C4semidirect
140. C2×C22⋊C8C2×C4semidirect
150. C2×#97D4semidirect
159. C2×C4×C8D4semidirect
187. #336C2×C4semidirect
188. #336C2×C4semidirect
189. #336C2×C4semidirect
190. #336C2×C4semidirect
687. C23#405semidirect

Maximal subgroups

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

subgroupindex
C22×#4052
C2×#22902
C2×#18702
C2×#18692
C2×#17492
C2×#17502
C2×C4×C22⋊C82
#109222
#109212
#108752
#108742
#107152
#107142
#106942