Finite Group Databasebeta

← #354297

Subgroups — #354297

Order 512.

2162 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#435C211yesmaximal, characteristic
2C22×#405C211yesmaximal, characteristic, complemented
3C2×#1869C211yesmaximal, characteristic
4C2×#1752C211yesmaximal, characteristic, complemented
5C2×#1753C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊C4C211yesmaximal, characteristic, complemented
7#13839C211yesmaximal, characteristic
8#10922C211yesmaximal, characteristic, complemented
9#10921C211yesmaximal, characteristic, complemented
10#10877C211yesmaximal, characteristic, complemented
11#10876C211yesmaximal, characteristic, complemented
12#10714C211yesmaximal, characteristic, complemented
13#10713C211yesmaximal, characteristic, complemented
14#10696C211yesmaximal, characteristic, complemented
15#10696C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic
21C2×#435—24no—
22C2×#435—24no—
23C2×#435C418yescomplemented
24C22×C4⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C2×#405—24no—
31C2×#405—24no—
32C2×#405—24no—
33C22×#97C2211yescharacteristic
34C22×#97C2211yescharacteristic
35C22×#97C2211yescharacteristic
36C22×#97C2211yescharacteristic
37C22×C4×C8C2211yescharacteristic
38C22×C4×C8C2211yescharacteristic
39C22×C4×C8C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43#1869C418yescomplemented
44#1753—24no—
45#1752—24no—
46C8×C22⋊C4—24no—
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic
59#1441C412yes—
60#1440C412yes—
61#1439C412yes—
62#1438C412yes—
63C4×#95C2211yescharacteristic
64C4×#95C2211yescharacteristic
65C23×D4C2×C411yescharacteristic
66C24×C4C2311yescharacteristic
67C24×C4C2311yescharacteristic
68C22×M16—22no—
69C22×M16—22no—
70C22×M16—22no—
71C22×M16—22no—
72C22×M16C2×C414yes—
73C22×M16D414yes—
74C22×M16D414yes—
75C23×C8—22no—
76C23×C8—22no—
77C23×C8—22no—
78C23×C8—22no—
79C23×C8—22no—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—22no—
83C23×C8—22no—
84C23×C8—22no—
85C23×C8—22no—
86C23×C8—22no—
87C23×C8C2×C414yes—
88C23×C8C2×C414yes—
89C23×C8C2311yescharacteristic
90C23×C8C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C2×C4×D4—22no—
98C2×C4×D4—22no—
99C2×C4×D4—22no—
100C2×C4×D4—22no—
101C2×C4×D4C2×C414yes—
102C2×C4×D4C2×C414yes—
103C2×#117—22no—
104C2×#117—22no—
105C2×#117—22no—
106C2×#117—22no—
107C2×#117—22no—
108C2×#117—22no—
109C22×C4⋊C4C2×C412yes—
110C22×C4⋊C4C2×C411yescharacteristic
111C22×C22⋊C4C2×C412yes—
112C22×C22⋊C4C2×C412yes—
113C22×C22⋊C4C2×C412yes—
114C22×C22⋊C4C2×C412yes—
115C22×C22⋊C4C2×C411yescharacteristic
116C22×C22⋊C4C2×C411yescharacteristic
117C22×C42C2311yescharacteristic
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121C22×C42C2311yescharacteristic
122#435—232no—
123C2×C4⋊C8—22no—
124C2×C4⋊C8—22no—
125C2×C4⋊C8C2×C414yes—
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⋊C8—22no—
136C2×C22⋊C8C2×C414yes—
137C2×C22⋊C8C2×C414yes—
138C2×C22⋊C8C2×C414yes—
139C2×C22⋊C8C2×C414yes—
140C2×C22⋊C8C2×C414yes—
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×#97—22no—
151C2×#97—22no—
152C2×#97C2×C414yes—
153C2×#97D414yescomplemented
154C2×C4×C8—22no—
155C2×C4×C8—22no—
156C2×C4×C8—22no—
157C2×C4×C8—22no—
158C2×C4×C8—22no—
159C2×C4×C8—22no—
160C2×C4×C8—22no—
161C2×C4×C8—22no—
162C2×C4×C8D414yescomplemented
163C4×C22⋊C4—22no—
164C4×C22⋊C4—22no—
165C4×C22⋊C4—22no—
166C4×C22⋊C4—22no—
167C4×C22⋊C4—22no—
168C4×C22⋊C4—22no—
169C2×#95C2×C412yes—
170C2×#95C2×C412yes—
171C2×#95C2×C412yes—
172C2×#95C2×C412yes—
173C2×#95C2×C412yes—
174C2×#95C2×C412yes—
175C2×#95C2×C412yes—
176#336—22no—
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#336C2×C414yes—
187#336C2×C414yes—
188C25C22×C411yescharacteristic
189C25C22×C411yescharacteristic
190C22×D4—22no—
191C22×D4—22no—
192C22×D4—24no—
193C22×D4—42no—
194C22×D4C4214yes—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
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—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4C22×C412yes—
216C23×C4C22×C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C22×C411yescharacteristic
219C23×C4C22×C412yes—
220C23×C4C22×C412yes—
221C23×C4C22×C412yes—
222C23×C4C22×C412yes—
223C23×C4C22×C412yes—
224C23×C4C22×C411yescharacteristic
225C23×C4C22×C412yes—
226C23×C4C22×C412yes—
227C23×C4C2×D412yes—
228C23×C4C2×D412yes—
229C23×C4#4112yes—
230C23×C4#4112yes—
231C23×C4C2411yescharacteristic
232C2×M16—28no—
233C2×M16—28no—
234C2×M16—28no—
235C2×M16—28no—
236C2×M16—28no—
237C2×M16—28no—
238C2×M16C22⋊C4116yescomplemented
239C22×C8—28no—
240C22×C8—28no—
241C22×C8—28no—
242C22×C8—28no—
243C22×C8—28no—
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—28no—
257C22×C8—28no—
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—21no—
271C22×C8—21no—
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—28no—
283C22×C8—28no—
284C22×C8—28no—
285C22×C8—44no—
286C22×C8—44no—
287C22×C8—44no—
288C22×C8—44no—
289C22×C8C22×C412yes—
290C22×C8C22×C412yes—
291C22×C8C22×C412yes—
292C22×C8C22×C412yes—
293C22×C8C22×C412yes—
294C22×C8C22×C412yes—
295C22×C8C22×C412yes—
296C22×C8C22×C412yes—
297C22×C8C2×D412yes—
298C22×C8C2×D412yes—
299C22×C8C2×D412yes—
300C22×C8C2×D412yes—
301C22×C8C2×D412yes—
302C22×C8C2×D412yes—
303C22×C8C2×D412yes—
304C22×C8C2×D412yes—
305C22×C8#4112yes—
306C22×C8#4112yes—
307C22×C8#4112yes—
308C22×C8#4112yes—
309C4×D4—28no—
310C4×D4—28no—
311C4×D4—28no—
312C4×D4—28no—
313#117—28no—
314#117—28no—
315#117—28no—
316#117—28no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4C4214yes—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4C4214yes—
340C2×C22⋊C4C4214yes—
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—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
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×C42C22×C412yes—
366C2×C42C22×C412yes—
367C2×C42C2×D412yes—
368C2×C42C2×D412yes—
369C2×C42#4112yes—
370C2×C42#4112yes—
371C4⋊C8—28no—
372C22⋊C8—28no—
373C22⋊C8—28no—
374C22⋊C8—28no—
375C22⋊C8—28no—
376C22⋊C8—28no—
377#97—28no—
378#97—28no—
379#97—28no—
380#97—44no—
381C4×C8—28no—
382C4×C8—28no—
383C4×C8—44no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—42no—
389#95—42no—
390#95—42no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24C2×C4212yes—
409C24C2×C4212yes—
410C24C4×D412yes—
411C24C4×D412yes—
412C24#13114yes—
413C24C23×C411yescharacteristic
414C2×D4—28no—
415C2×D4—28no—
416C2×D4—44no—
417C2×D4—48no—
418C2×D4—48no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
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—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
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—22no—
497C22×C4—22no—
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×C4C2×C4212yes—
515C22×C4C2×C4212yes—
516C22×C4C2×C4212yes—
517C22×C4C2×C4212yes—
518C22×C4C2×C22⋊C414yes—
519C22×C4#11714yes—
520C22×C4C4×D414yes—
521C22×C4C4×D414yes—
522C22×C4C4×D414yes—
523C22×C4C4×D414yes—
524C22×C4C4×D412yes—
525C22×C4C4×D412yes—
526C22×C4#13114yes—
527C22×C4C23×C411yescharacteristic
528C22×C4C23×C411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C22×C4C2×#4111yescharacteristic
536C22×C4C2×#4111yescharacteristic
537C22×C4C2×#4111yescharacteristic
538C22×C4C2×#4111yescharacteristic
539C22×C4C2×#4111yescharacteristic
540C22×C4C2×#4111yescharacteristic
541M16—232no—
542C2×C8—232no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
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—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—416no—
590C2×C8C2×C22⋊C414yes—
591C2×C8C2×C22⋊C414yes—
592C2×C8C4×D414yes—
593C2×C8C4×D414yes—
594C2×C8C4×D414yes—
595C2×C8C4×D414yes—
596C2×C8#12014yes—
597C2×C8#12114yes—
598C2×C8#12114yes—
599C2×C8#12314yes—
600C4⋊C4—216no—
601C4⋊C4—28no—
602C22⋊C4—216no—
603C22⋊C4—216no—
604C22⋊C4—28no—
605C22⋊C4—28no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—41no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23C4×C22⋊C414yes—
673C23#40514yescomplemented
674C23C22×C4211yescharacteristic
675C23C2×C4×D411yescharacteristic
676C23C2×C4×D411yescharacteristic
677C23C2×C4×D411yescharacteristic
678C23C2×C4×D411yescharacteristic
679C23C4×#4111yescharacteristic
680C23C4×#4111yescharacteristic
681C23C2×#13112yes—
682C23C2×#13112yes—
683C23#56812yes—
684C23#56812yes—
685D4—416no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
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—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4C4×C22⋊C414yes—
754C2×C4C22×C22⋊C411yescharacteristic
755C2×C4C2×#11711yescharacteristic
756C2×C4C2×C4×D411yescharacteristic
757C2×C4C2×C4×D411yescharacteristic
758C2×C4C2×C4×D411yescharacteristic
759C2×C4C2×C4×D411yescharacteristic
760C2×C4C2×C4×D411yescharacteristic
761C2×C4C2×C4×D411yescharacteristic
762C2×C4C4×#4111yescharacteristic
763C2×C4C4×#4111yescharacteristic
764C2×C4C4×#4111yescharacteristic
765C2×C4C4×#4111yescharacteristic
766C2×C4C2×#12011yescharacteristic
767C2×C4C2×#12111yescharacteristic
768C2×C4C2×#12111yescharacteristic
769C2×C4C2×#12311yescharacteristic
770C2×C4#52511yescharacteristic
771C2×C4#52511yescharacteristic
772C2×C4#52511yescharacteristic
773C2×C4#52511yescharacteristic
774C2×C4#52511yescharacteristic
775C2×C4#52511yescharacteristic
776C2×C4#52911yescharacteristic
777C2×C4#52911yescharacteristic
778C2×C4#52911yescharacteristic
779C2×C4#52911yescharacteristic
780C2×C4#53211yescharacteristic
781C2×C4#53211yescharacteristic
782C8—24no—
783C8—24no—
784C8—24no—
785C8—42no—
786C8—42no—
787C8—42no—
788C8—42no—
789C8#38618yes—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—44no—
803C22—44no—
804C22—42no—
805C22—42no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22C2×C4×C22⋊C411yescharacteristic
813C22C42×D411yescharacteristic
814C22C42×D411yescharacteristic
815C22C4×#12011yescharacteristic
816C22C4×#12111yescharacteristic
817C22C4×#12111yescharacteristic
818C22C4×#12311yescharacteristic
819C22C2×#40511yescharacteristic
820C22#287311yescharacteristic
821C22C4×#13111yescharacteristic
822C22#287511yescharacteristic
823C22#292912yes—
824C22#293212yes—
825C22#293312yes—
826C22#293312yes—
827C22#293312yes—
828C22#293312yes—
829C22#293512yes—
830C22#293512yes—
831C22#296612yes—
832C22#296712yes—
833C22#296812yes—
834C22#296812yes—
835C4—24no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—44no—
840C4—44no—
841C4—44no—
842C4—82no—
843C4C2×#38611yescharacteristic
844C4#229011yescharacteristic
845C4#229011yescharacteristic
846C4#229711yescharacteristic
847C4C4×#12011yescharacteristic
848C4C4×#12111yescharacteristic
849C4C4×#12111yescharacteristic
850C4C4×#12311yescharacteristic
851C2—44no—
852C2—44no—
853C2C4×#38611yescharacteristic
854C2#2038711yescharacteristic
855C2#2038911yescharacteristic
856C2#2048411yescharacteristic
857C2#2048811yescharacteristic
858C2#2049211yescharacteristic
859C2#2049311yescharacteristic
860C2#2144312yes—
861C2#2149212yes—
862C2#2149612yes—
863C2#2156812yes—
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
2. C22×#405C2semidirect
4. C2×#1752C2semidirect
5. C2×#1753C2semidirect
6. C2×C8×C22⋊C4C2semidirect
8. #10922C2semidirect
9. #10921C2semidirect
10. #10877C2semidirect
11. #10876C2semidirect
12. #10714C2semidirect
13. #10713C2semidirect
14. #10696C2semidirect
15. #10696C2semidirect
23. C2×#435C4semidirect
43. #1869C4semidirect
153. C2×#97D4semidirect
162. C2×C4×C8D4semidirect
238. C2×M16C22⋊C4semidirect
673. C23#405semidirect

Maximal subgroups

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

subgroupindex
C22×#4352
C22×#4052
C2×#18692
C2×#17522
C2×#17532
C2×C8×C22⋊C42
#138392
#109222
#109212
#108772
#108762
#107142
#107132
#106962