Finite Group Databasebeta

← #388403

Subgroups — #388403

Order 512.

1696 conjugacy classes of subgroups.

The subgroup lattice has 1147 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1955C211yesmaximal, characteristic, complemented
2C2×#1923C211yesmaximal, characteristic, complemented
3C2×#1869C211yesmaximal, characteristic, complemented
4C2×#1869C211yesmaximal, characteristic, complemented
5C4×#392C211yesmaximal, characteristic
6#11255C211yesmaximal, characteristic, complemented
7#11147C211yesmaximal, characteristic, complemented
8#10964C211yesmaximal, characteristic, complemented
9#10964C211yesmaximal, characteristic, complemented
10#10964C211yesmaximal, characteristic, complemented
11#10922C211yesmaximal, characteristic, complemented
12#10921C211yesmaximal, characteristic, complemented
13#10921C211yesmaximal, characteristic, complemented
14#10798C211yesmaximal, characteristic, complemented
15#10714C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27C22×C22⋊C8C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×#97C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34C2×#392C411yescharacteristic
35C2×C4×C22⋊C4C2211yescharacteristic
36C2×C4×C22⋊C4C2211yescharacteristic
37C2×C4×C22⋊C4C2211yescharacteristic
38#1955—24no—
39#1923—24no—
40#1869—24no—
41#1869—24no—
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
55#1444C411yescharacteristic
56#1439C411yescharacteristic
57#1439C411yescharacteristic
58#1439C411yescharacteristic
59#1438C411yescharacteristic
60#1438C411yescharacteristic
61#1438C411yescharacteristic
62C4×#95C2211yescharacteristic
63C23×D4C2×C411yescharacteristic
64C23×D4C2×C411yescharacteristic
65C23×D4C2×C411yescharacteristic
66C24×C4C2311yescharacteristic
67C24×C4C2311yescharacteristic
68C24×C4C2311yescharacteristic
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—41no—
73C23×C8—41no—
74C23×C8—41no—
75C23×C8—41no—
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C2×C4×D4—22no—
85C2×C4×D4—22no—
86C2×C4×D4—22no—
87C2×C4×D4—22no—
88C2×C4×D4—22no—
89C2×C4×D4—22no—
90C2×C4×D4—41no—
91C2×C4×D4—41no—
92C2×C4×D4—41no—
93C2×C4×D4—41no—
94C2×C4×D4—41no—
95C2×C4×D4—41no—
96C2×C4×D4—41no—
97C2×C4×D4—41no—
98C2×C4×D4—41no—
99C2×C4×D4—41no—
100C2×C4×D4—41no—
101C2×C4×D4—41no—
102C22×C4⋊C4C2×C411yescharacteristic
103C22×C4⋊C4C2×C411yescharacteristic
104C22×C4⋊C4C2×C411yescharacteristic
105C22×C22⋊C4C2×C411yescharacteristic
106C22×C22⋊C4C2×C411yescharacteristic
107C22×C22⋊C4C2×C411yescharacteristic
108C22×C22⋊C4C2×C411yescharacteristic
109C22×C22⋊C4C2×C411yescharacteristic
110C22×C22⋊C4C2×C411yescharacteristic
111C22×C22⋊C4C2×C411yescharacteristic
112C22×C22⋊C4C2×C411yescharacteristic
113C22×C22⋊C4C2×C411yescharacteristic
114C22×C22⋊C4C2×C411yescharacteristic
115C22×C22⋊C4C2×C411yescharacteristic
116C22×C22⋊C4C2×C411yescharacteristic
117C22×C42C2311yescharacteristic
118C22×C42C2311yescharacteristic
119C22×C42C2311yescharacteristic
120C22×C42C2311yescharacteristic
121C2×C4⋊C8—22no—
122C2×C4⋊C8—22no—
123C2×C4⋊C8—41no—
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⋊C8—22no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—22no—
140C2×C22⋊C8—41no—
141C2×C22⋊C8—41no—
142C2×C22⋊C8—41no—
143C2×C22⋊C8—41no—
144C2×C22⋊C8—41no—
145C2×C22⋊C8—41no—
146C2×C22⋊C8—41no—
147C2×C22⋊C8—41no—
148C2×C22⋊C8—41no—
149C2×C22⋊C8—41no—
150C2×C22⋊C8—41no—
151C2×C22⋊C8—41no—
152C2×C22⋊C8—41no—
153C2×C22⋊C8—41no—
154C2×C22⋊C8—41no—
155C2×C22⋊C8—41no—
156C2×C22⋊C8D414yescomplemented
157C2×#97—22no—
158C2×#97—22no—
159C2×#97—41no—
160C2×C4×C8—22no—
161C2×C4×C8—41no—
162C2×C4×C8—41no—
163#392—24no—
164C4×C22⋊C4—22no—
165C4×C22⋊C4—22no—
166C4×C22⋊C4—41no—
167C4×C22⋊C4—41no—
168C4×C22⋊C4—41no—
169C4×C22⋊C4—41no—
170C2×#95C2×C411yescharacteristic
171C2×#95C2×C411yescharacteristic
172C2×#95C2×C411yescharacteristic
173C2×#95C2×C411yescharacteristic
174C2×#95C2×C411yescharacteristic
175C2×#95C2×C411yescharacteristic
176C2×#95C2×C411yescharacteristic
177C2×#95C2×C411yescharacteristic
178C2×#95C2×C411yescharacteristic
179C2×#95C2×C411yescharacteristic
180#336—22no—
181#336—22no—
182#336—22no—
183#336—22no—
184#336—41no—
185#336—41no—
186#336—41no—
187#336—41no—
188#336—41no—
189#336—41no—
190#336—41no—
191#336—41no—
192#336D414yescomplemented
193C25C22×C411yescharacteristic
194C25C22×C411yescharacteristic
195C25C22×C411yescharacteristic
196C22×D4—22no—
197C22×D4—22no—
198C22×D4—22no—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—22no—
202C22×D4—22no—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—41no—
210C22×D4—41no—
211C22×D4—41no—
212C22×D4—41no—
213C22×D4—41no—
214C22×D4—41no—
215C22×D4—41no—
216C22×D4—41no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4C22×C411yescharacteristic
258C23×C4C22×C411yescharacteristic
259C23×C4C22×C411yescharacteristic
260C23×C4C22×C411yescharacteristic
261C23×C4C22×C411yescharacteristic
262C23×C4C22×C411yescharacteristic
263C23×C4C22×C411yescharacteristic
264C23×C4C22×C411yescharacteristic
265C23×C4C22×C411yescharacteristic
266C23×C4C22×C411yescharacteristic
267C23×C4C22×C411yescharacteristic
268C23×C4C2×D412yes—
269C23×C4#4112yes—
270C23×C4C2411yescharacteristic
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—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×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—21no—
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—44no—
322C22×C8—44no—
323C22×C8—44no—
324C22×C8—44no—
325C22×C8—44no—
326C22×C8—44no—
327C22×C8—44no—
328C22×C8C2×D412yes—
329C22×C8C2×D412yes—
330C22×C8C2×D412yes—
331C22×C8C2×D412yes—
332C22×C8#4112yes—
333C22×C8#4112yes—
334C4×D4—44no—
335C4×D4—44no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4—44no—
339C4×D4—44no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—44no—
344C4×D4—44no—
345C4×D4—44no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—41no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4—41no—
388C2×C22⋊C4—41no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4M1614yes—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42C2×D412yes—
414C2×C42#4112yes—
415C4⋊C8—44no—
416C22⋊C8—44no—
417C22⋊C8—44no—
418C22⋊C8—44no—
419C22⋊C8—44no—
420C22⋊C8—44no—
421C22⋊C8—44no—
422C22⋊C8—44no—
423C22⋊C8—44no—
424C22⋊C8—44no—
425C22⋊C8—44no—
426C22⋊C8—44no—
427#97—44no—
428C4×C8—44no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—41no—
434#95—41no—
435#95—41no—
436#95—41no—
437#95—41no—
438#95—41no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24C4×D412yes—
480C24C2×M1612yes—
481C24#13112yes—
482C24#13112yes—
483C24#13112yes—
484C24C23×C411yescharacteristic
485C2×D4—28no—
486C2×D4—28no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4C4×D412yes—
661C22×C4C4×D412yes—
662C22×C4C4×D412yes—
663C22×C4C2×M1612yes—
664C22×C4C2×M1612yes—
665C22×C4#13112yes—
666C22×C4#13112yes—
667C22×C4C22×D411yescharacteristic
668C22×C4C22×D411yescharacteristic
669C22×C4C2×#4111yescharacteristic
670C22×C4C2×#4111yescharacteristic
671C22×C4C2×#4111yescharacteristic
672C22×C4C2×#4111yescharacteristic
673C22×C4H(5,𝔽2)11yescharacteristic
674C22×C4H(5,𝔽2)11yescharacteristic
675C22×C4H(5,𝔽2)11yescharacteristic
676C22×C4H(5,𝔽2)11yescharacteristic
677C22×C4H(5,𝔽2)11yescharacteristic
678C22×C4H(5,𝔽2)11yescharacteristic
679C22×C4H(5,𝔽2)11yescharacteristic
680C22×C4H(5,𝔽2)11yescharacteristic
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—22no—
699C2×C8—416no—
700C2×C8—41no—
701C2×C8—41no—
702C2×C8—41no—
703C2×C8—41no—
704C2×C8—41no—
705C2×C8—41no—
706C2×C8—41no—
707C2×C8—41no—
708C2×C8—41no—
709C2×C8—41no—
710C2×C8—41no—
711C2×C8—41no—
712C2×C8—41no—
713C2×C8—41no—
714C2×C8—41no—
715C2×C8—41no—
716C2×C8—41no—
717C2×C8—41no—
718C2×C8—41no—
719C2×C8—41no—
720C2×C8—41no—
721C2×C8—41no—
722C2×C8—41no—
723C2×C8—41no—
724C2×C8—41no—
725C2×C8—41no—
726C2×C8—41no—
727C2×C8—41no—
728C2×C8—41no—
729C2×C8—41no—
730C2×C8—41no—
731C2×C8—41no—
732C2×C8—41no—
733C2×C8—41no—
734C2×C8—41no—
735C2×C8—41no—
736C2×C8—41no—
737C2×C8—41no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C22⋊C4—28no—
742C22⋊C4—44no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C22⋊C4—44no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—22no—
757C42—41no—
758C42—41no—
759C42—41no—
760C42—41no—
761C42—41no—
762C42—41no—
763C42—41no—
764C42—41no—
765C42—41no—
766C42—41no—
767C42—41no—
768C42—41no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23#43614yes—
874C23C2×C4×D411yescharacteristic
875C23C2×C4×D411yescharacteristic
876C23C4×#4111yescharacteristic
877C23#51811yescharacteristic
878C23#51811yescharacteristic
879C23#51811yescharacteristic
880C23#51811yescharacteristic
881C23C22×M1611yescharacteristic
882C23C2×#13111yescharacteristic
883C23C2×#13111yescharacteristic
884C23C2×#13111yescharacteristic
885C23C2×#13111yescharacteristic
886C23C2×#13111yescharacteristic
887C23#56811yescharacteristic
888C23#56811yescharacteristic
889D4—416no—
890D4—416no—
891D4—416no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—81no—
978C2×C4—81no—
979C2×C4—81no—
980C2×C4—81no—
981C2×C4—81no—
982C2×C4—81no—
983C2×C4—81no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—81no—
992C2×C4—81no—
993C2×C4#53411yescharacteristic
994C2×C4#53511yescharacteristic
995C2×C4#53511yescharacteristic
996C2×C4#53511yescharacteristic
997C2×C4#53811yescharacteristic
998C2×C4#53811yescharacteristic
999C2×C4#53811yescharacteristic
1000C2×C4#53811yescharacteristic
1001C2×C4#54011yescharacteristic
1002C2×C4#54011yescharacteristic
1003C2×C4#54011yescharacteristic
1004C2×C4#54011yescharacteristic
1005C2×C4D4211yescharacteristic
1006C2×C4#54611yescharacteristic
1007C2×C4#54611yescharacteristic
1008C2×C4#54611yescharacteristic
1009C2×C4#54611yescharacteristic
1010C2×C4#54611yescharacteristic
1011C2×C4#55011yescharacteristic
1012C2×C4#55111yescharacteristic
1013C2×C4#55311yescharacteristic
1014C2×C4#55311yescharacteristic
1015C2×C4#55311yescharacteristic
1016C2×C4#55511yescharacteristic
1017C2×C4#56011yescharacteristic
1018C2×C4#56011yescharacteristic
1019C2×C4#56011yescharacteristic
1020C2×C4H(3,𝔽4)11yescharacteristic
1021C8—42no—
1022C8—42no—
1023C8—42no—
1024C8—42no—
1025C8—42no—
1026C8—42no—
1027C8—81no—
1028C8—81no—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22#232111yescharacteristic
1075C22#232811yescharacteristic
1076C22#233311yescharacteristic
1077C22#235811yescharacteristic
1078C22#236311yescharacteristic
1079C22#236411yescharacteristic
1080C22#237511yescharacteristic
1081C22C2×#43611yescharacteristic
1082C22#292911yescharacteristic
1083C22#292911yescharacteristic
1084C22#292911yescharacteristic
1085C22#293311yescharacteristic
1086C22D4×M1611yescharacteristic
1087C22#293511yescharacteristic
1088C22#293511yescharacteristic
1089C22#296511yescharacteristic
1090C22#296611yescharacteristic
1091C22#296811yescharacteristic
1092C22#296811yescharacteristic
1093C22#297311yescharacteristic
1094C22#297411yescharacteristic
1095C22#297411yescharacteristic
1096C22#297411yescharacteristic
1097C22#297611yescharacteristic
1098C22#297611yescharacteristic
1099C22#297611yescharacteristic
1100C22#297711yescharacteristic
1101C22#297711yescharacteristic
1102C22#297711yescharacteristic
1103C22#297711yescharacteristic
1104C22#297711yescharacteristic
1105C22#297911yescharacteristic
1106C22#298011yescharacteristic
1107C22#298111yescharacteristic
1108C22#298111yescharacteristic
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—81no—
1117C4—81no—
1118C4—81no—
1119C4—81no—
1120C4#267011yescharacteristic
1121C4#267311yescharacteristic
1122C4#269911yescharacteristic
1123C4#270311yescharacteristic
1124C4#270311yescharacteristic
1125C4#271411yescharacteristic
1126C4#275311yescharacteristic
1127C4#275611yescharacteristic
1128C2—44no—
1129C2—82no—
1130C2—82no—
1131C2#1452011yescharacteristic
1132C2#2203211yescharacteristic
1133C2#2203711yescharacteristic
1134C2#2226111yescharacteristic
1135C2#2226611yescharacteristic
1136C2#2233311yescharacteristic
1137C2#2234011yescharacteristic
1138C2#2284311yescharacteristic
1139C2#2284811yescharacteristic
1140C2#2308511yescharacteristic
1141C2#2308911yescharacteristic
1142C2#2312011yescharacteristic
1143C2#2312311yescharacteristic
1144C2#2330711yescharacteristic
1145C2#2331011yescharacteristic
subgroupG/H
center, Frattini, cosocleC23×C4C24
commutator, socleC24C23×C4
prime radicalC2×#392C4
LCSG ▷ C24 ▷ 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. C2×#1955C2semidirect
2. C2×#1923C2semidirect
3. C2×#1869C2semidirect
4. C2×#1869C2semidirect
6. #11255C2semidirect
7. #11147C2semidirect
8. #10964C2semidirect
9. #10964C2semidirect
10. #10964C2semidirect
11. #10922C2semidirect
12. #10921C2semidirect
13. #10921C2semidirect
14. #10798C2semidirect
15. #10714C2semidirect
156. C2×C22⋊C8D4semidirect
192. #336D4semidirect

Maximal subgroups

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

subgroupindex
C2×#19552
C2×#19232
C2×#18692
C4×#3922
#112552
#111472
#109642
#109222
#109212
#107982
#107142