Finite Group Databasebeta

← #221728

Subgroups — #221728

Order 512.

1430 conjugacy classes of subgroups.

The subgroup lattice has 1021 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36107C211yesmaximal, characteristic
2#22554C211yesmaximal, characteristic, complemented
3C2×#1509C211yesmaximal, characteristic, complemented
4C22×#327C211yesmaximal, characteristic
5#13814C211yesmaximal, characteristic, complemented
6#9713C211yesmaximal, characteristic, complemented
7#9682C211yesmaximal, characteristic, complemented
8#9148C211yesmaximal, characteristic, complemented
9#9143C211yesmaximal, characteristic, complemented
10#9118C211yesmaximal, characteristic, complemented
11#9111C211yesmaximal, characteristic, complemented
12#8571C211yesmaximal, characteristic, complemented
13#8330C211yesmaximal, characteristic, complemented
14#8328C211yesmaximal, characteristic
15#8218C211yesmaximal, characteristic, complemented
16C2×#529C2211yescharacteristic
17C22×#121C2211yescharacteristic
18C2×#432C2211yescharacteristic, complemented
19C22×C22⋊C8C2211yescharacteristic
20#2854C2211yescharacteristic
21#2850C2211yescharacteristic
22#2848C2211yescharacteristic
23#2559—21no—
24#2490C411yescharacteristic, complemented
25#2480—21no—
26#2476—21no—
27#2444—21no—
28#2442C411yescharacteristic, complemented
29#2435C411yescharacteristic, complemented
30#2427C411yescharacteristic, complemented
31#2426C411yescharacteristic, complemented
32#2425—21no—
33#2420C411yescharacteristic, complemented
34#2405—21no—
35#2360C411yescharacteristic, complemented
36#2342—21no—
37D4×C22⋊C4—21no—
38D4×C22⋊C4C411yescharacteristic, complemented
39C4×#121C2211yescharacteristic
40C2×#385—21no—
41C2×C4×C4⋊C4C2211yescharacteristic, complemented
42C2×C4×C22⋊C4—21no—
43C2×C4×C22⋊C4C2211yescharacteristic
44C22×#95C2211yescharacteristic
45#1924—21no—
46#1924—21no—
47#1850—21no—
48#1817C2211yescharacteristic, complemented
49#1797C2211yescharacteristic, complemented
50#1779C2211yescharacteristic
51#1752—21no—
52#1749C2211yescharacteristic, complemented
53#1509—24no—
54C2×#328C2211yescharacteristic, complemented
55C2×#328C2211yescharacteristic, complemented
56C2×#328C2211yescharacteristic, complemented
57C2×#328C2211yescharacteristic, complemented
58C2×#327—24no—
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic
62C2×#327C2211yescharacteristic
63C2×#327C2211yescharacteristic
64C2×#327C2211yescharacteristic
65C2×#327C2211yescharacteristic
66C2×#327C2211yescharacteristic
67#1436—21no—
68#1436—21no—
69C4⋊#95C2211yescharacteristic, complemented
70#1434C2211yescharacteristic, complemented
71C22⋊#95C2211yescharacteristic
72C4×#95C2211yescharacteristic, complemented
73#1294C2211yescharacteristic, complemented
74#1294C2211yescharacteristic, complemented
75#1294C2211yescharacteristic, complemented
76#1294C2211yescharacteristic, complemented
77C23×D4—21no—
78C23×D4C2×C411yescharacteristic
79C24×C4—21no—
80C24×C4C2311yescharacteristic
81C23×C8—21no—
82#529—22no—
83#529—22no—
84#529—41no—
85#529—41no—
86C2×#126—21no—
87C2×#125C2×C411yescharacteristic, complemented
88C2×#124C2×C411yescharacteristic, complemented
89C2×#124C2×C411yescharacteristic, complemented
90C2×#123—21no—
91C2×#123—21no—
92C2×C22⋊Q8C2×C411yescharacteristic
93C2×C22⋊Q8C2×C411yescharacteristic
94C2×C22⋊Q8C2311yescharacteristic
95C2×#121—21no—
96C2×#121—21no—
97C2×#121—22no—
98C2×#121—22no—
99C2×#121—41no—
100C2×#121—41no—
101C2×#121C2×C411yescharacteristic
102C2×#121C2×C411yescharacteristic
103C2×#121C2311yescharacteristic
104C2×#121C2311yescharacteristic
105C2×C4×Q8C2×C411yescharacteristic, complemented
106C2×C4×D4—21no—
107C2×C4×D4—21no—
108C2×C4×D4C2×C411yescharacteristic, complemented
109C2×C4×D4C2×C411yescharacteristic, complemented
110C2×#117—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4C2×C411yescharacteristic
114C22×C22⋊C4—21no—
115C22×C22⋊C4—21no—
116C22×C22⋊C4—21no—
117C22×C22⋊C4D411yescharacteristic
118C22×C22⋊C4D411yescharacteristic
119C22×C42—21no—
120C22×C42—21no—
121C22×C42C2311yescharacteristic
122C22×C42C2311yescharacteristic
123#432—22no—
124#432—41no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127C2×C22⋊C8—22no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—41no—
132C2×C22⋊C8C2311yescharacteristic
133C2×C22⋊C8C2311yescharacteristic
134C2×C22⋊C8C2311yescharacteristic
135C2×C22⋊C8C2311yescharacteristic
136C2×#97—21no—
137C2×#97—21no—
138#400—21no—
139#398—21no—
140#397—21no—
141#397—21no—
142#397—21no—
143#396—21no—
144#394—21no—
145#394—21no—
146#394—21no—
147#394—21no—
148#394—21no—
149#394—21no—
150#391C2×C411yescharacteristic, complemented
151#390—21no—
152#390—21no—
153#390C2×C411yescharacteristic, complemented
154#390C2×C411yescharacteristic, complemented
155#390C2×C411yescharacteristic, complemented
156#390C2×C411yescharacteristic, complemented
157#389—21no—
158#389C2×C411yescharacteristic, complemented
159#389C2×C411yescharacteristic, complemented
160#389C2×C411yescharacteristic, complemented
161#388—21no—
162#388—21no—
163#388—21no—
164#388—21no—
165#388—21no—
166#388—21no—
167#388—21no—
168#387—21no—
169#386—21no—
170#386—21no—
171#386—21no—
172#386—21no—
173#386—21no—
174#386—21no—
175#386—21no—
176#386—21no—
177#385—28no—
178#385—21no—
179#385—21no—
180#385—21no—
181#385—21no—
182#385—21no—
183#382C2×C411yescharacteristic, complemented
184#381—21no—
185#380—21no—
186#380—21no—
187#380C2×C411yescharacteristic
188#380C2×C411yescharacteristic
189#380C2311yescharacteristic
190#379—21no—
191#379—21no—
192#379—21no—
193#379—21no—
194C4×C4⋊C4—22no—
195C4×C4⋊C4—41no—
196C4×C4⋊C4C2×C411yescharacteristic, complemented
197C4×C22⋊C4—21no—
198C4×C22⋊C4—21no—
199C4×C22⋊C4—44no—
200C4×C22⋊C4C2×C411yescharacteristic
201C4×C22⋊C4C2×C411yescharacteristic
202C4×C22⋊C4C2×C411yescharacteristic
203C4×C22⋊C4C2×C411yescharacteristic
204C4×C22⋊C4D411yescharacteristic
205C4×C22⋊C4D411yescharacteristic
206C4×C22⋊C4D411yescharacteristic
207C4×C22⋊C4D411yescharacteristic
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—22no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—41no—
216C2×#95D411yescharacteristic
217C2×#95D411yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222#336—21no—
223#336—21no—
224#336—21no—
225#336—21no—
226#328—22no—
227#328—22no—
228#328—41no—
229#328—41no—
230#327—22no—
231#327—22no—
232#327—22no—
233#327—22no—
234#327—22no—
235#327—41no—
236#327—41no—
237#327D414yes—
238C25—21no—
239C25C2×D411yescharacteristic
240C22×Q8C22×C411yescharacteristic
241C22×D4—21no—
242C22×D4—22no—
243C22×D4—21no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4—21no—
247C22×D4—41no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4—81no—
254C22×D4—81no—
255C22×D4—81no—
256C22×D4C22×C411yescharacteristic
257C22×D4C22×C411yescharacteristic
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—24no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—81no—
276C23×C4—81no—
277C23×C4—81no—
278C23×C4C22×C411yescharacteristic
279C23×C4C22×C411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2411yescharacteristic
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—42no—
293C22×C8—42no—
294C22×C8—81no—
295#126—42no—
296#126—42no—
297#125—22no—
298#125—41no—
299#124—22no—
300#124—41no—
301#124—81no—
302#123—42no—
303#123—42no—
304#123—81no—
305#123—81no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—42no—
311C22⋊Q8—81no—
312#121—21no—
313#121—21no—
314#121—22no—
315#121—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—22no—
320#121—42no—
321#121—42no—
322#121—41no—
323#121—41no—
324#121—42no—
325#121—42no—
326#121C2×D412yes—
327#121#4112yes—
328C4×Q8—22no—
329C4×Q8—41no—
330C4×D4—22no—
331C4×D4—41no—
332C4×D4—42no—
333C4×D4—42no—
334C4×D4—81no—
335C4×D4—81no—
336C4×D4—81no—
337#117—42no—
338#117—42no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—81no—
356C2×C4⋊C4—81no—
357C2×C4⋊C4C22×C411yescharacteristic
358C2×C4⋊C4C22×C411yescharacteristic
359C2×C4⋊C4C22×C411yescharacteristic
360C2×C4⋊C4C22×C411yescharacteristic
361C2×C4⋊C4C22×C411yescharacteristic
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4C22⋊C411yescharacteristic
396C2×C22⋊C4C22⋊C411yescharacteristic
397C2×C22⋊C4C22⋊C411yescharacteristic
398C2×C22⋊C4C22⋊C411yescharacteristic
399C2×C22⋊C4C22⋊C411yescharacteristic
400C2×C22⋊C4C22⋊C411yescharacteristic
401C2×C22⋊C4C22⋊C411yescharacteristic
402C2×C22⋊C4C22⋊C411yescharacteristic
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—81no—
414C2×C42—81no—
415C2×C42—81no—
416C2×C42C22×C411yescharacteristic
417C2×C42C22×C411yescharacteristic
418C2×C42C22×C411yescharacteristic
419C2×C42C22×C411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C4⋊C8—42no—
425C4⋊C8—81no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—42no—
434C22⋊C8—42no—
435C22⋊C8—81no—
436C22⋊C8C2×D412yes—
437#97—42no—
438#97—81no—
439#95—24no—
440#95—24no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—81no—
463#95C22⋊C411yescharacteristic
464#95C22⋊C411yescharacteristic
465#95C22⋊C411yescharacteristic
466#95C22⋊C411yescharacteristic
467#95C22⋊C411yescharacteristic
468#95C22⋊C411yescharacteristic
469#95C22⋊C411yescharacteristic
470#95C22⋊C411yescharacteristic
471#95C2×D412yes—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—21no—
479C24—21no—
480C24—41no—
481C24—41no—
482C24—42no—
483C24—42no—
484C24—42no—
485C24—42no—
486C24—81no—
487C24—81no—
488C24—81no—
489C24C2×C22⋊C411yescharacteristic
490C24C2×C22⋊C411yescharacteristic
491C24AGL(1,ℤ/8)12yes—
492C24#13712yes—
493C24C22×D411yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—42no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—42no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—81no—
524C2×D4—84no—
525C2×D4—84no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4—84no—
529C2×D4—84no—
530C2×D4—84no—
531C2×D4—84no—
532C2×D4C4×D412yes—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
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—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—48no—
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—48no—
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—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—82no—
620C22×C4—82no—
621C22×C4—81no—
622C22×C4—84no—
623C22×C4—84no—
624C22×C4—84no—
625C22×C4—84no—
626C22×C4—84no—
627C22×C4C2×C22⋊C411yescharacteristic
628C22×C4C2×C22⋊C411yescharacteristic
629C22×C4C2×C22⋊C411yescharacteristic
630C22×C4C2×C22⋊C411yescharacteristic
631C22×C4C2×C22⋊C411yescharacteristic
632C22×C4C2×C22⋊C411yescharacteristic
633C22×C4C2×C22⋊C411yescharacteristic
634C22×C4C2×C22⋊C411yescharacteristic
635C22×C4C2×C22⋊C411yescharacteristic
636C22×C4C2×C22⋊C411yescharacteristic
637C22×C4C23×C411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C2×#4111yescharacteristic
641C22×C4H(5,𝔽2)11yescharacteristic
642C22×C4H(5,𝔽2)11yescharacteristic
643C2×C8—22no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—84no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—48no—
668C4⋊C4—42no—
669C4⋊C4—41no—
670C4⋊C4—41no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—84no—
676C4⋊C4C4×D412yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—48no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—41no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—41no—
699C22⋊C4—41no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—81no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4#10414yes—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—41no—
723C42—41no—
724C42—41no—
725C42—41no—
726C42—42no—
727C42—81no—
728C42—84no—
729C42—84no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—84no—
775C23—84no—
776C23—84no—
777C23—84no—
778C23—162no—
779C23—162no—
780C23—162no—
781C23#41012yes—
782C23#41712yes—
783C23#41712yes—
784C23C2×#10412yes—
785C23C22×C22⋊C411yescharacteristic
786C23D4211yescharacteristic
787C23#54611yescharacteristic
788C23C2×AGL(1,ℤ/8)11yescharacteristic
789C23C2×#13711yescharacteristic
790C23#57611yescharacteristic
791C23#57711yescharacteristic
792Q8—81no—
793Q8—81no—
794D4—42no—
795D4—42no—
796D4—42no—
797D4—42no—
798D4—42no—
799D4—42no—
800D4—81no—
801D4—81no—
802D4—84no—
803D4—84no—
804D4—84no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—24no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—84no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—84no—
901C2×C4—816no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—81no—
906C2×C4—81no—
907C2×C4—81no—
908C2×C4—81no—
909C2×C4—81no—
910C2×C4—81no—
911C2×C4—81no—
912C2×C4—81no—
913C2×C4—81no—
914C2×C4—162no—
915C2×C4C2×#10412yes—
916C2×C4C2×#10412yes—
917C2×C4C2×C4×D411yescharacteristic
918C2×C4#51811yescharacteristic
919C2×C4D4211yescharacteristic
920C2×C4#54611yescharacteristic
921C8—42no—
922C8—81no—
923C8—81no—
924C8—81no—
925C22—21no—
926C22—21no—
927C22—21no—
928C22—22no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—22no—
933C22—22no—
934C22—21no—
935C22—21no—
936C22—22no—
937C22—21no—
938C22—21no—
939C22—22no—
940C22—21no—
941C22—21no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—44no—
947C22—44no—
948C22—44no—
949C22—44no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—168no—
969C22#150914yescomplemented
970C22D4×C22⋊C411yescharacteristic
971C22C2×#41011yescharacteristic
972C22#288311yescharacteristic
973C22C2×#41711yescharacteristic
974C22#289711yescharacteristic
975C22C22×#10411yescharacteristic
976C22#290111yescharacteristic
977C22#326411yescharacteristic
978C22#326611yescharacteristic
979C22#330611yescharacteristic
980C22#331411yescharacteristic
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—22no—
986C4—22no—
987C4—44no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—42no—
994C4—41no—
995C4—41no—
996C4—41no—
997C4—82no—
998C4—82no—
999C4—82no—
1000C4—81no—
1001C4—81no—
1002C4—81no—
1003C4—81no—
1004C4—81no—
1005C2—21no—
1006C2—21no—
1007C2—24no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—82no—
1012C2—161no—
1013C2C2×#150911yescharacteristic
1014C2#1754711yescharacteristic
1015C2#1760411yescharacteristic
1016C2#1762211yescharacteristic
1017C2#2240511yescharacteristic
1018C2#2241911yescharacteristic
1019C2D4×#10411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22554C2semidirect
3. C2×#1509C2semidirect
5. #13814C2semidirect
6. #9713C2semidirect
7. #9682C2semidirect
8. #9148C2semidirect
9. #9143C2semidirect
10. #9118C2semidirect
11. #9111C2semidirect
12. #8571C2semidirect
13. #8330C2semidirect
15. #8218C2semidirect
18. C2×#432C22semidirect
24. #2490C4semidirect
28. #2442C4semidirect
29. #2435C4semidirect
30. #2427C4semidirect
31. #2426C4semidirect
33. #2420C4semidirect
35. #2360C4semidirect
38. D4×C22⋊C4C4semidirect
41. C2×C4×C4⋊C4C22semidirect
48. #1817C22semidirect
49. #1797C22semidirect
52. #1749C22semidirect
54. C2×#328C22semidirect
55. C2×#328C22semidirect
56. C2×#328C22semidirect
57. C2×#328C22semidirect
69. C4⋊#95C22semidirect
70. #1434C22semidirect
72. C4×#95C22semidirect
73. #1294C22semidirect
74. #1294C22semidirect
75. #1294C22semidirect
76. #1294C22semidirect
87. C2×#125C2×C4semidirect
88. C2×#124C2×C4semidirect
89. C2×#124C2×C4semidirect
105. C2×C4×Q8C2×C4semidirect
108. C2×C4×D4C2×C4semidirect
109. C2×C4×D4C2×C4semidirect
150. #391C2×C4semidirect
153. #390C2×C4semidirect
154. #390C2×C4semidirect
155. #390C2×C4semidirect
156. #390C2×C4semidirect
158. #389C2×C4semidirect
159. #389C2×C4semidirect
160. #389C2×C4semidirect
183. #382C2×C4semidirect
196. C4×C4⋊C4C2×C4semidirect
969. C22#1509semidirect

Maximal subgroups

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

subgroupindex
#361072
#225542
C2×#15092
C22×#3272
#138142
#97132
#96822
#91482
#91432
#91182
#91112
#85712
#83302
#83282
#82182