Finite Group Databasebeta

← #221708

Subgroups — #221708

Order 512.

1760 conjugacy classes of subgroups.

The subgroup lattice has 1111 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36097C211yesmaximal, characteristic
2#22399C211yesmaximal, characteristic, complemented
3C2×#1504C211yesmaximal, characteristic, complemented
4C22×#328C211yesmaximal, characteristic, complemented
5D4×#95C211yesmaximal, characteristic, complemented
6#9713C211yesmaximal, characteristic, complemented
7#9682C211yesmaximal, characteristic, complemented
8#9147C211yesmaximal, characteristic, complemented
9#9143C211yesmaximal, characteristic, complemented
10#9115C211yesmaximal, characteristic, complemented
11#9113C211yesmaximal, characteristic, complemented
12#8578C211yesmaximal, characteristic, complemented
13#8331C211yesmaximal, characteristic, complemented
14#8329C211yesmaximal, characteristic, complemented
15#8219C211yesmaximal, characteristic, complemented
16C2×#548C411yescharacteristic, complemented
17C2×#525C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C4×D4—21no—
20C22×C4×D4C2211yescharacteristic
21C2×#435—21no—
22C2×#407C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24#2850C2211yescharacteristic
25#2848C2211yescharacteristic
26#2847C2211yescharacteristic
27#2540C411yescharacteristic, complemented
28#2536C411yescharacteristic, complemented
29#2472—21no—
30#2463—21no—
31#2461—21no—
32#2449—21no—
33#2443—21no—
34#2416C411yescharacteristic, complemented
35#2415C411yescharacteristic, complemented
36#2410—21no—
37#2409C411yescharacteristic, complemented
38#2407C411yescharacteristic, complemented
39#2361—21no—
40#2358—21no—
41#2352C411yescharacteristic, complemented
42C4×C22⋊Q8C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45#1955—21no—
46#1870—21no—
47#1869—21no—
48#1797C2211yescharacteristic
49#1779C2211yescharacteristic
50#1779C2211yescharacteristic
51#1749C2211yescharacteristic
52#1504—24no—
53C2×#328—24no—
54C2×#328C2211yescharacteristic
55C2×#328C2211yescharacteristic
56C2×#328C2211yescharacteristic
57C2×#328C2211yescharacteristic
58C2×#328C2211yescharacteristic
59C2×#328C2211yescharacteristic
60C2×#328C2211yescharacteristic
61C2×#328C2211yescharacteristic
62C2×#327C2211yescharacteristic
63C2×#327C2211yescharacteristic
64C2×#327C2211yescharacteristic
65C2×#327C2211yescharacteristic
66C4⋊#95—21no—
67C4⋊#95C2211yescharacteristic
68C22⋊#95—21no—
69C22⋊#95—21no—
70C22⋊#95C2211yescharacteristic
71C22⋊#95C2211yescharacteristic
72C4×#95C2211yescharacteristic
73#1294C2211yescharacteristic
74#1294C2211yescharacteristic
75#1294C2211yescharacteristic
76#1294C2211yescharacteristic
77C22×#41C2×C411yescharacteristic, complemented
78C23×Q8C2×C411yescharacteristic, complemented
79C23×D4D411yescharacteristic
80C24×C4—21no—
81C24×C4—21no—
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C22×M16—21no—
85C23×C8—21no—
86#548—44no—
87C2×#124—21no—
88C2×#124C2×C411yescharacteristic, complemented
89#525—22no—
90#525—22no—
91#525—41no—
92#525—41no—
93C2×#123—21no—
94C2×C22⋊Q8—21no—
95C2×C22⋊Q8—21no—
96C2×C22⋊Q8—21no—
97C2×C22⋊Q8—22no—
98C2×C22⋊Q8—22no—
99C2×C22⋊Q8—41no—
100C2×C22⋊Q8—41no—
101C2×C22⋊Q8C2×C411yescharacteristic, complemented
102C2×C22⋊Q8C2×C411yescharacteristic, complemented
103C2×C22⋊Q8C2×C411yescharacteristic, complemented
104C2×C22⋊Q8C2×C411yescharacteristic, complemented
105C2×C22⋊Q8C2×C411yescharacteristic, complemented
106C2×C22⋊Q8C2311yescharacteristic
107C2×C22⋊Q8C2311yescharacteristic
108C2×#121—21no—
109C2×#121—21no—
110C2×#121C2×C411yescharacteristic, complemented
111C2×#121C2×C411yescharacteristic, complemented
112C2×#121C2×C411yescharacteristic, complemented
113C2×#121C2311yescharacteristic
114C2×#120—21no—
115C2×#120—21no—
116C2×C4×Q8C2×C411yescharacteristic, complemented
117C2×C4×D4—28no—
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4—44no—
122C2×C4×D4—44no—
123C2×C4×D4—44no—
124C2×C4×D4C2×C411yescharacteristic
125C2×C4×D4C2×C411yescharacteristic
126C2×C4×D4C2×C411yescharacteristic
127C2×C4×D4C2×C411yescharacteristic
128C2×C4×D4D411yescharacteristic
129C2×C4×D4D411yescharacteristic
130C2×C4×D4D411yescharacteristic
131C2×C4×D4D411yescharacteristic
132C2×#117C2×C411yescharacteristic, complemented
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4C2×C411yescharacteristic, complemented
136C22×C4⋊C4D411yescharacteristic
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4D411yescharacteristic
141C22×C22⋊C4D411yescharacteristic
142C22×C42—21no—
143C22×C42C2311yescharacteristic
144#435—44no—
145C2×C4⋊C8—21no—
146#407—22no—
147#407—41no—
148C2×C22⋊C8—22no—
149C2×C22⋊C8—21no—
150C2×C22⋊C8—21no—
151C2×C22⋊C8—21no—
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C2×C22⋊C8—41no—
156C2×C22⋊C8C2311yescharacteristic
157C2×C22⋊C8C2311yescharacteristic
158C2×C22⋊C8C2311yescharacteristic
159C2×C22⋊C8C2311yescharacteristic
160C2×#97—21no—
161#399—21no—
162#398—21no—
163#397—21no—
164#396—21no—
165#395—21no—
166#394—21no—
167#394—21no—
168#394—21no—
169#394—21no—
170#393—21no—
171#392—21no—
172#392—21no—
173#391C2×C411yescharacteristic, complemented
174#391C2×C411yescharacteristic, complemented
175#390—21no—
176#390—21no—
177#390C2×C411yescharacteristic, complemented
178#389—21no—
179#389C2×C411yescharacteristic, complemented
180#388—21no—
181#388—21no—
182#388—21no—
183#388—21no—
184#388—21no—
185#388—21no—
186#387—21no—
187#387—21no—
188#386—21no—
189#386—21no—
190#386—21no—
191#386—21no—
192#386—21no—
193#386—21no—
194#386—21no—
195#386—21no—
196#386—21no—
197#385—21no—
198#385—21no—
199#385—21no—
200#385—21no—
201#385—21no—
202#385—21no—
203#382C2×C411yescharacteristic, complemented
204#380C2×C411yescharacteristic, complemented
205#380C2×C411yescharacteristic, complemented
206#380C2×C411yescharacteristic, complemented
207#380C2×C411yescharacteristic, complemented
208#380C2311yescharacteristic
209#379—21no—
210C4×C4⋊C4—21no—
211C4×C4⋊C4C2×C411yescharacteristic, complemented
212C4×C22⋊C4—21no—
213C4×C22⋊C4—21no—
214C2×#95—22no—
215C2×#95—22no—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95—41no—
223C2×#95—41no—
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228#336—21no—
229#336—21no—
230#328—22no—
231#328—22no—
232#328—22no—
233#328—22no—
234#328—22no—
235#328—41no—
236#328—41no—
237#328D414yescomplemented
238#327—22no—
239#327—22no—
240#327—41no—
241#327—41no—
242C25C2×D411yescharacteristic
243C25C2×D411yescharacteristic
244C2×#41—22no—
245C2×#41—41no—
246C2×#41—42no—
247C2×#41—81no—
248C22×Q8—21no—
249C22×Q8—22no—
250C22×Q8—41no—
251C22×Q8—42no—
252C22×Q8—81no—
253C22×Q8C22×C411yescharacteristic
254C22×Q8C22×C411yescharacteristic
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4C22⋊C411yescharacteristic
265C22×D4C22⋊C411yescharacteristic
266C22×D4C22⋊C411yescharacteristic
267C22×D4C22⋊C411yescharacteristic
268C22×D4C22×C411yescharacteristic
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—81no—
297C23×C4—81no—
298C23×C4—81no—
299C23×C4—81no—
300C23×C4—81no—
301C23×C4—81no—
302C23×C4C22×C411yescharacteristic
303C23×C4C22×C411yescharacteristic
304C23×C4C22×C411yescharacteristic
305C23×C4C22×C411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2411yescharacteristic
315C2×M16—42no—
316C2×M16—42no—
317C2×M16—81no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—42no—
323C22×C8—42no—
324C22×C8—81no—
325#124—42no—
326#124—44no—
327#123—42no—
328#123—42no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—22no—
338C22⋊Q8—42no—
339C22⋊Q8—42no—
340C22⋊Q8—41no—
341C22⋊Q8—41no—
342C22⋊Q8—41no—
343C22⋊Q8—42no—
344C22⋊Q8—42no—
345C22⋊Q8—44no—
346C22⋊Q8—42no—
347C22⋊Q8—81no—
348C22⋊Q8C2×D412yes—
349C22⋊Q8#4112yes—
350#121—21no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—22no—
355#121—41no—
356#121—42no—
357#121—44no—
358#121—44no—
359#121—81no—
360#120—42no—
361#120—42no—
362#120—42no—
363#120—42no—
364C4×Q8—42no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—42no—
368C4×D4—42no—
369C4×D4—42no—
370C4×D4—42no—
371C4×D4—42no—
372C4×D4—42no—
373C4×D4—42no—
374C4×D4—42no—
375C4×D4—44no—
376C4×D4—42no—
377C4×D4—42no—
378C4×D4—432no—
379#117—22no—
380#117—41no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—42no—
399C2×C4⋊C4C22⋊C411yescharacteristic
400C2×C4⋊C4C22⋊C411yescharacteristic
401C2×C4⋊C4C22⋊C411yescharacteristic
402C2×C4⋊C4C22⋊C411yescharacteristic
403C2×C4⋊C4C22×C411yescharacteristic
404C2×C4⋊C4C22×C411yescharacteristic
405C2×C4⋊C4C22×C411yescharacteristic
406C2×C4⋊C4C22×C411yescharacteristic
407C2×C4⋊C4C22×C411yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4—42no—
439C2×C22⋊C4C22⋊C411yescharacteristic
440C2×C22⋊C4C22⋊C411yescharacteristic
441C2×C22⋊C4C22⋊C411yescharacteristic
442C2×C22⋊C4C22⋊C411yescharacteristic
443C2×C22⋊C4C22⋊C411yescharacteristic
444C2×C22⋊C4C22⋊C411yescharacteristic
445C2×C22⋊C4C22⋊C411yescharacteristic
446C2×C22⋊C4C22⋊C411yescharacteristic
447C2×C42—24no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—42no—
452C2×C42—42no—
453C2×C42—42no—
454C2×C42C22×C411yescharacteristic
455C2×C42C22×C411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C4⋊C8—42no—
459C22⋊C8—21no—
460C22⋊C8—21no—
461C22⋊C8—21no—
462C22⋊C8—21no—
463C22⋊C8—21no—
464C22⋊C8—21no—
465C22⋊C8—21no—
466C22⋊C8—42no—
467C22⋊C8—42no—
468C22⋊C8—42no—
469C22⋊C8—42no—
470C22⋊C8—81no—
471C22⋊C8—81no—
472C22⋊C8C2×D412yes—
473#97—42no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—42no—
495#95—42no—
496#95—42no—
497#95—81no—
498#95—81no—
499#95—81no—
500#95C2×D412yes—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—41no—
517C24—41no—
518C24—41no—
519C24—41no—
520C24C2×C22⋊C411yescharacteristic
521C24C2×C22⋊C411yescharacteristic
522C24C2×C22⋊C411yescharacteristic
523C24C2×C22⋊C411yescharacteristic
524C24AGL(1,ℤ/8)12yes—
525C24#13712yes—
526C24C22×D411yescharacteristic
527#41—84no—
528#41—84no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—81no—
539C2×Q8—84no—
540C2×Q8—84no—
541C2×Q8C4×D412yescomplemented
542C2×D4—216no—
543C2×D4—216no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4#9914yes—
577C2×D4#10414yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
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—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—48no—
646C22×C4—48no—
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—48no—
659C22×C4—48no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—81no—
674C22×C4—82no—
675C22×C4—82no—
676C22×C4—82no—
677C22×C4—82no—
678C22×C4—82no—
679C22×C4—82no—
680C22×C4—82no—
681C22×C4—82no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4—84no—
685C22×C4—84no—
686C22×C4—84no—
687C22×C4—84no—
688C22×C4—84no—
689C22×C4—84no—
690C22×C4—84no—
691C22×C4—84no—
692C22×C4—84no—
693C22×C4—84no—
694C22×C4C2×C22⋊C411yescharacteristic
695C22×C4C2×C22⋊C411yescharacteristic
696C22×C4C2×C22⋊C411yescharacteristic
697C22×C4C2×C22⋊C411yescharacteristic
698C22×C4C2×C22⋊C411yescharacteristic
699C22×C4C2×C22⋊C411yescharacteristic
700C22×C4C2×C22⋊C411yescharacteristic
701C22×C4C2×C22⋊C411yescharacteristic
702C22×C4C23×C411yescharacteristic
703C22×C4C22×D411yescharacteristic
704C22×C4C22×D411yescharacteristic
705C22×C4C2×#4111yescharacteristic
706C22×C4H(5,𝔽2)11yescharacteristic
707C22×C4H(5,𝔽2)11yescharacteristic
708M16—84no—
709C2×C8—22no—
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—84no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—22no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—41no—
732C4⋊C4—41no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—41no—
738C4⋊C4—41no—
739C4⋊C4—48no—
740C4⋊C4—42no—
741C4⋊C4—41no—
742C4⋊C4—41no—
743C4⋊C4—42no—
744C4⋊C4—42no—
745C4⋊C4—81no—
746C4⋊C4C4×D412yescomplemented
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—41no—
754C22⋊C4—41no—
755C22⋊C4—41no—
756C22⋊C4—41no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—48no—
765C22⋊C4—48no—
766C22⋊C4—41no—
767C22⋊C4—41no—
768C22⋊C4—41no—
769C22⋊C4—41no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—41no—
775C22⋊C4—41no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C22⋊C4—81no—
782C42—22no—
783C42—22no—
784C42—41no—
785C42—41no—
786C42—42no—
787C42—48no—
788C42—42no—
789C42—81no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—24no—
799C23—24no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—22no—
819C23—22no—
820C23—24no—
821C23—24no—
822C23—22no—
823C23—22no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23C2×#9912yes—
856C23C2×#9912yes—
857C23#41712yes—
858C23#41712yes—
859C23C2×#10412yes—
860C23C2×#10412yes—
861C23C22×C22⋊C411yescharacteristic
862C23D4211yescharacteristic
863C23#54611yescharacteristic
864C23C2×AGL(1,ℤ/8)11yescharacteristic
865C23C2×#13711yescharacteristic
866C23#57711yescharacteristic
867C23#57811yescharacteristic
868Q8—42no—
869Q8—42no—
870Q8—81no—
871Q8—81no—
872Q8—84no—
873D4—28no—
874D4—28no—
875D4—28no—
876D4—28no—
877D4—81no—
878D4—81no—
879D4—84no—
880D4—84no—
881D4—81no—
882D4—81no—
883D4—84no—
884D4—81no—
885D4—81no—
886D4—162no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—24no—
898C2×C4—21no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—42no—
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—81no—
965C2×C4—81no—
966C2×C4—81no—
967C2×C4—81no—
968C2×C4—81no—
969C2×C4—81no—
970C2×C4—81no—
971C2×C4—81no—
972C2×C4—81no—
973C2×C4—81no—
974C2×C4—81no—
975C2×C4—81no—
976C2×C4—81no—
977C2×C4—81no—
978C2×C4—84no—
979C2×C4—84no—
980C2×C4—84no—
981C2×C4—816no—
982C2×C4—816no—
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—81no—
994C2×C4—81no—
995C2×C4C2×#9912yes—
996C2×C4C2×#10412yes—
997C2×C4C2×C4×D411yescharacteristic
998C2×C4#51811yescharacteristic
999C2×C4D4211yescharacteristic
1000C2×C4#54611yescharacteristic
1001C8—42no—
1002C8—81no—
1003C8—81no—
1004C8—81no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—22no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—22no—
1013C22—22no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—22no—
1020C22—21no—
1021C22—21no—
1022C22—22no—
1023C22—22no—
1024C22—22no—
1025C22—22no—
1026C22—22no—
1027C22—22no—
1028C22—22no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—44no—
1033C22—44no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—41no—
1041C22—41no—
1042C22—41no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—41no—
1047C22—41no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22#150414yescomplemented
1060C22D4×C22⋊C411yescharacteristic
1061C22C22×#9911yescharacteristic
1062C22#288311yescharacteristic
1063C22C2×#41711yescharacteristic
1064C22#289811yescharacteristic
1065C22C22×#10411yescharacteristic
1066C22#290111yescharacteristic
1067C22#326511yescharacteristic
1068C22#327011yescharacteristic
1069C22#330811yescharacteristic
1070C22#331611yescharacteristic
1071C4—22no—
1072C4—22no—
1073C4—21no—
1074C4—21no—
1075C4—21no—
1076C4—21no—
1077C4—44no—
1078C4—41no—
1079C4—41no—
1080C4—41no—
1081C4—41no—
1082C4—42no—
1083C4—42no—
1084C4—41no—
1085C4—41no—
1086C4—82no—
1087C4—82no—
1088C4—82no—
1089C4—81no—
1090C4—81no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C2—21no—
1095C2—21no—
1096C2—21no—
1097C2—21no—
1098C2—24no—
1099C2—42no—
1100C2—42no—
1101C2—42no—
1102C2—161no—
1103C2C2×#150411yescharacteristic
1104C2#1754811yescharacteristic
1105C2#1760811yescharacteristic
1106C2#1762211yescharacteristic
1107C2D4×#9911yescharacteristic
1108C2#2242111yescharacteristic
1109C2D4×#10411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#36097C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22399C2semidirect
3. C2×#1504C2semidirect
4. C22×#328C2semidirect
5. D4×#95C2semidirect
6. #9713C2semidirect
7. #9682C2semidirect
8. #9147C2semidirect
9. #9143C2semidirect
10. #9115C2semidirect
11. #9113C2semidirect
12. #8578C2semidirect
13. #8331C2semidirect
14. #8329C2semidirect
15. #8219C2semidirect
16. C2×#548C4semidirect
27. #2540C4semidirect
28. #2536C4semidirect
34. #2416C4semidirect
35. #2415C4semidirect
37. #2409C4semidirect
38. #2407C4semidirect
41. #2352C4semidirect
77. C22×#41C2×C4semidirect
78. C23×Q8C2×C4semidirect
88. C2×#124C2×C4semidirect
101. C2×C22⋊Q8C2×C4semidirect
102. C2×C22⋊Q8C2×C4semidirect
103. C2×C22⋊Q8C2×C4semidirect
104. C2×C22⋊Q8C2×C4semidirect
105. C2×C22⋊Q8C2×C4semidirect
110. C2×#121C2×C4semidirect
111. C2×#121C2×C4semidirect
112. C2×#121C2×C4semidirect
116. C2×C4×Q8C2×C4semidirect
132. C2×#117C2×C4semidirect
135. C22×C4⋊C4C2×C4semidirect
173. #391C2×C4semidirect
174. #391C2×C4semidirect
177. #390C2×C4semidirect
179. #389C2×C4semidirect
203. #382C2×C4semidirect
204. #380C2×C4semidirect
205. #380C2×C4semidirect
206. #380C2×C4semidirect
207. #380C2×C4semidirect
211. C4×C4⋊C4C2×C4semidirect
237. #328D4semidirect
541. C2×Q8C4×D4semidirect
746. C4⋊C4C4×D4semidirect
1059. C22#1504semidirect

Maximal subgroups

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

subgroupindex
#360972
#223992
C2×#15042
C22×#3282
D4×#952
#97132
#96822
#91472
#91432
#91152
#91132
#85782
#83312
#83292
#82192