Finite Group Databasebeta

← #221803

Subgroups — #221803

Order 512.

1535 conjugacy classes of subgroups.

The subgroup lattice has 1085 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36123C211yesmaximal, characteristic
2#22552C211yesmaximal, characteristic, complemented
3C2×#1517C211yesmaximal, characteristic, complemented
4C22×#327C211yesmaximal, characteristic, complemented
5#13896C211yesmaximal, characteristic, complemented
6#9715C211yesmaximal, characteristic, complemented
7#9680C211yesmaximal, characteristic, complemented
8#9156C211yesmaximal, characteristic, complemented
9#9147C211yesmaximal, characteristic, complemented
10#9114C211yesmaximal, characteristic, complemented
11#9113C211yesmaximal, characteristic, complemented
12#8571C211yesmaximal, characteristic, complemented
13#8332C211yesmaximal, characteristic, complemented
14#8328C211yesmaximal, characteristic, complemented
15#8220C211yesmaximal, characteristic, complemented
16C2×#546—21no—
17C2×#532C2211yescharacteristic
18C22×#121C2211yescharacteristic
19C2×#431C2211yescharacteristic, complemented
20C22×C22⋊C8C2211yescharacteristic
21#2856C2211yescharacteristic
22#2854C2211yescharacteristic
23#2847C2211yescharacteristic
24#2555—21no—
25#2543—21no—
26#2491C411yescharacteristic, complemented
27#2472—21no—
28#2464—21no—
29#2440C411yescharacteristic, complemented
30#2433C411yescharacteristic, complemented
31#2430—21no—
32#2428C411yescharacteristic, complemented
33#2428C411yescharacteristic, complemented
34#2422C411yescharacteristic, complemented
35#2410—21no—
36#2361C411yescharacteristic, complemented
37#2358—21no—
38D4×C22⋊C4C411yescharacteristic, complemented
39C4×#121C2211yescharacteristic
40C2×#385—21no—
41C2×#382C2211yescharacteristic, complemented
42C2×C4×C22⋊C4C2211yescharacteristic
43C22×#95C2211yescharacteristic
44#1923—21no—
45#1923—21no—
46#1850—21no—
47#1817C2211yescharacteristic, complemented
48#1797C2211yescharacteristic, complemented
49#1779C2211yescharacteristic
50C8×C22⋊C4—21no—
51C4×C22⋊C8C2211yescharacteristic, complemented
52#1517—24no—
53C2×#327—24no—
54C2×#327C2211yescharacteristic
55C2×#327C2211yescharacteristic
56C2×#327C2211yescharacteristic
57C2×#327C2211yescharacteristic
58C2×#327C2211yescharacteristic
59C2×#327C2211yescharacteristic
60C2×#327C2211yescharacteristic
61C2×#327C2211yescharacteristic
62C2×#327C2211yescharacteristic, complemented
63C2×#327C2211yescharacteristic, complemented
64C2×#327C2211yescharacteristic, complemented
65C2×#327C2211yescharacteristic, complemented
66#1442—21no—
67#1442—21no—
68C4⋊#95C2211yescharacteristic, complemented
69#1434C2211yescharacteristic, complemented
70#1434C2211yescharacteristic, complemented
71C22⋊#95—21no—
72C22⋊#95C2211yescharacteristic
73#1294C2211yescharacteristic, complemented
74#1294C2211yescharacteristic, complemented
75#1294C2211yescharacteristic, complemented
76#1294C2211yescharacteristic, complemented
77C22×#41—21no—
78C23×D4—21no—
79C23×D4C2×C411yescharacteristic
80C24×C4—21no—
81C24×C4C2311yescharacteristic
82C23×C8—21no—
83#546—44no—
84#546—44no—
85#532—22no—
86#532—22no—
87#532—41no—
88#532—41no—
89C2×C4⋊Q8C2×C411yescharacteristic, complemented
90C2×#127C2×C411yescharacteristic, complemented
91C2×#127C2×C411yescharacteristic, complemented
92C2×#124—21no—
93C2×#124—21no—
94C2×#123—21no—
95C2×#123—21no—
96C2×C22⋊Q8—21no—
97C2×#121—21no—
98C2×#121—21no—
99C2×#121—21no—
100C2×#121—21no—
101C2×#121—21no—
102C2×#121—21no—
103C2×#121—21no—
104C2×#121—22no—
105C2×#121—22no—
106C2×#121—41no—
107C2×#121—41no—
108C2×#121C2×C411yescharacteristic
109C2×#121C2×C411yescharacteristic
110C2×#121C2×C411yescharacteristic
111C2×#121C2×C411yescharacteristic
112C2×#121C2311yescharacteristic
113C2×#121C2311yescharacteristic
114C2×#121C2311yescharacteristic
115C2×#120—21no—
116C2×#120—21no—
117C2×#120—21no—
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4C2×C411yescharacteristic, complemented
122C2×C4×D4C2×C411yescharacteristic, complemented
123C2×C4×D4C2×C411yescharacteristic, complemented
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4C2×C411yescharacteristic
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4D411yescharacteristic
131C22×C22⋊C4D411yescharacteristic
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134#431—22no—
135#431—41no—
136C2×C4⋊C8—21no—
137C2×C4⋊C8—21no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—21no—
140C2×C22⋊C8—21no—
141C2×C22⋊C8—21no—
142C2×C22⋊C8—41no—
143C2×C22⋊C8C2311yescharacteristic
144C2×C22⋊C8C2311yescharacteristic
145C2×C22⋊C8C2311yescharacteristic
146C2×C22⋊C8C2311yescharacteristic
147C2×C4×C8—21no—
148C2×C4×C8—21no—
149#398—21no—
150#397—21no—
151#395—21no—
152#394—21no—
153#394—21no—
154#394—21no—
155#394—21no—
156#393—21no—
157#392—21no—
158#392—21no—
159#392—21no—
160#392—21no—
161#390—21no—
162#390—21no—
163#390C2×C411yescharacteristic, complemented
164#390C2×C411yescharacteristic, complemented
165#390C2×C411yescharacteristic, complemented
166#390C2×C411yescharacteristic, complemented
167#390C2×C411yescharacteristic, complemented
168#389C2×C411yescharacteristic, complemented
169#389C2×C411yescharacteristic, complemented
170#389C2×C411yescharacteristic, complemented
171#388—21no—
172#388—21no—
173#388—21no—
174#388—21no—
175#388—21no—
176#386—21no—
177#386—21no—
178#386—21no—
179#386—21no—
180#386—21no—
181#386—21no—
182#386—21no—
183#386—21no—
184#386—21no—
185#386—21no—
186#385—21no—
187#385—21no—
188#385—21no—
189#385—44no—
190#384C2×C411yescharacteristic, complemented
191#382—22no—
192#382—41no—
193#380C2×C411yescharacteristic
194#380C2×C411yescharacteristic
195#380C2311yescharacteristic
196#379—21no—
197C4×C4⋊C4C2×C411yescharacteristic, complemented
198C4×C22⋊C4—21no—
199C4×C22⋊C4C2×C411yescharacteristic
200C4×C22⋊C4C2×C411yescharacteristic
201C4×C22⋊C4C2×C411yescharacteristic
202C4×C22⋊C4C2×C411yescharacteristic
203C4×C22⋊C4D411yescharacteristic
204C4×C22⋊C4D411yescharacteristic
205C4×C22⋊C4D411yescharacteristic
206C4×C22⋊C4D411yescharacteristic
207C2×#95—22no—
208C2×#95—21no—
209C2×#95—21no—
210C2×#95—21no—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—41no—
217C2×#95D411yescharacteristic
218C2×#95D411yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223#336—21no—
224#336—21no—
225#336—21no—
226#336—21no—
227#327—22no—
228#327—22no—
229#327—22no—
230#327—22no—
231#327—22no—
232#327—22no—
233#327—22no—
234#327—41no—
235#327—41no—
236#327—41no—
237#327—41no—
238#327D414yescomplemented
239C25—21no—
240C25C2×D411yescharacteristic
241C2×#41—42no—
242C2×#41—42no—
243C2×#41—42no—
244C2×#41—42no—
245C2×#41—81no—
246C2×#41—81no—
247C22×Q8—21no—
248C22×D4—21no—
249C22×D4—22no—
250C22×D4—21no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—41no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—81no—
268C22×D4—81no—
269C22×D4—81no—
270C22×D4C22×C411yescharacteristic
271C22×D4C22×C411yescharacteristic
272C22×D4C22×C411yescharacteristic
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—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—81no—
292C23×C4—81no—
293C23×C4—81no—
294C23×C4C22×C411yescharacteristic
295C23×C4C22×C411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—42no—
309C22×C8—42no—
310C22×C8—81no—
311C4⋊Q8—22no—
312C4⋊Q8—41no—
313#127—22no—
314#127—41no—
315#127—81no—
316#124—42no—
317#124—42no—
318#124—44no—
319#123—42no—
320#123—42no—
321#123—44no—
322C22⋊Q8—44no—
323#121—21no—
324#121—21no—
325#121—22no—
326#121—21no—
327#121—21no—
328#121—21no—
329#121—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—22no—
335#121—42no—
336#121—42no—
337#121—41no—
338#121—41no—
339#121—42no—
340#121—42no—
341#121—42no—
342#121—42no—
343#121—42no—
344#121—42no—
345#121—42no—
346#121—44no—
347#121—44no—
348#121—81no—
349#121—81no—
350#121—81no—
351#121C2×D412yes—
352#121#4112yes—
353#120—44no—
354#120—42no—
355#120—42no—
356#120—44no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—42no—
360C4×D4—42no—
361C4×D4—41no—
362C4×D4—41no—
363C4×D4—42no—
364C4×D4—42no—
365C4×D4—44no—
366C4×D4—81no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—41no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—81no—
381C2×C4⋊C4—81no—
382C2×C4⋊C4C22×C411yescharacteristic
383C2×C4⋊C4C22×C411yescharacteristic
384C2×C4⋊C4C22×C411yescharacteristic
385C2×C4⋊C4C22×C411yescharacteristic
386C2×C4⋊C4C22×C411yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4C22⋊C411yescharacteristic
418C2×C22⋊C4C22⋊C411yescharacteristic
419C2×C22⋊C4C22⋊C411yescharacteristic
420C2×C22⋊C4C22⋊C411yescharacteristic
421C2×C22⋊C4C22⋊C411yescharacteristic
422C2×C22⋊C4C22⋊C411yescharacteristic
423C2×C22⋊C4C22⋊C411yescharacteristic
424C2×C22⋊C4C22⋊C411yescharacteristic
425C2×C22⋊C4D814yes—
426C2×C22⋊C4SD1614yes—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—81no—
433C2×C42C22×C411yescharacteristic
434C2×C42C22×C411yescharacteristic
435C2×C42C22×C411yescharacteristic
436C2×C42C22×C411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C4⋊C8—42no—
442C4⋊C8—81no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—42no—
451C22⋊C8—42no—
452C22⋊C8—81no—
453C22⋊C8C2×D412yes—
454C4×C8—42no—
455C4×C8—81no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—42no—
471#95—42no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95—81no—
476#95—81no—
477#95—81no—
478#95C22⋊C411yescharacteristic
479#95C22⋊C411yescharacteristic
480#95C22⋊C411yescharacteristic
481#95C22⋊C411yescharacteristic
482#95C22⋊C411yescharacteristic
483#95C22⋊C411yescharacteristic
484#95C22⋊C411yescharacteristic
485#95C22⋊C411yescharacteristic
486#95C2×D412yes—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—41no—
497C24—41no—
498C24—42no—
499C24—42no—
500C24—42no—
501C24—42no—
502C24—81no—
503C24—81no—
504C24—81no—
505C24C2×C22⋊C411yescharacteristic
506C24C2×C22⋊C411yescharacteristic
507C24C2×D812yes—
508C24C2×SD1612yes—
509C24C22×D411yescharacteristic
510#41—84no—
511#41—84no—
512#41—84no—
513#41—84no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—81no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—42no—
542C2×D4—41no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—84no—
570C2×D4—84no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—84no—
576C2×D4—84no—
577C2×D4—84no—
578C2×D4—84no—
579C2×D4C4×D412yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
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—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
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—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—48no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
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—81no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—82no—
662C22×C4—82no—
663C22×C4—82no—
664C22×C4—82no—
665C22×C4—81no—
666C22×C4—84no—
667C22×C4—84no—
668C22×C4—84no—
669C22×C4—84no—
670C22×C4—84no—
671C22×C4—84no—
672C22×C4C2×C22⋊C411yescharacteristic
673C22×C4C2×C22⋊C411yescharacteristic
674C22×C4C2×C22⋊C411yescharacteristic
675C22×C4C2×C22⋊C411yescharacteristic
676C22×C4C2×C22⋊C411yescharacteristic
677C22×C4C2×C22⋊C411yescharacteristic
678C22×C4C2×C22⋊C411yescharacteristic
679C22×C4C2×C22⋊C411yescharacteristic
680C22×C4C2×C22⋊C411yescharacteristic
681C22×C4C2×C22⋊C411yescharacteristic
682C22×C4C2×D812yes—
683C22×C4C2×D812yes—
684C22×C4C2×SD1612yes—
685C22×C4C2×SD1612yes—
686C22×C4C23×C411yescharacteristic
687C22×C4C22×D411yescharacteristic
688C22×C4C22×D411yescharacteristic
689C22×C4C2×#4111yescharacteristic
690C22×C4H(5,𝔽2)11yescharacteristic
691C22×C4H(5,𝔽2)11yescharacteristic
692C2×C8—22no—
693C2×C8—41no—
694C2×C8—41no—
695C2×C8—41no—
696C2×C8—41no—
697C2×C8—41no—
698C2×C8—41no—
699C2×C8—41no—
700C2×C8—41no—
701C2×C8—41no—
702C2×C8—41no—
703C2×C8—41no—
704C2×C8—84no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—41no—
713C4⋊C4—41no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4—42no—
717C4⋊C4—42no—
718C4⋊C4—81no—
719C4⋊C4—84no—
720C4⋊C4—84no—
721C4⋊C4C4×D412yes—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—41no—
727C22⋊C4—41no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4—42no—
734C22⋊C4—42no—
735C22⋊C4—41no—
736C22⋊C4—41no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4—41no—
740C22⋊C4—41no—
741C22⋊C4—41no—
742C22⋊C4—41no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C22⋊C4—81no—
751C22⋊C4—81no—
752C22⋊C4—81no—
753C22⋊C4—84no—
754C22⋊C4#10214yes—
755C22⋊C4#10214yes—
756C22⋊C4#10214yes—
757C22⋊C4#10214yes—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—41no—
767C42—41no—
768C42—41no—
769C42—41no—
770C42—42no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—24no—
790C23—24no—
791C23—22no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
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—84no—
823C23—84no—
824C23—84no—
825C23—84no—
826C23—162no—
827C23—162no—
828C23—162no—
829C23#41012yes—
830C23C2×#10212yes—
831C23C2×#10212yes—
832C23#42112yes—
833C23C22×C22⋊C411yescharacteristic
834C23D4211yescharacteristic
835C23#54611yescharacteristic
836C23C22×D811yescharacteristic
837C23C22×SD1611yescharacteristic
838C23#57611yescharacteristic
839C23#57711yescharacteristic
840Q8—84no—
841D4—42no—
842D4—42no—
843D4—42no—
844D4—42no—
845D4—42no—
846D4—42no—
847D4—84no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—84no—
853D4—84no—
854D4—84no—
855D4—84no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—84no—
865D4—162no—
866D4—162no—
867D4—162no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
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—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—42no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
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—42no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—84no—
938C2×C4—84no—
939C2×C4—81no—
940C2×C4—81no—
941C2×C4—81no—
942C2×C4—81no—
943C2×C4—81no—
944C2×C4—81no—
945C2×C4—84no—
946C2×C4—81no—
947C2×C4—81no—
948C2×C4—81no—
949C2×C4—81no—
950C2×C4—81no—
951C2×C4—81no—
952C2×C4—81no—
953C2×C4—816no—
954C2×C4—81no—
955C2×C4—81no—
956C2×C4—81no—
957C2×C4—81no—
958C2×C4—81no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—81no—
962C2×C4—81no—
963C2×C4—81no—
964C2×C4—81no—
965C2×C4—81no—
966C2×C4—81no—
967C2×C4—81no—
968C2×C4—81no—
969C2×C4—162no—
970C2×C4C2×#10212yes—
971C2×C4C2×#10212yes—
972C2×C4C2×#10212yes—
973C2×C4C2×#10212yes—
974C2×C4C2×C4×D411yescharacteristic
975C2×C4#51811yescharacteristic
976C2×C4D4211yescharacteristic
977C2×C4#54611yescharacteristic
978C8—42no—
979C8—81no—
980C8—81no—
981C8—81no—
982C22—21no—
983C22—22no—
984C22—21no—
985C22—22no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—22no—
991C22—21no—
992C22—21no—
993C22—22no—
994C22—21no—
995C22—21no—
996C22—22no—
997C22—21no—
998C22—21no—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—81no—
1015C22—81no—
1016C22—81no—
1017C22—81no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22—81no—
1022C22—81no—
1023C22—81no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—81no—
1031C22—81no—
1032C22—168no—
1033C22#151714yescomplemented
1034C22D4×C22⋊C411yescharacteristic
1035C22C2×#41011yescharacteristic
1036C22#288311yescharacteristic
1037C22C22×#10211yescharacteristic
1038C22#289711yescharacteristic
1039C22C2×#42111yescharacteristic
1040C22#290111yescharacteristic
1041C22D4×D811yescharacteristic
1042C22D4×SD1611yescharacteristic
1043C22#329411yescharacteristic
1044C22#329511yescharacteristic
1045C4—21no—
1046C4—21no—
1047C4—21no—
1048C4—21no—
1049C4—22no—
1050C4—22no—
1051C4—22no—
1052C4—22no—
1053C4—41no—
1054C4—41no—
1055C4—42no—
1056C4—41no—
1057C4—41no—
1058C4—41no—
1059C4—41no—
1060C4—82no—
1061C4—82no—
1062C4—81no—
1063C4—81no—
1064C4—81no—
1065C4—81no—
1066C4—161no—
1067C4—161no—
1068C2—21no—
1069C2—21no—
1070C2—24no—
1071C2—21no—
1072C2—21no—
1073C2—42no—
1074C2—82no—
1075C2—161no—
1076C2—161no—
1077C2C2×#151711yescharacteristic
1078C2#1759711yescharacteristic
1079C2#1760411yescharacteristic
1080C2#1761311yescharacteristic
1081C2#2240511yescharacteristic
1082C2D4×#10211yescharacteristic
1083C2#2243411yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radical#36123C2
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. #22552C2semidirect
3. C2×#1517C2semidirect
4. C22×#327C2semidirect
5. #13896C2semidirect
6. #9715C2semidirect
7. #9680C2semidirect
8. #9156C2semidirect
9. #9147C2semidirect
10. #9114C2semidirect
11. #9113C2semidirect
12. #8571C2semidirect
13. #8332C2semidirect
14. #8328C2semidirect
15. #8220C2semidirect
19. C2×#431C22semidirect
26. #2491C4semidirect
29. #2440C4semidirect
30. #2433C4semidirect
32. #2428C4semidirect
33. #2428C4semidirect
34. #2422C4semidirect
36. #2361C4semidirect
38. D4×C22⋊C4C4semidirect
41. C2×#382C22semidirect
47. #1817C22semidirect
48. #1797C22semidirect
51. C4×C22⋊C8C22semidirect
62. C2×#327C22semidirect
63. C2×#327C22semidirect
64. C2×#327C22semidirect
65. C2×#327C22semidirect
68. C4⋊#95C22semidirect
69. #1434C22semidirect
70. #1434C22semidirect
73. #1294C22semidirect
74. #1294C22semidirect
75. #1294C22semidirect
76. #1294C22semidirect
89. C2×C4⋊Q8C2×C4semidirect
90. C2×#127C2×C4semidirect
91. C2×#127C2×C4semidirect
121. C2×C4×D4C2×C4semidirect
122. C2×C4×D4C2×C4semidirect
123. C2×C4×D4C2×C4semidirect
163. #390C2×C4semidirect
164. #390C2×C4semidirect
165. #390C2×C4semidirect
166. #390C2×C4semidirect
167. #390C2×C4semidirect
168. #389C2×C4semidirect
169. #389C2×C4semidirect
170. #389C2×C4semidirect
190. #384C2×C4semidirect
197. C4×C4⋊C4C2×C4semidirect
238. #327D4semidirect
1033. C22#1517semidirect

Maximal subgroups

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

subgroupindex
#361232
#225522
C2×#15172
C22×#3272
#138962
#97152
#96802
#91562
#91472
#91142
#91132
#85712
#83322
#83282
#82202