Finite Group Databasebeta

← #163993

Subgroups — #163993

Order 512.

1222 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35256C211yesmaximal, characteristic
2#22471C211yesmaximal, characteristic, complemented
3#22469C211yesmaximal, characteristic, complemented
4#7730C211yesmaximal, characteristic, complemented
5#7724C211yesmaximal, characteristic, complemented
6#7710C211yesmaximal, characteristic, complemented
7#7704C211yesmaximal, characteristic, complemented
8#7690C211yesmaximal, characteristic, complemented
9#7684C211yesmaximal, characteristic, complemented
10#7670C211yesmaximal, characteristic, complemented
11#7664C211yesmaximal, characteristic, complemented
12#7592C211yesmaximal, characteristic, complemented
13#7578C211yesmaximal, characteristic, complemented
14#7578C211yesmaximal, characteristic, complemented
15C2×#1270C211yesmaximal, characteristic, complemented
16C2×#537C411yescharacteristic
17C2×#535C411yescharacteristic
18C2×#535C411yescharacteristic
19C2×C4×#41C2211yescharacteristic
20C2×#435—21no—
21C2×C8×D4—21no—
22#2856C2211yescharacteristic
23#2856C2211yescharacteristic
24#2850C2211yescharacteristic
25#2850C2211yescharacteristic
26#2620C411yescharacteristic
27#2620C411yescharacteristic
28#2619C411yescharacteristic
29#2619C411yescharacteristic
30#2428—21no—
31#2428—21no—
32#2426—21no—
33#2426—21no—
34#2424—21no—
35#2424—21no—
36#2424—21no—
37#2424—21no—
38#2317C411yescharacteristic
39#2297C2211yescharacteristic
40C2×#390C2211yescharacteristic
41#1985—21no—
42#1984—21no—
43#1870—21no—
44#1869—21no—
45#1869—21no—
46#1869—21no—
47#1817C2211yescharacteristic
48#1817C2211yescharacteristic
49#1817C2211yescharacteristic, complemented
50#1817C2211yescharacteristic, complemented
51#1797C2211yescharacteristic, complemented
52#1797C2211yescharacteristic, complemented
53#1749C2211yescharacteristic, complemented
54C4×C22⋊C8C2211yescharacteristic, complemented
55#1728C2211yescharacteristic, complemented
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58C2×#336C2211yescharacteristic, complemented
59#1272C2211yescharacteristic, complemented
60#1272C2211yescharacteristic, complemented
61#1272C2211yescharacteristic, complemented
62#1272C2211yescharacteristic, complemented
63#1270C2211yescharacteristic
64#1270C2211yescharacteristic
65#1270C2211yescharacteristic
66#1270C2211yescharacteristic
67#1270C2211yescharacteristic
68#1270C2211yescharacteristic
69#1270C2211yescharacteristic
70#1270C2211yescharacteristic
71#1270C2211yescharacteristic, complemented
72#1270C2211yescharacteristic, complemented
73#1270C2211yescharacteristic, complemented
74#1270C2211yescharacteristic, complemented
75C22×#41C2×C411yescharacteristic
76C22×#41C2×C411yescharacteristic
77C23×D4C2×C411yescharacteristic
78C22×M16—21no—
79C23×C8—21no—
80C23×C8—21no—
81C23×C8—21no—
82#537—44no—
83#535—44no—
84#535—44no—
85C2×#127—21no—
86C2×#127C2×C411yescharacteristic
87C2×#127C2×C411yescharacteristic
88C2×#124—21no—
89C2×#124C2×C411yescharacteristic
90C2×#124C2×C411yescharacteristic
91C2×C22⋊Q8—21no—
92C2×C22⋊Q8C2×C411yescharacteristic
93C2×C22⋊Q8C2×C411yescharacteristic
94C2×#121—21no—
95C2×#121—21no—
96C2×#121—21no—
97C2×#121—21no—
98C2×#121—21no—
99C2×#121—21no—
100C2×#121—21no—
101C2×#121—21no—
102C2×#121—21no—
103C2×#121C2×C411yescharacteristic
104C2×#121C2×C411yescharacteristic
105C2×#121C2×C411yescharacteristic
106C2×#121C2×C411yescharacteristic
107C2×#121C2×C411yescharacteristic
108C2×#121C2×C411yescharacteristic
109C2×#120—21no—
110C2×#120—21no—
111C2×#120—21no—
112C2×#120—21no—
113C4×#41—44no—
114C2×C4×Q8D411yescharacteristic
115C2×C4×Q8D411yescharacteristic
116C2×C4×D4D411yescharacteristic
117C2×C4×D4D411yescharacteristic
118C2×C4×D4D411yescharacteristic
119C2×C4×D4D411yescharacteristic
120C2×C4×D4D411yescharacteristic
121C2×C4×D4D411yescharacteristic
122C2×#117C2×C411yescharacteristic
123C2×#117C2×C411yescharacteristic
124C2×#117C2×C411yescharacteristic
125C2×#117C2×C411yescharacteristic
126C22×C4⋊C4C2×C411yescharacteristic
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132#435—44no—
133C8×D4—44no—
134C2×C4⋊C8—21no—
135C2×C4⋊C8—21no—
136C2×C22⋊C8—21no—
137C2×C22⋊C8—21no—
138C2×C22⋊C8—21no—
139C2×C22⋊C8—21no—
140C2×C22⋊C8—21no—
141C2×C22⋊C8—21no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8—21no—
144C2×#97—21no—
145C2×C4×C8—21no—
146#396—21no—
147#396—21no—
148#396—21no—
149#396—21no—
150#394—21no—
151#394—21no—
152#394—21no—
153#394—21no—
154#394—21no—
155#394—21no—
156#394—21no—
157#394—21no—
158#392—21no—
159#392—21no—
160#392—21no—
161#392—21no—
162#391C2×C411yescharacteristic
163#391C2311yescharacteristic
164#390—21no—
165#390—21no—
166#390—21no—
167#390—21no—
168#390—21no—
169#390—21no—
170#390C2×C411yescharacteristic
171#390C2×C411yescharacteristic
172#390C2×C411yescharacteristic
173#390C2311yescharacteristic
174#390C2311yescharacteristic
175#390C2311yescharacteristic
176#389—21no—
177#389—21no—
178#388—21no—
179#388—21no—
180#388—21no—
181#388—21no—
182#386—21no—
183#386—21no—
184#386—21no—
185#386—21no—
186#386—21no—
187#386—21no—
188#385—21no—
189#385—21no—
190#384C2×C411yescharacteristic
191#384C2×C411yescharacteristic
192#382C2×C411yescharacteristic
193#382C2×C411yescharacteristic
194C4×C22⋊C4—21no—
195C4×C22⋊C4—21no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—21no—
201#336—21no—
202#336—21no—
203#336—21no—
204#336C2311yescharacteristic
205#336C2311yescharacteristic
206#336C2311yescharacteristic
207#336C2311yescharacteristic
208#336C2311yescharacteristic
209#336C2311yescharacteristic
210#336C2311yescharacteristic
211#336C2311yescharacteristic
212C25—21no—
213C2×#41—24no—
214C2×#41—24no—
215C2×#41—24no—
216C2×#41—42no—
217C2×#41—42no—
218C2×#41—42no—
219C22×Q8C22⋊C411yescharacteristic
220C22×Q8C22×C411yescharacteristic
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—21no—
231C22×D4—21no—
232C22×D4—21no—
233C22×D4—24no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4C22⋊C411yescharacteristic
237C22×D4C22⋊C411yescharacteristic
238C22×D4C22⋊C411yescharacteristic
239C22×D4C22×C411yescharacteristic
240C22×D4C22×C411yescharacteristic
241C22×D4C22×C411yescharacteristic
242C23×C4—21no—
243C23×C4—21no—
244C23×C4C22×C411yescharacteristic
245C23×C4C22×C411yescharacteristic
246C23×C4C22×C411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4C2×D411yescharacteristic
249C23×C4C2×D411yescharacteristic
250C23×C4C2×D411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C2×M16—42no—
254C2×M16—42no—
255C2×M16—81no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—42no—
265C22×C8—42no—
266C22×C8—42no—
267C22×C8—42no—
268C22×C8—42no—
269C22×C8—42no—
270C22×C8—81no—
271C22×C8—81no—
272C22×C8—81no—
273#127—42no—
274#127—42no—
275#127—44no—
276#124—42no—
277#124—42no—
278#124—44no—
279C22⋊Q8—44no—
280C22⋊Q8—42no—
281C22⋊Q8—42no—
282#121—44no—
283#121—44no—
284#121—42no—
285#121—42no—
286#121—42no—
287#121—44no—
288#121—44no—
289#121—44no—
290#121—42no—
291#121—42no—
292#121—42no—
293#121—81no—
294#121—81no—
295#121—81no—
296#121—81no—
297#121—81no—
298#121—81no—
299#121—81no—
300#121—81no—
301#120—44no—
302#120—44no—
303#120—44no—
304#120—44no—
305C4×Q8—42no—
306C4×Q8—42no—
307C4×D4—24no—
308C4×D4—24no—
309C4×D4—42no—
310C4×D4—42no—
311C4×D4—42no—
312C4×D4—42no—
313#117—24no—
314#117—42no—
315#117—42no—
316#117—42no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4C22⋊C411yescharacteristic
326C2×C4⋊C4C22⋊C411yescharacteristic
327C2×C4⋊C4C22⋊C411yescharacteristic
328C2×C4⋊C4C22⋊C411yescharacteristic
329C2×C4⋊C4C22⋊C411yescharacteristic
330C2×C4⋊C4C22⋊C411yescharacteristic
331C2×C4⋊C4C22×C411yescharacteristic
332C2×C4⋊C4C22×C411yescharacteristic
333C2×C4⋊C4C22×C411yescharacteristic
334C2×C4⋊C4C22×C411yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—81no—
361C2×C22⋊C4—81no—
362C2×C22⋊C4—81no—
363C2×C22⋊C4—81no—
364C2×C22⋊C4C22⋊C411yescharacteristic
365C2×C22⋊C4C22⋊C411yescharacteristic
366C2×C22⋊C4C22⋊C411yescharacteristic
367C2×C22⋊C4C22⋊C411yescharacteristic
368C2×C22⋊C4C22⋊C411yescharacteristic
369C2×C22⋊C4C22⋊C411yescharacteristic
370C2×C42—21no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42C22×C411yescharacteristic
375C2×C42C22×C411yescharacteristic
376C2×C42C22×C411yescharacteristic
377C2×C42C2×D411yescharacteristic
378C2×C42C2×D411yescharacteristic
379C2×C42C2×D411yescharacteristic
380C2×C42C2×D411yescharacteristic
381C2×C42C2×D411yescharacteristic
382C2×C42C2×D411yescharacteristic
383C2×C42C2411yescharacteristic
384C4⋊C8—42no—
385C4⋊C8—42no—
386C22⋊C8—42no—
387C22⋊C8—42no—
388C22⋊C8—42no—
389C22⋊C8—42no—
390C22⋊C8—42no—
391C22⋊C8—42no—
392C22⋊C8—81no—
393C22⋊C8—81no—
394#97—42no—
395C4×C8—42no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—81no—
411C24—81no—
412C24—81no—
413C24—81no—
414C24C2×C22⋊C411yescharacteristic
415C24C2×C22⋊C411yescharacteristic
416C24C2×C22⋊C411yescharacteristic
417#41—416no—
418#41—88no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—88no—
459C2×D4—81no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4—81no—
467C2×D4—81no—
468C2×D4—81no—
469C2×D4—81no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4—81no—
473C2×D4—81no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4—81no—
479C2×D4#10014yes—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4C2×C22⋊C411yescharacteristic
524C22×C4C2×C22⋊C411yescharacteristic
525C22×C4C2×C22⋊C411yescharacteristic
526C22×C4C2×C22⋊C411yescharacteristic
527C22×C4C2×C22⋊C411yescharacteristic
528C22×C4C2×C22⋊C411yescharacteristic
529C22×C4C2×C22⋊C411yescharacteristic
530C22×C4C2×C22⋊C411yescharacteristic
531C22×C4C2×C22⋊C411yescharacteristic
532C22×C4#13114yes—
533C22×C4C23×C411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536M16—84no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—84no—
562C2×C8—84no—
563C2×C8—84no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4—81no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
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—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—81no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C22⋊C4#9914yes—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—41no—
623C42—41no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—42no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—162no—
671C23—162no—
672C23—162no—
673C23—162no—
674C23#40812yes—
675C23C2×#9912yes—
676C23C2×#10012yes—
677C23C2×#10012yes—
678C23C22×C22⋊C411yescharacteristic
679Q8—44no—
680Q8—82no—
681D4—28no—
682D4—44no—
683D4—44no—
684D4—82no—
685D4—82no—
686D4—82no—
687D4—84no—
688D4—84no—
689D4—162no—
690D4—162no—
691D4—162no—
692D4—162no—
693D4—162no—
694D4—162no—
695D4—162no—
696D4—162no—
697D4—162no—
698D4—162no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—28no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—84no—
759C2×C4—162no—
760C2×C4#40812yes—
761C2×C4C2×#9912yes—
762C2×C4C2×#9912yes—
763C2×C4C2×#10012yes—
764C2×C4C2×#13112yes—
765C2×C4#57611yescharacteristic
766C2×C4#57611yescharacteristic
767C2×C4#57711yescharacteristic
768C2×C4#57711yescharacteristic
769C8—42no—
770C8—42no—
771C8—81no—
772C8—81no—
773C8—81no—
774C8—81no—
775C8—81no—
776C8—81no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—168no—
819C22#147114yes—
820C22C2×#40811yescharacteristic
821C22C22×#9911yescharacteristic
822C22C22×#10011yescharacteristic
823C22#289711yescharacteristic
824C22#289711yescharacteristic
825C22#290111yescharacteristic
826C22#290111yescharacteristic
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—22no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—81no—
843C4—81no—
844C4—81no—
845C4—81no—
846C2—24no—
847C2—42no—
848C2—81no—
849C2—161no—
850C2—161no—
851C2—161no—
852C2C2×#147111yescharacteristic
853C2#1746811yescharacteristic
854C2#1748311yescharacteristic
855C2#1760311yescharacteristic
856C2#1760311yescharacteristic
857C2#1768511yescharacteristic
858C2#1777011yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radical#35256C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22471C2semidirect
3. #22469C2semidirect
4. #7730C2semidirect
5. #7724C2semidirect
6. #7710C2semidirect
7. #7704C2semidirect
8. #7690C2semidirect
9. #7684C2semidirect
10. #7670C2semidirect
11. #7664C2semidirect
12. #7592C2semidirect
13. #7578C2semidirect
14. #7578C2semidirect
15. C2×#1270C2semidirect
49. #1817C22semidirect
50. #1817C22semidirect
51. #1797C22semidirect
52. #1797C22semidirect
53. #1749C22semidirect
54. C4×C22⋊C8C22semidirect
55. #1728C22semidirect
58. C2×#336C22semidirect
59. #1272C22semidirect
60. #1272C22semidirect
61. #1272C22semidirect
62. #1272C22semidirect
71. #1270C22semidirect
72. #1270C22semidirect
73. #1270C22semidirect
74. #1270C22semidirect

Maximal subgroups

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

subgroupindex
#352562
#224712
#224692
#77302
#77242
#77102
#77042
#76902
#76842
#76702
#76642
#75922
#75782
C2×#12702