Finite Group Databasebeta

← #165171

Subgroups — #165171

Order 512.

1095 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36360C211yesmaximal, characteristic
2#22532C211yesmaximal, characteristic, complemented
3#20630C211yesmaximal, characteristic, complemented
4#7715C211yesmaximal, characteristic, complemented
5#7714C211yesmaximal, characteristic, complemented
6#7710C211yesmaximal, characteristic, complemented
7#7698C211yesmaximal, characteristic, complemented
8#7690C211yesmaximal, characteristic, complemented
9#7661C211yesmaximal, characteristic, complemented
10#7640C211yesmaximal, characteristic, complemented
11#7633C211yesmaximal, characteristic, complemented
12#7612C211yesmaximal, characteristic, complemented
13#7597C211yesmaximal, characteristic, complemented
14#7586C211yesmaximal, characteristic, complemented
15#7572C211yesmaximal, characteristic, complemented
16C2×#546C411yescharacteristic
17C2×C4×#41C2211yescharacteristic
18C2×#446—21no—
19C2×#424—21no—
20C2×#408—21no—
21#2855C2211yescharacteristic
22#2854C2211yescharacteristic
23#2850C2211yescharacteristic
24#2592C411yescharacteristic
25#2580C411yescharacteristic
26#2476—21no—
27#2471—21no—
28#2458—21no—
29#2456—21no—
30#2418—21no—
31#2417C411yescharacteristic
32#2414C411yescharacteristic
33#2408C411yescharacteristic
34#2407C411yescharacteristic
35#2404—21no—
36#2358—21no—
37#2352C411yescharacteristic
38#2342—21no—
39C4×#121C2211yescharacteristic
40#2297C2211yescharacteristic
41C2×#390C2211yescharacteristic
42#1955—21no—
43#1955—21no—
44#1954—21no—
45#1798—21no—
46#1798—21no—
47#1797C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic, complemented
51#1797C2211yescharacteristic, complemented
52#1797C2211yescharacteristic, complemented
53#1797C2211yescharacteristic, complemented
54#1749C2211yescharacteristic, complemented
55#1749C2211yescharacteristic, complemented
56C4×C22⋊C8C2211yescharacteristic
57#1728C2211yescharacteristic, complemented
58C2×#336C2211yescharacteristic, complemented
59#1272C2211yescharacteristic, complemented
60#1272C2211yescharacteristic, complemented
61#1272C2211yescharacteristic, complemented
62#1272C2211yescharacteristic, complemented
63#1271C2211yescharacteristic, complemented
64#1271C2211yescharacteristic, complemented
65#1271C2211yescharacteristic, complemented
66#1271C2211yescharacteristic, complemented
67#1270C2211yescharacteristic
68#1270C2211yescharacteristic
69#1270C2211yescharacteristic
70#1270C2211yescharacteristic
71#1270C2211yescharacteristic
72#1270C2211yescharacteristic
73#1270C2211yescharacteristic
74#1270C2211yescharacteristic
75C22×#41C2×C411yescharacteristic
76C22×#41D411yescharacteristic
77C23×D4C2×C411yescharacteristic
78C22×M16—21no—
79C23×C8—21no—
80#546—44no—
81C2×#124C2×C411yescharacteristic
82C2×#123—21no—
83C2×#123—21no—
84C2×C22⋊Q8C2×C411yescharacteristic
85C2×C22⋊Q8C2×C411yescharacteristic
86C2×#121—21no—
87C2×#121C2×C411yescharacteristic
88C2×#121C2×C411yescharacteristic
89C2×#121C2×C411yescharacteristic
90C2×#120—21no—
91C2×#120—21no—
92C4×#41—44no—
93C2×C4×Q8C2×C411yescharacteristic
94C2×C4×Q8D411yescharacteristic
95C2×C4×D4—21no—
96C2×C4×D4C2×C411yescharacteristic
97C2×C4×D4C2×C411yescharacteristic
98C2×C4×D4C2×C411yescharacteristic
99C2×C4×D4C2×C411yescharacteristic
100C2×C4×D4D411yescharacteristic
101C2×C4×D4D411yescharacteristic
102C2×C4×D4D411yescharacteristic
103C2×#117C2×C411yescharacteristic
104C2×#117D411yescharacteristic
105C2×#117D411yescharacteristic
106C2×#117D411yescharacteristic
107C22×C4⋊C4C2×C411yescharacteristic
108C22×C22⋊C4—21no—
109C22×C22⋊C4—21no—
110C22×C22⋊C4—21no—
111C22×C42C2311yescharacteristic
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114#446—44no—
115#424—44no—
116C2×C4⋊C8—21no—
117C2×C4⋊C8—21no—
118C2×C4⋊C8—21no—
119C2×C4⋊C8—21no—
120C2×C4⋊C8—21no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—21no—
123#408—44no—
124C2×C22⋊C8—21no—
125C2×C22⋊C8—21no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—21no—
128C2×C22⋊C8—21no—
129C2×C22⋊C8—21no—
130C2×C22⋊C8—21no—
131C2×C22⋊C8—21no—
132C2×C22⋊C8—21no—
133C2×C22⋊C8—21no—
134C2×#97—21no—
135C2×#97—21no—
136C2×C4×C8—21no—
137#399—21no—
138#398—21no—
139#397—21no—
140#396—21no—
141#394—21no—
142#394—21no—
143#394—21no—
144#393—21no—
145#393—21no—
146#392—21no—
147#392—21no—
148#392—21no—
149#391C2×C411yescharacteristic
150#391C2×C411yescharacteristic
151#391C2311yescharacteristic
152#390—21no—
153#390—21no—
154#390—21no—
155#390C2×C411yescharacteristic
156#390C2×C411yescharacteristic
157#390C2×C411yescharacteristic
158#390C2×C411yescharacteristic
159#390C2311yescharacteristic
160#390C2311yescharacteristic
161#389C2×C411yescharacteristic
162#389C2×C411yescharacteristic
163#389C2311yescharacteristic
164#388—21no—
165#388—21no—
166#388—21no—
167#388—21no—
168#388—21no—
169#388—21no—
170#388—21no—
171#388—21no—
172#388—21no—
173#387—21no—
174#387—21no—
175#387—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#385—21no—
186#385—21no—
187#385—21no—
188#385—21no—
189#382C2×C411yescharacteristic
190#381—21no—
191#380—21no—
192#380C2×C411yescharacteristic
193#380C2×C411yescharacteristic
194#380C2×C411yescharacteristic
195#379—21no—
196C4×C4⋊C4C2×C411yescharacteristic
197C4×C22⋊C4—21no—
198C4×C22⋊C4—21no—
199C4×C22⋊C4—21no—
200C4×C22⋊C4—21no—
201#336—21no—
202#336—21no—
203#336C2311yescharacteristic
204#336C2311yescharacteristic
205#336C2311yescharacteristic
206#336C2311yescharacteristic
207#336C2311yescharacteristic
208#336C2311yescharacteristic
209#336C2311yescharacteristic
210#336C2311yescharacteristic
211C25—21no—
212C2×#41—22no—
213C2×#41—22no—
214C2×#41—22no—
215C2×#41—42no—
216C2×#41—42no—
217C2×#41—41no—
218C2×#41—42no—
219C2×#41—81no—
220C22×Q8C22⋊C411yescharacteristic
221C22×Q8C22×C411yescharacteristic
222C22×D4—22no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—41no—
229C22×D4—42no—
230C22×D4—81no—
231C22×D4C22⋊C411yescharacteristic
232C22×D4C22⋊C411yescharacteristic
233C22×D4C22⋊C411yescharacteristic
234C22×D4C22×C411yescharacteristic
235C22×D4C22×C411yescharacteristic
236C23×C4—21no—
237C23×C4—21no—
238C23×C4—21no—
239C23×C4C22×C411yescharacteristic
240C23×C4C22×C411yescharacteristic
241C23×C4C22×C411yescharacteristic
242C23×C4C2×D411yescharacteristic
243C23×C4C2×D411yescharacteristic
244C23×C4C2×D411yescharacteristic
245C23×C4C2×D411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C2×M16—42no—
249C2×M16—42no—
250C2×M16—42no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—42no—
260C22×C8—42no—
261C22×C8—42no—
262#124—42no—
263#123—44no—
264#123—81no—
265#123—81no—
266C22⋊Q8—42no—
267C22⋊Q8—81no—
268#121—22no—
269#121—44no—
270#121—41no—
271#121—42no—
272#121—81no—
273#120—44no—
274#120—44no—
275C4×Q8—24no—
276C4×Q8—42no—
277C4×D4—24no—
278C4×D4—42no—
279C4×D4—42no—
280C4×D4—42no—
281C4×D4—42no—
282C4×D4—42no—
283C4×D4—42no—
284C4×D4—81no—
285C4×D4—81no—
286#117—24no—
287#117—42no—
288#117—42no—
289#117—81no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—81no—
297C2×C4⋊C4C22⋊C411yescharacteristic
298C2×C4⋊C4C22⋊C411yescharacteristic
299C2×C4⋊C4C22⋊C411yescharacteristic
300C2×C4⋊C4C22⋊C411yescharacteristic
301C2×C4⋊C4C22⋊C411yescharacteristic
302C2×C4⋊C4C22⋊C411yescharacteristic
303C2×C4⋊C4C22×C411yescharacteristic
304C2×C4⋊C4C22×C411yescharacteristic
305C2×C4⋊C4C22×C411yescharacteristic
306C2×C4⋊C4C22×C411yescharacteristic
307C2×C4⋊C4C22×C411yescharacteristic
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—81no—
336C2×C22⋊C4—81no—
337C2×C22⋊C4C22⋊C411yescharacteristic
338C2×C22⋊C4C22⋊C411yescharacteristic
339C2×C22⋊C4C22⋊C411yescharacteristic
340C2×C22⋊C4C22⋊C411yescharacteristic
341C2×C22⋊C4C22⋊C411yescharacteristic
342C2×C22⋊C4C22⋊C411yescharacteristic
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42—42no—
348C2×C42C22×C411yescharacteristic
349C2×C42C22×C411yescharacteristic
350C2×C42C22×C411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2×D411yescharacteristic
356C2×C42C2×D411yescharacteristic
357C2×C42C2411yescharacteristic
358C4⋊C8—42no—
359C4⋊C8—42no—
360C4⋊C8—42no—
361C4⋊C8—42no—
362C4⋊C8—42no—
363C4⋊C8—42no—
364C4⋊C8—42no—
365C22⋊C8—42no—
366C22⋊C8—42no—
367C22⋊C8—42no—
368C22⋊C8—42no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8—81no—
373C22⋊C8—81no—
374C22⋊C8—81no—
375#97—42no—
376#97—42no—
377C4×C8—42no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393C24—21no—
394C24—21no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24—81no—
400C24—81no—
401C24—81no—
402C24C2×C22⋊C411yescharacteristic
403C24C2×C22⋊C411yescharacteristic
404C24C2×C22⋊C411yescharacteristic
405#41—48no—
406#41—48no—
407#41—84no—
408#41—84no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—42no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—81no—
441C2×D4—84no—
442C2×D4—84no—
443C2×D4—81no—
444C2×D4—81no—
445C2×D4—81no—
446C2×D4—81no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4#13112yes—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4C2×C22⋊C411yescharacteristic
500C22×C4C2×C22⋊C411yescharacteristic
501C22×C4C2×C22⋊C411yescharacteristic
502C22×C4C2×C22⋊C411yescharacteristic
503C22×C4C2×C22⋊C411yescharacteristic
504C22×C4C2×C22⋊C411yescharacteristic
505C22×C4C2×C22⋊C411yescharacteristic
506C22×C4C2×C22⋊C411yescharacteristic
507C22×C4C2×C22⋊C411yescharacteristic
508C22×C4AGL(1,ℤ/8)12yes—
509C22×C4#13712yes—
510C22×C4C23×C411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C22×D411yescharacteristic
513M16—84no—
514C2×C8—22no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—84no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—42no—
553C4⋊C4—81no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4#9914yes—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C22⋊C4—81no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—81no—
603C42—81no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—84no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—162no—
642C23—162no—
643C23—162no—
644C23#41712yes—
645C23#42112yes—
646C23C22×C22⋊C411yescharacteristic
647Q8—44no—
648Q8—81no—
649Q8—81no—
650D4—44no—
651D4—44no—
652D4—42no—
653D4—42no—
654D4—44no—
655D4—84no—
656D4—81no—
657D4—81no—
658D4—84no—
659D4—84no—
660D4—162no—
661D4—162no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—84no—
728C2×C4—162no—
729C2×C4—162no—
730C2×C4C2×#9912yes—
731C2×C4C2×#9912yes—
732C2×C4C2×#9912yes—
733C2×C4#41712yes—
734C2×C4C2×#13111yescharacteristic
735C2×C4#56811yescharacteristic
736C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
737C2×C4C2×#13711yescharacteristic
738C2×C4#57611yescharacteristic
739C2×C4#57711yescharacteristic
740C8—42no—
741C8—81no—
742C8—81no—
743C8—81no—
744C8—81no—
745C8—81no—
746C8—81no—
747C8—81no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—168no—
784C22#288011yescharacteristic
785C22C22×#9911yescharacteristic
786C22#288811yescharacteristic
787C22C2×#41711yescharacteristic
788C22#289711yescharacteristic
789C22C2×#42111yescharacteristic
790C22#290111yescharacteristic
791C4—21no—
792C4—21no—
793C4—22no—
794C4—22no—
795C4—21no—
796C4—21no—
797C4—22no—
798C4—22no—
799C4—21no—
800C4—21no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—81no—
810C4—81no—
811C4—81no—
812C2—42no—
813C2—42no—
814C2—81no—
815C2—82no—
816C2—161no—
817C2#1741111yescharacteristic
818C2#1751211yescharacteristic
819C2#1752111yescharacteristic
820C2#1759211yescharacteristic
821C2#1761111yescharacteristic
822C2#1767911yescharacteristic
823C2#1776211yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radical#36360C2
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. #22532C2semidirect
3. #20630C2semidirect
4. #7715C2semidirect
5. #7714C2semidirect
6. #7710C2semidirect
7. #7698C2semidirect
8. #7690C2semidirect
9. #7661C2semidirect
10. #7640C2semidirect
11. #7633C2semidirect
12. #7612C2semidirect
13. #7597C2semidirect
14. #7586C2semidirect
15. #7572C2semidirect
50. #1797C22semidirect
51. #1797C22semidirect
52. #1797C22semidirect
53. #1797C22semidirect
54. #1749C22semidirect
55. #1749C22semidirect
57. #1728C22semidirect
58. C2×#336C22semidirect
59. #1272C22semidirect
60. #1272C22semidirect
61. #1272C22semidirect
62. #1272C22semidirect
63. #1271C22semidirect
64. #1271C22semidirect
65. #1271C22semidirect
66. #1271C22semidirect

Maximal subgroups

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

subgroupindex
#363602
#225322
#206302
#77152
#77142
#77102
#76982
#76902
#76612
#76402
#76332
#76122
#75972
#75862
#75722