Finite Group Databasebeta

← #164921

Subgroups — #164921

Order 512.

1378 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36260C211yesmaximal, characteristic
2#22785C211yesmaximal, characteristic, complemented
3#22698C211yesmaximal, characteristic, complemented
4#7724C211yesmaximal, characteristic, complemented
5#7719C211yesmaximal, characteristic, complemented
6#7684C211yesmaximal, characteristic, complemented
7#7679C211yesmaximal, characteristic, complemented
8#7664C211yesmaximal, characteristic, complemented
9#7664C211yesmaximal, characteristic, complemented
10#7640C211yesmaximal, characteristic, complemented
11#7621C211yesmaximal, characteristic, complemented
12#7606C211yesmaximal, characteristic, complemented
13#7587C211yesmaximal, characteristic, complemented
14#7572C211yesmaximal, characteristic, complemented
15C2×#1270C211yesmaximal, characteristic, complemented
16C2×#547C411yescharacteristic
17C2×#546—21no—
18C2×#546—21no—
19C2×D42C411yescharacteristic
20C2×#435—21no—
21#2858C2211yescharacteristic
22#2856C2211yescharacteristic
23#2856C2211yescharacteristic
24#2542C411yescharacteristic
25#2541C411yescharacteristic
26#2540—21no—
27#2540—21no—
28#2539—21no—
29#2539—21no—
30#2539—21no—
31#2539—21no—
32#2501C411yescharacteristic
33#2501C411yescharacteristic
34#2433C411yescharacteristic
35#2433C411yescharacteristic
36C4×#127C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C42×D4C2211yescharacteristic
40#1940—21no—
41#1923—21no—
42#1916—21no—
43#1869—21no—
44#1851—21no—
45#1850—21no—
46#1839C2211yescharacteristic, complemented
47#1831C2211yescharacteristic, complemented
48#1817C2211yescharacteristic, complemented
49#1797C2211yescharacteristic, complemented
50#1797C2211yescharacteristic, complemented
51#1797C2211yescharacteristic, complemented
52#1767C2211yescharacteristic, complemented
53C8×C22⋊C4—21no—
54C4×C22⋊C8C2211yescharacteristic, complemented
55#1744C2211yescharacteristic, complemented
56#1728C2211yescharacteristic, complemented
57C2×#336C2211yescharacteristic, complemented
58C2×#336C2211yescharacteristic, complemented
59#1270C2211yescharacteristic
60#1270C2211yescharacteristic
61#1270C2211yescharacteristic
62#1270C2211yescharacteristic
63#1270C2211yescharacteristic, complemented
64#1270C2211yescharacteristic, complemented
65#1270C2211yescharacteristic, complemented
66#1270C2211yescharacteristic, complemented
67#1270C2211yescharacteristic, complemented
68#1270C2211yescharacteristic, complemented
69#1270C2211yescharacteristic, complemented
70#1270C2211yescharacteristic, complemented
71#1270C2211yescharacteristic, complemented
72#1270C2211yescharacteristic, complemented
73#1270C2211yescharacteristic, complemented
74#1270C2211yescharacteristic, complemented
75C22×#41—21no—
76C23×D4—21no—
77C23×D4C2×C411yescharacteristic
78C23×D4C2×C411yescharacteristic
79C22×M16—21no—
80C23×C8—21no—
81C23×C8—21no—
82#547—44no—
83#546—44no—
84#546—44no—
85#546—44no—
86#546—44no—
87D42—44no—
88C2×C4⋊Q8C2×C411yescharacteristic
89C2×#127C2×C411yescharacteristic
90C2×#127C2×C411yescharacteristic
91C2×#127C2×C411yescharacteristic
92C2×#127C2×C411yescharacteristic
93C2×#124—21no—
94C2×#124—21no—
95C2×#123—21no—
96C2×#123—21no—
97C2×#123—21no—
98C2×#123—21no—
99C2×#123—21no—
100C2×#123—21no—
101C2×C22⋊Q8—21no—
102C2×C22⋊Q8—21no—
103C2×C22⋊Q8—21no—
104C2×#121—21no—
105C2×#121—21no—
106C2×#121—21no—
107C2×#121—21no—
108C2×#121—21no—
109C2×#121—21no—
110C2×#121—21no—
111C2×#121C2×C411yescharacteristic
112C2×#121C2×C411yescharacteristic
113C2×#121C2×C411yescharacteristic
114C2×#121C2×C411yescharacteristic
115C2×#120—21no—
116C2×#120—21no—
117C2×#120—21no—
118C2×#120—21no—
119C2×#120—21no—
120C2×#120—21no—
121C2×C4×D4—21no—
122C2×C4×D4—21no—
123C2×C4×D4C2×C411yescharacteristic
124C2×C4×D4C2×C411yescharacteristic
125C2×C4×D4C2×C411yescharacteristic
126C2×C4×D4D411yescharacteristic
127C2×C4×D4D411yescharacteristic
128C22×C4⋊C4C2×C411yescharacteristic
129C22×C4⋊C4C2×C411yescharacteristic
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136#435—44no—
137C2×C4⋊C8—21no—
138C2×C4⋊C8—21no—
139C2×C4⋊C8—21no—
140C2×C4⋊C8—21no—
141C2×C4⋊C8—21no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8—21no—
144C2×C22⋊C8—21no—
145C2×C22⋊C8—21no—
146C2×C22⋊C8—21no—
147C2×#97—21no—
148C2×C4×C8—21no—
149C2×C4×C8—21no—
150#399—21no—
151#399—21no—
152#399—21no—
153#399—21no—
154#399—21no—
155#399—21no—
156#392—21no—
157#392—21no—
158#392—21no—
159#392—21no—
160#392—21no—
161#392—21no—
162#390—21no—
163#390—21no—
164#390—21no—
165#390—21no—
166#390—21no—
167#390—21no—
168#390—21no—
169#390—21no—
170#390—21no—
171#390—21no—
172#390—21no—
173#390—21no—
174#390C2×C411yescharacteristic
175#390C2×C411yescharacteristic
176#390C2×C411yescharacteristic
177#390C2×C411yescharacteristic
178#390C2×C411yescharacteristic
179#390C2×C411yescharacteristic
180#390C2311yescharacteristic
181#390C2311yescharacteristic
182#390C2311yescharacteristic
183#390C2311yescharacteristic
184#384C2×C411yescharacteristic
185#384C2×C411yescharacteristic
186#384C2×C411yescharacteristic
187C4×C4⋊C4C2×C411yescharacteristic
188C4×C4⋊C4D411yescharacteristic
189C4×C4⋊C4D411yescharacteristic
190C4×C22⋊C4C2×C411yescharacteristic
191C4×C22⋊C4C2×C411yescharacteristic
192C4×C22⋊C4D411yescharacteristic
193C4×C22⋊C4D411yescharacteristic
194C4×C22⋊C4D411yescharacteristic
195C4×C22⋊C4D411yescharacteristic
196C43C2311yescharacteristic
197#336—21no—
198#336—21no—
199#336—21no—
200#336—21no—
201#336—21no—
202#336—21no—
203#336—21no—
204#336—21no—
205#336C2311yescharacteristic
206#336C2311yescharacteristic
207#336C2311yescharacteristic
208#336C2311yescharacteristic
209#336C2311yescharacteristic
210#336C2311yescharacteristic
211#336C2311yescharacteristic
212#336C2311yescharacteristic
213C25—21no—
214C25—21no—
215C2×#41—44no—
216C2×#41—44no—
217C2×#41—44no—
218C22×Q8—21no—
219C22×D4—22no—
220C22×D4—22no—
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—21no—
234C22×D4—21no—
235C22×D4—41no—
236C22×D4—41no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—81no—
243C22×D4—81no—
244C22×D4C22⋊C411yescharacteristic
245C22×D4C22×C411yescharacteristic
246C22×D4C22×C411yescharacteristic
247C22×D4C22×C411yescharacteristic
248C22×D4C22×C411yescharacteristic
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4C22×C411yescharacteristic
254C23×C4C22×C411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D411yescharacteristic
259C2×M16—42no—
260C2×M16—42no—
261C2×M16—81no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—42no—
271C22×C8—42no—
272C22×C8—42no—
273C22×C8—42no—
274C22×C8—81no—
275C22×C8—81no—
276C4⋊Q8—42no—
277#127—22no—
278#127—41no—
279#127—42no—
280#127—81no—
281#127—81no—
282#124—42no—
283#124—42no—
284#124—42no—
285#124—42no—
286#123—44no—
287#123—44no—
288#123—44no—
289#123—44no—
290#123—44no—
291#123—44no—
292C22⋊Q8—44no—
293C22⋊Q8—44no—
294C22⋊Q8—44no—
295#121—44no—
296#121—44no—
297#121—42no—
298#121—42no—
299#121—42no—
300#121—42no—
301#121—42no—
302#121—42no—
303#121—42no—
304#121—42no—
305#121—42no—
306#121—42no—
307#121—44no—
308#121—42no—
309#121—42no—
310#120—44no—
311#120—44no—
312#120—44no—
313#120—44no—
314#120—44no—
315#120—44no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—24no—
319C4×D4—42no—
320C4×D4—42no—
321C4×D4—42no—
322C4×D4—42no—
323C4×D4—42no—
324C4×D4—42no—
325C4×D4D814yes—
326C4×D4SD1614yes—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4C22⋊C411yescharacteristic
339C2×C4⋊C4C22⋊C411yescharacteristic
340C2×C4⋊C4C22⋊C411yescharacteristic
341C2×C4⋊C4C22×C411yescharacteristic
342C2×C4⋊C4C22×C411yescharacteristic
343C2×C4⋊C4C22×C411yescharacteristic
344C2×C4⋊C4C22×C411yescharacteristic
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—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4C22⋊C411yescharacteristic
380C2×C22⋊C4C22⋊C411yescharacteristic
381C2×C22⋊C4C22⋊C411yescharacteristic
382C2×C22⋊C4C22⋊C411yescharacteristic
383C2×C22⋊C4C22⋊C411yescharacteristic
384C2×C22⋊C4C22⋊C411yescharacteristic
385C2×C42—81no—
386C2×C42—81no—
387C2×C42C22×C411yescharacteristic
388C2×C42C22×C411yescharacteristic
389C2×C42C22×C411yescharacteristic
390C2×C42C22×C411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2411yescharacteristic
400C4⋊C8—42no—
401C4⋊C8—42no—
402C4⋊C8—81no—
403C4⋊C8—81no—
404C4⋊C8—81no—
405C22⋊C8—42no—
406C22⋊C8—42no—
407C22⋊C8—42no—
408C22⋊C8—42no—
409C22⋊C8—81no—
410#97—42no—
411C4×C8—42no—
412C4×C8—81no—
413#95C22⋊C411yescharacteristic
414#95C22⋊C411yescharacteristic
415#95C22⋊C411yescharacteristic
416#95C22⋊C411yescharacteristic
417#95C22⋊C411yescharacteristic
418#95C22⋊C411yescharacteristic
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—81no—
432C24—81no—
433C24—81no—
434C24—81no—
435C24—81no—
436C24—81no—
437C24C2×C22⋊C411yescharacteristic
438C24C2×C22⋊C411yescharacteristic
439#41—816no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—81no—
489C2×D4—81no—
490C2×D4—81no—
491C2×D4—81no—
492C2×D4—81no—
493C2×D4—81no—
494C2×D4—81no—
495C2×D4—81no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4—81no—
500C2×D4—81no—
501C2×D4—81no—
502C2×D4—84no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—816no—
507C2×D4#10214yes—
508C2×D4#13112yes—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4C2×C22⋊C411yescharacteristic
544C22×C4C2×C22⋊C411yescharacteristic
545C22×C4C2×C22⋊C411yescharacteristic
546C22×C4C2×C22⋊C411yescharacteristic
547C22×C4C2×C22⋊C411yescharacteristic
548C22×C4C2×C22⋊C411yescharacteristic
549C22×C4C2×C22⋊C411yescharacteristic
550C22×C4C2×C22⋊C411yescharacteristic
551C22×C4C2×C22⋊C411yescharacteristic
552C22×C4C2×C22⋊C411yescharacteristic
553C22×C4C2×D812yes—
554C22×C4C2×D812yes—
555C22×C4C2×SD1612yes—
556C22×C4C2×SD1612yes—
557C22×C4AGL(1,ℤ/8)12yes—
558C22×C4AGL(1,ℤ/8)12yes—
559C22×C4C23×C411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562M16—84no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8—41no—
584C2×C8—41no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—84no—
588C2×C8—84no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4#10214yes—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
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—41no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4#10014yes—
643C22⋊C4#10214yes—
644C22⋊C4#10214yes—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—22no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42C2×D812yes—
660C42C2×SD1612yes—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—162no—
708C23—162no—
709C23—162no—
710C23—162no—
711C23—162no—
712C23—162no—
713C23C2×#10012yes—
714C23C2×#10212yes—
715C23C2×#10212yes—
716C23#41812yes—
717C23C22×C22⋊C411yescharacteristic
718Q8—84no—
719D4—28no—
720D4—42no—
721D4—42no—
722D4—84no—
723D4—84no—
724D4—81no—
725D4—81no—
726D4—81no—
727D4—81no—
728D4—81no—
729D4—81no—
730D4—84no—
731D4—84no—
732D4—84no—
733D4—84no—
734D4—84no—
735D4—84no—
736D4—84no—
737D4—162no—
738D4—162no—
739D4—162no—
740D4—162no—
741D4—162no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—84no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4—84no—
799C2×C4C2×#10012yes—
800C2×C4C2×#10012yes—
801C2×C4C2×#10212yes—
802C2×C4C2×#10212yes—
803C2×C4C2×#10212yes—
804C2×C4C2×#10212yes—
805C2×C4#41812yes—
806C2×C4C2×#13111yescharacteristic
807C2×C4#56811yescharacteristic
808C2×C4C22×D811yescharacteristic
809C2×C4C22×SD1611yescharacteristic
810C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
811C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
812C8—42no—
813C8—42no—
814C8—81no—
815C8—81no—
816C8—81no—
817C8—81no—
818C8—81no—
819C8—81no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—168no—
862C22—168no—
863C22#154514yes—
864C22#288011yescharacteristic
865C22#288311yescharacteristic
866C22C22×#10011yescharacteristic
867C22C22×#10211yescharacteristic
868C22C2×#41811yescharacteristic
869C22#290111yescharacteristic
870C22#290111yescharacteristic
871C4—21no—
872C4—21no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—21no—
878C4—21no—
879C4—22no—
880C4—22no—
881C4—21no—
882C4—21no—
883C4—22no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—81no—
888C4—81no—
889C4—81no—
890C4—81no—
891C2—24no—
892C2—42no—
893C2—82no—
894C2—161no—
895C2—161no—
896C2—161no—
897C2#1742111yescharacteristic
898C2#1750711yescharacteristic
899C2#1751111yescharacteristic
900C2#1761311yescharacteristic
901C2#1762011yescharacteristic
902C2#1768511yescharacteristic
903C2C2×#154511yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radical#36260C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22785C2semidirect
3. #22698C2semidirect
4. #7724C2semidirect
5. #7719C2semidirect
6. #7684C2semidirect
7. #7679C2semidirect
8. #7664C2semidirect
9. #7664C2semidirect
10. #7640C2semidirect
11. #7621C2semidirect
12. #7606C2semidirect
13. #7587C2semidirect
14. #7572C2semidirect
15. C2×#1270C2semidirect
46. #1839C22semidirect
47. #1831C22semidirect
48. #1817C22semidirect
49. #1797C22semidirect
50. #1797C22semidirect
51. #1797C22semidirect
52. #1767C22semidirect
54. C4×C22⋊C8C22semidirect
55. #1744C22semidirect
56. #1728C22semidirect
57. C2×#336C22semidirect
58. C2×#336C22semidirect
63. #1270C22semidirect
64. #1270C22semidirect
65. #1270C22semidirect
66. #1270C22semidirect
67. #1270C22semidirect
68. #1270C22semidirect
69. #1270C22semidirect
70. #1270C22semidirect
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
#362602
#227852
#226982
#77242
#77192
#76842
#76792
#76642
#76402
#76212
#76062
#75872
#75722
C2×#12702