Finite Group Databasebeta

← #164512

Subgroups — #164512

Order 512.

1280 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36258C211yesmaximal, characteristic
2#22471C211yesmaximal, characteristic, complemented
3#20684C211yesmaximal, characteristic, complemented
4#7724C211yesmaximal, characteristic, complemented
5#7718C211yesmaximal, characteristic, complemented
6#7704C211yesmaximal, characteristic, complemented
7#7694C211yesmaximal, characteristic, complemented
8#7678C211yesmaximal, characteristic, complemented
9#7654C211yesmaximal, characteristic, complemented
10#7620C211yesmaximal, characteristic, complemented
11#7606C211yesmaximal, characteristic, complemented
12#7606C211yesmaximal, characteristic, complemented
13#7599C211yesmaximal, characteristic, complemented
14#7592C211yesmaximal, characteristic, complemented
15C2×#1270C211yesmaximal, characteristic, complemented
16C2×#546—21no—
17C2×D42C411yescharacteristic
18C2×C4×#41C2211yescharacteristic
19C2×#435—21no—
20C2×#408—21no—
21#2856C2211yescharacteristic
22#2854C2211yescharacteristic
23#2854C2211yescharacteristic
24#2548C411yescharacteristic
25#2538C411yescharacteristic
26#2426—21no—
27#2424—21no—
28#2424—21no—
29#2416C411yescharacteristic
30#2416C411yescharacteristic
31#2414—21no—
32#2411—21no—
33#2411—21no—
34#2408C411yescharacteristic
35#2408C411yescharacteristic
36D4×C4⋊C4C411yescharacteristic
37D4×C22⋊C4—21no—
38C4×#121C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41#1985—21no—
42#1870—21no—
43#1869—21no—
44#1818—21no—
45#1818—21no—
46#1817C2211yescharacteristic, complemented
47#1817C2211yescharacteristic, complemented
48#1817C2211yescharacteristic, complemented
49#1817C2211yescharacteristic, complemented
50#1817C2211yescharacteristic, complemented
51#1817C2211yescharacteristic, complemented
52#1797C2211yescharacteristic, complemented
53#1749C2211yescharacteristic, complemented
54#1729—21no—
55#1728C2211yescharacteristic, complemented
56#1728C2211yescharacteristic, complemented
57C2×#336C2211yescharacteristic, complemented
58C2×#336C2211yescharacteristic, complemented
59#1271C2211yescharacteristic, complemented
60#1271C2211yescharacteristic, complemented
61#1271C2211yescharacteristic, complemented
62#1271C2211yescharacteristic, complemented
63#1270C2211yescharacteristic
64#1270C2211yescharacteristic
65#1270C2211yescharacteristic
66#1270C2211yescharacteristic
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×#41D411yescharacteristic
76C23×D4—21no—
77C23×D4C2×C411yescharacteristic
78C23×D4C2×C411yescharacteristic
79C22×M16—21no—
80C22×M16—21no—
81C23×C8—21no—
82C23×C8—21no—
83#546—44no—
84#546—44no—
85D42—44no—
86C2×#127C2×C411yescharacteristic
87C2×#124—21no—
88C2×#123—21no—
89C2×#123—21no—
90C2×C22⋊Q8—21no—
91C2×#121—21no—
92C2×#121—21no—
93C2×#121—21no—
94C2×#121—21no—
95C2×#121—21no—
96C2×#121C2×C411yescharacteristic
97C2×#121C2×C411yescharacteristic
98C2×#121C2×C411yescharacteristic
99C2×#121C2×C411yescharacteristic
100C2×#121C2×C411yescharacteristic
101C2×#120—21no—
102C2×#120—21no—
103C2×#120—21no—
104C2×#120—21no—
105C4×#41—44no—
106C2×C4×Q8C2×C411yescharacteristic
107C2×C4×Q8D411yescharacteristic
108C2×C4×D4—21no—
109C2×C4×D4—21no—
110C2×C4×D4C2×C411yescharacteristic
111C2×C4×D4C2×C411yescharacteristic
112C2×C4×D4C2×C411yescharacteristic
113C2×C4×D4C2×C411yescharacteristic
114C2×C4×D4D411yescharacteristic
115C2×C4×D4D411yescharacteristic
116C2×C4×D4D411yescharacteristic
117C2×#117D411yescharacteristic
118C2×#117D411yescharacteristic
119C2×#117D411yescharacteristic
120C22×C4⋊C4C2×C411yescharacteristic
121C22×C4⋊C4C2×C411yescharacteristic
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C42C2311yescharacteristic
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129#435—44no—
130C2×C4⋊C8—21no—
131#408—44no—
132C2×C22⋊C8—21no—
133C2×C22⋊C8—21no—
134C2×C22⋊C8—21no—
135C2×C22⋊C8—21no—
136C2×C22⋊C8—21no—
137C2×C22⋊C8—21no—
138C2×C22⋊C8—21no—
139C2×C22⋊C8—21no—
140C2×#97—21no—
141#396—21no—
142#396—21no—
143#396—21no—
144#396—21no—
145#394—21no—
146#394—21no—
147#394—21no—
148#394—21no—
149#394—21no—
150#394—21no—
151#392—21no—
152#392—21no—
153#390—21no—
154#390—21no—
155#390—21no—
156#390—21no—
157#390—21no—
158#390—21no—
159#390—21no—
160#390C2×C411yescharacteristic
161#390C2×C411yescharacteristic
162#390C2×C411yescharacteristic
163#390C2×C411yescharacteristic
164#390C2×C411yescharacteristic
165#390C2×C411yescharacteristic
166#390C2311yescharacteristic
167#390C2311yescharacteristic
168#390C2311yescharacteristic
169#389—21no—
170#389C2×C411yescharacteristic
171#389C2×C411yescharacteristic
172#389C2311yescharacteristic
173#388—21no—
174#388—21no—
175#388—21no—
176#388—21no—
177#388—21no—
178#386—21no—
179#386—21no—
180#386—21no—
181#386—21no—
182#386—21no—
183#385—21no—
184#385—21no—
185#384C2×C411yescharacteristic
186#380—21no—
187#380C2×C411yescharacteristic
188#380C2×C411yescharacteristic
189#380C2×C411yescharacteristic
190#379—21no—
191#379—21no—
192C4×C4⋊C4C2×C411yescharacteristic
193C4×C22⋊C4—21no—
194#336—21no—
195#336—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—
213C25—21no—
214C2×#41—24no—
215C2×#41—22no—
216C2×#41—22no—
217C2×#41—42no—
218C22×Q8C22⋊C411yescharacteristic
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—41no—
231C22×D4—41no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—44no—
235C22×D4—44no—
236C22×D4—44no—
237C22×D4—81no—
238C22×D4—81no—
239C22×D4C22⋊C411yescharacteristic
240C22×D4C22⋊C411yescharacteristic
241C22×D4C22⋊C411yescharacteristic
242C22×D4C22×C411yescharacteristic
243C22×D4C22×C411yescharacteristic
244C22×D4C22×C411yescharacteristic
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4C22×C411yescharacteristic
249C23×C4C22×C411yescharacteristic
250C23×C4C22×C411yescharacteristic
251C23×C4C2×D411yescharacteristic
252C23×C4C2×D411yescharacteristic
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C2×M16—42no—
258C2×M16—42no—
259C2×M16—42no—
260C2×M16—42no—
261C2×M16—42no—
262C2×M16—81no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—42no—
272C22×C8—42no—
273C22×C8—42no—
274C22×C8—42no—
275C22×C8—42no—
276C22×C8—81no—
277#127—42no—
278#124—44no—
279#123—42no—
280#123—42no—
281#123—42no—
282#123—42no—
283C22⋊Q8—44no—
284#121—22no—
285#121—41no—
286#121—44no—
287#121—42no—
288#121—42no—
289#121—42no—
290#121—42no—
291#121—44no—
292#121—44no—
293#121—81no—
294#121—81no—
295#121—81no—
296#121—81no—
297#120—44no—
298#120—44no—
299#120—44no—
300#120—44no—
301C4×Q8—42no—
302C4×Q8—42no—
303C4×D4—24no—
304C4×D4—24no—
305C4×D4—42no—
306C4×D4—42no—
307C4×D4—42no—
308C4×D4—42no—
309C4×D4—42no—
310C4×D4—42no—
311C4×D4—42no—
312C4×D4—44no—
313#117—42no—
314#117—42no—
315#117—42no—
316C2×C4⋊C4—21no—
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—81no—
324C2×C4⋊C4—81no—
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×C4⋊C4C22×C411yescharacteristic
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—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—81no—
368C2×C22⋊C4—81no—
369C2×C22⋊C4—81no—
370C2×C22⋊C4—81no—
371C2×C22⋊C4C22⋊C411yescharacteristic
372C2×C22⋊C4C22⋊C411yescharacteristic
373C2×C22⋊C4C22⋊C411yescharacteristic
374C2×C22⋊C4C22⋊C411yescharacteristic
375C2×C22⋊C4C22⋊C411yescharacteristic
376C2×C22⋊C4C22⋊C411yescharacteristic
377C2×C42—21no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42C22×C411yescharacteristic
382C2×C42C22×C411yescharacteristic
383C2×C42C22×C411yescharacteristic
384C2×C42C2×D411yescharacteristic
385C2×C42C2×D411yescharacteristic
386C2×C42C2×D411yescharacteristic
387C2×C42C2×D411yescharacteristic
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C2×C42C2411yescharacteristic
391C4⋊C8—42no—
392C22⋊C8—42no—
393C22⋊C8—42no—
394C22⋊C8—42no—
395C22⋊C8—42no—
396C22⋊C8—42no—
397C22⋊C8—42no—
398C22⋊C8—42no—
399C22⋊C8—81no—
400#97—42no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—81no—
420C24—81no—
421C24—81no—
422C24—81no—
423C24—81no—
424C24—81no—
425C24C2×C22⋊C411yescharacteristic
426C24C2×C22⋊C411yescharacteristic
427C24C2×C22⋊C411yescharacteristic
428#41—48no—
429#41—48no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—41no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—22no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4—81no—
473C2×D4—81no—
474C2×D4—84no—
475C2×D4—84no—
476C2×D4—84no—
477C2×D4—84no—
478C2×D4—81no—
479C2×D4—81no—
480C2×D4—81no—
481C2×D4—81no—
482C2×D4—81no—
483C2×D4—816no—
484C2×D4#9914yes—
485C2×D4#13112yes—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×C22⋊C411yescharacteristic
535C22×C4C2×C22⋊C411yescharacteristic
536C22×C4C2×C22⋊C411yescharacteristic
537C22×C4C2×C22⋊C411yescharacteristic
538C22×C4C2×C22⋊C411yescharacteristic
539C22×C4C2×C22⋊C411yescharacteristic
540C22×C4C2×C22⋊C411yescharacteristic
541C22×C4C2×C22⋊C411yescharacteristic
542C22×C4C2×C22⋊C411yescharacteristic
543C22×C4AGL(1,ℤ/8)12yes—
544C22×C4AGL(1,ℤ/8)12yes—
545C22×C4C23×C411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548M16—84no—
549M16—84no—
550C2×C8—22no—
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—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
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—84no—
575C2×C8—84no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—42no—
593C4⋊C4—81no—
594C4⋊C4—81no—
595C4⋊C4—81no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
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—41no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C42—22no—
636C42—22no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—41no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—22no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
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—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—162no—
693C23—162no—
694C23—162no—
695C23—162no—
696C23—162no—
697C23—162no—
698C23C2×#9912yes—
699C23C2×#9912yes—
700C23#41812yes—
701C23#42112yes—
702C23C22×C22⋊C411yescharacteristic
703Q8—44no—
704D4—28no—
705D4—44no—
706D4—42no—
707D4—42no—
708D4—44no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—84no—
714D4—84no—
715D4—84no—
716D4—84no—
717D4—84no—
718D4—84no—
719D4—162no—
720D4—162no—
721D4—162no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
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—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—84no—
787C2×C4—162no—
788C2×C4—162no—
789C2×C4C2×#9912yes—
790C2×C4#41812yes—
791C2×C4C2×#13111yescharacteristic
792C2×C4#56811yescharacteristic
793C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
794C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
795C2×C4#57611yescharacteristic
796C2×C4#57711yescharacteristic
797C8—42no—
798C8—81no—
799C8—81no—
800C8—81no—
801C8—81no—
802C8—81no—
803C8—81no—
804C8—81no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—168no—
847C22—168no—
848C22#151014yes—
849C22#288011yescharacteristic
850C22C22×#9911yescharacteristic
851C22#288811yescharacteristic
852C22C2×#41811yescharacteristic
853C22#289711yescharacteristic
854C22C2×#42111yescharacteristic
855C22#290111yescharacteristic
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—22no—
861C4—22no—
862C4—21no—
863C4—21no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—41no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4—81no—
876C2—24no—
877C2—42no—
878C2—81no—
879C2—82no—
880C2—161no—
881C2—161no—
882C2#1741111yescharacteristic
883C2#1751111yescharacteristic
884C2#1752111yescharacteristic
885C2C2×#151011yescharacteristic
886C2#1760311yescharacteristic
887C2#1767911yescharacteristic
888C2#1775811yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radical#36258C2
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. #20684C2semidirect
4. #7724C2semidirect
5. #7718C2semidirect
6. #7704C2semidirect
7. #7694C2semidirect
8. #7678C2semidirect
9. #7654C2semidirect
10. #7620C2semidirect
11. #7606C2semidirect
12. #7606C2semidirect
13. #7599C2semidirect
14. #7592C2semidirect
15. C2×#1270C2semidirect
46. #1817C22semidirect
47. #1817C22semidirect
48. #1817C22semidirect
49. #1817C22semidirect
50. #1817C22semidirect
51. #1817C22semidirect
52. #1797C22semidirect
53. #1749C22semidirect
55. #1728C22semidirect
56. #1728C22semidirect
57. C2×#336C22semidirect
58. C2×#336C22semidirect
59. #1271C22semidirect
60. #1271C22semidirect
61. #1271C22semidirect
62. #1271C22semidirect
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
#362582
#224712
#206842
#77242
#77182
#77042
#76942
#76782
#76542
#76202
#76062
#75992
#75922
C2×#12702