Finite Group Databasebeta

← #165541

Subgroups — #165541

Order 512.

1324 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36260C211yesmaximal, characteristic
2#22837C211yesmaximal, characteristic, complemented
3#22786C211yesmaximal, characteristic, complemented
4#7724C211yesmaximal, characteristic, complemented
5#7719C211yesmaximal, characteristic, complemented
6#7704C211yesmaximal, characteristic, complemented
7#7704C211yesmaximal, characteristic, complemented
8#7684C211yesmaximal, characteristic, complemented
9#7679C211yesmaximal, characteristic, complemented
10#7626C211yesmaximal, characteristic, complemented
11#7621C211yesmaximal, characteristic, complemented
12#7606C211yesmaximal, characteristic, complemented
13#7592C211yesmaximal, characteristic, complemented
14#7587C211yesmaximal, characteristic, complemented
15#7572C211yesmaximal, characteristic, complemented
16C2×#547C411yescharacteristic
17C2×#546—21no—
18C2×#546—21no—
19C2×D42C411yescharacteristic
20#2858C2211yescharacteristic
21#2856C2211yescharacteristic
22#2856C2211yescharacteristic
23#2542C411yescharacteristic
24#2541C411yescharacteristic
25#2540—21no—
26#2540—21no—
27#2539—21no—
28#2539—21no—
29#2539—21no—
30#2539—21no—
31#2501C411yescharacteristic
32#2501C411yescharacteristic
33#2433C411yescharacteristic
34#2433C411yescharacteristic
35C4×#127C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C42×D4C2211yescharacteristic
39#1955—21no—
40#1924—21no—
41#1923—21no—
42#1923—21no—
43#1917—21no—
44#1870—21no—
45#1839C2211yescharacteristic, complemented
46#1831C2211yescharacteristic, complemented
47#1817C2211yescharacteristic, complemented
48#1817C2211yescharacteristic, complemented
49#1817C2211yescharacteristic, complemented
50#1797C2211yescharacteristic, complemented
51#1771—21no—
52#1767C2211yescharacteristic, complemented
53#1753—21no—
54#1749C2211yescharacteristic, complemented
55#1749C2211yescharacteristic, complemented
56C4×C22⋊C8C2211yescharacteristic, complemented
57#1744C2211yescharacteristic, complemented
58#1728C2211yescharacteristic, 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—
80#547—44no—
81#546—44no—
82#546—44no—
83#546—44no—
84#546—44no—
85D42—44no—
86C2×C4⋊Q8C2×C411yescharacteristic
87C2×#127C2×C411yescharacteristic
88C2×#127C2×C411yescharacteristic
89C2×#127C2×C411yescharacteristic
90C2×#127C2×C411yescharacteristic
91C2×#124—21no—
92C2×#124—21no—
93C2×#123—21no—
94C2×#123—21no—
95C2×#123—21no—
96C2×#123—21no—
97C2×#123—21no—
98C2×#123—21no—
99C2×C22⋊Q8—21no—
100C2×C22⋊Q8—21no—
101C2×C22⋊Q8—21no—
102C2×#121—21no—
103C2×#121—21no—
104C2×#121—21no—
105C2×#121—21no—
106C2×#121—21no—
107C2×#121—21no—
108C2×#121—21no—
109C2×#121C2×C411yescharacteristic
110C2×#121C2×C411yescharacteristic
111C2×#121C2×C411yescharacteristic
112C2×#121C2×C411yescharacteristic
113C2×#120—21no—
114C2×#120—21no—
115C2×#120—21no—
116C2×#120—21no—
117C2×#120—21no—
118C2×#120—21no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4C2×C411yescharacteristic
122C2×C4×D4C2×C411yescharacteristic
123C2×C4×D4C2×C411yescharacteristic
124C2×C4×D4D411yescharacteristic
125C2×C4×D4D411yescharacteristic
126C22×C4⋊C4C2×C411yescharacteristic
127C22×C4⋊C4C2×C411yescharacteristic
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C2×C4⋊C8—21no—
135C2×C4⋊C8—21no—
136C2×C4⋊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×#97—21no—
146C2×#97—21no—
147C2×C4×C8—21no—
148C2×C4×C8—21no—
149#399—21no—
150#399—21no—
151#399—21no—
152#399—21no—
153#399—21no—
154#399—21no—
155#392—21no—
156#392—21no—
157#392—21no—
158#392—21no—
159#392—21no—
160#392—21no—
161#390—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#390C2×C411yescharacteristic
174#390C2×C411yescharacteristic
175#390C2×C411yescharacteristic
176#390C2×C411yescharacteristic
177#390C2×C411yescharacteristic
178#390C2×C411yescharacteristic
179#390C2311yescharacteristic
180#390C2311yescharacteristic
181#390C2311yescharacteristic
182#390C2311yescharacteristic
183#384C2×C411yescharacteristic
184#384C2×C411yescharacteristic
185#384C2×C411yescharacteristic
186C4×C4⋊C4C2×C411yescharacteristic
187C4×C4⋊C4D411yescharacteristic
188C4×C4⋊C4D411yescharacteristic
189C4×C22⋊C4C2×C411yescharacteristic
190C4×C22⋊C4C2×C411yescharacteristic
191C4×C22⋊C4D411yescharacteristic
192C4×C22⋊C4D411yescharacteristic
193C4×C22⋊C4D411yescharacteristic
194C4×C22⋊C4D411yescharacteristic
195C43C2311yescharacteristic
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—44no—
215C2×#41—44no—
216C2×#41—44no—
217C22×Q8—21no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—21no—
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—41no—
235C22×D4—41no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—81no—
242C22×D4—81no—
243C22×D4C22⋊C411yescharacteristic
244C22×D4C22×C411yescharacteristic
245C22×D4C22×C411yescharacteristic
246C22×D4C22×C411yescharacteristic
247C22×D4C22×C411yescharacteristic
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4C22×C411yescharacteristic
253C23×C4C22×C411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C2×M16—42no—
259C2×M16—42no—
260C2×M16—81no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C4⋊Q8—42no—
270#127—22no—
271#127—41no—
272#127—42no—
273#127—81no—
274#127—81no—
275#124—42no—
276#124—42no—
277#124—42no—
278#124—42no—
279#123—44no—
280#123—44no—
281#123—44no—
282#123—44no—
283#123—44no—
284#123—44no—
285C22⋊Q8—44no—
286C22⋊Q8—44no—
287C22⋊Q8—44no—
288#121—44no—
289#121—44no—
290#121—44no—
291#121—42no—
292#121—42no—
293#121—42no—
294#121—42no—
295#121—42no—
296#121—42no—
297#121—42no—
298#121—42no—
299#121—42no—
300#121—42no—
301#121—42no—
302#121—42no—
303#120—44no—
304#120—44no—
305#120—44no—
306#120—44no—
307#120—44no—
308#120—44no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—24no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—42no—
315C4×D4—42no—
316C4×D4—42no—
317C4×D4—42no—
318C4×D4—42no—
319C4×D4—42no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4C22⋊C411yescharacteristic
332C2×C4⋊C4C22⋊C411yescharacteristic
333C2×C4⋊C4C22⋊C411yescharacteristic
334C2×C4⋊C4C22×C411yescharacteristic
335C2×C4⋊C4C22×C411yescharacteristic
336C2×C4⋊C4C22×C411yescharacteristic
337C2×C4⋊C4C22×C411yescharacteristic
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—21no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4C22⋊C411yescharacteristic
373C2×C22⋊C4C22⋊C411yescharacteristic
374C2×C22⋊C4C22⋊C411yescharacteristic
375C2×C22⋊C4C22⋊C411yescharacteristic
376C2×C22⋊C4C22⋊C411yescharacteristic
377C2×C22⋊C4C22⋊C411yescharacteristic
378C2×C42—81no—
379C2×C42—81no—
380C2×C42C22×C411yescharacteristic
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×C42C2×D411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2411yescharacteristic
393C4⋊C8—42no—
394C4⋊C8—42no—
395C4⋊C8—81no—
396C22⋊C8—42no—
397C22⋊C8—42no—
398C22⋊C8—42no—
399C22⋊C8—42no—
400C22⋊C8—81no—
401C22⋊C8—81no—
402C22⋊C8—81no—
403#97—42no—
404#97—81no—
405#97—81no—
406C4×C8—42no—
407C4×C8—81no—
408#95C22⋊C411yescharacteristic
409#95C22⋊C411yescharacteristic
410#95C22⋊C411yescharacteristic
411#95C22⋊C411yescharacteristic
412#95C22⋊C411yescharacteristic
413#95C22⋊C411yescharacteristic
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—81no—
427C24—81no—
428C24—81no—
429C24—81no—
430C24—81no—
431C24—81no—
432C24C2×C22⋊C411yescharacteristic
433C24C2×C22⋊C411yescharacteristic
434#41—816no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
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—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—81no—
485C2×D4—81no—
486C2×D4—81no—
487C2×D4—81no—
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—84no—
499C2×D4—84no—
500C2×D4—84no—
501C2×D4—84no—
502C2×D4—816no—
503C2×D4#13112yes—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—41no—
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—42no—
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×C4C2×C22⋊C411yescharacteristic
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×C4AGL(1,ℤ/8)12yes—
553C22×C4AGL(1,ℤ/8)12yes—
554C22×C4C23×C411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557M16—84no—
558C2×C8—22no—
559C2×C8—22no—
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—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
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—42no—
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—41no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—41no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4#10014yes—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—22no—
643C42—41no—
644C42—41no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42AGL(1,ℤ/8)12yes—
653C42AGL(1,ℤ/8)12yes—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—22no—
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—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—84no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—162no—
703C23—162no—
704C23—162no—
705C23—162no—
706C23—162no—
707C23—162no—
708C23C2×#10012yes—
709C23#41812yes—
710C23C22×C22⋊C411yescharacteristic
711Q8—84no—
712D4—28no—
713D4—42no—
714D4—42no—
715D4—84no—
716D4—84no—
717D4—81no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—81no—
722D4—81no—
723D4—84no—
724D4—84no—
725D4—84no—
726D4—84no—
727D4—84no—
728D4—84no—
729D4—84no—
730D4—162no—
731D4—162no—
732D4—162no—
733D4—162no—
734D4—162no—
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—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—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
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—41no—
783C2×C4—41no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—84no—
791C2×C4—84no—
792C2×C4—84no—
793C2×C4—84no—
794C2×C4C2×#10012yes—
795C2×C4C2×#10012yes—
796C2×C4#41812yes—
797C2×C4#41812yes—
798C2×C4#41812yes—
799C2×C4C2×#13111yescharacteristic
800C2×C4#56811yescharacteristic
801C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
802C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
803C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
804C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
805C8—42no—
806C8—42no—
807C8—81no—
808C8—81no—
809C8—81no—
810C8—81no—
811C8—81no—
812C8—81no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—42no—
828C22—42no—
829C22—42no—
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—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—168no—
856C22—168no—
857C22#288011yescharacteristic
858C22#288311yescharacteristic
859C22C22×#10011yescharacteristic
860C22C2×#41811yescharacteristic
861C22C2×#41811yescharacteristic
862C22#290111yescharacteristic
863C22#290111yescharacteristic
864C4—21no—
865C4—21no—
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—21no—
871C4—21no—
872C4—22no—
873C4—21no—
874C4—21no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4—81no—
884C2—42no—
885C2—42no—
886C2—82no—
887C2—161no—
888C2—161no—
889C2—161no—
890C2#1742111yescharacteristic
891C2#1751111yescharacteristic
892C2#1751111yescharacteristic
893C2#1762011yescharacteristic
894C2#1762611yescharacteristic
895C2#1768511yescharacteristic
896C2#1774111yescharacteristic
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. #22837C2semidirect
3. #22786C2semidirect
4. #7724C2semidirect
5. #7719C2semidirect
6. #7704C2semidirect
7. #7704C2semidirect
8. #7684C2semidirect
9. #7679C2semidirect
10. #7626C2semidirect
11. #7621C2semidirect
12. #7606C2semidirect
13. #7592C2semidirect
14. #7587C2semidirect
15. #7572C2semidirect
45. #1839C22semidirect
46. #1831C22semidirect
47. #1817C22semidirect
48. #1817C22semidirect
49. #1817C22semidirect
50. #1797C22semidirect
52. #1767C22semidirect
54. #1749C22semidirect
55. #1749C22semidirect
56. C4×C22⋊C8C22semidirect
57. #1744C22semidirect
58. #1728C22semidirect
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
#228372
#227862
#77242
#77192
#77042
#76842
#76792
#76262
#76212
#76062
#75922
#75872
#75722