Finite Group Databasebeta

← #6497467

Subgroups — #6497467

Order 512.

1951 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3165C211yesmaximal, characteristic, complemented
2C2×#2965C211yesmaximal, characteristic
3#35316C211yesmaximal, characteristic
4#35297C211yesmaximal, characteristic
5#33212C211yesmaximal, characteristic, complemented
6#33210C211yesmaximal, characteristic, complemented
7#33209C211yesmaximal, characteristic, complemented
8#33207C211yesmaximal, characteristic, complemented
9#29878C211yesmaximal, characteristic, complemented
10#29877C211yesmaximal, characteristic, complemented
11#29877C211yesmaximal, characteristic, complemented
12#29876C211yesmaximal, characteristic, complemented
13#28714C214yesmaximal, complemented
14#28685C214yesmaximal, complemented
15#27670C214yesmaximal, complemented
16#27669C214yesmaximal, complemented
17#21835C211yesmaximal, characteristic, complemented
18#21834C211yesmaximal, characteristic, complemented
19#20824C211yesmaximal, characteristic, complemented
20C2×#536—21no—
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×C4×#41C2211yescharacteristic
24#3165—28no—
25C2×#501C2214yes—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#498C2211yescharacteristic
29C2×#498C2211yescharacteristic
30#2965—28no—
31C2×#446C2212yes—
32C2×#436C2212yes—
33C2×#435C2212yes—
34C2×#435C2212yes—
35C2×#431C2211yescharacteristic
36C2×#431C2211yescharacteristic
37C2×#431C2211yescharacteristic
38C2×#428C2214yes—
39C2×C4×M16C2211yescharacteristic
40C2×C4×M16C2211yescharacteristic
41C22×C4×C8C2211yescharacteristic
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2625—21no—
51#2621—21no—
52#2621—21no—
53#2616—21no—
54#2584C2212yes—
55#2581—21no—
56#2562C2212yes—
57#2547—21no—
58#2547C2212yes—
59#2546—21no—
60#2546C2212yes—
61#2536—21no—
62#2486—21no—
63#2486—21no—
64#2486C2212yes—
65#2486C2212yes—
66#2485C2212yes—
67#2485C2212yes—
68#2415—21no—
69#2415—21no—
70#2323—21no—
71#2323—21no—
72#2310—21no—
73#2285C2211yescharacteristic
74#2285C2211yescharacteristic
75#2088C2214yes—
76#2088C2214yes—
77#2087C2214yes—
78#2086C2214yes—
79#2077C2214yes—
80#2077C2214yes—
81#2076C2214yes—
82#2075C2214yes—
83#1990C2211yescharacteristic
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1990C2211yescharacteristic
89#1990C2211yescharacteristic
90#1990C2211yescharacteristic
91#1989C2214yes—
92#1987C2214yes—
93#1944C2214yes—
94#1943C2214yes—
95#1942C2214yes—
96#1941C2214yes—
97#1845C2211yescharacteristic
98#1844C2211yescharacteristic
99#1834C2211yescharacteristic
100#1834C2211yescharacteristic
101#1825C2214yes—
102#1824C2214yes—
103#1809C2214yes—
104#1809C2214yes—
105#1809C2214yes—
106#1808C2214yes—
107#1807C2214yes—
108#1776C2214yes—
109C22×#41D411yescharacteristic
110C23×Q8—21no—
111C22×M16C2312yes—
112C22×M16C2312yes—
113C23×C8C2312yes—
114#536—48no—
115#533—24no—
116#533—24no—
117C2×C4⋊Q8—22no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—21no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—24no—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2312yes—
127C2×#125C2312yes—
128C2×#124—22no—
129C2×#123—22no—
130C2×#123—22no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C4×#41—24no—
142C4×#41—24no—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8D411yescharacteristic
146C2×C4×Q8C2311yescharacteristic
147C2×C4×D4D411yescharacteristic
148C2×C4×D4D411yescharacteristic
149C2×C4×D4D411yescharacteristic
150C2×C4×D4C2311yescharacteristic
151C2×C4×D4C2311yescharacteristic
152C2×C4×D4C2311yescharacteristic
153C2×#117—21no—
154C2×#117—21no—
155C2×#117D411yescharacteristic
156C2×#117D411yescharacteristic
157C2×#117D411yescharacteristic
158C2×#117C2312yes—
159C22×C4⋊C4—21no—
160C22×C4⋊C4C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#501—216no—
165#500—24no—
166#500—24no—
167#498—24no—
168#498—24no—
169#446—28no—
170#436—28no—
171#435—28no—
172#435—28no—
173#431—24no—
174#431—24no—
175#431—24no—
176#428—216no—
177C2×#107C2314yes—
178C2×#107C2314yes—
179C2×#107C2314yes—
180C2×#106C2314yes—
181C2×#106C2314yes—
182C2×#106C2314yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C4×M16—24no—
190C4×M16D418yes—
191C2×#97C2312yes—
192C2×#97C2312yes—
193C2×C4×C8—24no—
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2312yes—
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199#400—22no—
200#398—22no—
201#398—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#397—22no—
206#397—22no—
207#397—22no—
208#397—22no—
209#397—22no—
210#397—22no—
211#395—22no—
212#394—22no—
213#394—22no—
214#394—22no—
215#391—22no—
216#391—22no—
217#391—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#389—22no—
226#389—22no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#387—22no—
248#387—22no—
249#384C2311yescharacteristic
250#384C2311yescharacteristic
251#384C2311yescharacteristic
252#384C2311yescharacteristic
253#382—21no—
254#382—21no—
255#381—22no—
256#381—22no—
257#380—21no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270#380C2312yes—
271#380C2312yes—
272#380C2312yes—
273#380C2312yes—
274#380C2312yes—
275#380C2312yes—
276#380C2312yes—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2312yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
289#340C2314yes—
290#340C2314yes—
291C2×#41—24no—
292C2×#41—24no—
293C2×#41—42no—
294C22×Q8—21no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—22no—
299C22×Q8—44no—
300C22×Q8—44no—
301C22×Q8—44no—
302C22×Q8C2×D411yescharacteristic
303C22×D4C2×D411yescharacteristic
304C22×D4C2×D411yescharacteristic
305C22×D4C2×D411yescharacteristic
306C23×C4—22no—
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C2×M16—24no—
317C2×M16—24no—
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—24no—
321C2×M16C2×D418yes—
322C22×C8—24no—
323C22×C8—24no—
324C22×C8—24no—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—24no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—24no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—48no—
340C4⋊Q8—44no—
341C4⋊Q8—44no—
342#125—24no—
343#125—24no—
344#124—48no—
345#123—48no—
346#123—48no—
347C22⋊Q8—44no—
348C22⋊Q8—44no—
349C22⋊Q8—44no—
350C22⋊Q8—44no—
351C22⋊Q8—44no—
352C22⋊Q8—44no—
353C22⋊Q8—44no—
354C22⋊Q8—44no—
355C22⋊Q8—82no—
356C22⋊Q8—82no—
357C4×Q8—24no—
358C4×Q8—22no—
359C4×Q8—22no—
360C4×Q8—44no—
361C4×Q8—44no—
362C4×D4—24no—
363C4×D4—24no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—24no—
369C4×D4—22no—
370C4×D4—22no—
371#117—24no—
372#117—24no—
373#117—24no—
374#117—24no—
375#117—24no—
376#117—44no—
377#117—82no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2412yes—
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4C2×D411yescharacteristic
431C2×C22⋊C4C2×D411yescharacteristic
432C2×C22⋊C4C2×D411yescharacteristic
433C2×C22⋊C4C2×D411yescharacteristic
434C2×C22⋊C4C2×D411yescharacteristic
435C2×C22⋊C4C2×D411yescharacteristic
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D414yes—
450C2×C42#4114yes—
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455#107—28no—
456#107—28no—
457#107—28no—
458#106—28no—
459#106—28no—
460#106—28no—
461C4⋊C8—24no—
462C4⋊C8—24no—
463C4⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8—24no—
466C22⋊C8—24no—
467#97—24no—
468#97C2×D418yes—
469C4×C8—24no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8C2×D414yes—
473C4×C8C2×D414yes—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494C24C22×D411yescharacteristic
495C24C22×D411yescharacteristic
496C24C22×D411yescharacteristic
497#41—416no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—41no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—44no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—816no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—41no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4#12114yes—
563C22×C4#12114yes—
564C22×C4AGL(1,ℤ/8)14yes—
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D412yes—
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C2×#4112yes—
578C22×C4C2511yescharacteristic
579M16—216no—
580M16—48no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—48no—
590C2×C8C22×D414yes—
591C2×C8C22×D414yes—
592C2×C82−1+414yes—
593C2×C82−1+414yes—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—82no—
635C4⋊C4—82no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—82no—
651C22⋊C4—82no—
652C22⋊C4—82no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—44no—
662C42—44no—
663C42—82no—
664C42#12114yes—
665C42#12114yes—
666C42C22×D412yes—
667C42C22×D412yes—
668C42C2×#4112yes—
669C42C2×#4112yes—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23C2×#12112yes—
690C23C2×AGL(1,ℤ/8)12yes—
691C23C23×D411yescharacteristic
692Q8—44no—
693Q8—88no—
694Q8—84no—
695Q8—84no—
696Q8—84no—
697Q8—84no—
698D4—44no—
699D4—44no—
700D4—44no—
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—24no—
710C2×C4—24no—
711C2×C4—28no—
712C2×C4—28no—
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—44no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—88no—
761C2×C4C2×#12112yes—
762C2×C4C2×#12112yes—
763C2×C4C2×#12112yes—
764C2×C4C2×#12112yes—
765C2×C4C2×#12112yes—
766C2×C4C2×AGL(1,ℤ/8)12yes—
767C2×C4C2×AGL(1,ℤ/8)12yes—
768C2×C4#57512yes—
769C2×C4#57712yes—
770C2×C4#57812yes—
771C2×C4C23×D411yescharacteristic
772C2×C4C22×#4111yescharacteristic
773C2×C4C2×2−1+412yes—
774C2×C4C2×2−1+412yes—
775C8—24no—
776C8—42no—
777C8—42no—
778C8#53618yescomplemented
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22C22×#12111yescharacteristic
801C22#349911yescharacteristic
802C22#349911yescharacteristic
803C22C22×AGL(1,ℤ/8)11yescharacteristic
804C22C2×#57511yescharacteristic
805C22C2×#57711yescharacteristic
806C22C2×#57811yescharacteristic
807C4—22no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4#305514yes—
825C4#306314yes—
826C4C2×#53612yes—
827C4#350912yes—
828C2—42no—
829C2—42no—
830C2—81no—
831C2#3531611yescharacteristic
832C2C2×#305511yescharacteristic
833C2C2×#306311yescharacteristic
834C2#6247711yescharacteristic
835C2#6247911yescharacteristic
836C2#6248211yescharacteristic
837C2#6248311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3165C2semidirect
5. #33212C2semidirect
6. #33210C2semidirect
7. #33209C2semidirect
8. #33207C2semidirect
9. #29878C2semidirect
10. #29877C2semidirect
11. #29877C2semidirect
12. #29876C2semidirect
13. #28714C2semidirect
14. #28685C2semidirect
15. #27670C2semidirect
16. #27669C2semidirect
17. #21835C2semidirect
18. #21834C2semidirect
19. #20824C2semidirect
778. C8#536semidirect

Maximal subgroups

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

subgroupindex
C2×#31652
C2×#29652
#353162
#352972
#332122
#332102
#332092
#332072
#298782
#298772
#298762
#287142
#286852
#276702
#276692
#218352
#218342
#208242