Finite Group Databasebeta

← #6477194

Subgroups — #6477194

Order 512.

1834 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic
2#36625C211yesmaximal, characteristic
3#33209C211yesmaximal, characteristic, complemented
4#33207C211yesmaximal, characteristic, complemented
5#33043C211yesmaximal, characteristic, complemented
6#33043C211yesmaximal, characteristic, complemented
7#30361C214yesmaximal, complemented
8#29158C214yesmaximal, complemented
9#27962C211yesmaximal, characteristic, complemented
10#27908C211yesmaximal, characteristic, complemented
11#27877C211yesmaximal, characteristic, complemented
12#27875C211yesmaximal, characteristic, complemented
13#25904C211yesmaximal, characteristic, complemented
14#25812C211yesmaximal, characteristic, complemented
15#25674C211yesmaximal, characteristic, complemented
16#25672C211yesmaximal, characteristic, complemented
17#24554C214yesmaximal
18#22077C214yesmaximal, complemented
19C2×C4×C22⋊C8C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#500C2211yescharacteristic, complemented
24C2×#498C2211yescharacteristic, complemented
25C2×#487C2211yescharacteristic, complemented
26C2×#487C2211yescharacteristic, complemented
27C2×#485C2214yes—
28C22×C22⋊C8C2212yes—
29C22×C4×C8C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2855—21no—
40#2855—21no—
41#2855—21no—
42#2855C2212yes—
43#2851—21no—
44#2851—21no—
45#2851C2212yes—
46#2851C2212yes—
47#2848—21no—
48#2848—21no—
49#2848—21no—
50#2848C2212yes—
51C4×C22⋊Q8—21no—
52C4×C22⋊Q8—21no—
53C4×C22⋊Q8—21no—
54C4×C22⋊Q8—21no—
55C4×C22⋊Q8—21no—
56C4×C22⋊Q8—21no—
57C4×C22⋊Q8C2212yes—
58C4×C22⋊Q8C2212yes—
59#2296—21no—
60#2296C2212yes—
61#2285C2211yescharacteristic
62#2285C2211yescharacteristic
63#2280—21no—
64#2280C2212yes—
65#2101C2214yescomplemented
66#2097C2214yescomplemented
67#2077C2214yes—
68#2075C2214yes—
69#2059C2214yescomplemented
70#2036C2214yes—
71#2035C2214yes—
72#2026C2214yescomplemented
73#1990C2211yescharacteristic, complemented
74#1990C2211yescharacteristic, complemented
75#1990C2211yescharacteristic, complemented
76#1990C2211yescharacteristic, complemented
77#1990C2211yescharacteristic, complemented
78#1990C2211yescharacteristic, complemented
79#1956C2211yescharacteristic, complemented
80#1956C2211yescharacteristic, complemented
81#1942C2214yescomplemented
82#1941C2214yescomplemented
83#1933C2214yescomplemented
84#1933C2214yescomplemented
85#1920C2214yescomplemented
86#1918C2214yescomplemented
87#1892C2214yes—
88#1892C2214yes—
89#1873C2214yes—
90#1865C2214yescomplemented
91#1863C2214yescomplemented
92#1854C2214yes—
93#1845C2211yescharacteristic, complemented
94#1844C2211yescharacteristic, complemented
95#1834C2211yescharacteristic, complemented
96#1834C2211yescharacteristic, complemented
97#1825C2214yes—
98#1808C2214yes—
99#1807C2214yes—
100C4×C22⋊C8C2211yescharacteristic
101C4×C22⋊C8C2211yescharacteristic
102C4×C22⋊C8C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2212yes—
106C2×#336C2212yes—
107C24×C4D411yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4C2311yescharacteristic
110C23×C8C2312yes—
111C23×C8C2312yes—
112#533—42no—
113#533—42no—
114#533—42no—
115#533—42no—
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×#125—21no—
121C2×#125C2312yes—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—21no—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×C4×Q8—21no—
135C2×C4×Q8—21no—
136C2×C4×Q8—21no—
137C2×C4×Q8C2312yes—
138C2×#117—21no—
139C2×#117—21no—
140C2×#117C2312yes—
141C2×#117C2312yes—
142C22×C42—42no—
143C22×C42—42no—
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#500—42no—
157#498—42no—
158#487—42no—
159#487—42no—
160#485—216no—
161C2×#107C2314yes—
162C2×#107C2314yes—
163C2×#106C2314yes—
164C2×#106C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×C22⋊C8—28no—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C4×C8—42no—
175C2×C4×C8—42no—
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2312yes—
181C2×C4×C8C2312yes—
182#391—21no—
183#391—21no—
184#391—21no—
185#391—21no—
186#391—21no—
187#391—21no—
188#391C2312yes—
189#391C2312yes—
190#389—21no—
191#389—21no—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389C2312yes—
201#389C2312yes—
202#389C2312yes—
203#389C2312yes—
204#389C2312yes—
205#389C2312yes—
206#387—22no—
207#387—22no—
208#387—22no—
209#387—22no—
210#387—22no—
211#387—22no—
212#387—22no—
213#387—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#385—22no—
220#385—22no—
221#385—22no—
222#385—22no—
223#385—22no—
224#385—22no—
225#385—22no—
226#384C2311yescharacteristic
227#384C2311yescharacteristic
228#384C2311yescharacteristic
229#384C2311yescharacteristic
230#382—21no—
231#382C2312yes—
232#381—22no—
233#381—22no—
234#380—21no—
235#380—21no—
236#380—21no—
237#380—21no—
238#380—21no—
239#380—21no—
240#380—21no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380—21no—
245#380—21no—
246#380—21no—
247#380C2312yes—
248#380C2312yes—
249#380C2312yes—
250#380C2312yes—
251#380C2312yes—
252#380C2312yes—
253#380C2312yes—
254#379—22no—
255#379—22no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—22no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4—22no—
263C4×C4⋊C4C2312yes—
264C4×C22⋊C4—22no—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—22no—
267C4×C22⋊C4—22no—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280C25C2×D411yescharacteristic
281C22×Q8—21no—
282C22×Q8—21no—
283C22×Q8—21no—
284C22×Q8C2412yes—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—41no—
294C23×C4—41no—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C22×C8—24no—
314C22×C8—24no—
315C22×C8—24no—
316C22×C8—24no—
317C22×C8—42no—
318C22×C8—42no—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331#125—42no—
332#125—42no—
333#125—44no—
334C22⋊Q8—28no—
335C22⋊Q8—28no—
336C22⋊Q8—42no—
337C22⋊Q8—42no—
338C22⋊Q8—44no—
339C22⋊Q8—44no—
340C22⋊Q8—44no—
341C22⋊Q8—44no—
342C22⋊Q8—44no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345C22⋊Q8—44no—
346C22⋊Q8—44no—
347C4×Q8—42no—
348C4×Q8—42no—
349C4×Q8—44no—
350C4×Q8—44no—
351C4×Q8—44no—
352#117—28no—
353#117—42no—
354#117—42no—
355#117—44no—
356#117—44no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—41no—
418C2×C42—41no—
419C2×C42—41no—
420C2×C42—41no—
421C2×C42—41no—
422C2×C42—41no—
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439#107—28no—
440#107—44no—
441#106—28no—
442#106—44no—
443#103—28no—
444#103—28no—
445#103—44no—
446#103—44no—
447C22⋊C8—24no—
448C22⋊C8—24no—
449C22⋊C8—24no—
450C22⋊C8#4118yes—
451C4×C8—22no—
452C4×C8—22no—
453C4×C8—22no—
454C4×C8—22no—
455C4×C8—42no—
456C4×C8—42no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—41no—
483C24—41no—
484C24C22×D411yescharacteristic
485C24C22×D411yescharacteristic
486C24C22×D411yescharacteristic
487C2×Q8—24no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—24no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—42no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
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—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—416no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—416no—
564C22×C4#13514yes—
565C22×C4#13514yes—
566C22×C4#13714yes—
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C2×#4114yes—
579C22×C42−1+414yes—
580C22×C4C2511yescharacteristic
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—22no—
590C2×C8—22no—
591C2×C8—48no—
592C2×C8—48no—
593C2×C8C2×#4114yes—
594C2×C8C2×#4114yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—42no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—44no—
661C42—44no—
662C42—44no—
663C42—44no—
664C42H(5,𝔽2)12yes—
665C42H(5,𝔽2)12yes—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—28no—
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—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23#53212yes—
690C23#53612yes—
691C23C2×#13512yes—
692C23C2×#13512yes—
693C23C2×#13712yes—
694C23C23×D411yescharacteristic
695Q8—44no—
696Q8—44no—
697Q8—84no—
698Q8—84no—
699Q8—84no—
700C2×C4—21no—
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—21no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
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—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
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—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4#53212yes—
768C2×C4#53412yes—
769C2×C4#53412yes—
770C2×C4#53612yes—
771C2×C4C2×#13512yes—
772C2×C4C2×#13512yes—
773C2×C4C2×#13512yes—
774C2×C4C2×#13512yes—
775C2×C4C2×#13712yes—
776C2×C4C2×#13712yes—
777C2×C4#57512yes—
778C2×C4C22×#4112yes—
779C2×C4C2×H(5,𝔽2)11yescharacteristic
780C2×C4C2×H(5,𝔽2)11yescharacteristic
781C2×C4C2×2−1+412yes—
782C8—24no—
783C8—24no—
784C8—42no—
785C8—42no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—416no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22#323114yes—
808C22C2×#53211yescharacteristic
809C22C2×#53411yescharacteristic
810C22C2×#53611yescharacteristic
811C22C22×#13511yescharacteristic
812C22C22×#13511yescharacteristic
813C22C22×#13711yescharacteristic
814C22C2×#57511yescharacteristic
815C4—22no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4—82no—
832C4#319014yes—
833C4#319114yes—
834C4#352012yes—
835C4#352012yes—
836C2—24no—
837C2—42no—
838C2—42no—
839C2#3508511yescharacteristic
840C2#6067311yescharacteristic
841C2#6070111yescharacteristic
842C2C2×#319011yescharacteristic
843C2C2×#319111yescharacteristic
844C2C2×#323111yescharacteristic
845C2#6084611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33209C2semidirect
4. #33207C2semidirect
5. #33043C2semidirect
6. #33043C2semidirect
7. #30361C2semidirect
8. #29158C2semidirect
9. #27962C2semidirect
10. #27908C2semidirect
11. #27877C2semidirect
12. #27875C2semidirect
13. #25904C2semidirect
14. #25812C2semidirect
15. #25674C2semidirect
16. #25672C2semidirect
18. #22077C2semidirect
23. C2×#500C22semidirect
24. C2×#498C22semidirect
25. C2×#487C22semidirect
26. C2×#487C22semidirect
65. #2101C22semidirect
66. #2097C22semidirect
69. #2059C22semidirect
72. #2026C22semidirect
73. #1990C22semidirect
74. #1990C22semidirect
75. #1990C22semidirect
76. #1990C22semidirect
77. #1990C22semidirect
78. #1990C22semidirect
79. #1956C22semidirect
80. #1956C22semidirect
81. #1942C22semidirect
82. #1941C22semidirect
83. #1933C22semidirect
84. #1933C22semidirect
85. #1920C22semidirect
86. #1918C22semidirect
90. #1865C22semidirect
91. #1863C22semidirect
93. #1845C22semidirect
94. #1844C22semidirect
95. #1834C22semidirect
96. #1834C22semidirect

Maximal subgroups

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

subgroupindex
#366252
#332092
#332072
#330432
#303612
#291582
#279622
#279082
#278772
#278752
#259042
#258122
#256742
#256722
#245542
#220772
C2×C4×C22⋊C82