Finite Group Databasebeta

← #6476961

Subgroups — #6476961

Order 512.

2120 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2#36624C211yesmaximal, characteristic
3#33172C211yesmaximal, characteristic, complemented
4#33170C211yesmaximal, characteristic, complemented
5#33043C211yesmaximal, characteristic, complemented
6#33042C211yesmaximal, characteristic, complemented
7#30321C214yesmaximal, complemented
8#28576C214yesmaximal, complemented
9#27975C211yesmaximal, characteristic, complemented
10#27949C211yesmaximal, characteristic, complemented
11#27891C211yesmaximal, characteristic, complemented
12#27889C211yesmaximal, characteristic, complemented
13#25857C211yesmaximal, characteristic, complemented
14#25719C211yesmaximal, characteristic, complemented
15#25600C211yesmaximal, characteristic, complemented
16#25598C211yesmaximal, characteristic, complemented
17#24383C214yesmaximal, complemented
18#22042C214yesmaximal, complemented
19C2×C4×C22⋊C8C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#525C2212yes—
23C23×C42C2211yescharacteristic
24C2×#494C2211yescharacteristic, complemented
25C2×#492C2211yescharacteristic, complemented
26C2×#487C2211yescharacteristic, complemented
27C2×#486C2211yescharacteristic, complemented
28C2×#467C2214yes—
29C2×#465C2214yes—
30C2×#452C2214yes—
31C22×C22⋊C8C2212yes—
32C22×C4×C8C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2857C2211yescharacteristic
40#2856C2211yescharacteristic
41#2856C2211yescharacteristic
42#2855—21no—
43#2855C2212yes—
44#2854—21no—
45#2854—21no—
46#2851—21no—
47#2851—21no—
48#2850C2212yes—
49#2850C2212yes—
50#2848—21no—
51#2848C2212yes—
52#2847—21no—
53#2847—21no—
54C4×C22⋊Q8—21no—
55C4×C22⋊Q8—21no—
56C4×C22⋊Q8C2212yes—
57C4×C22⋊Q8C2212yes—
58C4×#121—21no—
59C4×#121—21no—
60C4×#121—21no—
61C4×#121—21no—
62#2297C2212yes—
63#2296—21no—
64#2285C2211yescharacteristic
65#2285C2211yescharacteristic
66#2280—21no—
67#2085C2214yescomplemented
68#2074C2214yescomplemented
69#2042C2214yescomplemented
70#2035C2214yes—
71#2033C2214yes—
72#2015C2214yescomplemented
73#2001C2214yes—
74#2000C2214yes—
75#1990C2211yescharacteristic, complemented
76#1990C2211yescharacteristic, complemented
77#1969C2214yescomplemented
78#1968C2214yescomplemented
79#1957C2211yescharacteristic, complemented
80#1957C2211yescharacteristic, complemented
81#1956C2211yescharacteristic, complemented
82#1956C2211yescharacteristic, complemented
83#1956C2211yescharacteristic, complemented
84#1956C2211yescharacteristic, complemented
85#1934C2214yescomplemented
86#1933C2214yescomplemented
87#1927C2214yescomplemented
88#1925C2214yescomplemented
89#1893C2214yes—
90#1892C2214yes—
91#1880C2214yescomplemented
92#1878C2214yescomplemented
93#1873C2214yes—
94#1854C2214yes—
95#1845C2211yescharacteristic, complemented
96#1844C2211yescharacteristic, complemented
97#1834C2211yescharacteristic, complemented
98#1834C2211yescharacteristic, complemented
99#1788C2214yes—
100C4×C22⋊C8C2211yescharacteristic
101C4×C22⋊C8C2211yescharacteristic
102C4×C22⋊C8C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2212yes—
105C4×C22⋊C8C2211yescharacteristic
106C2×#336C2212yes—
107C22×#41C2312yes—
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111C22×Q16C2314yes—
112C22×SD16C2314yes—
113C23×C8C2312yes—
114C23×C8C2312yes—
115#533—42no—
116#533—42no—
117#532—42no—
118#532—42no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×#127C2311yescharacteristic
123C2×#125—21no—
124C2×#124C2312yes—
125#525—48no—
126C2×#123—22no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×C22⋊Q8C2312yes—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121—21no—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×#120—22no—
144C2×C4×Q8—21no—
145C2×C4×Q8C2312yes—
146C2×C4×D4—22no—
147C2×C4×D4—22no—
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×#117—21no—
151C2×#117—21no—
152C2×#117C2312yes—
153C22×C42—42no—
154C22×C42—42no—
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#494—42no—
168#492—42no—
169#487—42no—
170#486—42no—
171#467—48no—
172#465—48no—
173#452—216no—
174C2×#107C2314yes—
175C2×#106C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×C22⋊C8—28no—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C4×C8—42no—
190C2×C4×C8—42no—
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2311yescharacteristic
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2312yes—
196C2×C4×C8C2312yes—
197#391—21no—
198#391—21no—
199#391C2312yes—
200#391C2312yes—
201#391C2312yes—
202#391C2312yes—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390C2312yes—
208#390C2312yes—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389C2312yes—
220#389C2312yes—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#387—22no—
226#387—22no—
227#387—22no—
228#387—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#386—22no—
234#386—22no—
235#385—22no—
236#385—22no—
237#385—22no—
238#385—22no—
239#385—22no—
240#385—22no—
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#384C2311yescharacteristic
244#384C2311yescharacteristic
245#382—21no—
246#382C2312yes—
247#381—22no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—21no—
254#380—21no—
255#380—21no—
256#380—21no—
257#380—21no—
258#380—21no—
259#380—21no—
260#380—21no—
261#380C2312yes—
262#380C2312yes—
263#380C2312yes—
264#379—22no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—22no—
269C4×C4⋊C4—22no—
270C4×C4⋊C4C2312yes—
271C4×C22⋊C4—22no—
272C4×C22⋊C4—22no—
273C4×C22⋊C4—22no—
274C4×C22⋊C4—22no—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#336C2312yes—
280#336C2312yes—
281#336C2312yes—
282#336C2312yes—
283C25C2×D411yescharacteristic
284C2×#41—28no—
285C2×#41—44no—
286C2×#41—42no—
287C2×#41—42no—
288C22×Q8—21no—
289C22×Q8C2412yes—
290C22×Q8C2412yes—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4C2412yes—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—22no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—41no—
307C23×C4—41no—
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C2×Q16—28no—
327C2×Q16—44no—
328C2×Q16—44no—
329C2×SD16—28no—
330C2×SD16—44no—
331C2×SD16—44no—
332C22×C8—24no—
333C22×C8—24no—
334C22×C8—24no—
335C22×C8—24no—
336C22×C8—42no—
337C22×C8—42no—
338C22×C8C2412yes—
339C22×C8C2412yes—
340C22×C8C2412yes—
341C22×C8C2412yes—
342C4⋊Q8—22no—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348#127—22no—
349#127—22no—
350#125—44no—
351#124—42no—
352#124—42no—
353#123—48no—
354C22⋊Q8—28no—
355C22⋊Q8—28no—
356C22⋊Q8—28no—
357C22⋊Q8—44no—
358C22⋊Q8—42no—
359C22⋊Q8—42no—
360C22⋊Q8—44no—
361C22⋊Q8—44no—
362C22⋊Q8—44no—
363#121—28no—
364#121—44no—
365#121—44no—
366#121—44no—
367#121—44no—
368#121—44no—
369#121—44no—
370#121—44no—
371#120—48no—
372C4×Q8—42no—
373C4×Q8—42no—
374C4×Q8—44no—
375C4×D4—44no—
376C4×D4—44no—
377C4×D4—48no—
378C4×D4—48no—
379#117—44no—
380#117—44no—
381#117—44no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
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—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C4⋊C4C2412yes—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
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×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—42no—
439C2×C42—42no—
440C2×C42—41no—
441C2×C42—41no—
442C2×C42—41no—
443C2×C42—41no—
444C2×C42—41no—
445C2×C42—41no—
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2411yescharacteristic
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462#107—44no—
463#106—44no—
464#103—28no—
465#103—44no—
466#103—44no—
467#103—44no—
468#103—44no—
469#102—28no—
470#102—44no—
471#102—44no—
472C22⋊C8—24no—
473C22⋊C8—24no—
474C22⋊C8—24no—
475C22⋊C8#4118yes—
476C4×C8—22no—
477C4×C8—22no—
478C4×C8—22no—
479C4×C8—22no—
480C4×C8—42no—
481C4×C8—42no—
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—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—41no—
505C24—41no—
506C24C22×D411yescharacteristic
507C24C22×D411yescharacteristic
508C24C22×D411yescharacteristic
509#41—88no—
510#41—88no—
511C2×Q8—24no—
512C2×Q8—24no—
513C2×Q8—24no—
514C2×Q8—22no—
515C2×Q8—24no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×D4—24no—
523C2×D4—22no—
524C2×D4—24no—
525C2×D4—22no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—416no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—416no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4#13514yes—
608C22×C4#13514yes—
609C22×C4#13714yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C2×#4114yes—
622C22×C4H(5,𝔽2)14yes—
623C22×C4C2511yescharacteristic
624Q16—88no—
625SD16—88no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—48no—
637C2×C8—48no—
638C2×C8C2×#4114yes—
639C2×C8C2×#4114yes—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—21no—
696C42—41no—
697C42—41no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—41no—
702C42—44no—
703C42—44no—
704C42—44no—
705C42H(5,𝔽2)12yes—
706C42H(5,𝔽2)12yes—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—28no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23#53212yes—
738C23#53512yes—
739C23C2×#13512yes—
740C23C2×#13512yes—
741C23C2×#13712yes—
742C23C23×D411yescharacteristic
743Q8—44no—
744Q8—44no—
745Q8—44no—
746Q8—44no—
747Q8—84no—
748D4—44no—
749D4—44no—
750D4—88no—
751D4—88no—
752D4—88no—
753D4—84no—
754D4—84no—
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—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—88no—
820C2×C4#53212yes—
821C2×C4#53412yes—
822C2×C4#53412yes—
823C2×C4#53512yes—
824C2×C4C2×#13512yes—
825C2×C4C2×#13512yes—
826C2×C4C2×#13512yes—
827C2×C4C2×#13512yes—
828C2×C4C2×#13712yes—
829C2×C4C2×#13712yes—
830C2×C4#57512yes—
831C2×C4C22×#4112yes—
832C2×C4C2×H(5,𝔽2)11yescharacteristic
833C2×C4C2×H(5,𝔽2)11yescharacteristic
834C2×C4C2×H(5,𝔽2)12yes—
835C8—24no—
836C8—24no—
837C8—42no—
838C8—42no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—416no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22#321014yes—
868C22C2×#53211yescharacteristic
869C22C2×#53411yescharacteristic
870C22C2×#53511yescharacteristic
871C22C22×#13511yescharacteristic
872C22C22×#13511yescharacteristic
873C22C22×#13711yescharacteristic
874C22C2×#57511yescharacteristic
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4#319014yes—
892C4#319114yes—
893C4#351912yes—
894C4#351912yes—
895C2—24no—
896C2—42no—
897C2—42no—
898C2—162no—
899C2#3507811yescharacteristic
900C2#6067311yescharacteristic
901C2#6070111yescharacteristic
902C2C2×#319011yescharacteristic
903C2C2×#319111yescharacteristic
904C2C2×#321011yescharacteristic
905C2#6078211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
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
1. #36625C2semidirect
3. #33172C2semidirect
4. #33170C2semidirect
5. #33043C2semidirect
6. #33042C2semidirect
7. #30321C2semidirect
8. #28576C2semidirect
9. #27975C2semidirect
10. #27949C2semidirect
11. #27891C2semidirect
12. #27889C2semidirect
13. #25857C2semidirect
14. #25719C2semidirect
15. #25600C2semidirect
16. #25598C2semidirect
17. #24383C2semidirect
18. #22042C2semidirect
19. C2×C4×C22⋊C8C2semidirect
24. C2×#494C22semidirect
25. C2×#492C22semidirect
26. C2×#487C22semidirect
27. C2×#486C22semidirect
67. #2085C22semidirect
68. #2074C22semidirect
69. #2042C22semidirect
72. #2015C22semidirect
75. #1990C22semidirect
76. #1990C22semidirect
77. #1969C22semidirect
78. #1968C22semidirect
79. #1957C22semidirect
80. #1957C22semidirect
81. #1956C22semidirect
82. #1956C22semidirect
83. #1956C22semidirect
84. #1956C22semidirect
85. #1934C22semidirect
86. #1933C22semidirect
87. #1927C22semidirect
88. #1925C22semidirect
91. #1880C22semidirect
92. #1878C22semidirect
95. #1845C22semidirect
96. #1844C22semidirect
97. #1834C22semidirect
98. #1834C22semidirect

Maximal subgroups

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

subgroupindex
#366252
#366242
#331722
#331702
#330432
#330422
#303212
#285762
#279752
#279492
#278912
#278892
#258572
#257192
#256002
#255982
#243832
#220422
C2×C4×C22⋊C82