Finite Group Databasebeta

← #6473038

Subgroups — #6473038

Order 512.

2448 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3189C211yesmaximal, characteristic, complemented
2C2×#3187C211yesmaximal, characteristic
3C2×#2850C211yesmaximal, characteristic
4C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
5#33110C212yesmaximal, complemented
6#32909C212yesmaximal, complemented
7#29761C212yesmaximal, complemented
8#29719C212yesmaximal, complemented
9#28576C214yesmaximal, complemented
10#28124C212yesmaximal, complemented
11#28123C212yesmaximal, complemented
12#27653C212yesmaximal, complemented
13#24755C214yesmaximal, complemented
14#24217C212yesmaximal, complemented
15#21759C211yesmaximal, characteristic, complemented
16#21758C211yesmaximal, characteristic
17C2×#1797C211yesmaximal, characteristic, complemented
18C22×#124C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic, complemented
23C23×C42C2211yescharacteristic
24#3189—28no—
25#3187—28no—
26C2×#484C2212yes—
27C2×#484C2212yescomplemented
28C2×#481C2212yes—
29C2×#483C2212yes—
30C2×#467C2214yescomplemented
31C2×#465C2214yes—
32C2×#464C2214yescomplemented
33C2×#451C2212yes—
34C2×#451C2212yescomplemented
35C2×#448C2212yes—
36C2×#450C2212yes—
37C22×C4⋊C8C2212yescomplemented
38C22×C22⋊C8C2211yescharacteristic
39C22×C22⋊C8C2211yescharacteristic
40#2850—21no—
41#2850—21no—
42#2850—21no—
43#2850—21no—
44#2850C2212yes—
45#2850C2212yes—
46#2850C2212yes—
47#2850C2212yes—
48C4×C22⋊Q8—21no—
49C4×C22⋊Q8—21no—
50C4×C22⋊Q8—21no—
51C4×C22⋊Q8—21no—
52C4×C22⋊Q8C2212yes—
53C4×C22⋊Q8C2212yes—
54C4×C22⋊Q8C2212yescomplemented
55C4×C22⋊Q8C2212yescomplemented
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic, complemented
58C2×#390C2211yescharacteristic
59C2×#389C2211yescharacteristic, complemented
60C2×#388—21no—
61C2×#388—21no—
62C2×#387—21no—
63C2×#386—21no—
64C2×#386—21no—
65C2×#385—21no—
66C2×#382C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×C4×C4⋊C4—21no—
69C2×C4×C4⋊C4C2211yescharacteristic, complemented
70C2×C4×C22⋊C4—21no—
71#2085C2214yescomplemented
72#2074C2214yescomplemented
73#2067C2214yescomplemented
74#2066C2214yescomplemented
75#2056C2214yescomplemented
76#2055C2214yescomplemented
77#2042C2214yescomplemented
78#2015C2214yescomplemented
79#1983C2214yescomplemented
80#1949C2214yescomplemented
81#1927C2214yescomplemented
82#1925C2214yescomplemented
83#1893C2214yes—
84#1892C2214yescomplemented
85#1880C2214yescomplemented
86#1878C2214yescomplemented
87#1874C2212yes—
88#1874C2212yes—
89#1872C2212yescomplemented
90#1872C2212yescomplemented
91#1824C2212yes—
92#1823C2212yes—
93#1805C2214yescomplemented
94#1797C2212yes—
95#1797C2212yes—
96#1797C2212yescomplemented
97#1797C2212yescomplemented
98#1787C2212yes—
99#1786C2212yes—
100C2×#336C2212yescomplemented
101C23×Q8C2311yescharacteristic
102C23×Q8C2311yescharacteristic
103C23×D4—21no—
104C23×D4C2311yescharacteristic
105C24×C4D411yescharacteristic
106C24×C4D411yescharacteristic
107C24×C4C2311yescharacteristic
108C22×Q16C2314yes—
109C22×SD16C2314yes—
110C23×C8C2312yes—
111C23×C8C2312yes—
112C2×#124—21no—
113C2×#124—21no—
114C2×#124—44no—
115C2×#124C2312yes—
116C2×#124C2312yes—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—21no—
121C2×C22⋊Q8—21no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8D418yes—
125C2×C22⋊Q8C2312yes—
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2312yes—
128C2×C22⋊Q8C2312yes—
129C2×#121—21no—
130C2×#121—21no—
131C2×#121—24no—
132C2×#121—24no—
133C2×#121C2312yes—
134C2×#121C2312yes—
135C2×C4×Q8—21no—
136C2×C4×Q8—21no—
137C2×C4×Q8—44no—
138C2×C4×Q8C2312yes—
139C2×C4×Q8C2312yes—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C42—21no—
158C22×C42—21no—
159C22×C42—44no—
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42D411yescharacteristic
164C22×C42D411yescharacteristic
165C22×C42D411yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#484—28no—
173#484—28no—
174#483—28no—
175#481—28no—
176#467—216no—
177#465—216no—
178#464—48no—
179#451—28no—
180#451—28no—
181#450—28no—
182#448—28no—
183C2×#107C2314yes—
184C2×#106C2314yes—
185C2×C4⋊C8—44no—
186C2×C4⋊C8C2314yes—
187C2×C4⋊C8C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#102C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×C22⋊C8—24no—
197C2×C22⋊C8—24no—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200C2×C22⋊C8C2312yes—
201C2×C22⋊C8C2312yes—
202#391—21no—
203#391—21no—
204#391—21no—
205#391—21no—
206#391C2312yes—
207#391C2312yes—
208#391C2312yes—
209#391C2312yes—
210#390—21no—
211#390—21no—
212#390C2312yes—
213#390C2312yes—
214#389—21no—
215#389—21no—
216#389C2312yes—
217#389C2312yes—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#387—22no—
227#387—22no—
228#387—22no—
229#387—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#386—22no—
238#385—22no—
239#385—22no—
240#385—22no—
241#385—22no—
242#382—21no—
243#382—21no—
244#382C2312yes—
245#382C2312yes—
246#380—21no—
247#380—21no—
248#380C2312yes—
249#380C2312yes—
250C4×C4⋊C4—22no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4—22no—
253C4×C4⋊C4—22no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C4×C22⋊C4—22no—
259C4×C22⋊C4—22no—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C2×#95—21no—
263C2×#95—21no—
264C2×#95—21no—
265C2×#95—21no—
266C2×#95—21no—
267C2×#95—21no—
268C2×#95—21no—
269C2×#95—21no—
270C2×#95—21no—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#336C2314yes—
276#336C2314yes—
277C25—21no—
278C25C2×D411yescharacteristic
279C22×Q8—21no—
280C22×Q8—21no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8—42no—
285C22×Q8—42no—
286C22×Q8—42no—
287C22×Q8—42no—
288C22×Q8C2×D414yes—
289C22×Q8C2412yes—
290C22×Q8C2412yes—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—21no—
295C22×D4—22no—
296C22×D4—42no—
297C22×D4—42no—
298C22×D4—44no—
299C22×D4—44no—
300C22×D4—44no—
301C22×D4C2412yes—
302C23×C4—24no—
303C23×C4—24no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4—42no—
314C23×C4—42no—
315C23×C4—42no—
316C23×C4—42no—
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4C2×D411yescharacteristic
331C23×C4C2×D411yescharacteristic
332C23×C4C2×D414yes—
333C23×C4#4114yes—
334C23×C4C2411yescharacteristic
335C23×C4C2411yescharacteristic
336C23×C4C2411yescharacteristic
337C2×Q16—28no—
338C2×Q16—44no—
339C2×Q16—44no—
340C2×SD16—28no—
341C2×SD16—44no—
342C2×SD16—44no—
343C22×C8—24no—
344C22×C8—24no—
345C22×C8—42no—
346C22×C8—42no—
347C22×C8—42no—
348C22×C8—42no—
349C22×C8C2414yes—
350C22×C8C2414yes—
351#124—28no—
352#124—44no—
353#124—44no—
354#124—44no—
355C22⋊Q8—28no—
356C22⋊Q8—28no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359C22⋊Q8—24no—
360C22⋊Q8—24no—
361C22⋊Q8—24no—
362C22⋊Q8—24no—
363C22⋊Q8—44no—
364C22⋊Q8—44no—
365C22⋊Q8C2×D418yes—
366C22⋊Q8C2×D418yes—
367#121—24no—
368#121—24no—
369#121—24no—
370#121—24no—
371#121—44no—
372#121—44no—
373C4×Q8—28no—
374C4×Q8—44no—
375C4×Q8—44no—
376C4×Q8—44no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—44no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4C2×D414yes—
402C2×C4⋊C4C2412yes—
403C2×C4⋊C4C2412yes—
404C2×C4⋊C4C2412yes—
405C2×C4⋊C4C2412yes—
406C2×C4⋊C4C2412yes—
407C2×C22⋊C4—28no—
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—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C42—24no—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—42no—
439C2×C42—42no—
440C2×C42—42no—
441C2×C42—42no—
442C2×C42—42no—
443C2×C42—42no—
444C2×C42—42no—
445C2×C42—42no—
446C2×C42—42no—
447C2×C42—44no—
448C2×C42—44no—
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×C42C2×D411yescharacteristic
459C2×C42C2×D411yescharacteristic
460C2×C42C2×D411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465#107—28no—
466#106—28no—
467C4⋊C8—28no—
468C4⋊C8—44no—
469#103—28no—
470#103—28no—
471#103—28no—
472#103—44no—
473#103—44no—
474#102—28no—
475#102—44no—
476#102—44no—
477C22⋊C8—24no—
478C22⋊C8—24no—
479C22⋊C8—24no—
480C22⋊C8—24no—
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—
494#95—22no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499C24—22no—
500C24—41no—
501C24—41no—
502C24—41no—
503C24—41no—
504C24—42no—
505C24—42no—
506C24—42no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24#12114yes—
512C24#13514yes—
513C24#13714yes—
514C24C22×D411yescharacteristic
515C24C22×D411yescharacteristic
516C24C22×D411yescharacteristic
517C2×Q8—24no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—24no—
522C2×Q8—24no—
523C2×Q8—24no—
524C2×Q8—24no—
525C2×Q8—48no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×Q8—48no—
529C2×Q8—42no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—84no—
533C2×Q8—84no—
534C2×Q8C22×D414yes—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—42no—
548C2×D4—84no—
549C2×D4—84no—
550C2×D4—816no—
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—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
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—22no—
579C22×C4—22no—
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—22no—
589C22×C4—22no—
590C22×C4—48no—
591C22×C4—48no—
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—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—416no—
611C22×C4—416no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4#12114yes—
632C22×C4#12114yes—
633C22×C4#12114yes—
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C2×#4112yes—
649C22×C4C2×#4112yes—
650C22×C4C2×#4112yes—
651C22×C4C2511yescharacteristic
652Q16—88no—
653SD16—88no—
654C2×C8—24no—
655C2×C8—24no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—24no—
660C2×C8—84no—
661C2×C8—84no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—24no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—42no—
673C4⋊C4—44no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C4⋊C4C22×D414yes—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—41no—
709C42—41no—
710C42—41no—
711C42—41no—
712C42—41no—
713C42—41no—
714C42—44no—
715C42—44no—
716C42—44no—
717C42—44no—
718C42H(5,𝔽2)14yes—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—84no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23—84no—
749C23—84no—
750C23—84no—
751C23#464116yescomplemented
752C23C2×#12112yes—
753C23C2×#12112yes—
754C23C2×#12112yes—
755C23C2×#13512yes—
756C23C2×#13512yes—
757C23C2×#13512yes—
758C23C2×#13712yes—
759C23C2×#13712yes—
760C23C2×#13712yes—
761C23C23×D411yescharacteristic
762Q8—28no—
763Q8—48no—
764Q8—44no—
765Q8—44no—
766Q8—44no—
767Q8—84no—
768D4—44no—
769D4—44no—
770D4—84no—
771D4—88no—
772D4—88no—
773C2×C4—28no—
774C2×C4—28no—
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—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—48no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—48no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—84no—
844C2×C4—84no—
845C2×C4—84no—
846C2×C4—84no—
847C2×C4—84no—
848C2×C4C2×#12112yes—
849C2×C4C2×#12112yes—
850C2×C4C2×#12112yes—
851C2×C4#53412yes—
852C2×C4#53412yes—
853C2×C4#57512yes—
854C2×C4#57512yes—
855C2×C4C23×D411yescharacteristic
856C2×C4C22×#4111yescharacteristic
857C2×C4C2×H(5,𝔽2)12yes—
858C2×C4#58512yes—
859C8—44no—
860C8—44no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—416no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—168no—
888C22C2×#46414yes—
889C22C2×#46414yes—
890C22C2×#46414yes—
891C22C22×#12111yescharacteristic
892C22C2×#53411yescharacteristic
893C22#344911yescharacteristic
894C22C22×#13511yescharacteristic
895C22C22×#13711yescharacteristic
896C22C2×#57511yescharacteristic
897C22C2×#57511yescharacteristic
898C4—22no—
899C4—22no—
900C4—22no—
901C4—22no—
902C4—22no—
903C4—22no—
904C4—22no—
905C4—41no—
906C4—41no—
907C4—41no—
908C4—41no—
909C4—44no—
910C4—44no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4—82no—
916C4#349612yes—
917C4#350512yes—
918C2—24no—
919C2—24no—
920C2—24no—
921C2—162no—
922C2#3500011yescharacteristic
923C2C22×#46411yescharacteristic
924C2#6041511yescharacteristic
925C2#6073411yescharacteristic
926C2#6075111yescharacteristic
927C2#6094511yescharacteristic
928C2#6096011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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. C2×#3189C2semidirect
4. C2×C4×C22⋊Q8C2semidirect
5. #33110C2semidirect
6. #32909C2semidirect
7. #29761C2semidirect
8. #29719C2semidirect
9. #28576C2semidirect
10. #28124C2semidirect
11. #28123C2semidirect
12. #27653C2semidirect
13. #24755C2semidirect
14. #24217C2semidirect
15. #21759C2semidirect
17. C2×#1797C2semidirect
22. C22×C4×Q8C22semidirect
27. C2×#484C22semidirect
30. C2×#467C22semidirect
32. C2×#464C22semidirect
34. C2×#451C22semidirect
37. C22×C4⋊C8C22semidirect
54. C4×C22⋊Q8C22semidirect
55. C4×C22⋊Q8C22semidirect
57. C2×#391C22semidirect
59. C2×#389C22semidirect
69. C2×C4×C4⋊C4C22semidirect
71. #2085C22semidirect
72. #2074C22semidirect
73. #2067C22semidirect
74. #2066C22semidirect
75. #2056C22semidirect
76. #2055C22semidirect
77. #2042C22semidirect
78. #2015C22semidirect
79. #1983C22semidirect
80. #1949C22semidirect
81. #1927C22semidirect
82. #1925C22semidirect
84. #1892C22semidirect
85. #1880C22semidirect
86. #1878C22semidirect
89. #1872C22semidirect
90. #1872C22semidirect
93. #1805C22semidirect
96. #1797C22semidirect
97. #1797C22semidirect
100. C2×#336C22semidirect
751. C23#464semidirect

Maximal subgroups

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

subgroupindex
C2×#31892
C2×#31872
C2×#28502
C2×C4×C22⋊Q82
#331102
#329092
#297612
#297192
#285762
#281242
#281232
#276532
#247552
#242172
#217592
#217582
C2×#17972