Finite Group Databasebeta

← #6469964

Subgroups — #6469964

Order 512.

4995 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#535C211yesmaximal, characteristic, complemented
2C2×#3194C211yesmaximal, characteristic, complemented
3C2×#3188C211yesmaximal, characteristic, complemented
4#35251C211yesmaximal, characteristic, complemented
5#32984C211yesmaximal, characteristic, complemented
6#32980C211yesmaximal, characteristic, complemented
7#32881C211yesmaximal, characteristic, complemented
8#32878C211yesmaximal, characteristic, complemented
9#29598C211yesmaximal, characteristic, complemented
10#29596C211yesmaximal, characteristic, complemented
11#29594C211yesmaximal, characteristic, complemented
12#29592C211yesmaximal, characteristic, complemented
13#24394C214yesmaximal, complemented
14#24390C214yesmaximal, complemented
15#24015C214yesmaximal, complemented
16#23924C214yesmaximal, complemented
17#21764C211yesmaximal, characteristic, complemented
18#21758C211yesmaximal, characteristic, complemented
19#20581C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C24×D4C2211yescharacteristic
22C2×#537C2212yescomplemented
23C2×#535—22no—
24C2×#535—22no—
25C2×#535—28no—
26C2×#535—28no—
27C2×#535C2214yes—
28C2×#535C2214yes—
29C22×#127—21no—
30C22×#124—21no—
31C2×#525C2211yescharacteristic, complemented
32C22×#121C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C22×#121C2211yescharacteristic
36C22×#120—21no—
37C22×#120—21no—
38C22×#117C2211yescharacteristic
39#3194—28no—
40#3188—28no—
41C2×#484C2211yescharacteristic, complemented
42C2×#481C2211yescharacteristic, complemented
43C2×#482C2212yescomplemented
44C2×#482C2212yescomplemented
45C2×#483C2211yescharacteristic, complemented
46C2×#480C2211yescharacteristic, complemented
47C2×#469C2212yescomplemented
48C2×#468C2212yescomplemented
49C2×#466C2212yescomplemented
50C2×#465C2212yescomplemented
51C2×#449C2212yescomplemented
52C2×#449C2212yescomplemented
53C2×#450C2211yescharacteristic
54C2×#450C2211yescharacteristic
55C2×#450C2214yescomplemented
56C2×#447C2211yescharacteristic
57C2×#447C2211yescharacteristic
58C2×#447C2214yescomplemented
59C2×#408C2214yescomplemented
60C2×#407C2211yescharacteristic, complemented
61C22×C22⋊C8C2211yescharacteristic, complemented
62#2848C2211yescharacteristic
63#2848C2211yescharacteristic, complemented
64#2847C2211yescharacteristic
65#2847C2211yescharacteristic, complemented
66#2616C2212yescomplemented
67#2615C2212yescomplemented
68#2430—22no—
69#2410—21no—
70#2410—21no—
71#2409—21no—
72#2408—21no—
73#2407—22no—
74#2311C2212yescomplemented
75C2×#380C2211yescharacteristic, complemented
76#2034C2214yescomplemented
77#2034C2214yescomplemented
78#2033C2214yescomplemented
79#2033C2214yescomplemented
80#2000C2214yescomplemented
81#2000C2214yescomplemented
82#1999C2214yescomplemented
83#1999C2214yescomplemented
84#1895C2214yescomplemented
85#1893C2214yescomplemented
86#1875C2214yescomplemented
87#1874C2214yescomplemented
88#1874C2214yescomplemented
89#1873C2214yescomplemented
90#1854C2214yescomplemented
91#1854C2214yescomplemented
92#1824C2211yescharacteristic, complemented
93#1824C2211yescharacteristic, complemented
94#1823C2211yescharacteristic, complemented
95#1823C2211yescharacteristic, complemented
96#1786C2211yescharacteristic
97#1786C2211yescharacteristic
98#1786C2211yescharacteristic
99#1786C2211yescharacteristic
100#1786C2214yescomplemented
101#1786C2214yescomplemented
102#1780C2214yescomplemented
103#1779C2211yescharacteristic
104#1779C2211yescharacteristic
105#1779C2211yescharacteristic, complemented
106#1779C2211yescharacteristic, complemented
107C26—21no—
108C22×#41—24no—
109C22×#41—24no—
110C22×#41—48no—
111C22×#41D412yes—
112C22×#41D412yes—
113C22×#41C2312yes—
114C22×#41C2312yes—
115C22×#41C2311yescharacteristic, complemented
116C23×Q8D411yescharacteristic
117C23×D4—21no—
118C23×D4—21no—
119C23×D4—21no—
120C23×D4—21no—
121C23×D4—24no—
122C23×D4—24no—
123C23×D4—21no—
124C23×D4—22no—
125C23×D4—48no—
126C23×D4D411yescharacteristic
127C23×D4D411yescharacteristic
128C23×D4D411yescharacteristic
129C23×D4C2314yes—
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C22×SD16C2312yes—
136C22×SD16C2312yes—
137C22×D8C2312yes—
138C22×D8C2312yes—
139C22×M16C2312yescomplemented
140C23×C8C2312yescomplemented
141#537—48no—
142#535—232no—
143#535—232no—
144#535—216no—
145#535—216no—
146#535—216no—
147#535—216no—
148C2×#127—216no—
149C2×#127—24no—
150C2×#127—24no—
151C2×#124—216no—
152C2×#124—24no—
153C2×#124—24no—
154#525—24no—
155#525—24no—
156C2×#123—21no—
157C2×C22⋊Q8—22no—
158C2×C22⋊Q8C2311yescharacteristic
159C2×C22⋊Q8C2312yes—
160C2×C22⋊Q8C2311yescharacteristic, complemented
161C2×C22⋊Q8C2312yescomplemented
162C2×#121—24no—
163C2×#121—24no—
164C2×#121—24no—
165C2×#121—24no—
166C2×#121—22no—
167C2×#121—22no—
168C2×#121—21no—
169C2×#121—21no—
170C2×#121—21no—
171C2×#121—21no—
172C2×#121—22no—
173C2×#121—22no—
174C2×#121—22no—
175C2×#121—24no—
176C2×#121—24no—
177C2×#121D418yescomplemented
178C2×#121D418yescomplemented
179C2×#121C2311yescharacteristic
180C2×#121C2312yes—
181C2×#121C2314yes—
182C2×#121C2314yes—
183C2×#121C2312yes—
184C2×#121C2312yes—
185C2×#121C2312yes—
186C2×#121C2312yes—
187C2×#121C2311yescharacteristic, complemented
188C2×#121C2312yescomplemented
189C2×#120—216no—
190C2×#120—216no—
191C2×#120—24no—
192C2×#120—24no—
193C2×#120—24no—
194C2×#120—24no—
195C2×#120—21no—
196C2×#120—21no—
197C2×#120—21no—
198C2×C4×D4—21no—
199C2×C4×D4—21no—
200C2×#117—22no—
201C2×#117—24no—
202C2×#117—24no—
203C2×#117C2314yes—
204C2×#117C2311yescharacteristic, complemented
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2312yescomplemented
208C22×C22⋊C4—21no—
209C22×C22⋊C4—21no—
210C22×C22⋊C4—21no—
211C22×C22⋊C4—21no—
212C22×C22⋊C4—21no—
213C22×C22⋊C4—21no—
214C22×C42—21no—
215#484—24no—
216#483—24no—
217#482—28no—
218#482—28no—
219#481—24no—
220#480—24no—
221#469—28no—
222#468—28no—
223#466—28no—
224#465—28no—
225#450—24no—
226#450—24no—
227#450—48no—
228#449—28no—
229#449—28no—
230#447—24no—
231#447—24no—
232#447—48no—
233C2×#107C2312yescomplemented
234C2×#107C2312yescomplemented
235C2×#106C2312yescomplemented
236C2×#106C2312yescomplemented
237C2×#103C2312yescomplemented
238C2×#103C2312yescomplemented
239C2×#102C2312yes—
240C2×#102C2312yes—
241C2×#102C2312yes—
242C2×#102C2312yes—
243C2×#102C2314yes—
244C2×#102C2314yes—
245C2×#102C2314yes—
246C2×#102C2314yes—
247C2×#102C2312yescomplemented
248C2×#102C2312yescomplemented
249#408—48no—
250#407—24no—
251C2×C22⋊C8—24no—
252C2×C22⋊C8C2311yescharacteristic
253C2×C22⋊C8C2311yescharacteristic
254C2×C22⋊C8C2311yescharacteristic
255C2×C22⋊C8C2311yescharacteristic
256C2×C22⋊C8C2314yes—
257C2×C22⋊C8C2314yes—
258C2×C22⋊C8C2312yescomplemented
259C2×C22⋊C8C2312yescomplemented
260C2×C22⋊C8C2314yescomplemented
261C2×C22⋊C8C2314yescomplemented
262#395—22no—
263#394—22no—
264#394—22no—
265#394—22no—
266#393—22no—
267#392—22no—
268#392—22no—
269#392—22no—
270#391—22no—
271#390—22no—
272#386—22no—
273#386—22no—
274#386—22no—
275#386—21no—
276#386—22no—
277#386—21no—
278#385—22no—
279#385—21no—
280#385—22no—
281#385—21no—
282#380—21no—
283#380—21no—
284#380C2312yes—
285#380C2312yes—
286#380C2311yescharacteristic
287#380C2311yescharacteristic
288#380C2312yescomplemented
289#380C2312yescomplemented
290#380C2312yescomplemented
291#379—21no—
292#379—21no—
293C2×#95—21no—
294#340C2314yescomplemented
295#340C2314yescomplemented
296#340C2314yescomplemented
297#340C2314yescomplemented
298C25—28no—
299C25—21no—
300C25—21no—
301C25—24no—
302C25—48no—
303C25—82no—
304C25—82no—
305C25—84no—
306C25C2×D411yescharacteristic
307C25C2×D411yescharacteristic
308C25C2×D411yescharacteristic
309C2×#41—28no—
310C2×#41—28no—
311C2×#41—24no—
312C2×#41—24no—
313C2×#41—24no—
314C2×#41—24no—
315C2×#41—28no—
316C2×#41—28no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—44no—
320C2×#41—44no—
321C2×#41—44no—
322C2×#41—44no—
323C2×#41—44no—
324C2×#41—44no—
325C2×#41—44no—
326C2×#41—432no—
327C2×#41—432no—
328C22×Q8—24no—
329C22×Q8—44no—
330C22×Q8C2×D412yes—
331C22×Q8C2×D412yes—
332C22×Q8C2411yescharacteristic
333C22×D4—28no—
334C22×D4—216no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—28no—
338C22×D4—28no—
339C22×D4—28no—
340C22×D4—28no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—28no—
348C22×D4—28no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—24no—
360C22×D4—28no—
361C22×D4—28no—
362C22×D4—44no—
363C22×D4—44no—
364C22×D4—44no—
365C22×D4—44no—
366C22×D4—44no—
367C22×D4—432no—
368C22×D4—432no—
369C22×D4—48no—
370C22×D4—48no—
371C22×D4—48no—
372C22×D4—44no—
373C22×D4—44no—
374C22×D4—82no—
375C22×D4—82no—
376C22×D4—82no—
377C22×D4—82no—
378C22×D4—84no—
379C22×D4—84no—
380C22×D4C2×D412yes—
381C22×D4C2×D412yes—
382C22×D4C2×D412yes—
383C22×D4C2×D412yes—
384C22×D4C2×D412yes—
385C22×D4C2×D412yes—
386C22×D4C2×D414yes—
387C22×D4C2×D414yes—
388C22×D4C2411yescharacteristic
389C22×D4C2412yes—
390C22×D4C2412yes—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—28no—
394C23×C4—21no—
395C23×C4—21no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—21no—
400C23×C4—44no—
401C23×C4—44no—
402C23×C4C2×D412yes—
403C23×C4C2×D411yescharacteristic
404C23×C4C2×D411yescharacteristic
405C23×C4C2×D412yes—
406C23×C4C2×D411yescharacteristic
407C23×C4C2×D411yescharacteristic
408C23×C4C2×D411yescharacteristic
409C23×C4C2×D414yes—
410C23×C4C2×D414yes—
411C23×C4C2412yes—
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2412yes—
416C2×SD16—24no—
417C2×SD16—24no—
418C2×SD16—44no—
419C2×SD16—44no—
420C2×D8—24no—
421C2×D8—24no—
422C2×D8—44no—
423C2×D8—44no—
424C2×M16—24no—
425C2×M16—44no—
426C22×C8—24no—
427C22×C8—44no—
428C22×C8C2412yes—
429C22×C8C2412yes—
430C22×C8C2412yes—
431C22×C8C2412yes—
432#127—232no—
433#127—232no—
434#124—232no—
435#124—232no—
436#123—44no—
437C22⋊Q8—22no—
438C22⋊Q8—22no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8—28no—
442C22⋊Q8—44no—
443C22⋊Q8—48no—
444#121—216no—
445#121—216no—
446#121—28no—
447#121—28no—
448#121—28no—
449#121—28no—
450#121—28no—
451#121—28no—
452#121—24no—
453#121—24no—
454#121—24no—
455#121—24no—
456#121—28no—
457#121—28no—
458#121—22no—
459#121—22no—
460#121—22no—
461#121—22no—
462#121—28no—
463#121—44no—
464#121—48no—
465#121—48no—
466#121—48no—
467#121C2×D418yes—
468#121C2×D418yes—
469#121C2×D418yes—
470#121C2×D418yes—
471#120—232no—
472#120—232no—
473#120—232no—
474#120—232no—
475#120—44no—
476#120—82no—
477#120—82no—
478C4×D4—44no—
479C4×D4—44no—
480#117—216no—
481#117—28no—
482#117—28no—
483#117—22no—
484#117—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—44no—
495C2×C4⋊C4C2×D414yes—
496C2×C4⋊C4C2×D414yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2411yescharacteristic
500C2×C4⋊C4C2411yescharacteristic
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C22⋊C4—28no—
504C2×C22⋊C4—28no—
505C2×C22⋊C4—28no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—28no—
508C2×C22⋊C4—28no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—82no—
532C2×C42—28no—
533C2×C42—24no—
534C2×C42—21no—
535#107—24no—
536#107—24no—
537#106—24no—
538#106—24no—
539#103—24no—
540#103—24no—
541#102—24no—
542#102—24no—
543#102—24no—
544#102—24no—
545#102—24no—
546#102—24no—
547#102—44no—
548#102—44no—
549#102—44no—
550#102—44no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—24no—
554C22⋊C8—22no—
555C22⋊C8—22no—
556C22⋊C8—24no—
557C22⋊C8—28no—
558C22⋊C8—28no—
559C22⋊C8—44no—
560C22⋊C8—44no—
561#95—21no—
562#95—21no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95—22no—
568C24—22no—
569C24—24no—
570C24—22no—
571C24—22no—
572C24—216no—
573C24—24no—
574C24—24no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—44no—
589C24—44no—
590C24—432no—
591C24—48no—
592C24—44no—
593C24—44no—
594C24—48no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—42no—
599C24—84no—
600C24—84no—
601C24—84no—
602C24—84no—
603C24—816no—
604C24—816no—
605C24—832no—
606C24—832no—
607C24#12014yes—
608C24C22×D412yes—
609C24C22×D411yescharacteristic
610C24C22×D411yescharacteristic
611C24C22×D412yes—
612C24C22×D411yescharacteristic
613#41—416no—
614#41—416no—
615#41—416no—
616#41—416no—
617#41—432no—
618#41—432no—
619#41—84no—
620#41—84no—
621C2×Q8—24no—
622C2×Q8—24no—
623C2×Q8—24no—
624C2×Q8—24no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—24no—
628C2×Q8—42no—
629C2×Q8—42no—
630C2×Q8—416no—
631C2×D4—216no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—24no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—216no—
641C2×D4—216no—
642C2×D4—28no—
643C2×D4—28no—
644C2×D4—28no—
645C2×D4—28no—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—416no—
664C2×D4—416no—
665C2×D4—416no—
666C2×D4—416no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—432no—
674C2×D4—464no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4—416no—
681C2×D4—416no—
682C2×D4—416no—
683C2×D4—44no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—82no—
693C2×D4—84no—
694C2×D4—84no—
695C2×D4—84no—
696C2×D4—84no—
697C2×D4—816no—
698C2×D4—82no—
699C2×D4—82no—
700C2×D4—84no—
701C2×D4—82no—
702C2×D4—82no—
703C2×D4—84no—
704C2×D4—816no—
705C2×D4—816no—
706C2×D4—816no—
707C2×D4—82no—
708C2×D4—82no—
709C2×D4—82no—
710C2×D4—82no—
711C2×D4C22×D414yes—
712C2×D4C22×D414yes—
713C22×C4—216no—
714C22×C4—216no—
715C22×C4—22no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—24no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—48no—
742C22×C4—48no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—48no—
750C22×C4—48no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—44no—
756C22×C4—42no—
757C22×C4—82no—
758C22×C4—82no—
759C22×C4#12014yes—
760C22×C4#12014yes—
761C22×C4#12014yes—
762C22×C4C22×D412yes—
763C22×C4C22×D411yescharacteristic
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D411yescharacteristic
766C22×C4C22×D412yes—
767C22×C4C22×D412yes—
768C22×C4C22×D412yes—
769C22×C4C22×D412yes—
770C22×C4C22×D412yes—
771C22×C4C22×D412yes—
772C22×C4C22×D412yes—
773C22×C4H(5,𝔽2)18yes—
774C22×C4C2511yescharacteristic
775SD16—84no—
776SD16—84no—
777D8—84no—
778D8—84no—
779M16—84no—
780C2×C8—22no—
781C2×C8—22no—
782C2×C8—22no—
783C2×C8—22no—
784C2×C8—24no—
785C2×C8—24no—
786C2×C8—24no—
787C2×C8—24no—
788C2×C8—84no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—24no—
798C4⋊C4—24no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—42no—
802C4⋊C4—42no—
803C4⋊C4—44no—
804C4⋊C4C22×D414yes—
805C4⋊C4C22×D414yes—
806C22⋊C4—216no—
807C22⋊C4—216no—
808C22⋊C4—216no—
809C22⋊C4—28no—
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—28no—
813C22⋊C4—44no—
814C22⋊C4—44no—
815C22⋊C4—42no—
816C22⋊C4—42no—
817C22⋊C4—42no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—44no—
824C22⋊C4—82no—
825C22⋊C4—82no—
826C22⋊C4—82no—
827C22⋊C4—82no—
828C22⋊C4—82no—
829C42—216no—
830C42—42no—
831C23—22no—
832C23—22no—
833C23—28no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—21no—
843C23—22no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—22no—
848C23—28no—
849C23—22no—
850C23—22no—
851C23—24no—
852C23—24no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—44no—
859C23—44no—
860C23—48no—
861C23—48no—
862C23—44no—
863C23—44no—
864C23—48no—
865C23—48no—
866C23—432no—
867C23—44no—
868C23—48no—
869C23—48no—
870C23—44no—
871C23—44no—
872C23—44no—
873C23—44no—
874C23—44no—
875C23—44no—
876C23—48no—
877C23—48no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—41no—
884C23—42no—
885C23—41no—
886C23—41no—
887C23—84no—
888C23—84no—
889C23—84no—
890C23—84no—
891C23—88no—
892C23—88no—
893C23—88no—
894C23—88no—
895C23—816no—
896C23—816no—
897C23—816no—
898C23—816no—
899C23—8128no—
900C23—816no—
901C23—816no—
902C23C2×#12012yes—
903C23C2×#12012yes—
904C23C2×#12012yes—
905C23#53414yes—
906C23#57612yes—
907C23#57712yes—
908C23C23×D411yescharacteristic
909Q8—48no—
910Q8—48no—
911Q8—42no—
912Q8—42no—
913D4—24no—
914D4—24no—
915D4—24no—
916D4—24no—
917D4—48no—
918D4—48no—
919D4—48no—
920D4—48no—
921D4—48no—
922D4—48no—
923D4—432no—
924D4—48no—
925D4—48no—
926D4—44no—
927D4—44no—
928D4—42no—
929D4—42no—
930D4—88no—
931D4—88no—
932D4—88no—
933D4—88no—
934D4—816no—
935D4—816no—
936D4—84no—
937D4—84no—
938D4—84no—
939D4—164no—
940D4—164no—
941C2×C4—28no—
942C2×C4—216no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—28no—
953C2×C4—28no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—44no—
962C2×C4—44no—
963C2×C4—44no—
964C2×C4—48no—
965C2×C4—44no—
966C2×C4—48no—
967C2×C4—44no—
968C2×C4—48no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—44no—
972C2×C4—44no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—84no—
987C2×C4—164no—
988C2×C4C2×#12012yes—
989C2×C4C2×#12012yes—
990C2×C4C2×#12012yes—
991C2×C4#53414yes—
992C2×C4C23×D411yescharacteristic
993C2×C4C23×D411yescharacteristic
994C2×C4C2×H(5,𝔽2)14yes—
995C8—42no—
996C8—42no—
997C8—42no—
998C8—42no—
999C22—24no—
1000C22—24no—
1001C22—22no—
1002C22—22no—
1003C22—24no—
1004C22—24no—
1005C22—24no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—416no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—44no—
1027C22—44no—
1028C22—42no—
1029C22—44no—
1030C22—44no—
1031C22—42no—
1032C22—44no—
1033C22—44no—
1034C22—88no—
1035C22—88no—
1036C22—816no—
1037C22—816no—
1038C22—864no—
1039C22—84no—
1040C22—84no—
1041C22—84no—
1042C22—84no—
1043C22—82no—
1044C22—82no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22#301214yes—
1049C22C22×#12011yescharacteristic
1050C22C2×#53412yes—
1051C22C2×#57611yescharacteristic
1052C22C2×#57711yescharacteristic
1053C22#358512yes—
1054C4—22no—
1055C4—24no—
1056C4—22no—
1057C4—22no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—82no—
1062C4—82no—
1063C4—81no—
1064C4—81no—
1065C4—81no—
1066C4#348412yes—
1067C4#348412yes—
1068C2—24no—
1069C2—44no—
1070C2—42no—
1071C2—42no—
1072C2—82no—
1073C2—84no—
1074C2—84no—
1075C2—161no—
1076C2#3498011yescharacteristic
1077C2C2×#301211yescharacteristic
1078C2#6036711yescharacteristic
1079C2#6075612yes—
1080C2#6075712yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#535C2semidirect
2. C2×#3194C2semidirect
3. C2×#3188C2semidirect
4. #35251C2semidirect
5. #32984C2semidirect
6. #32980C2semidirect
7. #32881C2semidirect
8. #32878C2semidirect
9. #29598C2semidirect
10. #29596C2semidirect
11. #29594C2semidirect
12. #29592C2semidirect
13. #24394C2semidirect
14. #24390C2semidirect
15. #24015C2semidirect
16. #23924C2semidirect
17. #21764C2semidirect
18. #21758C2semidirect
19. #20581C2semidirect
22. C2×#537C22semidirect
31. C2×#525C22semidirect
41. C2×#484C22semidirect
42. C2×#481C22semidirect
43. C2×#482C22semidirect
44. C2×#482C22semidirect
45. C2×#483C22semidirect
46. C2×#480C22semidirect
47. C2×#469C22semidirect
48. C2×#468C22semidirect
49. C2×#466C22semidirect
50. C2×#465C22semidirect
51. C2×#449C22semidirect
52. C2×#449C22semidirect
55. C2×#450C22semidirect
58. C2×#447C22semidirect
59. C2×#408C22semidirect
60. C2×#407C22semidirect
61. C22×C22⋊C8C22semidirect
63. #2848C22semidirect
65. #2847C22semidirect
66. #2616C22semidirect
67. #2615C22semidirect
74. #2311C22semidirect
75. C2×#380C22semidirect
76. #2034C22semidirect
77. #2034C22semidirect
78. #2033C22semidirect
79. #2033C22semidirect
80. #2000C22semidirect
81. #2000C22semidirect
82. #1999C22semidirect
83. #1999C22semidirect
84. #1895C22semidirect
85. #1893C22semidirect
86. #1875C22semidirect
87. #1874C22semidirect
88. #1874C22semidirect
89. #1873C22semidirect
90. #1854C22semidirect
91. #1854C22semidirect
92. #1824C22semidirect
93. #1824C22semidirect
94. #1823C22semidirect
95. #1823C22semidirect
100. #1786C22semidirect
101. #1786C22semidirect
102. #1780C22semidirect
105. #1779C22semidirect
106. #1779C22semidirect
115. C22×#41C23semidirect
139. C22×M16C23semidirect
140. C23×C8C23semidirect
160. C2×C22⋊Q8C23semidirect
161. C2×C22⋊Q8C23semidirect
177. C2×#121D4semidirect
178. C2×#121D4semidirect
187. C2×#121C23semidirect
188. C2×#121C23semidirect
204. C2×#117C23semidirect
207. C22×C4⋊C4C23semidirect
233. C2×#107C23semidirect
234. C2×#107C23semidirect
235. C2×#106C23semidirect
236. C2×#106C23semidirect
237. C2×#103C23semidirect
238. C2×#103C23semidirect
247. C2×#102C23semidirect
248. C2×#102C23semidirect
258. C2×C22⋊C8C23semidirect
259. C2×C22⋊C8C23semidirect
260. C2×C22⋊C8C23semidirect
261. C2×C22⋊C8C23semidirect
288. #380C23semidirect
289. #380C23semidirect
290. #380C23semidirect
294. #340C23semidirect
295. #340C23semidirect
296. #340C23semidirect
297. #340C23semidirect

Maximal subgroups

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

subgroupindex
C22×#5352
C2×#31942
C2×#31882
#352512
#329842
#329802
#328812
#328782
#295982
#295962
#295942
#295922
#243942
#243902
#240152
#239242
#217642
#217582
#205812