Finite Group Databasebeta

← #6438789

Subgroups — #6438789

Order 512.

3356 conjugacy classes of subgroups.

The subgroup lattice has 1023 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#468C211yesmaximal, characteristic, complemented
2C2×#3042C211yesmaximal, characteristic, complemented
3C2×#3006C211yesmaximal, characteristic
4C2×#2896C211yesmaximal, characteristic, complemented
5#35305C211yesmaximal, characteristic, complemented
6#34204C211yesmaximal, characteristic, complemented
7#25104C214yesmaximal, complemented
8#25101C214yesmaximal, complemented
9#25099C214yesmaximal, complemented
10#25094C214yesmaximal, complemented
11#23611C211yesmaximal, characteristic, complemented
12#23544C211yesmaximal, characteristic, complemented
13#23512C211yesmaximal, characteristic, complemented
14#23424C211yesmaximal, characteristic, complemented
15#21262C211yesmaximal, characteristic, complemented
16#21067C211yesmaximal, characteristic, complemented
17#20929C211yesmaximal, characteristic, complemented
18#20911C211yesmaximal, characteristic, complemented
19#20835C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×AGL(1,ℤ/8)C2211yescharacteristic
22C22×AGL(1,ℤ/8)C2211yescharacteristic
23C23×SD16C2211yescharacteristic, complemented
24C23×M16C2211yescharacteristic
25C2×#536C2211yescharacteristic
26C2×#536C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C2×#518C2211yescharacteristic, complemented
30C22×#117C2211yescharacteristic
31C2×#468—28no—
32C2×#468C2214yes—
33C2×#468C2214yescomplemented
34#3042—28no—
35C2×#463C2214yescomplemented
36C2×#461C2214yescomplemented
37#3006—28no—
38C2×#449C2212yes—
39C2×#449C2212yes—
40C2×#448C2212yes—
41C2×#447C2212yes—
42C22×#107C2211yescharacteristic, complemented
43C2×#424C2211yescharacteristic, complemented
44C2×#424C2211yescharacteristic, complemented
45#2896—28no—
46C2×#417C2211yescharacteristic
47C2×#417C2211yescharacteristic
48C2×#417C2212yescomplemented
49C2×#417C2212yescomplemented
50C2×#419C2211yescharacteristic, complemented
51C2×#419C2212yescomplemented
52C2×#419C2211yescharacteristic, complemented
53C2×#418C2212yescomplemented
54C2×#416C2211yescharacteristic
55C2×#416C2211yescharacteristic
56C2×#416C2211yescharacteristic
57C2×#416C2211yescharacteristic
58C22×#103C2211yescharacteristic, complemented
59C22×#102C2211yescharacteristic, complemented
60C2×#407C2211yescharacteristic
61#2848—22no—
62#2616—22no—
63#2435C2212yescomplemented
64#2434C2212yescomplemented
65#2432C2212yescomplemented
66#2432C2212yescomplemented
67#2406—22no—
68#2405—22no—
69#2363C2214yes—
70#2361C2214yescomplemented
71#2342—22no—
72D4×C22⋊C4—22no—
73#2324—22no—
74#2316C2211yescharacteristic, complemented
75#2311C2211yescharacteristic
76#2311C2211yescharacteristic
77#2309C2211yescharacteristic, complemented
78C4×#121—22no—
79#2280C2211yescharacteristic
80#2274C2211yescharacteristic, complemented
81#2068C2214yescomplemented
82#2067C2214yescomplemented
83#2055C2214yescomplemented
84#2054C2214yescomplemented
85#2043C2214yescomplemented
86#2042C2214yescomplemented
87#2013C2214yescomplemented
88#2012C2214yescomplemented
89#1983C2214yescomplemented
90#1981C2214yescomplemented
91#1928C2214yescomplemented
92#1925C2214yescomplemented
93#1879C2214yescomplemented
94#1877C2214yescomplemented
95#1873C2214yescomplemented
96#1872C2214yescomplemented
97#1851C2214yescomplemented
98#1851C2214yescomplemented
99#1736C2211yescharacteristic, complemented
100#1736C2211yescharacteristic, complemented
101#1729C2211yescharacteristic, complemented
102#1729C2211yescharacteristic, complemented
103C22×#41—21no—
104C22×#41—21no—
105C22×#41—24no—
106C22×#41—24no—
107C22×#41—24no—
108C22×#41—24no—
109C22×#41—42no—
110C22×#41—42no—
111C22×#41C2311yescharacteristic
112C22×#41C2311yescharacteristic
113C22×#41C2311yescharacteristic
114C22×#41C2311yescharacteristic
115C23×Q8C2311yescharacteristic
116C23×Q8C2311yescharacteristic
117C23×D4—21no—
118C23×D4—21no—
119C23×D4C2311yescharacteristic
120C23×D4C2311yescharacteristic
121C24×C4—21no—
122C24×C4C2311yescharacteristic
123C2×AGL(1,ℤ/8)—24no—
124C2×AGL(1,ℤ/8)—24no—
125C2×AGL(1,ℤ/8)—24no—
126C2×AGL(1,ℤ/8)—24no—
127C2×AGL(1,ℤ/8)—42no—
128C2×AGL(1,ℤ/8)—42no—
129C22×SD16—24no—
130C22×SD16—24no—
131C22×SD16—42no—
132C22×SD16C2312yes—
133C22×SD16C2312yes—
134C22×SD16C2314yes—
135C22×D8C2312yes—
136C22×D8C2312yes—
137C22×M16—24no—
138C22×M16—24no—
139C22×M16—42no—
140C22×M16C2311yescharacteristic
141C22×M16C2311yescharacteristic
142C22×M16C2312yes—
143C22×M16C2312yes—
144C23×C8C2311yescharacteristic
145C23×C8C2311yescharacteristic
146#536—24no—
147#536—24no—
148#536—42no—
149#536—42no—
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2312yes—
152C2×#124C2312yes—
153C2×#124C2312yes—
154C2×#123—22no—
155C2×#123—22no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—22no—
159C2×C22⋊Q8—22no—
160C2×C22⋊Q8—24no—
161C2×C22⋊Q8—24no—
162C2×C22⋊Q8C2312yes—
163C2×C22⋊Q8C2312yes—
164C2×#121—21no—
165C2×#121—21no—
166C2×#121—24no—
167C2×#121D418yes—
168C2×#121C2312yes—
169C2×#121C2312yes—
170#518—24no—
171#518—42no—
172C2×C4×D4—22no—
173C2×C4×D4—24no—
174C2×C4×D4C2314yes—
175C2×#117—21no—
176C2×#117—21no—
177C2×#117—24no—
178C2×#117—42no—
179C2×#117C2311yescharacteristic
180C2×#117C2312yes—
181C2×#117C2311yescharacteristic
182C2×#117C2311yescharacteristic
183C2×#117C2311yescharacteristic
184C22×C4⋊C4—21no—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C22⋊C4—21no—
189C22×C22⋊C4—21no—
190C22×C22⋊C4—21no—
191C22×C22⋊C4—22no—
192C22×C42—21no—
193#468—216no—
194#468—216no—
195#463—216no—
196#461—216no—
197#449—28no—
198#449—28no—
199#448—28no—
200#447—28no—
201C2×#107—24no—
202C2×#107C2314yes—
203#424—24no—
204#424—42no—
205C2×C4⋊C8C2314yes—
206C2×C4⋊C8C2314yes—
207#419—24no—
208#419—28no—
209#419—42no—
210#418—28no—
211#417—24no—
212#417—24no—
213#417—28no—
214#417—28no—
215#416—24no—
216#416—24no—
217#416—24no—
218#416D418yescomplemented
219C2×#103—24no—
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2312yes—
223C2×#103C2314yes—
224C2×#103C2312yes—
225C2×#103C2314yes—
226C2×#103C2312yes—
227C2×#103C2314yes—
228C2×#103C2312yes—
229C2×#102—24no—
230C2×#102C2312yes—
231C2×#102C2314yes—
232C2×#102C2312yes—
233C2×#102C2312yes—
234C2×#102C2312yes—
235C2×#102C2312yes—
236C2×#102C2312yes—
237#407—24no—
238C2×C22⋊C8C2312yes—
239C2×C22⋊C8C2312yes—
240#395—24no—
241#394—24no—
242#394—24no—
243#394—24no—
244#391C2312yes—
245#391C2312yes—
246#390—22no—
247#390—24no—
248#390C2314yes—
249#390C2312yes—
250#390C2312yes—
251#389—22no—
252#389C2314yes—
253#388—24no—
254#388—24no—
255#386—22no—
256#386—22no—
257#386—24no—
258#386—24no—
259#385—24no—
260#385—24no—
261#385—24no—
262#385—24no—
263#381D412yes—
264#380—22no—
265#380—22no—
266#380—22no—
267#380D412yes—
268#380D412yes—
269#379—22no—
270#379—24no—
271#379D412yes—
272C4×C4⋊C4—22no—
273C4×C4⋊C4C2314yes—
274C4×C22⋊C4—22no—
275C4×C22⋊C4—24no—
276C4×C22⋊C4C2312yes—
277C4×C22⋊C4C2312yes—
278#340C2314yes—
279#340C2314yes—
280#336C2314yes—
281#336C2314yes—
282C25—21no—
283C25—21no—
284C25C2×D411yescharacteristic
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—232no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—44no—
305C2×#41—44no—
306C2×#41—41no—
307C2×#41—41no—
308C2×#41—41no—
309C2×#41—41no—
310C2×#41—44no—
311C2×#41—44no—
312C2×#41—416no—
313C2×#41—416no—
314C2×#41—416no—
315C2×#41—44no—
316C2×#41—44no—
317C2×#41C2×D414yes—
318C2×#41#4114yes—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—41no—
332C22×Q8—41no—
333C22×Q8C2412yes—
334C22×Q8C2411yescharacteristic
335C22×Q8C2411yescharacteristic
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—28no—
342C22×D4—22no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4—22no—
346C22×D4—21no—
347C22×D4—22no—
348C22×D4—21no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—41no—
355C22×D4—41no—
356C22×D4—44no—
357C22×D4—44no—
358C22×D4—44no—
359C22×D4—84no—
360C22×D4C2×D414yes—
361C22×D4C2412yes—
362C22×D4C2411yescharacteristic
363C22×D4C2411yescharacteristic
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—22no—
374C23×C4—21no—
375C23×C4—21no—
376C23×C4—21no—
377C23×C4—24no—
378C23×C4—44no—
379C23×C4—44no—
380C23×C4—44no—
381C23×C4C2×D411yescharacteristic
382C23×C4C2×D411yescharacteristic
383C23×C4C2×D411yescharacteristic
384C23×C4C2×D414yes—
385C23×C4#4114yes—
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389AGL(1,ℤ/8)—416no—
390AGL(1,ℤ/8)—416no—
391C2×SD16—24no—
392C2×SD16—24no—
393C2×SD16—28no—
394C2×SD16—24no—
395C2×SD16—24no—
396C2×SD16—28no—
397C2×SD16—44no—
398C2×SD16—42no—
399C2×SD16—42no—
400C2×SD16—416no—
401C2×D8—24no—
402C2×D8—24no—
403C2×D8—24no—
404C2×D8—24no—
405C2×D8—42no—
406C2×D8—42no—
407C2×M16—24no—
408C2×M16—24no—
409C2×M16—22no—
410C2×M16—22no—
411C2×M16—22no—
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—22no—
415C2×M16—24no—
416C2×M16—24no—
417C2×M16—42no—
418C2×M16—42no—
419C2×M16—416no—
420C22×C8—22no—
421C22×C8—22no—
422C22×C8—22no—
423C22×C8—22no—
424C22×C8—22no—
425C22×C8C2×D414yes—
426C22×C8C2412yes—
427C22×C8C2412yes—
428C22×C8C2412yes—
429C22×C8C2412yes—
430C4⋊Q8—24no—
431C4⋊Q8—24no—
432C4⋊Q8—42no—
433C4⋊Q8—42no—
434#124—24no—
435#124—24no—
436#124—42no—
437#124—42no—
438#123—48no—
439#123—48no—
440C22⋊Q8—24no—
441C22⋊Q8—24no—
442C22⋊Q8—24no—
443C22⋊Q8—24no—
444C22⋊Q8—48no—
445C22⋊Q8—48no—
446C22⋊Q8—44no—
447C22⋊Q8—44no—
448#121—28no—
449#121—28no—
450#121—24no—
451#121—24no—
452#121C2×D418yes—
453#121C2×D418yes—
454C4×D4—28no—
455C4×D4—44no—
456C4×D4—48no—
457C4×D4—88no—
458#117—22no—
459#117—22no—
460#117—22no—
461#117—22no—
462#117—22no—
463#117—22no—
464#117—22no—
465#117—24no—
466#117—44no—
467#117—44no—
468#117—42no—
469#117C2×D414yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—44no—
484C2×C4⋊C4C2×D412yes—
485C2×C4⋊C4C2×D412yes—
486C2×C4⋊C4C2×D414yes—
487C2×C4⋊C4C2412yes—
488C2×C4⋊C4C2412yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2412yes—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—28no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—48no—
507C2×C22⋊C4—44no—
508C2×C22⋊C4—44no—
509C2×C22⋊C4C2×D412yes—
510C2×C22⋊C4C2×D412yes—
511C2×C22⋊C4C2×D414yes—
512C2×C22⋊C4C2×D414yes—
513C2×C42—21no—
514C2×C42—22no—
515C2×C42—21no—
516C2×C42—24no—
517C2×C42—44no—
518C2×C42C2412yes—
519C2×C42C2412yes—
520#107—28no—
521C4⋊C8—28no—
522C4⋊C8—44no—
523#103—24no—
524#103—24no—
525#103—28no—
526#103—24no—
527#103—24no—
528#103—24no—
529#103—28no—
530#103—44no—
531#103C2×D418yescomplemented
532#102—28no—
533#102—24no—
534#102—24no—
535#102—24no—
536#102—24no—
537#102—24no—
538#102C2×D418yescomplemented
539C22⋊C8—24no—
540C22⋊C8—24no—
541#95—24no—
542#95—24no—
543#95—24no—
544#95—24no—
545#95C2×D414yes—
546#95C2×D414yes—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—21no—
551C24—21no—
552C24—24no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—44no—
558C24—42no—
559C24—42no—
560C24—42no—
561C24—82no—
562C24—82no—
563C24—82no—
564C24#12114yes—
565C24C22×D411yescharacteristic
566C24C22×D411yescharacteristic
567C24C22×D411yescharacteristic
568#41—28no—
569#41—28no—
570#41—28no—
571#41—28no—
572#41—28no—
573#41—28no—
574#41—44no—
575#41—44no—
576#41—44no—
577#41—44no—
578#41—432no—
579#41—432no—
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584#41—44no—
585#41—44no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—28no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—22no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—42no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8—42no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—44no—
616C2×Q8C22×D412yes—
617C2×Q8C2×#4112yes—
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—28no—
623C2×D4—24no—
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—22no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—44no—
642C2×D4—44no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—44no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—48no—
651C2×D4—432no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—44no—
660C2×D4—44no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—84no—
664C2×D4—816no—
665C2×D4C22×D412yes—
666C2×D4C22×D414yes—
667C2×D4C2×#4112yes—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—28no—
671C22×C4—28no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—28no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—48no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—432no—
704C22×C4—44no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—44no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—84no—
718C22×C4—84no—
719C22×C4—82no—
720C22×C4—82no—
721C22×C4—82no—
722C22×C4#12114yes—
723C22×C4#12114yes—
724C22×C4#12114yes—
725C22×C4C22×D414yes—
726C22×C4C22×D414yes—
727C22×C4C22×D411yescharacteristic
728C22×C4C22×D411yescharacteristic
729C22×C4C22×D412yes—
730C22×C4C22×D412yes—
731C22×C4C22×D411yescharacteristic
732C22×C4C22×D412yes—
733C22×C4C22×D412yes—
734C22×C4C2×#4112yes—
735C22×C4C2×#4112yes—
736C22×C4C2×#4112yes—
737C22×C4C2×#4112yes—
738C22×C4H(5,𝔽2)12yes—
739C22×C4H(5,𝔽2)12yes—
740C22×C4C2511yescharacteristic
741SD16—416no—
742SD16—48no—
743SD16—48no—
744D8—48no—
745D8—48no—
746M16—48no—
747M16—48no—
748M16—44no—
749M16—44no—
750C2×C8—28no—
751C2×C8—22no—
752C2×C8—22no—
753C2×C8—22no—
754C2×C8—22no—
755C2×C8—22no—
756C2×C8—22no—
757C2×C8—22no—
758C2×C8—22no—
759C2×C8—22no—
760C2×C8—22no—
761C2×C8—22no—
762C2×C8—44no—
763C2×C8C22×D414yes—
764C4⋊C4—24no—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—22no—
771C4⋊C4—22no—
772C4⋊C4—22no—
773C4⋊C4—44no—
774C4⋊C4—48no—
775C4⋊C4—48no—
776C4⋊C4—42no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—84no—
780C4⋊C4C22×D414yes—
781C4⋊C4C22×D414yes—
782C22⋊C4—24no—
783C22⋊C4—24no—
784C22⋊C4—24no—
785C22⋊C4—28no—
786C22⋊C4—28no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—48no—
790C22⋊C4—44no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—42no—
796C22⋊C4—84no—
797C22⋊C4—84no—
798C22⋊C4—84no—
799C22⋊C4—84no—
800C42—24no—
801C42—22no—
802C42—22no—
803C42—22no—
804C42—22no—
805C42—44no—
806C42—42no—
807C42—84no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—28no—
819C23—24no—
820C23—22no—
821C23—22no—
822C23—44no—
823C23—44no—
824C23—48no—
825C23—42no—
826C23—42no—
827C23—44no—
828C23—44no—
829C23—42no—
830C23—42no—
831C23—41no—
832C23—41no—
833C23—42no—
834C23—41no—
835C23—41no—
836C23—42no—
837C23—48no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—88no—
845C23—88no—
846C23—164no—
847C23—164no—
848C23C2×#12112yes—
849C23C2×#12112yes—
850C23C2×#12112yes—
851C23D4212yes—
852C23#54612yes—
853C23C23×D411yescharacteristic
854Q8—22no—
855Q8—22no—
856Q8—22no—
857Q8—22no—
858Q8—48no—
859Q8—41no—
860Q8—41no—
861Q8—41no—
862Q8—41no—
863Q8—42no—
864Q8—42no—
865Q8—42no—
866Q8—42no—
867Q8—84no—
868D4—22no—
869D4—22no—
870D4—22no—
871D4—24no—
872D4—22no—
873D4—24no—
874D4—48no—
875D4—416no—
876D4—48no—
877D4—48no—
878D4—48no—
879D4—48no—
880D4—42no—
881D4—48no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—88no—
888C2×C4—28no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—28no—
896C2×C4—28no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—48no—
916C2×C4—42no—
917C2×C4—44no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—48no—
924C2×C4—48no—
925C2×C4—42no—
926C2×C4—44no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—84no—
934C2×C4—88no—
935C2×C4—84no—
936C2×C4—84no—
937C2×C4—168no—
938C2×C4C2×#12112yes—
939C2×C4C2×#12112yes—
940C2×C4C2×#12112yes—
941C2×C4#52514yes—
942C2×C4#53814yes—
943C2×C4D4212yes—
944C2×C4D4214yes—
945C2×C4#54612yes—
946C2×C4#54614yes—
947C2×C4C23×D411yescharacteristic
948C2×C4C23×D411yescharacteristic
949C2×C4C22×#4111yescharacteristic
950C2×C4C22×#4111yescharacteristic
951C2×C4C2×H(5,𝔽2)11yescharacteristic
952C2×C4C2×H(5,𝔽2)11yescharacteristic
953C8—24no—
954C8—42no—
955C8—42no—
956C8—42no—
957C22—22no—
958C22—22no—
959C22—24no—
960C22—24no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—44no—
972C22—44no—
973C22—42no—
974C22—42no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—88no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—84no—
985C22—82no—
986C22—82no—
987C22—84no—
988C22—168no—
989C22#242414yes—
990C22C22×#12111yescharacteristic
991C22C2×D4211yescharacteristic
992C22C2×#54611yescharacteristic
993C22#358512yes—
994C22#358612yes—
995C4—22no—
996C4—22no—
997C4—44no—
998C4—42no—
999C4—42no—
1000C4—44no—
1001C4—44no—
1002C4—44no—
1003C4—82no—
1004C4—82no—
1005C4—82no—
1006C4#242414yes—
1007C4C2×#52511yescharacteristic
1008C4C2×#53811yescharacteristic
1009C4C2×D4211yescharacteristic
1010C4C2×#54611yescharacteristic
1011C2—24no—
1012C2—42no—
1013C2—42no—
1014C2—82no—
1015C2—82no—
1016C2—84no—
1017C2C2×#242411yescharacteristic
1018C2#6042311yescharacteristic
1019C2#6042711yescharacteristic
1020C2#6106212yes—
1021C2#6118212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#468C2semidirect
2. C2×#3042C2semidirect
4. C2×#2896C2semidirect
5. #35305C2semidirect
6. #34204C2semidirect
7. #25104C2semidirect
8. #25101C2semidirect
9. #25099C2semidirect
10. #25094C2semidirect
11. #23611C2semidirect
12. #23544C2semidirect
13. #23512C2semidirect
14. #23424C2semidirect
15. #21262C2semidirect
16. #21067C2semidirect
17. #20929C2semidirect
18. #20911C2semidirect
19. #20835C2semidirect
23. C23×SD16C22semidirect
29. C2×#518C22semidirect
33. C2×#468C22semidirect
35. C2×#463C22semidirect
36. C2×#461C22semidirect
42. C22×#107C22semidirect
43. C2×#424C22semidirect
44. C2×#424C22semidirect
48. C2×#417C22semidirect
49. C2×#417C22semidirect
50. C2×#419C22semidirect
51. C2×#419C22semidirect
52. C2×#419C22semidirect
53. C2×#418C22semidirect
58. C22×#103C22semidirect
59. C22×#102C22semidirect
63. #2435C22semidirect
64. #2434C22semidirect
65. #2432C22semidirect
66. #2432C22semidirect
70. #2361C22semidirect
74. #2316C22semidirect
77. #2309C22semidirect
80. #2274C22semidirect
81. #2068C22semidirect
82. #2067C22semidirect
83. #2055C22semidirect
84. #2054C22semidirect
85. #2043C22semidirect
86. #2042C22semidirect
87. #2013C22semidirect
88. #2012C22semidirect
89. #1983C22semidirect
90. #1981C22semidirect
91. #1928C22semidirect
92. #1925C22semidirect
93. #1879C22semidirect
94. #1877C22semidirect
95. #1873C22semidirect
96. #1872C22semidirect
97. #1851C22semidirect
98. #1851C22semidirect
99. #1736C22semidirect
100. #1736C22semidirect
101. #1729C22semidirect
102. #1729C22semidirect
218. #416D4semidirect
531. #103C2×D4semidirect
538. #102C2×D4semidirect

Maximal subgroups

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

subgroupindex
C22×#4682
C2×#30422
C2×#30062
C2×#28962
#353052
#342042
#251042
#251012
#250992
#250942
#236112
#235442
#235122
#234242
#212622
#210672
#209292
#209112
#208352