Finite Group Databasebeta

← #6440514

Subgroups — #6440514

Order 512.

3080 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3006C211yesmaximal, characteristic
2C2×#2896C211yesmaximal, characteristic, complemented
3C2×#2500C211yesmaximal, characteristic, complemented
4C22⋊C4×#41C211yesmaximal, characteristic, complemented
5#24541C214yesmaximal, complemented
6#24539C214yesmaximal, complemented
7#24537C214yesmaximal, complemented
8#24535C214yesmaximal, complemented
9#23631C211yesmaximal, characteristic, complemented
10#23630C211yesmaximal, characteristic, complemented
11#23546C211yesmaximal, characteristic, complemented
12#23546C211yesmaximal, characteristic, complemented
13#20973C211yesmaximal, characteristic, complemented
14#20928C211yesmaximal, characteristic, complemented
15#20928C211yesmaximal, characteristic, complemented
16#20837C211yesmaximal, characteristic, complemented
17#20701C211yesmaximal, characteristic, complemented
18#20649C211yesmaximal, characteristic, complemented
19#20648C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×AGL(1,ℤ/8)C2211yescharacteristic
22C22×AGL(1,ℤ/8)C2211yescharacteristic
23C23×M16C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C2×C4×#41C2211yescharacteristic
27C22×#117C2211yescharacteristic
28#3006—28no—
29C2×#449C2212yes—
30C2×#449C2212yes—
31C2×#448C2212yes—
32C2×#447C2212yes—
33C2×#423C2211yescharacteristic, complemented
34C2×#423C2211yescharacteristic, complemented
35#2896—28no—
36C2×#417C2211yescharacteristic
37C2×#417C2211yescharacteristic
38C2×#417C2211yescharacteristic
39C2×#417C2211yescharacteristic
40C2×#417C2211yescharacteristic
41C2×#417C2211yescharacteristic
42C2×#419C2212yescomplemented
43C2×#418C2212yescomplemented
44C2×#418C2211yescharacteristic, complemented
45C2×#418C2211yescharacteristic, complemented
46C2×#416C2212yescomplemented
47C2×#416C2212yescomplemented
48C2×#407C2211yescharacteristic
49#2500—21no—
50#2500—21no—
51#2500—21no—
52#2500—21no—
53#2500C2214yes—
54#2500C2214yescomplemented
55C2×#394—22no—
56#2341C2212yescomplemented
57Q8×C22⋊C4C2212yescomplemented
58#2339—22no—
59#2339C2212yescomplemented
60D4×C22⋊C4—22no—
61D4×C22⋊C4C2212yescomplemented
62#2297—21no—
63#2297—21no—
64#2297C2211yescharacteristic
65#2297C2211yescharacteristic
66C2×#390C2211yescharacteristic, complemented
67C2×#390C2211yescharacteristic, complemented
68C2×#388—22no—
69C2×#384C2211yescharacteristic, complemented
70C2×#382C2211yescharacteristic, complemented
71#2280—21no—
72#2280C2211yescharacteristic
73C2×C4×C22⋊C4—21no—
74C2×C4×C22⋊C4C2211yescharacteristic
75#2074C2214yescomplemented
76#2073C2214yescomplemented
77#2072C2214yescomplemented
78#2071C2214yescomplemented
79#2055C2214yescomplemented
80#2055C2214yescomplemented
81#2054C2214yescomplemented
82#2054C2214yescomplemented
83#1895C2214yes—
84#1893C2214yescomplemented
85#1880C2214yescomplemented
86#1880C2214yescomplemented
87#1879C2214yescomplemented
88#1879C2214yescomplemented
89#1851C2214yescomplemented
90#1850C2214yescomplemented
91#1825C2214yescomplemented
92#1825C2214yescomplemented
93#1805C2214yescomplemented
94#1804C2214yescomplemented
95#1803C2214yescomplemented
96#1802C2214yescomplemented
97#1736C2211yescharacteristic, complemented
98#1736C2211yescharacteristic, complemented
99#1736C2211yescharacteristic, complemented
100#1736C2211yescharacteristic, complemented
101#1736C2211yescharacteristic, complemented
102#1736C2211yescharacteristic, complemented
103#1728C2211yescharacteristic, complemented
104#1728C2211yescharacteristic, complemented
105C22×#41—21no—
106C22×#41—21no—
107C22×#41—24no—
108C22×#41—24no—
109C22×#41—24no—
110C22×#41—42no—
111C22×#41—42no—
112C22×#41D418yes—
113C22×#41C2311yescharacteristic
114C22×#41C2311yescharacteristic
115C22×#41C2311yescharacteristic
116C22×#41C2311yescharacteristic
117C23×Q8C2311yescharacteristic
118C23×D4—21no—
119C23×D4—21no—
120C23×D4C2311yescharacteristic
121C23×D4C2311yescharacteristic
122C24×C4—21no—
123C24×C4C2311yescharacteristic
124C2×AGL(1,ℤ/8)—24no—
125C2×AGL(1,ℤ/8)—24no—
126C2×AGL(1,ℤ/8)—24no—
127C2×AGL(1,ℤ/8)—24no—
128C2×AGL(1,ℤ/8)—42no—
129C2×AGL(1,ℤ/8)—42no—
130C22×SD16C2312yes—
131C22×SD16C2312yes—
132C22×D8C2312yes—
133C22×D8C2312yes—
134C22×M16—24no—
135C22×M16—42no—
136C22×M16—42no—
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C22×M16C2311yescharacteristic
140C22×M16C2311yescharacteristic
141C22×M16C2312yes—
142C23×C8C2312yes—
143C2×#121—21no—
144C2×#121—21no—
145C2×#121—24no—
146C2×#121—24no—
147C2×#121C2312yes—
148C2×#121C2312yes—
149C4×#41—24no—
150C4×#41—24no—
151C4×#41—42no—
152C4×#41—42no—
153C2×C4×Q8C2312yes—
154C2×C4×Q8C2312yes—
155C2×C4×D4—22no—
156C2×C4×D4—22no—
157C2×C4×D4C2312yes—
158C2×C4×D4C2312yes—
159C2×#117—21no—
160C2×#117—21no—
161C2×#117—21no—
162C2×#117—21no—
163C2×#117—24no—
164C2×#117—24no—
165C2×#117C2312yes—
166C2×#117C2312yes—
167C2×#117C2311yescharacteristic
168C2×#117C2311yescharacteristic
169C22×C4⋊C4—22no—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C22⋊C4—21no—
174C22×C22⋊C4—22no—
175C22×C22⋊C4—21no—
176C22×C22⋊C4—22no—
177C22×C22⋊C4—22no—
178C22×C22⋊C4D412yes—
179C22×C42—21no—
180C22×C42—21no—
181C22×C42—21no—
182C22×C42C2311yescharacteristic
183C22×C42C2311yescharacteristic
184#449—28no—
185#449—28no—
186#448—28no—
187#447—28no—
188#423—42no—
189#423—42no—
190C2×C4⋊C8C2314yes—
191C2×C4⋊C8C2314yes—
192#419—28no—
193#418—28no—
194#418—42no—
195#418—42no—
196#417—24no—
197#417—24no—
198#417—24no—
199#417—24no—
200#417—24no—
201#417—24no—
202#416—28no—
203#416—28no—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2312yes—
215C2×#102C2312yes—
216C2×#102C2314yes—
217C2×#102C2314yes—
218#407—24no—
219C2×C22⋊C8C2312yes—
220C2×C22⋊C8C2312yes—
221#394—24no—
222#394—24no—
223#394—24no—
224#394—24no—
225#391—22no—
226#391—22no—
227#391C2312yes—
228#391C2312yes—
229#390—22no—
230#390—22no—
231#390—21no—
232#390—21no—
233#390—21no—
234#390—21no—
235#390C2312yes—
236#390C2312yes—
237#390C2314yes—
238#390C2314yes—
239#388—24no—
240#388—24no—
241#388—24no—
242#388—24no—
243#386—22no—
244#386—22no—
245#386—22no—
246#386—22no—
247#386—22no—
248#386—22no—
249#384—21no—
250#384—21no—
251#384C2314yes—
252#382—21no—
253#382—21no—
254#382C2314yes—
255#381—21no—
256#381—22no—
257#380—22no—
258#380—22no—
259#380C2312yes—
260#380C2312yes—
261#379—21no—
262#379—22no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—22no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—21no—
268C4×C22⋊C4—21no—
269C4×C22⋊C4—21no—
270C4×C22⋊C4—22no—
271C4×C22⋊C4D411yescharacteristic
272C4×C22⋊C4D411yescharacteristic
273C4×C22⋊C4D411yescharacteristic
274C4×C22⋊C4D411yescharacteristic
275C4×C22⋊C4C2312yes—
276C4×C22⋊C4C2312yes—
277C2×#95—22no—
278C2×#95—22no—
279C2×#95D412yes—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#336C2314yes—
287#336C2314yes—
288C25—21no—
289C25—21no—
290C25C2×D411yescharacteristic
291C2×#41—28no—
292C2×#41—28no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—232no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—44no—
309C2×#41—44no—
310C2×#41—41no—
311C2×#41—41no—
312C2×#41—41no—
313C2×#41—41no—
314C2×#41—44no—
315C2×#41—44no—
316C2×#41—416no—
317C2×#41—416no—
318C2×#41—416no—
319C2×#41C2×D414yes—
320C2×#41C2×D414yes—
321C2×#41C2×D414yes—
322C2×#41C2×D414yes—
323C2×#41#4114yes—
324C2×#41#4114yes—
325C22×Q8—21no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—41no—
330C22×Q8—41no—
331C22×Q8C2×D414yes—
332C22×Q8C2411yescharacteristic
333C22×Q8C2411yescharacteristic
334C22×D4—21no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—28no—
338C22×D4—21no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—21no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—41no—
353C22×D4—41no—
354C22×D4—44no—
355C22×D4—44no—
356C22×D4—44no—
357C22×D4—84no—
358C22×D4C2×D414yes—
359C22×D4C2412yes—
360C22×D4C2411yescharacteristic
361C22×D4C2411yescharacteristic
362C23×C4—21no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—21no—
368C23×C4—28no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4—21no—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—44no—
378C23×C4—44no—
379C23×C4C2×D412yes—
380C23×C4C2×D411yescharacteristic
381C23×C4C2×D411yescharacteristic
382C23×C4C2×D411yescharacteristic
383C23×C4C2×D414yes—
384C23×C4C2×D412yes—
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—24no—
394C2×SD16—24no—
395C2×SD16—42no—
396C2×SD16—42no—
397C2×D8—24no—
398C2×D8—24no—
399C2×D8—24no—
400C2×D8—24no—
401C2×D8—42no—
402C2×D8—42no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—24no—
406C2×M16—22no—
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—22no—
410C2×M16—22no—
411C2×M16—22no—
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—22no—
415C2×M16—22no—
416C2×M16—42no—
417C2×M16—42no—
418C2×M16—416no—
419C22×C8—24no—
420C22×C8—42no—
421C22×C8—42no—
422C22×C8C2412yes—
423C22×C8C2412yes—
424C22×C8C2412yes—
425C22×C8C2412yes—
426#121—24no—
427#121—24no—
428#121—24no—
429#121—24no—
430#121—44no—
431#121—44no—
432C4×Q8—24no—
433C4×Q8—24no—
434C4×Q8—42no—
435C4×Q8—42no—
436C4×D4—24no—
437C4×D4—24no—
438C4×D4—42no—
439C4×D4—42no—
440C4×D4—48no—
441C4×D4—48no—
442#117—24no—
443#117—24no—
444#117—24no—
445#117—24no—
446#117—22no—
447#117—22no—
448#117—22no—
449#117—22no—
450#117—44no—
451#117—44no—
452#117—44no—
453#117—44no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—84no—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2412yes—
471C2×C4⋊C4C2412yes—
472C2×C4⋊C4C2412yes—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—44no—
492C2×C22⋊C4—48no—
493C2×C22⋊C4—48no—
494C2×C22⋊C4—44no—
495C2×C22⋊C4—44no—
496C2×C22⋊C4—84no—
497C2×C22⋊C4C2×D412yes—
498C2×C22⋊C4C2×D412yes—
499C2×C22⋊C4C2×D412yes—
500C2×C22⋊C4C2×D412yes—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—44no—
512C2×C42—44no—
513C2×C42—44no—
514C2×C42C2×D411yescharacteristic
515C2×C42C2×D411yescharacteristic
516C2×C42C2×D411yescharacteristic
517C2×C42C2×D411yescharacteristic
518C2×C42C2412yes—
519C2×C42C2412yes—
520C4⋊C8—44no—
521C4⋊C8—44no—
522#103—24no—
523#103—24no—
524#103—24no—
525#103—24no—
526#103—24no—
527#103—24no—
528#102—24no—
529#102—24no—
530#102—24no—
531#102—24no—
532#102—24no—
533#102—24no—
534#102—44no—
535#102—44no—
536C22⋊C8—24no—
537C22⋊C8—24no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—24no—
542#95—24no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95C2×D412yes—
547#95C2×D412yes—
548#95C2×D412yes—
549#95C2×D412yes—
550C24—21no—
551C24—22no—
552C24—22no—
553C24—21no—
554C24—24no—
555C24—22no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—42no—
560C24—44no—
561C24—44no—
562C24—44no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—82no—
567C24#12114yes—
568C24C22×D411yescharacteristic
569C24C22×D411yescharacteristic
570C24C22×D411yescharacteristic
571#41—28no—
572#41—28no—
573#41—28no—
574#41—28no—
575#41—28no—
576#41—28no—
577#41—28no—
578#41—432no—
579#41—44no—
580#41—44no—
581#41—432no—
582#41—44no—
583#41—44no—
584#41—44no—
585#41—44no—
586#41—44no—
587#41—44no—
588#41#123116yes—
589C2×Q8—24no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—28no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—42no—
600C2×Q8—42no—
601C2×Q8—44no—
602C2×Q8—44no—
603C2×Q8—44no—
604C2×Q8C22×D412yes—
605C2×Q8C22×D412yes—
606C2×Q8C2×#4112yes—
607C2×Q8C2×#4112yes—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—28no—
612C2×D4—24no—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—432no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—42no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—44no—
650C2×D4—44no—
651C2×D4—84no—
652C2×D4—84no—
653C2×D4—816no—
654C2×D4C22×D412yes—
655C2×D4C22×D412yes—
656C2×D4C2×#4112yes—
657C2×D4C2×#4112yes—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—24no—
662C22×C4—28no—
663C22×C4—28no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—28no—
671C22×C4—28no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—24no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—432no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—44no—
715C22×C4—82no—
716C22×C4—82no—
717C22×C4#12114yes—
718C22×C4#12114yes—
719C22×C4#12114yes—
720C22×C4C22×D412yes—
721C22×C4C22×D412yes—
722C22×C4C22×D412yes—
723C22×C4C22×D411yescharacteristic
724C22×C4C22×D411yescharacteristic
725C22×C4C22×D412yes—
726C22×C4C22×D412yes—
727C22×C4C22×D412yes—
728C22×C4C22×D411yescharacteristic
729C22×C4C22×D412yes—
730C22×C4C2×#4112yes—
731C22×C4C2×#4112yes—
732C22×C4C2×#4112yes—
733C22×C4C2×#4112yes—
734C22×C4C2×#4112yes—
735C22×C4H(5,𝔽2)12yes—
736C22×C4H(5,𝔽2)12yes—
737C22×C4C2511yescharacteristic
738SD16—48no—
739SD16—48no—
740D8—48no—
741D8—48no—
742M16—48no—
743M16—44no—
744M16—44no—
745M16—44no—
746M16—44no—
747C2×C8—22no—
748C2×C8—22no—
749C2×C8—22no—
750C2×C8—22no—
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—48no—
760C4⋊C4—22no—
761C4⋊C4—22no—
762C4⋊C4—22no—
763C4⋊C4—22no—
764C4⋊C4—22no—
765C4⋊C4—22no—
766C4⋊C4—22no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—42no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—84no—
776C4⋊C4—84no—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—48no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C22⋊C4—42no—
789C22⋊C4—42no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4—48no—
794C22⋊C4—82no—
795C22⋊C4—82no—
796C22⋊C4—84no—
797C22⋊C4—84no—
798C22⋊C4—82no—
799C42—22no—
800C42—22no—
801C42—22no—
802C42—22no—
803C42—22no—
804C42—22no—
805C42—22no—
806C42—22no—
807C42—44no—
808C42—44no—
809C42—44no—
810C42—44no—
811C42—42no—
812C42—42no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—22no—
825C23—22no—
826C23—28no—
827C23—22no—
828C23—44no—
829C23—44no—
830C23—48no—
831C23—48no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—41no—
836C23—41no—
837C23—42no—
838C23—44no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—44no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—88no—
848C23—88no—
849C23—84no—
850C23—88no—
851C23—88no—
852C23—84no—
853C23C2×#12112yes—
854C23C2×#12112yes—
855C23C2×#12112yes—
856C23#54612yes—
857C23#54612yes—
858C23C23×D411yescharacteristic
859Q8—22no—
860Q8—22no—
861Q8—22no—
862Q8—22no—
863Q8—22no—
864Q8—48no—
865Q8—41no—
866Q8—41no—
867Q8C2×#12314yes—
868D4—216no—
869D4—22no—
870D4—22no—
871D4—22no—
872D4—22no—
873D4—22no—
874D4—48no—
875D4—48no—
876D4—48no—
877D4—48no—
878D4—42no—
879D4—42no—
880D4—41no—
881D4—41no—
882D4—42no—
883D4—42no—
884D4—88no—
885D4—88no—
886D4—84no—
887D4C2×#12314yes—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—28no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—28no—
901C2×C4—28no—
902C2×C4—216no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—48no—
920C2×C4—48no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—48no—
926C2×C4—44no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—44no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—44no—
938C2×C4—88no—
939C2×C4—84no—
940C2×C4—88no—
941C2×C4—84no—
942C2×C4—84no—
943C2×C4—84no—
944C2×C4C2×#12112yes—
945C2×C4C2×#12112yes—
946C2×C4C2×#12112yes—
947C2×C4C2×#12314yes—
948C2×C4#53414yes—
949C2×C4#54612yes—
950C2×C4#54612yes—
951C2×C4#55114yes—
952C2×C4#55114yes—
953C2×C4#57514yes—
954C2×C4C23×D411yescharacteristic
955C2×C4C22×#4111yescharacteristic
956C2×C4C22×#4111yescharacteristic
957C2×C4C22×#4111yescharacteristic
958C2×C4C2×H(5,𝔽2)11yescharacteristic
959C2×C4C2×H(5,𝔽2)11yescharacteristic
960C8—42no—
961C8—42no—
962C8—42no—
963C8—42no—
964C22—22no—
965C22—24no—
966C22—24no—
967C22—22no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—24no—
973C22—22no—
974C22—22no—
975C22—42no—
976C22—44no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—88no—
987C22—816no—
988C22—82no—
989C22—82no—
990C22—82no—
991C22—82no—
992C22—84no—
993C22—84no—
994C22—82no—
995C22—168no—
996C22#241214yes—
997C22C22×#12111yescharacteristic
998C22C2×#54611yescharacteristic
999C22C2×#54611yescharacteristic
1000C22C2×#57512yes—
1001C22#358512yes—
1002C4—22no—
1003C4—22no—
1004C4—24no—
1005C4—24no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—42no—
1010C4—82no—
1011C4—82no—
1012C4—82no—
1013C4—82no—
1014C4—82no—
1015C4#241214yes—
1016C4C22×#12311yescharacteristic
1017C4C2×#53411yescharacteristic
1018C4C2×#55111yescharacteristic
1019C4C2×#55111yescharacteristic
1020C2—24no—
1021C2—42no—
1022C2—42no—
1023C2—44no—
1024C2—82no—
1025C2—162no—
1026C2C2×#241211yescharacteristic
1027C2#6041511yescharacteristic
1028C2#6042611yescharacteristic
1029C2#6116412yes—
1030C2#6116612yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2896C2semidirect
3. C2×#2500C2semidirect
4. C22⋊C4×#41C2semidirect
5. #24541C2semidirect
6. #24539C2semidirect
7. #24537C2semidirect
8. #24535C2semidirect
9. #23631C2semidirect
10. #23630C2semidirect
11. #23546C2semidirect
12. #23546C2semidirect
13. #20973C2semidirect
14. #20928C2semidirect
15. #20928C2semidirect
16. #20837C2semidirect
17. #20701C2semidirect
18. #20649C2semidirect
19. #20648C2semidirect
33. C2×#423C22semidirect
34. C2×#423C22semidirect
42. C2×#419C22semidirect
43. C2×#418C22semidirect
44. C2×#418C22semidirect
45. C2×#418C22semidirect
46. C2×#416C22semidirect
47. C2×#416C22semidirect
54. #2500C22semidirect
56. #2341C22semidirect
57. Q8×C22⋊C4C22semidirect
59. #2339C22semidirect
61. D4×C22⋊C4C22semidirect
66. C2×#390C22semidirect
67. C2×#390C22semidirect
69. C2×#384C22semidirect
70. C2×#382C22semidirect
75. #2074C22semidirect
76. #2073C22semidirect
77. #2072C22semidirect
78. #2071C22semidirect
79. #2055C22semidirect
80. #2055C22semidirect
81. #2054C22semidirect
82. #2054C22semidirect
84. #1893C22semidirect
85. #1880C22semidirect
86. #1880C22semidirect
87. #1879C22semidirect
88. #1879C22semidirect
89. #1851C22semidirect
90. #1850C22semidirect
91. #1825C22semidirect
92. #1825C22semidirect
93. #1805C22semidirect
94. #1804C22semidirect
95. #1803C22semidirect
96. #1802C22semidirect
97. #1736C22semidirect
98. #1736C22semidirect
99. #1736C22semidirect
100. #1736C22semidirect
101. #1736C22semidirect
102. #1736C22semidirect
103. #1728C22semidirect
104. #1728C22semidirect

Maximal subgroups

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

subgroupindex
C2×#30062
C2×#28962
C2×#25002
C22⋊C4×#412
#245412
#245392
#245372
#245352
#236312
#236302
#235462
#209732
#209282
#208372
#207012
#206492
#206482