Finite Group Databasebeta

← #6475290

Subgroups — #6475290

Order 512.

2134 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C4×#525C211yesmaximal, characteristic
3#33153C212yesmaximal, complemented
4#32958C212yesmaximal, complemented
5#29971C212yesmaximal, complemented
6#29955C212yesmaximal, complemented
7#29243C212yesmaximal, complemented
8#29237C212yesmaximal, complemented
9#29159C212yesmaximal, complemented
10#29157C212yesmaximal, complemented
11#27680C211yesmaximal, characteristic, complemented
12#27677C211yesmaximal, characteristic, complemented
13#24837C212yesmaximal, complemented
14#24836C212yesmaximal, complemented
15#24302C211yesmaximal, characteristic, complemented
16#24299C211yesmaximal, characteristic, complemented
17#21941C212yesmaximal, complemented
18#21763C212yesmaximal
19C2×#1797C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C2×#525C2211yescharacteristic
22C22×C22⋊Q8—21no—
23C2×C4×#41C2211yescharacteristic
24C23×C42C2211yescharacteristic
25C2×#477C2212yescomplemented
26C2×#476C2212yescomplemented
27C22×C4⋊C8C2212yes—
28C22×C22⋊C8C2212yes—
29#2857—21no—
30#2857—21no—
31#2857—21no—
32#2857—21no—
33#2857C2212yes—
34#2857C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37C4×C22⋊Q8C2211yescharacteristic
38C4×C22⋊Q8C2211yescharacteristic
39C4×C22⋊Q8C2211yescharacteristic
40C4×C22⋊Q8C2211yescharacteristic
41C4×#123—21no—
42C4×#123—21no—
43C4×#121C2211yescharacteristic
44C4×#121C2211yescharacteristic
45C4×#121C2211yescharacteristic
46C4×#121C2211yescharacteristic
47C4×#120—21no—
48C4×#120—21no—
49#2297C2211yescharacteristic
50#2296C2211yescharacteristic
51C2×#391—21no—
52C2×#389—21no—
53C2×#389C2212yes—
54#2290—21no—
55#2290—21no—
56C2×#384C2211yescharacteristic
57#2280C2211yescharacteristic
58C2×#380—21no—
59C2×#380C2212yes—
60C42×D4—21no—
61C42×D4—21no—
62C4×#117C2211yescharacteristic
63#2099C2212yescomplemented
64#2099C2212yescomplemented
65#2096C2212yescomplemented
66#2093C2212yescomplemented
67#2088C2214yescomplemented
68#2087C2214yescomplemented
69#2068C2214yescomplemented
70#2065C2214yescomplemented
71#2058C2212yescomplemented
72#2057C2212yescomplemented
73#2024C2212yescomplemented
74#2023C2212yescomplemented
75#1987C2212yescomplemented
76#1987C2212yescomplemented
77#1948C2212yescomplemented
78#1947C2212yescomplemented
79#1919C2214yescomplemented
80#1918C2214yescomplemented
81#1893C2214yes—
82#1892C2214yes—
83#1874C2212yes—
84#1874C2212yes—
85#1872C2212yes—
86#1872C2212yes—
87#1865C2214yescomplemented
88#1862C2214yescomplemented
89#1854C2214yes—
90#1854C2214yes—
91#1853C2212yes—
92#1853C2212yes—
93#1852C2212yes—
94#1852C2212yes—
95#1825C2214yes—
96#1808C2214yes—
97#1807C2214yes—
98#1803C2212yescomplemented
99#1802C2212yescomplemented
100#1797C2212yes—
101#1797C2211yescharacteristic
102#1797C2211yescharacteristic
103#1797C2212yes—
104#1797C2212yes—
105#1788C2214yes—
106C2×#336C2212yes—
107C22×#41C2311yescharacteristic
108C23×Q8—21no—
109C24×C4D411yescharacteristic
110C24×C4D411yescharacteristic
111C24×C4C2311yescharacteristic
112C23×C8C2314yes—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—44no—
116C2×C4⋊Q8C2312yes—
117C2×C4⋊Q8C2312yes—
118#525—24no—
119#525Q818yescomplemented
120C2×#123—21no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—22no—
125C2×C22⋊Q8—48no—
126C2×C22⋊Q8C2311yescharacteristic
127C2×C22⋊Q8C2311yescharacteristic
128C2×#121C2311yescharacteristic
129C2×#121C2311yescharacteristic
130C2×#120—21no—
131C4×#41—44no—
132C2×C4×Q8C2311yescharacteristic
133C2×C4×Q8C2311yescharacteristic
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4C2311yescharacteristic
143C2×C4×D4C2311yescharacteristic
144C2×#117—21no—
145C2×#117C2311yescharacteristic
146C2×#117C2311yescharacteristic
147C2×#117C2311yescharacteristic
148C22×C4⋊C4—21no—
149C22×C4⋊C4—22no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C22⋊C4—22no—
155C22×C42—21no—
156C22×C42—44no—
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169#477—44no—
170#476—44no—
171C2×#107C2314yes—
172C2×#107C2314yes—
173C2×#106C2314yes—
174C2×#106C2314yes—
175C2×C4⋊C8—44no—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×C22⋊C8—28no—
184C2×C22⋊C8C2314yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187#391—22no—
188#391—22no—
189#391—22no—
190#391—22no—
191#391C2311yescharacteristic
192#391C2311yescharacteristic
193#390C2311yescharacteristic
194#390C2311yescharacteristic
195#389—22no—
196#389—22no—
197#389—22no—
198#389—22no—
199#389—22no—
200#389—22no—
201#389C2311yescharacteristic
202#389C2311yescharacteristic
203#389C2314yes—
204#389C2311yescharacteristic
205#389C2311yescharacteristic
206#389C2314yes—
207#388—21no—
208#388—21no—
209#388—21no—
210#388—21no—
211#387—21no—
212#387—21no—
213#387—21no—
214#387—21no—
215#386—21no—
216#386—21no—
217#386—21no—
218#386—21no—
219#386—21no—
220#386—21no—
221#385—21no—
222#385—21no—
223#385—21no—
224#385—21no—
225#385—21no—
226#385—21no—
227#384—21no—
228#384—21no—
229#384C2312yes—
230#384C2312yes—
231#381—21no—
232#380—22no—
233#380—22no—
234#380—22no—
235#380—22no—
236#380—22no—
237#380—22no—
238#380C2311yescharacteristic
239#380C2314yes—
240#380C2311yescharacteristic
241#380C2314yes—
242#380C2311yescharacteristic
243#380C2311yescharacteristic
244#379—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4C2311yescharacteristic
252C4×C4⋊C4C2311yescharacteristic
253C4×C4⋊C4C2311yescharacteristic
254C4×C4⋊C4C2311yescharacteristic
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—21no—
268C4×C22⋊C4—21no—
269#376—21no—
270C2×#95—22no—
271C2×#95—22no—
272C43—21no—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#336C2312yes—
282#336C2312yes—
283#336C2314yes—
284C25C2×D411yescharacteristic
285C2×#41—22no—
286C2×#41—42no—
287C2×#41—42no—
288C2×#41C2×Q814yescomplemented
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8—44no—
292C22×Q8—44no—
293C22×Q8—44no—
294C22×Q8C2411yescharacteristic
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C2411yescharacteristic
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—21no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4—42no—
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×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×Q814yes—
328C23×C4#4114yes—
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C22×C8—28no—
333C22×C8—44no—
334C22×C8—44no—
335C22×C8C2414yes—
336C22×C8C2414yes—
337C4⋊Q8—24no—
338C4⋊Q8—24no—
339C4⋊Q8—44no—
340C4⋊Q8—44no—
341C4⋊Q8—44no—
342#123—28no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—48no—
346C22⋊Q8—48no—
347C22⋊Q8—48no—
348C22⋊Q8—48no—
349C22⋊Q8C2×Q814yes—
350C22⋊Q8C2×Q814yescomplemented
351#121—22no—
352#121—22no—
353#121C2×Q814yes—
354#121C2×Q814yescomplemented
355#120—28no—
356C4×Q8—24no—
357C4×Q8—42no—
358C4×D4—28no—
359C4×D4—28no—
360C4×D4—24no—
361C4×D4—42no—
362C4×D4—44no—
363C4×D4—44no—
364C4×D4—44no—
365C4×D4—44no—
366C4×D4—44no—
367C4×D4—44no—
368#117—22no—
369#117—44no—
370#117—42no—
371#117—42no—
372#117C2×Q814yescomplemented
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—48no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4C2414yes—
398C2×C4⋊C4C2414yes—
399C2×C4⋊C4C2411yescharacteristic
400C2×C4⋊C4C2411yescharacteristic
401C2×C4⋊C4C2411yescharacteristic
402C2×C4⋊C4C2411yescharacteristic
403C2×C4⋊C4C2411yescharacteristic
404C2×C4⋊C4C2411yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—48no—
425C2×C42—21no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—42no—
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—44no—
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×C42C2×D411yescharacteristic
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463#107—44no—
464#107—44no—
465#106—44no—
466#106—44no—
467C4⋊C8—24no—
468C4⋊C8—24no—
469C4⋊C8—44no—
470#103—44no—
471#103—44no—
472#102—44no—
473#102—44no—
474C22⋊C8—28no—
475C22⋊C8—24no—
476C22⋊C8—24no—
477#95—24no—
478#95—24no—
479#95—24no—
480#95—24no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—21no—
502C24—41no—
503C24—41no—
504C24C22⋊Q814yes—
505C24C22×D411yescharacteristic
506C24C22×D411yescharacteristic
507C24C22×D411yescharacteristic
508#41—48no—
509#41—48no—
510C2×Q8—21no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—816no—
520C2×Q8C22×Q812yes—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—21no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4C22×Q812yes—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
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—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—416no—
592C22×C4—42no—
593C22×C4—416no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4C22⋊Q814yes—
608C22×C4C22⋊Q814yes—
609C22×C4C22⋊Q814yes—
610C22×C4#13514yes—
611C22×C4AGL(1,ℤ/8)14yes—
612C22×C4#13714yes—
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×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×Q812yes—
625C22×C4C22×Q812yes—
626C22×C4C22×Q812yes—
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4C2×#4112yes—
630C22×C4C2511yescharacteristic
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C2×C8—88no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—48no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—44no—
658C4⋊C4—42no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—42no—
662C4⋊C4—44no—
663C4⋊C4—48no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4C22×Q812yes—
667C4⋊C4C22×Q812yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—48no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—48no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C42—24no—
688C42—22no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—41no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—41no—
702C42—41no—
703C42—42no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42—42no—
708C42—42no—
709C42—42no—
710C42—42no—
711C42H(5,𝔽2)14yes—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—28no—
721C23—28no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23C2×C22⋊Q812yes—
741C23C2×C22⋊Q812yes—
742C23C2×C22⋊Q812yes—
743C23C2×#13512yes—
744C23C2×AGL(1,ℤ/8)12yes—
745C23C2×#13712yes—
746C23#57512yes—
747C23C23×D411yescharacteristic
748Q8—24no—
749Q8—42no—
750Q8—88no—
751Q8—88no—
752D4—24no—
753D4—48no—
754D4—48no—
755D4—48no—
756D4—42no—
757C2×C4—28no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—48no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—44no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—44no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—44no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—44no—
819C2×C4—41no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—44no—
828C2×C4—84no—
829C2×C4—88no—
830C2×C4—88no—
831C2×C4—84no—
832C2×C4C2×C22⋊Q812yes—
833C2×C4C2×C22⋊Q812yes—
834C2×C4C2×C22⋊Q812yes—
835C2×C4#53412yes—
836C2×C4#53412yes—
837C2×C4C2×#13512yes—
838C2×C4C2×#13512yes—
839C2×C4C2×AGL(1,ℤ/8)12yes—
840C2×C4C2×AGL(1,ℤ/8)12yes—
841C2×C4C2×#13712yes—
842C2×C4C2×#13712yes—
843C2×C4C23×Q811yescharacteristic
844C2×C4C22×#4111yescharacteristic
845C2×C4C2×H(5,𝔽2)12yes—
846C2×C4#58512yes—
847C8—44no—
848C8—44no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—416no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22#307614yes—
877C22#307914yes—
878C22C22×C22⋊Q811yescharacteristic
879C22C2×#53411yescharacteristic
880C22#344911yescharacteristic
881C22C22×#13511yescharacteristic
882C22C22×AGL(1,ℤ/8)11yescharacteristic
883C22C22×#13711yescharacteristic
884C22C2×#57511yescharacteristic
885C4—22no—
886C4—22no—
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—42no—
895C4—42no—
896C4—41no—
897C4—42no—
898C4—81no—
899C4—84no—
900C4—81no—
901C4—81no—
902C4—81no—
903C4—84no—
904C4#319014yes—
905C4#350112yes—
906C4#350512yes—
907C2—24no—
908C2—24no—
909C2—42no—
910C2—82no—
911C2#3501011yescharacteristic
912C2C2×#307611yescharacteristic
913C2C2×#307911yescharacteristic
914C2C2×#319011yescharacteristic
915C2#6075011yescharacteristic
916C2#6094611yescharacteristic
917C2#6096311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
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×#2857C2semidirect
3. #33153C2semidirect
4. #32958C2semidirect
5. #29971C2semidirect
6. #29955C2semidirect
7. #29243C2semidirect
8. #29237C2semidirect
9. #29159C2semidirect
10. #29157C2semidirect
11. #27680C2semidirect
12. #27677C2semidirect
13. #24837C2semidirect
14. #24836C2semidirect
15. #24302C2semidirect
16. #24299C2semidirect
17. #21941C2semidirect
19. C2×#1797C2semidirect
25. C2×#477C22semidirect
26. C2×#476C22semidirect
63. #2099C22semidirect
64. #2099C22semidirect
65. #2096C22semidirect
66. #2093C22semidirect
67. #2088C22semidirect
68. #2087C22semidirect
69. #2068C22semidirect
70. #2065C22semidirect
71. #2058C22semidirect
72. #2057C22semidirect
73. #2024C22semidirect
74. #2023C22semidirect
75. #1987C22semidirect
76. #1987C22semidirect
77. #1948C22semidirect
78. #1947C22semidirect
79. #1919C22semidirect
80. #1918C22semidirect
87. #1865C22semidirect
88. #1862C22semidirect
98. #1803C22semidirect
99. #1802C22semidirect
119. #525Q8semidirect
288. C2×#41C2×Q8semidirect
350. C22⋊Q8C2×Q8semidirect
354. #121C2×Q8semidirect
372. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C4×#5252
#331532
#329582
#299712
#299552
#292432
#292372
#291592
#291572
#276802
#276772
#248372
#248362
#243022
#242992
#219412
#217632
C2×#17972