Finite Group Databasebeta

← #6441636

Subgroups — #6441636

Order 512.

2676 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3092C211yesmaximal, characteristic, complemented
2C2×#3055C211yesmaximal, characteristic
3C2×#2501C211yesmaximal, characteristic, complemented
4#34136C211yesmaximal, characteristic, complemented
5#25221C214yesmaximal, complemented
6#25217C214yesmaximal, complemented
7#25204C214yesmaximal, complemented
8#25200C214yesmaximal, complemented
9#23658C211yesmaximal, characteristic, complemented
10#23630C211yesmaximal, characteristic, complemented
11#23618C211yesmaximal, characteristic, complemented
12#23546C211yesmaximal, characteristic, complemented
13#21171C211yesmaximal, characteristic, complemented
14#21060C211yesmaximal, characteristic, complemented
15#20928C211yesmaximal, characteristic, complemented
16#20912C211yesmaximal, characteristic, complemented
17#20837C211yesmaximal, characteristic, complemented
18#20648C211yesmaximal, characteristic, complemented
19C2×#1736C211yesmaximal, characteristic, complemented
20C22×AGL(1,ℤ/8)C2211yescharacteristic
21C23×M16C2211yescharacteristic
22C2×#525C2211yescharacteristic
23C22×#123—22no—
24C22×#121C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#3092—28no—
29C2×#484C2212yescomplemented
30C2×#481C2212yescomplemented
31C2×#483C2212yescomplemented
32C2×#480C2212yescomplemented
33#3055—28no—
34C2×#469C2212yes—
35C2×#468C2212yes—
36C2×#466C2212yes—
37C2×#465C2212yes—
38C2×#428C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#423C2211yescharacteristic
42C2×#423C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#417C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×#418C2211yescharacteristic
48C2×#418C2211yescharacteristic
49C2×#407C2211yescharacteristic
50#2501—21no—
51#2501—21no—
52#2501—21no—
53#2501—21no—
54#2501C2214yes—
55#2501C2214yes—
56C2×#399—22no—
57#2363C2212yescomplemented
58#2362C2212yescomplemented
59#2361C2212yescomplemented
60#2360C2212yescomplemented
61#2359—22no—
62#2358—22no—
63#2297C2211yescharacteristic
64#2296C2211yescharacteristic
65#2293—21no—
66C2×#390C2211yescharacteristic
67C2×#390C2211yescharacteristic
68#2290—21no—
69#2290—21no—
70C2×#384C2211yescharacteristic
71C2×#384C2211yescharacteristic
72C42×D4—21no—
73C4×#117C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75#2084C2214yescomplemented
76#2083C2214yescomplemented
77#2072C2214yescomplemented
78#2071C2214yescomplemented
79#2067C2214yescomplemented
80#2065C2214yescomplemented
81#2055C2214yescomplemented
82#2054C2214yescomplemented
83#1948C2214yescomplemented
84#1947C2214yescomplemented
85#1926C2214yescomplemented
86#1925C2214yescomplemented
87#1880C2214yescomplemented
88#1879C2214yescomplemented
89#1875C2214yes—
90#1874C2214yes—
91#1851C2214yescomplemented
92#1850C2214yescomplemented
93#1803C2214yescomplemented
94#1802C2214yescomplemented
95#1736C2211yescharacteristic
96#1736C2211yescharacteristic
97#1736C2211yescharacteristic
98#1736C2211yescharacteristic
99#1736C2211yescharacteristic
100#1736C2211yescharacteristic
101#1736C2214yescomplemented
102C2×#340C2214yescomplemented
103#1728C2211yescharacteristic
104#1728C2211yescharacteristic
105C22×#41C2311yescharacteristic
106C23×D4—21no—
107C23×D4C2311yescharacteristic
108C24×C4—21no—
109C24×C4C2311yescharacteristic
110C2×AGL(1,ℤ/8)—24no—
111C2×AGL(1,ℤ/8)—24no—
112C2×AGL(1,ℤ/8)—42no—
113C22×SD16C2312yes—
114C22×D8C2312yes—
115C22×M16—24no—
116C22×M16—24no—
117C22×M16—42no—
118C22×M16C2311yescharacteristic
119C22×M16C2311yescharacteristic
120C22×M16C2311yescharacteristic
121C22×M16C2312yes—
122C22×M16C2311yescharacteristic
123C23×C8C2312yes—
124#525—24no—
125#525D418yes—
126C2×#123—21no—
127C2×#123—24no—
128C2×#123—24no—
129C2×#123—24no—
130C2×#123—24no—
131C2×#123—416no—
132C2×C22⋊Q8C2311yescharacteristic
133C2×C22⋊Q8C2311yescharacteristic
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—24no—
137C2×#121—24no—
138C2×#121C2312yes—
139C2×#121C2312yes—
140C2×#121C2311yescharacteristic
141C2×#121C2311yescharacteristic
142C2×#120—21no—
143C4×#41—24no—
144C4×#41—42no—
145C2×C4×Q8C2312yes—
146C2×C4×D4—21no—
147C2×C4×D4—21no—
148C2×C4×D4—22no—
149C2×C4×D4—22no—
150C2×C4×D4C2312yes—
151C2×#117—21no—
152C2×#117—21no—
153C2×#117—21no—
154C2×#117—24no—
155C2×#117—42no—
156C2×#117C2311yescharacteristic
157C2×#117C2312yes—
158C2×#117C2311yescharacteristic
159C2×#117C2311yescharacteristic
160C22×C4⋊C4—24no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—22no—
164C22×C4⋊C4—22no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C22⋊C4—21no—
174C22×C22⋊C4—21no—
175C22×C22⋊C4—22no—
176C22×C22⋊C4—22no—
177C22×C22⋊C4D412yes—
178C22×C42—21no—
179C22×C42—21no—
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182#484—28no—
183#483—28no—
184#481—28no—
185#480—28no—
186#469—28no—
187#468—28no—
188#466—28no—
189#465—28no—
190#428—24no—
191#428—24no—
192#428—24no—
193C2×#107C2312yes—
194C2×#107C2312yes—
195C2×#107C2312yes—
196C2×#106C2312yes—
197C2×#106C2312yes—
198C2×#106C2312yes—
199#423—24no—
200#423—42no—
201C2×C4⋊C8C2314yes—
202C2×C4⋊C8C2314yes—
203#418—24no—
204#418—24no—
205#418—42no—
206#417—24no—
207#417—24no—
208#417—24no—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#103C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2312yes—
215C2×#102C2312yes—
216C2×#102C2312yes—
217C2×#102C2314yes—
218C2×#102C2314yes—
219#407—24no—
220C2×C22⋊C8C2312yes—
221C2×C22⋊C8C2312yes—
222#399—24no—
223#399—24no—
224#399—24no—
225#399—24no—
226#391C2312yes—
227#390—22no—
228#390—21no—
229#390—21no—
230#390—21no—
231#390—21no—
232#390C2312yes—
233#390C2314yes—
234#390C2314yes—
235#389—22no—
236#389C2312yes—
237#389C2312yes—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#387—22no—
243#387—22no—
244#386—22no—
245#386—22no—
246#386—22no—
247#385—22no—
248#385—22no—
249#385—22no—
250#384—21no—
251#384—21no—
252#384—21no—
253#384—21no—
254#384C2314yes—
255#384C2314yes—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—22no—
259C4×C4⋊C4C2312yes—
260C4×C4⋊C4C2312yes—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—22no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—22no—
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4D411yescharacteristic
269C4×C22⋊C4D411yescharacteristic
270C4×C22⋊C4C2312yes—
271C4×C22⋊C4C2312yes—
272#376—21no—
273C2×#95D412yes—
274C43—21no—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#336C2314yes—
282#336C2314yes—
283C25—21no—
284C25C2×D411yescharacteristic
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—22no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41C2×D414yes—
291C22×Q8C2411yescharacteristic
292C22×D4—21no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—21no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—48no—
305C22×D4—44no—
306C22×D4C2412yes—
307C22×D4C2411yescharacteristic
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—21no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—48no—
321C23×C4—44no—
322C23×C4C2×D412yes—
323C23×C4C2×D412yes—
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D414yes—
328C23×C4#4114yes—
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332AGL(1,ℤ/8)—416no—
333C2×SD16—24no—
334C2×SD16—24no—
335C2×SD16—42no—
336C2×D8—24no—
337C2×D8—24no—
338C2×D8—42no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—24no—
343C2×M16—22no—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—22no—
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—24no—
352C2×M16—42no—
353C2×M16—416no—
354C2×M16#4114yes—
355C22×C8—24no—
356C22×C8—24no—
357C22×C8—42no—
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2412yes—
361C22×C8C2412yes—
362#123—28no—
363#123—416no—
364#123—416no—
365#123—416no—
366#123—416no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8C2×D414yes—
370C22⋊Q8C2×D414yes—
371#121—22no—
372#121—22no—
373#121—24no—
374#121—24no—
375#121—24no—
376#121—24no—
377#121—44no—
378#121—44no—
379#121C2×D414yes—
380#121C2×D414yes—
381#120—28no—
382C4×Q8—24no—
383C4×Q8—42no—
384C4×D4—28no—
385C4×D4—28no—
386C4×D4—24no—
387C4×D4—42no—
388C4×D4—48no—
389C4×D4—48no—
390#117—22no—
391#117—22no—
392#117—22no—
393#117—22no—
394#117—24no—
395#117—44no—
396#117—44no—
397#117—44no—
398#117—42no—
399#117C2×D414yes—
400#117#4114yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—42no—
428C2×C4⋊C4—48no—
429C2×C4⋊C4—48no—
430C2×C4⋊C4—44no—
431C2×C4⋊C4—44no—
432C2×C4⋊C4—44no—
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2412yes—
435C2×C4⋊C4C2412yes—
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—28no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—44no—
459C2×C22⋊C4—48no—
460C2×C22⋊C4—48no—
461C2×C22⋊C4—44no—
462C2×C22⋊C4C2×D412yes—
463C2×C22⋊C4C2×D412yes—
464C2×C22⋊C4C2×D412yes—
465C2×C22⋊C4C2×D412yes—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—21no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—44no—
478C2×C42—44no—
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2412yes—
484C2×C42C2412yes—
485#107—24no—
486#107—24no—
487#107—24no—
488#106—24no—
489#106—24no—
490#106—24no—
491C4⋊C8—28no—
492C4⋊C8—44no—
493#103—24no—
494#103—24no—
495#103—24no—
496#102—24no—
497#102—24no—
498#102—24no—
499#102—24no—
500#102—24no—
501#102—28no—
502#102—44no—
503C22⋊C8—24no—
504C22⋊C8—24no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95C2×D412yes—
512#95C2×D412yes—
513#95C2×D412yes—
514#95C2×D412yes—
515C24—22no—
516C24—22no—
517C24—24no—
518C24—21no—
519C24—22no—
520C24—42no—
521C24—44no—
522C24—44no—
523C24—42no—
524C24—42no—
525C24—42no—
526C24#12114yes—
527C24C22×D411yescharacteristic
528C24C22×D411yescharacteristic
529C24C22×D411yescharacteristic
530#41—28no—
531#41—28no—
532#41—44no—
533#41—44no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8C22×D412yes—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—44no—
557C2×D4—48no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—48no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—42no—
566C2×D4—44no—
567C2×D4—42no—
568C2×D4—82no—
569C2×D4—816no—
570C2×D4C22×D412yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—48no—
612C22×C4—42no—
613C22×C4—44no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—48no—
619C22×C4—44no—
620C22×C4—82no—
621C22×C4—82no—
622C22×C4—816no—
623C22×C4#12114yes—
624C22×C4#12114yes—
625C22×C4#12114yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D412yes—
636C22×C4C2×#4112yes—
637C22×C4C2×#4112yes—
638C22×C4C2×#4112yes—
639C22×C4C2×#4112yes—
640C22×C4C2×#4112yes—
641C22×C4H(5,𝔽2)12yes—
642C22×C42−1+412yes—
643C22×C4C2511yescharacteristic
644SD16—48no—
645D8—48no—
646M16—28no—
647M16—48no—
648M16—44no—
649M16—44no—
650M16—44no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—48no—
663C2×C8C2×#4114yes—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—48no—
680C4⋊C4—48no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—48no—
687C4⋊C4—48no—
688C4⋊C4—44no—
689C4⋊C4—82no—
690C4⋊C4C22×D412yes—
691C4⋊C4C22×D412yes—
692C4⋊C4C2×#4114yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—48no—
705C22⋊C4—48no—
706C22⋊C4—42no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—44no—
712C22⋊C4—82no—
713C22⋊C4AGL(1,ℤ/8)18yescomplemented
714C42—24no—
715C42—22no—
716C42—22no—
717C42—24no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—44no—
725C42—44no—
726C42—42no—
727C42—44no—
728C42—82no—
729C23—22no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—28no—
736C23—21no—
737C23—21no—
738C23—28no—
739C23—22no—
740C23—22no—
741C23—44no—
742C23—48no—
743C23—48no—
744C23—42no—
745C23—41no—
746C23—41no—
747C23—42no—
748C23—44no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—44no—
753C23—84no—
754C23—84no—
755C23—88no—
756C23—88no—
757C23—84no—
758C23C2×#12112yes—
759C23C2×#12112yes—
760C23C2×#12112yes—
761C23#54612yes—
762C23#54712yes—
763C23C2×AGL(1,ℤ/8)14yes—
764C23C23×D411yescharacteristic
765Q8—22no—
766Q8—22no—
767Q8—41no—
768Q8—41no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—41no—
774D4—42no—
775D4—41no—
776D4—42no—
777D4—42no—
778D4—42no—
779D4—84no—
780D4—88no—
781D4—88no—
782D4—84no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—28no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—48no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—88no—
831C2×C4—88no—
832C2×C4—84no—
833C2×C4—84no—
834C2×C4—88no—
835C2×C4—84no—
836C2×C4—88no—
837C2×C4C2×#12112yes—
838C2×C4C2×#12112yes—
839C2×C4C2×#12112yes—
840C2×C4#52914yes—
841C2×C4#53914yes—
842C2×C4#54612yes—
843C2×C4#54614yes—
844C2×C4#54712yes—
845C2×C4#54714yes—
846C2×C4C2×AGL(1,ℤ/8)14yes—
847C2×C4C2×AGL(1,ℤ/8)14yes—
848C2×C4C23×D411yescharacteristic
849C2×C4C22×#4111yescharacteristic
850C2×C4C22×#4111yescharacteristic
851C2×C4C22×#4111yescharacteristic
852C2×C4C2×H(5,𝔽2)11yescharacteristic
853C2×C4C2×2−1+411yescharacteristic
854C8—24no—
855C8—42no—
856C8—42no—
857C8—42no—
858C22—22no—
859C22—22no—
860C22—24no—
861C22—24no—
862C22—22no—
863C22—24no—
864C22—24no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—416no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—84no—
879C22—82no—
880C22—84no—
881C22—82no—
882C22—168no—
883C22#242514yes—
884C22#303814yes—
885C22C22×#12111yescharacteristic
886C22C2×#54611yescharacteristic
887C22C2×#54711yescharacteristic
888C22C22×AGL(1,ℤ/8)12yes—
889C22#358612yes—
890C4—24no—
891C4—22no—
892C4—22no—
893C4—24no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—44no—
899C4—42no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4#242514yes—
905C4C2×#52911yescharacteristic
906C4C2×#53911yescharacteristic
907C4C2×#54611yescharacteristic
908C4C2×#54711yescharacteristic
909C2—24no—
910C2—24no—
911C2—42no—
912C2—82no—
913C2—162no—
914C2C2×#242511yescharacteristic
915C2C2×#303811yescharacteristic
916C2#6042711yescharacteristic
917C2#6116112yes—
918C2#6125212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3055C2
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
1. C2×#3092C2semidirect
3. C2×#2501C2semidirect
4. #34136C2semidirect
5. #25221C2semidirect
6. #25217C2semidirect
7. #25204C2semidirect
8. #25200C2semidirect
9. #23658C2semidirect
10. #23630C2semidirect
11. #23618C2semidirect
12. #23546C2semidirect
13. #21171C2semidirect
14. #21060C2semidirect
15. #20928C2semidirect
16. #20912C2semidirect
17. #20837C2semidirect
18. #20648C2semidirect
19. C2×#1736C2semidirect
29. C2×#484C22semidirect
30. C2×#481C22semidirect
31. C2×#483C22semidirect
32. C2×#480C22semidirect
57. #2363C22semidirect
58. #2362C22semidirect
59. #2361C22semidirect
60. #2360C22semidirect
75. #2084C22semidirect
76. #2083C22semidirect
77. #2072C22semidirect
78. #2071C22semidirect
79. #2067C22semidirect
80. #2065C22semidirect
81. #2055C22semidirect
82. #2054C22semidirect
83. #1948C22semidirect
84. #1947C22semidirect
85. #1926C22semidirect
86. #1925C22semidirect
87. #1880C22semidirect
88. #1879C22semidirect
91. #1851C22semidirect
92. #1850C22semidirect
93. #1803C22semidirect
94. #1802C22semidirect
101. #1736C22semidirect
102. C2×#340C22semidirect
713. C22⋊C4AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×#30922
C2×#30552
C2×#25012
#341362
#252212
#252172
#252042
#252002
#236582
#236302
#236182
#235462
#211712
#210602
#209282
#209122
#208372
#206482
C2×#17362