Finite Group Databasebeta

← C4×#3094 #6373051

Subgroups — C4×#3094 #6373051

Order 512.

2836 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3094C211yesmaximal, characteristic
2C2×C4×#121C211yesmaximal, characteristic
3C2×C4×#117C211yesmaximal, characteristic, complemented
4#21582C214yesmaximal, complemented
5#21580C212yesmaximal, complemented
6#21578C212yesmaximal, complemented
7C4×#482C214yesmaximal, complemented
8C4×#481C212yesmaximal, complemented
9C4×#480C212yesmaximal, complemented
10#21060C212yesmaximal, complemented
11#21034C212yesmaximal, complemented
12#20912C211yesmaximal, characteristic
13#20846C211yesmaximal, characteristic, complemented
14#20702C211yesmaximal, characteristic, complemented
15C4×#428C212yesmaximal, complemented
16C4×#418C212yesmaximal, complemented
17C4×#407C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4—21no—
20C22×C4×D4C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#3094C4116yesdirect product factor
25C2×#481C2212yes—
26C2×#482C2214yes—
27C2×#480C2212yes—
28C2×#428C2212yes—
29C2×#428C2212yes—
30C2×#418C2212yes—
31C2×#418C2212yes—
32C2×#407C2211yescharacteristic
33C2×#407C2211yescharacteristic
34C2×C4×M16C2212yes—
35C4×#121—21no—
36C4×#121—21no—
37C4×#121—21no—
38C4×#121—21no—
39C4×#121C2212yes—
40C4×#121C2212yes—
41C4×#121C2212yes—
42C4×#121C2212yes—
43C2×#390C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#388—21no—
46C2×#386—21no—
47C2×#380C2211yescharacteristic
48C4×#117—21no—
49C4×#117—21no—
50C4×#117—21no—
51C4×#117—21no—
52C4×#117C2212yes—
53C4×#117C2212yes—
54C4×#117C2212yescomplemented
55C4×#117C2212yescomplemented
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic, complemented
58C2×C4×C4⋊C4C2211yescharacteristic, complemented
59C2×C4×C4⋊C4C2211yescharacteristic, complemented
60C2×C4×C4⋊C4C2211yescharacteristic, complemented
61C2×C4×C22⋊C4—21no—
62C2×C4×C22⋊C4—21no—
63C2×C4×C22⋊C4—21no—
64C2×#376—21no—
65C2×C43—21no—
66#1926C2214yescomplemented
67#1926C2214yescomplemented
68#1925C2214yescomplemented
69#1925C2214yescomplemented
70#1921C2214yescomplemented
71#1920C2214yescomplemented
72#1919C2214yescomplemented
73#1918C2214yescomplemented
74#1875C2214yes—
75#1874C2212yes—
76#1874C2212yes—
77#1854C2214yescomplemented
78#1853C2212yescomplemented
79#1852C2212yescomplemented
80#1825C2214yescomplemented
81#1824C2212yescomplemented
82#1823C2212yescomplemented
83#1776C2214yescomplemented
84#1776C2214yescomplemented
85C4×#107C2214yescomplemented
86C4×#106C2214yescomplemented
87#1762C2214yescomplemented
88#1762C2214yescomplemented
89C4×#102C2214yescomplemented
90C4×#102C2214yescomplemented
91#1749C2212yescomplemented
92#1749C2212yescomplemented
93C4×C22⋊C8C2212yescomplemented
94C4×C22⋊C8C2212yescomplemented
95#1736C2212yes—
96#1736C2212yes—
97#1736C2212yes—
98#1736C2212yes—
99#1728C2212yes—
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C24×C4D411yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4C2311yescharacteristic
106C22×M16C2312yes—
107C22×M16C2312yes—
108C2×#121—21no—
109C2×#121—21no—
110C2×#121—24no—
111C2×#121C2×C418yes—
112C2×#121C2312yes—
113C2×#121C2312yes—
114C2×C4×D4—22no—
115C2×C4×D4—22no—
116C2×C4×D4—22no—
117C2×C4×D4—22no—
118C2×C4×D4—21no—
119C2×C4×D4—21no—
120C2×C4×D4—28no—
121C2×C4×D4—48no—
122C2×C4×D4C2312yes—
123C2×C4×D4C2312yes—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117—21no—
128C2×#117—24no—
129C2×#117—28no—
130C2×#117C2×C418yescomplemented
131C2×#117C2312yes—
132C2×#117C2312yes—
133C2×#117C2312yes—
134C2×#117C2312yes—
135C22×C4⋊C4—21no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C42—21no—
151C22×C42—21no—
152C22×C42—28no—
153C22×C42—21no—
154C22×C42—21no—
155C22×C42—21no—
156C22×C42—21no—
157C22×C42—21no—
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42D411yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#482C2×C4132yescomplemented
171#481C2×C4116yescomplemented
172#480C2×C4116yescomplemented
173#428—28no—
174#428C2×C4116yescomplemented
175C2×#107C2314yes—
176C2×#107C2314yes—
177C2×#106C2314yes—
178C2×#106C2314yes—
179#418—28no—
180#418C2×C4116yescomplemented
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×#102C2314yes—
185#407—24no—
186#407C2×C418yescomplemented
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C4×M16—28no—
192C2×#97C2314yes—
193C2×C4×C8C2314yes—
194#390—21no—
195#390—21no—
196#390C2312yes—
197#390C2312yes—
198#389—21no—
199#389—21no—
200#389C2312yes—
201#389C2312yes—
202#388—22no—
203#388—22no—
204#388—22no—
205#388—22no—
206#386—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#380—21no—
211#380—21no—
212#380C2312yes—
213#380C2312yes—
214C4×C4⋊C4—21no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4C2312yes—
225C4×C4⋊C4C2312yes—
226C4×C4⋊C4C2312yes—
227C4×C4⋊C4C2312yes—
228C4×C4⋊C4C2312yes—
229C4×C4⋊C4C2312yes—
230C4×C4⋊C4C2312yes—
231C4×C4⋊C4C2312yes—
232C4×C4⋊C4C2312yes—
233C4×C4⋊C4C2312yes—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246#376—22no—
247#376—22no—
248#376—22no—
249#376—22no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254C2×#95—21no—
255C2×#95—21no—
256C2×#95—21no—
257C43—22no—
258C43—22no—
259C43—22no—
260C43—22no—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#336C2314yes—
270#336C2314yes—
271C25—21no—
272C25C2×D411yescharacteristic
273C22×D4—28no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—21no—
277C22×D4—24no—
278C22×D4—24no—
279C22×D4—22no—
280C22×D4—44no—
281C22×D4—44no—
282C22×D4C22×C414yes—
283C22×D4C2412yes—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—44no—
302C23×C4—44no—
303C23×C4—44no—
304C23×C4C22×C414yes—
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
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×C4#4114yes—
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C2×M16—24no—
325C2×M16—24no—
326C2×M16—24no—
327C2×M16—24no—
328C2×M16—24no—
329C2×M16C22×C418yes—
330C22×C8C2414yes—
331C22×C8C2414yes—
332#121—28no—
333#121—28no—
334#121—24no—
335#121—24no—
336#121C22×C418yes—
337#121C22×C418yes—
338C4×D4—28no—
339C4×D4—28no—
340C4×D4—48no—
341C4×D4—48no—
342C4×D4—48no—
343C4×D4—48no—
344C4×D4—44no—
345C4×D4—44no—
346#117—28no—
347#117—28no—
348#117—28no—
349#117—28no—
350#117—24no—
351#117—24no—
352#117—24no—
353#117—24no—
354#117—24no—
355#117C22×C418yes—
356#117C22×C418yescomplemented
357#117#4118yes—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4C22×C414yes—
376C2×C4⋊C4C22×C414yescomplemented
377C2×C4⋊C4C22×C414yescomplemented
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C42—28no—
407C2×C42—28no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—44no—
434C2×C42—44no—
435C2×C42—44no—
436C2×C42—44no—
437C2×C42—44no—
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42#4118yes—
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455#107—28no—
456#107C22×C4116yescomplemented
457#106—28no—
458#106C22×C4116yescomplemented
459#102—28no—
460#102—28no—
461#102C22×C4116yescomplemented
462#102C22×C4116yescomplemented
463C22⋊C8—24no—
464C22⋊C8—24no—
465C22⋊C8C22×C418yescomplemented
466C22⋊C8C22×C418yescomplemented
467#97—28no—
468C4×C8—28no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—24no—
488C24—22no—
489C24—41no—
490C24—41no—
491C24—42no—
492C24—42no—
493C24—42no—
494C24—42no—
495C24—42no—
496C24—42no—
497C24C4×D414yes—
498C24C22×D411yescharacteristic
499C24C22×D411yescharacteristic
500C24C22×D411yescharacteristic
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—24no—
504C2×D4—216no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—22no—
508C2×D4—44no—
509C2×D4—432no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—48no—
516C2×D4C23×C414yes—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—216no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—216no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
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—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
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—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—416no—
575C22×C4—416no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—816no—
599C22×C4C4×D414yes—
600C22×C4C4×D414yes—
601C22×C4C4×D414yes—
602C22×C4#12314yes—
603C22×C4#12314yes—
604C22×C4AGL(1,ℤ/8)14yes—
605C22×C4C23×C412yes—
606C22×C4C23×C412yes—
607C22×C4C23×C412yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4114yes—
623C22×C4C2×#4114yes—
624C22×C4C2511yescharacteristic
625M16—216no—
626M16—48no—
627C2×C8—24no—
628C2×C8—24no—
629C2×C8—24no—
630C2×C8—24no—
631C2×C8—24no—
632C2×C8C23×C418yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—44no—
646C4⋊C4—42no—
647C4⋊C4—42no—
648C4⋊C4—44no—
649C4⋊C4C23×C414yes—
650C4⋊C4C23×C414yes—
651C4⋊C4C23×C414yes—
652C4⋊C4C2×#4114yes—
653C4⋊C4C2×#4114yes—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—28no—
658C22⋊C4—28no—
659C22⋊C4—28no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C42—28no—
669C42—28no—
670C42—28no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—22no—
679C42—22no—
680C42—22no—
681C42—28no—
682C42—22no—
683C42—22no—
684C42—44no—
685C42—44no—
686C42—44no—
687C42—44no—
688C42—44no—
689C42—44no—
690C42—44no—
691C42—44no—
692C42—44no—
693C42—44no—
694C42#12314yes—
695C42#12314yes—
696C42C2×#4114yes—
697C42C2×#4114yes—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—28no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—28no—
714C23—24no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—48no—
721C23—48no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—48no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23C2×C4×D412yes—
734C23C2×C4×D412yes—
735C23C2×C4×D412yes—
736C23C2×#12312yes—
737C23#52512yes—
738C23C2×AGL(1,ℤ/8)12yes—
739C23#57512yes—
740C23C23×D411yescharacteristic
741D4—28no—
742D4—416no—
743D4—416no—
744D4—44no—
745D4—48no—
746C2×C4—28no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—48no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—48no—
793C2×C4—48no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—88no—
812C2×C4—84no—
813C2×C4—84no—
814C2×C4—88no—
815C2×C4C2×C4×D412yes—
816C2×C4C2×C4×D412yes—
817C2×C4C2×C4×D412yes—
818C2×C4C4×#4118yes—
819C2×C4C2×#12312yes—
820C2×C4C2×#12312yes—
821C2×C4C2×#12312yes—
822C2×C4C2×#12312yes—
823C2×C4C2×#12312yes—
824C2×C4#52512yes—
825C2×C4#52918yes—
826C2×C4C2×AGL(1,ℤ/8)12yes—
827C2×C4C2×AGL(1,ℤ/8)12yes—
828C2×C4#57512yes—
829C2×C4#57512yes—
830C2×C4C24×C411yescharacteristic
831C2×C4C22×#4112yes—
832C2×C4C22×#4112yes—
833C2×C4C22×#4111yescharacteristic
834C8—28no—
835C8—44no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—416no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—816no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22C4×#12314yes—
865C22C4×AGL(1,ℤ/8)14yes—
866C22C22×C4×D411yescharacteristic
867C22C22×#12311yescharacteristic
868C22C2×#52511yescharacteristic
869C22C22×AGL(1,ℤ/8)11yescharacteristic
870C22C2×#57511yescharacteristic
871C22C2×#57511yescharacteristic
872C22C2×#57511yescharacteristic
873C4—22no—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—41no—
881C4—41no—
882C4—44no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—44no—
887C4—82no—
888C4—82no—
889C4C4×#12314yes—
890C4#309414yesdirect product factor
891C4C2×C4×#4112yes—
892C4C2×#52912yes—
893C2—24no—
894C2—24no—
895C2—42no—
896C2—84no—
897C2C2×C4×#12311yescharacteristic
898C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
899C2C4×#57511yescharacteristic
900C2C2×#309411yescharacteristic
901C2#6051111yescharacteristic
902C2#6056111yescharacteristic
903C2#6056311yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC22×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×C4×#117C2semidirect
4. #21582C2semidirect
5. #21580C2semidirect
6. #21578C2semidirect
7. C4×#482C2semidirect
8. C4×#481C2semidirect
9. C4×#480C2semidirect
10. #21060C2semidirect
11. #21034C2semidirect
13. #20846C2semidirect
14. #20702C2semidirect
15. C4×#428C2semidirect
16. C4×#418C2semidirect
17. C4×#407C2semidirect
24. #3094C4direct (N × H)
54. C4×#117C22semidirect
55. C4×#117C22semidirect
57. C2×C4×C4⋊C4C22semidirect
58. C2×C4×C4⋊C4C22semidirect
59. C2×C4×C4⋊C4C22semidirect
60. C2×C4×C4⋊C4C22semidirect
66. #1926C22semidirect
67. #1926C22semidirect
68. #1925C22semidirect
69. #1925C22semidirect
70. #1921C22semidirect
71. #1920C22semidirect
72. #1919C22semidirect
73. #1918C22semidirect
77. #1854C22semidirect
78. #1853C22semidirect
79. #1852C22semidirect
80. #1825C22semidirect
81. #1824C22semidirect
82. #1823C22semidirect
83. #1776C22semidirect
84. #1776C22semidirect
85. C4×#107C22semidirect
86. C4×#106C22semidirect
87. #1762C22semidirect
88. #1762C22semidirect
89. C4×#102C22semidirect
90. C4×#102C22semidirect
91. #1749C22semidirect
92. #1749C22semidirect
93. C4×C22⋊C8C22semidirect
94. C4×C22⋊C8C22semidirect
130. C2×#117C2×C4semidirect
170. #482C2×C4semidirect
171. #481C2×C4semidirect
172. #480C2×C4semidirect
174. #428C2×C4semidirect
180. #418C2×C4semidirect
186. #407C2×C4semidirect
356. #117C22×C4semidirect
376. C2×C4⋊C4C22×C4semidirect
377. C2×C4⋊C4C22×C4semidirect
456. #107C22×C4semidirect
458. #106C22×C4semidirect
461. #102C22×C4semidirect
462. #102C22×C4semidirect
465. C22⋊C8C22×C4semidirect
466. C22⋊C8C22×C4semidirect
890. C4#3094direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#30942
C2×C4×#1212
C2×C4×#1172
#215822
#215802
#215782
C4×#4822
C4×#4812
C4×#4802
#210602
#210342
#209122
#208462
#207022
C4×#4282
C4×#4182
C4×#4072