Finite Group Databasebeta

← C2×#33006 #6629199

Subgroups — C2×#33006 #6629199

Order 512.

4808 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#41C211yesmaximal, characteristic, complemented
2C22×#482C211yesmaximal, characteristic, complemented
3C22×#449C211yesmaximal, characteristic
4C2×#2854C211yesmaximal, characteristic, complemented
5#33006C2116yesmaximal, direct product factor
6C2×#1880C211yesmaximal, characteristic, complemented
7C2×#1880C211yesmaximal, characteristic, complemented
8C2×#1879C211yesmaximal, characteristic, complemented
9C2×#1879C211yesmaximal, characteristic, complemented
10C2×#1865C211yesmaximal, characteristic, complemented
11C2×#1863C211yesmaximal, characteristic, complemented
12C2×#1864C211yesmaximal, characteristic, complemented
13C2×#1862C211yesmaximal, characteristic, complemented
14C2×#1825C211yesmaximal, characteristic, complemented
15C2×#1817C211yesmaximal, characteristic, complemented
16C2×#1788C211yesmaximal, characteristic, complemented
17C23×#41C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×D8C2211yescharacteristic
20C22×#123—21no—
21C22×#121C2211yescharacteristic
22C2×C4×#41—24no—
23C2×C4×#41—28no—
24C2×C4×#41—28no—
25C2×C4×#41C2218yescomplemented
26C22×C4×Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×D4—21no—
29C22×C4×D4—21no—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×#117—21no—
33C22×#117C2211yescharacteristic
34C23×C42—21no—
35C23×C42C2211yescharacteristic
36C2×#482—28no—
37C2×#482C2218yescomplemented
38C2×#449—28no—
39C2×#449C2218yes—
40C22×#107C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×C22⋊C8C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52#2854—24no—
53#2854C2218yescomplemented
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#388—21no—
59C2×#388—21no—
60C2×#386—21no—
61C2×#380C2211yescharacteristic
62#1880C2218yescomplemented
63#1880C2218yescomplemented
64#1879C2218yescomplemented
65#1879C2218yescomplemented
66#1865C2218yescomplemented
67#1864C2218yescomplemented
68#1863C2218yescomplemented
69#1862C2218yescomplemented
70#1825C2218yescomplemented
71#1817C2218yescomplemented
72#1788C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C22×#41—24no—
82C22×#41—24no—
83C22×#41—24no—
84C22×#41—24no—
85C22×#41—24no—
86C22×#41—22no—
87C22×#41D418yes—
88C22×#41C2314yes—
89C23×Q8C2311yescharacteristic
90C23×D4—21no—
91C23×D4—21no—
92C23×D4C2311yescharacteristic
93C23×D4C2311yescharacteristic
94C24×C4—21no—
95C24×C4—21no—
96C24×C4—21no—
97C24×C4D411yescharacteristic
98C24×C4D411yescharacteristic
99C24×C4C2311yescharacteristic
100C22×SD16—24no—
101C22×SD16—24no—
102C22×SD16—24no—
103C22×SD16C2314yes—
104C22×D8—24no—
105C22×D8—24no—
106C22×D8—24no—
107C22×D8C2314yes—
108C23×C8C2311yescharacteristic
109C23×C8C2311yescharacteristic
110C23×C8C2311yescharacteristic
111C23×C8C2311yescharacteristic
112C2×#123—28no—
113C2×#123—48no—
114C2×#121—22no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121C2314yes—
118C4×#41—264no—
119C4×#41—232no—
120C4×#41—232no—
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8—22no—
126C2×C4×Q8—22no—
127C2×C4×Q8C2314yes—
128C2×C4×Q8C2314yes—
129C2×C4×D4—216no—
130C2×C4×D4—216no—
131C2×C4×D4—24no—
132C2×C4×D4—24no—
133C2×C4×D4—28no—
134C2×C4×D4—28no—
135C2×C4×D4—24no—
136C2×C4×D4—24no—
137C2×C4×D4—22no—
138C2×C4×D4—22no—
139C2×C4×D4C2314yes—
140C2×C4×D4C2314yes—
141C2×#117—216no—
142C2×#117—24no—
143C2×#117—22no—
144C2×#117—28no—
145C2×#117D418yes—
146C2×#117C2314yes—
147C22×C4⋊C4—21no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4—21no—
159C22×C22⋊C4—21no—
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C42—216no—
166C22×C42—21no—
167C22×C42—21no—
168C22×C42—21no—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42—28no—
172C22×C42D414yes—
173C22×C42D411yescharacteristic
174C22×C42D411yescharacteristic
175C22×C42C2314yes—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178#482—232no—
179#449—232no—
180C2×#107—24no—
181C2×#107C2314yes—
182C2×#106—24no—
183C2×#106C2314yes—
184C2×#103—24no—
185C2×#103—24no—
186C2×#103—24no—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#102—24no—
191C2×#102—24no—
192C2×#102—24no—
193C2×#102—24no—
194C2×#102—24no—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×#102C2314yes—
199C2×#102C2314yes—
200C2×C22⋊C8—24no—
201C2×C22⋊C8—24no—
202C2×C22⋊C8C2314yes—
203C2×C22⋊C8C2314yes—
204#390—22no—
205#390—22no—
206#390C2314yes—
207#390C2314yes—
208#389—22no—
209#389—22no—
210#389C2314yes—
211#389C2314yes—
212#388—28no—
213#388—28no—
214#386—28no—
215#380—22no—
216#380C2314yes—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220#340C2314yes—
221#340C2314yes—
222#340C2314yes—
223#340C2314yes—
224#336C2314yes—
225#336C2314yes—
226#336C2314yes—
227#336C2314yes—
228C25—21no—
229C25—21no—
230C25C2×D411yescharacteristic
231C2×#41—232no—
232C2×#41—232no—
233C2×#41—216no—
234C2×#41—216no—
235C2×#41—232no—
236C2×#41—28no—
237C2×#41—28no—
238C2×#41—232no—
239C2×#41—28no—
240C2×#41—28no—
241C2×#41—216no—
242C2×#41—28no—
243C2×#41C2×D4116yes—
244C22×Q8—22no—
245C22×Q8—21no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8C2×D414yes—
249C22×Q8#4114yes—
250C22×Q8#4114yes—
251C22×Q8C2412yes—
252C22×D4—28no—
253C22×D4—28no—
254C22×D4—28no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—21no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—21no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4C2×D414yes—
272C22×D4#4114yes—
273C22×D4#4114yes—
274C22×D4C2412yes—
275C22×D4C2412yes—
276C23×C4—28no—
277C23×C4—28no—
278C23×C4—21no—
279C23×C4—28no—
280C23×C4—24no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—28no—
286C23×C4—28no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—44no—
301C23×C4—44no—
302C23×C4—44no—
303C23×C4—44no—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D414yes—
307C23×C4C2×D414yes—
308C23×C4C2×D412yes—
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D414yes—
311C23×C4C2×D414yes—
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2412yes—
315C23×C4C2411yescharacteristic
316C2×SD16—28no—
317C2×SD16—28no—
318C2×SD16—28no—
319C2×SD16—416no—
320C2×D8—28no—
321C2×D8—28no—
322C2×D8—28no—
323C2×D8—416no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8C2412yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C22×C8C2412yes—
340#123—432no—
341#121—28no—
342#121—28no—
343#121—48no—
344C4×Q8—216no—
345C4×Q8—216no—
346C4×Q8—28no—
347C4×Q8—28no—
348C4×Q8—28no—
349C4×Q8—28no—
350C4×D4—264no—
351C4×D4—264no—
352C4×D4—216no—
353C4×D4—216no—
354C4×D4—28no—
355C4×D4—28no—
356C4×D4—28no—
357C4×D4—28no—
358#117—264no—
359#117—216no—
360#117—28no—
361#117C2×D4116yes—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4C2×D414yes—
384C2×C4⋊C4C2×D414yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C42—28no—
409C2×C42—28no—
410C2×C42—264no—
411C2×C42—24no—
412C2×C42—28no—
413C2×C42—216no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—28no—
423C2×C42—28no—
424C2×C42C2×D414yes—
425C2×C42C2×D412yes—
426C2×C42C2×D412yes—
427C2×C42C2×D414yes—
428C2×C42C2412yes—
429C2×C42C2412yes—
430#107—28no—
431#106—28no—
432#103—28no—
433#103—28no—
434#103—28no—
435#102—28no—
436#102—28no—
437#102—28no—
438#102—28no—
439#102—28no—
440C22⋊C8—28no—
441C22⋊C8—28no—
442#95—24no—
443#95—24no—
444#95—24no—
445C24—24no—
446C24—22no—
447C24—22no—
448C24—24no—
449C24—24no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24#12014yes—
468C24C22×D412yes—
469C24C22×D411yescharacteristic
470#41—2128no—
471#41—232no—
472#41—232no—
473#41—232no—
474#41—232no—
475C2×Q8—24no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8#123116yescomplemented
485C2×Q8C22×D414yes—
486C2×Q8C2×#4114yes—
487C2×Q8C2×#4114yes—
488C2×D4—264no—
489C2×D4—216no—
490C2×D4—216no—
491C2×D4—216no—
492C2×D4—24no—
493C2×D4—28no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—42no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—816no—
518C2×D4#123116yescomplemented
519C2×D4C22×D414yes—
520C2×D4C2×#4114yes—
521C2×D4C2×#4114yes—
522C22×C4—264no—
523C22×C4—216no—
524C22×C4—216no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—216no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—216no—
547C22×C4—216no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—416no—
568C22×C4—416no—
569C22×C4—432no—
570C22×C4—432no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—48no—
578C22×C4—48no—
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#12014yes—
589C22×C4#12018yes—
590C22×C4#13514yes—
591C22×C4AGL(1,ℤ/8)14yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D414yes—
596C22×C4C22×D414yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4C2511yescharacteristic
607SD16—416no—
608D8—416no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—44no—
622C2×C8—44no—
623C2×C8—44no—
624C2×C8—44no—
625C4⋊C4—216no—
626C4⋊C4—216no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—48no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—48no—
642C4⋊C4C22×D414yes—
643C4⋊C4C22×D414yes—
644C22⋊C4—216no—
645C22⋊C4—216no—
646C22⋊C4—216no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C42—216no—
654C42—216no—
655C42—28no—
656C42—216no—
657C42—28no—
658C42—24no—
659C42—24no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C23—28no—
665C23—216no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—28no—
672C23—28no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—44no—
678C23—48no—
679C23—44no—
680C23—48no—
681C23—44no—
682C23—48no—
683C23—44no—
684C23—48no—
685C23—48no—
686C23—48no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23—84no—
704C23—84no—
705C23C2×#12014yes—
706C23C2×#12012yes—
707C23#52512yes—
708C23#52512yes—
709C23C2×#13512yes—
710C23C2×AGL(1,ℤ/8)12yes—
711C23#57512yes—
712C23#57512yes—
713C23C23×D411yescharacteristic
714Q8—216no—
715Q8—24no—
716Q8—24no—
717Q8—24no—
718Q8C2×#12318yescomplemented
719D4—264no—
720D4—216no—
721D4—24no—
722D4—24no—
723D4—24no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—816no—
729D4—84no—
730D4C2×#12318yescomplemented
731C2×C4—264no—
732C2×C4—28no—
733C2×C4—216no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—216no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—416no—
759C2×C4—416no—
760C2×C4—432no—
761C2×C4—432no—
762C2×C4—44no—
763C2×C4—48no—
764C2×C4—44no—
765C2×C4—48no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4—84no—
782C2×C4C2×#12014yes—
783C2×C4C2×#12012yes—
784C2×C4C2×#12314yes—
785C2×C4C2×#12314yes—
786C2×C4#52512yes—
787C2×C4#52512yes—
788C2×C4#52514yes—
789C2×C4#52514yes—
790C2×C4C2×#13514yes—
791C2×C4C2×AGL(1,ℤ/8)14yes—
792C2×C4C23×D411yescharacteristic
793C2×C4C23×D411yescharacteristic
794C2×C4C22×#4111yescharacteristic
795C2×C4C22×#4111yescharacteristic
796C2×C4C22×#4111yescharacteristic
797C2×C4C22×#4111yescharacteristic
798C8—42no—
799C8—42no—
800C8—42no—
801C8—42no—
802C22—24no—
803C22—28no—
804C22—24no—
805C22—24no—
806C22—42no—
807C22—44no—
808C22—42no—
809C22—44no—
810C22—42no—
811C22—44no—
812C22—42no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—416no—
817C22—432no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—168no—
826C22#284914yes—
827C22#300214yes—
828C22#300614yes—
829C22#310214yes—
830C22#310614yes—
831C22#311114yes—
832C22#311514yes—
833C22C22×#12011yescharacteristic
834C22C2×#52511yescharacteristic
835C22C2×#52511yescharacteristic
836C22C22×#13511yescharacteristic
837C22C22×AGL(1,ℤ/8)11yescharacteristic
838C22C2×#57511yescharacteristic
839C22C2×#57511yescharacteristic
840C4—24no—
841C4—28no—
842C4—24no—
843C4—24no—
844C4—42no—
845C4—44no—
846C4—42no—
847C4—44no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4#284914yes—
852C4C22×#12311yescharacteristic
853C4C22×#12311yescharacteristic
854C4C2×#52511yescharacteristic
855C4C2×#52511yescharacteristic
856C2—44no—
857C2—48no—
858C2—162no—
859C2#3300618yesdirect product factor
860C2C2×#284911yescharacteristic
861C2C2×#300211yescharacteristic
862C2C2×#300611yescharacteristic
863C2C2×#310211yescharacteristic
864C2C2×#310611yescharacteristic
865C2C2×#311511yescharacteristic
866C2C2×#311111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×C4×#41C2semidirect
2. C22×#482C2semidirect
4. C2×#2854C2semidirect
5. #33006C2direct (N × H)
6. C2×#1880C2semidirect
7. C2×#1880C2semidirect
8. C2×#1879C2semidirect
9. C2×#1879C2semidirect
10. C2×#1865C2semidirect
11. C2×#1863C2semidirect
12. C2×#1864C2semidirect
13. C2×#1862C2semidirect
14. C2×#1825C2semidirect
15. C2×#1817C2semidirect
16. C2×#1788C2semidirect
25. C2×C4×#41C22semidirect
37. C2×#482C22semidirect
53. #2854C22semidirect
62. #1880C22semidirect
63. #1880C22semidirect
64. #1879C22semidirect
65. #1879C22semidirect
66. #1865C22semidirect
67. #1864C22semidirect
68. #1863C22semidirect
69. #1862C22semidirect
70. #1825C22semidirect
71. #1817C22semidirect
72. #1788C22semidirect
484. C2×Q8#123semidirect
518. C2×D4#123semidirect
718. Q8C2×#123semidirect
730. D4C2×#123semidirect
859. C2#33006direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×#412
C22×#4822
C22×#4492
C2×#28542
#330062
C2×#18802
C2×#18792
C2×#18652
C2×#18632
C2×#18642
C2×#18622
C2×#18252
C2×#18172
C2×#17882