Finite Group Databasebeta

← C2×#23583 #6432019

Subgroups — C2×#23583 #6432019

Order 512.

3806 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#542C211yesmaximal, characteristic, complemented
2C22×#442C211yesmaximal, characteristic, complemented
3C22×C4×SD16C211yesmaximal, characteristic, complemented
4C2×#2324C211yesmaximal, characteristic, complemented
5#23583C2116yesmaximal, direct product factor
6C2×#2058C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2034C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2023C211yesmaximal, characteristic, complemented
11C2×#2012C211yesmaximal, characteristic, complemented
12C2×#2000C211yesmaximal, characteristic, complemented
13C2×#1999C211yesmaximal, characteristic
14C2×#1763C211yesmaximal, characteristic, complemented
15C2×C4×#102C211yesmaximal, characteristic, complemented
16C2×#1750C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×D8C2211yescharacteristic
19C2×#542—28no—
20C2×#542—28no—
21C2×#542—24no—
22C2×#542C2218yescomplemented
23C22×C4⋊Q8C2211yescharacteristic
24C22×#126—21no—
25C22×#124—21no—
26C22×#124C2211yescharacteristic
27C22×#123—21no—
28C22×C22⋊Q8—21no—
29C22×C22⋊Q8C2211yescharacteristic
30C22×#121C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#442—28no—
37C2×#442C2218yescomplemented
38C2×C4×SD16—28no—
39C2×C4×SD16C2218yescomplemented
40C22×#106C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×C22⋊C8C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52C22×#97C2211yescharacteristic
53C22×C4×C8C2211yescharacteristic
54#2324—24no—
55#2324C2218yescomplemented
56C2×#390—21no—
57C2×#390C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#388—21no—
60C2×#386—21no—
61C2×#385—21no—
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64#2058C2218yescomplemented
65#2042C2218yescomplemented
66#2035C2218yescomplemented
67#2034C2218yescomplemented
68#2023C2218yescomplemented
69#2012C2218yescomplemented
70#2000C2218yescomplemented
71#1999C2218yes—
72#1763C2218yescomplemented
73C4×#102C2218yescomplemented
74#1750C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8—21no—
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4—21no—
85C23×D4C2311yescharacteristic
86C23×D4C2311yescharacteristic
87C24×C4—21no—
88C24×C4—21no—
89C24×C4C2311yescharacteristic
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16—24no—
93C22×SD16C2314yes—
94C22×D8—24no—
95C22×D8—24no—
96C22×D8—24no—
97C22×D8C2314yes—
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C23×C8C2311yescharacteristic
101C23×C8C2311yescharacteristic
102#542—264no—
103#542—232no—
104#542—232no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—22no—
108C2×C4⋊Q8C2314yes—
109C2×#126—216no—
110C2×#126—28no—
111C2×#124—216no—
112C2×#124—24no—
113C2×#124—24no—
114C2×#124—28no—
115C2×#124—22no—
116C2×#124C2314yes—
117C2×#123—216no—
118C2×#123—28no—
119C2×C22⋊Q8—216no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—28no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8C2314yes—
125C2×#121—24no—
126C2×#121—24no—
127C2×#121—22no—
128C2×#121—22no—
129C2×#121—24no—
130C2×#121—24no—
131C2×#121C2314yes—
132C2×#121C2314yes—
133C2×C4×Q8—24no—
134C2×C4×Q8—22no—
135C2×C4×Q8D418yescomplemented
136C2×C4×Q8C2314yes—
137C2×C4×D4—22no—
138C2×C4×D4—24no—
139C2×C4×D4—22no—
140C2×C4×D4—24no—
141C2×C4×D4—24no—
142C2×C4×D4D418yescomplemented
143C2×C4×D4C2314yes—
144C2×C4×D4C2314yes—
145C2×#117—24no—
146C2×#117—24no—
147C2×#117D414yes—
148C2×#117C2314yes—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4D411yescharacteristic
154C22×C4⋊C4D411yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C22⋊C4—21no—
167C22×C22⋊C4—21no—
168C22×C22⋊C4—21no—
169C22×C22⋊C4—21no—
170C22×C22⋊C4D411yescharacteristic
171C22×C22⋊C4D411yescharacteristic
172C22×C42—21no—
173C22×C42—21no—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176#442—232no—
177C4×SD16—232no—
178C2×#106—24no—
179C2×#106—24no—
180C2×#106C2314yes—
181C2×#106C2314yes—
182C2×#103—24no—
183C2×#103—24no—
184C2×#103—24no—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#102—24no—
189C2×#102—24no—
190C2×#102—24no—
191C2×#102—24no—
192C2×#102—24no—
193C2×#102C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×C22⋊C8—24no—
199C2×C22⋊C8—24no—
200C2×C22⋊C8C2314yes—
201C2×C22⋊C8C2314yes—
202C2×#97—24no—
203C2×#97C2314yes—
204C2×C4×C8—24no—
205C2×C4×C8C2314yes—
206#390—28no—
207#390—22no—
208#390C2314yes—
209#389—22no—
210#389C2314yes—
211#388—28no—
212#386—28no—
213#385—28no—
214#380—22no—
215#380C2314yes—
216C4×C4⋊C4—22no—
217C4×C4⋊C4C2314yes—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221#340C2314yes—
222#340C2314yes—
223#340C2314yes—
224#340C2314yes—
225#336C2314yes—
226#336C2314yes—
227C25—21no—
228C25—21no—
229C25C2×D411yescharacteristic
230C22×Q8—28no—
231C22×Q8—22no—
232C22×Q8—21no—
233C22×Q8—24no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—82no—
239C22×Q8—82no—
240C22×Q8C2×D414yes—
241C22×Q8C2412yes—
242C22×D4—28no—
243C22×D4—28no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—21no—
249C22×D4—22no—
250C22×D4—21no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—82no—
259C22×D4—82no—
260C22×D4—82no—
261C22×D4—82no—
262C22×D4C2×D414yes—
263C22×D4#4114yes—
264C22×D4C2412yes—
265C22×D4C2412yes—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—28no—
277C23×C4—24no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—24no—
281C23×C4—44no—
282C23×C4—82no—
283C23×C4—82no—
284C23×C4—82no—
285C23×C4—82no—
286C23×C4C2×D412yes—
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C2×SD16—232no—
295C2×SD16—28no—
296C2×SD16—28no—
297C2×SD16—28no—
298C2×D8—232no—
299C2×D8—28no—
300C2×D8—28no—
301C2×D8—28no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8#4114yes—
313C22×C8#4114yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C4⋊Q8—216no—
319C4⋊Q8—28no—
320C4⋊Q8—28no—
321#126—264no—
322#124—264no—
323#124—216no—
324#124—28no—
325#124—28no—
326#123—264no—
327C22⋊Q8—264no—
328C22⋊Q8—216no—
329C22⋊Q8—28no—
330C22⋊Q8—28no—
331#121—216no—
332#121—216no—
333#121—28no—
334#121—28no—
335#121—28no—
336#121—28no—
337C4×Q8—216no—
338C4×Q8—28no—
339C4×Q8C2×D4116yescomplemented
340C4×D4—216no—
341C4×D4—28no—
342C4×D4—28no—
343C4×D4—28no—
344C4×D4—48no—
345C4×D4C2×D4116yescomplemented
346#117—216no—
347#117—28no—
348#117—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—82no—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4C2×D414yes—
373C2×C4⋊C4C2×D414yes—
374C2×C4⋊C4C2×D414yes—
375C2×C4⋊C4#4114yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
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—44no—
400C2×C22⋊C4—82no—
401C2×C22⋊C4—82no—
402C2×C22⋊C4—82no—
403C2×C22⋊C4C2×D414yes—
404C2×C22⋊C4C2×D414yes—
405C2×C42—28no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—82no—
411C2×C42C2×D412yes—
412C2×C42C2×D412yes—
413C2×C42C2×D414yes—
414C2×C42C2×D414yes—
415C2×C42C2412yes—
416C2×C42C2412yes—
417#106—28no—
418#106—28no—
419#103—28no—
420#103—28no—
421#103—28no—
422#102—28no—
423#102—28no—
424#102—28no—
425#102—28no—
426#102—28no—
427C22⋊C8—28no—
428C22⋊C8—28no—
429#97—28no—
430C4×C8—28no—
431#95—24no—
432#95—24no—
433#95—24no—
434C24—22no—
435C24—24no—
436C24—24no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24C22×D412yes—
458C24C22×D411yescharacteristic
459C2×Q8—216no—
460C2×Q8—24no—
461C2×Q8—22no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—44no—
469C2×Q8—42no—
470C2×Q8—44no—
471C2×Q8—42no—
472C2×Q8—84no—
473C2×Q8—84no—
474C2×Q8—816no—
475C2×Q8C22×D414yes—
476C2×D4—216no—
477C2×D4—216no—
478C2×D4—24no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—24no—
483C2×D4—28no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—44no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—84no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—816no—
507C2×D4—816no—
508C2×D4C22×D414yes—
509C2×D4C2×#4114yes—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—216no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—48no—
562C22×C4—816no—
563C22×C4—84no—
564C22×C4—84no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4—816no—
568C22×C4#12014yes—
569C22×C4#12014yes—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D412yes—
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C2×#4112yes—
579C22×C4C2×#4112yes—
580C22×C4C2×#4112yes—
581C22×C4C2×#4112yes—
582C22×C4C2511yescharacteristic
583SD16—232no—
584D8—232no—
585C2×C8—28no—
586C2×C8—28no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—44no—
598C2×C8—44no—
599C2×C8C2×#4114yes—
600C2×C8C2×#4114yes—
601C4⋊C4—216no—
602C4⋊C4—216no—
603C4⋊C4—216no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—84no—
619C4⋊C4C22×D414yes—
620C4⋊C4C22×D414yes—
621C4⋊C4C2×#4114yes—
622C22⋊C4—216no—
623C22⋊C4—216no—
624C22⋊C4—216no—
625C22⋊C4—216no—
626C22⋊C4—216no—
627C22⋊C4—216no—
628C22⋊C4—28no—
629C22⋊C4—28no—
630C22⋊C4—48no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C42—216no—
635C42—24no—
636C42—22no—
637C42—22no—
638C42—84no—
639C42#12018yes—
640C42C22×D414yes—
641C42C22×D414yes—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—44no—
652C23—48no—
653C23—44no—
654C23—48no—
655C23—44no—
656C23—48no—
657C23—48no—
658C23—44no—
659C23—42no—
660C23—44no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—44no—
665C23—48no—
666C23—48no—
667C23—44no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23C2×#12012yes—
685C23#52512yes—
686C23#53212yes—
687C23#57612yes—
688C23#57712yes—
689C23#57712yes—
690C23#57712yes—
691C23C23×D411yescharacteristic
692Q8—24no—
693Q8—24no—
694Q8—48no—
695Q8—42no—
696Q8—42no—
697Q8—816no—
698D4—24no—
699D4—24no—
700D4—24no—
701D4—24no—
702D4—48no—
703D4—48no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—816no—
709D4—816no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—48no—
730C2×C4—44no—
731C2×C4—48no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—48no—
737C2×C4—48no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—48no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—816no—
756C2×C4—816no—
757C2×C4—84no—
758C2×C4—84no—
759C2×C4C2×#12014yes—
760C2×C4C2×#12014yes—
761C2×C4C2×#12012yes—
762C2×C4#52512yes—
763C2×C4#52514yes—
764C2×C4#52514yes—
765C2×C4#53212yes—
766C2×C4#53214yes—
767C2×C4#53214yes—
768C2×C4C23×D411yescharacteristic
769C2×C4C23×D411yescharacteristic
770C2×C4C22×#4111yescharacteristic
771C2×C4C22×#4111yescharacteristic
772C2×C4C22×#4111yescharacteristic
773C2×C4C22×#4111yescharacteristic
774C8—24no—
775C8—24no—
776C8—42no—
777C8—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—44no—
782C22—42no—
783C22—44no—
784C22—42no—
785C22—44no—
786C22—44no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—88no—
796C22—816no—
797C22—816no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22#238814yes—
803C22#301014yes—
804C22#301214yes—
805C22#311814yes—
806C22#312514yes—
807C22#317314yes—
808C22#317914yes—
809C22C22×#12011yescharacteristic
810C22C2×#52511yescharacteristic
811C22C2×#53211yescharacteristic
812C22C2×#57611yescharacteristic
813C22C2×#57711yescharacteristic
814C22C2×#57711yescharacteristic
815C22C2×#57711yescharacteristic
816C4—24no—
817C4—24no—
818C4—44no—
819C4—42no—
820C4—42no—
821C4—44no—
822C4—44no—
823C4—42no—
824C4—44no—
825C4—82no—
826C4—82no—
827C4#238814yes—
828C4C2×#52511yescharacteristic
829C4C2×#52511yescharacteristic
830C4C2×#53211yescharacteristic
831C4C2×#53211yescharacteristic
832C2—82no—
833C2—84no—
834C2—84no—
835C2#2358318yesdirect product factor
836C2C2×#238811yescharacteristic
837C2C2×#301011yescharacteristic
838C2C2×#301211yescharacteristic
839C2C2×#311811yescharacteristic
840C2C2×#312511yescharacteristic
841C2C2×#317311yescharacteristic
842C2C2×#317911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#542C2semidirect
2. C22×#442C2semidirect
3. C22×C4×SD16C2semidirect
4. C2×#2324C2semidirect
5. #23583C2direct (N × H)
6. C2×#2058C2semidirect
7. C2×#2042C2semidirect
8. C2×#2034C2semidirect
9. C2×#2035C2semidirect
10. C2×#2023C2semidirect
11. C2×#2012C2semidirect
12. C2×#2000C2semidirect
14. C2×#1763C2semidirect
15. C2×C4×#102C2semidirect
16. C2×#1750C2semidirect
22. C2×#542C22semidirect
37. C2×#442C22semidirect
39. C2×C4×SD16C22semidirect
55. #2324C22semidirect
64. #2058C22semidirect
65. #2042C22semidirect
66. #2035C22semidirect
67. #2034C22semidirect
68. #2023C22semidirect
69. #2012C22semidirect
70. #2000C22semidirect
72. #1763C22semidirect
73. C4×#102C22semidirect
74. #1750C22semidirect
135. C2×C4×Q8D4semidirect
142. C2×C4×D4D4semidirect
339. C4×Q8C2×D4semidirect
345. C4×D4C2×D4semidirect
835. C2#23583direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5422
C22×#4422
C22×C4×SD162
C2×#23242
#235832
C2×#20582
C2×#20422
C2×#20342
C2×#20352
C2×#20232
C2×#20122
C2×#20002
C2×#19992
C2×#17632
C2×C4×#1022
C2×#17502