Finite Group Databasebeta

← C2×#25099 #6438760

Subgroups — C2×#25099 #6438760

Order 512.

3460 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#468C211yesmaximal, characteristic
2C22×#461C211yesmaximal, characteristic, complemented
3C22×#448C211yesmaximal, characteristic
4C22×#419C211yesmaximal, characteristic, complemented
5C2×#2434C211yesmaximal, characteristic, complemented
6C2×#2363C211yesmaximal, characteristic
7#25099C2116yesmaximal, direct product factor
8C2×#2068C211yesmaximal, characteristic, complemented
9C2×#2055C211yesmaximal, characteristic, complemented
10C2×#2043C211yesmaximal, characteristic, complemented
11C2×#2013C211yesmaximal, characteristic, complemented
12C2×#1981C211yesmaximal, characteristic, complemented
13C2×#1928C211yesmaximal, characteristic, complemented
14C2×#1877C211yesmaximal, characteristic, complemented
15C2×#1873C211yesmaximal, characteristic, complemented
16C2×#1851C211yesmaximal, characteristic, complemented
17C24×Q8C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C23×SD16C2211yescharacteristic
21C23×M16C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C2×#468—28no—
29C2×#468C2218yes—
30C2×#461—28no—
31C2×#461C2218yescomplemented
32C2×#448—28no—
33C2×#448C2218yes—
34C22×#107C2211yescharacteristic
35C22×C4⋊C8C2211yescharacteristic
36C22×C4⋊C8C2211yescharacteristic
37C2×#419—28no—
38C2×#419C2218yescomplemented
39C22×#103C2211yescharacteristic
40C22×#103C2211yescharacteristic
41C22×#103C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×C22⋊C8C2211yescharacteristic
50#2434—24no—
51#2434C2218yescomplemented
52C2×#395—21no—
53C2×#395—21no—
54#2363—24no—
55#2363C2218yes—
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#390—21no—
59C2×#390C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#388—21no—
62C2×#386—21no—
63C2×#385—21no—
64C2×#385—21no—
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4—21no—
67C2×C4×C22⋊C4C2211yescharacteristic
68#2068C2218yescomplemented
69#2055C2218yescomplemented
70#2043C2218yescomplemented
71#2013C2218yescomplemented
72#1981C2218yescomplemented
73#1928C2218yescomplemented
74#1877C2218yescomplemented
75#1873C2218yescomplemented
76#1851C2218yescomplemented
77C2×#340C2211yescharacteristic
78C2×#340C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8—21no—
82C23×Q8—22no—
83C23×Q8—24no—
84C23×Q8—24no—
85C23×Q8—24no—
86C23×Q8—24no—
87C23×Q8—42no—
88C23×Q8—42no—
89C23×Q8C2311yescharacteristic
90C23×Q8C2311yescharacteristic
91C23×Q8C2311yescharacteristic
92C23×Q8C2314yes—
93C23×D4—21no—
94C23×D4C2311yescharacteristic
95C24×C4—21no—
96C24×C4—21no—
97C24×C4C2311yescharacteristic
98C22×SD16—24no—
99C22×SD16—24no—
100C22×SD16—24no—
101C22×SD16—24no—
102C22×SD16—24no—
103C22×SD16—24no—
104C22×SD16—42no—
105C22×SD16—42no—
106C22×SD16—42no—
107C22×SD16C2314yes—
108C22×SD16C2314yes—
109C22×SD16C2314yes—
110C22×M16—24no—
111C22×M16—24no—
112C22×M16—42no—
113C22×M16C2314yes—
114C23×C8C2311yescharacteristic
115C23×C8C2311yescharacteristic
116C23×C8C2311yescharacteristic
117C23×C8C2311yescharacteristic
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—22no—
121C2×C4⋊Q8—22no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8—42no—
124C2×C4⋊Q8C2314yes—
125C2×C4⋊Q8C2314yes—
126C2×C22⋊Q8—22no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8C2314yes—
130C2×#121—22no—
131C2×#121—24no—
132C2×#121D418yes—
133C2×#121C2314yes—
134C2×C4×D4—24no—
135C2×C4×D4—22no—
136C2×C4×D4—42no—
137C2×C4×D4C2314yes—
138C2×#117—22no—
139C2×#117—24no—
140C2×#117—42no—
141C2×#117C2314yes—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C22⋊C4D411yescharacteristic
159C22×C22⋊C4D411yescharacteristic
160C22×C42—21no—
161C22×C42—21no—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#468—232no—
165#461—232no—
166#448—232no—
167C2×#107—24no—
168C2×#107C2314yes—
169C2×C4⋊C8—24no—
170C2×C4⋊C8—42no—
171C2×C4⋊C8C2314yes—
172C2×C4⋊C8C2314yes—
173#419—232no—
174C2×#103—24no—
175C2×#103—24no—
176C2×#103—24no—
177C2×#103—24no—
178C2×#103—24no—
179C2×#103—24no—
180C2×#103—24no—
181C2×#103—42no—
182C2×#103D418yescomplemented
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#102—24no—
193C2×#102C2314yes—
194C2×C22⋊C8—24no—
195C2×C22⋊C8C2314yes—
196#395—28no—
197#395—28no—
198#391—22no—
199#391—22no—
200#391C2314yes—
201#391C2314yes—
202#390—28no—
203#390—22no—
204#390C2314yes—
205#389—22no—
206#389C2314yes—
207#388—28no—
208#386—28no—
209#385—28no—
210#385—28no—
211C4×C4⋊C4—22no—
212C4×C4⋊C4C2314yes—
213C4×C22⋊C4—28no—
214C4×C22⋊C4D414yes—
215C4×C22⋊C4C2314yes—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221C2×#95—21no—
222C2×#95D411yescharacteristic
223C2×#95D411yescharacteristic
224#340C2314yes—
225#340C2314yes—
226#336C2314yes—
227#336C2314yes—
228C25—21no—
229C25C2×D411yescharacteristic
230C22×Q8—21no—
231C22×Q8—21no—
232C22×Q8—21no—
233C22×Q8—24no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—232no—
237C22×Q8—28no—
238C22×Q8—28no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—28no—
245C22×Q8—28no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—44no—
256C22×Q8—44no—
257C22×Q8—44no—
258C22×Q8—44no—
259C22×Q8—48no—
260C22×Q8—416no—
261C22×Q8—48no—
262C22×Q8—416no—
263C22×Q8—416no—
264C22×Q8—44no—
265C22×Q8—48no—
266C22×Q8C2×D414yes—
267C22×Q8#4114yes—
268C22×Q8C2412yes—
269C22×Q8C2412yes—
270C22×Q8C2412yes—
271C22×D4—28no—
272C22×D4—24no—
273C22×D4—22no—
274C22×D4—21no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—82no—
280C22×D4—82no—
281C22×D4C2×D414yes—
282C22×D4C2412yes—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—24no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—24no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4—44no—
299C23×C4—44no—
300C23×C4—44no—
301C23×C4—82no—
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D412yes—
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D414yes—
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4#4114yes—
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C2×SD16—28no—
313C2×SD16—28no—
314C2×SD16—28no—
315C2×SD16—28no—
316C2×SD16—28no—
317C2×SD16—28no—
318C2×SD16—44no—
319C2×SD16—44no—
320C2×SD16—44no—
321C2×SD16—416no—
322C2×SD16—416no—
323C2×SD16—416no—
324C2×M16—28no—
325C2×M16—28no—
326C2×M16—44no—
327C2×M16—416no—
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×C8—22no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8C2×D414yes—
340C22×C8C2412yes—
341C22×C8C2412yes—
342C22×C8C2412yes—
343C22×C8C2412yes—
344C4⋊Q8—28no—
345C4⋊Q8—28no—
346C4⋊Q8—44no—
347C4⋊Q8—44no—
348C4⋊Q8—48no—
349C4⋊Q8—48no—
350C22⋊Q8—28no—
351C22⋊Q8—28no—
352C22⋊Q8—48no—
353#121—216no—
354#121—28no—
355#121C2×D4116yes—
356C4×D4—28no—
357C4×D4—44no—
358C4×D4—48no—
359#117—28no—
360#117—44no—
361#117—48no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—82no—
384C2×C4⋊C4C2×D414yes—
385C2×C4⋊C4C2×D414yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C22⋊C4—28no—
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—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—82no—
404C2×C22⋊C4C2×D414yes—
405C2×C22⋊C4C2×D414yes—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—44no—
413C2×C42—82no—
414C2×C42C2×D412yes—
415C2×C42C2×D412yes—
416C2×C42C2412yes—
417C2×C42C2412yes—
418#107—28no—
419C4⋊C8—28no—
420C4⋊C8—44no—
421#103—28no—
422#103—28no—
423#103—28no—
424#103—28no—
425#103—28no—
426#103—28no—
427#103—28no—
428#103—44no—
429#103C2×D4116yescomplemented
430#102—28no—
431C22⋊C8—28no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95C2×D414yes—
439#95C2×D414yes—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—24no—
447C24—22no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24#12114yes—
455C24C22×D412yes—
456C24C22×D411yescharacteristic
457C2×Q8—24no—
458C2×Q8—24no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—232no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—48no—
481C2×Q8—48no—
482C2×Q8—416no—
483C2×Q8—416no—
484C2×Q8—432no—
485C2×Q8—464no—
486C2×Q8—416no—
487C2×Q8—48no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—44no—
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8C22×D414yes—
504C2×Q8C2×#4114yes—
505C2×D4—216no—
506C2×D4—24no—
507C2×D4—28no—
508C2×D4—28no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—816no—
519C2×D4—84no—
520C2×D4—84no—
521C2×D4C22×D414yes—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—24no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—24no—
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—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—432no—
559C22×C4—48no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—48no—
578C22×C4—84no—
579C22×C4—816no—
580C22×C4#12114yes—
581C22×C4#12118yes—
582C22×C4#13714yes—
583C22×C4#13714yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4C2511yescharacteristic
599SD16—416no—
600SD16—416no—
601SD16—416no—
602M16—416no—
603C2×C8—28no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—44no—
616C2×C8—44no—
617C2×C8—44no—
618C2×C8C22×D414yes—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—42no—
632C4⋊C4—48no—
633C4⋊C4—42no—
634C4⋊C4—84no—
635C4⋊C4C22×D414yes—
636C4⋊C4C22×D414yes—
637C22⋊C4—216no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—84no—
645C42—24no—
646C42—24no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—48no—
652C42—84no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—28no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—48no—
668C23—42no—
669C23—42no—
670C23—48no—
671C23—48no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23C2×#12114yes—
681C23C2×#12112yes—
682C23D4212yes—
683C23#54612yes—
684C23C2×#13712yes—
685C23C2×#13712yes—
686C23#57712yes—
687C23#57712yes—
688C23C23×D411yescharacteristic
689Q8—24no—
690Q8—24no—
691Q8—24no—
692Q8—24no—
693Q8—432no—
694Q8—48no—
695Q8—48no—
696Q8—42no—
697Q8—42no—
698Q8—42no—
699Q8—42no—
700Q8—42no—
701Q8—42no—
702Q8—42no—
703Q8—42no—
704Q8—84no—
705D4—24no—
706D4—24no—
707D4—42no—
708D4—48no—
709D4—42no—
710D4—816no—
711C2×C4—28no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—216no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—432no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—48no—
740C2×C4—48no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—48no—
744C2×C4—44no—
745C2×C4—48no—
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—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—816no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4C2×#12114yes—
764C2×C4C2×#12112yes—
765C2×C4#52514yes—
766C2×C4#53814yes—
767C2×C4D4212yes—
768C2×C4D4214yes—
769C2×C4#54612yes—
770C2×C4#54614yes—
771C2×C4C2×#13714yes—
772C2×C4C2×#13714yes—
773C2×C4C23×D411yescharacteristic
774C2×C4C23×D411yescharacteristic
775C2×C4C22×#4111yescharacteristic
776C2×C4C22×#4111yescharacteristic
777C2×C4C2×H(5,𝔽2)11yescharacteristic
778C2×C4C2×H(5,𝔽2)11yescharacteristic
779C8—24no—
780C8—42no—
781C8—42no—
782C8—42no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—416no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—816no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22#242414yes—
800C22#303914yes—
801C22#304214yes—
802C22#326614yes—
803C22#327814yes—
804C22#332014yes—
805C22#332914yes—
806C22C22×#12111yescharacteristic
807C22C2×D4211yescharacteristic
808C22C2×#54611yescharacteristic
809C22C22×#13711yescharacteristic
810C22C22×#13711yescharacteristic
811C22C2×#57711yescharacteristic
812C22C2×#57711yescharacteristic
813C4—24no—
814C4—24no—
815C4—24no—
816C4—44no—
817C4—44no—
818C4—44no—
819C4—44no—
820C4—42no—
821C4—42no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4#242414yes—
826C4C2×#52511yescharacteristic
827C4C2×#53811yescharacteristic
828C4C2×D4211yescharacteristic
829C4C2×#54611yescharacteristic
830C2—44no—
831C2—84no—
832C2#2509918yesdirect product factor
833C2C2×#242411yescharacteristic
834C2C2×#303911yescharacteristic
835C2C2×#304211yescharacteristic
836C2C2×#326611yescharacteristic
837C2C2×#327811yescharacteristic
838C2C2×#332011yescharacteristic
839C2C2×#332911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#461C2semidirect
4. C22×#419C2semidirect
5. C2×#2434C2semidirect
7. #25099C2direct (N × H)
8. C2×#2068C2semidirect
9. C2×#2055C2semidirect
10. C2×#2043C2semidirect
11. C2×#2013C2semidirect
12. C2×#1981C2semidirect
13. C2×#1928C2semidirect
14. C2×#1877C2semidirect
15. C2×#1873C2semidirect
16. C2×#1851C2semidirect
31. C2×#461C22semidirect
38. C2×#419C22semidirect
51. #2434C22semidirect
68. #2068C22semidirect
69. #2055C22semidirect
70. #2043C22semidirect
71. #2013C22semidirect
72. #1981C22semidirect
73. #1928C22semidirect
74. #1877C22semidirect
75. #1873C22semidirect
76. #1851C22semidirect
182. C2×#103D4semidirect
429. #103C2×D4semidirect
832. C2#25099direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4682
C22×#4612
C22×#4482
C22×#4192
C2×#24342
C2×#23632
#250992
C2×#20682
C2×#20552
C2×#20432
C2×#20132
C2×#19812
C2×#19282
C2×#18772
C2×#18732
C2×#18512