Finite Group Databasebeta

← C2×#26945 #6443536

Subgroups — C2×#26945 #6443536

Order 512.

2798 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#484C211yesmaximal, characteristic, complemented
2C22×#461C211yesmaximal, characteristic, complemented
3C2×#2429C211yesmaximal, characteristic, complemented
4C2×#2361C211yesmaximal, characteristic
5#26945C2116yesmaximal, direct product factor
6C2×#2086C211yesmaximal, characteristic, complemented
7C2×#2043C211yesmaximal, characteristic, complemented
8C2×#2000C211yesmaximal, characteristic
9C2×#2000C211yesmaximal, characteristic
10C2×#1973C211yesmaximal, characteristic, complemented
11C2×#1928C211yesmaximal, characteristic, complemented
12C2×#1924C211yesmaximal, characteristic, complemented
13C2×#1880C211yesmaximal, characteristic, complemented
14C2×#1872C211yesmaximal, characteristic, complemented
15C2×#1862C211yesmaximal, characteristic, complemented
16C2×#1763C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C22×C4⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×C4×D4—21no—
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C2×#484—28no—
28C2×#484C2218yescomplemented
29C2×#461—28no—
30C2×#461C2218yescomplemented
31C22×#107C2211yescharacteristic
32C22×#107C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#103C2211yescharacteristic
39C22×#103C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×#97C2211yescharacteristic
45#2429—24no—
46#2429C2218yescomplemented
47C2×#398—21no—
48C2×#396—21no—
49#2361—24no—
50#2361C2218yes—
51C2×#391C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389—21no—
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#388—21no—
57C2×#388—21no—
58C2×#386—21no—
59C2×#385—21no—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#2086C2218yescomplemented
63#2043C2218yescomplemented
64#2000C2218yes—
65#2000C2218yes—
66#1973C2218yescomplemented
67#1928C2218yescomplemented
68#1924C2218yescomplemented
69#1880C2218yescomplemented
70#1872C2218yescomplemented
71#1862C2218yescomplemented
72#1763C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×Q8C2311yescharacteristic
81C23×D4—21no—
82C23×D4C2311yescharacteristic
83C24×C4—21no—
84C24×C4—21no—
85C24×C4C2311yescharacteristic
86C22×SD16—24no—
87C22×SD16—24no—
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—42no—
91C22×SD16—42no—
92C22×SD16C2314yes—
93C22×SD16C2314yes—
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—22no—
100C2×C4⋊Q8—42no—
101C2×C4⋊Q8C2314yes—
102C2×C22⋊Q8—22no—
103C2×C22⋊Q8—22no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—42no—
107C2×C22⋊Q8—42no—
108C2×C22⋊Q8C2314yes—
109C2×C22⋊Q8C2314yes—
110C2×#121—24no—
111C2×#121—22no—
112C2×#121—24no—
113C2×#121C2314yes—
114C2×C4×Q8—22no—
115C2×C4×Q8—24no—
116C2×C4×Q8—42no—
117C2×C4×Q8C2314yes—
118C2×C4×D4—28no—
119C2×C4×D4—24no—
120C2×C4×D4—22no—
121C2×C4×D4—42no—
122C2×C4×D4—48no—
123C2×C4×D4C2314yes—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—22no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—42no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4D411yescharacteristic
148C22×C22⋊C4D411yescharacteristic
149C22×C42—21no—
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#484—232no—
154#461—232no—
155C2×#107—24no—
156C2×#107—24no—
157C2×#107C2314yes—
158C2×#107C2314yes—
159C2×C4⋊C8—24no—
160C2×C4⋊C8C2314yes—
161C2×#103—24no—
162C2×#103—24no—
163C2×#103—24no—
164C2×#103—24no—
165C2×#103—42no—
166C2×#103D418yescomplemented
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#102—24no—
174C2×#102—42no—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8—24no—
178C2×C22⋊C8—42no—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2314yes—
181C2×#97—42no—
182C2×#97C2314yes—
183#398—28no—
184#396—28no—
185#391—22no—
186#391C2314yes—
187#390—22no—
188#390C2314yes—
189#389—22no—
190#389—22no—
191#389—28no—
192#389C2314yes—
193#389C2314yes—
194#388—28no—
195#388—28no—
196#386—28no—
197#385—28no—
198C4×C4⋊C4—22no—
199C4×C4⋊C4C2314yes—
200C4×C22⋊C4D414yes—
201C4×C22⋊C4C2314yes—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25C2×D411yescharacteristic
217C22×Q8—21no—
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8C2×D414yes—
231C22×Q8C2412yes—
232C22×Q8C2412yes—
233C22×D4—28no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—21no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4#4114yes—
244C22×D4C2412yes—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4—82no—
265C23×C4—82no—
266C23×C4C2×D412yes—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C2×SD16—28no—
275C2×SD16—28no—
276C2×SD16—28no—
277C2×SD16—28no—
278C2×SD16—44no—
279C2×SD16—44no—
280C2×SD16—416no—
281C2×SD16—416no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8C2×D414yes—
294C22×C8C2412yes—
295C22×C8C2412yes—
296C22×C8C2412yes—
297C22×C8C2412yes—
298C4⋊Q8—28no—
299C4⋊Q8—44no—
300C4⋊Q8—48no—
301C22⋊Q8—28no—
302C22⋊Q8—28no—
303C22⋊Q8—44no—
304C22⋊Q8—44no—
305C22⋊Q8—48no—
306C22⋊Q8—48no—
307#121—216no—
308#121—28no—
309#121—28no—
310C4×Q8—28no—
311C4×Q8—44no—
312C4×Q8—48no—
313C4×D4—28no—
314C4×D4—44no—
315C4×D4—48no—
316C4×D4—432no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—48no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4#4114yes—
350C2×C4⋊C4#4114yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—82no—
370C2×C22⋊C4C2×D414yes—
371C2×C22⋊C4C2×D414yes—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—44no—
379C2×C42—44no—
380C2×C42C2×D412yes—
381C2×C42C2×D412yes—
382C2×C42C2412yes—
383C2×C42C2412yes—
384#107—28no—
385#107—28no—
386C4⋊C8—28no—
387#103—28no—
388#103—28no—
389#103—28no—
390#103—28no—
391#103—44no—
392#103C2×D4116yescomplemented
393#102—28no—
394#102—44no—
395C22⋊C8—28no—
396C22⋊C8—44no—
397#97—44no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95C2×D414yes—
404#95C2×D414yes—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—22no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24#13714yes—
420C24C22×D412yes—
421C24C22×D411yescharacteristic
422C2×Q8—24no—
423C2×Q8—22no—
424C2×Q8—28no—
425C2×Q8—28no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8—44no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8C22×D414yes—
448C2×D4—216no—
449C2×D4—24no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—48no—
458C2×D4—432no—
459C2×D4—48no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4C2×#4114yes—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—48no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—48no—
524C22×C4—84no—
525C22×C4—816no—
526C22×C4—84no—
527C22×C4—816no—
528C22×C4AGL(1,ℤ/8)14yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D412yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4112yes—
539C22×C4H(5,𝔽2)12yes—
540C22×C4H(5,𝔽2)12yes—
541C22×C4C2511yescharacteristic
542SD16—416no—
543SD16—416no—
544C2×C8—28no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—44no—
557C2×C8—44no—
558C2×C8—44no—
559C2×C8C22×D414yes—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—48no—
571C4⋊C4—48no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4C22×D414yes—
581C4⋊C4C2×#4114yes—
582C4⋊C4C2×#4114yes—
583C22⋊C4—216no—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—84no—
591C42—24no—
592C42—24no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—48no—
598C42—48no—
599C23—28no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—28no—
604C23—28no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—48no—
614C23—48no—
615C23—42no—
616C23—42no—
617C23—48no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—84no—
623C23—84no—
624C23—84no—
625C23—84no—
626C23#52512yes—
627C23D4212yes—
628C23#54612yes—
629C23C2×AGL(1,ℤ/8)12yes—
630C23C2×#13714yes—
631C23C2×#13712yes—
632C23#57712yes—
633C23#57812yes—
634C23C23×D411yescharacteristic
635Q8—24no—
636Q8—24no—
637Q8—42no—
638Q8—42no—
639Q8—48no—
640Q8—42no—
641Q8—42no—
642Q8—42no—
643Q8—42no—
644Q8—84no—
645D4—24no—
646D4—24no—
647D4—432no—
648D4—42no—
649D4—42no—
650D4—48no—
651C2×C4—22no—
652C2×C4—28no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—44no—
671C2×C4—48no—
672C2×C4—48no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—44no—
676C2×C4—48no—
677C2×C4—48no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—48no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—816no—
701C2×C4—816no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4—84no—
705C2×C4#52512yes—
706C2×C4#53214yes—
707C2×C4#54014yes—
708C2×C4D4212yes—
709C2×C4#54614yes—
710C2×C4#54612yes—
711C2×C4#55314yes—
712C2×C4C2×AGL(1,ℤ/8)14yes—
713C2×C4C23×D411yescharacteristic
714C2×C4C22×#4111yescharacteristic
715C2×C4C22×#4111yescharacteristic
716C2×C4C22×#4111yescharacteristic
717C2×C4C2×H(5,𝔽2)11yescharacteristic
718C2×C4C2×H(5,𝔽2)11yescharacteristic
719C8—24no—
720C8—42no—
721C8—42no—
722C8—42no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—416no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—816no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22#246414yes—
740C22#311014yes—
741C22#312014yes—
742C22#326514yes—
743C22#327014yes—
744C22#332014yes—
745C22#333014yes—
746C22C2×#52511yescharacteristic
747C22C2×D4211yescharacteristic
748C22C2×#54611yescharacteristic
749C22C22×AGL(1,ℤ/8)11yescharacteristic
750C22C22×#13711yescharacteristic
751C22C2×#57711yescharacteristic
752C22C2×#57811yescharacteristic
753C4—24no—
754C4—44no—
755C4—42no—
756C4—42no—
757C4—44no—
758C4—44no—
759C4—42no—
760C4—42no—
761C4—44no—
762C4—82no—
763C4—82no—
764C4—82no—
765C4#246414yes—
766C4C2×#53211yescharacteristic
767C4C2×#54011yescharacteristic
768C4C2×#54611yescharacteristic
769C4C2×#55311yescharacteristic
770C2—44no—
771C2—84no—
772C2#2694518yesdirect product factor
773C2C2×#246411yescharacteristic
774C2C2×#311011yescharacteristic
775C2C2×#312011yescharacteristic
776C2C2×#326511yescharacteristic
777C2C2×#327011yescharacteristic
778C2C2×#332011yescharacteristic
779C2C2×#333011yescharacteristic
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
1. C22×#484C2semidirect
2. C22×#461C2semidirect
3. C2×#2429C2semidirect
5. #26945C2direct (N × H)
6. C2×#2086C2semidirect
7. C2×#2043C2semidirect
10. C2×#1973C2semidirect
11. C2×#1928C2semidirect
12. C2×#1924C2semidirect
13. C2×#1880C2semidirect
14. C2×#1872C2semidirect
15. C2×#1862C2semidirect
16. C2×#1763C2semidirect
28. C2×#484C22semidirect
30. C2×#461C22semidirect
46. #2429C22semidirect
62. #2086C22semidirect
63. #2043C22semidirect
66. #1973C22semidirect
67. #1928C22semidirect
68. #1924C22semidirect
69. #1880C22semidirect
70. #1872C22semidirect
71. #1862C22semidirect
72. #1763C22semidirect
166. C2×#103D4semidirect
392. #103C2×D4semidirect
772. C2#26945direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4842
C22×#4612
C2×#24292
C2×#23612
#269452
C2×#20862
C2×#20432
C2×#20002
C2×#19732
C2×#19282
C2×#19242
C2×#18802
C2×#18722
C2×#18622
C2×#17632