Finite Group Databasebeta

← C2×#30558 #7501157

Subgroups — C2×#30558 #7501157

Order 512.

2660 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#482C211yesmaximal, characteristic, complemented
2C22×#465C211yesmaximal, characteristic, complemented
3C2×#2535C211yesmaximal, characteristic
4C2×#2415C211yesmaximal, characteristic, complemented
5#30558C2116yesmaximal, direct product factor
6C2×#2097C211yesmaximal, characteristic, complemented
7C2×#2085C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#2033C211yesmaximal, characteristic, complemented
11C2×#2000C211yesmaximal, characteristic, complemented
12C2×#1877C211yesmaximal, characteristic, complemented
13C2×#1869C211yesmaximal, characteristic, complemented
14C2×#1864C211yesmaximal, characteristic, complemented
15C2×#1854C211yesmaximal, characteristic, complemented
16C2×#1807C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C24×C8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C2×#482—28no—
27C2×#482C2218yescomplemented
28C2×#465—28no—
29C2×#465C2218yescomplemented
30C22×#107C2211yescharacteristic
31C22×#107C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×#106C2211yescharacteristic
34C22×#106C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#103C2211yescharacteristic
37C22×#103C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44#2535—24no—
45#2535C2218yes—
46#2415—24no—
47#2415C2218yescomplemented
48C2×#397—21no—
49C2×#397—21no—
50C2×#394—21no—
51C2×#392—21no—
52C2×#391C2211yescharacteristic
53C2×#389—21no—
54C2×#389C2211yescharacteristic
55C2×#388—21no—
56C2×#386—21no—
57C2×#386—21no—
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62#2097C2218yescomplemented
63#2085C2218yescomplemented
64#2036C2218yescomplemented
65#2035C2218yescomplemented
66#2033C2218yescomplemented
67#2000C2218yescomplemented
68#1877C2218yescomplemented
69#1869C2218yescomplemented
70#1864C2218yescomplemented
71#1854C2218yescomplemented
72#1807C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4D411yescharacteristic
83C23×D4C2311yescharacteristic
84C24×C4—21no—
85C24×C4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C22×SD16—24no—
88C22×SD16—24no—
89C22×SD16—42no—
90C22×SD16C2314yes—
91C23×C8—24no—
92C23×C8—24no—
93C23×C8—42no—
94C23×C8C2311yescharacteristic
95C23×C8C2311yescharacteristic
96C23×C8C2314yes—
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C2×C22⋊Q8—22no—
100C2×C22⋊Q8—22no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—42no—
103C2×C22⋊Q8—42no—
104C2×C22⋊Q8—42no—
105C2×C22⋊Q8C2314yes—
106C2×C22⋊Q8C2314yes—
107C2×#121—22no—
108C2×#121—22no—
109C2×#121—24no—
110C2×#121—24no—
111C2×#121—42no—
112C2×#121—42no—
113C2×#121C2314yes—
114C2×#121C2314yes—
115C2×C4×D4—22no—
116C2×C4×D4—42no—
117C2×C4×D4—42no—
118C2×C4×D4—42no—
119C2×C4×D4—42no—
120C2×C4×D4D414yes—
121C2×C4×D4C2314yes—
122C2×C4×D4C2314yes—
123C2×#117—22no—
124C2×#117—24no—
125C2×#117—42no—
126C2×#117C2314yes—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4D411yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4D411yescharacteristic
147C22×C22⋊C4D411yescharacteristic
148C22×C42—21no—
149C22×C42C2311yescharacteristic
150#482—232no—
151#465—232no—
152C2×#107—24no—
153C2×#107—42no—
154C2×#107C2314yes—
155C2×#107C2314yes—
156C2×#106—24no—
157C2×#106—24no—
158C2×#106—42no—
159C2×#106C2314yes—
160C2×#106C2314yes—
161C2×#106C2314yes—
162C2×#103—24no—
163C2×#103—42no—
164C2×#103—42no—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102—24no—
169C2×#102—42no—
170C2×#102D418yescomplemented
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×C22⋊C8—24no—
175C2×C22⋊C8—24no—
176C2×C22⋊C8—42no—
177C2×C22⋊C8C2314yes—
178C2×C22⋊C8C2314yes—
179C2×C22⋊C8C2314yes—
180#397—28no—
181#397—28no—
182#394—28no—
183#392—28no—
184#391—22no—
185#391C2314yes—
186#389—28no—
187#389—22no—
188#389C2314yes—
189#388—28no—
190#386—28no—
191#386—28no—
192#382—22no—
193#382C2314yes—
194#380—22no—
195#380—22no—
196#380—22no—
197#380C2314yes—
198#380C2314yes—
199#380C2314yes—
200C2×#95—21no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95—21no—
208#340C2314yes—
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#336C2314yes—
213#336C2314yes—
214C25—21no—
215C25C2×D411yescharacteristic
216C25C2×D411yescharacteristic
217C22×Q8—21no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8C2412yes—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—21no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4—44no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—82no—
241C22×D4—82no—
242C22×D4C2×D414yes—
243C22×D4C2×D414yes—
244C22×D4C2412yes—
245C23×C4—21no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—24no—
265C23×C4—44no—
266C23×C4—82no—
267C23×C4—82no—
268C23×C4C2×D412yes—
269C23×C4C2×D412yes—
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C2×SD16—28no—
278C2×SD16—28no—
279C2×SD16—44no—
280C2×SD16—416no—
281C22×C8—22no—
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—28no—
292C22×C8—28no—
293C22×C8—44no—
294C22×C8—416no—
295C22×C8C2×D414yes—
296C22×C8#4114yes—
297C22×C8C2412yes—
298C22×C8C2412yes—
299C22×C8C2412yes—
300C22×C8C2412yes—
301C22⋊Q8—28no—
302C22⋊Q8—44no—
303C22⋊Q8—44no—
304C22⋊Q8—44no—
305C22⋊Q8—48no—
306C22⋊Q8—48no—
307#121—28no—
308#121—28no—
309#121—44no—
310#121—44no—
311#121—48no—
312#121—48no—
313C4×D4—44no—
314C4×D4—44no—
315C4×D4—48no—
316C4×D4—44no—
317C4×D4—44no—
318C4×D4—48no—
319#117—28no—
320#117—44no—
321#117—48no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4C2×D414yes—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
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—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—82no—
373C2×C22⋊C4—82no—
374C2×C22⋊C4C2×D414yes—
375C2×C22⋊C4C2×D414yes—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42—44no—
380C2×C42C2×D412yes—
381C2×C42C2412yes—
382#107—28no—
383#107—44no—
384#106—28no—
385#106—28no—
386#106—44no—
387#103—28no—
388#103—44no—
389#103—44no—
390#102—28no—
391#102—44no—
392#102C2×D4116yescomplemented
393C22⋊C8—28no—
394C22⋊C8—28no—
395C22⋊C8—44no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24#13514yes—
426C24C22×D412yes—
427C24C22×D412yes—
428C24C22×D411yescharacteristic
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×D4—28no—
443C2×D4—28no—
444C2×D4—24no—
445C2×D4—28no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—416no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—42no—
459C2×D4—44no—
460C2×D4—42no—
461C2×D4—44no—
462C2×D4—84no—
463C2×D4—84no—
464C2×D4—816no—
465C2×D4—816no—
466C2×D4C22×D414yes—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
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—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—48no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—84no—
535C22×C4—84no—
536C22×C4—816no—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D412yes—
543C22×C4C2×#4112yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C4H(5,𝔽2)12yes—
547C22×C42−1+412yes—
548C22×C4C2511yescharacteristic
549SD16—416no—
550C2×C8—28no—
551C2×C8—28no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—416no—
563C2×C8—44no—
564C2×C8—44no—
565C2×C8C22×D414yes—
566C2×C8C2×#4114yes—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—44no—
580C4⋊C4—48no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4C22×D414yes—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—84no—
599C22⋊C4—84no—
600C42—24no—
601C42—22no—
602C42—22no—
603C42—48no—
604C23—28no—
605C23—22no—
606C23—28no—
607C23—22no—
608C23—22no—
609C23—28no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—44no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—48no—
629C23—42no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—44no—
634C23—48no—
635C23—48no—
636C23—44no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23#53412yes—
646C23D4212yes—
647C23#54712yes—
648C23C2×#13514yes—
649C23C2×#13512yes—
650C23#57512yes—
651C23#57712yes—
652C23#57712yes—
653C23C23×D411yescharacteristic
654Q8—42no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—84no—
659D4—24no—
660D4—24no—
661D4—416no—
662D4—48no—
663D4—42no—
664D4—42no—
665D4—816no—
666D4—816no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—48no—
689C2×C4—42no—
690C2×C4—42no—
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—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—816no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4#53412yes—
723C2×C4#53714yes—
724C2×C4#54014yes—
725C2×C4D4212yes—
726C2×C4#54614yes—
727C2×C4#54712yes—
728C2×C4#56214yes—
729C2×C4C23×D411yescharacteristic
730C2×C4C22×#4111yescharacteristic
731C2×C4C2×H(5,𝔽2)11yescharacteristic
732C2×C4C2×H(5,𝔽2)11yescharacteristic
733C2×C4C2×H(5,𝔽2)11yescharacteristic
734C2×C4C2×2−1+411yescharacteristic
735C8—24no—
736C8—24no—
737C8—42no—
738C8—42no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—416no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—44no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—44no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—88no—
762C22—816no—
763C22#267114yes—
764C22#319114yes—
765C22#320014yes—
766C22#326714yes—
767C22#328214yes—
768C22#333714yes—
769C22#335014yes—
770C22C2×#53411yescharacteristic
771C22C2×D4211yescharacteristic
772C22C2×#54711yescharacteristic
773C22C22×#13511yescharacteristic
774C22C2×#57511yescharacteristic
775C22C2×#57711yescharacteristic
776C22C2×#57711yescharacteristic
777C4—42no—
778C4—42no—
779C4—44no—
780C4—42no—
781C4—42no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4#267114yes—
789C4C2×#53711yescharacteristic
790C4C2×#54011yescharacteristic
791C4C2×#54611yescharacteristic
792C4C2×#56211yescharacteristic
793C2—44no—
794C2—82no—
795C2—84no—
796C2#3055818yesdirect product factor
797C2C2×#267111yescharacteristic
798C2C2×#319111yescharacteristic
799C2C2×#320011yescharacteristic
800C2C2×#326711yescharacteristic
801C2C2×#328211yescharacteristic
802C2C2×#333711yescharacteristic
803C2C2×#335011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#482C2semidirect
2. C22×#465C2semidirect
4. C2×#2415C2semidirect
5. #30558C2direct (N × H)
6. C2×#2097C2semidirect
7. C2×#2085C2semidirect
8. C2×#2036C2semidirect
9. C2×#2035C2semidirect
10. C2×#2033C2semidirect
11. C2×#2000C2semidirect
12. C2×#1877C2semidirect
13. C2×#1869C2semidirect
14. C2×#1864C2semidirect
15. C2×#1854C2semidirect
16. C2×#1807C2semidirect
27. C2×#482C22semidirect
29. C2×#465C22semidirect
47. #2415C22semidirect
62. #2097C22semidirect
63. #2085C22semidirect
64. #2036C22semidirect
65. #2035C22semidirect
66. #2033C22semidirect
67. #2000C22semidirect
68. #1877C22semidirect
69. #1869C22semidirect
70. #1864C22semidirect
71. #1854C22semidirect
72. #1807C22semidirect
170. C2×#102D4semidirect
392. #102C2×D4semidirect
796. C2#30558direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4822
C22×#4652
C2×#25352
C2×#24152
#305582
C2×#20972
C2×#20852
C2×#20362
C2×#20352
C2×#20332
C2×#20002
C2×#18772
C2×#18692
C2×#18642
C2×#18542
C2×#18072