Finite Group Databasebeta

← C2×#31302 #7504323

Subgroups — C2×#31302 #7504323

Order 512.

2998 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2497C211yesmaximal, characteristic, complemented
2C2×#2435C211yesmaximal, characteristic
3#31302C2116yesmaximal, direct product factor
4C2×#2093C211yesmaximal, characteristic, complemented
5C2×#2067C211yesmaximal, characteristic, complemented
6C2×#2042C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2036C211yesmaximal, characteristic, complemented
9C2×#2036C211yesmaximal, characteristic, complemented
10C2×#1983C211yesmaximal, characteristic, complemented
11C2×#1959C211yesmaximal, characteristic, complemented
12C2×#1936C211yesmaximal, characteristic, complemented
13C2×#1925C211yesmaximal, characteristic, complemented
14C2×#1924C211yesmaximal, characteristic, complemented
15C2×#1786C211yesmaximal, characteristic
16C2×#1786C211yesmaximal, characteristic
17C24×D4C2211yescharacteristic
18C22×#124C2211yescharacteristic
19C22×#124C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#107C2211yescharacteristic, complemented
22C22×#107C2211yescharacteristic, complemented
23C22×C4⋊C8C2211yescharacteristic, complemented
24C22×#103C2211yescharacteristic, complemented
25C22×#103C2211yescharacteristic, complemented
26C22×#103C2211yescharacteristic, complemented
27C22×#103C2211yescharacteristic, complemented
28C22×#102C2211yescharacteristic
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×C22⋊C8C2211yescharacteristic
37C22×C22⋊C8C2211yescharacteristic
38C22×#97C2211yescharacteristic, complemented
39#2497—24no—
40#2497C2218yescomplemented
41#2435—24no—
42#2435C2218yes—
43C2×#400—21no—
44C2×#396—21no—
45C2×#394—21no—
46C2×#394—21no—
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2211yescharacteristic, complemented
50C2×#389C2211yescharacteristic, complemented
51C2×#388—21no—
52C2×#387—21no—
53C2×#384C2211yescharacteristic, complemented
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#379—21no—
57C2×#379—21no—
58C2×C4×C4⋊C4C2211yescharacteristic, complemented
59C2×C4×C22⋊C4C2211yescharacteristic
60#2093C2218yescomplemented
61#2067C2218yescomplemented
62#2042C2218yescomplemented
63#2042C2218yescomplemented
64#2036C2218yescomplemented
65#2036C2218yescomplemented
66#1983C2218yescomplemented
67#1959C2218yescomplemented
68#1936C2218yescomplemented
69#1925C2218yescomplemented
70#1924C2218yescomplemented
71#1786C2218yes—
72#1786C2218yes—
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#336C2211yescharacteristic, complemented
76C2×#336C2211yescharacteristic, complemented
77C26—21no—
78C23×Q8C2311yescharacteristic
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—21no—
82C23×D4—22no—
83C23×D4—42no—
84C23×D4—42no—
85C23×D4—42no—
86C23×D4—42no—
87C23×D4C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2314yes—
90C24×C4C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C2×#124—24no—
96C2×#124—24no—
97C2×#124—22no—
98C2×#124—22no—
99C2×#124—42no—
100C2×#124—42no—
101C2×#124C2314yes—
102C2×#124C2314yes—
103C2×C22⋊Q8—22no—
104C2×C22⋊Q8—42no—
105C2×C22⋊Q8—42no—
106C2×C22⋊Q8C2314yes—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C22⋊C4—21no—
118C22×C22⋊C4—21no—
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4D411yescharacteristic
129C22×C22⋊C4D411yescharacteristic
130C22×C42—21no—
131C22×C42C2311yescharacteristic
132C22×C42C2311yescharacteristic
133C2×#107—42no—
134C2×#107—42no—
135C2×#107C2314yescomplemented
136C2×#107C2314yescomplemented
137C2×C4⋊C8—42no—
138C2×C4⋊C8C2314yescomplemented
139C2×#103—42no—
140C2×#103—42no—
141C2×#103—42no—
142C2×#103—42no—
143C2×#103C2314yescomplemented
144C2×#103C2314yescomplemented
145C2×#103C2314yescomplemented
146C2×#103C2314yescomplemented
147C2×#102—24no—
148C2×#102—24no—
149C2×#102—42no—
150C2×#102—42no—
151C2×#102—42no—
152C2×#102—42no—
153C2×#102—42no—
154C2×#102—42no—
155C2×#102C2314yes—
156C2×#102C2314yes—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×C22⋊C8—42no—
164C2×C22⋊C8—42no—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2314yes—
167C2×#97—42no—
168C2×#97C2314yescomplemented
169#400—28no—
170#396—28no—
171#394—28no—
172#394—28no—
173#390—22no—
174#390—22no—
175#390C2314yes—
176#390C2314yes—
177#389—22no—
178#389—22no—
179#389C2314yescomplemented
180#389C2314yescomplemented
181#388—28no—
182#387—28no—
183#384—22no—
184#384C2314yescomplemented
185#380—22no—
186#380—22no—
187#380C2314yes—
188#380C2314yes—
189#379—28no—
190#379—28no—
191C4×C4⋊C4—22no—
192C4×C4⋊C4C2314yescomplemented
193C4×C22⋊C4D414yes—
194C4×C22⋊C4C2314yes—
195C2×#95—21no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95D411yescharacteristic
201C2×#95D411yescharacteristic
202#340C2314yescomplemented
203#340C2314yescomplemented
204#336C2314yescomplemented
205#336C2314yescomplemented
206C25—21no—
207C25—21no—
208C25—24no—
209C25—44no—
210C25—44no—
211C25—44no—
212C25—44no—
213C25—44no—
214C25—82no—
215C25—82no—
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—28no—
226C22×D4—28no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—48no—
245C22×D4—48no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—48no—
250C22×D4—416no—
251C22×D4—416no—
252C22×D4—416no—
253C22×D4—416no—
254C22×D4#4114yes—
255C22×D4#4114yes—
256C22×D4C2412yes—
257C22×D4C2412yes—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4C2×D412yes—
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—22no—
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×C8C2412yes—
291C22×C8C2412yes—
292C22×C8C2412yes—
293C22×C8C2412yes—
294#124—28no—
295#124—28no—
296#124—44no—
297#124—44no—
298#124—48no—
299#124—48no—
300C22⋊Q8—44no—
301C22⋊Q8—44no—
302C22⋊Q8—48no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—82no—
326C2×C4⋊C4—82no—
327C2×C4⋊C4—82no—
328C2×C4⋊C4C2412yes—
329C2×C4⋊C4C2412yes—
330C2×C4⋊C4C2412yes—
331C2×C4⋊C4C2412yes—
332C2×C4⋊C4C2412yes—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—82no—
352C2×C22⋊C4—82no—
353C2×C22⋊C4—82no—
354C2×C22⋊C4—82no—
355C2×C22⋊C4—82no—
356C2×C22⋊C4—82no—
357C2×C22⋊C4C2×D414yes—
358C2×C22⋊C4C2×D414yes—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—82no—
365C2×C42C2×D412yes—
366C2×C42C2×D412yes—
367C2×C42C2412yes—
368C2×C42C2412yes—
369#107—44no—
370#107—44no—
371C4⋊C8—44no—
372#103—44no—
373#103—44no—
374#103—44no—
375#103—44no—
376#102—28no—
377#102—28no—
378#102—44no—
379#102—44no—
380#102—44no—
381#102—44no—
382#102—44no—
383#102—44no—
384C22⋊C8—44no—
385C22⋊C8—44no—
386#97—44no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95C2×D414yes—
393#95C2×D414yes—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—24no—
401C24—24no—
402C24—22no—
403C24—22no—
404C24—48no—
405C24—48no—
406C24—48no—
407C24—48no—
408C24—432no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—48no—
422C24—84no—
423C24—84no—
424C24—816no—
425C24—816no—
426C24—816no—
427C24—816no—
428C24—816no—
429C24—816no—
430C24#13714yes—
431C24C22×D412yes—
432C24C22×D411yescharacteristic
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—24no—
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—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—416no—
466C2×D4—416no—
467C2×D4—416no—
468C2×D4—432no—
469C2×D4—464no—
470C2×D4—416no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4C2×#4114yes—
480C2×D4C2×#4114yes—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
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—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
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—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×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D411yescharacteristic
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C4H(5,𝔽2)12yes—
542C22×C4H(5,𝔽2)12yes—
543C22×C4H(5,𝔽2)12yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C4C2511yescharacteristic
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—22no—
557C2×C8—22no—
558C2×C8—44no—
559C2×C8—44no—
560C2×C8—44no—
561C2×C8—44no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—84no—
580C4⋊C4—84no—
581C4⋊C4—84no—
582C22⋊C4—28no—
583C22⋊C4—44no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—84no—
590C22⋊C4—84no—
591C22⋊C4—84no—
592C22⋊C4—84no—
593C22⋊C4—84no—
594C22⋊C4—84no—
595C42—24no—
596C42—24no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—84no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—28no—
606C23—28no—
607C23—28no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—432no—
618C23—42no—
619C23—42no—
620C23—48no—
621C23—48no—
622C23—42no—
623C23—42no—
624C23—48no—
625C23—48no—
626C23—48no—
627C23—48no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—816no—
637C23—816no—
638C23—816no—
639C23—816no—
640C23—816no—
641C23—8128no—
642C23—816no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23#53512yes—
652C23#54612yes—
653C23#54612yes—
654C23C2×#13714yes—
655C23C2×#13712yes—
656C23#57512yes—
657C23#57612yes—
658C23#57612yes—
659C23C23×D411yescharacteristic
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—84no—
665D4—24no—
666D4—24no—
667D4—24no—
668D4—24no—
669D4—432no—
670D4—42no—
671D4—42no—
672D4—48no—
673D4—48no—
674D4—42no—
675D4—42no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—48no—
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—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—84no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4#53512yes—
726C2×C4#53814yes—
727C2×C4#53814yes—
728C2×C4#54612yes—
729C2×C4#54612yes—
730C2×C4#55114yes—
731C2×C4#56014yes—
732C2×C4C22×#4111yescharacteristic
733C2×C4C22×#4111yescharacteristic
734C2×C4C2×H(5,𝔽2)11yescharacteristic
735C2×C4C2×H(5,𝔽2)11yescharacteristic
736C2×C4C2×H(5,𝔽2)11yescharacteristic
737C2×C4C2×H(5,𝔽2)11yescharacteristic
738C8—42no—
739C8—42no—
740C8—42no—
741C8—42no—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—864no—
757C22—816no—
758C22—816no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22#268514yes—
768C22#321514yes—
769C22#322014yes—
770C22#331414yes—
771C22#331414yes—
772C22#331914yes—
773C22#332214yes—
774C22C2×#53511yescharacteristic
775C22C2×#54611yescharacteristic
776C22C2×#54611yescharacteristic
777C22C22×#13711yescharacteristic
778C22C2×#57511yescharacteristic
779C22C2×#57611yescharacteristic
780C22C2×#57611yescharacteristic
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4#268514yes—
793C4C2×#53811yescharacteristic
794C4C2×#53811yescharacteristic
795C4C2×#55111yescharacteristic
796C4C2×#56011yescharacteristic
797C2—44no—
798C2—84no—
799C2—84no—
800C2#3130218yesdirect product factor
801C2C2×#268511yescharacteristic
802C2C2×#321511yescharacteristic
803C2C2×#322011yescharacteristic
804C2C2×#331411yescharacteristic
805C2C2×#331411yescharacteristic
806C2C2×#331911yescharacteristic
807C2C2×#332211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24×D4C22
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. C2×#2497C2semidirect
3. #31302C2direct (N × H)
4. C2×#2093C2semidirect
5. C2×#2067C2semidirect
6. C2×#2042C2semidirect
7. C2×#2042C2semidirect
8. C2×#2036C2semidirect
9. C2×#2036C2semidirect
10. C2×#1983C2semidirect
11. C2×#1959C2semidirect
12. C2×#1936C2semidirect
13. C2×#1925C2semidirect
14. C2×#1924C2semidirect
21. C22×#107C22semidirect
22. C22×#107C22semidirect
23. C22×C4⋊C8C22semidirect
24. C22×#103C22semidirect
25. C22×#103C22semidirect
26. C22×#103C22semidirect
27. C22×#103C22semidirect
38. C22×#97C22semidirect
40. #2497C22semidirect
49. C2×#389C22semidirect
50. C2×#389C22semidirect
53. C2×#384C22semidirect
58. C2×C4×C4⋊C4C22semidirect
60. #2093C22semidirect
61. #2067C22semidirect
62. #2042C22semidirect
63. #2042C22semidirect
64. #2036C22semidirect
65. #2036C22semidirect
66. #1983C22semidirect
67. #1959C22semidirect
68. #1936C22semidirect
69. #1925C22semidirect
70. #1924C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#336C22semidirect
76. C2×#336C22semidirect
135. C2×#107C23semidirect
136. C2×#107C23semidirect
138. C2×C4⋊C8C23semidirect
143. C2×#103C23semidirect
144. C2×#103C23semidirect
145. C2×#103C23semidirect
146. C2×#103C23semidirect
168. C2×#97C23semidirect
179. #389C23semidirect
180. #389C23semidirect
184. #384C23semidirect
192. C4×C4⋊C4C23semidirect
202. #340C23semidirect
203. #340C23semidirect
204. #336C23semidirect
205. #336C23semidirect
800. C2#31302direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24972
C2×#24352
#313022
C2×#20932
C2×#20672
C2×#20422
C2×#20362
C2×#19832
C2×#19592
C2×#19362
C2×#19252
C2×#19242
C2×#17862