Finite Group Databasebeta

← #188457

Subgroups — #188457

Order 512.

1692 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#525C211yesmaximal, characteristic
2#20626C211yesmaximal, characteristic, complemented
3C2×#1504C212yesmaximal
4C2×#1434C211yesmaximal, characteristic, complemented
5#8576C212yesmaximal, complemented
6#8575C212yesmaximal, complemented
7#8574C212yesmaximal, complemented
8#8573C212yesmaximal, complemented
9#8020C212yesmaximal, complemented
10C2×#525C2211yescharacteristic
11C2×C4×#41C411yescharacteristic, complemented
12C23×C42C2211yescharacteristic
13C2×#423—21no—
14C2×#407C2212yes—
15C4×C22⋊Q8C411yescharacteristic, complemented
16C4×C22⋊Q8C411yescharacteristic, complemented
17C4×C22⋊Q8C2211yescharacteristic
18C4×C22⋊Q8C2211yescharacteristic
19C4×#123—21no—
20C4×#123—21no—
21C4×#121C411yescharacteristic, complemented
22C4×#121C411yescharacteristic, complemented
23C4×#121C2211yescharacteristic
24C4×#121C2211yescharacteristic
25C4×#120—21no—
26C4×#120—21no—
27#2297C411yescharacteristic, complemented
28#2296C411yescharacteristic, complemented
29#2290—21no—
30#2290—21no—
31#2280C2211yescharacteristic
32C42×D4—21no—
33C42×D4—21no—
34C4×#117C411yescharacteristic, complemented
35C22×#95—21no—
36C22×#95—21no—
37C22×#95C2212yes—
38#1797—21no—
39#1797—21no—
40#1797C2212yes—
41#1797C2212yes—
42#1728—21no—
43#1504—28no—
44C2×#328C2214yes—
45C2×#327C2214yes—
46#1434—21no—
47#1434—21no—
48#1434C2212yes—
49#1434C2212yes—
50#1294C2214yes—
51#1294C2214yes—
52C22×#41C2×C411yescharacteristic
53C24×C4—22no—
54C24×C4D411yescharacteristic
55C24×C4D411yescharacteristic
56C24×C4C2311yescharacteristic
57C22×M16—22no—
58#525—22no—
59#525—22no—
60#525D414yes—
61#525Q814yes—
62C2×#123—21no—
63C2×C22⋊Q8C2×C411yescharacteristic
64C2×C22⋊Q8C2311yescharacteristic
65C2×#121C2×C411yescharacteristic
66C2×#121C2311yescharacteristic
67C2×#120—21no—
68C4×#41—44no—
69C2×C4×Q8C2×C411yescharacteristic, complemented
70C2×C4×Q8C2×C411yescharacteristic, complemented
71C2×C4×D4—21no—
72C2×C4×D4—21no—
73C2×C4×D4—21no—
74C2×C4×D4—21no—
75C2×C4×D4—21no—
76C2×C4×D4—21no—
77C2×C4×D4—21no—
78C2×C4×D4—21no—
79C2×C4×D4C2×C411yescharacteristic, complemented
80C2×C4×D4C2×C411yescharacteristic, complemented
81C2×#117—21no—
82C2×#117C2×C411yescharacteristic
83C2×#117C2×C411yescharacteristic
84C2×#117C2×C411yescharacteristic
85C22×C42—21no—
86C22×C42—44no—
87C22×C42C2×C411yescharacteristic
88C22×C42C2×C411yescharacteristic
89C22×C42C2×C411yescharacteristic
90C22×C42C2×C411yescharacteristic
91C22×C42D411yescharacteristic
92C22×C42D411yescharacteristic
93C22×C42D411yescharacteristic
94C22×C42D411yescharacteristic
95C22×C42D411yescharacteristic
96C22×C42D411yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99#423—44no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102#407—24no—
103#407—24no—
104C2×C22⋊C8—22no—
105C2×C22⋊C8C2314yes—
106#391C2×C411yescharacteristic, complemented
107#391C2×C411yescharacteristic, complemented
108#390C2×C411yescharacteristic, complemented
109#390C2×C411yescharacteristic, complemented
110#389C2×C411yescharacteristic, complemented
111#389C2×C411yescharacteristic, complemented
112#389C2×C411yescharacteristic, complemented
113#389C2×C411yescharacteristic, complemented
114#388—21no—
115#388—21no—
116#388—21no—
117#388—21no—
118#387—21no—
119#387—21no—
120#387—21no—
121#387—21no—
122#386—21no—
123#386—21no—
124#386—21no—
125#386—21no—
126#386—21no—
127#386—21no—
128#385—21no—
129#385—21no—
130#385—21no—
131#385—21no—
132#385—21no—
133#385—21no—
134#381—21no—
135#380C2×C411yescharacteristic
136#380C2×C411yescharacteristic
137#380C2311yescharacteristic
138#380C2311yescharacteristic
139#379—21no—
140C4×C4⋊C4—21no—
141C4×C4⋊C4—21no—
142C4×C4⋊C4—21no—
143C4×C4⋊C4—21no—
144C4×C4⋊C4—21no—
145C4×C4⋊C4—21no—
146C4×C4⋊C4C2×C411yescharacteristic, complemented
147C4×C4⋊C4C2×C411yescharacteristic, complemented
148C4×C4⋊C4C2×C411yescharacteristic, complemented
149C4×C4⋊C4C2×C411yescharacteristic, complemented
150C4×C22⋊C4—21no—
151C4×C22⋊C4—21no—
152C4×C22⋊C4—21no—
153C4×C22⋊C4—21no—
154C4×C22⋊C4—21no—
155C4×C22⋊C4—21no—
156C4×C22⋊C4—21no—
157C4×C22⋊C4—21no—
158C4×C22⋊C4—21no—
159C4×C22⋊C4—21no—
160C4×C22⋊C4—21no—
161C4×C22⋊C4—21no—
162C4×C22⋊C4—21no—
163C4×C22⋊C4—21no—
164#376—21no—
165C2×#95—28no—
166C2×#95—22no—
167C2×#95—22no—
168C2×#95—24no—
169C2×#95—24no—
170C2×#95—22no—
171C2×#95—22no—
172C2×#95—22no—
173C2×#95—44no—
174C2×#95C2314yes—
175C43—21no—
176#336—22no—
177#336—22no—
178#328—28no—
179#327—28no—
180C25C2×D411yescharacteristic
181C2×#41—22no—
182C2×#41—42no—
183C2×#41—42no—
184C2×#41C4⋊C414yes—
185C22×Q8C22×C411yescharacteristic
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4C22×C411yescharacteristic
190C23×C4—24no—
191C23×C4—24no—
192C23×C4—21no—
193C23×C4—28no—
194C23×C4—24no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
202C23×C4—42no—
203C23×C4—44no—
204C23×C4—44no—
205C23×C4—44no—
206C23×C4—44no—
207C23×C4—44no—
208C23×C4—44no—
209C23×C4C22⋊C411yescharacteristic
210C23×C4C22⋊C411yescharacteristic
211C23×C4C22⋊C411yescharacteristic
212C23×C4C22⋊C411yescharacteristic
213C23×C4C22⋊C411yescharacteristic
214C23×C4C22⋊C411yescharacteristic
215C23×C4C22⋊C411yescharacteristic
216C23×C4C22⋊C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C22×C411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
223C23×C4C2×D411yescharacteristic
224C23×C4C2×D411yescharacteristic
225C23×C4C2×D411yescharacteristic
226C23×C4C2×D412yes—
227C23×C4C2×Q812yes—
228C23×C4#4112yes—
229C23×C4#4112yes—
230C23×C4C2411yescharacteristic
231C2×M16—44no—
232C2×M16—44no—
233C2×M16—44no—
234C22×C8—24no—
235#123—24no—
236#123—24no—
237C22⋊Q8—22no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8C4⋊C414yes—
241C22⋊Q8C2×D412yes—
242C22⋊Q8C2×Q812yes—
243#121—22no—
244#121—21no—
245#121—21no—
246#121C4⋊C414yes—
247#121C2×D412yes—
248#121C2×Q812yes—
249#120—24no—
250#120—24no—
251C4×Q8—42no—
252C4×Q8—42no—
253C4×D4—24no—
254C4×D4—24no—
255C4×D4—24no—
256C4×D4—24no—
257C4×D4—42no—
258C4×D4—42no—
259C4×D4—44no—
260C4×D4—44no—
261C4×D4—44no—
262C4×D4—44no—
263C4×D4—44no—
264C4×D4—44no—
265#117—22no—
266#117—44no—
267#117—42no—
268#117—42no—
269#117C4⋊C414yes—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4C22×C411yescharacteristic
279C2×C4⋊C4C22×C411yescharacteristic
280C2×C4⋊C4C22×C411yescharacteristic
281C2×C4⋊C4C22×C411yescharacteristic
282C2×C4⋊C4C22×C411yescharacteristic
283C2×C4⋊C4C22×C411yescharacteristic
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C42—24no—
302C2×C42—24no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—42no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42—42no—
316C2×C42—42no—
317C2×C42—42no—
318C2×C42—42no—
319C2×C42—42no—
320C2×C42—44no—
321C2×C42—42no—
322C2×C42—42no—
323C2×C42C22⋊C411yescharacteristic
324C2×C42C22⋊C411yescharacteristic
325C2×C42C22⋊C411yescharacteristic
326C2×C42C22⋊C411yescharacteristic
327C2×C42C22⋊C411yescharacteristic
328C2×C42C22⋊C411yescharacteristic
329C2×C42C22⋊C411yescharacteristic
330C2×C42C22⋊C411yescharacteristic
331C2×C42C22×C411yescharacteristic
332C2×C42C22×C411yescharacteristic
333C2×C42C22×C411yescharacteristic
334C2×C42C22×C411yescharacteristic
335C2×C42C2×D411yescharacteristic
336C2×C42C2×D411yescharacteristic
337C2×C42C2×D411yescharacteristic
338C2×C42C2×D411yescharacteristic
339C4⋊C8—44no—
340C4⋊C8—44no—
341C22⋊C8—24no—
342C22⋊C8—24no—
343C22⋊C8—44no—
344#95—28no—
345#95—28no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—24no—
363#95—24no—
364#95—44no—
365#95—44no—
366#95—44no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—21no—
374C24C2×C22⋊C411yescharacteristic
375C24C2×C22⋊C411yescharacteristic
376C24#12112yes—
377C24C22⋊Q812yes—
378C24C22×D411yescharacteristic
379#41—48no—
380#41—48no—
381C2×Q8—21no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8C2×C4⋊C412yes—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—21no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4C2×C4⋊C412yes—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—28no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—44no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—41no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—416no—
465C22×C4—416no—
466C22×C4—44no—
467C22×C4—416no—
468C22×C4—416no—
469C22×C4—416no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—44no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—88no—
478C22×C4—88no—
479C22×C4—88no—
480C22×C4—88no—
481C22×C4#9914yes—
482C22×C4#10414yes—
483C22×C4C2×C22⋊C411yescharacteristic
484C22×C4C2×C22⋊C411yescharacteristic
485C22×C4C2×C22⋊C411yescharacteristic
486C22×C4C2×C22⋊C411yescharacteristic
487C22×C4C2×C22⋊C411yescharacteristic
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C4⋊C412yes—
494C22×C4C2×C4⋊C412yes—
495C22×C4#11712yes—
496C22×C4#11712yes—
497C22×C4#12112yes—
498C22×C4#12112yes—
499C22×C4#12112yes—
500C22×C4C22⋊Q812yes—
501C22×C4C22⋊Q812yes—
502C22×C4C22⋊Q812yes—
503C22×C4C23×C411yescharacteristic
504C22×C4C22×D411yescharacteristic
505C22×C4C22×D411yescharacteristic
506C22×C4C22×Q811yescharacteristic
507C22×C4C2×#4111yescharacteristic
508C22×C4C2×#4111yescharacteristic
509M16—88no—
510C2×C8—44no—
511C2×C8—44no—
512C2×C8—44no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—24no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4C2×C4⋊C412yes—
529C4⋊C4C2×C4⋊C412yes—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—24no—
533C22⋊C4—24no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—24no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C42—24no—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—22no—
558C42—41no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—42no—
567C42—42no—
568C42—42no—
569C42—42no—
570C42—42no—
571C42—42no—
572C42—42no—
573C42—42no—
574C23—28no—
575C23—28no—
576C23—28no—
577C23—28no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—24no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23#38012yes—
604C23#38012yes—
605C23C2×#9912yes—
606C23#41012yes—
607C23C2×#10412yes—
608C23#42112yes—
609C23C22×C22⋊C411yescharacteristic
610C23C2×#12111yescharacteristic
611C23C2×C22⋊Q811yescharacteristic
612C23#57512yes—
613C23#57512yes—
614Q8—42no—
615Q8—42no—
616D4—42no—
617D4—42no—
618D4—48no—
619D4—44no—
620D4—48no—
621D4—44no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—48no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—48no—
687C2×C4—48no—
688C2×C4—48no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—84no—
702C2×C4—84no—
703C2×C4—832no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4—84no—
707C2×C4—84no—
708C2×C4#38012yes—
709C2×C4#38012yes—
710C2×C4C2×#9912yes—
711C2×C4C2×#9912yes—
712C2×C4C2×#10412yes—
713C2×C4C2×#10412yes—
714C2×C4C22×C4⋊C411yescharacteristic
715C2×C4C2×#11711yescharacteristic
716C2×C4C2×#12111yescharacteristic
717C2×C4C2×C22⋊Q811yescharacteristic
718C8—84no—
719C22—216no—
720C22—216no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—21no—
728C22—21no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—21no—
733C22—21no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22#179914yes—
749C22#180614yes—
750C22C2×#38011yescharacteristic
751C22C22×#9911yescharacteristic
752C22C2×#41011yescharacteristic
753C22#289611yescharacteristic
754C22#289611yescharacteristic
755C22C22×#10411yescharacteristic
756C22C2×#42111yescharacteristic
757C22#304012yes—
758C22#308012yes—
759C4—22no—
760C4—22no—
761C4—21no—
762C4—22no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—41no—
770C4—41no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—41no—
775C4—41no—
776C4—88no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C2—22no—
782C2—24no—
783C2—22no—
784C2—24no—
785C2—82no—
786C2#1754111yescharacteristic
787C2#1754211yescharacteristic
788C2#1758711yescharacteristic
789C2#1759311yescharacteristic
790C2C2×#179911yescharacteristic
791C2#2064911yescharacteristic
792C2C2×#180611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #20626C2semidirect
4. C2×#1434C2semidirect
5. #8576C2semidirect
6. #8575C2semidirect
7. #8574C2semidirect
8. #8573C2semidirect
9. #8020C2semidirect
11. C2×C4×#41C4semidirect
15. C4×C22⋊Q8C4semidirect
16. C4×C22⋊Q8C4semidirect
21. C4×#121C4semidirect
22. C4×#121C4semidirect
27. #2297C4semidirect
28. #2296C4semidirect
34. C4×#117C4semidirect
69. C2×C4×Q8C2×C4semidirect
70. C2×C4×Q8C2×C4semidirect
79. C2×C4×D4C2×C4semidirect
80. C2×C4×D4C2×C4semidirect
106. #391C2×C4semidirect
107. #391C2×C4semidirect
108. #390C2×C4semidirect
109. #390C2×C4semidirect
110. #389C2×C4semidirect
111. #389C2×C4semidirect
112. #389C2×C4semidirect
113. #389C2×C4semidirect
146. C4×C4⋊C4C2×C4semidirect
147. C4×C4⋊C4C2×C4semidirect
148. C4×C4⋊C4C2×C4semidirect
149. C4×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C4×#5252
#206262
C2×#15042
C2×#14342
#85762
#85752
#85742
#85732
#80202