Finite Group Databasebeta

← #188443

Subgroups — #188443

Order 512.

1602 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#525C211yesmaximal, characteristic
2C2×#1797C211yesmaximal, characteristic, complemented
3C2×#1501C212yesmaximal
4C4×#380C211yesmaximal, characteristic, complemented
5#8578C212yesmaximal, complemented
6#8577C212yesmaximal, complemented
7#8574C212yesmaximal, complemented
8#8573C212yesmaximal, complemented
9#8012C212yesmaximal, complemented
10C2×#525C2211yescharacteristic
11C2×C4×#41C411yescharacteristic, complemented
12C23×C42C2211yescharacteristic
13C22×C4⋊C8—21no—
14C22×C22⋊C8C2212yes—
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
32C2×#380—21no—
33C42×D4—21no—
34C42×D4—21no—
35C4×#117C411yescharacteristic, complemented
36C2×C4×C4⋊C4—21no—
37C2×C4×C22⋊C4C2212yes—
38#1797—21no—
39#1797—21no—
40#1797C2212yes—
41#1797C2212yes—
42C2×#336—21no—
43#1501—28no—
44C2×#328C2214yes—
45C2×#327C2214yes—
46C4⋊#95C2212yes—
47#1434C2212yes—
48C22⋊#95—21no—
49C4×#95—21no—
50#1294C2214yes—
51#1294C2214yes—
52C22×#41C2×C411yescharacteristic
53C24×C4D411yescharacteristic
54C24×C4D411yescharacteristic
55C24×C4C2311yescharacteristic
56C23×C8—22no—
57#525—22no—
58#525—22no—
59#525D414yes—
60#525Q814yes—
61C2×#123—21no—
62C2×C22⋊Q8C2×C411yescharacteristic
63C2×C22⋊Q8C2311yescharacteristic
64C2×#121C2×C411yescharacteristic
65C2×#121C2311yescharacteristic
66C2×#120—21no—
67C4×#41—44no—
68C2×C4×Q8C2×C411yescharacteristic
69C2×C4×Q8C2×C411yescharacteristic
70C2×C4×D4—21no—
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×D4C2×C411yescharacteristic
79C2×C4×D4C2×C411yescharacteristic
80C2×#117—21no—
81C2×#117C2×C411yescharacteristic
82C2×#117C2×C411yescharacteristic
83C2×#117C2×C411yescharacteristic
84C22×C4⋊C4—22no—
85C22×C22⋊C4—22no—
86C22×C42—21no—
87C22×C42—22no—
88C22×C42—44no—
89C22×C42C2×C411yescharacteristic
90C22×C42C2×C411yescharacteristic
91C22×C42C2×C411yescharacteristic
92C22×C42C2×C411yescharacteristic
93C22×C42D411yescharacteristic
94C22×C42D411yescharacteristic
95C22×C42D411yescharacteristic
96C22×C42D411yescharacteristic
97C22×C42D411yescharacteristic
98C22×C42D411yescharacteristic
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—44no—
104C2×C22⋊C8—24no—
105C2×C22⋊C8—24no—
106C2×C22⋊C8—22no—
107C2×C22⋊C8C2314yes—
108#391C2×C411yescharacteristic
109#391C2×C411yescharacteristic
110#390C2×C411yescharacteristic
111#390C2×C411yescharacteristic
112#389C2×C411yescharacteristic
113#389C2×C411yescharacteristic
114#389C2×C411yescharacteristic
115#389C2×C411yescharacteristic
116#388—21no—
117#388—21no—
118#388—21no—
119#388—21no—
120#387—21no—
121#387—21no—
122#387—21no—
123#387—21no—
124#386—21no—
125#386—21no—
126#386—21no—
127#386—21no—
128#386—21no—
129#386—21no—
130#385—21no—
131#385—21no—
132#385—21no—
133#385—21no—
134#385—21no—
135#385—21no—
136#381—21no—
137#380—28no—
138#380C2×C411yescharacteristic
139#380C2×C411yescharacteristic
140#380C2311yescharacteristic
141#380C2311yescharacteristic
142#379—21no—
143C4×C4⋊C4—21no—
144C4×C4⋊C4—21no—
145C4×C4⋊C4—21no—
146C4×C4⋊C4—21no—
147C4×C4⋊C4—21no—
148C4×C4⋊C4—21no—
149C4×C4⋊C4—44no—
150C4×C4⋊C4C2×C411yescharacteristic
151C4×C4⋊C4C2×C411yescharacteristic
152C4×C4⋊C4C2×C411yescharacteristic
153C4×C4⋊C4C2×C411yescharacteristic
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—
164C4×C22⋊C4—21no—
165C4×C22⋊C4—21no—
166C4×C22⋊C4—21no—
167C4×C22⋊C4—21no—
168C4×C22⋊C4—24no—
169C4×C22⋊C4—24no—
170#376—21no—
171C2×#95—22no—
172C2×#95—22no—
173C2×#95—22no—
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⋊C414yescomplemented
185C22×Q8C22×C411yescharacteristic
186C22×D4—21no—
187C22×D4—21no—
188C22×D4—21no—
189C22×D4C22×C411yescharacteristic
190C23×C4—24no—
191C23×C4—21no—
192C23×C4—24no—
193C23×C4—24no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
202C23×C4C22⋊C411yescharacteristic
203C23×C4C22⋊C411yescharacteristic
204C23×C4C22⋊C411yescharacteristic
205C23×C4C22⋊C411yescharacteristic
206C23×C4C22⋊C411yescharacteristic
207C23×C4C22⋊C411yescharacteristic
208C23×C4C22⋊C411yescharacteristic
209C23×C4C22⋊C411yescharacteristic
210C23×C4C22×C411yescharacteristic
211C23×C4C22×C411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D412yes—
220C23×C4C2×Q812yes—
221C23×C4#4112yes—
222C23×C4#4112yes—
223C23×C4C2411yescharacteristic
224C22×C8—24no—
225C22×C8—44no—
226C22×C8—44no—
227C22×C8—44no—
228#123—24no—
229#123—24no—
230C22⋊Q8—22no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8C4⋊C414yescomplemented
234C22⋊Q8C2×D412yes—
235C22⋊Q8C2×Q812yes—
236#121—22no—
237#121—21no—
238#121—21no—
239#121C4⋊C414yescomplemented
240#121C2×D412yes—
241#121C2×Q812yes—
242#120—24no—
243#120—24no—
244C4×Q8—42no—
245C4×Q8—42no—
246C4×D4—24no—
247C4×D4—24no—
248C4×D4—24no—
249C4×D4—24no—
250C4×D4—42no—
251C4×D4—42no—
252C4×D4—44no—
253C4×D4—44no—
254C4×D4—44no—
255C4×D4—44no—
256C4×D4—44no—
257C4×D4—44no—
258#117—22no—
259#117—44no—
260#117—42no—
261#117—42no—
262#117C4⋊C414yescomplemented
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—44no—
274C2×C4⋊C4C22×C411yescharacteristic
275C2×C4⋊C4C22×C411yescharacteristic
276C2×C4⋊C4C22×C411yescharacteristic
277C2×C4⋊C4C22×C411yescharacteristic
278C2×C4⋊C4C22×C411yescharacteristic
279C2×C4⋊C4C22×C411yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—28no—
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—44no—
299C2×C22⋊C4—44no—
300C2×C42—21no—
301C2×C42—24no—
302C2×C42—24no—
303C2×C42—24no—
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—42no—
321C2×C42—44no—
322C2×C42—44no—
323C2×C42—44no—
324C2×C42—44no—
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×C42C22×C411yescharacteristic
336C2×C42C22×C411yescharacteristic
337C2×C42C2×D411yescharacteristic
338C2×C42C2×D411yescharacteristic
339C2×C42C2×D411yescharacteristic
340C2×C42C2×D411yescharacteristic
341C4⋊C8—44no—
342C4⋊C8—44no—
343C22⋊C8—24no—
344C22⋊C8—24no—
345C22⋊C8—44no—
346#95—28no—
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—21no—
363#95—24no—
364#95—24no—
365#95—44no—
366#95—44no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—41no—
373C24—41no—
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—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—28no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—44no—
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—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—416no—
459C22×C4—416no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4#10414yes—
475C22×C4C2×C22⋊C411yescharacteristic
476C22×C4C2×C22⋊C411yescharacteristic
477C22×C4C2×C22⋊C411yescharacteristic
478C22×C4C2×C22⋊C411yescharacteristic
479C22×C4C2×C22⋊C411yescharacteristic
480C22×C4C2×C22⋊C411yescharacteristic
481C22×C4C2×C22⋊C411yescharacteristic
482C22×C4C2×C22⋊C411yescharacteristic
483C22×C4C2×C22⋊C411yescharacteristic
484C22×C4C2×C22⋊C411yescharacteristic
485C22×C4C2×C4⋊C412yes—
486C22×C4C2×C4⋊C412yes—
487C22×C4#11712yes—
488C22×C4#11712yes—
489C22×C4#12112yes—
490C22×C4#12112yes—
491C22×C4#12112yes—
492C22×C4C22⋊Q812yes—
493C22×C4C22⋊Q812yes—
494C22×C4C22⋊Q812yes—
495C22×C4#13514yes—
496C22×C4C23×C411yescharacteristic
497C22×C4C22×D411yescharacteristic
498C22×C4C22×D411yescharacteristic
499C22×C4C22×Q811yescharacteristic
500C22×C4C2×#4111yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C2×C8—44no—
503C2×C8—44no—
504C2×C8—44no—
505C2×C8—88no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—24no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—416no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4C2×C4⋊C412yes—
523C4⋊C4C2×C4⋊C412yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—24no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—416no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C42—24no—
545C42—22no—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—22no—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—41no—
555C42—41no—
556C42—41no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42—42no—
561C42—42no—
562C42—42no—
563C42—42no—
564C42—42no—
565C42—42no—
566C42—42no—
567C42—42no—
568C42—88no—
569C42#9914yes—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—24no—
588C23—22no—
589C23—42no—
590C23—42no—
591C23—44no—
592C23—44no—
593C23—44no—
594C23—44no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23#38012yes—
602C23#38012yes—
603C23C2×#10412yes—
604C23#42112yes—
605C23C22×C22⋊C411yescharacteristic
606C23C2×#12111yescharacteristic
607C23C2×C22⋊Q811yescharacteristic
608C23C2×#13512yes—
609C23#57512yes—
610Q8—42no—
611Q8—42no—
612D4—42no—
613D4—42no—
614D4—48no—
615D4—44no—
616D4—48no—
617D4—44no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
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—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—44no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—44no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—48no—
678C2×C4—48no—
679C2×C4—48no—
680C2×C4—48no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—84no—
694C2×C4—84no—
695C2×C4—84no—
696C2×C4—84no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4#38012yes—
700C2×C4#38012yes—
701C2×C4C2×#9912yes—
702C2×C4C2×#9912yes—
703C2×C4C2×#9912yes—
704C2×C4#41012yes—
705C2×C4#41612yes—
706C2×C4#41612yes—
707C2×C4C2×#10412yes—
708C2×C4C2×#10412yes—
709C2×C4C22×C4⋊C411yescharacteristic
710C2×C4C2×#11711yescharacteristic
711C2×C4C2×#12111yescharacteristic
712C2×C4C2×C22⋊Q811yescharacteristic
713C8—84no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—21no—
719C22—21no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—21no—
727C22—21no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—48no—
732C22—48no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22#180614yes—
745C22C2×#38011yescharacteristic
746C22C22×#9911yescharacteristic
747C22C2×#41011yescharacteristic
748C22C2×#41611yescharacteristic
749C22#289611yescharacteristic
750C22C22×#10411yescharacteristic
751C22C2×#42111yescharacteristic
752C22#303512yes—
753C22#307612yes—
754C4—22no—
755C4—22no—
756C4—22no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—42no—
770C4—88no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4—81no—
775C4#179914yes—
776C2—22no—
777C2—22no—
778C2—24no—
779C2—42no—
780C2—82no—
781C2#1753311yescharacteristic
782C2#1754211yescharacteristic
783C2#1756011yescharacteristic
784C2#1757211yescharacteristic
785C2C2×#179911yescharacteristic
786C2#2064511yescharacteristic
787C2C2×#180611yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1797C2semidirect
4. C4×#380C2semidirect
5. #8578C2semidirect
6. #8577C2semidirect
7. #8574C2semidirect
8. #8573C2semidirect
9. #8012C2semidirect
11. C2×C4×#41C4semidirect
15. C4×C22⋊Q8C4semidirect
16. C4×C22⋊Q8C4semidirect
21. C4×#121C4semidirect
22. C4×#121C4semidirect
27. #2297C4semidirect
28. #2296C4semidirect
35. C4×#117C4semidirect
184. C2×#41C4⋊C4semidirect
233. C22⋊Q8C4⋊C4semidirect
239. #121C4⋊C4semidirect
262. #117C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C4×#5252
C2×#17972
C2×#15012
C4×#3802
#85782
#85772
#85742
#85732
#80122