Finite Group Databasebeta

← #360763

Subgroups — #360763

Order 512.

1714 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic
2C2×#1854C211yesmaximal, characteristic
3C2×#1853C211yesmaximal, characteristic
4C2×#1847C211yesmaximal, characteristic, complemented
5C2×#1844C211yesmaximal, characteristic, complemented
6C2×#1809C211yesmaximal, characteristic
7C2×#1753C211yesmaximal, characteristic
8#13880C211yesmaximal, characteristic
9#13879C211yesmaximal, characteristic
10#11325C211yesmaximal, characteristic, complemented
11#11324C211yesmaximal, characteristic, complemented
12#11323C211yesmaximal, characteristic, complemented
13#11323C211yesmaximal, characteristic, complemented
14#10863C211yesmaximal, characteristic, complemented
15#10862C211yesmaximal, characteristic, complemented
16C23×M16C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C23×C4⋊C4C2211yescharacteristic
19C2×#428—24no—
20C2×#428—24no—
21C2×#428—24no—
22C22×#107C2211yescharacteristic
23C22×#107C2211yescharacteristic
24C22×#107C2211yescharacteristic
25C22×#107C2211yescharacteristic
26C22×#106C2211yescharacteristic
27C22×#106C2211yescharacteristic
28C22×#106C2211yescharacteristic
29C22×#106C2211yescharacteristic
30C22×#106C2211yescharacteristic
31C22×#106C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C22×#97C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35C2×#385—22no—
36C2×#384C2211yescharacteristic
37C2×#384C2211yescharacteristic
38C2×#384C2211yescharacteristic
39C2×#382C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×C4×C22⋊C4C2211yescharacteristic
43#1854—24no—
44#1853—24no—
45#1847—24no—
46#1844—24no—
47#1809—24no—
48#1753C418yescomplemented
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1444—22no—
58#1439—22no—
59#1436—22no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C24×C4—21no—
65C24×C4C2311yescharacteristic
66C22×M16—22no—
67C22×M16—22no—
68C22×M16—22no—
69C22×M16—22no—
70C22×M16C2×C414yes—
71C22×M16D414yes—
72C22×M16Q814yes—
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C2×#117—22no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—22no—
81C2×#117—41no—
82C2×#117—41no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—22no—
86C22×C4⋊C4—22no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—22no—
89C22×C4⋊C4—22no—
90C22×C4⋊C4—22no—
91C22×C4⋊C4—41no—
92C22×C4⋊C4—41no—
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C22⋊C4—21no—
102C22×C22⋊C4—21no—
103C22×C22⋊C4—21no—
104C22×C22⋊C4D412yes—
105C22×C42—21no—
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108#428—232no—
109C2×#107—22no—
110C2×#107—22no—
111C2×#107—22no—
112C2×#107—22no—
113C2×#107—22no—
114C2×#107—22no—
115C2×#107—22no—
116C2×#107—22no—
117C2×#107—22no—
118C2×#107—22no—
119C2×#107—41no—
120C2×#107D414yes—
121C2×#106—22no—
122C2×#106—22no—
123C2×#106—22no—
124C2×#106—22no—
125C2×#106—22no—
126C2×#106—22no—
127C2×#106—22no—
128C2×#106—22no—
129C2×#106—22no—
130C2×#106—22no—
131C2×#106—22no—
132C2×#106—22no—
133C2×#106—22no—
134C2×#106—22no—
135C2×#106—41no—
136C2×#106—41no—
137C2×#106—41no—
138C2×#106D414yes—
139C2×C22⋊C8C2×C414yes—
140C2×C22⋊C8D414yes—
141C2×C22⋊C8Q814yes—
142C2×#97—22no—
143C2×#97—22no—
144C2×#97C2×C414yescomplemented
145C2×C4×C8—22no—
146C2×C4×C8—22no—
147C2×C4×C8C2×C414yescomplemented
148#385—48no—
149#384—22no—
150#384—22no—
151#384—22no—
152#384—41no—
153#384—41no—
154#384—41no—
155#382—22no—
156#382—41no—
157#380—22no—
158#380—22no—
159#380—22no—
160#380—22no—
161C4×C22⋊C4C2×C414yes—
162C4×C22⋊C4Q814yes—
163C2×#95—22no—
164C2×#95—22no—
165C2×#95—22no—
166C2×#95—21no—
167C2×#95—22no—
168C2×#95—21no—
169C2×#95—22no—
170C2×#95D412yes—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#336C2×C414yescomplemented
178#336C2×C414yescomplemented
179C25C2×D411yescharacteristic
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—44no—
200C23×C4—82no—
201C23×C4C22×C412yes—
202C23×C4C2×D412yes—
203C23×C4C2×D411yescharacteristic
204C23×C4C2×D412yes—
205C23×C4C2×D412yes—
206C23×C4C2×D412yes—
207C23×C4C2×Q812yes—
208C23×C4C2×Q812yes—
209C23×C4C2×Q812yes—
210C23×C4C2411yescharacteristic
211C2×M16—28no—
212C2×M16—28no—
213C2×M16—28no—
214C2×M16—28no—
215C2×M16—28no—
216C2×M16—28no—
217C2×M16C4⋊C4116yescomplemented
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8C22×C412yes—
231C22×C8C22×C412yes—
232C22×C8C22×C412yes—
233C22×C8C22×C412yes—
234C22×C8C2×D412yes—
235C22×C8C2×D412yes—
236C22×C8C2×D412yes—
237C22×C8C2×D412yes—
238C22×C8C2×D412yes—
239C22×C8C2×D412yes—
240C22×C8C2×Q812yes—
241C22×C8C2×Q812yes—
242C22×C8C2×Q812yes—
243C22×C8C2×Q812yes—
244C22×C8#4112yes—
245C22×C8#4112yes—
246#117—28no—
247#117—44no—
248#117—44no—
249#117—44no—
250C2×C4⋊C4—28no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
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—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—82no—
308C2×C4⋊C4—82no—
309C2×C4⋊C4—82no—
310C2×C4⋊C4C2×D412yes—
311C2×C4⋊C4C2×D412yes—
312C2×C4⋊C4C2×D412yes—
313C2×C4⋊C4C2×D412yes—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—82no—
323C2×C22⋊C4C4⋊C418yes—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—42no—
333C2×C42—42no—
334C2×C42—42no—
335C2×C42C22×C412yes—
336C2×C42C22×C412yes—
337C2×C42C2×Q812yes—
338C2×C42C2×Q812yes—
339#107—28no—
340#107—28no—
341#107—44no—
342#107—44no—
343#106—28no—
344#106—28no—
345#106—44no—
346#106—44no—
347#106—44no—
348#106—44no—
349C22⋊C8C4⋊C4116yescomplemented
350#97—28no—
351C4×C8—28no—
352#95—44no—
353#95—44no—
354#95—42no—
355#95—42no—
356#95—44no—
357#95—44no—
358#95—82no—
359#95C4⋊C418yes—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24—22no—
368C24C2×C4⋊C412yes—
369C24#12712yes—
370C24C4⋊Q812yes—
371C24C22×D411yescharacteristic
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
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—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—48no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
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—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—88no—
452C22×C4—88no—
453C22×C4—84no—
454C22×C4—84no—
455C22×C4C2×C4⋊C414yes—
456C22×C4C2×C4⋊C414yes—
457C22×C4C2×C4⋊C414yes—
458C22×C4C2×C4⋊C412yes—
459C22×C4C2×C4⋊C414yes—
460C22×C4#12712yes—
461C22×C4C4⋊Q814yes—
462C22×C4C4⋊Q814yes—
463C22×C4C4⋊Q812yes—
464C22×C4AGL(1,ℤ/8)14yes—
465C22×C4#13714yes—
466C22×C4C23×C411yescharacteristic
467C22×C4C22×D411yescharacteristic
468C22×C4C22×D411yescharacteristic
469C22×C4C22×D411yescharacteristic
470C22×C4C22×D411yescharacteristic
471C22×C4C22×Q811yescharacteristic
472C22×C4C22×Q811yescharacteristic
473C22×C4C22×Q811yescharacteristic
474C22×C4C2×#4111yescharacteristic
475C22×C4C2×#4111yescharacteristic
476C22×C4H(5,𝔽2)11yescharacteristic
477C22×C4H(5,𝔽2)11yescharacteristic
478C22×C42−1+411yescharacteristic
479C22×C42−1+411yescharacteristic
480M16—232no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8C2×C4⋊C414yes—
500C2×C8C2×C4⋊C414yes—
501C2×C8C2×C4⋊C414yes—
502C2×C8C2×C4⋊C414yes—
503C2×C8C4×D414yes—
504C2×C8C4×D414yes—
505C2×C8#12014yes—
506C2×C8C22⋊Q814yes—
507C2×C8C22⋊Q814yes—
508C2×C8#12314yes—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—48no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—88no—
543C4⋊C4—88no—
544C4⋊C4—88no—
545C22⋊C4—216no—
546C22⋊C4—48no—
547C22⋊C4—84no—
548C22⋊C4—84no—
549C42—22no—
550C42—22no—
551C42—22no—
552C42—22no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—48no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23#38414yes—
581C23C22×C4⋊C411yescharacteristic
582C23C2×#12711yescharacteristic
583C23C2×C4⋊Q811yescharacteristic
584C23D4211yescharacteristic
585C23D4211yescharacteristic
586C23#54711yescharacteristic
587C23#54711yescharacteristic
588C23C2×AGL(1,ℤ/8)12yes—
589C23C2×#13712yes—
590C23#57712yes—
591C23#57712yes—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—816no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—81no—
636C2×C4—82no—
637C2×C4—82no—
638C2×C4—82no—
639C2×C4—82no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4—82no—
643C2×C4—82no—
644C2×C4—81no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—82no—
655C2×C4—82no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4#38414yes—
661C2×C4#42818yescomplemented
662C2×C4C22×C4⋊C411yescharacteristic
663C2×C4C22×C4⋊C411yescharacteristic
664C2×C4C2×C4×D411yescharacteristic
665C2×C4C2×C4×D411yescharacteristic
666C2×C4#52011yescharacteristic
667C2×C4#52011yescharacteristic
668C2×C4C2×#12011yescharacteristic
669C2×C4C2×C22⋊Q811yescharacteristic
670C2×C4C2×C22⋊Q811yescharacteristic
671C2×C4C2×#12311yescharacteristic
672C2×C4C2×C4⋊Q811yescharacteristic
673C2×C4C2×C4⋊Q811yescharacteristic
674C2×C4#53511yescharacteristic
675C2×C4#53611yescharacteristic
676C2×C4#54411yescharacteristic
677C2×C4#54411yescharacteristic
678C2×C4D4211yescharacteristic
679C2×C4D4211yescharacteristic
680C2×C4#54711yescharacteristic
681C2×C4#54711yescharacteristic
682C2×C4D4×Q811yescharacteristic
683C2×C4D4×Q811yescharacteristic
684C2×C4D4×Q811yescharacteristic
685C2×C4D4×Q811yescharacteristic
686C2×C4#55411yescharacteristic
687C2×C4#55411yescharacteristic
688C2×C4#55411yescharacteristic
689C2×C4#55411yescharacteristic
690C8—24no—
691C8—24no—
692C8—24no—
693C8#38518yescomplemented
694C22—24no—
695C22—24no—
696C22—24no—
697C22—42no—
698C22—42no—
699C22—44no—
700C22—44no—
701C22—42no—
702C22—42no—
703C22—44no—
704C22—44no—
705C22C2×#38411yescharacteristic
706C22D4×C4⋊C411yescharacteristic
707C22D4×C4⋊C411yescharacteristic
708C22#243311yescharacteristic
709C22#244011yescharacteristic
710C22#244011yescharacteristic
711C22#250111yescharacteristic
712C22C2×#42812yes—
713C22#291212yes—
714C22#315111yescharacteristic
715C22#315211yescharacteristic
716C22#315411yescharacteristic
717C22#315411yescharacteristic
718C22#316312yes—
719C22#316512yes—
720C22#326512yes—
721C22#326612yes—
722C22#327212yes—
723C22#327812yes—
724C22#334412yes—
725C22#334512yes—
726C22#335412yes—
727C22#335612yes—
728C4—24no—
729C4—28no—
730C4—44no—
731C4—82no—
732C4—82no—
733C4—82no—
734C4—82no—
735C4—161no—
736C4—161no—
737C4—161no—
738C4—161no—
739C4C2×#38511yescharacteristic
740C4#231711yescharacteristic
741C4D4×C4⋊C411yescharacteristic
742C4D4×C4⋊C411yescharacteristic
743C4#243411yescharacteristic
744C4#244011yescharacteristic
745C4#244011yescharacteristic
746C4#250211yescharacteristic
747C2—44no—
748C2#1388011yescharacteristic
749C2#2080011yescharacteristic
750C2#2080211yescharacteristic
751C2#2265912yes—
752C2#2266312yes—
753C2#2579011yescharacteristic
754C2#2579111yescharacteristic
755C2#2607212yes—
756C2#2607812yes—
757C2#2794011yescharacteristic
758C2#2794111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1847C2semidirect
5. C2×#1844C2semidirect
10. #11325C2semidirect
11. #11324C2semidirect
12. #11323C2semidirect
13. #11323C2semidirect
14. #10863C2semidirect
15. #10862C2semidirect
48. #1753C4semidirect
144. C2×#97C2×C4semidirect
147. C2×C4×C8C2×C4semidirect
177. #336C2×C4semidirect
178. #336C2×C4semidirect
217. C2×M16C4⋊C4semidirect
349. C22⋊C8C4⋊C4semidirect
661. C2×C4#428semidirect
693. C8#385semidirect

Maximal subgroups

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

subgroupindex
C22×#4282
C2×#18542
C2×#18532
C2×#18472
C2×#18442
C2×#18092
C2×#17532
#138802
#138792
#113252
#113242
#113232
#108632
#108622