Finite Group Databasebeta

← #222001

Subgroups — #222001

Order 512.

1237 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36122C211yesmaximal, characteristic
2#22795C211yesmaximal, characteristic, complemented
3#22648C211yesmaximal, characteristic, complemented
4C2×#1546C211yesmaximal, characteristic, complemented
5C2×#1540C211yesmaximal, characteristic, complemented
6#9704C211yesmaximal, characteristic, complemented
7#9698C211yesmaximal, characteristic, complemented
8#9141C211yesmaximal, characteristic, complemented
9#9134C211yesmaximal, characteristic, complemented
10#9131C211yesmaximal, characteristic, complemented
11#9130C211yesmaximal, characteristic, complemented
12#8586C211yesmaximal, characteristic, complemented
13#8341C211yesmaximal, characteristic, complemented
14#8340C211yesmaximal, characteristic, complemented
15#8236C211yesmaximal, characteristic, complemented
16C2×#548—21no—
17C2×#532C2211yescharacteristic
18C22×C4⋊Q8C2211yescharacteristic
19C2×#435—21no—
20C2×#431C2211yescharacteristic
21C2×#431C2211yescharacteristic
22C2×#423C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24#2858C2211yescharacteristic
25#2857C2211yescharacteristic
26#2856C2211yescharacteristic
27#2545—21no—
28#2491—21no—
29#2491C412yes—
30#2452—21no—
31#2452C412yes—
32#2436—21no—
33#2432—21no—
34#2416—21no—
35#2416C412yes—
36#2361—21no—
37#2361C412yes—
38C4×C4⋊Q8C2211yescharacteristic
39C42×D4C2211yescharacteristic
40#1954—21no—
41#1940—21no—
42#1923—21no—
43#1923—21no—
44#1851—21no—
45#1850—21no—
46#1842C2211yescharacteristic
47#1842C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1797C2211yescharacteristic
52C8×C4⋊C4—21no—
53#1767C2211yescharacteristic
54C4×C4⋊C8C2211yescharacteristic
55#1546—24no—
56#1540—24no—
57C2×#332C2211yescharacteristic
58C2×#332C2211yescharacteristic
59C2×#332C2211yescharacteristic
60C2×#332C2211yescharacteristic
61C2×#332C2211yescharacteristic
62C2×#332C2211yescharacteristic
63C2×#332C2211yescharacteristic
64C2×#332C2211yescharacteristic
65C2×#331C2211yescharacteristic
66C2×#331C2211yescharacteristic
67C2×#331C2211yescharacteristic
68C2×#331C2211yescharacteristic
69#1296C2211yescharacteristic
70#1296C2211yescharacteristic
71#1296C2211yescharacteristic
72#1296C2211yescharacteristic
73C22×#41—21no—
74C23×Q8—21no—
75C22×M16—21no—
76C23×C8—21no—
77#548—44no—
78#548—44no—
79#532—22no—
80#532—22no—
81#532—41no—
82#532—41no—
83C2×C4⋊Q8—22no—
84C2×C4⋊Q8—22no—
85C2×C4⋊Q8—21no—
86C2×C4⋊Q8—21no—
87C2×C4⋊Q8—41no—
88C2×C4⋊Q8—41no—
89C2×C4⋊Q8C2×C412yes—
90C2×C4⋊Q8C2311yescharacteristic
91C2×C4⋊Q8C2311yescharacteristic
92C2×#127C2311yescharacteristic
93C2×#124—22no—
94C2×#124—21no—
95C2×#124—21no—
96C2×#124—21no—
97C2×C22⋊Q8—21no—
98C2×C22⋊Q8—22no—
99C2×#121—22no—
100C2×#121—21no—
101C2×#121—21no—
102C2×#121—21no—
103C2×#121C2×C412yes—
104C2×#121C2×C412yes—
105C2×C4×Q8—21no—
106C2×C4×D4—22no—
107C2×C4×D4—21no—
108C2×C4×D4C2×C412yes—
109C2×C4×D4C2×C411yescharacteristic
110C2×C4×D4D411yescharacteristic
111C2×C4×D4D411yescharacteristic
112C22×C4⋊C4—21no—
113C22×C4⋊C4C2×C412yes—
114C22×C42C2311yescharacteristic
115C22×C42C2311yescharacteristic
116#435—44no—
117#431—22no—
118#431—22no—
119#431—41no—
120#431—41no—
121#423—22no—
122#423—41no—
123C2×C4⋊C8—22no—
124C2×C4⋊C8—21no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127C2×C4⋊C8—21no—
128C2×C4⋊C8—21no—
129C2×C4⋊C8—21no—
130C2×C4⋊C8—41no—
131C2×C4⋊C8C2311yescharacteristic
132C2×C4⋊C8C2311yescharacteristic
133C2×C4⋊C8C2311yescharacteristic
134C2×C4⋊C8C2311yescharacteristic
135C2×C4⋊C8C2311yescharacteristic
136C2×C4⋊C8C2311yescharacteristic
137C2×C4⋊C8C2311yescharacteristic
138C2×C4⋊C8C2311yescharacteristic
139C2×C22⋊C8—21no—
140C2×C22⋊C8—21no—
141C2×C22⋊C8—21no—
142C2×C22⋊C8—21no—
143C2×C22⋊C8—21no—
144C2×C22⋊C8—21no—
145C2×#97—21no—
146C2×C4×C8—21no—
147C2×C4×C8—21no—
148C2×C4×C8—21no—
149#396—22no—
150#396—22no—
151#394—22no—
152#394—22no—
153#393—22no—
154#393—22no—
155#391—21no—
156#391—21no—
157#390—21no—
158#390—21no—
159#390—21no—
160#390—21no—
161#390C2×C412yes—
162#390C2×C412yes—
163#390C2×C412yes—
164#389—21no—
165#389—21no—
166#389C2×C412yes—
167#389C2×C412yes—
168#388—22no—
169#388—22no—
170#386—22no—
171#386—22no—
172#385—22no—
173#385—22no—
174#384C2311yescharacteristic
175#380—21no—
176#380C2×C412yes—
177C4×C4⋊C4—21no—
178C4×C4⋊C4C2×C412yes—
179C4×C4⋊C4C2×C411yescharacteristic
180C4×C4⋊C4D411yescharacteristic
181C4×C4⋊C4D411yescharacteristic
182C4×C22⋊C4C2×C411yescharacteristic
183C4×C22⋊C4C2×C411yescharacteristic
184C4×C22⋊C4D411yescharacteristic
185C4×C22⋊C4D411yescharacteristic
186C4×C22⋊C4D411yescharacteristic
187C4×C22⋊C4D411yescharacteristic
188C43C2311yescharacteristic
189#336—21no—
190#336—21no—
191#336—21no—
192#336—21no—
193#336—21no—
194#336—21no—
195#332—22no—
196#332—22no—
197#332—22no—
198#332—22no—
199#332—22no—
200#332—41no—
201#332—41no—
202#332D414yescomplemented
203#331—22no—
204#331—22no—
205#331—41no—
206#331—41no—
207C2×#41—42no—
208C2×#41—42no—
209C2×#41—42no—
210C2×#41—42no—
211C2×#41—81no—
212C2×#41—81no—
213C22×Q8—22no—
214C22×Q8—21no—
215C22×Q8—21no—
216C22×Q8—42no—
217C22×Q8—42no—
218C22×Q8—42no—
219C22×Q8—42no—
220C22×Q8—81no—
221C22×Q8—81no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4C22⋊C411yescharacteristic
227C22×D4C22×C412yes—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4C22×C411yescharacteristic
231C23×C4C22×C411yescharacteristic
232C23×C4C2×D411yescharacteristic
233C23×C4C2×D411yescharacteristic
234C23×C4C2×D411yescharacteristic
235C23×C4C2×D411yescharacteristic
236C2×M16—42no—
237C2×M16—42no—
238C2×M16—81no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—42no—
248C22×C8—42no—
249C22×C8—81no—
250C4⋊Q8—24no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—42no—
258C4⋊Q8—42no—
259C4⋊Q8—42no—
260C4⋊Q8—42no—
261C4⋊Q8—42no—
262C4⋊Q8C2×D412yes—
263C4⋊Q8#4112yes—
264#127—21no—
265#127—21no—
266#127—21no—
267#127—21no—
268#124—42no—
269#124—42no—
270#124—48no—
271#124—42no—
272#124—42no—
273#124—81no—
274#124—81no—
275C22⋊Q8—42no—
276C22⋊Q8—42no—
277C22⋊Q8—48no—
278#121—24no—
279#121—42no—
280#121—42no—
281#121—42no—
282#121—42no—
283#121—42no—
284#121—48no—
285#121—42no—
286#121—42no—
287#121—44no—
288C4×Q8—42no—
289C4×Q8—42no—
290C4×D4—24no—
291C4×D4—42no—
292C4×D4—42no—
293C4×D4—42no—
294C4×D4—41no—
295C4×D4—41no—
296C4×D4—42no—
297C4×D4—48no—
298C4×D4D814yes—
299C4×D4SD1614yes—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4C22⋊C411yescharacteristic
313C2×C4⋊C4C22⋊C411yescharacteristic
314C2×C4⋊C4C22⋊C411yescharacteristic
315C2×C4⋊C4C22×C412yes—
316C2×C4⋊C4C22×C412yes—
317C2×C4⋊C4C22×C412yes—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4C22⋊C411yescharacteristic
329C2×C22⋊C4C22⋊C411yescharacteristic
330C2×C22⋊C4C22⋊C411yescharacteristic
331C2×C22⋊C4C22⋊C411yescharacteristic
332C2×C22⋊C4C22⋊C411yescharacteristic
333C2×C22⋊C4C22⋊C411yescharacteristic
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—22no—
343C2×C42C22×C411yescharacteristic
344C2×C42C22×C411yescharacteristic
345C2×C42C22×C411yescharacteristic
346C2×C42C22×C411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C2×C42C2×D411yescharacteristic
354C2×C42C2×D411yescharacteristic
355C2×C42C2411yescharacteristic
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—21no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8—21no—
370C4⋊C8—42no—
371C4⋊C8—42no—
372C4⋊C8—42no—
373C4⋊C8—42no—
374C4⋊C8—81no—
375C4⋊C8—81no—
376C4⋊C8C2×D412yes—
377C4⋊C8C2×D412yes—
378C22⋊C8—42no—
379C22⋊C8—42no—
380C22⋊C8—42no—
381C22⋊C8—42no—
382C22⋊C8—81no—
383C22⋊C8—81no—
384#97—42no—
385C4×C8—42no—
386C4×C8—42no—
387C4×C8—42no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95C22⋊C411yescharacteristic
393#95C22⋊C411yescharacteristic
394#95C22⋊C411yescharacteristic
395#95C22⋊C411yescharacteristic
396#95C22⋊C411yescharacteristic
397#95C22⋊C411yescharacteristic
398C24—22no—
399C24C2×C22⋊C411yescharacteristic
400C24C2×C22⋊C411yescharacteristic
401#41—84no—
402#41—84no—
403#41—84no—
404#41—84no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—44no—
419C2×Q8—82no—
420C2×Q8—84no—
421C2×Q8—84no—
422C2×Q8—84no—
423C2×Q8—84no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—44no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—44no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—82no—
448C2×D4#10214yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—82no—
485C22×C4—82no—
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×C22⋊C411yescharacteristic
494C22×C4C2×C22⋊C411yescharacteristic
495C22×C4C2×C22⋊C411yescharacteristic
496C22×C4C2×D812yes—
497C22×C4C2×D812yes—
498C22×C4C2×SD1612yes—
499C22×C4C2×SD1612yes—
500C22×C4C23×C411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×D411yescharacteristic
503M16—84no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—84no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—41no—
536C4⋊C4—44no—
537C4⋊C4—44no—
538C4⋊C4—42no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—44no—
546C4⋊C4—44no—
547C4⋊C4#10214yes—
548C4⋊C4C4×D414yes—
549C22⋊C4—22no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—44no—
554C22⋊C4—44no—
555C22⋊C4—44no—
556C22⋊C4—44no—
557C22⋊C4—44no—
558C22⋊C4—44no—
559C22⋊C4—44no—
560C22⋊C4—44no—
561C22⋊C4—82no—
562C22⋊C4—82no—
563C22⋊C4#10214yes—
564C22⋊C4#10214yes—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—41no—
584C42—41no—
585C42—44no—
586C42C2×D812yes—
587C42C2×SD1612yes—
588C42C22×D411yescharacteristic
589C42C2×#4111yescharacteristic
590C42H(5,𝔽2)11yescharacteristic
591C42H(5,𝔽2)11yescharacteristic
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23C2×#10212yes—
612C23C2×#10212yes—
613C23C22×C22⋊C411yescharacteristic
614Q8—42no—
615Q8—42no—
616Q8—42no—
617Q8—42no—
618Q8—88no—
619Q8—81no—
620Q8—81no—
621Q8—81no—
622Q8—81no—
623D4—44no—
624D4—82no—
625D4—82no—
626D4—88no—
627D4—88no—
628D4—81no—
629D4—81no—
630D4—81no—
631D4—81no—
632D4—81no—
633D4—81no—
634D4—81no—
635D4—81no—
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—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—24no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—88no—
693C2×C4—88no—
694C2×C4#41312yes—
695C2×C4C2×#10212yes—
696C2×C4C2×#10212yes—
697C2×C4C2×#10212yes—
698C2×C4C2×#10212yes—
699C2×C4C2×C4×D411yescharacteristic
700C2×C4#51811yescharacteristic
701C2×C4D4211yescharacteristic
702C2×C4D4211yescharacteristic
703C2×C4#54611yescharacteristic
704C2×C4#54611yescharacteristic
705C2×C4C22×D811yescharacteristic
706C2×C4C22×SD1611yescharacteristic
707C2×C4#57511yescharacteristic
708C2×C4#57511yescharacteristic
709C2×C4#57611yescharacteristic
710C2×C4#57711yescharacteristic
711C2×C4#57711yescharacteristic
712C2×C4#57811yescharacteristic
713C8—42no—
714C8—42no—
715C8—81no—
716C8—81no—
717C8—81no—
718C8—81no—
719C8—81no—
720C8—81no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22D4×C22⋊C411yescharacteristic
743C22C2×#41311yescharacteristic
744C22#288911yescharacteristic
745C22C22×#10211yescharacteristic
746C22#289611yescharacteristic
747C22#289711yescharacteristic
748C22#289811yescharacteristic
749C4—22no—
750C4—22no—
751C4—21no—
752C4—21no—
753C4—22no—
754C4—22no—
755C4—22no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—44no—
760C4—41no—
761C4—41no—
762C4—82no—
763C4—82no—
764C4#326911yescharacteristic
765C4#327111yescharacteristic
766C4D4×D811yescharacteristic
767C4D4×SD1611yescharacteristic
768C4#329411yescharacteristic
769C4#329511yescharacteristic
770C4#331311yescharacteristic
771C4#332111yescharacteristic
772C2—42no—
773C2—42no—
774C2—162no—
775C2#1770411yescharacteristic
776C2#1772111yescharacteristic
777C2#1776911yescharacteristic
778C2#1777211yescharacteristic
779C2#2241011yescharacteristic
780C2D4×#10211yescharacteristic
781C2#2242611yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radical#36122C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22795C2semidirect
3. #22648C2semidirect
4. C2×#1546C2semidirect
5. C2×#1540C2semidirect
6. #9704C2semidirect
7. #9698C2semidirect
8. #9141C2semidirect
9. #9134C2semidirect
10. #9131C2semidirect
11. #9130C2semidirect
12. #8586C2semidirect
13. #8341C2semidirect
14. #8340C2semidirect
15. #8236C2semidirect
202. #332D4semidirect

Maximal subgroups

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

subgroupindex
#361222
#227952
#226482
C2×#15462
C2×#15402
#97042
#96982
#91412
#91342
#91312
#91302
#85862
#83412
#83402
#82362