Finite Group Databasebeta

← #385239

Subgroups — #385239

Order 512.

1041 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1945C211yesmaximal, characteristic, complemented
2#21148C211yesmaximal, characteristic, complemented
3C2×#1937C211yesmaximal, characteristic
4C2×#1929C211yesmaximal, characteristic
5#20872C211yesmaximal, characteristic
6C2×#1806C211yesmaximal, characteristic
7#20630C211yesmaximal, characteristic
8#11329C211yesmaximal, characteristic, complemented
9#11326C211yesmaximal, characteristic, complemented
10#11226C211yesmaximal, characteristic, complemented
11#11221C211yesmaximal, characteristic, complemented
12#11125C211yesmaximal, characteristic
13#11068C211yesmaximal, characteristic
14#10887C211yesmaximal, characteristic, complemented
15#10874C211yesmaximal, characteristic, complemented
16C2×C4×#41C2211yescharacteristic
17C22×#108C2211yescharacteristic
18C22×#108C2211yescharacteristic
19C2×#427C2211yescharacteristic
20C2×#424C2211yescharacteristic
21C2×#424C2211yescharacteristic
22C2×#424C2211yescharacteristic
23C2×#424C2211yescharacteristic
24C2×#423C2211yescharacteristic
25C22×#104C2211yescharacteristic
26C22×#104C2211yescharacteristic
27C2×#416C2211yescharacteristic
28C2×#416C2211yescharacteristic
29C2×#408C2211yescharacteristic
30C2×#408C2211yescharacteristic
31C2×#405C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33#2296C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35#1945—24no—
36#1940—21no—
37#1940—21no—
38#1939—21no—
39#1939—21no—
40#1937—24no—
41#1929—24no—
42#1865C411yescharacteristic, complemented
43#1865C411yescharacteristic, complemented
44#1864C411yescharacteristic, complemented
45#1864C411yescharacteristic, complemented
46#1863C411yescharacteristic, complemented
47#1863C411yescharacteristic, complemented
48#1862C411yescharacteristic, complemented
49#1862C411yescharacteristic, complemented
50#1806—24no—
51#1798—21no—
52#1798—21no—
53#1797—21no—
54#1797—21no—
55C2×#341C2211yescharacteristic
56C2×#341C2211yescharacteristic
57#1735C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64#1729C2211yescharacteristic
65#1728C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C2×#336C2211yescharacteristic
70C2×#336C2211yescharacteristic
71C22×#41C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C4×#41—22no—
81C4×#41—22no—
82C4×#41—41no—
83C4×#41—41no—
84C2×C4×Q8C2×C411yescharacteristic
85C2×C4×Q8C2×C411yescharacteristic
86C2×C4×D4—21no—
87C2×C4×D4—21no—
88C2×C4×D4C2×C411yescharacteristic
89C2×C4×D4C2×C411yescharacteristic
90C2×#117—21no—
91C2×#117C2311yescharacteristic
92C2×#117C2311yescharacteristic
93C2×#117C2311yescharacteristic
94C22×C4⋊C4—21no—
95C22×C42—21no—
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C2×#108—22no—
100C2×#108—22no—
101C2×#108—41no—
102C2×#108—41no—
103C2×#108—41no—
104C2×#108—41no—
105#427—22no—
106#427—22no—
107C2×#107C2×C411yescharacteristic
108C2×#107C2×C411yescharacteristic
109C2×#106C2×C411yescharacteristic
110C2×#106C2×C411yescharacteristic
111#424—22no—
112#424—22no—
113#424—22no—
114#424—22no—
115#424—41no—
116#424—41no—
117#424—41no—
118#424—41no—
119#423—22no—
120#423—41no—
121C2×C4⋊C8—21no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8—21no—
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—21no—
131C2×#104—22no—
132C2×#104—22no—
133C2×#104—22no—
134C2×#104—22no—
135C2×#104—41no—
136C2×#104—41no—
137#416—41no—
138#416—41no—
139#416D414yes—
140#416Q814yes—
141C2×#103C2×C411yescharacteristic
142C2×#103C2×C411yescharacteristic
143C2×#103C2×C411yescharacteristic
144C2×#103C2×C411yescharacteristic
145C2×#102C2×C411yescharacteristic
146C2×#102C2×C411yescharacteristic
147C2×#102C2×C411yescharacteristic
148C2×#102C2×C411yescharacteristic
149#408—22no—
150#408—22no—
151#408—41no—
152#408—41no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C2×C22⋊C8—21no—
156C2×C22⋊C8—21no—
157#405—22no—
158#405—41no—
159C2×#97—21no—
160C2×C4×C8—22no—
161C2×C4×C8—21no—
162C2×C4×C8—22no—
163C2×C4×C8—41no—
164#389C2×C411yescharacteristic
165#389C2×C411yescharacteristic
166#389C2×C411yescharacteristic
167#389C2×C411yescharacteristic
168#385—21no—
169#385—21no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4—21no—
172C4×C4⋊C4—22no—
173C4×C4⋊C4—41no—
174C2×#95—21no—
175#341—22no—
176#341—41no—
177#340C2×C411yescharacteristic
178#340C2×C411yescharacteristic
179#340C2×C411yescharacteristic
180#340C2×C411yescharacteristic
181#339—22no—
182#339—22no—
183#339—22no—
184#339—22no—
185#339—41no—
186#339D414yes—
187#336—22no—
188#336—21no—
189#336—21no—
190#336—21no—
191#336—21no—
192#336—41no—
193#336—41no—
194#336C2×C411yescharacteristic
195#336C2×C411yescharacteristic
196#336C2×C411yescharacteristic
197#336C2×C411yescharacteristic
198#336D411yescharacteristic
199#336D411yescharacteristic
200#336D411yescharacteristic
201#336D411yescharacteristic
202C2×#41—21no—
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41—21no—
207C2×#41—21no—
208C2×#41—21no—
209C2×#41—21no—
210C2×#41—21no—
211C2×#41—21no—
212C2×#41C2×D412yes—
213C2×#41C2×Q812yes—
214C22×Q8C22×C411yescharacteristic
215C22×D4—21no—
216C22×D4C22×C411yescharacteristic
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4#4111yescharacteristic
223C23×C4#4111yescharacteristic
224C23×C4C2411yescharacteristic
225C2×M16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16C2×D412yes—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8C22×C411yescharacteristic
276C22×C8C22×C411yescharacteristic
277C22×C8C22×C411yescharacteristic
278C22×C8C22×C411yescharacteristic
279C22×C8C2×D411yescharacteristic
280C22×C8C2×D411yescharacteristic
281C22×C8C2×D411yescharacteristic
282C22×C8C2×D411yescharacteristic
283C22×C8C2×D412yes—
284C22×C8C2×Q812yes—
285C4×Q8—22no—
286C4×Q8—22no—
287C4×Q8—41no—
288C4×Q8—41no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4—41no—
292C4×D4—41no—
293C4×D4—42no—
294C4×D4—42no—
295C4×D4—42no—
296C4×D4—42no—
297#117—21no—
298#117—21no—
299#117—21no—
300#117—21no—
301#117—21no—
302#117—21no—
303#117—21no—
304#117—21no—
305#117—42no—
306#117—42no—
307#117C2×D412yes—
308#117C2×D412yes—
309#117C2×Q812yes—
310#117#4112yes—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4C22×C411yescharacteristic
321C2×C4⋊C4C22×C411yescharacteristic
322C2×C4⋊C4C22×C411yescharacteristic
323C2×C4⋊C4C22×C411yescharacteristic
324C2×C4⋊C4C22×C411yescharacteristic
325C2×C4⋊C4C22×C411yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
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—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—42no—
352C2×C42—42no—
353C2×C42C22×C411yescharacteristic
354C2×C42C22×C411yescharacteristic
355C2×C42C2×D412yes—
356C2×C42C2×D411yescharacteristic
357C2×C42C2×D411yescharacteristic
358#108—44no—
359#108—44no—
360#107—22no—
361#107—22no—
362#106—22no—
363#106—22no—
364C4⋊C8—42no—
365C4⋊C8—42no—
366C4⋊C8—42no—
367C4⋊C8—42no—
368C4⋊C8—42no—
369C4⋊C8—42no—
370C4⋊C8—42no—
371C4⋊C8—42no—
372C4⋊C8—42no—
373C4⋊C8—42no—
374#104—44no—
375#104—44no—
376#103—41no—
377#103—41no—
378#103C4⋊C414yescomplemented
379#103C4⋊C414yescomplemented
380#102—41no—
381#102—41no—
382#102C4⋊C414yescomplemented
383#102C4⋊C414yescomplemented
384C22⋊C8—42no—
385C22⋊C8—42no—
386C22⋊C8—42no—
387C22⋊C8—42no—
388#97—42no—
389C4×C8—44no—
390C4×C8—42no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—42no—
396C24—21no—
397C24C2×#4111yescharacteristic
398#41—22no—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—41no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8C2×C4⋊C412yes—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4C2×C4⋊C412yes—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4C4×D411yescharacteristic
474C22×C4C4×D411yescharacteristic
475C22×C4C4×D411yescharacteristic
476C22×C4C4×D411yescharacteristic
477C22×C4C23×C411yescharacteristic
478C22×C4C22×D411yescharacteristic
479C22×C4C22×D411yescharacteristic
480C22×C4C22×D411yescharacteristic
481C22×C4C22×Q811yescharacteristic
482C22×C4C2×#4111yescharacteristic
483C22×C4H(5,𝔽2)11yescharacteristic
484C22×C4H(5,𝔽2)11yescharacteristic
485C22×C4H(5,𝔽2)11yescharacteristic
486C22×C4H(5,𝔽2)11yescharacteristic
487C22×C42−1+411yescharacteristic
488C22×C42−1+411yescharacteristic
489C22×C42−1+411yescharacteristic
490C22×C42−1+411yescharacteristic
491M16—22no—
492M16—22no—
493M16—41no—
494M16—41no—
495M16—41no—
496M16—41no—
497M16—41no—
498M16—41no—
499M16—41no—
500M16—41no—
501M16—41no—
502M16—41no—
503M16—41no—
504M16—41no—
505M16—41no—
506M16—41no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—22no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8C2×C4⋊C412yes—
558C2×C8C2×C4⋊C412yes—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—48no—
571C4⋊C4—42no—
572C4⋊C4—81no—
573C4⋊C4—81no—
574C4⋊C4C2×C4⋊C412yes—
575C4⋊C4C2×C4⋊C412yes—
576C4⋊C4C4×D412yes—
577C4⋊C4C4×D412yes—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—22no—
591C42—21no—
592C42—21no—
593C42—22no—
594C42—22no—
595C42—21no—
596C42—21no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—42no—
601C42—42no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—41no—
606C42—41no—
607C42—41no—
608C42—41no—
609C42—41no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23C2×C4×D411yescharacteristic
622C23#54111yescharacteristic
623C23#54211yescharacteristic
624C23#54611yescharacteristic
625C23#54711yescharacteristic
626C23#55111yescharacteristic
627C23#55411yescharacteristic
628Q8—22no—
629Q8—22no—
630Q8—41no—
631Q8—41no—
632D4—22no—
633D4—22no—
634D4—42no—
635D4—42no—
636D4—42no—
637D4—42no—
638D4—41no—
639D4—41no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—84no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—84no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4#44312yes—
697C2×C4C22×C4⋊C411yescharacteristic
698C2×C4C2×C4×D411yescharacteristic
699C2×C4#51811yescharacteristic
700C2×C4#51911yescharacteristic
701C2×C4#52011yescharacteristic
702C2×C4#52011yescharacteristic
703C2×C4#53611yescharacteristic
704C2×C4#53611yescharacteristic
705C2×C4#53711yescharacteristic
706C2×C4#53711yescharacteristic
707C2×C4#53711yescharacteristic
708C2×C4#53711yescharacteristic
709C2×C4#54111yescharacteristic
710C2×C4#54211yescharacteristic
711C2×C4#54411yescharacteristic
712C2×C4#54411yescharacteristic
713C2×C4D4211yescharacteristic
714C2×C4D4211yescharacteristic
715C2×C4D4211yescharacteristic
716C2×C4#54611yescharacteristic
717C2×C4#54711yescharacteristic
718C2×C4D4×Q811yescharacteristic
719C2×C4D4×Q811yescharacteristic
720C2×C4#55411yescharacteristic
721C2×C4#56011yescharacteristic
722C2×C4#56211yescharacteristic
723C2×C4#56211yescharacteristic
724C2×C4#56311yescharacteristic
725C8—22no—
726C8—22no—
727C8—41no—
728C8—41no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—42no—
734C8—81no—
735C8—81no—
736C8—81no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22#232311yescharacteristic
757C22D4×C4⋊C411yescharacteristic
758C22#235811yescharacteristic
759C22#267211yescharacteristic
760C22#270411yescharacteristic
761C22#272211yescharacteristic
762C22#274211yescharacteristic
763C22C2×#44311yescharacteristic
764C22#295511yescharacteristic
765C22#295611yescharacteristic
766C22#295711yescharacteristic
767C4—22no—
768C4—44no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—41no—
773C4—41no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—82no—
778C4—81no—
779C4—81no—
780C4#231611yescharacteristic
781C4#232311yescharacteristic
782C4D4×C4⋊C411yescharacteristic
783C4#237611yescharacteristic
784C4#267211yescharacteristic
785C4#267511yescharacteristic
786C4#267711yescharacteristic
787C4#270411yescharacteristic
788C2—21no—
789C2—21no—
790C2—21no—
791C2—21no—
792C2—82no—
793C2#1440211yescharacteristic
794C2#2213011yescharacteristic
795C2#2213211yescharacteristic
796C2#2268711yescharacteristic
797C2#2268811yescharacteristic
798C2#2288811yescharacteristic
799C2#2288911yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×#336 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#1945C2semidirect
2. #21148C2semidirect
8. #11329C2semidirect
9. #11326C2semidirect
10. #11226C2semidirect
11. #11221C2semidirect
14. #10887C2semidirect
15. #10874C2semidirect
42. #1865C4semidirect
43. #1865C4semidirect
44. #1864C4semidirect
45. #1864C4semidirect
46. #1863C4semidirect
47. #1863C4semidirect
48. #1862C4semidirect
49. #1862C4semidirect
378. #103C4⋊C4semidirect
379. #103C4⋊C4semidirect
382. #102C4⋊C4semidirect
383. #102C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19452
#211482
C2×#19372
C2×#19292
#208722
C2×#18062
#206302
#113292
#113262
#112262
#112212
#111252
#110682
#108872
#108742