Finite Group Databasebeta

← #372930

Subgroups — #372930

Order 512.

970 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21050C211yesmaximal, characteristic
2#20699C211yesmaximal, characteristic
3#20379C211yesmaximal, characteristic
4#11291C211yesmaximal, characteristic, complemented
5#11258C211yesmaximal, characteristic, complemented
6#11201C211yesmaximal, characteristic
7#11097C211yesmaximal, characteristic
8#10922C211yesmaximal, characteristic
9#10910C211yesmaximal, characteristic, complemented
10#10887C211yesmaximal, characteristic, complemented
11#10819C211yesmaximal, characteristic, complemented
12#10809C211yesmaximal, characteristic, complemented
13#10809C211yesmaximal, characteristic, complemented
14#10733C211yesmaximal, characteristic
15#10707C211yesmaximal, characteristic, complemented
16C22×#117C2211yescharacteristic
17C22×#108C2211yescharacteristic
18C2×#424C2211yescharacteristic
19C2×#407C2211yescharacteristic
20C2×#407C2211yescharacteristic
21C22×C22⋊C8C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C2×#405C2211yescharacteristic
24C2×#405C2211yescharacteristic
25C2×#405C2211yescharacteristic
26C22×#97C2211yescharacteristic
27#2280C2211yescharacteristic
28C2×C4×C22⋊C4C2211yescharacteristic
29#1924—21no—
30#1924—21no—
31#1923—21no—
32#1923—21no—
33#1825C411yescharacteristic, complemented
34#1825C411yescharacteristic, complemented
35#1825C411yescharacteristic, complemented
36#1825C411yescharacteristic, complemented
37#1824C411yescharacteristic, complemented
38#1824C411yescharacteristic, complemented
39#1823C411yescharacteristic, complemented
40#1823C411yescharacteristic, complemented
41#1750—21no—
42#1750—21no—
43#1749—21no—
44C4×C22⋊C8—21no—
45C2×#341C2211yescharacteristic
46C2×#341C2211yescharacteristic
47C2×#341C2211yescharacteristic
48#1735C2211yescharacteristic
49#1735C2211yescharacteristic
50#1735C2211yescharacteristic
51#1735C2211yescharacteristic
52C2×#339C2211yescharacteristic
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60#1729C2211yescharacteristic
61#1729C2211yescharacteristic
62#1729C2211yescharacteristic
63#1729C2211yescharacteristic
64C2×#336C2211yescharacteristic
65C2×#336C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C24×C4C2311yescharacteristic
68C22×M16C2311yescharacteristic
69C22×M16C2311yescharacteristic
70C22×M16C2311yescharacteristic
71C22×M16C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C2×#117—21no—
77C2×#117—21no—
78C2×#117—22no—
79C2×#117—22no—
80C2×#117—41no—
81C2×#117—41no—
82C2×#117C2×C411yescharacteristic
83C2×#117C2×C411yescharacteristic
84C2×#117C2311yescharacteristic
85C2×#117C2311yescharacteristic
86C2×#117C2311yescharacteristic
87C2×#117C2311yescharacteristic
88C22×C4⋊C4C2×C411yescharacteristic
89C22×C4⋊C4C2×C411yescharacteristic
90C22×C22⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C42—21no—
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C2×#108—22no—
96C2×#108—41no—
97C2×#108—41no—
98#424—22no—
99#424—41no—
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102#407—22no—
103#407—22no—
104#407—22no—
105#407—41no—
106C2×C22⋊C8—21no—
107C2×C22⋊C8—21no—
108C2×C22⋊C8—22no—
109C2×C22⋊C8—22no—
110C2×C22⋊C8—21no—
111C2×C22⋊C8—21no—
112C2×C22⋊C8—41no—
113C2×C22⋊C8—41no—
114C2×C22⋊C8C2×C411yescharacteristic
115C2×C22⋊C8C2×C411yescharacteristic
116C2×C22⋊C8C2×C411yescharacteristic
117C2×C22⋊C8C2×C411yescharacteristic
118C2×C22⋊C8D411yescharacteristic
119C2×C22⋊C8D411yescharacteristic
120C2×C22⋊C8D411yescharacteristic
121C2×C22⋊C8D411yescharacteristic
122#405—22no—
123#405—22no—
124#405—22no—
125#405—22no—
126#405—41no—
127#405—41no—
128C2×#97—21no—
129C2×#97—21no—
130C2×#97—21no—
131C2×#97—22no—
132C2×#97—22no—
133C2×#97—41no—
134C2×C4×C8—21no—
135C2×C4×C8—21no—
136C2×C4×C8—21no—
137#381—21no—
138#380C2×C411yescharacteristic
139#380C2×C411yescharacteristic
140#380C2×C411yescharacteristic
141#380C2×C411yescharacteristic
142#379—21no—
143C4×C22⋊C4—21no—
144C4×C22⋊C4—21no—
145C4×C22⋊C4—22no—
146C4×C22⋊C4—41no—
147C2×#95—21no—
148#341—22no—
149#341—22no—
150#341—41no—
151#340C2×C411yescharacteristic
152#340C2×C411yescharacteristic
153#340C2×C411yescharacteristic
154#340C2×C411yescharacteristic
155#340C2×C411yescharacteristic
156#340C2×C411yescharacteristic
157#340C2×C411yescharacteristic
158#340C2×C411yescharacteristic
159#340C2×C411yescharacteristic
160#340C2×C411yescharacteristic
161#340C2×C411yescharacteristic
162#340C2×C411yescharacteristic
163#340C2×C411yescharacteristic
164#340C2×C411yescharacteristic
165#340C2×C411yescharacteristic
166#340C2×C411yescharacteristic
167#339—22no—
168#339—22no—
169#339—22no—
170#339—22no—
171#339—22no—
172#339—41no—
173#339—41no—
174#339—41no—
175#336—21no—
176#336—21no—
177#336—21no—
178#336—21no—
179#336—21no—
180#336—21no—
181#336—21no—
182#336—21no—
183#336—22no—
184#336—41no—
185#336—41no—
186C25#4111yescharacteristic
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—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4C22×C411yescharacteristic
204C23×C4C22×C411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4#4111yescharacteristic
208C23×C4C2411yescharacteristic
209C2×M16—21no—
210C2×M16—21no—
211C2×M16—21no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16#4112yes—
231C2×M16#4112yes—
232C2×M16#4112yes—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
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—21no—
248C22×C8—21no—
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×C8C22×C411yescharacteristic
260C22×C8C22×C411yescharacteristic
261C22×C8C22×C411yescharacteristic
262C22×C8C22×C411yescharacteristic
263C22×C8C2×D411yescharacteristic
264C22×C8C2×D411yescharacteristic
265C22×C8C2×D411yescharacteristic
266C22×C8C2×D411yescharacteristic
267C22×C8#4112yes—
268C22×C8#4112yes—
269#117—21no—
270#117—21no—
271#117—21no—
272#117—21no—
273#117—21no—
274#117—21no—
275#117—21no—
276#117—21no—
277#117—21no—
278#117—21no—
279#117—21no—
280#117—21no—
281#117—21no—
282#117—21no—
283#117—22no—
284#117—22no—
285#117—42no—
286#117—42no—
287#117—42no—
288#117—42no—
289#117—41no—
290#117—41no—
291#117#4112yes—
292#117#4112yes—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4C22×C411yescharacteristic
300C2×C4⋊C4C22×C411yescharacteristic
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C4⋊C4C22×C411yescharacteristic
304C2×C4⋊C4C22×C411yescharacteristic
305C2×C4⋊C4C22×C411yescharacteristic
306C2×C4⋊C4C22×C411yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C42—21no—
323C2×C42—21no—
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—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42#4112yes—
342#108—44no—
343C4⋊C8—42no—
344C4⋊C8—42no—
345C22⋊C8—24no—
346C22⋊C8—24no—
347C22⋊C8—22no—
348C22⋊C8—22no—
349C22⋊C8—22no—
350C22⋊C8—22no—
351C22⋊C8—41no—
352C22⋊C8—41no—
353C22⋊C8—41no—
354C22⋊C8—41no—
355C22⋊C8—42no—
356C22⋊C8—42no—
357#97—44no—
358#97—42no—
359#97—42no—
360#97—42no—
361C4×C8—42no—
362C4×C8—42no—
363C4×C8—42no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—42no—
369C24—22no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24C4×D411yescharacteristic
380C24C4×D411yescharacteristic
381C24C2×#4111yescharacteristic
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
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—42no—
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—42no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4C4×D411yescharacteristic
457C22×C4C4×D411yescharacteristic
458C22×C4C23×C411yescharacteristic
459C22×C4C22×D411yescharacteristic
460C22×C4C2×#4111yescharacteristic
461C22×C4C2×#4111yescharacteristic
462C22×C4C2×#4111yescharacteristic
463C22×C4C2×#4111yescharacteristic
464C22×C4C2×#4111yescharacteristic
465C22×C4C2×#4111yescharacteristic
466C22×C4C2×#4111yescharacteristic
467C22×C4C2×#4111yescharacteristic
468C22×C4H(5,𝔽2)11yescharacteristic
469C22×C4H(5,𝔽2)11yescharacteristic
470C22×C4H(5,𝔽2)11yescharacteristic
471C22×C42−1+411yescharacteristic
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—41no—
479M16—41no—
480M16—41no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16—41no—
487M16—41no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—22no—
515C2×C8—21no—
516C2×C8—21no—
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—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8#12312yes—
539C2×C8#12312yes—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4#11712yes—
557C4⋊C4#11712yes—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—48no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—42no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—42no—
578C42—42no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C23—21no—
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—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—81no—
619C23—81no—
620C23—81no—
621C23—81no—
622C23—81no—
623C23—81no—
624C23#44412yes—
625C23C2×C4×D411yescharacteristic
626C23#52911yescharacteristic
627C23#52911yescharacteristic
628C23#55111yescharacteristic
629C23#55111yescharacteristic
630C23#55111yescharacteristic
631C23#55211yescharacteristic
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
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—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4C2×#11711yescharacteristic
699C2×C4C4×#4111yescharacteristic
700C2×C4C4×#4111yescharacteristic
701C2×C4C4×#4111yescharacteristic
702C2×C4#51811yescharacteristic
703C2×C4#52011yescharacteristic
704C2×C4C2×#12311yescharacteristic
705C2×C4#52511yescharacteristic
706C2×C4#52911yescharacteristic
707C2×C4#52911yescharacteristic
708C2×C4#52911yescharacteristic
709C2×C4#52911yescharacteristic
710C2×C4#53811yescharacteristic
711C2×C4#53911yescharacteristic
712C2×C4#54011yescharacteristic
713C2×C4#54211yescharacteristic
714C2×C4#54611yescharacteristic
715C2×C4#54611yescharacteristic
716C2×C4#54611yescharacteristic
717C2×C4#54711yescharacteristic
718C2×C4#55111yescharacteristic
719C2×C4#55211yescharacteristic
720C2×C4#55211yescharacteristic
721C2×C4#55311yescharacteristic
722C2×C4#55311yescharacteristic
723C2×C4#55511yescharacteristic
724C2×C4#55511yescharacteristic
725C2×C4#55911yescharacteristic
726C8—22no—
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C8—42no—
735C8—42no—
736C8—42no—
737C8—81no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22C4×#12311yescharacteristic
769C22#234211yescharacteristic
770C22#235911yescharacteristic
771C22#251511yescharacteristic
772C22#252611yescharacteristic
773C22#257211yescharacteristic
774C22#257511yescharacteristic
775C22C2×#44411yescharacteristic
776C22#295511yescharacteristic
777C22#295611yescharacteristic
778C22#295711yescharacteristic
779C4—41no—
780C4—41no—
781C4—42no—
782C4—42no—
783C4—82no—
784C4—82no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4—81no—
789C4—81no—
790C4—81no—
791C4#229811yescharacteristic
792C4#233511yescharacteristic
793C4#234611yescharacteristic
794C4#237411yescharacteristic
795C4#241911yescharacteristic
796C4#242011yescharacteristic
797C4#245911yescharacteristic
798C4#246811yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—42no—
804C2—81no—
805C2#1410311yescharacteristic
806C2#2159311yescharacteristic
807C2#2159411yescharacteristic
808C2#2258611yescharacteristic
809C2#2258811yescharacteristic
810C2#2294911yescharacteristic
811C2#2295011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11291C2semidirect
5. #11258C2semidirect
9. #10910C2semidirect
10. #10887C2semidirect
11. #10819C2semidirect
12. #10809C2semidirect
13. #10809C2semidirect
15. #10707C2semidirect
33. #1825C4semidirect
34. #1825C4semidirect
35. #1825C4semidirect
36. #1825C4semidirect
37. #1824C4semidirect
38. #1824C4semidirect
39. #1823C4semidirect
40. #1823C4semidirect

Maximal subgroups

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

subgroupindex
#210502
#206992
#203792
#112912
#112582
#112012
#110972
#109222
#109102
#108872
#108192
#108092
#107332
#107072