Finite Group Databasebeta

← #371385

Subgroups — #371385

Order 512.

1168 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2924C211yesmaximal, characteristic
2C2×#1945C211yesmaximal, characteristic, complemented
3#21053C211yesmaximal, characteristic
4C2×#1922C211yesmaximal, characteristic, complemented
5#20843C211yesmaximal, characteristic
6#11291C211yesmaximal, characteristic, complemented
7#11221C211yesmaximal, characteristic, complemented
8#11201C211yesmaximal, characteristic
9#11097C211yesmaximal, characteristic
10#10921C211yesmaximal, characteristic
11#10910C211yesmaximal, characteristic, complemented
12#10909C211yesmaximal, characteristic, complemented
13#10887C211yesmaximal, characteristic, complemented
14#10733C211yesmaximal, characteristic
15#10706C211yesmaximal, characteristic, complemented
16C22×#117C2211yescharacteristic
17#2924—24no—
18#2924—24no—
19C2×#433—21no—
20C2×#433—21no—
21C2×#432—21no—
22C2×#431—21no—
23C22×#108C2211yescharacteristic
24C2×#427C2211yescharacteristic
25C2×#427C2211yescharacteristic
26C2×#424C2211yescharacteristic
27C2×#424C2211yescharacteristic
28C2×#424C2211yescharacteristic
29C2×#407C2211yescharacteristic
30C2×#407C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C22×C22⋊C8C2211yescharacteristic
33C2×#405C2211yescharacteristic
34C2×#405C2211yescharacteristic
35C2×#405C2211yescharacteristic
36C22×C4×C8C2211yescharacteristic
37#2280C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39#1945—24no—
40#1924—21no—
41#1924—21no—
42#1923—21no—
43#1923—21no—
44#1922—24no—
45#1854C411yescharacteristic, complemented
46#1854C411yescharacteristic, complemented
47#1854C411yescharacteristic, complemented
48#1854C411yescharacteristic, complemented
49#1853C411yescharacteristic, complemented
50#1853C411yescharacteristic, complemented
51#1852C411yescharacteristic, complemented
52#1852C411yescharacteristic, complemented
53C2×#341C2211yescharacteristic
54C2×#341C2211yescharacteristic
55C2×#341C2211yescharacteristic
56#1735C2211yescharacteristic
57#1735C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63C2×#339C2211yescharacteristic
64C2×#339C2211yescharacteristic
65C2×#339C2211yescharacteristic
66#1729C2211yescharacteristic
67#1729C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C2×#336C2211yescharacteristic
70C2×#336C2211yescharacteristic
71C24×C4C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80C2×#117—21no—
81C2×#117—21no—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117C2×C411yescharacteristic
87C2×#117C2×C411yescharacteristic
88C2×#117C2311yescharacteristic
89C2×#117C2311yescharacteristic
90C2×#117C2311yescharacteristic
91C2×#117C2311yescharacteristic
92C22×C4⋊C4C2×C411yescharacteristic
93C22×C4⋊C4C2×C411yescharacteristic
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C42—21no—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99#433—28no—
100#433—28no—
101#432—28no—
102#431—28no—
103C2×#108—22no—
104C2×#108—22no—
105C2×#108—41no—
106#427—22no—
107#427—22no—
108#427—22no—
109#427—22no—
110C2×#107C2×C411yescharacteristic
111C2×#107C2×C411yescharacteristic
112C2×#107C2×C411yescharacteristic
113C2×#107C2×C411yescharacteristic
114C2×#106C2×C411yescharacteristic
115C2×#106C2×C411yescharacteristic
116C2×#106C2×C411yescharacteristic
117C2×#106C2×C411yescharacteristic
118#424—22no—
119#424—22no—
120#424—22no—
121#424—22no—
122#424—22no—
123#424D414yes—
124C2×C4⋊C8—21no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127C2×C4⋊C8—21no—
128C2×C4⋊C8—21no—
129C2×C4⋊C8—21no—
130#407—22no—
131#407—22no—
132#407—22no—
133#407—41no—
134C2×C22⋊C8—21no—
135C2×C22⋊C8—21no—
136C2×C22⋊C8—22no—
137C2×C22⋊C8—22no—
138C2×C22⋊C8—22no—
139C2×C22⋊C8—22no—
140C2×C22⋊C8—21no—
141C2×C22⋊C8—21no—
142C2×C22⋊C8C2×C411yescharacteristic
143C2×C22⋊C8C2×C411yescharacteristic
144C2×C22⋊C8C2×C411yescharacteristic
145C2×C22⋊C8C2×C411yescharacteristic
146C2×C22⋊C8D411yescharacteristic
147C2×C22⋊C8D411yescharacteristic
148C2×C22⋊C8D411yescharacteristic
149C2×C22⋊C8D411yescharacteristic
150#405—22no—
151#405—22no—
152#405—22no—
153#405—22no—
154#405—41no—
155#405D414yes—
156C2×#97—21no—
157C2×#97—21no—
158C2×#97—21no—
159C2×C4×C8—21no—
160C2×C4×C8—21no—
161C2×C4×C8—22no—
162C2×C4×C8—21no—
163C2×C4×C8—22no—
164C2×C4×C8—41no—
165#381—21no—
166#380C2×C411yescharacteristic
167#380C2×C411yescharacteristic
168#380C2×C411yescharacteristic
169#380C2×C411yescharacteristic
170#379—21no—
171C4×C22⋊C4—21no—
172C4×C22⋊C4—21no—
173C4×C22⋊C4—22no—
174C4×C22⋊C4—41no—
175C2×#95—21no—
176#341—22no—
177#341—22no—
178#341—22no—
179#340C2×C411yescharacteristic
180#340C2×C411yescharacteristic
181#340C2×C411yescharacteristic
182#340C2×C411yescharacteristic
183#340C2×C411yescharacteristic
184#340C2×C411yescharacteristic
185#340C2×C411yescharacteristic
186#340C2×C411yescharacteristic
187#339—22no—
188#339—22no—
189#339—22no—
190#339—22no—
191#339—22no—
192#339—22no—
193#339—22no—
194#339—41no—
195#336—22no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—22no—
201#336—22no—
202C25#4111yescharacteristic
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4C22×C411yescharacteristic
220C23×C4C22×C411yescharacteristic
221C23×C4C2×D411yescharacteristic
222C23×C4C2×D411yescharacteristic
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×M16C2×D412yes—
247C2×M16C2×D412yes—
248C2×M16#4112yes—
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×C8C22×C411yescharacteristic
274C22×C8C22×C411yescharacteristic
275C22×C8C22×C411yescharacteristic
276C22×C8C22×C411yescharacteristic
277C22×C8C2×D411yescharacteristic
278C22×C8C2×D411yescharacteristic
279C22×C8C2×D412yes—
280C22×C8C2×D412yes—
281C22×C8C2×D411yescharacteristic
282C22×C8C2×D411yescharacteristic
283C22×C8#4112yes—
284C22×C8#4112yes—
285#117—24no—
286#117—24no—
287#117—24no—
288#117—24no—
289#117—21no—
290#117—21no—
291#117—21no—
292#117—21no—
293#117—22no—
294#117—22no—
295#117—22no—
296#117—22no—
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#117C2×D412yes—
306#117C2×D412yes—
307#117#4112yes—
308#117#4112yes—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4C22×C411yescharacteristic
316C2×C4⋊C4C22×C411yescharacteristic
317C2×C4⋊C4C22×C411yescharacteristic
318C2×C4⋊C4C22×C411yescharacteristic
319C2×C4⋊C4C22×C411yescharacteristic
320C2×C4⋊C4C22×C411yescharacteristic
321C2×C4⋊C4C22×C411yescharacteristic
322C2×C4⋊C4C22×C411yescharacteristic
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C42—24no—
339C2×C42—24no—
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—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42#4112yes—
358#108—44no—
359#107—22no—
360#107—22no—
361#107—22no—
362#107—22no—
363#106—22no—
364#106—22no—
365#106—22no—
366#106—22no—
367C4⋊C8—24no—
368C4⋊C8—24no—
369C4⋊C8—24no—
370C4⋊C8—24no—
371C4⋊C8—42no—
372C4⋊C8—42no—
373C22⋊C8—24no—
374C22⋊C8—24no—
375C22⋊C8—22no—
376C22⋊C8—22no—
377C22⋊C8—22no—
378C22⋊C8—22no—
379C22⋊C8—22no—
380C22⋊C8—22no—
381C22⋊C8—22no—
382C22⋊C8—22no—
383C22⋊C8—42no—
384C22⋊C8—42no—
385#97—24no—
386#97—24no—
387#97—42no—
388C4×C8—24no—
389C4×C8—24no—
390C4×C8—44no—
391C4×C8—42no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—42no—
397C24—22no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24C4×D411yescharacteristic
408C24C4×D411yescharacteristic
409C24C2×#4111yescharacteristic
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—42no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—42no—
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—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—81no—
483C22×C4—81no—
484C22×C4C4×D411yescharacteristic
485C22×C4C4×D411yescharacteristic
486C22×C4C23×C411yescharacteristic
487C22×C4C22×D411yescharacteristic
488C22×C4C22×D411yescharacteristic
489C22×C4C22×D411yescharacteristic
490C22×C4C2×#4111yescharacteristic
491C22×C4C2×#4111yescharacteristic
492C22×C4C2×#4111yescharacteristic
493C22×C4C2×#4111yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4H(5,𝔽2)11yescharacteristic
497C22×C42−1+411yescharacteristic
498C22×C42−1+411yescharacteristic
499C22×C42−1+411yescharacteristic
500M16—22no—
501M16—22no—
502M16—22no—
503M16—22no—
504M16—22no—
505M16—22no—
506M16—41no—
507M16—41no—
508M16—41no—
509M16—41no—
510M16—41no—
511M16—41no—
512M16—41no—
513M16—41no—
514M16—41no—
515M16—41no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—22no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—21no—
542C2×C8—22no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
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×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8#11712yes—
565C2×C8#11712yes—
566C2×C8#12012yes—
567C2×C8#12012yes—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4C4×D412yes—
583C4⋊C4C4×D412yes—
584C4⋊C4C4×D412yes—
585C4⋊C4C4×D412yes—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—48no—
593C22⋊C4—42no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—42no—
599C22⋊C4—81no—
600C22⋊C4—81no—
601C42—24no—
602C42—24no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—41no—
610C42—41no—
611C42—41no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—81no—
647C23—81no—
648C23—81no—
649C23—81no—
650C23—81no—
651C23—81no—
652C23#44312yes—
653C23C2×C4×D411yescharacteristic
654C23#52511yescharacteristic
655C23#52511yescharacteristic
656C23#55111yescharacteristic
657C23#55211yescharacteristic
658C23#55211yescharacteristic
659C23#55211yescharacteristic
660C2×C4—24no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—48no—
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—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4C2×#11711yescharacteristic
727C2×C4C2×C4×D411yescharacteristic
728C2×C4C2×C4×D411yescharacteristic
729C2×C4C4×#4111yescharacteristic
730C2×C4#51911yescharacteristic
731C2×C4#52011yescharacteristic
732C2×C4C2×#12011yescharacteristic
733C2×C4#52511yescharacteristic
734C2×C4#52911yescharacteristic
735C2×C4#52911yescharacteristic
736C2×C4#53211yescharacteristic
737C2×C4#53211yescharacteristic
738C2×C4#53611yescharacteristic
739C2×C4#53711yescharacteristic
740C2×C4#54111yescharacteristic
741C2×C4#54211yescharacteristic
742C2×C4#54611yescharacteristic
743C2×C4#54611yescharacteristic
744C2×C4#54711yescharacteristic
745C2×C4#54711yescharacteristic
746C2×C4#54711yescharacteristic
747C2×C4#54711yescharacteristic
748C2×C4#54811yescharacteristic
749C2×C4#54811yescharacteristic
750C2×C4#55211yescharacteristic
751C2×C4#55211yescharacteristic
752C2×C4#55311yescharacteristic
753C2×C4#55611yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—22no—
758C8—42no—
759C8—41no—
760C8—41no—
761C8—42no—
762C8—42no—
763C8—41no—
764C8—41no—
765C8—81no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22C4×#12011yescharacteristic
797C22#234411yescharacteristic
798C22#235911yescharacteristic
799C22#247511yescharacteristic
800C22#247711yescharacteristic
801C22#260111yescharacteristic
802C22#261111yescharacteristic
803C22C2×#44311yescharacteristic
804C22#295511yescharacteristic
805C22#295611yescharacteristic
806C22#295711yescharacteristic
807C4—44no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—82no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4#229311yescharacteristic
820C4#232311yescharacteristic
821C4#235211yescharacteristic
822C4#236211yescharacteristic
823C4#243011yescharacteristic
824C4#243211yescharacteristic
825C4#247011yescharacteristic
826C4#247811yescharacteristic
827C2—21no—
828C2—21no—
829C2—21no—
830C2—21no—
831C2—42no—
832C2—81no—
833C2#1407211yescharacteristic
834C2#2146611yescharacteristic
835C2#2146811yescharacteristic
836C2#2260611yescharacteristic
837C2#2260811yescharacteristic
838C2#2294811yescharacteristic
839C2#2294911yescharacteristic
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
2. C2×#1945C2semidirect
4. C2×#1922C2semidirect
6. #11291C2semidirect
7. #11221C2semidirect
11. #10910C2semidirect
12. #10909C2semidirect
13. #10887C2semidirect
15. #10706C2semidirect
45. #1854C4semidirect
46. #1854C4semidirect
47. #1854C4semidirect
48. #1854C4semidirect
49. #1853C4semidirect
50. #1853C4semidirect
51. #1852C4semidirect
52. #1852C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29242
C2×#19452
#210532
C2×#19222
#208432
#112912
#112212
#112012
#110972
#109212
#109102
#109092
#108872
#107332
#107062