Finite Group Databasebeta

← #373910

Subgroups — #373910

Order 512.

1284 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1922C211yesmaximal, characteristic, complemented
2#20843C211yesmaximal, characteristic
3#20836C211yesmaximal, characteristic
4#20379C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6#11376C211yesmaximal, characteristic, complemented
7#11317C211yesmaximal, characteristic, complemented
8#11291C211yesmaximal, characteristic, complemented
9#11221C211yesmaximal, characteristic, complemented
10#10909C211yesmaximal, characteristic, complemented
11#10887C211yesmaximal, characteristic, complemented
12#10809C211yesmaximal, characteristic, complemented
13#10734C211yesmaximal, characteristic
14#10719C211yesmaximal, characteristic
15#10712C211yesmaximal, characteristic
16C23×M16C2211yescharacteristic
17C22×#117C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C2×#427C2211yescharacteristic
20C2×#427C2211yescharacteristic
21C2×#424C2211yescharacteristic
22C2×#424C2211yescharacteristic
23C2×#407C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C22⋊C8C2211yescharacteristic
26C2×#405C2211yescharacteristic
27C2×#405C2211yescharacteristic
28#2280C2211yescharacteristic
29#1922—24no—
30#1854C411yescharacteristic, complemented
31#1854C411yescharacteristic, complemented
32#1854C411yescharacteristic, complemented
33#1854C411yescharacteristic, complemented
34#1853C411yescharacteristic, complemented
35#1853C411yescharacteristic, complemented
36#1852C411yescharacteristic, complemented
37#1852C411yescharacteristic, complemented
38#1851—21no—
39#1851—21no—
40#1850—21no—
41#1850—21no—
42#1750—21no—
43#1750—21no—
44#1749—21no—
45C4×C22⋊C8—21no—
46C2×#341C2211yescharacteristic
47C2×#341C2211yescharacteristic
48C2×#341C2211yescharacteristic
49C2×#341C2211yescharacteristic
50#1735C2211yescharacteristic
51#1735C2211yescharacteristic
52C2×#339—24no—
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61#1729C2211yescharacteristic
62#1729C2211yescharacteristic
63#1729C2211yescharacteristic
64#1729C2211yescharacteristic
65C2×#336C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C24×C4—21no—
70C24×C4C2311yescharacteristic
71C22×M16—21no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16—41no—
77C22×M16—41no—
78C22×M16C2311yescharacteristic
79C22×M16C2311yescharacteristic
80C22×M16C2311yescharacteristic
81C22×M16C2311yescharacteristic
82C23×C8—21no—
83C23×C8C2311yescharacteristic
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C2×#117—21no—
88C2×#117—21no—
89C2×#117—22no—
90C2×#117—22no—
91C2×#117—41no—
92C2×#117—41no—
93C2×#117C2×C411yescharacteristic
94C2×#117C2×C411yescharacteristic
95C2×#117C2311yescharacteristic
96C2×#117C2311yescharacteristic
97C2×#117C2311yescharacteristic
98C2×#117C2311yescharacteristic
99C22×C4⋊C4C2×C411yescharacteristic
100C22×C4⋊C4C2×C411yescharacteristic
101C22×C22⋊C4—21no—
102C22×C42—22no—
103C22×C42—22no—
104C22×C42—22no—
105C22×C42—21no—
106C22×C42—22no—
107C22×C42—21no—
108C22×C42—41no—
109C22×C42—41no—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112#427—22no—
113#427—22no—
114#427—41no—
115#427—41no—
116C2×#107C2×C411yescharacteristic, complemented
117C2×#107C2×C411yescharacteristic, complemented
118C2×#107C2×C411yescharacteristic, complemented
119C2×#107C2×C411yescharacteristic, complemented
120C2×#106C2×C411yescharacteristic, complemented
121C2×#106C2×C411yescharacteristic, complemented
122C2×#106C2×C411yescharacteristic, complemented
123C2×#106C2×C411yescharacteristic, complemented
124#424—22no—
125#424—22no—
126#424—41no—
127#424—41no—
128C2×C4⋊C8—21no—
129C2×C4⋊C8—21no—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132#407—22no—
133#407Q814yes—
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⋊C8C2×C411yescharacteristic
141C2×C22⋊C8C2×C411yescharacteristic
142C2×C22⋊C8C2×C411yescharacteristic
143C2×C22⋊C8C2×C411yescharacteristic
144C2×C22⋊C8D411yescharacteristic
145C2×C22⋊C8D411yescharacteristic
146C2×C22⋊C8D411yescharacteristic
147C2×C22⋊C8D411yescharacteristic
148#405—22no—
149#405—22no—
150#405—41no—
151#405—41no—
152C2×#97—21no—
153C2×#97—21no—
154C2×C4×C8—21no—
155C2×C4×C8—21no—
156#381—21no—
157#380C2×C411yescharacteristic
158#380C2×C411yescharacteristic
159#380C2×C411yescharacteristic
160#380C2×C411yescharacteristic
161#379—21no—
162C4×C22⋊C4—21no—
163C4×C22⋊C4—21no—
164#341—22no—
165#341—22no—
166#341—41no—
167#341—41no—
168#340C2×C411yescharacteristic, complemented
169#340C2×C411yescharacteristic, complemented
170#340C2×C411yescharacteristic, complemented
171#340C2×C411yescharacteristic, complemented
172#340C2×C411yescharacteristic, complemented
173#340C2×C411yescharacteristic, complemented
174#340C2×C411yescharacteristic, complemented
175#340C2×C411yescharacteristic, complemented
176#339—22no—
177#339—22no—
178#339—22no—
179#339—22no—
180#339—22no—
181#339—41no—
182#339—41no—
183#339D414yes—
184#336—21no—
185#336—21no—
186#336—21no—
187#336—21no—
188#336—21no—
189#336—21no—
190#336—21no—
191#336—21no—
192#336—22no—
193#336—22no—
194#336—41no—
195#336—41no—
196C25#4111yescharacteristic
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—24no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—42no—
211C23×C4—42no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4C22×C411yescharacteristic
217C23×C4C22×C411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2×Q812yes—
221C23×C4#4112yes—
222C23×C4#4112yes—
223C23×C4#4111yescharacteristic
224C23×C4#4112yes—
225C23×C4C2411yescharacteristic
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—28no—
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—42no—
248C2×M16—42no—
249C2×M16—44no—
250C2×M16—44no—
251C2×M16—44no—
252C2×M16—42no—
253C2×M16C2×D412yes—
254C2×M16C2×Q812yes—
255C2×M16C2×Q812yes—
256C2×M16#4112yes—
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×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—42no—
286C22×C8—42no—
287C22×C8—42no—
288C22×C8C22×C411yescharacteristic
289C22×C8C22×C411yescharacteristic
290C22×C8C22×C411yescharacteristic
291C22×C8C22×C411yescharacteristic
292C22×C8C2×D411yescharacteristic
293C22×C8C2×D411yescharacteristic
294C22×C8C2×D411yescharacteristic
295C22×C8C2×D411yescharacteristic
296#117—21no—
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—21no—
306#117—21no—
307#117—21no—
308#117—21no—
309#117—21no—
310#117—22no—
311#117—22no—
312#117—42no—
313#117—42no—
314#117—42no—
315#117—42no—
316#117—41no—
317#117—41no—
318#117C2×D412yes—
319#117#4112yes—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4C22×C411yescharacteristic
327C2×C4⋊C4C22×C411yescharacteristic
328C2×C4⋊C4C22×C411yescharacteristic
329C2×C4⋊C4C22×C411yescharacteristic
330C2×C4⋊C4C22×C411yescharacteristic
331C2×C4⋊C4C22×C411yescharacteristic
332C2×C4⋊C4C22×C411yescharacteristic
333C2×C4⋊C4C22×C411yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C42—21no—
347C2×C42—28no—
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—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42—44no—
366C2×C42—44no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—44no—
370C2×C42—42no—
371C2×C42C2×D412yes—
372C2×C42#4112yes—
373#107—22no—
374#107—22no—
375#107—41no—
376#107—41no—
377#106—22no—
378#106—22no—
379#106—41no—
380#106—41no—
381C4⋊C8—42no—
382C4⋊C8—42no—
383C4⋊C8—42no—
384C4⋊C8—42no—
385C22⋊C8—22no—
386C22⋊C8—22no—
387C22⋊C8—22no—
388C22⋊C8—22no—
389C22⋊C8—24no—
390C22⋊C8—24no—
391C22⋊C8—22no—
392C22⋊C8—22no—
393C22⋊C8—22no—
394C22⋊C8—22no—
395#97—42no—
396#97—42no—
397C4×C8—42no—
398C4×C8—42no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—22no—
408C24—22no—
409C24—41no—
410C24—41no—
411C24C4×D411yescharacteristic
412C24C4×D411yescharacteristic
413C24#12512yes—
414C24#12612yes—
415C24C2×#4111yescharacteristic
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—48no—
467C22×C4—48no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—48no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—48no—
476C22×C4—48no—
477C22×C4—48no—
478C22×C4—48no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4#11712yes—
488C22×C4#11712yes—
489C22×C4C4×D411yescharacteristic
490C22×C4C4×D411yescharacteristic
491C22×C4C4×Q812yes—
492C22×C4C4×Q812yes—
493C22×C4C22⋊Q812yes—
494C22×C4C22⋊Q812yes—
495C22×C4#12312yes—
496C22×C4#12312yes—
497C22×C4#12512yes—
498C22×C4#12612yes—
499C22×C4C23×C411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×Q811yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4C2×#4111yescharacteristic
508C22×C4C2×#4111yescharacteristic
509C22×C4H(5,𝔽2)11yescharacteristic
510C22×C4H(5,𝔽2)11yescharacteristic
511C22×C4H(5,𝔽2)11yescharacteristic
512C22×C42−1+411yescharacteristic
513M16—22no—
514M16—22no—
515M16—22no—
516M16—22no—
517M16—22no—
518M16—22no—
519M16—22no—
520M16—22no—
521M16—48no—
522M16—41no—
523M16—41no—
524M16—41no—
525M16—41no—
526M16—41no—
527M16—41no—
528M16—41no—
529M16—41no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—22no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—22no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—48no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—41no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4C4×D412yes—
600C4⋊C4C4×D412yes—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—42no—
622C42—42no—
623C42—48no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23#38712yes—
665C23#38712yes—
666C23#44312yes—
667C23#44412yes—
668C23C2×C4×D411yescharacteristic
669C23C2×#12511yescharacteristic
670C23C2×#12611yescharacteristic
671C23#54611yescharacteristic
672C23#55111yescharacteristic
673C23#55111yescharacteristic
674C23#55211yescharacteristic
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—432no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4#38712yes—
741C2×C4#38712yes—
742C2×C4C2×#11711yescharacteristic
743C2×C4C2×C4×D411yescharacteristic
744C2×C4C2×C4×Q811yescharacteristic
745C2×C4C4×#4111yescharacteristic
746C2×C4#51811yescharacteristic
747C2×C4#52011yescharacteristic
748C2×C4C2×C22⋊Q811yescharacteristic
749C2×C4C2×#12311yescharacteristic
750C2×C4#52511yescharacteristic
751C2×C4#52511yescharacteristic
752C2×C4#52911yescharacteristic
753C2×C4#52911yescharacteristic
754C2×C4#53811yescharacteristic
755C2×C4#53811yescharacteristic
756C2×C4#53911yescharacteristic
757C2×C4#53911yescharacteristic
758C2×C4D4211yescharacteristic
759C2×C4#54611yescharacteristic
760C2×C4#54611yescharacteristic
761C2×C4#54611yescharacteristic
762C2×C4#54711yescharacteristic
763C2×C4D4×Q811yescharacteristic
764C2×C4#55111yescharacteristic
765C2×C4#55111yescharacteristic
766C2×C4#55211yescharacteristic
767C2×C4#55411yescharacteristic
768C2×C4#55411yescharacteristic
769C2×C4#55411yescharacteristic
770C8—41no—
771C8—41no—
772C8—41no—
773C8—41no—
774C8—42no—
775C8—42no—
776C8—41no—
777C8—41no—
778C8—42no—
779C8—42no—
780C8—41no—
781C8—41no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—22no—
787C22—22no—
788C22—21no—
789C22—22no—
790C22—21no—
791C22—21no—
792C22—22no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—22no—
797C22—21no—
798C22—21no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—44no—
804C22—44no—
805C22—44no—
806C22—44no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22#192214yescomplemented
812C22C2×#38711yescharacteristic
813C22#235811yescharacteristic
814C22#235911yescharacteristic
815C22#247311yescharacteristic
816C22#248011yescharacteristic
817C22#249311yescharacteristic
818C22#250511yescharacteristic
819C22C2×#44311yescharacteristic
820C22C2×#44411yescharacteristic
821C22#295611yescharacteristic
822C22#295611yescharacteristic
823C4—22no—
824C4—22no—
825C4—44no—
826C4—44no—
827C4—42no—
828C4—42no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4—81no—
835C4#229011yescharacteristic
836C4#231811yescharacteristic
837C4#236011yescharacteristic
838C4#236811yescharacteristic
839C4#241811yescharacteristic
840C4#241911yescharacteristic
841C4#244911yescharacteristic
842C4#245011yescharacteristic
843C2—21no—
844C2—24no—
845C2—21no—
846C2—21no—
847C2—21no—
848C2—42no—
849C2#1413111yescharacteristic
850C2C2×#192211yescharacteristic
851C2#2104211yescharacteristic
852C2#2288611yescharacteristic
853C2#2288811yescharacteristic
854C2#2294811yescharacteristic
855C2#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
1. C2×#1922C2semidirect
6. #11376C2semidirect
7. #11317C2semidirect
8. #11291C2semidirect
9. #11221C2semidirect
10. #10909C2semidirect
11. #10887C2semidirect
12. #10809C2semidirect
30. #1854C4semidirect
31. #1854C4semidirect
32. #1854C4semidirect
33. #1854C4semidirect
34. #1853C4semidirect
35. #1853C4semidirect
36. #1852C4semidirect
37. #1852C4semidirect
116. C2×#107C2×C4semidirect
117. C2×#107C2×C4semidirect
118. C2×#107C2×C4semidirect
119. C2×#107C2×C4semidirect
120. C2×#106C2×C4semidirect
121. C2×#106C2×C4semidirect
122. C2×#106C2×C4semidirect
123. C2×#106C2×C4semidirect
168. #340C2×C4semidirect
169. #340C2×C4semidirect
170. #340C2×C4semidirect
171. #340C2×C4semidirect
172. #340C2×C4semidirect
173. #340C2×C4semidirect
174. #340C2×C4semidirect
175. #340C2×C4semidirect
811. C22#1922semidirect

Maximal subgroups

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

subgroupindex
C2×#19222
#208432
#208362
#203792
C22×#3392
#113762
#113172
#112912
#112212
#109092
#108872
#108092
#107342
#107192
#107122