Finite Group Databasebeta

← #390396

Subgroups — #390396

Order 512.

1286 conjugacy classes of subgroups.

The subgroup lattice has 939 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23479C211yesmaximal, characteristic
2C2×#1929C211yesmaximal, characteristic, complemented
3#21053C211yesmaximal, characteristic, complemented
4C2×#1896C211yesmaximal, characteristic
5#20899C211yesmaximal, characteristic
6#11376C211yesmaximal, characteristic, complemented
7#11291C211yesmaximal, characteristic, complemented
8#11258C211yesmaximal, characteristic, complemented
9#11097C211yesmaximal, characteristic, complemented
10#11068C211yesmaximal, characteristic, complemented
11#10909C211yesmaximal, characteristic, complemented
12#10791C211yesmaximal, characteristic, complemented
13#10791C211yesmaximal, characteristic, complemented
14#10719C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C22×#131C2211yescharacteristic
17C2×#525C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×#108C2211yescharacteristic
20C2×#427C2211yescharacteristic
21C2×#424C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C22×#104C2211yescharacteristic
24C2×#416C2211yescharacteristic
25C2×#416C2211yescharacteristic
26C2×#408C2211yescharacteristic
27C2×#407C2211yescharacteristic
28C2×#407C2211yescharacteristic
29C22×C22⋊C8C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C2×#405C2211yescharacteristic
32#2280C2211yescharacteristic
33#2036C411yescharacteristic, complemented
34#2036C411yescharacteristic, complemented
35#2035C411yescharacteristic, complemented
36#2035C411yescharacteristic, complemented
37#2034C411yescharacteristic, complemented
38#2034C411yescharacteristic, complemented
39#2033C411yescharacteristic, complemented
40#2033C411yescharacteristic, complemented
41#1929—24no—
42#1924—21no—
43#1924—21no—
44#1923—21no—
45#1923—21no—
46#1896—24no—
47#1870—21no—
48#1870—21no—
49#1869—21no—
50#1869—21no—
51C2×#341C2211yescharacteristic
52C2×#341C2211yescharacteristic
53C2×#341C2211yescharacteristic
54#1735C2211yescharacteristic
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
69C22×#41C2311yescharacteristic
70C24×C4—21no—
71C24×C4C2311yescharacteristic
72C2×#131—22no—
73C2×#131—22no—
74C2×#131—41no—
75C2×#131—41no—
76C2×#131—41no—
77C2×#131—41no—
78C22×M16—21no—
79C22×M16C2311yescharacteristic
80C22×M16C2311yescharacteristic
81C22×M16C2311yescharacteristic
82C22×M16C2311yescharacteristic
83C23×C8—21no—
84C23×C8C2311yescharacteristic
85C23×C8C2311yescharacteristic
86C23×C8C2311yescharacteristic
87C23×C8C2311yescharacteristic
88#525—22no—
89#525—22no—
90#525—41no—
91#525—41no—
92C2×#123—21no—
93C2×C22⋊Q8C2×C411yescharacteristic
94C2×C22⋊Q8C2×C411yescharacteristic
95C2×#121C2×C411yescharacteristic
96C2×#121C2×C411yescharacteristic
97C2×#120—21no—
98C2×C4×D4—21no—
99C2×C4×D4—21no—
100C2×#117C2311yescharacteristic
101C2×#117C2311yescharacteristic
102C2×#117C2311yescharacteristic
103C22×C42—22no—
104C22×C42—22no—
105C22×C42—21no—
106C22×C42—41no—
107C22×C42—41no—
108C22×C42—41no—
109C22×C42—41no—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C2×#108—22no—
113C2×#108—41no—
114C2×#108—41no—
115#427—41no—
116#427—41no—
117C2×#107C2×C411yescharacteristic, complemented
118C2×#107C2×C411yescharacteristic, complemented
119C2×#106C2×C411yescharacteristic, complemented
120C2×#106C2×C411yescharacteristic, complemented
121#424—41no—
122#424—41no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×#104—22no—
126C2×#104—22no—
127C2×#104—41no—
128C2×#104—41no—
129C2×#104—41no—
130C2×#104D414yes—
131#416—22no—
132#416—22no—
133#416—41no—
134#416—41no—
135C2×#103C2×C411yescharacteristic, complemented
136C2×#103C2×C411yescharacteristic, complemented
137C2×#103C2×C411yescharacteristic, complemented
138C2×#103C2×C411yescharacteristic, complemented
139C2×#102C2×C411yescharacteristic, complemented
140C2×#102C2×C411yescharacteristic, complemented
141C2×#102C2×C411yescharacteristic, complemented
142C2×#102C2×C411yescharacteristic, complemented
143#408—22no—
144#408—41no—
145#407—22no—
146#407—22no—
147#407—41no—
148#407—41no—
149C2×C22⋊C8—21no—
150C2×C22⋊C8—21no—
151C2×C22⋊C8—21no—
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C2×C22⋊C8—41no—
156C2×C22⋊C8—41no—
157C2×C22⋊C8—41no—
158C2×C22⋊C8—41no—
159C2×C22⋊C8C2×C411yescharacteristic
160C2×C22⋊C8C2×C411yescharacteristic
161C2×C22⋊C8C2×C411yescharacteristic
162C2×C22⋊C8C2×C411yescharacteristic
163C2×C22⋊C8D411yescharacteristic
164C2×C22⋊C8D411yescharacteristic
165C2×C22⋊C8D411yescharacteristic
166C2×C22⋊C8D411yescharacteristic
167#405—22no—
168#405—41no—
169C2×#97—21no—
170C2×C4×C8—21no—
171#381—21no—
172#380C2×C411yescharacteristic
173#380C2×C411yescharacteristic
174#380C2×C411yescharacteristic
175#380C2×C411yescharacteristic
176#379—21no—
177C4×C22⋊C4—21no—
178C4×C22⋊C4—21no—
179#341—22no—
180#341—41no—
181#341—41no—
182#340C2×C411yescharacteristic, complemented
183#340C2×C411yescharacteristic, complemented
184#340C2×C411yescharacteristic, complemented
185#340C2×C411yescharacteristic, complemented
186#339—22no—
187#339—22no—
188#339—22no—
189#339—41no—
190#339—41no—
191#339—41no—
192#336—21no—
193#336—21no—
194#336—21no—
195#336—21no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—22no—
201#336—22no—
202#336—41no—
203#336—41no—
204C25#4111yescharacteristic
205C2×#41—21no—
206C2×#41—21no—
207C2×#41—21no—
208C2×#41—21no—
209C2×#41—21no—
210C2×#41—21no—
211C2×#41—21no—
212C2×#41—21no—
213C2×#41—21no—
214C2×#41—21no—
215C2×#41C2×D412yes—
216C2×#41#4112yes—
217C22×Q8C22×C411yescharacteristic
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4C22×C411yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—21no—
237C23×C4—24no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4C22×C411yescharacteristic
245C23×C4C22×C411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4#4111yescharacteristic
249C23×C4C2411yescharacteristic
250#131—44no—
251#131—44no—
252#131—44no—
253#131—44no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16—21no—
273C2×M16—21no—
274C2×M16—21no—
275C2×M16—21no—
276C2×M16—42no—
277C2×M16—42no—
278C2×M16—42no—
279C2×M16C2×D412yes—
280C2×M16#4112yes—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—21no—
309C22×C8—42no—
310C22×C8—42no—
311C22×C8—42no—
312C22×C8C22×C411yescharacteristic
313C22×C8C22×C411yescharacteristic
314C22×C8C22×C411yescharacteristic
315C22×C8C22×C411yescharacteristic
316C22×C8C2×D411yescharacteristic
317C22×C8C2×D411yescharacteristic
318C22×C8C2×D411yescharacteristic
319C22×C8C2×D411yescharacteristic
320#123—42no—
321#123—42no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—41no—
325C22⋊Q8—41no—
326#121—22no—
327#121—22no—
328#121—41no—
329#121—41no—
330#120—42no—
331#120—42no—
332C4×D4—42no—
333C4×D4—42no—
334C4×D4—42no—
335C4×D4—42no—
336#117—21no—
337#117—21no—
338#117—21no—
339#117—21no—
340#117—21no—
341#117—21no—
342#117—21no—
343#117—21no—
344#117—21no—
345#117—21no—
346#117—21no—
347#117—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4C22×C411yescharacteristic
351C2×C4⋊C4C22×C411yescharacteristic
352C2×C4⋊C4C22×C411yescharacteristic
353C2×C4⋊C4C22×C411yescharacteristic
354C2×C4⋊C4C22×C411yescharacteristic
355C2×C4⋊C4C22×C411yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—44no—
381C2×C42—44no—
382C2×C42—44no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—44no—
387C2×C42C2×D412yes—
388C2×C42#4112yes—
389#108—44no—
390#107—41no—
391#107—41no—
392#106—41no—
393#106—41no—
394C4⋊C8—42no—
395C4⋊C8—42no—
396#104—44no—
397#104—44no—
398#103—22no—
399#103—22no—
400#103—41no—
401#103—41no—
402#102—22no—
403#102—22no—
404#102—41no—
405#102—41no—
406C22⋊C8—41no—
407C22⋊C8—41no—
408C22⋊C8—41no—
409C22⋊C8—41no—
410C22⋊C8—41no—
411C22⋊C8—41no—
412C22⋊C8—41no—
413C22⋊C8—41no—
414C22⋊C8—42no—
415C22⋊C8—42no—
416C22⋊C8—42no—
417C22⋊C8—42no—
418C22⋊C8—42no—
419C22⋊C8—42no—
420#97—42no—
421C4×C8—42no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—41no—
436C24—41no—
437C24C4×D411yescharacteristic
438C24C4×D411yescharacteristic
439C24C2×#4111yescharacteristic
440#41—22no—
441#41—22no—
442#41—22no—
443#41—22no—
444#41—22no—
445#41—22no—
446#41—22no—
447#41—22no—
448#41—41no—
449#41—41no—
450#41—41no—
451#41—41no—
452#41—41no—
453#41—41no—
454#41—41no—
455#41—41no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8C4×D412yes—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—81no—
478C2×D4—81no—
479C2×D4C4×D412yes—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4C4×D411yescharacteristic
561C22×C4C4×D411yescharacteristic
562C22×C4C23×C411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C2×#4111yescharacteristic
566C22×C4C2×#4111yescharacteristic
567C22×C4C2×#4111yescharacteristic
568C22×C4H(5,𝔽2)11yescharacteristic
569C22×C4H(5,𝔽2)11yescharacteristic
570C22×C4H(5,𝔽2)11yescharacteristic
571C22×C4H(5,𝔽2)11yescharacteristic
572C22×C4H(5,𝔽2)11yescharacteristic
573C22×C4H(5,𝔽2)11yescharacteristic
574C22×C42−1+411yescharacteristic
575C22×C42−1+411yescharacteristic
576M16—22no—
577M16—22no—
578M16—22no—
579M16—22no—
580M16—48no—
581M16—41no—
582M16—41no—
583M16—41no—
584M16—41no—
585M16—41no—
586M16—41no—
587M16—41no—
588M16—41no—
589M16—41no—
590M16—41no—
591M16—41no—
592M16—41no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—22no—
611C2×C8—21no—
612C2×C8—22no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—48no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—81no—
673C22⋊C4—81no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—22no—
678C42—48no—
679C42—41no—
680C42—41no—
681C42—41no—
682C42—41no—
683C42—41no—
684C42—41no—
685C42—41no—
686C42—41no—
687C42—41no—
688C42—41no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—24no—
694C23—24no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23#44312yes—
729C23#44412yes—
730C23C2×C4×D411yescharacteristic
731C23#53811yescharacteristic
732C23#53911yescharacteristic
733C23#54611yescharacteristic
734C23#55111yescharacteristic
735C23#55111yescharacteristic
736C23#55211yescharacteristic
737Q8—22no—
738Q8—22no—
739Q8—41no—
740Q8—41no—
741D4—22no—
742D4—22no—
743D4—42no—
744D4—42no—
745D4—42no—
746D4—42no—
747D4—41no—
748D4—41no—
749D4—84no—
750D4—84no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—432no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4C2×C4×D411yescharacteristic
818C2×C4C4×#4111yescharacteristic
819C2×C4#51811yescharacteristic
820C2×C4#51811yescharacteristic
821C2×C4#52011yescharacteristic
822C2×C4#52011yescharacteristic
823C2×C4#53411yescharacteristic
824C2×C4#53411yescharacteristic
825C2×C4#53711yescharacteristic
826C2×C4#53711yescharacteristic
827C2×C4#53811yescharacteristic
828C2×C4#53811yescharacteristic
829C2×C4#53811yescharacteristic
830C2×C4#53911yescharacteristic
831C2×C4#54011yescharacteristic
832C2×C4#54011yescharacteristic
833C2×C4D4211yescharacteristic
834C2×C4#54611yescharacteristic
835C2×C4#54611yescharacteristic
836C2×C4#54611yescharacteristic
837C2×C4#54711yescharacteristic
838C2×C4#54711yescharacteristic
839C2×C4#55111yescharacteristic
840C2×C4#55211yescharacteristic
841C2×C4H(3,𝔽4)11yescharacteristic
842C2×C4#56211yescharacteristic
843C2×C4#56211yescharacteristic
844C2×C4#56311yescharacteristic
845C8—41no—
846C8—41no—
847C8—41no—
848C8—41no—
849C8—41no—
850C8—41no—
851C8—42no—
852C8—41no—
853C8—41no—
854C8—42no—
855C8—81no—
856C8—81no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22#232511yescharacteristic
895C22#235811yescharacteristic
896C22#235911yescharacteristic
897C22#268411yescharacteristic
898C22#269511yescharacteristic
899C22#274311yescharacteristic
900C22#274311yescharacteristic
901C22C2×#44311yescharacteristic
902C22C2×#44411yescharacteristic
903C22#295611yescharacteristic
904C22#295611yescharacteristic
905C4—44no—
906C4—44no—
907C4—41no—
908C4—41no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4—81no—
915C4—81no—
916C4#232511yescharacteristic
917C4#233311yescharacteristic
918C4#235911yescharacteristic
919C4#237911yescharacteristic
920C4#267111yescharacteristic
921C4#267111yescharacteristic
922C4#268411yescharacteristic
923C4#269511yescharacteristic
924C2—21no—
925C2—21no—
926C2—21no—
927C2—21no—
928C2—42no—
929C2—42no—
930C2—82no—
931C2#1457111yescharacteristic
932C2#2220411yescharacteristic
933C2#2220711yescharacteristic
934C2#2288611yescharacteristic
935C2#2288811yescharacteristic
936C2#2294811yescharacteristic
937C2#2295011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC2×#525C22
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×#1929C2semidirect
3. #21053C2semidirect
6. #11376C2semidirect
7. #11291C2semidirect
8. #11258C2semidirect
9. #11097C2semidirect
10. #11068C2semidirect
11. #10909C2semidirect
12. #10791C2semidirect
13. #10791C2semidirect
14. #10719C2semidirect
15. #10712C2semidirect
33. #2036C4semidirect
34. #2036C4semidirect
35. #2035C4semidirect
36. #2035C4semidirect
37. #2034C4semidirect
38. #2034C4semidirect
39. #2033C4semidirect
40. #2033C4semidirect
117. C2×#107C2×C4semidirect
118. C2×#107C2×C4semidirect
119. C2×#106C2×C4semidirect
120. C2×#106C2×C4semidirect
135. C2×#103C2×C4semidirect
136. C2×#103C2×C4semidirect
137. C2×#103C2×C4semidirect
138. C2×#103C2×C4semidirect
139. C2×#102C2×C4semidirect
140. C2×#102C2×C4semidirect
141. C2×#102C2×C4semidirect
142. C2×#102C2×C4semidirect
182. #340C2×C4semidirect
183. #340C2×C4semidirect
184. #340C2×C4semidirect
185. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
#234792
C2×#19292
#210532
C2×#18962
#208992
#113762
#112912
#112582
#110972
#110682
#109092
#107912
#107192
#107122