Finite Group Databasebeta

← #383792

Subgroups — #383792

Order 512.

1085 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3076C211yesmaximal, characteristic
2#21304C211yesmaximal, characteristic, complemented
3C2×#1938C211yesmaximal, characteristic
4C2×#1929C211yesmaximal, characteristic
5#20684C211yesmaximal, characteristic
6#11386C211yesmaximal, characteristic, complemented
7#11376C211yesmaximal, characteristic, complemented
8#11233C211yesmaximal, characteristic, complemented
9#11221C211yesmaximal, characteristic, complemented
10#11191C211yesmaximal, characteristic
11#11191C211yesmaximal, characteristic
12#10909C211yesmaximal, characteristic, complemented
13#10877C211yesmaximal, characteristic, complemented
14#10860C211yesmaximal, characteristic, complemented
15#10790C211yesmaximal, characteristic
16C2×#533C2211yescharacteristic
17C2×C4×#41C2211yescharacteristic
18#3076—24no—
19#3076—24no—
20C2×#479C411yescharacteristic, complemented
21C2×#479C411yescharacteristic, complemented
22C2×#477C411yescharacteristic, complemented
23C2×#475C411yescharacteristic, complemented
24C2×#478C411yescharacteristic, complemented
25C2×#478C411yescharacteristic, complemented
26C2×#476C411yescharacteristic, complemented
27C2×#474C411yescharacteristic, complemented
28C22×#108C2211yescharacteristic
29C2×#427C2211yescharacteristic
30C2×#427C2211yescharacteristic
31C2×#424C2211yescharacteristic
32C22×C4⋊C8C2211yescharacteristic
33C22×#104C2211yescharacteristic
34C22×#104C2211yescharacteristic
35C2×#416C2211yescharacteristic
36C2×#416C2211yescharacteristic
37C2×#408C2211yescharacteristic
38C2×#408C2211yescharacteristic
39C2×#405C2211yescharacteristic
40C22×#97C2211yescharacteristic
41#1985—21no—
42#1985—21no—
43#1984—21no—
44#1984—21no—
45#1938—24no—
46#1929—24no—
47#1818—21no—
48#1818—21no—
49#1817—21no—
50#1817—21no—
51C2×#341C2211yescharacteristic
52C2×#341C2211yescharacteristic
53C2×#341C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60#1729C2211yescharacteristic
61#1729C2211yescharacteristic
62#1729C2211yescharacteristic
63#1729C2211yescharacteristic
64#1728C2211yescharacteristic
65#1728C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C2×#336C2211yescharacteristic
70C4×#95C2211yescharacteristic
71C22×#41C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80#533—22no—
81#533—22no—
82#533—41no—
83#533—41no—
84C2×C4⋊Q8C2×C411yescharacteristic
85C2×C4⋊Q8C2×C411yescharacteristic
86C2×#125C2×C411yescharacteristic
87C2×#125C2×C411yescharacteristic
88C2×C22⋊Q8—21no—
89C2×C22⋊Q8—21no—
90C4×#41—22no—
91C4×#41—22no—
92C4×#41—41no—
93C4×#41—41no—
94C2×C4×Q8—21no—
95C2×C4×Q8—21no—
96C2×C4×Q8C2×C411yescharacteristic
97C2×C4×Q8C2×C411yescharacteristic
98C2×C4×D4—21no—
99C2×C4×D4—21no—
100C2×C4×D4C2×C411yescharacteristic
101C2×C4×D4C2×C411yescharacteristic
102C2×#117—21no—
103C2×#117C2311yescharacteristic
104C2×#117C2311yescharacteristic
105C2×#117C2311yescharacteristic
106C22×C42—21no—
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110#479—24no—
111#479—24no—
112#478—24no—
113#478—24no—
114#477—24no—
115#476—24no—
116#475—24no—
117#474—24no—
118C2×#108—22no—
119C2×#108—22no—
120C2×#108—41no—
121#427—22no—
122#427—22no—
123#427—22no—
124#427—22no—
125C2×#107C2×C411yescharacteristic
126C2×#107C2×C411yescharacteristic
127C2×#107C2×C411yescharacteristic
128C2×#107C2×C411yescharacteristic
129C2×#106C2×C411yescharacteristic
130C2×#106C2×C411yescharacteristic
131C2×#106C2×C411yescharacteristic
132C2×#106C2×C411yescharacteristic
133#424—22no—
134#424—41no—
135C2×C4⋊C8—22no—
136C2×C4⋊C8—22no—
137C2×C4⋊C8—21no—
138C2×C4⋊C8—21no—
139C2×C4⋊C8C2×C411yescharacteristic
140C2×C4⋊C8C2×C411yescharacteristic
141C2×C4⋊C8C2×C411yescharacteristic
142C2×C4⋊C8C2×C411yescharacteristic
143C2×#104—22no—
144C2×#104—22no—
145C2×#104—22no—
146C2×#104—22no—
147C2×#104—41no—
148C2×#104—41no—
149#416—22no—
150#416—22no—
151#416D414yes—
152#416D414yes—
153C2×#103C2×C411yescharacteristic
154C2×#103C2×C411yescharacteristic
155C2×#103C2×C411yescharacteristic
156C2×#103C2×C411yescharacteristic
157C2×#102C2×C411yescharacteristic
158C2×#102C2×C411yescharacteristic
159C2×#102C2×C411yescharacteristic
160C2×#102C2×C411yescharacteristic
161#408—22no—
162#408—22no—
163#408—41no—
164#408—41no—
165C2×C22⋊C8—21no—
166C2×C22⋊C8—21no—
167C2×C22⋊C8—21no—
168C2×C22⋊C8—21no—
169#405—22no—
170#405—41no—
171C2×#97—22no—
172C2×#97—21no—
173C2×#97—22no—
174C2×#97—41no—
175C2×C4×C8—21no—
176C2×#95—21no—
177C2×#95—21no—
178#341—22no—
179#341—22no—
180#341—41no—
181#339—22no—
182#339—22no—
183#339—41no—
184#339—41no—
185#339—41no—
186#339—41no—
187#336—21no—
188#336—21no—
189#336—21no—
190#336—21no—
191#336—22no—
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—41no—
202#336D411yescharacteristic
203#336D411yescharacteristic
204#336D411yescharacteristic
205#336D411yescharacteristic
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×#41—21no—
216C2×#41C2×D412yes—
217C2×#41C2×D412yes—
218C22×Q8—21no—
219C22×Q8—21no—
220C22×Q8C22×C411yescharacteristic
221C22×D4—21no—
222C22×D4C22×C411yescharacteristic
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4#4111yescharacteristic
229C23×C4#4111yescharacteristic
230C23×C4C2411yescharacteristic
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×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16#4112yes—
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×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8C22×C411yescharacteristic
282C22×C8C22×C411yescharacteristic
283C22×C8C22×C411yescharacteristic
284C22×C8C22×C411yescharacteristic
285C22×C8C2×D411yescharacteristic
286C22×C8C2×D411yescharacteristic
287C22×C8C2×D411yescharacteristic
288C22×C8C2×D411yescharacteristic
289C22×C8C2×D412yes—
290C22×C8C2×D412yes—
291C4⋊Q8—22no—
292C4⋊Q8—22no—
293C4⋊Q8—41no—
294C4⋊Q8—41no—
295#125—22no—
296#125—22no—
297#125—41no—
298#125—41no—
299C22⋊Q8—42no—
300C22⋊Q8—42no—
301C22⋊Q8—42no—
302C22⋊Q8—42no—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×Q8—42no—
306C4×Q8—42no—
307C4×Q8—42no—
308C4×Q8—42no—
309C4×Q8—41no—
310C4×Q8—41no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—41no—
314C4×D4—41no—
315C4×D4—42no—
316C4×D4—42no—
317C4×D4—42no—
318C4×D4—42no—
319#117—21no—
320#117—21no—
321#117—21no—
322#117—21no—
323#117—21no—
324#117—21no—
325#117—21no—
326#117—21no—
327#117—21no—
328#117—21no—
329#117—42no—
330#117—42no—
331#117C2×D412yes—
332#117C2×D412yes—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4C22×C411yescharacteristic
342C2×C4⋊C4C22×C411yescharacteristic
343C2×C4⋊C4C22×C411yescharacteristic
344C2×C4⋊C4C22×C411yescharacteristic
345C2×C4⋊C4C22×C411yescharacteristic
346C2×C4⋊C4C22×C411yescharacteristic
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—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—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42C22×C411yescharacteristic
375C2×C42C22×C411yescharacteristic
376C2×C42C2×D411yescharacteristic
377C2×C42C2×D411yescharacteristic
378C2×C42#4112yes—
379#108—44no—
380#107—22no—
381#107—22no—
382#107—22no—
383#107—22no—
384#106—22no—
385#106—22no—
386#106—22no—
387#106—22no—
388C4⋊C8—22no—
389C4⋊C8—22no—
390C4⋊C8—22no—
391C4⋊C8—22no—
392C4⋊C8—42no—
393C4⋊C8—42no—
394#104—44no—
395#104—44no—
396#103—22no—
397#103—22no—
398#103C22⋊C414yes—
399#103C22⋊C414yes—
400#102—22no—
401#102—22no—
402#102C22⋊C414yes—
403#102C22⋊C414yes—
404C22⋊C8—42no—
405C22⋊C8—42no—
406C22⋊C8—42no—
407C22⋊C8—42no—
408#97—44no—
409#97—42no—
410C4×C8—42no—
411#95—42no—
412#95—42no—
413C24—21no—
414C24C2×#4111yescharacteristic
415#41—22no—
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—41no—
424#41—41no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8—42no—
439C2×Q8—42no—
440C2×Q8—81no—
441C2×Q8—81no—
442C2×Q8C2×C22⋊C412yes—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×C22⋊C412yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—42no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4C4×D411yescharacteristic
497C22×C4C4×D411yescharacteristic
498C22×C4C4×D411yescharacteristic
499C22×C4C4×D411yescharacteristic
500C22×C4C23×C411yescharacteristic
501C22×C4C22×D411yescharacteristic
502C22×C4C22×D411yescharacteristic
503C22×C4C22×D411yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4H(5,𝔽2)11yescharacteristic
507C22×C4H(5,𝔽2)11yescharacteristic
508C22×C4H(5,𝔽2)11yescharacteristic
509C22×C42−1+411yescharacteristic
510C22×C42−1+411yescharacteristic
511C22×C42−1+411yescharacteristic
512C22×C42−1+411yescharacteristic
513C22×C42−1+411yescharacteristic
514M16—22no—
515M16—22no—
516M16—41no—
517M16—41no—
518M16—41no—
519M16—41no—
520M16—41no—
521M16—41no—
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—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—22no—
557C2×C8—41no—
558C2×C8—41no—
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×C8C2×C22⋊C412yes—
581C2×C8C2×C22⋊C412yes—
582C4⋊C4—21no—
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—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4C2×C22⋊C412yes—
601C4⋊C4C2×C22⋊C412yes—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—22no—
615C42—22no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—22no—
621C42—22no—
622C42—42no—
623C42—42no—
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—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C2×C4×D411yescharacteristic
646C23#54111yescharacteristic
647C23#54211yescharacteristic
648C23#54611yescharacteristic
649C23#54611yescharacteristic
650C23#55211yescharacteristic
651C23#55611yescharacteristic
652Q8—22no—
653Q8—22no—
654Q8—41no—
655Q8—41no—
656Q8—84no—
657Q8—84no—
658D4—22no—
659D4—22no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—41no—
665D4—41no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
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—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—84no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—84no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4#44412yes—
723C2×C4C22×C22⋊C411yescharacteristic
724C2×C4C4×#4111yescharacteristic
725C2×C4#51811yescharacteristic
726C2×C4#51911yescharacteristic
727C2×C4#51911yescharacteristic
728C2×C4#52011yescharacteristic
729C2×C4#53611yescharacteristic
730C2×C4#53611yescharacteristic
731C2×C4#53611yescharacteristic
732C2×C4#53611yescharacteristic
733C2×C4#53611yescharacteristic
734C2×C4#53711yescharacteristic
735C2×C4#53911yescharacteristic
736C2×C4#53911yescharacteristic
737C2×C4#54211yescharacteristic
738C2×C4#54211yescharacteristic
739C2×C4D4211yescharacteristic
740C2×C4D4211yescharacteristic
741C2×C4#54611yescharacteristic
742C2×C4#54611yescharacteristic
743C2×C4#54711yescharacteristic
744C2×C4#54711yescharacteristic
745C2×C4#54711yescharacteristic
746C2×C4#54811yescharacteristic
747C2×C4#56211yescharacteristic
748C2×C4#56211yescharacteristic
749C2×C4#56311yescharacteristic
750C2×C4#56311yescharacteristic
751C8—22no—
752C8—22no—
753C8—41no—
754C8—41no—
755C8—41no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—42no—
760C8—81no—
761C8—81no—
762C8—81no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22#232311yescharacteristic
783C22D4×C22⋊C411yescharacteristic
784C22#236211yescharacteristic
785C22#268711yescharacteristic
786C22#268911yescharacteristic
787C22#269811yescharacteristic
788C22#270011yescharacteristic
789C22C2×#44411yescharacteristic
790C22#295511yescharacteristic
791C22#295611yescharacteristic
792C22#295711yescharacteristic
793C4—22no—
794C4—42no—
795C4—41no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—82no—
801C4—82no—
802C4—81no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4#231011yescharacteristic
807C4#233211yescharacteristic
808C4#233911yescharacteristic
809C4#237811yescharacteristic
810C4#267211yescharacteristic
811C4#267411yescharacteristic
812C4#268011yescharacteristic
813C4#268111yescharacteristic
814C2—21no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—82no—
819C2#1436411yescharacteristic
820C2#2213111yescharacteristic
821C2#2213211yescharacteristic
822C2#2245211yescharacteristic
823C2#2245311yescharacteristic
824C2#2308111yescharacteristic
825C2#2308211yescharacteristic
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
2. #21304C2semidirect
6. #11386C2semidirect
7. #11376C2semidirect
8. #11233C2semidirect
9. #11221C2semidirect
12. #10909C2semidirect
13. #10877C2semidirect
14. #10860C2semidirect
20. C2×#479C4semidirect
21. C2×#479C4semidirect
22. C2×#477C4semidirect
23. C2×#475C4semidirect
24. C2×#478C4semidirect
25. C2×#478C4semidirect
26. C2×#476C4semidirect
27. C2×#474C4semidirect

Maximal subgroups

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

subgroupindex
C2×#30762
#213042
C2×#19382
C2×#19292
#206842
#113862
#113762
#112332
#112212
#111912
#109092
#108772
#108602
#107902