Finite Group Databasebeta

← #367696

Subgroups — #367696

Order 512.

1020 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
1#21050C211yesmaximal, characteristic
2C2×#1922C211yesmaximal, characteristic, complemented
3#20843C211yesmaximal, characteristic
4C2×#1826C211yesmaximal, characteristic
5#20379C211yesmaximal, characteristic
6#11317C211yesmaximal, characteristic, complemented
7#11221C211yesmaximal, characteristic, complemented
8#11201C211yesmaximal, characteristic
9#11097C211yesmaximal, characteristic
10#10922C211yesmaximal, characteristic
11#10910C211yesmaximal, characteristic, complemented
12#10909C211yesmaximal, characteristic, complemented
13#10860C211yesmaximal, characteristic, complemented
14#10809C211yesmaximal, characteristic, complemented
15#10707C211yesmaximal, characteristic, complemented
16C22×#117C2211yescharacteristic
17C22×#108C2211yescharacteristic
18C2×#427C2211yescharacteristic
19C2×#427C2211yescharacteristic
20C2×#424C2211yescharacteristic
21C2×#407C2211yescharacteristic
22C2×#407C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C2×#405C2211yescharacteristic
26C2×#405C2211yescharacteristic
27C2×#405C2211yescharacteristic
28C22×#97C2211yescharacteristic
29#2280C2211yescharacteristic
30C2×C4×C22⋊C4C2211yescharacteristic
31#1924—21no—
32#1924—21no—
33#1923—21no—
34#1923—21no—
35#1922—24no—
36#1854C411yescharacteristic, complemented
37#1854C411yescharacteristic, complemented
38#1854C411yescharacteristic, complemented
39#1854C411yescharacteristic, complemented
40#1853C411yescharacteristic, complemented
41#1853C411yescharacteristic, complemented
42#1852C411yescharacteristic, complemented
43#1852C411yescharacteristic, complemented
44#1826—24no—
45#1750—21no—
46#1750—21no—
47#1749—21no—
48C4×C22⋊C8—21no—
49C2×#341C2211yescharacteristic
50C2×#341C2211yescharacteristic
51C2×#341C2211yescharacteristic
52#1735C2211yescharacteristic
53#1735C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62#1729C2211yescharacteristic
63#1729C2211yescharacteristic
64#1729C2211yescharacteristic
65#1729C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C24×C4C2311yescharacteristic
70C22×M16C2311yescharacteristic
71C22×M16C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C2×#117—21no—
79C2×#117—21no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—41no—
83C2×#117—41no—
84C2×#117C2×C411yescharacteristic
85C2×#117C2×C411yescharacteristic
86C2×#117C2311yescharacteristic
87C2×#117C2311yescharacteristic
88C2×#117C2311yescharacteristic
89C2×#117C2311yescharacteristic
90C22×C4⋊C4C2×C411yescharacteristic
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C42—21no—
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C2×#108—22no—
98C2×#108—22no—
99C2×#108—41no—
100#427—22no—
101#427—22no—
102#427—41no—
103#427—41no—
104C2×#107C2×C411yescharacteristic
105C2×#107C2×C411yescharacteristic
106C2×#107C2×C411yescharacteristic
107C2×#107C2×C411yescharacteristic
108C2×#106C2×C411yescharacteristic
109C2×#106C2×C411yescharacteristic
110C2×#106C2×C411yescharacteristic
111C2×#106C2×C411yescharacteristic
112#424—22no—
113#424—41no—
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116#407—22no—
117#407—22no—
118#407—22no—
119#407—41no—
120C2×C22⋊C8—21no—
121C2×C22⋊C8—21no—
122C2×C22⋊C8—22no—
123C2×C22⋊C8—22no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8—21no—
127C2×C22⋊C8—21no—
128C2×C22⋊C8C2×C411yescharacteristic
129C2×C22⋊C8C2×C411yescharacteristic
130C2×C22⋊C8C2×C411yescharacteristic
131C2×C22⋊C8C2×C411yescharacteristic
132C2×C22⋊C8D411yescharacteristic
133C2×C22⋊C8D411yescharacteristic
134C2×C22⋊C8D411yescharacteristic
135C2×C22⋊C8D411yescharacteristic
136#405—22no—
137#405—22no—
138#405—22no—
139#405—22no—
140#405—41no—
141#405—41no—
142C2×#97—21no—
143C2×#97—21no—
144C2×#97—21no—
145C2×#97—22no—
146C2×#97—22no—
147C2×#97—41no—
148C2×C4×C8—21no—
149C2×C4×C8—21no—
150C2×C4×C8—21no—
151#381—21no—
152#380C2×C411yescharacteristic
153#380C2×C411yescharacteristic
154#380C2×C411yescharacteristic
155#380C2×C411yescharacteristic
156#379—21no—
157C4×C22⋊C4—21no—
158C4×C22⋊C4—21no—
159C4×C22⋊C4—22no—
160C4×C22⋊C4—41no—
161C2×#95—21no—
162#341—22no—
163#341—22no—
164#341—22no—
165#340C2×C411yescharacteristic
166#340C2×C411yescharacteristic
167#340C2×C411yescharacteristic
168#340C2×C411yescharacteristic
169#340C2×C411yescharacteristic
170#340C2×C411yescharacteristic
171#340C2×C411yescharacteristic
172#340C2×C411yescharacteristic
173#339—22no—
174#339—22no—
175#339—22no—
176#339—22no—
177#339—22no—
178#339—22no—
179#339—41no—
180#339D414yes—
181#336—21no—
182#336—21no—
183#336—21no—
184#336—21no—
185#336—21no—
186#336—21no—
187#336—21no—
188#336—21no—
189#336—22no—
190#336—22no—
191#336—22no—
192C25#4111yescharacteristic
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×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4C22×C411yescharacteristic
210C23×C4C22×C411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4#4111yescharacteristic
214C23×C4C2411yescharacteristic
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—21no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16C2×D412yes—
237C2×M16#4112yes—
238C2×M16#4112yes—
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×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8C22×C411yescharacteristic
264C22×C8C22×C411yescharacteristic
265C22×C8C22×C411yescharacteristic
266C22×C8C22×C411yescharacteristic
267C22×C8C2×D411yescharacteristic
268C22×C8C2×D411yescharacteristic
269C22×C8C2×D411yescharacteristic
270C22×C8C2×D411yescharacteristic
271C22×C8#4112yes—
272C22×C8#4112yes—
273C22×C8#4112yes—
274C22×C8#4112yes—
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—21no—
284#117—21no—
285#117—21no—
286#117—21no—
287#117—21no—
288#117—21no—
289#117—22no—
290#117—22no—
291#117—42no—
292#117—42no—
293#117—42no—
294#117—42no—
295#117—41no—
296#117—41no—
297#117C2×D412yes—
298#117#4112yes—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4C22×C411yescharacteristic
306C2×C4⋊C4C22×C411yescharacteristic
307C2×C4⋊C4C22×C411yescharacteristic
308C2×C4⋊C4C22×C411yescharacteristic
309C2×C4⋊C4C22×C411yescharacteristic
310C2×C4⋊C4C22×C411yescharacteristic
311C2×C4⋊C4C22×C411yescharacteristic
312C2×C4⋊C4C22×C411yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
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—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—42no—
346C2×C42—42no—
347C2×C42C2×D412yes—
348#108—44no—
349#107—22no—
350#107—22no—
351#107—41no—
352#107—41no—
353#106—22no—
354#106—22no—
355#106—41no—
356#106—41no—
357C4⋊C8—42no—
358C4⋊C8—42no—
359C22⋊C8—24no—
360C22⋊C8—24no—
361C22⋊C8—22no—
362C22⋊C8—22no—
363C22⋊C8—22no—
364C22⋊C8—22no—
365C22⋊C8—22no—
366C22⋊C8—22no—
367C22⋊C8—22no—
368C22⋊C8—22no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371#97—42no—
372#97—42no—
373#97—44no—
374#97—42no—
375C4×C8—42no—
376C4×C8—42no—
377C4×C8—42no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—42no—
383C24—22no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24C4×D411yescharacteristic
394C24C4×D411yescharacteristic
395C24C2×#4111yescharacteristic
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—21no—
415C22×C4—21no—
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—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
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—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—42no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4—81no—
470C22×C4C4×D411yescharacteristic
471C22×C4C4×D411yescharacteristic
472C22×C4C23×C411yescharacteristic
473C22×C4C22×D411yescharacteristic
474C22×C4C22×D411yescharacteristic
475C22×C4C2×#4111yescharacteristic
476C22×C4C2×#4111yescharacteristic
477C22×C4C2×#4111yescharacteristic
478C22×C4C2×#4111yescharacteristic
479C22×C4C2×#4111yescharacteristic
480C22×C4C2×#4111yescharacteristic
481C22×C4C2×#4111yescharacteristic
482C22×C4H(5,𝔽2)11yescharacteristic
483C22×C4H(5,𝔽2)11yescharacteristic
484C22×C42−1+411yescharacteristic
485C22×C42−1+411yescharacteristic
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—22no—
491M16—22no—
492M16—41no—
493M16—41no—
494M16—41no—
495M16—41no—
496M16—41no—
497M16—41no—
498M16—41no—
499M16—41no—
500M16—41no—
501M16—41no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—22no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8#11712yes—
551C2×C8#11712yes—
552C2×C8#12312yes—
553C2×C8#12312yes—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4C4×D412yes—
571C4⋊C4C4×D412yes—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—48no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C22⋊C4—42no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—42no—
592C42—42no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23#44412yes—
639C23C2×C4×D411yescharacteristic
640C23#52911yescharacteristic
641C23#52911yescharacteristic
642C23#54611yescharacteristic
643C23#55111yescharacteristic
644C23#55211yescharacteristic
645C23#55211yescharacteristic
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
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—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
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—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
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—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4C2×#11711yescharacteristic
713C2×C4C2×C4×D411yescharacteristic
714C2×C4C4×#4111yescharacteristic
715C2×C4C4×#4111yescharacteristic
716C2×C4#51811yescharacteristic
717C2×C4#51911yescharacteristic
718C2×C4C2×#12311yescharacteristic
719C2×C4#52511yescharacteristic
720C2×C4#52911yescharacteristic
721C2×C4#52911yescharacteristic
722C2×C4#53211yescharacteristic
723C2×C4#53211yescharacteristic
724C2×C4#53911yescharacteristic
725C2×C4#53911yescharacteristic
726C2×C4#54211yescharacteristic
727C2×C4#54211yescharacteristic
728C2×C4D4211yescharacteristic
729C2×C4#54611yescharacteristic
730C2×C4#54711yescharacteristic
731C2×C4#54711yescharacteristic
732C2×C4#54711yescharacteristic
733C2×C4#54811yescharacteristic
734C2×C4#55111yescharacteristic
735C2×C4#55111yescharacteristic
736C2×C4#55211yescharacteristic
737C2×C4#55311yescharacteristic
738C2×C4#55311yescharacteristic
739C2×C4#55611yescharacteristic
740C8—22no—
741C8—22no—
742C8—22no—
743C8—22no—
744C8—41no—
745C8—41no—
746C8—42no—
747C8—42no—
748C8—42no—
749C8—41no—
750C8—41no—
751C8—81no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22C4×#12311yescharacteristic
783C22#234411yescharacteristic
784C22#235811yescharacteristic
785C22#251511yescharacteristic
786C22#252711yescharacteristic
787C22#255311yescharacteristic
788C22#255811yescharacteristic
789C22C2×#44411yescharacteristic
790C22#295511yescharacteristic
791C22#295611yescharacteristic
792C22#295711yescharacteristic
793C4—42no—
794C4—42no—
795C4—41no—
796C4—41no—
797C4—82no—
798C4—82no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4—81no—
803C4—81no—
804C4—81no—
805C4#229311yescharacteristic
806C4#233211yescharacteristic
807C4#235311yescharacteristic
808C4#236211yescharacteristic
809C4#241911yescharacteristic
810C4#242211yescharacteristic
811C4#246111yescharacteristic
812C4#246611yescharacteristic
813C2—21no—
814C2—21no—
815C2—21no—
816C2—21no—
817C2—42no—
818C2—81no—
819C2#1400811yescharacteristic
820C2#2159311yescharacteristic
821C2#2159411yescharacteristic
822C2#2260711yescharacteristic
823C2#2260811yescharacteristic
824C2#2288611yescharacteristic
825C2#2288911yescharacteristic
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×#1922C2semidirect
6. #11317C2semidirect
7. #11221C2semidirect
11. #10910C2semidirect
12. #10909C2semidirect
13. #10860C2semidirect
14. #10809C2semidirect
15. #10707C2semidirect
36. #1854C4semidirect
37. #1854C4semidirect
38. #1854C4semidirect
39. #1854C4semidirect
40. #1853C4semidirect
41. #1853C4semidirect
42. #1852C4semidirect
43. #1852C4semidirect

Maximal subgroups

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

subgroupindex
#210502
C2×#19222
#208432
C2×#18262
#203792
#113172
#112212
#112012
#110972
#109222
#109102
#109092
#108602
#108092
#107072