Finite Group Databasebeta

← #6477222

Subgroups — #6477222

Order 512.

1655 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35297C211yesmaximal, characteristic
2#35279C211yesmaximal, characteristic
3#33210C211yesmaximal, characteristic, complemented
4#33207C211yesmaximal, characteristic, complemented
5#33049C211yesmaximal, characteristic, complemented
6#33043C211yesmaximal, characteristic, complemented
7#30374C214yesmaximal, complemented
8#29170C214yesmaximal, complemented
9#27962C211yesmaximal, characteristic, complemented
10#27908C211yesmaximal, characteristic, complemented
11#27878C211yesmaximal, characteristic, complemented
12#27875C211yesmaximal, characteristic, complemented
13#25902C211yesmaximal, characteristic, complemented
14#25811C211yesmaximal, characteristic, complemented
15#25672C211yesmaximal, characteristic, complemented
16#25672C211yesmaximal, characteristic, complemented
17#24569C214yesmaximal
18#22092C214yesmaximal, complemented
19C4×#408C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C2×C4×#41C2211yescharacteristic
23C2×#498C2211yescharacteristic
24C2×#498C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#485C2214yes—
28C2×#408C2212yes—
29C2×C4×M16C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2628C2212yes—
40#2628C2212yes—
41#2625C2212yes—
42#2616C2212yes—
43#2584—21no—
44#2581—21no—
45#2568—21no—
46#2567—21no—
47#2563—21no—
48#2562—21no—
49#2542—21no—
50#2536—21no—
51#2487—21no—
52#2487—21no—
53#2485—21no—
54#2485—21no—
55#2415—21no—
56#2415—21no—
57#2409—21no—
58#2409—21no—
59#2323C2212yes—
60#2323C2212yes—
61#2317C2212yes—
62#2311C2212yes—
63#2285C2211yescharacteristic
64#2285C2211yescharacteristic
65#2101C2214yes—
66#2097C2214yes—
67#2077C2214yes—
68#2076C2214yes—
69#2058C2214yes—
70#2035C2214yes—
71#2035C2214yes—
72#2024C2214yes—
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1943C2214yes—
82#1941C2214yes—
83#1935C2214yes—
84#1933C2214yes—
85#1921C2214yes—
86#1920C2214yes—
87#1894C2214yes—
88#1892C2214yes—
89#1872C2214yes—
90#1865C2214yes—
91#1865C2214yes—
92#1853C2214yes—
93#1845C2211yescharacteristic
94#1844C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97#1825C2214yes—
98#1809C2214yes—
99#1807C2214yes—
100#1750C2212yes—
101#1750C2212yes—
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1729C2212yes—
107C22×#41C2311yescharacteristic
108C23×Q8—21no—
109C22×M16C2312yes—
110C23×C8C2312yes—
111#533—42no—
112#533—42no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—42no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2312yes—
122C2×#125—21no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2312yes—
133C4×#41—42no—
134C4×#41—42no—
135C2×C4×Q8—21no—
136C2×C4×Q8D411yescharacteristic
137C2×C4×Q8D411yescharacteristic
138C2×C4×Q8C2312yes—
139C2×C4×D4D411yescharacteristic
140C2×C4×D4D411yescharacteristic
141C2×C4×D4D411yescharacteristic
142C2×C4×D4D411yescharacteristic
143C2×C4×D4D411yescharacteristic
144C2×C4×D4D411yescharacteristic
145C2×#117—21no—
146C2×#117—21no—
147C2×#117C2312yes—
148C2×#117C2311yescharacteristic
149C2×#117C2311yescharacteristic
150C2×#117C2311yescharacteristic
151C22×C4⋊C4—21no—
152C22×C4⋊C4C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#498—42no—
157#498—42no—
158#487—42no—
159#487—42no—
160#485—216no—
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×#106C2314yes—
164C2×#106C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169#408—28no—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C4×M16—42no—
175C2×#97C2312yes—
176C2×C4×C8—42no—
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2312yes—
182#400—22no—
183#400—22no—
184#400—22no—
185#399—22no—
186#399—22no—
187#398—22no—
188#397—22no—
189#397—22no—
190#395—22no—
191#395—22no—
192#395—22no—
193#394—22no—
194#394—22no—
195#394—22no—
196#393—22no—
197#393—22no—
198#391—22no—
199#391—21no—
200#391—21no—
201#391—21no—
202#391—21no—
203#391—21no—
204#391—21no—
205#391C2312yes—
206#391C2312yes—
207#390—22no—
208#389—22no—
209#389—22no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389C2312yes—
221#389C2312yes—
222#389C2312yes—
223#389C2312yes—
224#389C2312yes—
225#389C2312yes—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#387—22no—
231#387—22no—
232#386—22no—
233#386—22no—
234#385—22no—
235#385—22no—
236#384—22no—
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#382—22no—
242#382—21no—
243#382C2312yes—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—21no—
254#380—21no—
255#380—21no—
256#380—21no—
257#380C2312yes—
258#380C2312yes—
259#380C2312yes—
260#380C2312yes—
261#380C2312yes—
262#380C2312yes—
263#380C2312yes—
264C4×C4⋊C4—21no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4—21no—
267C4×C4⋊C4C2312yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280C2×#41—24no—
281C2×#41—24no—
282C2×#41—41no—
283C2×#41—41no—
284C22×Q8—21no—
285C22×Q8—21no—
286C22×Q8—21no—
287C22×Q8—22no—
288C22×Q8—44no—
289C22×Q8—82no—
290C22×Q8—82no—
291C22×Q8C2×D411yescharacteristic
292C22×Q8C2412yes—
293C22×D4C2×D411yescharacteristic
294C22×D4C2×D411yescharacteristic
295C22×D4C2×D411yescharacteristic
296C23×C4—22no—
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C2×M16—24no—
307C2×M16—24no—
308C2×M16—42no—
309C22×C8—24no—
310C22×C8—24no—
311C22×C8—42no—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—42no—
325C4⋊Q8—42no—
326C4⋊Q8—44no—
327C4⋊Q8—44no—
328#125—44no—
329C22⋊Q8—28no—
330C22⋊Q8—28no—
331C22⋊Q8—42no—
332C22⋊Q8—42no—
333C22⋊Q8—44no—
334C22⋊Q8—82no—
335C22⋊Q8—82no—
336C22⋊Q8—82no—
337C22⋊Q8—82no—
338C22⋊Q8—82no—
339C22⋊Q8—82no—
340C4×Q8—42no—
341C4×Q8—42no—
342C4×Q8—42no—
343C4×Q8—42no—
344C4×Q8—44no—
345C4×D4—42no—
346C4×D4—42no—
347C4×D4—42no—
348C4×D4—42no—
349C4×D4—42no—
350C4×D4—42no—
351#117—28no—
352#117—41no—
353#117—41no—
354#117—41no—
355#117—41no—
356#117—41no—
357#117—41no—
358#117—44no—
359#117—82no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D411yescharacteristic
391C2×C4⋊C4C2×D411yescharacteristic
392C2×C4⋊C4C2×D411yescharacteristic
393C2×C4⋊C4C2×D411yescharacteristic
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4C2×D411yescharacteristic
413C2×C22⋊C4C2×D411yescharacteristic
414C2×C22⋊C4C2×D411yescharacteristic
415C2×C22⋊C4C2×D411yescharacteristic
416C2×C22⋊C4C2×D411yescharacteristic
417C2×C22⋊C4C2×D411yescharacteristic
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437#107—28no—
438#106—28no—
439#106—44no—
440#106—44no—
441#103—28no—
442#103—28no—
443#103—44no—
444#103—44no—
445C22⋊C8—24no—
446C22⋊C8—24no—
447C22⋊C8—24no—
448C22⋊C8#4118yes—
449#97—42no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8—22no—
453C4×C8—22no—
454C4×C8—42no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475C24C22×D411yescharacteristic
476C24C22×D411yescharacteristic
477C24C22×D411yescharacteristic
478#41—48no—
479#41—48no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—24no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—24no—
486C2×Q8—41no—
487C2×Q8—44no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—82no—
498C2×Q8—82no—
499C2×Q8—816no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—44no—
546C22×C4—82no—
547C22×C4—82no—
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C2×#4114yes—
560C22×C42−1+414yes—
561C22×C4C2511yescharacteristic
562M16—48no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—48no—
574C2×C8C2×#4114yes—
575C2×C8C2×#4114yes—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—82no—
612C4⋊C4—82no—
613C4⋊C4—82no—
614C4⋊C4—82no—
615C4⋊C4—82no—
616C4⋊C4—82no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—82no—
628C22⋊C4—82no—
629C22⋊C4—82no—
630C22⋊C4—82no—
631C22⋊C4—82no—
632C22⋊C4—82no—
633C22⋊C4—82no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—44no—
647C42—44no—
648C42—82no—
649C42H(5,𝔽2)12yes—
650C42H(5,𝔽2)12yes—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23#53212yes—
671C23#53612yes—
672C23C23×D411yescharacteristic
673Q8—44no—
674Q8—44no—
675Q8—44no—
676Q8—88no—
677Q8—84no—
678Q8—84no—
679Q8—84no—
680D4—44no—
681D4—44no—
682D4—44no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—88no—
745C2×C4#53212yes—
746C2×C4#53412yes—
747C2×C4#53412yes—
748C2×C4#53612yes—
749C2×C4#57712yes—
750C2×C4#57712yes—
751C2×C4#57712yes—
752C2×C4#57812yes—
753C2×C4C22×#4112yes—
754C2×C4C2×H(5,𝔽2)11yescharacteristic
755C2×C4C2×H(5,𝔽2)11yescharacteristic
756C2×C4C2×2−1+412yes—
757C8—24no—
758C8—24no—
759C8—42no—
760C8—42no—
761C22—22no—
762C22—22no—
763C22—22no—
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—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22C2×#53211yescharacteristic
783C22C2×#53411yescharacteristic
784C22C2×#53611yescharacteristic
785C22C2×#57711yescharacteristic
786C22C2×#57711yescharacteristic
787C22C2×#57711yescharacteristic
788C22C2×#57811yescharacteristic
789C4—22no—
790C4—22no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4#320014yes—
807C4#320114yes—
808C4#352012yes—
809C4#352012yes—
810C2—42no—
811C2—42no—
812C2—81no—
813C2#3508511yescharacteristic
814C2#6071611yescharacteristic
815C2#6072311yescharacteristic
816C2C2×#320011yescharacteristic
817C2C2×#320111yescharacteristic
818C2#6087811yescharacteristic
819C2#6088111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #33210C2semidirect
4. #33207C2semidirect
5. #33049C2semidirect
6. #33043C2semidirect
7. #30374C2semidirect
8. #29170C2semidirect
9. #27962C2semidirect
10. #27908C2semidirect
11. #27878C2semidirect
12. #27875C2semidirect
13. #25902C2semidirect
14. #25811C2semidirect
15. #25672C2semidirect
16. #25672C2semidirect
18. #22092C2semidirect

Maximal subgroups

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

subgroupindex
#352972
#352792
#332102
#332072
#330492
#330432
#303742
#291702
#279622
#279082
#278782
#278752
#259022
#258112
#256722
#245692
#220922
C4×#4082