Finite Group Databasebeta

← #6798237

Subgroups — #6798237

Order 512.

1873 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#36194C211yesmaximal, characteristic, complemented
2#36122C211yesmaximal, characteristic
3#33230C211yesmaximal, characteristic, complemented
4#30546C214yesmaximal, complemented
5#30537C214yesmaximal, complemented
6#29808C211yesmaximal, characteristic, complemented
7#29807C211yesmaximal, characteristic, complemented
8#29141C211yesmaximal, characteristic, complemented
9#28444C211yesmaximal, characteristic, complemented
10#27890C211yesmaximal, characteristic, complemented
11#27889C211yesmaximal, characteristic, complemented
12#25722C211yesmaximal, characteristic, complemented
13#25719C211yesmaximal, characteristic, complemented
14#24641C214yesmaximal, complemented
15#24258C214yesmaximal, complemented
16#21805C211yesmaximal, characteristic, complemented
17#21804C211yesmaximal, characteristic, complemented
18#21691C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×#548C2212yes—
21C2×#532C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#494C2211yescharacteristic
24C2×#494C2211yescharacteristic
25C2×#492C2211yescharacteristic
26C2×#489C2214yes—
27C2×#464C2214yes—
28C2×#452C2214yes—
29C2×#451C2214yes—
30C2×#441C2214yes—
31C2×#431C2211yescharacteristic
32C2×#431C2211yescharacteristic
33#2868C2211yescharacteristic
34#2858C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2856C2211yescharacteristic
39#2571—21no—
40#2563—21no—
41#2545C2212yes—
42#2538C2212yes—
43#2497—21no—
44#2497—21no—
45#2492C2212yes—
46#2492C2212yes—
47#2491—21no—
48#2491—21no—
49#2452—21no—
50#2452—21no—
51#2439—21no—
52#2439—21no—
53#2436C2212yes—
54#2432C2212yes—
55#2416—21no—
56#2416—21no—
57#2369—21no—
58#2361—21no—
59#2361—21no—
60#2355C2212yes—
61#2354—21no—
62C4×C4⋊Q8C2211yescharacteristic
63C4×C4⋊Q8C2211yescharacteristic
64#2285C2211yescharacteristic
65#2285C2211yescharacteristic
66C42×D4C2211yescharacteristic
67#2056C2214yes—
68#2055C2214yes—
69#2035C2214yes—
70#2034C2214yes—
71#2024C2214yes—
72#2016C2214yes—
73#2015C2214yes—
74#2015C2214yes—
75#2001C2214yes—
76#2000C2214yes—
77#1983C2214yes—
78#1981C2214yes—
79#1971C2214yes—
80#1959C2214yes—
81#1957C2211yescharacteristic
82#1957C2211yescharacteristic
83#1957C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1956C2211yescharacteristic
87#1956C2211yescharacteristic
88#1956C2211yescharacteristic
89#1956C2211yescharacteristic
90#1956C2211yescharacteristic
91#1955C2212yes—
92#1940C2212yes—
93#1927C2214yes—
94#1926C2214yes—
95#1924C2212yes—
96#1924C2212yes—
97#1844C2211yescharacteristic
98#1834C2211yescharacteristic
99#1834C2211yescharacteristic
100#1803C2214yes—
101#1788C2214yes—
102#1787C2214yes—
103C4×C4⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×#41C2312yes—
108C23×Q8C2312yes—
109C22×Q16C2314yes—
110C22×Q16C2314yes—
111C22×SD16C2314yes—
112#548—48no—
113#532—24no—
114#532—42no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8—21no—
120C2×C4⋊Q8—42no—
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2312yes—
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2312yes—
126C2×#127C2311yescharacteristic
127C2×#124—22no—
128C2×#124C2312yes—
129C2×#124C2312yes—
130C2×#124C2312yes—
131C2×C22⋊Q8—22no—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×C22⋊Q8C2312yes—
135C2×#121—22no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121C2312yes—
141C2×C4×Q8C2312yes—
142C2×C4×Q8C2312yes—
143C2×C4×D4—22no—
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4D411yescharacteristic
147C2×C4×D4D411yescharacteristic
148C2×C4×D4C2311yescharacteristic
149C2×#117—21no—
150C2×#117—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#494—24no—
156#494—42no—
157#492—42no—
158#489—48no—
159#464—48no—
160#452—48no—
161#451—48no—
162#441—48no—
163#431—42no—
164#431—42no—
165C2×#106C2314yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×#97C2312yes—
184C2×#97C2312yes—
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2311yescharacteristic
188C2×C4×C8C2311yescharacteristic
189#400—22no—
190#400—22no—
191#396—22no—
192#396—22no—
193#396—22no—
194#396—22no—
195#394—22no—
196#394—22no—
197#393—22no—
198#393—22no—
199#393—22no—
200#393—22no—
201#391—22no—
202#391—22no—
203#391C2312yes—
204#391C2312yes—
205#391C2312yes—
206#391C2312yes—
207#391C2312yes—
208#390—22no—
209#390—21no—
210#390—21no—
211#390—21no—
212#390—21no—
213#390—21no—
214#390—21no—
215#390C2312yes—
216#389—22no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#387—22no—
232#387—22no—
233#386—22no—
234#386—22no—
235#385—22no—
236#385—22no—
237#384—21no—
238#384—21no—
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#384C2312yes—
242#384C2311yescharacteristic
243#384C2311yescharacteristic
244#382—22no—
245#382—21no—
246#382—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#380C2312yes—
256#380C2312yes—
257C4×C4⋊C4—22no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4—21no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4—21no—
264C4×C4⋊C4D411yescharacteristic
265C4×C4⋊C4D411yescharacteristic
266C4×C4⋊C4C2312yes—
267C4×C4⋊C4C2312yes—
268C4×C4⋊C4C2311yescharacteristic
269C4×C22⋊C4D411yescharacteristic
270C4×C22⋊C4D411yescharacteristic
271C4×C22⋊C4D411yescharacteristic
272C4×C22⋊C4D411yescharacteristic
273C4×C22⋊C4C2311yescharacteristic
274C4×C22⋊C4C2311yescharacteristic
275C43C2311yescharacteristic
276#340C2314yes—
277#340C2314yes—
278#336C2312yes—
279#336C2312yes—
280#336C2312yes—
281C2×#41—24no—
282C2×#41—42no—
283C2×#41—44no—
284C2×#41—44no—
285C22×Q8—22no—
286C22×Q8—22no—
287C22×Q8—24no—
288C22×Q8—42no—
289C22×Q8—44no—
290C22×Q8—44no—
291C22×Q8C2412yes—
292C22×Q8C2412yes—
293C22×Q8C2412yes—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C2×D411yescharacteristic
299C22×D4C2412yes—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C2×Q16—28no—
309C2×Q16—28no—
310C2×Q16—44no—
311C2×Q16—44no—
312C2×Q16—44no—
313C2×Q16—44no—
314C2×SD16—44no—
315C2×SD16—44no—
316C2×SD16—44no—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C4⋊Q8—24no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—44no—
328C4⋊Q8—44no—
329C4⋊Q8—44no—
330C4⋊Q8—42no—
331C4⋊Q8—44no—
332C4⋊Q8—82no—
333C4⋊Q8#4114yes—
334#127—22no—
335#127—22no—
336#124—24no—
337#124—28no—
338#124—42no—
339#124—44no—
340#124—48no—
341C22⋊Q8—44no—
342C22⋊Q8—48no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345#121—44no—
346#121—44no—
347#121—44no—
348#121—44no—
349#121—48no—
350#121—44no—
351C4×Q8—28no—
352C4×Q8—28no—
353C4×D4—24no—
354C4×D4—24no—
355C4×D4—44no—
356C4×D4—44no—
357C4×D4—42no—
358C4×D4—48no—
359#117—82no—
360#117—82no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
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⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C22⋊C4C2×D411yescharacteristic
413C2×C22⋊C4C2×D411yescharacteristic
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435#106—44no—
436C4⋊C8—24no—
437C4⋊C8—42no—
438C4⋊C8—42no—
439#103—28no—
440#103—44no—
441#103—44no—
442#103—44no—
443#103—44no—
444#103—44no—
445#103—44no—
446#102—28no—
447#102—44no—
448#102—44no—
449C22⋊C8—24no—
450C22⋊C8—24no—
451C22⋊C8—42no—
452C22⋊C8—42no—
453#97—24no—
454#97—24no—
455C4×C8—22no—
456C4×C8—22no—
457C4×C8—22no—
458C4×C8—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#95C2×D411yescharacteristic
474#95C2×D411yescharacteristic
475#95C2×D411yescharacteristic
476#95C2×D411yescharacteristic
477#95C2×D411yescharacteristic
478#95C2×D411yescharacteristic
479C24—22no—
480C24C22×D411yescharacteristic
481C24C22×D411yescharacteristic
482#41—88no—
483#41—88no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—24no—
488C2×Q8—24no—
489C2×Q8—24no—
490C2×Q8—24no—
491C2×Q8—24no—
492C2×Q8—24no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—82no—
499C2×Q8—82no—
500C2×Q8—82no—
501C2×Q8—88no—
502C2×Q8—88no—
503C2×Q8C2×#4114yes—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—22no—
510C2×D4—41no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—82no—
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—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—82no—
554C22×C4—82no—
555C22×C4#13714yes—
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C2511yescharacteristic
569Q16—416no—
570Q16—88no—
571SD16—88no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8H(5,𝔽2)14yes—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—22no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—41no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
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—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—82no—
630C22⋊C4—82no—
631C22⋊C4—82no—
632C22⋊C4—82no—
633C22⋊C4—82no—
634C22⋊C4—82no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—21no—
644C42—21no—
645C42—22no—
646C42—21no—
647C42—21no—
648C42—44no—
649C42—44no—
650C42—82no—
651C42—82no—
652C42C2×#4112yes—
653C42H(5,𝔽2)14yes—
654C42H(5,𝔽2)12yes—
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—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23C2×#13712yes—
676C23C23×D411yescharacteristic
677Q8—28no—
678Q8—44no—
679Q8—44no—
680Q8—44no—
681Q8—44no—
682Q8—44no—
683Q8—88no—
684Q8—164no—
685D4—44no—
686D4—44no—
687D4—44no—
688D4—88no—
689D4—88no—
690D4—84no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—28no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—24no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
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—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—88no—
749C2×C4—88no—
750C2×C4#53512yes—
751C2×C4#53512yes—
752C2×C4#54612yes—
753C2×C4#54612yes—
754C2×C4C2×#13712yes—
755C2×C4C2×#13712yes—
756C2×C4#57512yes—
757C2×C4#57712yes—
758C2×C4#57812yes—
759C2×C4C22×#4111yescharacteristic
760C2×C4C2×H(5,𝔽2)12yes—
761C2×C4C2×H(5,𝔽2)12yes—
762C2×C4C2×H(5,𝔽2)11yescharacteristic
763C8—24no—
764C8—42no—
765C8—42no—
766C8—42no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22C2×#53511yescharacteristic
789C22C2×#54611yescharacteristic
790C22#349811yescharacteristic
791C22C22×#13711yescharacteristic
792C22C2×#57511yescharacteristic
793C22C2×#57711yescharacteristic
794C22C2×#57811yescharacteristic
795C4—22no—
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—44no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4#331314yes—
813C4#331614yes—
814C4#351912yes—
815C4#354912yes—
816C2—42no—
817C2—81no—
818C2—162no—
819C2#3895311yescharacteristic
820C2#6080411yescharacteristic
821C2#6082411yescharacteristic
822C2C2×#331611yescharacteristic
823C2C2×#331311yescharacteristic
824C2#6242411yescharacteristic
825C2#6242711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36122C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36194C2semidirect
3. #33230C2semidirect
4. #30546C2semidirect
5. #30537C2semidirect
6. #29808C2semidirect
7. #29807C2semidirect
8. #29141C2semidirect
9. #28444C2semidirect
10. #27890C2semidirect
11. #27889C2semidirect
12. #25722C2semidirect
13. #25719C2semidirect
14. #24641C2semidirect
15. #24258C2semidirect
16. #21805C2semidirect
17. #21804C2semidirect
18. #21691C2semidirect
19. #21265C2semidirect

Maximal subgroups

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

subgroupindex
#361942
#361222
#332302
#305462
#305372
#298082
#298072
#291412
#284442
#278902
#278892
#257222
#257192
#246412
#242582
#218052
#218042
#216912
#212652