Finite Group Databasebeta

← #6763417

Subgroups — #6763417

Order 512.

1836 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36180C211yesmaximal, characteristic, complemented
2#36149C211yesmaximal, characteristic
3#33049C211yesmaximal, characteristic, complemented
4#31858C214yesmaximal, complemented
5#31650C214yesmaximal, complemented
6#30205C211yesmaximal, characteristic, complemented
7#29808C211yesmaximal, characteristic, complemented
8#29139C211yesmaximal, characteristic, complemented
9#28616C211yesmaximal, characteristic, complemented
10#27972C211yesmaximal, characteristic, complemented
11#27960C211yesmaximal, characteristic, complemented
12#25719C211yesmaximal, characteristic, complemented
13#25597C211yesmaximal, characteristic, complemented
14#24548C214yesmaximal, complemented
15#23981C214yesmaximal, complemented
16#22268C211yesmaximal, characteristic, complemented
17#21859C211yesmaximal, characteristic, complemented
18#21200C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#554C2212yes—
21C2×#532C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×#494C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#452C2214yes—
27C2×#431C2211yescharacteristic
28C2×#417C2214yes—
29C2×C4×M16C2211yescharacteristic
30#2868C2211yescharacteristic
31#2862C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2567C2212yes—
37#2552—21no—
38#2552—21no—
39#2535—21no—
40#2502C2212yes—
41#2502C2212yes—
42#2447—21no—
43#2447C2212yes—
44#2440—21no—
45#2440—21no—
46#2440—21no—
47#2440—21no—
48#2427—21no—
49#2427C2212yes—
50#2420—21no—
51#2420—21no—
52#2407—21no—
53#2407C2212yes—
54#2349—21no—
55D4×C4⋊C4—21no—
56D4×C4⋊C4—21no—
57#2339—21no—
58#2339C2212yes—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2099C2214yes—
65#2072C2214yes—
66#2072C2214yes—
67#2056C2214yes—
68#2056C2214yes—
69#2024C2214yes—
70#2023C2214yes—
71#2015C2214yes—
72#2001C2214yes—
73#2000C2214yes—
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1959C2214yes—
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1935C2214yes—
86#1924C2212yes—
87#1917C2212yes—
88#1894C2214yes—
89#1880C2214yes—
90#1878C2214yes—
91#1877C2214yes—
92#1877C2214yes—
93#1874C2214yes—
94#1872C2214yes—
95#1870C2212yes—
96#1851C2212yes—
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1834C2211yescharacteristic
100#1823C2214yes—
101#1802C2214yes—
102#1802C2214yes—
103C4×C4⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C22×#41—21no—
108C22×#41C2312yes—
109C22×Q16C2314yes—
110C22×SD16C2314yes—
111C22×M16C2312yes—
112#554—48no—
113#532—24no—
114#532—24no—
115#532—42no—
116#532—42no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—21no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2311yescharacteristic
122C2×C4⋊Q8C2312yes—
123C2×#127C2311yescharacteristic
124C2×#125—22no—
125C2×#124—21no—
126C2×#124C2312yes—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8—22no—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×C22⋊Q8C2312yes—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121C2312yes—
137C2×C4×Q8C2312yes—
138C2×C4×D4—22no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4—21no—
144C2×C4×D4D411yescharacteristic
145C2×C4×D4D411yescharacteristic
146C2×C4×D4C2312yes—
147C2×C4×D4C2312yes—
148C2×C4×D4C2311yescharacteristic
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#494—42no—
158#492—24no—
159#487—42no—
160#452—48no—
161#431—42no—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2312yes—
164#417—48no—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C4×M16—42no—
177C2×#97C2312yes—
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182#398—22no—
183#398—22no—
184#398—22no—
185#398—22no—
186#397—22no—
187#397—22no—
188#397—22no—
189#395—22no—
190#395—22no—
191#394—22no—
192#394—22no—
193#392—22no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391C2312yes—
198#391C2312yes—
199#391C2312yes—
200#391C2312yes—
201#391C2312yes—
202#391C2312yes—
203#390—21no—
204#390—21no—
205#390C2312yes—
206#389—22no—
207#389—22no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389C2312yes—
218#386—22no—
219#386—22no—
220#386—22no—
221#386—22no—
222#385—22no—
223#385—22no—
224#385—22no—
225#385—22no—
226#385—22no—
227#385—22no—
228#384—21no—
229#384—21no—
230#384—21no—
231#384—21no—
232#384—21no—
233#384—21no—
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#384C2312yes—
237#384C2312yes—
238#384C2312yes—
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#382—21no—
242#382—21no—
243#381—22no—
244#381—22no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—22no—
253#380C2312yes—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4D411yescharacteristic
257C4×C4⋊C4D411yescharacteristic
258C4×C4⋊C4C2311yescharacteristic
259C4×C22⋊C4D411yescharacteristic
260C4×C22⋊C4D411yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4C2311yescharacteristic
264C4×C22⋊C4C2311yescharacteristic
265C2×#95—22no—
266C43C2311yescharacteristic
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C2×#41—24no—
279C2×#41—28no—
280C2×#41—42no—
281C2×#41—44no—
282C2×#41—44no—
283C2×#41—44no—
284C2×#41—82no—
285C22×Q8—21no—
286C22×Q8—22no—
287C22×Q8C2412yes—
288C22×Q8C2412yes—
289C22×D4—22no—
290C22×D4—22no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C2×D411yescharacteristic
294C22×D4C2412yes—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C2×Q16—44no—
307C2×Q16—44no—
308C2×Q16—44no—
309C2×SD16—28no—
310C2×SD16—44no—
311C2×SD16—44no—
312C2×M16—24no—
313C2×M16—42no—
314C2×M16—42no—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—44no—
326C4⋊Q8—82no—
327C4⋊Q8—82no—
328#127—22no—
329#127#4114yes—
330#125—48no—
331#124—24no—
332#124—42no—
333#124—44no—
334C22⋊Q8—28no—
335C22⋊Q8—48no—
336C22⋊Q8—48no—
337C22⋊Q8—44no—
338C22⋊Q8—44no—
339C22⋊Q8—82no—
340#121—24no—
341#121—42no—
342#121—44no—
343#121—44no—
344#121—44no—
345C4×Q8—44no—
346C4×D4—24no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—42no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4—44no—
354C4×D4—44no—
355C4×D4—48no—
356C4×D4—44no—
357C4×D4—82no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
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—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
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—22no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—82no—
388C2×C4⋊C4—82no—
389C2×C4⋊C4—82no—
390C2×C4⋊C4—82no—
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×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⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C22⋊C4C2×D411yescharacteristic
413C2×C22⋊C4C2×D411yescharacteristic
414C2×C22⋊C4C2×D411yescharacteristic
415C2×C22⋊C4C2×D411yescharacteristic
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C4⋊C8—42no—
435C4⋊C8—42no—
436#103—44no—
437#103—44no—
438#103—44no—
439#103—44no—
440#103—44no—
441#102—44no—
442#102—44no—
443#102—44no—
444C22⋊C8—24no—
445C22⋊C8—42no—
446C22⋊C8—42no—
447#97—42no—
448C4×C8—22no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—22no—
452#95—22no—
453#95—22no—
454#95—22no—
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#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472C24—22no—
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475#41—416no—
476#41—88no—
477#41—816no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—24no—
483C2×Q8—22no—
484C2×Q8—24no—
485C2×Q8—24no—
486C2×Q8—44no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—82no—
491C2×Q8—82no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—24no—
498C2×D4—22no—
499C2×D4—24no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—82no—
509C2×D4—82no—
510C2×D4C2×#4114yes—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
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—21no—
526C22×C4—21no—
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—22no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—82no—
544C22×C4—82no—
545C22×C4—82no—
546C22×C4—82no—
547C22×C4—82no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4#13714yes—
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
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×C4H(5,𝔽2)14yes—
565C22×C4C2511yescharacteristic
566Q16—88no—
567SD16—88no—
568M16—48no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
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—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—22no—
589C4⋊C4—24no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
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—82no—
610C4⋊C4—82no—
611C4⋊C4—82no—
612C4⋊C4—82no—
613C4⋊C4—82no—
614C4⋊C4—82no—
615C4⋊C4—82no—
616C4⋊C4—82no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
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—22no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—22no—
646C42—22no—
647C42—44no—
648C42#13714yes—
649C42C2×#4112yes—
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—24no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23#53512yes—
671C23C2×#13712yes—
672C23C23×D411yescharacteristic
673Q8—44no—
674Q8—44no—
675Q8—44no—
676Q8—44no—
677Q8—84no—
678Q8—164no—
679D4—28no—
680D4—28no—
681D4—48no—
682D4—44no—
683D4—48no—
684D4—88no—
685D4—88no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—28no—
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—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—44no—
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—88no—
742C2×C4—88no—
743C2×C4—164no—
744C2×C4—164no—
745C2×C4—164no—
746C2×C4#53512yes—
747C2×C4#54612yes—
748C2×C4#54612yes—
749C2×C4C2×#13712yes—
750C2×C4C2×#13712yes—
751C2×C4C2×#13712yes—
752C2×C4C2×#13712yes—
753C2×C4C2×#13712yes—
754C2×C4#57612yes—
755C2×C4#57712yes—
756C2×C4C22×#4111yescharacteristic
757C2×C4C2×H(5,𝔽2)12yes—
758C2×C4C2×H(5,𝔽2)11yescharacteristic
759C2×C4#58512yes—
760C8—42no—
761C8—42no—
762C8—42no—
763C8—42no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22C2×#53511yescharacteristic
786C22C2×#54611yescharacteristic
787C22#350011yescharacteristic
788C22C22×#13711yescharacteristic
789C22C22×#13711yescharacteristic
790C22C2×#57611yescharacteristic
791C22C2×#57711yescharacteristic
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4#331414yes—
810C4#333114yes—
811C4#351312yes—
812C4#354212yes—
813C2—42no—
814C2—42no—
815C2—84no—
816C2#3808211yescharacteristic
817C2#6080011yescharacteristic
818C2#6082211yescharacteristic
819C2C2×#331411yescharacteristic
820C2C2×#333111yescharacteristic
821C2#6253711yescharacteristic
822C2#6254211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36149C2
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. #36180C2semidirect
3. #33049C2semidirect
4. #31858C2semidirect
5. #31650C2semidirect
6. #30205C2semidirect
7. #29808C2semidirect
8. #29139C2semidirect
9. #28616C2semidirect
10. #27972C2semidirect
11. #27960C2semidirect
12. #25719C2semidirect
13. #25597C2semidirect
14. #24548C2semidirect
15. #23981C2semidirect
16. #22268C2semidirect
17. #21859C2semidirect
18. #21200C2semidirect
19. #21102C2semidirect

Maximal subgroups

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

subgroupindex
#361802
#361492
#330492
#318582
#316502
#302052
#298082
#291392
#286162
#279722
#279602
#257192
#255972
#245482
#239812
#222682
#218592
#212002
#211022