Finite Group Databasebeta

← #6475514

Subgroups — #6475514

Order 512.

1826 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35280C211yesmaximal, characteristic, complemented
2#35273C211yesmaximal, characteristic
3#33049C211yesmaximal, characteristic, complemented
4#33048C211yesmaximal, characteristic, complemented
5#33043C211yesmaximal, characteristic, complemented
6#33042C211yesmaximal, characteristic, complemented
7#30191C214yesmaximal, complemented
8#29342C214yesmaximal, complemented
9#29119C214yesmaximal, complemented
10#27973C211yesmaximal, characteristic, complemented
11#27972C211yesmaximal, characteristic, complemented
12#27961C211yesmaximal, characteristic, complemented
13#27960C211yesmaximal, characteristic, complemented
14#25905C211yesmaximal, characteristic, complemented
15#25904C211yesmaximal, characteristic, complemented
16#25857C211yesmaximal, characteristic, complemented
17#25857C211yesmaximal, characteristic, complemented
18#21772C214yesmaximal, complemented
19C4×#408C211yesmaximal, characteristic, complemented
20C2×#537C2212yes—
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×C4×#41C2211yescharacteristic
24C2×#487C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#408C2212yes—
29C2×C4×M16C2211yescharacteristic
30C22×C4×C8C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2856C2211yescharacteristic
39#2629C2212yes—
40#2629C2212yes—
41#2620C2212yes—
42#2620C2212yes—
43#2582—21no—
44#2582—21no—
45#2538—21no—
46#2538—21no—
47#2538—21no—
48#2538—21no—
49#2537—21no—
50#2537—21no—
51#2417—21no—
52#2417—21no—
53#2417—21no—
54#2417—21no—
55#2416—21no—
56#2416—21no—
57#2416—21no—
58#2416—21no—
59#2316C2212yes—
60#2311C2212yes—
61#2311C2212yes—
62C2×#384C2211yescharacteristic
63C2×#384C2211yescharacteristic
64#2100C2214yes—
65#2099C2214yes—
66#2072C2214yes—
67#2071C2214yes—
68#2042C2214yes—
69#2042C2214yes—
70#2026C2214yes—
71#2025C2214yes—
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1957C2211yescharacteristic
77#1957C2211yescharacteristic
78#1956C2211yescharacteristic
79#1956C2211yescharacteristic
80#1936C2214yes—
81#1935C2214yes—
82#1934C2214yes—
83#1933C2214yes—
84#1895C2214yes—
85#1894C2214yes—
86#1893C2214yes—
87#1892C2214yes—
88#1875C2214yes—
89#1874C2214yes—
90#1873C2214yes—
91#1872C2214yes—
92#1834C2211yescharacteristic
93#1834C2211yescharacteristic
94#1834C2211yescharacteristic
95#1834C2211yescharacteristic
96#1824C2214yes—
97#1823C2214yes—
98#1788C2214yes—
99#1788C2214yes—
100#1750C2212yes—
101#1750C2212yes—
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1729C2212yes—
107C22×#41C2312yes—
108C22×#41C2311yescharacteristic
109C22×M16C2312yes—
110C23×C8C2312yes—
111#537—216no—
112#533—42no—
113#533—42no—
114#532—42no—
115#532—42no—
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×#127C2311yescharacteristic
120C2×#125C2312yes—
121C2×#124C2312yes—
122C2×C22⋊Q8—22no—
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⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×#121—22no—
132C2×#121—22no—
133C2×#121—22no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—21no—
140C2×#121C2312yes—
141C2×#121C2312yes—
142C4×#41—42no—
143C4×#41—42no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8D411yescharacteristic
147C2×C4×Q8D411yescharacteristic
148C2×C4×D4—21no—
149C2×C4×D4—21no—
150C2×C4×D4D411yescharacteristic
151C2×C4×D4D411yescharacteristic
152C2×C4×D4D411yescharacteristic
153C2×C4×D4D411yescharacteristic
154C2×C4×D4D411yescharacteristic
155C2×C4×D4D411yescharacteristic
156C2×#117C2312yes—
157C2×#117C2311yescharacteristic
158C2×#117C2311yescharacteristic
159C2×#117C2311yescharacteristic
160C22×C4⋊C4—21no—
161C22×C4⋊C4—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169#487—42no—
170#487—42no—
171#486—42no—
172#486—42no—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×#102C2314yes—
181#408—28no—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C4×M16—42no—
187C2×#97C2312yes—
188C2×C4×C8—42no—
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2311yescharacteristic
191C2×C4×C8C2311yescharacteristic
192C2×C4×C8C2311yescharacteristic
193C2×C4×C8C2312yes—
194#398—22no—
195#398—22no—
196#398—22no—
197#398—22no—
198#396—22no—
199#396—22no—
200#396—22no—
201#396—22no—
202#396—22no—
203#396—22no—
204#396—22no—
205#396—22no—
206#394—22no—
207#394—22no—
208#394—22no—
209#394—22no—
210#391—22no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391C2312yes—
216#391C2312yes—
217#390—22no—
218#390—21no—
219#390—21no—
220#390—21no—
221#390—21no—
222#390C2312yes—
223#390C2312yes—
224#389—22no—
225#389—22no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#386—22no—
239#386—22no—
240#386—22no—
241#386—22no—
242#384—21no—
243#384—21no—
244#384—21no—
245#384—21no—
246#384C2312yes—
247#384C2311yescharacteristic
248#384C2311yescharacteristic
249#384C2311yescharacteristic
250#384C2311yescharacteristic
251#384C2312yes—
252#380—21no—
253#380—21no—
254#380—21no—
255#380—21no—
256#380—21no—
257#380—21no—
258#380—21no—
259#380—21no—
260#380—22no—
261#380—22no—
262#380—22no—
263#380—22no—
264#380C2312yes—
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
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—28no—
281C2×#41—41no—
282C2×#41—41no—
283C2×#41—42no—
284C2×#41—42no—
285C2×#41—42no—
286C2×#41—44no—
287C2×#41#4118yes—
288C22×Q8—21no—
289C22×Q8—21no—
290C22×Q8C2×D411yescharacteristic
291C22×Q8C2412yes—
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4C2×D411yescharacteristic
298C22×D4C2×D411yescharacteristic
299C22×D4C2×D411yescharacteristic
300C22×D4C2412yes—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C2×M16—24no—
314C2×M16—42no—
315C2×M16—42no—
316C22×C8—24no—
317C22×C8—42no—
318C22×C8—42no—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C22×C8C2412yes—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329#127—22no—
330#127—22no—
331#125—42no—
332#125—42no—
333#124—42no—
334#124—42no—
335C22⋊Q8—28no—
336C22⋊Q8—28no—
337C22⋊Q8—44no—
338C22⋊Q8—44no—
339C22⋊Q8—48no—
340C22⋊Q8—82no—
341C22⋊Q8—82no—
342C22⋊Q8—82no—
343C22⋊Q8—82no—
344#121—28no—
345#121—28no—
346#121—44no—
347#121—44no—
348#121—48no—
349#121—48no—
350#121—48no—
351#121—82no—
352#121—82no—
353#121—82no—
354#121—82no—
355C4×Q8—42no—
356C4×Q8—42no—
357C4×Q8—44no—
358C4×Q8—44no—
359C4×D4—42no—
360C4×D4—42no—
361C4×D4—42no—
362C4×D4—42no—
363C4×D4—42no—
364C4×D4—42no—
365C4×D4—44no—
366C4×D4—44no—
367#117—41no—
368#117—41no—
369#117—41no—
370#117—41no—
371#117—41no—
372#117—41no—
373#117—42no—
374#117—42no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—82no—
404C2×C4⋊C4—82no—
405C2×C4⋊C4—82no—
406C2×C4⋊C4—82no—
407C2×C4⋊C4C2×D411yescharacteristic
408C2×C4⋊C4C2×D411yescharacteristic
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2×D411yescharacteristic
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4C2×D411yescharacteristic
435C2×C22⋊C4C2×D411yescharacteristic
436C2×C22⋊C4C2×D411yescharacteristic
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457#103—44no—
458#103—44no—
459#103—44no—
460#103—44no—
461#102—44no—
462#102—44no—
463#102—44no—
464#102—44no—
465C22⋊C8—24no—
466C22⋊C8—24no—
467C22⋊C8—24no—
468C22⋊C8—24no—
469#97—42no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8—22no—
474C4×C8—42no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487C24—22no—
488C24C22×D411yescharacteristic
489C24C22×D411yescharacteristic
490C24C22×D411yescharacteristic
491#41—48no—
492#41—48no—
493#41—88no—
494#41—88no—
495C2×Q8—24no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—24no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8#12414yes—
508C2×D4—24no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—24no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—82no—
530C2×D4—82no—
531C2×D4—82no—
532C2×D4—82no—
533C2×D4#12414yes—
534C2×D4#12414yes—
535C2×D4#12414yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C2×#4114yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4114yes—
593C22×C4C2511yescharacteristic
594M16—48no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—48no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—82no—
641C4⋊C4—82no—
642C4⋊C4—82no—
643C4⋊C4—82no—
644C4⋊C4—82no—
645C4⋊C4—82no—
646C4⋊C4—82no—
647C4⋊C4—82no—
648C22⋊C4—41no—
649C22⋊C4—41no—
650C22⋊C4—41no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C22⋊C4—82no—
665C22⋊C4—82no—
666C22⋊C4—82no—
667C22⋊C4—82no—
668C22⋊C4—82no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—44no—
682C42H(5,𝔽2)12yes—
683C42H(5,𝔽2)12yes—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23C2×#12412yes—
710C23C2×#12412yes—
711C23C2×#12412yes—
712C23C23×D411yescharacteristic
713Q8—44no—
714Q8—44no—
715Q8—44no—
716Q8—84no—
717Q8—84no—
718D4—44no—
719D4—44no—
720D4—44no—
721D4—44no—
722D4—44no—
723D4—88no—
724D4—84no—
725D4—84no—
726D4—164no—
727D4—164no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—88no—
786C2×C4—164no—
787C2×C4—164no—
788C2×C4C2×#12412yes—
789C2×C4C2×#12412yes—
790C2×C4C2×#12412yes—
791C2×C4#53412yes—
792C2×C4#53412yes—
793C2×C4#57612yes—
794C2×C4#57712yes—
795C2×C4#57712yes—
796C2×C4#57812yes—
797C2×C4C22×#4112yes—
798C2×C4C2×H(5,𝔽2)11yescharacteristic
799C2×C4C2×H(5,𝔽2)11yescharacteristic
800C2×C4#58512yes—
801C8—42no—
802C8—42no—
803C8—42no—
804C8—42no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22C22×#12411yescharacteristic
834C22C2×#53411yescharacteristic
835C22#344911yescharacteristic
836C22C2×#57611yescharacteristic
837C22C2×#57711yescharacteristic
838C22C2×#57711yescharacteristic
839C22C2×#57811yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4—82no—
856C4#320314yes—
857C4#320414yes—
858C4#350512yes—
859C4#350512yes—
860C2—42no—
861C2—42no—
862C2—42no—
863C2—162no—
864C2#3501911yescharacteristic
865C2#6062211yescharacteristic
866C2#6062311yescharacteristic
867C2C2×#320311yescharacteristic
868C2C2×#320411yescharacteristic
869C2#6100611yescharacteristic
870C2#6100811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35273C2
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
1. #35280C2semidirect
3. #33049C2semidirect
4. #33048C2semidirect
5. #33043C2semidirect
6. #33042C2semidirect
7. #30191C2semidirect
8. #29342C2semidirect
9. #29119C2semidirect
10. #27973C2semidirect
11. #27972C2semidirect
12. #27961C2semidirect
13. #27960C2semidirect
14. #25905C2semidirect
15. #25904C2semidirect
16. #25857C2semidirect
17. #25857C2semidirect
18. #21772C2semidirect
19. C4×#408C2semidirect

Maximal subgroups

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

subgroupindex
#352802
#352732
#330492
#330482
#330432
#330422
#301912
#293422
#291192
#279732
#279722
#279612
#279602
#259052
#259042
#258572
#217722
C4×#4082