Finite Group Databasebeta

← #6660698

Subgroups — #6660698

Order 512.

2043 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2#36621C211yesmaximal, characteristic
3#32725C212yesmaximal, complemented
4#32723C212yesmaximal, complemented
5#30244C212yesmaximal, complemented
6#30190C212yesmaximal, complemented
7#29957C212yesmaximal, complemented
8#29926C212yesmaximal, complemented
9#29719C212yesmaximal, complemented
10#29665C212yesmaximal, complemented
11#27680C211yesmaximal, characteristic, complemented
12#27677C211yesmaximal, characteristic, complemented
13#24752C212yesmaximal, complemented
14#24751C212yesmaximal, complemented
15#24381C212yesmaximal
16#24380C212yesmaximal, complemented
17#24212C211yesmaximal, characteristic, complemented
18#24209C211yesmaximal, characteristic, complemented
19C2×#1797C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C2×#529C2211yescharacteristic
22C22×C22⋊Q8C2212yes—
23C23×C42C2211yescharacteristic
24C2×#467C2214yes—
25C2×#465C2214yes—
26C2×#462C2212yescomplemented
27C2×#461C2212yescomplemented
28C2×#451C2212yes—
29C2×#448C2212yes—
30C22×C4⋊C8C2212yes—
31C22×C22⋊C8C2212yes—
32#2857—21no—
33#2857—21no—
34#2857—21no—
35#2857—21no—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2855C2211yescharacteristic
41#2854C2211yescharacteristic
42#2853—21no—
43#2852—21no—
44#2852—21no—
45#2851C2211yescharacteristic
46#2851C2211yescharacteristic
47#2850C2211yescharacteristic
48#2850C2211yescharacteristic
49#2849—21no—
50#2848C2211yescharacteristic
51#2847C2211yescharacteristic
52C4×C22⋊Q8C2211yescharacteristic
53C4×C22⋊Q8C2211yescharacteristic
54C4×#123—21no—
55C4×#121C2211yescharacteristic
56C4×#121C2211yescharacteristic
57C4×#120—21no—
58C2×#391C2212yes—
59C2×#389—21no—
60C2×#389—21no—
61#2290—21no—
62#2290—21no—
63C2×#384C2211yescharacteristic
64#2283C2211yescharacteristic
65C2×#380—21no—
66C2×#380—21no—
67#2099C2212yescomplemented
68#2099C2212yescomplemented
69#2097C2214yescomplemented
70#2096C2212yescomplemented
71#2093C2212yescomplemented
72#2074C2214yescomplemented
73#2068C2214yescomplemented
74#2066C2214yescomplemented
75#2056C2214yescomplemented
76#2055C2214yescomplemented
77#2043C2212yescomplemented
78#2043C2212yescomplemented
79#2036C2214yes—
80#2035C2214yes—
81#2026C2214yescomplemented
82#2016C2212yescomplemented
83#2015C2214yescomplemented
84#2013C2212yescomplemented
85#2001C2214yes—
86#2000C2214yes—
87#1981C2212yescomplemented
88#1981C2212yescomplemented
89#1948C2212yescomplemented
90#1947C2212yescomplemented
91#1892C2214yes—
92#1892C2214yes—
93#1874C2212yes—
94#1872C2212yes—
95#1853C2212yes—
96#1852C2212yes—
97#1803C2212yescomplemented
98#1802C2212yescomplemented
99#1797C2212yes—
100#1797C2211yescharacteristic
101#1797C2211yescharacteristic
102#1797C2212yes—
103#1797C2212yes—
104#1787C2212yes—
105#1787C2212yes—
106C2×#336C2212yes—
107C23×Q8C2312yes—
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111C22×Q16C2314yes—
112C22×SD16C2314yes—
113C23×C8C2314yes—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—44no—
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2312yes—
119#529—44no—
120C2×#126—21no—
121C2×#125C2311yescharacteristic
122C2×#124C2311yescharacteristic
123C2×#123—21no—
124C2×#123—21no—
125C2×C22⋊Q8—22no—
126C2×C22⋊Q8—22no—
127C2×C22⋊Q8—48no—
128C2×C22⋊Q8C2311yescharacteristic
129C2×C22⋊Q8C2311yescharacteristic
130C2×C22⋊Q8C2314yes—
131C2×C22⋊Q8C2311yescharacteristic
132C2×C22⋊Q8C2314yes—
133C2×#121C2311yescharacteristic
134C2×#121C2311yescharacteristic
135C2×#121C2311yescharacteristic
136C2×#120—21no—
137C2×C4×Q8C2311yescharacteristic
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4C2311yescharacteristic
142C2×#117—21no—
143C22×C4⋊C4—22no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C4⋊C4C2312yes—
149C22×C22⋊C4—22no—
150C22×C42—44no—
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#467—48no—
164#465—48no—
165#462—44no—
166#461—44no—
167#451—44no—
168#448—44no—
169C2×#107C2314yes—
170C2×#106C2314yes—
171C2×C4⋊C8—44no—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2314yes—
175C2×#103C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#103C2314yes—
182C2×#102C2314yes—
183C2×C22⋊C8—44no—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2314yes—
187#391—22no—
188#391—22no—
189#391C2314yes—
190#391C2311yescharacteristic
191#391C2314yes—
192#391C2311yescharacteristic
193#390C2311yescharacteristic
194#390C2311yescharacteristic
195#389—22no—
196#389—22no—
197#389—22no—
198#389—22no—
199#389—22no—
200#389—22no—
201#389—22no—
202#389—22no—
203#389C2311yescharacteristic
204#389C2311yescharacteristic
205#389C2311yescharacteristic
206#389C2311yescharacteristic
207#388—21no—
208#388—21no—
209#388—21no—
210#388—21no—
211#388—21no—
212#388—21no—
213#388—21no—
214#388—21no—
215#387—21no—
216#387—21no—
217#387—21no—
218#387—21no—
219#387—21no—
220#387—21no—
221#387—21no—
222#387—21no—
223#386—21no—
224#386—21no—
225#386—21no—
226#386—21no—
227#386—21no—
228#386—21no—
229#386—21no—
230#386—21no—
231#386—21no—
232#386—21no—
233#385—21no—
234#385—21no—
235#385—21no—
236#385—21no—
237#385—21no—
238#385—21no—
239#385—21no—
240#385—21no—
241#385—21no—
242#385—21no—
243#384—21no—
244#384—21no—
245#384C2312yes—
246#384C2312yes—
247#383—21no—
248#382C2311yescharacteristic
249#382C2311yescharacteristic
250#381—21no—
251#381—21no—
252#380—22no—
253#380—22no—
254#380—22no—
255#380—22no—
256#380—22no—
257#380—22no—
258#380—22no—
259#380—22no—
260#380C2311yescharacteristic
261#380C2311yescharacteristic
262#380C2311yescharacteristic
263#380C2311yescharacteristic
264#380C2311yescharacteristic
265#380C2311yescharacteristic
266#379—21no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4C2311yescharacteristic
270C4×C4⋊C4C2311yescharacteristic
271C4×C22⋊C4—21no—
272C4×C22⋊C4—21no—
273C4×C22⋊C4—21no—
274C4×C22⋊C4—21no—
275C4×C22⋊C4—21no—
276#376—21no—
277C2×#95—22no—
278C2×#95—22no—
279#340C2314yes—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#336C2314yes—
284#336C2312yes—
285#336C2312yes—
286C25C2×D411yescharacteristic
287C22×Q8—22no—
288C22×Q8—24no—
289C22×Q8—24no—
290C22×Q8—44no—
291C22×Q8—44no—
292C22×Q8C2411yescharacteristic
293C22×Q8C2414yes—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4C2411yescharacteristic
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—21no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C23×C4C2411yescharacteristic
329C2×Q16—44no—
330C2×Q16—44no—
331C2×Q16—44no—
332C2×SD16—44no—
333C2×SD16—44no—
334C2×SD16—44no—
335C22×C8—28no—
336C22×C8—44no—
337C22×C8—44no—
338C22×C8C2414yes—
339C22×C8C2414yes—
340C4⋊Q8—24no—
341C4⋊Q8—24no—
342C4⋊Q8—44no—
343C4⋊Q8—44no—
344C4⋊Q8—44no—
345#126—44no—
346#125—42no—
347#124—42no—
348#123—44no—
349#123—44no—
350C22⋊Q8—28no—
351C22⋊Q8—28no—
352C22⋊Q8—22no—
353C22⋊Q8—24no—
354C22⋊Q8—22no—
355C22⋊Q8—44no—
356C22⋊Q8—44no—
357C22⋊Q8—42no—
358C22⋊Q8—48no—
359C22⋊Q8—48no—
360#121—22no—
361#121—24no—
362#121—22no—
363#121—42no—
364#120—44no—
365C4×Q8—24no—
366C4×D4—24no—
367C4×D4—44no—
368C4×D4—44no—
369C4×D4—44no—
370#117—44no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4—44no—
394C2×C4⋊C4—48no—
395C2×C4⋊C4—44no—
396C2×C4⋊C4—44no—
397C2×C4⋊C4—44no—
398C2×C4⋊C4C2414yes—
399C2×C4⋊C4C2411yescharacteristic
400C2×C4⋊C4C2411yescharacteristic
401C2×C4⋊C4C2411yescharacteristic
402C2×C4⋊C4C2411yescharacteristic
403C2×C4⋊C4C2411yescharacteristic
404C2×C4⋊C4C2411yescharacteristic
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—48no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—24no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—42no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—42no—
439C2×C42—42no—
440C2×C42—42no—
441C2×C42—42no—
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457C2×C42C2411yescharacteristic
458#107—44no—
459#106—44no—
460C4⋊C8—24no—
461C4⋊C8—24no—
462C4⋊C8—44no—
463#103—44no—
464#103—44no—
465#103—44no—
466#103—44no—
467#103—44no—
468#103—44no—
469#103—44no—
470#102—44no—
471C22⋊C8—24no—
472C22⋊C8—24no—
473C22⋊C8—44no—
474#95—24no—
475#95—24no—
476#95—24no—
477#95—24no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—21no—
503C24—41no—
504C24—41no—
505C24#13714yes—
506C24C22×D411yescharacteristic
507C24C22×D411yescharacteristic
508C24C22×D411yescharacteristic
509C2×Q8—22no—
510C2×Q8—24no—
511C2×Q8—24no—
512C2×Q8—24no—
513C2×Q8—24no—
514C2×Q8—24no—
515C2×Q8—22no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—24no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×Q8—44no—
522C2×Q8—88no—
523C2×Q8—88no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
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—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
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—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—416no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—416no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4#13514yes—
612C22×C4#13714yes—
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4H(5,𝔽2)14yes—
625C22×C4H(5,𝔽2)12yes—
626C22×C42−1+412yes—
627C22×C4C2511yescharacteristic
628Q16—88no—
629SD16—88no—
630C2×C8—24no—
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—88no—
637C4⋊C4—24no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—48no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—42no—
659C4⋊C4—48no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—44no—
667C4⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—48no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—48no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C42—22no—
690C42—22no—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—22no—
697C42—22no—
698C42—41no—
699C42—41no—
700C42—41no—
701C42—41no—
702C42—41no—
703C42—41no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42H(5,𝔽2)14yes—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—28no—
720C23—28no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#53512yes—
737C23#53712yes—
738C23C2×#13512yes—
739C23C2×#13712yes—
740C23C2×#13712yes—
741C23C2×#13712yes—
742C23C2×#13712yes—
743C23C23×D411yescharacteristic
744Q8—42no—
745Q8—44no—
746Q8—44no—
747Q8—44no—
748Q8—42no—
749Q8—44no—
750Q8—88no—
751D4—42no—
752D4—42no—
753D4—84no—
754D4—84no—
755D4—84no—
756C2×C4—28no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—44no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—44no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—44no—
827C2×C4—41no—
828C2×C4—88no—
829C2×C4—88no—
830C2×C4—84no—
831C2×C4#53412yes—
832C2×C4#53412yes—
833C2×C4#53512yes—
834C2×C4#53712yes—
835C2×C4C2×#13512yes—
836C2×C4C2×#13512yes—
837C2×C4C2×#13712yes—
838C2×C4C2×#13712yes—
839C2×C4#57512yes—
840C2×C4C2×H(5,𝔽2)12yes—
841C2×C4C2×H(5,𝔽2)12yes—
842C2×C4C2×H(5,𝔽2)11yescharacteristic
843C2×C4C2×2−1+411yescharacteristic
844C8—44no—
845C8—44no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—416no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22#321814yes—
874C22#324814yes—
875C22C2×#53411yescharacteristic
876C22C2×#53511yescharacteristic
877C22C2×#53711yescharacteristic
878C22C22×#13511yescharacteristic
879C22C22×#13711yescharacteristic
880C22C22×#13711yescharacteristic
881C22C2×#57511yescharacteristic
882C4—22no—
883C4—22no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—22no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—81no—
893C4—84no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—84no—
898C4—81no—
899C4—81no—
900C4—81no—
901C4#319014yes—
902C4#353612yes—
903C4#353712yes—
904C2—24no—
905C2—24no—
906C2—42no—
907C2—161no—
908C2#3743911yescharacteristic
909C2C2×#319011yescharacteristic
910C2#6075111yescharacteristic
911C2#6078211yescharacteristic
912C2C2×#321811yescharacteristic
913C2C2×#324811yescharacteristic
914C2#6091811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2847C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2857C2semidirect
3. #32725C2semidirect
4. #32723C2semidirect
5. #30244C2semidirect
6. #30190C2semidirect
7. #29957C2semidirect
8. #29926C2semidirect
9. #29719C2semidirect
10. #29665C2semidirect
11. #27680C2semidirect
12. #27677C2semidirect
13. #24752C2semidirect
14. #24751C2semidirect
16. #24380C2semidirect
17. #24212C2semidirect
18. #24209C2semidirect
19. C2×#1797C2semidirect
26. C2×#462C22semidirect
27. C2×#461C22semidirect
67. #2099C22semidirect
68. #2099C22semidirect
69. #2097C22semidirect
70. #2096C22semidirect
71. #2093C22semidirect
72. #2074C22semidirect
73. #2068C22semidirect
74. #2066C22semidirect
75. #2056C22semidirect
76. #2055C22semidirect
77. #2043C22semidirect
78. #2043C22semidirect
81. #2026C22semidirect
82. #2016C22semidirect
83. #2015C22semidirect
84. #2013C22semidirect
87. #1981C22semidirect
88. #1981C22semidirect
89. #1948C22semidirect
90. #1947C22semidirect
97. #1803C22semidirect
98. #1802C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
#366212
#327252
#327232
#302442
#301902
#299572
#299262
#297192
#296652
#276802
#276772
#247522
#247512
#243812
#243802
#242122
#242092
C2×#17972