Finite Group Databasebeta

← #6469421

Subgroups — #6469421

Order 512.

1654 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34220C211yesmaximal, characteristic
2C2×#2331C211yesmaximal, characteristic, complemented
3#29403C212yesmaximal, complemented
4#29400C212yesmaximal, complemented
5#29282C212yesmaximal, complemented
6#28212C212yesmaximal, complemented
7#27653C211yesmaximal, characteristic, complemented
8#27651C211yesmaximal, characteristic
9#27613C211yesmaximal, characteristic, complemented
10#27611C211yesmaximal, characteristic, complemented
11#24301C211yesmaximal, characteristic, complemented
12#24299C211yesmaximal, characteristic
13#24067C211yesmaximal, characteristic
14#24066C211yesmaximal, characteristic
15#23845C212yesmaximal, complemented
16#23827C212yesmaximal, complemented
17#21626C212yesmaximal, complemented
18#21623C212yesmaximal, complemented
19#21581C211yesmaximal, characteristic, complemented
20#21578C211yesmaximal, characteristic
21C4×#481C211yesmaximal, characteristic
22C4×#483C211yesmaximal, characteristic, complemented
23#20779C211yesmaximal, characteristic, complemented
24C22×C4⋊Q8C2211yescharacteristic
25C2×#529C2211yescharacteristic
26C2×#484C2211yescharacteristic
27C2×#481C2211yescharacteristic
28C2×#483C2211yescharacteristic
29C2×#480C2211yescharacteristic
30C2×#475C2212yes—
31C2×#476C2212yes—
32#2373—21no—
33#2373—21no—
34#2359—21no—
35#2359—21no—
36#2353—21no—
37#2349—21no—
38#2346—21no—
39#2343—21no—
40#2331—21no—
41#2331—21no—
42#2331—21no—
43#2331—21no—
44#2331C2212yes—
45#2331C2212yes—
46#2331C2212yes—
47#2331C2212yes—
48#2330C2211yescharacteristic
49#2330C2211yescharacteristic
50#2326C2211yescharacteristic
51#2326C2211yescharacteristic
52#2320C2211yescharacteristic
53#2319C2211yescharacteristic
54C4×C22⋊Q8C2211yescharacteristic
55C4×C22⋊Q8C2211yescharacteristic
56C4×#121C2211yescharacteristic
57C4×#121C2211yescharacteristic
58C2×#391—21no—
59C2×#391—21no—
60C2×#389C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#387—21no—
63C2×#387—21no—
64#2285C2211yescharacteristic
65C2×#382C2211yescharacteristic
66#2276C2211yescharacteristic
67#2275C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×#376C2211yescharacteristic
71#2100C2212yes—
72#2099C2212yes—
73#2085C2212yes—
74#2085C2212yes—
75#2084C2212yes—
76#2084C2212yes—
77#2074C2212yes—
78#2073C2212yes—
79#2059C2212yes—
80#2059C2212yes—
81#2058C2212yes—
82#2058C2212yes—
83#2042C2212yes—
84#2042C2212yes—
85#2024C2212yes—
86#2023C2212yes—
87#1988C2212yes—
88#1987C2212yes—
89#1949C2212yes—
90#1949C2212yes—
91#1927C2212yes—
92#1927C2212yes—
93#1926C2212yes—
94#1926C2212yes—
95#1921C2212yes—
96#1920C2212yes—
97#1920C2212yes—
98#1920C2212yes—
99#1919C2212yes—
100#1919C2212yes—
101#1919C2212yes—
102#1918C2212yes—
103#1874C2211yescharacteristic
104#1874C2211yescharacteristic
105#1872C2211yescharacteristic
106#1872C2211yescharacteristic
107#1865C2212yes—
108#1864C2212yes—
109#1863C2212yes—
110#1862C2212yes—
111#1853C2211yescharacteristic
112#1853C2211yescharacteristic
113#1853C2211yescharacteristic
114#1853C2211yescharacteristic
115#1840C2212yes—
116#1832C2212yes—
117#1824C2211yescharacteristic
118#1824C2211yescharacteristic
119#1823C2211yescharacteristic
120#1823C2211yescharacteristic
121#1817C2211yescharacteristic
122#1817C2211yescharacteristic
123#1805C2212yes—
124#1804C2212yes—
125#1797C2211yescharacteristic
126#1797C2211yescharacteristic
127#1776C2212yes—
128#1776C2212yes—
129C4×#106C2212yes—
130C4×#106C2212yes—
131#1768C2212yes—
132#1763C2212yes—
133#1762C2212yes—
134C4×#103C2212yes—
135C4×#102C2212yes—
136#1749C2211yescharacteristic
137C4×C22⋊C8C2211yescharacteristic
138#1746C2212yes—
139C23×Q8—21no—
140C2×C4⋊Q8—28no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8C2312yes—
144C2×C4⋊Q8C2312yes—
145#529—24no—
146#529—24no—
147C2×#126—21no—
148C2×#125C2311yescharacteristic
149C2×#124C2311yescharacteristic
150C2×#123—21no—
151C2×C22⋊Q8C2311yescharacteristic
152C2×#121C2311yescharacteristic
153C2×C4×Q8C2311yescharacteristic
154C2×C4×Q8C2311yescharacteristic
155C2×C4×Q8C2311yescharacteristic
156C2×C4×D4—21no—
157C2×C4×D4—21no—
158C2×C4×D4—21no—
159C2×C4×D4C2311yescharacteristic
160C2×C4×D4C2311yescharacteristic
161C2×C4×D4C2311yescharacteristic
162C2×#117—21no—
163C2×#117—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C42—21no—
172C22×C42—21no—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176#484—24no—
177#483—24no—
178#481—24no—
179#480—24no—
180#476—28no—
181#475—28no—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×C22⋊C8C2311yescharacteristic
201C2×C22⋊C8C2311yescharacteristic
202C2×C22⋊C8C2311yescharacteristic
203C2×C22⋊C8C2311yescharacteristic
204C2×#97C2312yes—
205C2×C4×C8C2312yes—
206#391—22no—
207#391—22no—
208#391—22no—
209#391—22no—
210#391—22no—
211#391—22no—
212#391—22no—
213#391—22no—
214#391C2311yescharacteristic
215#391C2311yescharacteristic
216#390C2311yescharacteristic
217#390C2311yescharacteristic
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#389C2311yescharacteristic
227#389C2311yescharacteristic
228#389C2312yes—
229#389C2312yes—
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2312yes—
233#389C2312yes—
234#388—21no—
235#388—21no—
236#388—21no—
237#388—21no—
238#388—21no—
239#388—21no—
240#388—21no—
241#388—21no—
242#387—21no—
243#387—21no—
244#387—21no—
245#387—21no—
246#387—21no—
247#387—21no—
248#387—21no—
249#387—21no—
250#387—22no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#386—21no—
259#386—21no—
260#385—21no—
261#385—21no—
262#385—21no—
263#385—21no—
264#385—21no—
265#385—21no—
266#384C2311yescharacteristic
267#384C2311yescharacteristic
268#383—21no—
269#382—21no—
270#382—21no—
271#382—21no—
272#382—21no—
273#382C2312yes—
274#382C2312yes—
275#381—21no—
276#380—21no—
277#380—21no—
278#380C2311yescharacteristic
279#380C2311yescharacteristic
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4C2311yescharacteristic
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2312yes—
298C4×C4⋊C4C2312yes—
299C4×C4⋊C4C2312yes—
300C4×C22⋊C4—21no—
301C4×C22⋊C4—21no—
302C4×C22⋊C4—21no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—21no—
305C4×C22⋊C4—21no—
306C4×C22⋊C4—21no—
307#376—21no—
308#376D411yescharacteristic
309#376D411yescharacteristic
310#376D411yescharacteristic
311#376D411yescharacteristic
312#376C2311yescharacteristic
313#376C2311yescharacteristic
314#376C2311yescharacteristic
315#376C2311yescharacteristic
316C2×#95—21no—
317C2×#95—21no—
318C2×#95—21no—
319C2×#95—21no—
320C2×#95—21no—
321C2×#95—21no—
322C2×#95—21no—
323C2×#95D411yescharacteristic
324C2×#95D411yescharacteristic
325C2×#95D411yescharacteristic
326C2×#95D411yescharacteristic
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351C22×Q8—28no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—82no—
355C22×Q8—82no—
356C22×Q8C2411yescharacteristic
357C22×D4—21no—
358C22×D4C2411yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371C23×C4C2×D411yescharacteristic
372C23×C4C2411yescharacteristic
373C22×C8C2412yes—
374C22×C8C2412yes—
375C22×C8C2412yes—
376C22×C8C2412yes—
377C4⋊Q8—28no—
378C4⋊Q8—28no—
379C4⋊Q8—24no—
380C4⋊Q8—24no—
381C4⋊Q8—24no—
382C4⋊Q8#4118yes—
383#126—28no—
384#125—22no—
385#125—22no—
386#124—22no—
387#124—22no—
388#123—28no—
389C22⋊Q8—22no—
390C22⋊Q8#4114yes—
391#121—22no—
392#121#4114yes—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—24no—
396C4×Q8—24no—
397C4×D4—28no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—24no—
401C4×D4—24no—
402C4×D4—82no—
403C4×D4—82no—
404#117—28no—
405#117—82no—
406C2×C4⋊C4—28no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—82no—
438C2×C4⋊C4—82no—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C42—21no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—24no—
466C2×C42—24no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—82no—
480C2×C42—82no—
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42C2411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493#107—24no—
494#107—24no—
495#106—24no—
496#106—24no—
497#106—24no—
498#106—24no—
499#106—24no—
500#106—24no—
501C4⋊C8—24no—
502C4⋊C8—24no—
503#103—24no—
504#103—24no—
505#103—24no—
506#103—24no—
507#102—24no—
508#102—24no—
509#102—24no—
510#102—24no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515#97—24no—
516C4×C8—24no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552#95C2×D411yescharacteristic
553#95C2×D411yescharacteristic
554#95C2×D411yescharacteristic
555#95C2×D411yescharacteristic
556#95C2×D411yescharacteristic
557#95C2×D411yescharacteristic
558#95C2×D411yescharacteristic
559#95C2×D411yescharacteristic
560#95C2×D411yescharacteristic
561C24—21no—
562C24C22×D411yescharacteristic
563C2×Q8—28no—
564C2×Q8—28no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—82no—
570C2×Q8—82no—
571C2×Q8—82no—
572C2×Q8—816no—
573C2×Q8C2×#4112yes—
574C2×D4—24no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4C2×#4112yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—81no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4—81no—
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C2×#4112yes—
647C22×C4C2×#4112yes—
648C22×C4C2511yescharacteristic
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—28no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—28no—
668C4⋊C4—24no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—81no—
688C4⋊C4—81no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4—82no—
693C4⋊C4—81no—
694C4⋊C4—81no—
695C4⋊C4—81no—
696C4⋊C4—81no—
697C4⋊C4C2×#4114yes—
698C4⋊C4C2×#4114yes—
699C4⋊C4C2×#4112yes—
700C4⋊C4C2×#4112yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—24no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—22no—
726C42—22no—
727C42—42no—
728C42—42no—
729C42—81no—
730C42—81no—
731C42—82no—
732C42—82no—
733C42—82no—
734C42—82no—
735C42—81no—
736C42—81no—
737C42—81no—
738C42—81no—
739C42C2×#4114yes—
740C422−1+414yes—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—22no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23#52512yes—
753C23#57712yes—
754C23#57712yes—
755C23C23×D411yescharacteristic
756Q8—24no—
757Q8—42no—
758Q8—88no—
759Q8—88no—
760D4—24no—
761D4—48no—
762D4—42no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
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—21no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—48no—
809C2×C4—48no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—44no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—82no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4—84no—
843C2×C4—162no—
844C2×C4—162no—
845C2×C4#52512yes—
846C2×C4#52512yes—
847C2×C4#52512yes—
848C2×C4#53612yes—
849C2×C4#53612yes—
850C2×C4C22×#4111yescharacteristic
851C2×C4C22×#4111yescharacteristic
852C2×C4C22×#4112yes—
853C2×C4C2×2−1+412yes—
854C8—42no—
855C8—42no—
856C8—42no—
857C8—42no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22#312514yes—
872C22C2×#52511yescharacteristic
873C22C2×#52511yescharacteristic
874C22C2×#53611yescharacteristic
875C22C2×#57711yescharacteristic
876C22C2×#57711yescharacteristic
877C22#358511yescharacteristic
878C22#358611yescharacteristic
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—22no—
884C4—41no—
885C4—41no—
886C4—42no—
887C4—41no—
888C4—41no—
889C4—42no—
890C4—42no—
891C4—41no—
892C4—44no—
893C4—44no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—82no—
898C4—82no—
899C4—81no—
900C4—81no—
901C4—81no—
902C4—81no—
903C4#348212yes—
904C4#348212yes—
905C2—24no—
906C2—82no—
907C2#3497111yescharacteristic
908C2C2×#312511yescharacteristic
909C2#6056711yescharacteristic
910C2#6057911yescharacteristic
911C2#6058211yescharacteristic
912C2#6087211yescharacteristic
913C2#6087311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#376 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2331C2semidirect
3. #29403C2semidirect
4. #29400C2semidirect
5. #29282C2semidirect
6. #28212C2semidirect
7. #27653C2semidirect
9. #27613C2semidirect
10. #27611C2semidirect
11. #24301C2semidirect
15. #23845C2semidirect
16. #23827C2semidirect
17. #21626C2semidirect
18. #21623C2semidirect
19. #21581C2semidirect
22. C4×#483C2semidirect
23. #20779C2semidirect

Maximal subgroups

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

subgroupindex
#342202
C2×#23312
#294032
#294002
#292822
#282122
#276532
#276512
#276132
#276112
#243012
#242992
#240672
#240662
#238452
#238272
#216262
#216232
#215812
#215782
C4×#4812
C4×#4832
#207792