Finite Group Databasebeta

← #6499228

Subgroups — #6499228

Order 512.

1400 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2647C211yesmaximal, characteristic
2#34221C211yesmaximal, characteristic
3#33077C212yesmaximal, complemented
4#33075C212yesmaximal, complemented
5#30005C212yesmaximal, complemented
6#30004C212yesmaximal, complemented
7#29244C211yesmaximal, characteristic
8#29244C211yesmaximal, characteristic
9#29243C211yesmaximal, characteristic
10#29243C211yesmaximal, characteristic
11#29241C211yesmaximal, characteristic
12#29241C211yesmaximal, characteristic
13#29240C211yesmaximal, characteristic
14#29240C211yesmaximal, characteristic
15#29205C212yesmaximal, complemented
16#29202C212yesmaximal, complemented
17#29189C212yesmaximal, complemented
18#29187C212yesmaximal, complemented
19#21987C211yesmaximal, characteristic
20#21983C211yesmaximal, characteristic
21#21866C211yesmaximal, characteristic
22#21860C211yesmaximal, characteristic
23#20814C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C2×#432C2211yescharacteristic
26C2×#431C2211yescharacteristic
27#2647—21no—
28#2647—21no—
29#2647—21no—
30#2647—21no—
31#2647C2212yes—
32#2647C2212yes—
33#2647C2212yes—
34#2647C2212yes—
35C2×#400—21no—
36C2×#400—21no—
37C2×#398—21no—
38C2×#398—21no—
39#2371—21no—
40#2371—21no—
41#2368—21no—
42#2368—21no—
43#2356—21no—
44#2356—21no—
45#2343—21no—
46#2343—21no—
47#2331C2211yescharacteristic
48#2331C2211yescharacteristic
49#2327C2211yescharacteristic
50#2327C2211yescharacteristic
51#2320C2211yescharacteristic
52#2320C2211yescharacteristic
53C4×C22⋊Q8C2211yescharacteristic
54C4×C22⋊Q8C2211yescharacteristic
55C4×C22⋊Q8C2211yescharacteristic
56C4×C22⋊Q8C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#384C2211yescharacteristic
62#2283C2211yescharacteristic
63C2×#382C2211yescharacteristic
64#2276C2211yescharacteristic
65#2276C2211yescharacteristic
66C2×#376C2211yescharacteristic
67#2088C2212yes—
68#2088C2212yes—
69#2088C2212yes—
70#2088C2212yes—
71#2087C2212yes—
72#2087C2212yes—
73#2086C2212yes—
74#2086C2212yes—
75#2068C2212yes—
76#2068C2212yes—
77#2068C2212yes—
78#2068C2212yes—
79#2066C2212yes—
80#2066C2212yes—
81#2066C2212yes—
82#2066C2212yes—
83#1993C2212yes—
84#1990C2212yes—
85#1960C2212yes—
86#1956C2212yes—
87#1949C2212yes—
88#1949C2212yes—
89#1948C2212yes—
90#1947C2212yes—
91#1921C2212yes—
92#1921C2212yes—
93#1920C2212yes—
94#1920C2212yes—
95#1919C2212yes—
96#1919C2212yes—
97#1918C2212yes—
98#1918C2212yes—
99#1872C2211yescharacteristic
100#1872C2211yescharacteristic
101#1872C2211yescharacteristic
102#1872C2211yescharacteristic
103#1872C2211yescharacteristic
104#1872C2211yescharacteristic
105#1872C2211yescharacteristic
106#1872C2211yescharacteristic
107#1865C2212yes—
108#1865C2212yes—
109#1865C2212yes—
110#1865C2212yes—
111#1863C2212yes—
112#1863C2212yes—
113#1863C2212yes—
114#1863C2212yes—
115#1853C2211yescharacteristic
116#1853C2211yescharacteristic
117#1853C2211yescharacteristic
118#1853C2211yescharacteristic
119#1852C2211yescharacteristic
120#1852C2211yescharacteristic
121#1852C2211yescharacteristic
122#1852C2211yescharacteristic
123#1847C2212yes—
124#1846C2212yes—
125#1843C2212yes—
126#1836C2212yes—
127#1835C2212yes—
128#1832C2212yes—
129#1805C2212yes—
130#1805C2212yes—
131#1803C2212yes—
132#1803C2212yes—
133#1797C2211yescharacteristic
134#1797C2211yescharacteristic
135#1797C2211yescharacteristic
136#1797C2211yescharacteristic
137#1768C2212yes—
138#1768C2212yes—
139#533—24no—
140#533Q818yes—
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2311yescharacteristic
143C2×#125—21no—
144C2×C22⋊Q8—21no—
145C2×C22⋊Q8C2311yescharacteristic
146C2×C22⋊Q8C2311yescharacteristic
147C2×C4×Q8—21no—
148C2×C4×Q8C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2311yescharacteristic
154C2×#117—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#432—24no—
169#431—24no—
170C2×#107C2312yes—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×#103C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×C22⋊C8C2311yescharacteristic
193C2×C22⋊C8C2311yescharacteristic
194C2×C22⋊C8C2311yescharacteristic
195C2×C22⋊C8C2311yescharacteristic
196C2×#97C2312yes—
197C2×C4×C8C2312yes—
198#400—22no—
199#400—22no—
200#400—22no—
201#400—22no—
202#400—22no—
203#400—22no—
204#400—22no—
205#400—22no—
206#398—22no—
207#398—22no—
208#398—22no—
209#398—22no—
210#398—22no—
211#398—22no—
212#398—22no—
213#398—22no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391C2311yescharacteristic
219#391C2311yescharacteristic
220#391C2311yescharacteristic
221#391C2311yescharacteristic
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2311yescharacteristic
233#389C2311yescharacteristic
234#389C2312yes—
235#389C2312yes—
236#389C2312yes—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
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—21no—
251#387—21no—
252#387—21no—
253#387—21no—
254#387—21no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#385—21no—
263#385—21no—
264#385—21no—
265#385—21no—
266#384—21no—
267#384—21no—
268#384C2312yes—
269#384C2312yes—
270#383—21no—
271#383—21no—
272#383—21no—
273#382—21no—
274#382—21no—
275#382—21no—
276#382—21no—
277#382C2312yes—
278#382C2311yescharacteristic
279#382C2311yescharacteristic
280#382C2312yes—
281#381—21no—
282#380C2311yescharacteristic
283#380C2311yescharacteristic
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⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2311yescharacteristic
300C4×C22⋊C4—21no—
301C4×C22⋊C4—21no—
302C4×C22⋊C4—21no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—21no—
305#376—21no—
306#376—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×#95D411yescharacteristic
323C2×#95D411yescharacteristic
324C2×#95D411yescharacteristic
325C2×#95D411yescharacteristic
326#340C2312yes—
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#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346C22×Q8—21no—
347C22×Q8C2411yescharacteristic
348C22×Q8C2411yescharacteristic
349C23×C4—21no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4C2×D411yescharacteristic
354C23×C4C2×D411yescharacteristic
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2411yescharacteristic
360C22×C8C2412yes—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2412yes—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8C2×Q814yes—
367C4⋊Q8C2×Q814yes—
368#125—28no—
369C22⋊Q8—28no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8C2×Q814yes—
373C22⋊Q8C2×Q814yes—
374C4×Q8—28no—
375C4×Q8—22no—
376C4×Q8—22no—
377C4×Q8—42no—
378C4×Q8—42no—
379C4×Q8—42no—
380C4×Q8—42no—
381C4×Q8C2×Q814yes—
382C4×Q8C2×Q814yes—
383#117—28no—
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—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—82no—
420C2×C4⋊C4—82no—
421C2×C4⋊C4—82no—
422C2×C4⋊C4—82no—
423C2×C4⋊C4—82no—
424C2×C4⋊C4—82no—
425C2×C4⋊C4C2412yes—
426C2×C4⋊C4C2412yes—
427C2×C4⋊C4C2412yes—
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2411yescharacteristic
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—42no—
452C2×C42—42no—
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2×Q814yes—
460C2×C42#4114yes—
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464C2×C42C2411yescharacteristic
465C2×C42C2411yescharacteristic
466C2×C42C2411yescharacteristic
467#107—42no—
468#107—42no—
469#107—42no—
470#107—42no—
471#106—42no—
472#106—42no—
473#106—42no—
474#106—42no—
475C4⋊C8—24no—
476C4⋊C8—24no—
477C4⋊C8—42no—
478C4⋊C8—42no—
479C4⋊C8—42no—
480C4⋊C8—42no—
481#103—42no—
482#103—42no—
483#103—42no—
484#103—42no—
485#103—42no—
486#103—42no—
487#103—42no—
488#103—42no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493#97—24no—
494C4×C8—24no—
495#95—22no—
496#95—22no—
497#95—22no—
498#95—22no—
499#95—22no—
500#95—22no—
501#95—22no—
502#95—22no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95C2×D411yescharacteristic
532#95C2×D411yescharacteristic
533#95C2×D411yescharacteristic
534#95C2×D411yescharacteristic
535#95C2×D411yescharacteristic
536#95C2×D411yescharacteristic
537#95C2×D411yescharacteristic
538#95C2×D411yescharacteristic
539#95C2×D411yescharacteristic
540#95C2×D411yescharacteristic
541#95C2×D411yescharacteristic
542#95C2×D411yescharacteristic
543#95C2×D411yescharacteristic
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547C24C22×D411yescharacteristic
548C2×Q8—24no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—81no—
556C2×Q8—81no—
557C2×Q8C22×Q812yes—
558C2×Q8C22×Q812yes—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4C22⋊Q814yes—
602C22×C4C22⋊Q814yes—
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×Q812yes—
617C22×C4C2×#4112yes—
618C22×C4C2511yescharacteristic
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—81no—
661C4⋊C4—81no—
662C4⋊C4—81no—
663C4⋊C4—81no—
664C4⋊C4—82no—
665C4⋊C4—82no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—82no—
670C4⋊C4—82no—
671C4⋊C4—82no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4C22×Q812yes—
677C4⋊C4C22×Q812yes—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C42—24no—
683C42—24no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—41no—
689C42—41no—
690C42—41no—
691C42—41no—
692C42—42no—
693C42—42no—
694C42—42no—
695C42—42no—
696C42—81no—
697C42—81no—
698C42—81no—
699C42—81no—
700C42—81no—
701C42—81no—
702C42C22⋊Q814yes—
703C42C22⋊Q814yes—
704C42C22×Q812yes—
705C42C22×Q812yes—
706C42C2×#4112yes—
707C42C2×#4112yes—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23C2×C22⋊Q812yes—
713C23#57712yes—
714C23#57812yes—
715C23C23×D411yescharacteristic
716Q8—24no—
717Q8—24no—
718Q8—42no—
719Q8—42no—
720Q8—84no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—28no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
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—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—44no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—82no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4—82no—
799C2×C4—84no—
800C2×C4—84no—
801C2×C4—84no—
802C2×C4—84no—
803C2×C4C2×C22⋊Q812yes—
804C2×C4C2×C22⋊Q812yes—
805C2×C4C2×C22⋊Q812yes—
806C2×C4C2×C22⋊Q812yes—
807C2×C4C2×C22⋊Q812yes—
808C2×C4C23×Q811yescharacteristic
809C2×C4C22×#4111yescharacteristic
810C2×C4#58512yes—
811C2×C4#58512yes—
812C8—42no—
813C8—42no—
814C8—42no—
815C8—42no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22#308214yes—
823C22C22×C22⋊Q811yescharacteristic
824C22#344911yescharacteristic
825C22#344911yescharacteristic
826C22C2×#57711yescharacteristic
827C22C2×#57811yescharacteristic
828C22#358511yescharacteristic
829C22#358611yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—42no—
836C4—42no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—42no—
846C4—42no—
847C4—81no—
848C4—82no—
849C4—81no—
850C4—82no—
851C4—82no—
852C4—81no—
853C4—82no—
854C4—81no—
855C4#350412yes—
856C4#351212yes—
857C2—24no—
858C2#3533311yescharacteristic
859C2C2×#308211yescharacteristic
860C2#6049311yescharacteristic
861C2#6097711yescharacteristic
862C2#6097911yescharacteristic
863C2#6098111yescharacteristic
864C2#6098311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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
3. #33077C2semidirect
4. #33075C2semidirect
5. #30005C2semidirect
6. #30004C2semidirect
15. #29205C2semidirect
16. #29202C2semidirect
17. #29189C2semidirect
18. #29187C2semidirect

Maximal subgroups

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

subgroupindex
C2×#26472
#342212
#330772
#330752
#300052
#300042
#292442
#292432
#292412
#292402
#292052
#292022
#291892
#291872
#219872
#219832
#218662
#218602
#208142