Finite Group Databasebeta

← #6568713

Subgroups — #6568713

Order 512.

1516 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36363C211yesmaximal, characteristic
2#36180C211yesmaximal, characteristic
3#30233C211yesmaximal, characteristic, complemented
4#30199C211yesmaximal, characteristic, complemented
5#30190C211yesmaximal, characteristic, complemented
6#29335C211yesmaximal, characteristic, complemented
7#29332C211yesmaximal, characteristic, complemented
8#29219C211yesmaximal, characteristic, complemented
9#29126C211yesmaximal, characteristic, complemented
10#27965C211yesmaximal, characteristic, complemented
11#27960C211yesmaximal, characteristic, complemented
12#27832C212yesmaximal, complemented
13#27746C212yesmaximal, complemented
14#27721C212yesmaximal, complemented
15#27707C212yesmaximal, complemented
16#27697C212yesmaximal, complemented
17#27697C212yesmaximal, complemented
18#23823C211yesmaximal, characteristic, complemented
19#23745C211yesmaximal, characteristic, complemented
20C2×#2099C211yesmaximal, characteristic, complemented
21#22497C212yesmaximal
22#22497C212yesmaximal
23#20559C211yesmaximal, characteristic
24C2×#554C2212yes—
25C2×#435C2212yes—
26#2868C2211yescharacteristic
27#2864C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic
31#2851C2211yescharacteristic
32#2586—21no—
33#2585—21no—
34#2570C2211yescharacteristic
35#2567C2212yes—
36#2552—21no—
37#2552—21no—
38#2550C2211yescharacteristic
39#2522—21no—
40#2502C2212yes—
41#2502C2212yes—
42#2465—21no—
43#2450—21no—
44#2449—21no—
45#2441C2211yescharacteristic
46#2440—21no—
47#2440—21no—
48#2440—21no—
49#2440—21no—
50#2440C2211yescharacteristic
51#2440C2211yescharacteristic
52#2439C2211yescharacteristic
53#2368—21no—
54#2360—21no—
55#2352C2211yescharacteristic
56#2352C2211yescharacteristic
57D4×C4⋊C4—21no—
58D4×C4⋊C4—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61#2296C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#384C2211yescharacteristic
64C2×#384C2211yescharacteristic
65C42×D4C2211yescharacteristic
66#2100C2212yes—
67#2100C2212yes—
68#2100C2212yes—
69#2100C2212yes—
70#2099C2211yescharacteristic
71#2099C2211yescharacteristic
72#2099C2211yescharacteristic
73#2099C2211yescharacteristic
74#2099C2211yescharacteristic
75#2099C2211yescharacteristic
76#2099C2211yescharacteristic
77#2099C2211yescharacteristic
78#2099C2211yescharacteristic
79#2099C2211yescharacteristic
80#2099C2211yescharacteristic
81#2099C2212yes—
82#2099C2211yescharacteristic
83#2099C2212yes—
84#2074C2212yes—
85#2072C2212yes—
86#2072C2212yes—
87#2043C2211yescharacteristic
88#2043C2211yescharacteristic
89#2043C2211yescharacteristic
90#2043C2211yescharacteristic
91#2026C2212yes—
92#2024C2212yes—
93#2024C2212yes—
94#1993C2212yes—
95#1993C2212yes—
96#1992C2212yes—
97#1990C2212yes—
98#1990C2212yes—
99#1988C2212yes—
100#1988C2212yes—
101#1935C2212yes—
102#1935C2212yes—
103#1933C2212yes—
104#1933C2212yes—
105#1933C2212yes—
106#1933C2212yes—
107#1894C2212yes—
108#1894C2212yes—
109#1892C2212yes—
110#1892C2212yes—
111#1873C2212yes—
112#1873C2212yes—
113#1872C2212yes—
114#1872C2212yes—
115#1836C2212yes—
116#1834C2212yes—
117#1834C2212yes—
118#1824C2212yes—
119#1824C2212yes—
120#1823C2212yes—
121#1823C2212yes—
122#1805C2212yes—
123#1805C2212yes—
124#1771C2212yes—
125C4×C4⋊C8C2211yescharacteristic
126#1763C2212yes—
127#1763C2212yes—
128#1753C2212yes—
129C8×C22⋊C4C2212yes—
130#1749C2211yescharacteristic
131C4×C22⋊C8C2211yescharacteristic
132#1745C2211yescharacteristic
133#1736C2212yes—
134#1736C2212yes—
135C2×#340C2212yes—
136C2×#340C2212yes—
137#1728C2211yescharacteristic
138C2×#336C2211yescharacteristic
139C22×M16C2312yes—
140C23×C8C2312yes—
141#554—28no—
142#554—28no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2312yes—
147C2×C4⋊Q8C2311yescharacteristic
148C2×C4⋊Q8C2311yescharacteristic
149C2×#125—22no—
150C2×#125C2311yescharacteristic
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8—21no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—22no—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8C2312yes—
157C2×C22⋊Q8C2312yes—
158C2×C4×Q8—21no—
159C2×C4×Q8C2312yes—
160C2×C4×D4—22no—
161C2×C4×D4D411yescharacteristic
162C2×C4×D4D411yescharacteristic
163C2×C4×D4C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C22×C4⋊C4—21no—
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4—21no—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177#435—28no—
178C2×C4⋊C8C2312yes—
179C2×#103C2312yes—
180C2×#103C2312yes—
181C2×#103C2312yes—
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#103C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×#97C2312yes—
190C2×#97C2312yes—
191C2×C4×C8C2312yes—
192C2×C4×C8C2312yes—
193#400—21no—
194#399—21no—
195#398—21no—
196#398—21no—
197#398—21no—
198#398—21no—
199#398—22no—
200#398—22no—
201#398—22no—
202#398—22no—
203#396—21no—
204#396—21no—
205#395—21no—
206#395—22no—
207#395—22no—
208#395—21no—
209#395—21no—
210#393—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391C2312yes—
216#391C2312yes—
217#391C2312yes—
218#389—22no—
219#389—22no—
220#389—21no—
221#389—21no—
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#389—21no—
231#389—21no—
232#389C2311yescharacteristic
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#389C2311yescharacteristic
242#388—21no—
243#388—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#386—21no—
257#386—21no—
258#385—21no—
259#385—21no—
260#385—21no—
261#385—21no—
262#385—22no—
263#385—22no—
264#385—22no—
265#385—22no—
266#385—21no—
267#385—21no—
268#384—21no—
269#384—21no—
270#384—21no—
271#384—21no—
272#384—21no—
273#384—21no—
274#384C2311yescharacteristic
275#384C2311yescharacteristic
276#384C2312yes—
277#384C2312yes—
278#384C2311yescharacteristic
279#384C2311yescharacteristic
280#384C2311yescharacteristic
281#384C2312yes—
282#382C2311yescharacteristic
283#382C2311yescharacteristic
284#382C2311yescharacteristic
285#380—21no—
286#380—21no—
287#380—21no—
288#380—21no—
289#380—21no—
290#380C2311yescharacteristic
291#380C2311yescharacteristic
292#380C2311yescharacteristic
293#380C2311yescharacteristic
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4D411yescharacteristic
300C4×C4⋊C4D411yescharacteristic
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C22⋊C4—21no—
305C4×C22⋊C4—21no—
306C4×C22⋊C4D411yescharacteristic
307C4×C22⋊C4D411yescharacteristic
308C4×C22⋊C4D411yescharacteristic
309C4×C22⋊C4D411yescharacteristic
310C4×C22⋊C4C2311yescharacteristic
311C4×C22⋊C4C2311yescharacteristic
312C2×#95—21no—
313C43C2311yescharacteristic
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
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#336C2312yes—
339#336C2312yes—
340#336C2312yes—
341#336C2311yescharacteristic
342#336C2311yescharacteristic
343#336C2311yescharacteristic
344#336C2311yescharacteristic
345C22×Q8—21no—
346C22×Q8—22no—
347C22×Q8—21no—
348C22×Q8C2412yes—
349C22×D4C2×D411yescharacteristic
350C23×C4—21no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—21no—
354C23×C4C2×D411yescharacteristic
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2411yescharacteristic
359C23×C4C2411yescharacteristic
360C2×M16—24no—
361C2×M16—42no—
362C2×M16—42no—
363C22×C8—24no—
364C22×C8—42no—
365C22×C8—42no—
366C22×C8C2412yes—
367C22×C8C2412yes—
368C22×C8C2412yes—
369C22×C8C2412yes—
370C4⋊Q8—22no—
371C4⋊Q8—24no—
372C4⋊Q8—24no—
373C4⋊Q8—41no—
374C4⋊Q8—42no—
375C4⋊Q8—42no—
376C4⋊Q8—82no—
377C4⋊Q8—82no—
378#125—42no—
379#125—48no—
380C22⋊Q8—24no—
381C22⋊Q8—24no—
382C22⋊Q8—24no—
383C22⋊Q8—24no—
384C22⋊Q8—48no—
385C22⋊Q8—48no—
386C22⋊Q8—44no—
387C22⋊Q8—44no—
388C22⋊Q8—82no—
389C4×Q8—24no—
390C4×Q8—24no—
391C4×Q8—82no—
392C4×D4—24no—
393C4×D4—24no—
394C4×D4—48no—
395C4×D4#4118yes—
396#117—22no—
397#117—41no—
398#117—42no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—82no—
447C2×C4⋊C4—82no—
448C2×C4⋊C4—82no—
449C2×C4⋊C4—82no—
450C2×C4⋊C4—82no—
451C2×C4⋊C4C2×D411yescharacteristic
452C2×C4⋊C4C2×D411yescharacteristic
453C2×C4⋊C4C2×D411yescharacteristic
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2411yescharacteristic
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2411yescharacteristic
462C2×C4⋊C4C2411yescharacteristic
463C2×C4⋊C4C2411yescharacteristic
464C2×C4⋊C4C2411yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4C2×D411yescharacteristic
474C2×C22⋊C4C2×D411yescharacteristic
475C2×C22⋊C4C2×D411yescharacteristic
476C2×C22⋊C4C2×D411yescharacteristic
477C2×C22⋊C4C2×D411yescharacteristic
478C2×C22⋊C4C2×D411yescharacteristic
479C2×C42—21no—
480C2×C42—22no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—42no—
485C2×C42—42no—
486C2×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2×D411yescharacteristic
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C4⋊C8—24no—
500#103—24no—
501#103—42no—
502#103—42no—
503#103—42no—
504#103—42no—
505#103—42no—
506#103—42no—
507#103—42no—
508C22⋊C8—24no—
509C22⋊C8—24no—
510#97—24no—
511#97—42no—
512C4×C8—42no—
513C4×C8—42no—
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—22no—
526#95—22no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
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#95C2×D411yescharacteristic
543#95C2×D411yescharacteristic
544#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548C24C22×D411yescharacteristic
549C24C22×D411yescharacteristic
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—42no—
557C2×Q8—44no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—81no—
561C2×Q8—81no—
562C2×Q8—81no—
563C2×Q8—82no—
564C2×Q8—82no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4#12414yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—42no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—82no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
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×C4C2×#4114yes—
623C22×C4C2×#4114yes—
624C22×C4C2511yescharacteristic
625M16—84no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—84no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—81no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—81no—
688C4⋊C4—81no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—81no—
692C4⋊C4—81no—
693C4⋊C4—81no—
694C4⋊C4—81no—
695C4⋊C4—81no—
696C4⋊C4—82no—
697C4⋊C4—82no—
698C4⋊C4#12414yes—
699C4⋊C42−1+412yes—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—42no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4#12414yes—
711C22⋊C4#12414yes—
712C22⋊C4#13714yes—
713C22⋊C4#13714yes—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—21no—
719C42—21no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—41no—
724C42—41no—
725C42—41no—
726C42—41no—
727C42—42no—
728C42—44no—
729C42—81no—
730C42—81no—
731C42—81no—
732C42C2×#4114yes—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23C2×#12412yes—
744C23C2×#12412yes—
745C23C2×#13712yes—
746C23C2×#13712yes—
747C23C23×D411yescharacteristic
748Q8—42no—
749Q8—42no—
750Q8—42no—
751Q8—42no—
752Q8—84no—
753Q8—162no—
754Q8—164no—
755D4—28no—
756C2×C4—21no—
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—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
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—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—84no—
827C2×C4—162no—
828C2×C4—164no—
829C2×C4—164no—
830C2×C4C2×#12412yes—
831C2×C4C2×#12412yes—
832C2×C4C2×#12412yes—
833C2×C4C2×#12412yes—
834C2×C4C2×#13712yes—
835C2×C4C2×#13712yes—
836C2×C4C2×#13712yes—
837C2×C4C2×#13712yes—
838C2×C4#57612yes—
839C2×C4#57712yes—
840C2×C4C22×#4112yes—
841C2×C4C2×2−1+411yescharacteristic
842C2×C4#58512yes—
843C2×C4#58511yescharacteristic
844C8—42no—
845C8—42no—
846C8—42no—
847C8—42no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22#313914yes—
862C22C22×#12411yescharacteristic
863C22#348511yescharacteristic
864C22#348911yescharacteristic
865C22C22×#13711yescharacteristic
866C22C22×#13711yescharacteristic
867C22C2×#57611yescharacteristic
868C22C2×#57711yescharacteristic
869C4—22no—
870C4—22no—
871C4—22no—
872C4—22no—
873C4—22no—
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—41no—
880C4—41no—
881C4—42no—
882C4—81no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4#351512yes—
894C4#352112yes—
895C2—24no—
896C2—42no—
897C2#3604211yescharacteristic
898C2C2×#313911yescharacteristic
899C2#6062211yescharacteristic
900C2#6172611yescharacteristic
901C2#6173511yescharacteristic
902C2#6212711yescharacteristic
903C2#6213111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
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
3. #30233C2semidirect
4. #30199C2semidirect
5. #30190C2semidirect
6. #29335C2semidirect
7. #29332C2semidirect
8. #29219C2semidirect
9. #29126C2semidirect
10. #27965C2semidirect
11. #27960C2semidirect
12. #27832C2semidirect
13. #27746C2semidirect
14. #27721C2semidirect
15. #27707C2semidirect
16. #27697C2semidirect
17. #27697C2semidirect
18. #23823C2semidirect
19. #23745C2semidirect
20. C2×#2099C2semidirect

Maximal subgroups

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

subgroupindex
#363632
#361802
#302332
#301992
#301902
#293352
#293322
#292192
#291262
#279652
#279602
#278322
#277462
#277212
#277072
#276972
#238232
#237452
C2×#20992
#224972
#205592