Finite Group Databasebeta

← #6490379

Subgroups — #6490379

Order 512.

1447 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34619C211yesmaximal, characteristic
2#34216C211yesmaximal, characteristic, complemented
3#33104C212yesmaximal, complemented
4#33102C212yesmaximal
5#30100C212yesmaximal, complemented
6#30068C212yesmaximal, complemented
7#29526C212yesmaximal, complemented
8#29524C212yesmaximal, complemented
9#29342C212yesmaximal
10#29308C212yesmaximal, complemented
11#29276C211yesmaximal, characteristic, complemented
12#29272C211yesmaximal, characteristic, complemented
13#28203C211yesmaximal, characteristic, complemented
14#28203C211yesmaximal, characteristic, complemented
15#27682C211yesmaximal, characteristic, complemented
16#27679C211yesmaximal, characteristic
17#24301C211yesmaximal, characteristic, complemented
18#24298C211yesmaximal, characteristic
19#22118C211yesmaximal, characteristic, complemented
20#22116C211yesmaximal, characteristic, complemented
21#22112C211yesmaximal, characteristic, complemented
22#22110C211yesmaximal, characteristic, complemented
23#20786C211yesmaximal, characteristic, complemented
24C22×C4⋊Q8C2211yescharacteristic
25C2×#475C2211yescharacteristic
26C2×#475C2211yescharacteristic
27C2×#474C2211yescharacteristic
28C2×#474C2211yescharacteristic
29#2654—21no—
30#2653—21no—
31#2650—21no—
32#2649—21no—
33#2647C2211yescharacteristic
34#2645C2211yescharacteristic
35#2644C2211yescharacteristic
36#2640C2211yescharacteristic
37#2628C2211yescharacteristic
38#2625C2211yescharacteristic
39#2624C2211yescharacteristic
40#2620C2211yescharacteristic
41#2401—21no—
42#2398—21no—
43#2396—21no—
44#2395—21no—
45#2369—21no—
46#2369—21no—
47#2365—21no—
48#2365—21no—
49#2345—21no—
50#2345—21no—
51Q8×C22⋊C4—21no—
52Q8×C22⋊C4—21no—
53#2331C2212yes—
54#2331C2212yes—
55#2316C2212yes—
56C4×C4⋊Q8C2211yescharacteristic
57C4×C4⋊Q8C2211yescharacteristic
58C4×C4⋊Q8C2211yescharacteristic
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61C4×#124C2211yescharacteristic
62C4×C22⋊Q8C2211yescharacteristic
63C4×#121C2211yescharacteristic
64#2295C2211yescharacteristic
65#2293C2211yescharacteristic
66#2285C2211yescharacteristic
67#2274C2212yes—
68C4×#117C2211yescharacteristic
69#2101C2212yes—
70#2101C2212yes—
71#2100C2212yes—
72#2099C2212yes—
73#2097C2212yes—
74#2092C2212yes—
75#2085C2212yes—
76#2085C2212yes—
77#2058C2212yes—
78#2058C2212yes—
79#2057C2212yes—
80#2057C2212yes—
81#2042C2212yes—
82#2042C2212yes—
83#2024C2212yes—
84#2023C2212yes—
85#1988C2211yescharacteristic
86#1988C2211yescharacteristic
87#1988C2211yescharacteristic
88#1988C2211yescharacteristic
89#1948C2211yescharacteristic
90#1948C2211yescharacteristic
91#1947C2211yescharacteristic
92#1947C2211yescharacteristic
93#1944C2212yes—
94#1943C2212yes—
95#1942C2212yes—
96#1941C2212yes—
97#1936C2212yes—
98#1935C2212yes—
99#1934C2212yes—
100#1933C2212yes—
101#1928C2212yes—
102#1928C2212yes—
103#1928C2212yes—
104#1927C2212yes—
105#1926C2212yes—
106#1926C2212yes—
107#1926C2212yes—
108#1925C2212yes—
109#1921C2212yes—
110#1920C2212yes—
111#1920C2212yes—
112#1920C2212yes—
113#1919C2212yes—
114#1918C2212yes—
115#1918C2212yes—
116#1918C2212yes—
117#1875C2212yes—
118#1874C2212yes—
119#1873C2212yes—
120#1872C2212yes—
121#1854C2212yes—
122#1854C2212yes—
123#1853C2212yes—
124#1852C2212yes—
125#1840C2212yes—
126#1831C2211yescharacteristic
127#1831C2211yescharacteristic
128#1818C2212yes—
129#1803C2211yescharacteristic
130#1803C2211yescharacteristic
131#1802C2211yescharacteristic
132#1802C2211yescharacteristic
133#1797C2211yescharacteristic
134#1797C2211yescharacteristic
135#1767C2211yescharacteristic
136C4×C4⋊C8C2211yescharacteristic
137#1750C2212yes—
138#1746C2212yes—
139C23×Q8—21no—
140C2×C4⋊Q8—24no—
141C2×C4⋊Q8—24no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8C2312yes—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×#124C2311yescharacteristic
149C2×C22⋊Q8C2311yescharacteristic
150C2×#121C2311yescharacteristic
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8C2311yescharacteristic
157C2×C4×D4—21no—
158C2×C4×D4C2311yescharacteristic
159C2×#117—21no—
160C2×#117C2312yes—
161C2×#117C2311yescharacteristic
162C2×#117C2311yescharacteristic
163C22×C4⋊C4—21no—
164C22×C4⋊C4C2312yes—
165C22×C42C2311yescharacteristic
166#475—24no—
167#475—24no—
168#474—24no—
169#474—24no—
170C2×#107C2312yes—
171C2×#107C2312yes—
172C2×#107C2312yes—
173C2×#107C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#106C2312yes—
178C2×C4⋊C8C2311yescharacteristic
179C2×C4⋊C8C2311yescharacteristic
180C2×C4⋊C8C2311yescharacteristic
181C2×C4⋊C8C2311yescharacteristic
182C2×#103C2312yes—
183C2×#103C2312yes—
184C2×#103C2312yes—
185C2×#103C2312yes—
186C2×#102C2312yes—
187C2×#102C2312yes—
188C2×#102C2312yes—
189C2×#102C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×#97C2312yes—
193C2×C4×C8C2312yes—
194#401—21no—
195#400—21no—
196#400—21no—
197#400—21no—
198#400—21no—
199#400—21no—
200#400—21no—
201#400—21no—
202#399—21no—
203#399—21no—
204#398—21no—
205#398—21no—
206#398—21no—
207#397—21no—
208#397—21no—
209#397—21no—
210#397—21no—
211#397—21no—
212#397—21no—
213#397—21no—
214#397—21no—
215#396—21no—
216#396—21no—
217#396—21no—
218#395—21no—
219#394—21no—
220#394—21no—
221#394—21no—
222#394—21no—
223#393—21no—
224#393—21no—
225#393—21no—
226#391—21no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—22no—
232#391—22no—
233#391—22no—
234#391—22no—
235#391C2311yescharacteristic
236#391C2311yescharacteristic
237#391C2311yescharacteristic
238#391C2311yescharacteristic
239#390C2311yescharacteristic
240#390C2311yescharacteristic
241#390C2311yescharacteristic
242#390C2311yescharacteristic
243#389—22no—
244#389—22no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389C2312yes—
251#389C2312yes—
252#389C2312yes—
253#389C2312yes—
254#389C2311yescharacteristic
255#389C2311yescharacteristic
256#389C2311yescharacteristic
257#389C2311yescharacteristic
258#389C2311yescharacteristic
259#389C2311yescharacteristic
260#389C2311yescharacteristic
261#389C2311yescharacteristic
262#388—21no—
263#388—21no—
264#388—21no—
265#388—21no—
266#388—21no—
267#387—21no—
268#387—21no—
269#387—21no—
270#387—22no—
271#387—22no—
272#387—22no—
273#387—22no—
274#386—21no—
275#385—21no—
276#384C2311yescharacteristic
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#382C2312yes—
280#382C2311yescharacteristic
281#380—21no—
282#380—21no—
283#380—22no—
284#380—22no—
285#380C2311yescharacteristic
286#380C2311yescharacteristic
287C4×C4⋊C4—22no—
288C4×C4⋊C4—22no—
289C4×C4⋊C4—21no—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4D411yescharacteristic
299C4×C4⋊C4D411yescharacteristic
300C4×C4⋊C4D411yescharacteristic
301C4×C4⋊C4D411yescharacteristic
302C4×C4⋊C4C2312yes—
303C4×C4⋊C4C2312yes—
304C4×C4⋊C4C2312yes—
305C4×C4⋊C4C2312yes—
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C22⋊C4—21no—
309C4×C22⋊C4—22no—
310C4×C22⋊C4—22no—
311C4×C22⋊C4—21no—
312C4×C22⋊C4—21no—
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315C4×C22⋊C4D411yescharacteristic
316C4×C22⋊C4D411yescharacteristic
317C4×C22⋊C4D411yescharacteristic
318C4×C22⋊C4D411yescharacteristic
319#376—21no—
320#376C2311yescharacteristic
321#376C2311yescharacteristic
322C43C2311yescharacteristic
323C43C2311yescharacteristic
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#340C2312yes—
339#340C2312yes—
340#336C2312yes—
341#336C2312yes—
342#336C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348C22×Q8—28no—
349C22×Q8—21no—
350C22×Q8—21no—
351C22×Q8—22no—
352C22×Q8—21no—
353C22×Q8—82no—
354C22×Q8—82no—
355C22×Q8C2411yescharacteristic
356C22×D4—21no—
357C22×D4C2411yescharacteristic
358C23×C4—22no—
359C23×C4—21no—
360C23×C4C2×D411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4C2411yescharacteristic
363C22×C8C2412yes—
364C22×C8C2412yes—
365C22×C8C2412yes—
366C22×C8C2412yes—
367C4⋊Q8—28no—
368C4⋊Q8—28no—
369C4⋊Q8—24no—
370C4⋊Q8—24no—
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373C4⋊Q8—41no—
374C4⋊Q8—41no—
375C4⋊Q8#4114yes—
376C4⋊Q8#4114yes—
377#124—41no—
378#124—41no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381#121—22no—
382#121—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—82no—
386C4×Q8—82no—
387C4×Q8—82no—
388C4×Q8—82no—
389C4×Q8—82no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—82no—
393#117—22no—
394#117—22no—
395#117—41no—
396#117—41no—
397#117—42no—
398#117—42no—
399#117—82no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
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—21no—
416C2×C4⋊C4—21no—
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—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D411yescharacteristic
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2412yes—
433C2×C4⋊C4C2412yes—
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2411yescharacteristic
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
459C2×C22⋊C4C2×D411yescharacteristic
460C2×C22⋊C4C2×D411yescharacteristic
461C2×C22⋊C4C2×D411yescharacteristic
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—22no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488#107—24no—
489#107—24no—
490#107—42no—
491#107—42no—
492#106—24no—
493#106—24no—
494#106—42no—
495#106—42no—
496C4⋊C8—22no—
497C4⋊C8—22no—
498C4⋊C8—22no—
499C4⋊C8—22no—
500#103—24no—
501#103—24no—
502#103—42no—
503#103—42no—
504#102—24no—
505#102—24no—
506#102—42no—
507#102—42no—
508C22⋊C8—24no—
509C22⋊C8—24no—
510#97—42no—
511C4×C8—42no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—22no—
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—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
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#95C2×D411yescharacteristic
545#95C2×D411yescharacteristic
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552C24—21no—
553C24C22×D411yescharacteristic
554C2×Q8—28no—
555C2×Q8—24no—
556C2×Q8—24no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8—42no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—81no—
569C2×Q8—81no—
570C2×Q8—82no—
571C2×Q8—82no—
572C2×Q8—816no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4C22×D411yescharacteristic
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×C42−1+412yes—
623C22×C42−1+412yes—
624C22×C4C2511yescharacteristic
625C2×C8—22no—
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—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—41no—
662C4⋊C4—41no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—81no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—81no—
676C4⋊C4—81no—
677C4⋊C4—81no—
678C4⋊C4—81no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4—81no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4C2×#4114yes—
685C4⋊C4C2×#4114yes—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—44no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—81no—
697C22⋊C4—81no—
698C22⋊C4—81no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C22⋊C4—81no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—81no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—41no—
723C42—41no—
724C42—41no—
725C42—41no—
726C42—44no—
727C42—42no—
728C42—42no—
729C42—42no—
730C42—82no—
731C42—82no—
732C42—82no—
733C42—82no—
734C42C2×#4112yes—
735C42C2×#4112yes—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23#53612yes—
750C23C23×D411yescharacteristic
751Q8—48no—
752Q8—48no—
753Q8—41no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8—88no—
758Q8—84no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—84no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
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—24no—
785C2×C4—24no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
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—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—88no—
838C2×C4—84no—
839C2×C4#52512yes—
840C2×C4#52512yes—
841C2×C4#53612yes—
842C2×C4#57612yes—
843C2×C4#57712yes—
844C2×C4C22×#4111yescharacteristic
845C2×C4C22×#4111yescharacteristic
846C2×C4C2×2−1+411yescharacteristic
847C2×C4C2×2−1+411yescharacteristic
848C2×C4#58511yescharacteristic
849C2×C4#58511yescharacteristic
850C8—42no—
851C8—42no—
852C8—42no—
853C8—42no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22C2×#52511yescharacteristic
869C22C2×#53611yescharacteristic
870C22#344911yescharacteristic
871C22C2×#57611yescharacteristic
872C22C2×#57711yescharacteristic
873C22#358611yescharacteristic
874C22#358611yescharacteristic
875C4—22no—
876C4—22no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—44no—
883C4—44no—
884C4—41no—
885C4—41no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—82no—
890C4—81no—
891C4—81no—
892C4—82no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4#311814yes—
899C4#351611yescharacteristic
900C4#351611yescharacteristic
901C4#351611yescharacteristic
902C4#351611yescharacteristic
903C2—42no—
904C2—161no—
905C2#3524511yescharacteristic
906C2C2×#311811yescharacteristic
907C2#6056611yescharacteristic
908C2#6088811yescharacteristic
909C2#6088911yescharacteristic
910C2#6098811yescharacteristic
911C2#6099211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34216C2semidirect
3. #33104C2semidirect
5. #30100C2semidirect
6. #30068C2semidirect
7. #29526C2semidirect
8. #29524C2semidirect
10. #29308C2semidirect
11. #29276C2semidirect
12. #29272C2semidirect
13. #28203C2semidirect
14. #28203C2semidirect
15. #27682C2semidirect
17. #24301C2semidirect
19. #22118C2semidirect
20. #22116C2semidirect
21. #22112C2semidirect
22. #22110C2semidirect
23. #20786C2semidirect

Maximal subgroups

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

subgroupindex
#346192
#342162
#331042
#331022
#301002
#300682
#295262
#295242
#293422
#293082
#292762
#292722
#282032
#276822
#276792
#243012
#242982
#221182
#221162
#221122
#221102
#207862