Finite Group Databasebeta

← #6810626

Subgroups — #6810626

Order 512.

1757 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3336C211yesmaximal, characteristic, complemented
2C2×#3177C211yesmaximal, characteristic, complemented
3#42803C212yesmaximal
4#33216C211yesmaximal, characteristic, complemented
5#30652C212yesmaximal, complemented
6#30649C212yesmaximal, complemented
7#30580C212yesmaximal, complemented
8#30577C212yesmaximal, complemented
9#29701C212yesmaximal, complemented
10#28535C211yesmaximal, characteristic, complemented
11#28228C211yesmaximal, characteristic, complemented
12#28228C211yesmaximal, characteristic, complemented
13#28226C211yesmaximal, characteristic, complemented
14#26067C211yesmaximal, characteristic, complemented
15#26066C211yesmaximal, characteristic, complemented
16#25415C211yesmaximal, characteristic, complemented
17#25415C211yesmaximal, characteristic, complemented
18#24826C212yesmaximal, complemented
19#24781C211yesmaximal, characteristic, complemented
20#24779C211yesmaximal, characteristic, complemented
21#24139C212yesmaximal, complemented
22C4⋊C4×Q16C211yesmaximal, characteristic, complemented
23#21491C211yesmaximal, characteristic
24C2×#552C2212yes—
25C2×#541C2212yes—
26#3336—28no—
27#3177—28no—
28C2×#499C2211yescharacteristic
29C2×#499C2211yescharacteristic
30C2×#494C2211yescharacteristic
31C2×#491C2212yes—
32C2×#485C2212yes—
33C2×#483C2212yes—
34C2×#479C2212yes—
35C2×#479C2212yes—
36C2×#470C2212yes—
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#467C2211yescharacteristic
41C2×#467C2211yescharacteristic
42C2×#467C2211yescharacteristic
43C2×#441C2212yes—
44C2×C4×Q16C2211yescharacteristic
45C2×C4×Q16C2211yescharacteristic
46C2×C4×Q16C2211yescharacteristic
47C2×C4×Q16C2211yescharacteristic
48C2×C8×D4C2211yescharacteristic
49C2×C8×D4C2211yescharacteristic
50C2×C8×D4C2211yescharacteristic
51C2×#427C2211yescharacteristic
52C22×#107C2211yescharacteristic
53C2×#405C2211yescharacteristic
54#2823—22no—
55#2726—22no—
56#2725—22no—
57#2707—22no—
58#2705—22no—
59#2664—22no—
60#2629—22no—
61#2629C2212yes—
62#2601—22no—
63#2565C2212yes—
64#2538C2212yes—
65#2538C2212yes—
66#2536C2212yes—
67#2442C2212yes—
68#2441C2212yes—
69#2429C2212yes—
70#2429C2212yes—
71#2417C2212yes—
72#2415C2212yes—
73#2392C2211yescharacteristic
74Q8×C4⋊C4C2212yes—
75#2097C2212yes—
76#2096C2212yes—
77#2085C2212yes—
78#2084C2212yes—
79#2068C2212yes—
80#2066C2212yes—
81#2059C2212yes—
82#2059C2212yes—
83#2043C2212yes—
84#2043C2212yes—
85#2036C2212yes—
86#2036C2212yes—
87#2036C2212yes—
88#2036C2212yes—
89#2036C2212yes—
90#2035C2212yes—
91#2035C2212yes—
92#2035C2212yes—
93#2001C2212yes—
94#2001C2212yes—
95#1992C2212yes—
96#1969C2211yescharacteristic
97#1969C2211yescharacteristic
98#1955C2211yescharacteristic
99#1943C2212yes—
100#1942C2211yescharacteristic
101#1942C2211yescharacteristic
102#1942C2211yescharacteristic
103#1942C2211yescharacteristic
104#1940C2211yescharacteristic
105#1924C2211yescharacteristic
106#1924C2211yescharacteristic
107#1878C2212yes—
108#1878C2212yes—
109#1873C2212yes—
110#1872C2212yes—
111#1870C2211yescharacteristic
112#1870C2211yescharacteristic
113#1863C2212yes—
114#1863C2212yes—
115#1854C2212yes—
116#1853C2212yes—
117#1846C2211yescharacteristic
118#1845C2211yescharacteristic
119#1845C2211yescharacteristic
120#1809C2212yes—
121#1808C2211yescharacteristic
122#1808C2211yescharacteristic
123#1808C2211yescharacteristic
124#1808C2211yescharacteristic
125#1805C2212yes—
126#1803C2212yes—
127#1803C2212yes—
128#1803C2212yes—
129#1798C2211yescharacteristic
130C8×C4⋊C4C2211yescharacteristic
131C8×C22⋊C4C2211yescharacteristic
132C8×C22⋊C4C2211yescharacteristic
133C22×Q16C2311yescharacteristic
134C22×Q16C2312yes—
135C22×Q16C2311yescharacteristic
136C22×M16C2311yescharacteristic
137C23×C8C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C23×C8C2311yescharacteristic
140#552—28no—
141#552—44no—
142#541—28no—
143#541—44no—
144C2×C4⋊Q8C2312yes—
145C2×#126—22no—
146C2×#126—22no—
147C2×#126—22no—
148C2×#125—22no—
149C2×#125—22no—
150C2×#125—22no—
151C2×#125C2312yes—
152C2×#125C2312yes—
153C2×#123—22no—
154C2×C22⋊Q8C2312yes—
155C2×C22⋊Q8C2312yes—
156C2×C22⋊Q8C2312yes—
157C2×C22⋊Q8C2312yes—
158C2×C22⋊Q8C2312yes—
159C2×C22⋊Q8C2312yes—
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2312yes—
162C2×C4×Q8C2312yes—
163C2×C4×Q8C2312yes—
164C2×C4×D4C2311yescharacteristic
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2311yescharacteristic
167C2×#117—22no—
168C2×#117C2312yes—
169C2×#117C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171#499—24no—
172#499—24no—
173#494—24no—
174#491—28no—
175#485—28no—
176#483—28no—
177#479—28no—
178#479—44no—
179#470—28no—
180#467—24no—
181#467—24no—
182#467—24no—
183#467—24no—
184#467—42no—
185#467—42no—
186#441—28no—
187C4×Q16—24no—
188C4×Q16—42no—
189C4×Q16—42no—
190C4×Q16D418yescomplemented
191C8×D4—24no—
192C8×D4—42no—
193C8×D4—42no—
194#427—24no—
195C2×#107—24no—
196C2×#107C2312yes—
197C2×#107C2311yescharacteristic
198C2×#107C2311yescharacteristic
199C2×#107C2311yescharacteristic
200C2×#107C2311yescharacteristic
201C2×#107C2311yescharacteristic
202C2×#107C2312yes—
203C2×#107C2312yes—
204C2×#107C2311yescharacteristic
205C2×#106C2312yes—
206C2×#106C2312yes—
207C2×#106C2312yes—
208C2×#106C2312yes—
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2311yescharacteristic
211C2×C4⋊C8C2311yescharacteristic
212C2×C4⋊C8C2311yescharacteristic
213C2×#103C2312yes—
214C2×#103C2312yes—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#103C2312yes—
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2312yes—
223C2×#103C2312yes—
224C2×#103C2312yes—
225C2×C22⋊C8C2311yescharacteristic
226C2×C22⋊C8C2311yescharacteristic
227C2×C22⋊C8C2311yescharacteristic
228C2×C22⋊C8C2311yescharacteristic
229C2×C22⋊C8C2311yescharacteristic
230C2×C22⋊C8C2311yescharacteristic
231C2×C22⋊C8C2311yescharacteristic
232C2×C22⋊C8C2311yescharacteristic
233#405—24no—
234C2×#97C2311yescharacteristic
235C2×#97C2311yescharacteristic
236C2×C4×C8C2311yescharacteristic
237C2×C4×C8C2311yescharacteristic
238C2×C4×C8C2311yescharacteristic
239C2×C4×C8C2311yescharacteristic
240#400—22no—
241#399—22no—
242#398—22no—
243#398—22no—
244#398—22no—
245#398—22no—
246#398—22no—
247#398—22no—
248#398—22no—
249#398—22no—
250#398—22no—
251#398D411yescharacteristic
252#397—22no—
253#397D411yescharacteristic
254#396—22no—
255#396—22no—
256#396—22no—
257#396—22no—
258#396—22no—
259#396—22no—
260#396—22no—
261#396—22no—
262#396—22no—
263#396—22no—
264#396D411yescharacteristic
265#396D411yescharacteristic
266#394—22no—
267#394—22no—
268#394D411yescharacteristic
269#394D411yescharacteristic
270#394D411yescharacteristic
271#392D411yescharacteristic
272#391C2312yes—
273#391C2312yes—
274#390—22no—
275#390—22no—
276#389—22no—
277#389—22no—
278#389—22no—
279#389—22no—
280#389—22no—
281#389—22no—
282#389—22no—
283#389—22no—
284#389C2312yes—
285#389C2312yes—
286#389C2312yes—
287#389C2312yes—
288#388—22no—
289#388—22no—
290#388—22no—
291#388—22no—
292#388—22no—
293#387—22no—
294#387—22no—
295#387—22no—
296#386—22no—
297#385—22no—
298#384—22no—
299#384C2312yes—
300#384C2312yes—
301#382C2312yes—
302#380—22no—
303#380—22no—
304#380C2312yes—
305#380C2312yes—
306#380C2312yes—
307#380C2312yes—
308C4×C4⋊C4—22no—
309C4×C4⋊C4C2311yescharacteristic
310C4×C22⋊C4C2311yescharacteristic
311C4×C22⋊C4C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#336C2311yescharacteristic
321#336C2311yescharacteristic
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2311yescharacteristic
325#336C2311yescharacteristic
326C22×Q8C2412yes—
327C22×Q8C2412yes—
328C22×D4C2×D411yescharacteristic
329C22×D4C2×D411yescharacteristic
330C22×D4C2×D411yescharacteristic
331C23×C4—22no—
332C23×C4C2411yescharacteristic
333C23×C4C2411yescharacteristic
334C23×C4C2411yescharacteristic
335C2×Q16—24no—
336C2×Q16—22no—
337C2×Q16—22no—
338C2×Q16—22no—
339C2×Q16—22no—
340C2×Q16—24no—
341C2×Q16—22no—
342C2×Q16—42no—
343C2×Q16C2×D414yes—
344C2×M16—22no—
345C2×M16—22no—
346C2×M16—41no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C4⋊Q8—24no—
365C4⋊Q8—42no—
366#126—48no—
367#126—48no—
368#126—48no—
369#125—24no—
370#125—24no—
371#125—24no—
372#125—42no—
373#125—48no—
374#125—48no—
375#125—48no—
376#123—48no—
377C22⋊Q8—24no—
378C22⋊Q8—24no—
379C22⋊Q8—24no—
380C22⋊Q8—24no—
381C22⋊Q8—42no—
382C22⋊Q8—42no—
383C22⋊Q8—42no—
384C22⋊Q8—42no—
385C22⋊Q8—42no—
386C22⋊Q8—42no—
387C22⋊Q8—42no—
388C22⋊Q8—42no—
389C4×Q8—24no—
390C4×Q8—24no—
391C4×Q8—24no—
392C4×Q8—42no—
393C4×Q8—42no—
394C4×Q8—42no—
395C4×Q8—42no—
396C4×Q8C2×D418yes—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—41no—
400C4×D4—41no—
401C4×D4—41no—
402C4×D4—41no—
403#117—22no—
404#117—22no—
405#117—24no—
406#117—48no—
407#117—42no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D411yescharacteristic
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4C2×D411yescharacteristic
460C2×C22⋊C4C2×D411yescharacteristic
461C2×C22⋊C4C2×D411yescharacteristic
462C2×C22⋊C4C2×D411yescharacteristic
463C2×C22⋊C4C2×D411yescharacteristic
464C2×C22⋊C4C2×D411yescharacteristic
465C2×C22⋊C4C2×D411yescharacteristic
466C2×C22⋊C4C2×D411yescharacteristic
467C2×C22⋊C4C2×D411yescharacteristic
468C2×C22⋊C4C2×D411yescharacteristic
469C2×C22⋊C4C2×D411yescharacteristic
470C2×C22⋊C4C2×D411yescharacteristic
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42C2411yescharacteristic
477C2×C42C2411yescharacteristic
478C2×C42C2411yescharacteristic
479C2×C42C2411yescharacteristic
480#107—22no—
481#107—22no—
482#107—22no—
483#107—22no—
484#107—22no—
485#107—24no—
486#107—42no—
487#107—42no—
488#107C2×D414yes—
489#106—24no—
490#106—24no—
491#106—24no—
492#106—42no—
493C4⋊C8—22no—
494C4⋊C8—22no—
495C4⋊C8—41no—
496C4⋊C8—41no—
497#103—24no—
498#103—24no—
499#103—24no—
500#103—24no—
501#103—24no—
502#103—42no—
503#103—42no—
504#103—42no—
505#103—42no—
506#103—42no—
507#103—42no—
508#103C2×D418yes—
509C22⋊C8—22no—
510C22⋊C8—22no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8—41no—
514C22⋊C8—41no—
515C22⋊C8—41no—
516C22⋊C8—41no—
517#97—22no—
518#97—22no—
519C4×C8—22no—
520C4×C8—22no—
521C4×C8—22no—
522C4×C8C2×D414yes—
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—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95C2×D411yescharacteristic
538#95C2×D411yescharacteristic
539#95C2×D411yescharacteristic
540#95C2×D411yescharacteristic
541#95C2×D411yescharacteristic
542#95C2×D411yescharacteristic
543C24C22×D411yescharacteristic
544C24C22×D411yescharacteristic
545C24C22×D411yescharacteristic
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8C22×D414yes—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
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—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—82no—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C22×D411yescharacteristic
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C2511yescharacteristic
608Q16—28no—
609Q16—48no—
610Q16—44no—
611M16—44no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—44no—
632C2×C8—44no—
633C2×C8—44no—
634C2×C8C22×D412yes—
635C2×C8C22×D412yes—
636C2×C8H(5,𝔽2)12yes—
637C2×C82−1+412yes—
638C2×C82−1+412yes—
639C4⋊C4—28no—
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—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—41no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—82no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4—82no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4—82no—
678C4⋊C4—82no—
679C4⋊C4—82no—
680C4⋊C4—82no—
681C4⋊C4—82no—
682C4⋊C4C22×D414yes—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—41no—
690C22⋊C4—41no—
691C22⋊C4—41no—
692C22⋊C4—41no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C22⋊C4—82no—
703C22⋊C4—82no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C42—28no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—44no—
714C42—44no—
715C42—82no—
716C42—82no—
717C42C22×D412yes—
718C42H(5,𝔽2)12yes—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23#57812yes—
740C23C23×D411yescharacteristic
741Q8—24no—
742Q8—24no—
743Q8—42no—
744Q8—42no—
745Q8—42no—
746Q8—42no—
747Q8—42no—
748Q8—42no—
749D4—44no—
750D4—44no—
751D4—44no—
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—21no—
763C2×C4—21no—
764C2×C4—24no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—24no—
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—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—88no—
819C2×C4D4212yes—
820C2×C4D4212yes—
821C2×C4#57812yes—
822C2×C4C23×D411yescharacteristic
823C2×C4C2×H(5,𝔽2)11yescharacteristic
824C2×C4C2×H(5,𝔽2)11yescharacteristic
825C2×C4C2×2−1+411yescharacteristic
826C2×C4C2×2−1+411yescharacteristic
827C2×C4#58511yescharacteristic
828C8—22no—
829C8—22no—
830C8—41no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—41no—
835C8#53714yes—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22C2×D4211yescharacteristic
858C22#349611yescharacteristic
859C22#349911yescharacteristic
860C22C2×#57811yescharacteristic
861C22C2×#57811yescharacteristic
862C22#358411yescharacteristic
863C22#358411yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—41no—
868C4—41no—
869C4—41no—
870C4—41no—
871C4—44no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—44no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4C2×#53711yescharacteristic
884C4#348911yescharacteristic
885C4#354711yescharacteristic
886C4#354811yescharacteristic
887C2—42no—
888C2—81no—
889C2—81no—
890C2#3934011yescharacteristic
891C2#6105711yescharacteristic
892C2#6108611yescharacteristic
893C2#6227111yescharacteristic
894C2#6227611yescharacteristic
895C2#6249311yescharacteristic
896C2#6249611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#392D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3336C2semidirect
2. C2×#3177C2semidirect
4. #33216C2semidirect
5. #30652C2semidirect
6. #30649C2semidirect
7. #30580C2semidirect
8. #30577C2semidirect
9. #29701C2semidirect
10. #28535C2semidirect
11. #28228C2semidirect
12. #28228C2semidirect
13. #28226C2semidirect
14. #26067C2semidirect
15. #26066C2semidirect
16. #25415C2semidirect
17. #25415C2semidirect
18. #24826C2semidirect
19. #24781C2semidirect
20. #24779C2semidirect
21. #24139C2semidirect
22. C4⋊C4×Q16C2semidirect
190. C4×Q16D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33362
C2×#31772
#428032
#332162
#306522
#306492
#305802
#305772
#297012
#285352
#282282
#282262
#260672
#260662
#254152
#248262
#247812
#247792
#241392
C4⋊C4×Q162
#214912