Finite Group Databasebeta

← #6865048

Subgroups — #6865048

Order 512.

1629 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36505C211yesmaximal, characteristic
2#34952C211yesmaximal, characteristic
3#32954C211yesmaximal, characteristic, complemented
4#32265C212yesmaximal, complemented
5#32008C212yesmaximal, complemented
6#31267C212yesmaximal, complemented
7#30411C212yesmaximal, complemented
8#30174C212yesmaximal, complemented
9#29417C212yesmaximal, complemented
10#29158C212yesmaximal, complemented
11#28228C211yesmaximal, characteristic, complemented
12#28142C211yesmaximal, characteristic, complemented
13#27877C211yesmaximal, characteristic, complemented
14#27628C211yesmaximal, characteristic, complemented
15#25341C211yesmaximal, characteristic, complemented
16#25341C211yesmaximal, characteristic, complemented
17#25063C211yesmaximal, characteristic, complemented
18#24997C211yesmaximal, characteristic, complemented
19#24332C211yesmaximal, characteristic, complemented
20#24332C211yesmaximal, characteristic, complemented
21#22469C211yesmaximal, characteristic
22#22183C212yesmaximal, complemented
23C4×#451C211yesmaximal, characteristic, complemented
24C2×#557C2211yescharacteristic
25C2×C4×#41C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C2×#475C2211yescharacteristic
28C2×#475C2211yescharacteristic
29C2×#467C2212yes—
30C2×#451C2211yescharacteristic
31C2×C4×Q16C2211yescharacteristic
32C2×C4×Q16C2211yescharacteristic
33C2×C8×D4C2211yescharacteristic
34C2×C8×D4C2211yescharacteristic
35#2857C2211yescharacteristic
36#2851C2212yes—
37#2582C2211yescharacteristic
38#2582C2211yescharacteristic
39#2581—21no—
40#2580—21no—
41#2579—22no—
42#2562C2212yes—
43#2547C2211yescharacteristic
44#2538C2211yescharacteristic
45#2538C2211yescharacteristic
46#2538C2211yescharacteristic
47#2536C2212yes—
48#2487C2212yes—
49#2475—22no—
50#2460—22no—
51#2446—21no—
52#2432—21no—
53#2409C2212yes—
54#2396—22no—
55#2367—21no—
56#2362—21no—
57#2355C2211yescharacteristic
58C4×C22⋊Q8C2212yes—
59C4×C22⋊Q8C2212yes—
60C4×C22⋊Q8C2212yes—
61C4×C22⋊Q8C2211yescharacteristic
62#2297—21no—
63#2296—21no—
64#2285C2211yescharacteristic
65#2101C2212yes—
66#2097C2212yes—
67#2085C2212yes—
68#2077C2212yes—
69#2077C2212yes—
70#2077C2212yes—
71#2076C2212yes—
72#2075C2212yes—
73#2075C2212yes—
74#2074C2212yes—
75#2059C2212yes—
76#2059C2212yes—
77#2036C2212yes—
78#2036C2212yes—
79#2035C2212yes—
80#2035C2212yes—
81#2035C2212yes—
82#2026C2212yes—
83#2026C2212yes—
84#2001C2212yes—
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1984C2211yescharacteristic
88#1984C2211yescharacteristic
89#1948C2211yescharacteristic
90#1948C2211yescharacteristic
91#1928C2212yes—
92#1927C2212yes—
93#1927C2212yes—
94#1920C2212yes—
95#1919C2212yes—
96#1918C2212yes—
97#1918C2212yes—
98#1918C2212yes—
99#1892C2212yes—
100#1892C2212yes—
101#1892C2212yes—
102#1892C2212yes—
103#1878C2212yes—
104#1878C2212yes—
105#1878C2211yescharacteristic
106#1878C2211yescharacteristic
107#1872C2211yescharacteristic
108#1869C2212yes—
109#1869C2212yes—
110#1865C2212yes—
111#1865C2212yes—
112#1865C2212yes—
113#1865C2212yes—
114#1863C2211yescharacteristic
115#1863C2211yescharacteristic
116#1853C2212yes—
117#1852C2211yescharacteristic
118#1845C2211yescharacteristic
119#1834C2211yescharacteristic
120#1817C2212yes—
121#1808C2212yes—
122#1807C2212yes—
123#1807C2212yes—
124#1803C2211yescharacteristic
125#1803C2211yescharacteristic
126#1803C2211yescharacteristic
127#1803C2211yescharacteristic
128#1797C2211yescharacteristic
129#1787C2211yescharacteristic
130#1787C2212yes—
131C4×#103C2211yescharacteristic
132C4×#103C2211yescharacteristic
133C4×C22⋊C8C2211yescharacteristic
134C2×#336C2212yes—
135C22×#41D411yescharacteristic
136C23×Q8C2311yescharacteristic
137C22×Q16C2311yescharacteristic
138C22×Q16C2311yescharacteristic
139C23×C8C2312yes—
140C23×C8C2312yes—
141#557—42no—
142#557—42no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×#125—22no—
146C2×#125C2312yes—
147C2×#124—21no—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8C2311yescharacteristic
150C2×C22⋊Q8C2312yes—
151C2×C22⋊Q8C2312yes—
152C2×C22⋊Q8C2312yes—
153C4×#41—42no—
154C4×#41—42no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8—42no—
159C2×C4×Q8—42no—
160C2×C4×Q8D411yescharacteristic
161C2×C4×Q8C2311yescharacteristic
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×Q8C2311yescharacteristic
165C2×C4×Q8C2311yescharacteristic
166C2×C4×Q8C2312yes—
167C2×C4×Q8C2311yescharacteristic
168C2×C4×D4D412yes—
169C2×C4×D4D411yescharacteristic
170C2×C4×D4C2311yescharacteristic
171C2×C4×D4C2312yes—
172C2×#117—21no—
173C2×#117D411yescharacteristic
174C2×#117D412yes—
175C22×C4⋊C4—21no—
176C22×C4⋊C4C2311yescharacteristic
177C22×C42—21no—
178C22×C42C2311yescharacteristic
179C22×C42C2312yes—
180#475—42no—
181#475—42no—
182#467—28no—
183#451—24no—
184C4×Q16—42no—
185C4×Q16—42no—
186C8×D4—42no—
187C8×D4—42no—
188C2×#107C2312yes—
189C2×#107C2311yescharacteristic
190C2×#107C2311yescharacteristic
191C2×#107C2312yes—
192C2×#106C2312yes—
193C2×#106C2312yes—
194C2×#106C2312yes—
195C2×#106C2312yes—
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2311yescharacteristic
208C2×#103C2311yescharacteristic
209C2×#103C2311yescharacteristic
210C2×#103C2311yescharacteristic
211C2×#103C2311yescharacteristic
212C2×C22⋊C8C2311yescharacteristic
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219#400—22no—
220#400—22no—
221#399—22no—
222#398—22no—
223#398—22no—
224#398—22no—
225#397—22no—
226#396—22no—
227#396—22no—
228#396—22no—
229#395—22no—
230#394—22no—
231#394—22no—
232#393—22no—
233#391—21no—
234#391—21no—
235#391—21no—
236#391—21no—
237#391—21no—
238#391C2312yes—
239#391C2312yes—
240#391C2311yescharacteristic
241#390—21no—
242#390—21no—
243#390—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389C2312yes—
251#389C2312yes—
252#389C2311yescharacteristic
253#389C2312yes—
254#388—22no—
255#388—22no—
256#388—22no—
257#388—22no—
258#387—22no—
259#387—22no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—21no—
265#386—22no—
266#386—22no—
267#385—22no—
268#385—22no—
269#385—22no—
270#385—22no—
271#385—22no—
272#385—21no—
273#385—22no—
274#385—22no—
275#384C2311yescharacteristic
276#384C2311yescharacteristic
277#384C2311yescharacteristic
278#382—21no—
279#382C2312yes—
280#380—21no—
281#380—21no—
282#380C2311yescharacteristic
283#380C2312yes—
284#380C2312yes—
285#380C2312yes—
286#380C2312yes—
287#380C2312yes—
288#380C2312yes—
289#380C2312yes—
290C4×C4⋊C4—21no—
291C4×C4⋊C4—22no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—22no—
295C4×C4⋊C4—22no—
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2312yes—
299C4×C22⋊C4—21no—
300C4×C22⋊C4—22no—
301C4×C22⋊C4—22no—
302C4×C22⋊C4—22no—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2312yes—
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2311yescharacteristic
323#336C2312yes—
324#336C2312yes—
325#336C2311yescharacteristic
326C2×#41—24no—
327C2×#41—24no—
328C2×#41—42no—
329C22×Q8—21no—
330C22×Q8—21no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—41no—
334C22×Q8—41no—
335C22×Q8—41no—
336C22×Q8—41no—
337C22×Q8C2×D411yescharacteristic
338C22×Q8C2411yescharacteristic
339C22×Q8C2411yescharacteristic
340C22×Q8C2411yescharacteristic
341C22×D4C2×D412yes—
342C22×D4C2×D411yescharacteristic
343C23×C4—21no—
344C23×C4—21no—
345C23×C4C2×D412yes—
346C23×C4C2×D411yescharacteristic
347C23×C4C2×D411yescharacteristic
348C23×C4C2×D412yes—
349C23×C4C2411yescharacteristic
350C23×C4C2412yes—
351C2×Q16—22no—
352C2×Q16—22no—
353C2×Q16—41no—
354C2×Q16—41no—
355C2×Q16—41no—
356C2×Q16#4114yescomplemented
357C22×C8—24no—
358C22×C8—42no—
359C22×C8—42no—
360C22×C8—42no—
361C22×C8—42no—
362C22×C8—42no—
363C22×C8C2411yescharacteristic
364C22×C8C2412yes—
365C22×C8C2412yes—
366C22×C8C2411yescharacteristic
367C22×C8C2411yescharacteristic
368C22×C8C2411yescharacteristic
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371C4⋊Q8—44no—
372#125—42no—
373#125—42no—
374#125—48no—
375#124—44no—
376C22⋊Q8—22no—
377C22⋊Q8—24no—
378C22⋊Q8—24no—
379C22⋊Q8—24no—
380C22⋊Q8—42no—
381C22⋊Q8—42no—
382C22⋊Q8—41no—
383C22⋊Q8—42no—
384C22⋊Q8—44no—
385C4×Q8—22no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—41no—
394C4×Q8—41no—
395C4×Q8—41no—
396C4×Q8—41no—
397C4×Q8—42no—
398C4×Q8—42no—
399C4×Q8—42no—
400C4×Q8—44no—
401C4×Q8—44no—
402C4×Q8—44no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—42no—
406C4×D4—42no—
407C4×D4—42no—
408C4×D4—44no—
409#117—44no—
410#117—42no—
411#117—44no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—41no—
437C2×C4⋊C4—41no—
438C2×C4⋊C4—44no—
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D412yes—
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D412yes—
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2411yescharacteristic
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4C2×D412yes—
465C2×C22⋊C4C2×D412yes—
466C2×C22⋊C4C2×D412yes—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—22no—
478C2×C42—42no—
479C2×C42—42no—
480C2×C42—44no—
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D412yes—
484C2×C42C2×D412yes—
485C2×C42C2412yes—
486C2×C42C2411yescharacteristic
487C2×C42C2411yescharacteristic
488#107—24no—
489#107—42no—
490#107—41no—
491#107—41no—
492#106—42no—
493#106—42no—
494#106—42no—
495#106—42no—
496C4⋊C8—22no—
497C4⋊C8—22no—
498#103—22no—
499#103—24no—
500#103—24no—
501#103—22no—
502#103—22no—
503#103—41no—
504#103—42no—
505#103—42no—
506#103—41no—
507#103—41no—
508#103—41no—
509#103—41no—
510#103—42no—
511#103—42no—
512C22⋊C8—22no—
513C22⋊C8—42no—
514C22⋊C8—41no—
515C22⋊C8—42no—
516C22⋊C8—42no—
517C4×C8—22no—
518C4×C8—22no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—21no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—21no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—21no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542C24C22×D411yescharacteristic
543C24C22×D412yes—
544#41—416no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
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—44no—
567C2×Q8—44no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8C2×#4112yes—
574C2×Q8C2×#4112yes—
575C2×Q82−1+412yes—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—42no—
581C2×D4#13714yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—42no—
612C22×C4—42no—
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—81no—
622C22×C4—81no—
623C22×C4#13514yes—
624C22×C4C22×D412yes—
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D412yes—
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D412yes—
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C2511yescharacteristic
633Q16—44no—
634Q16—44no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—22no—
651C2×C8—21no—
652C2×C8—84no—
653C2×C8—84no—
654C2×C8C2×#4112yes—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—24no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—21no—
675C4⋊C4—22no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—44no—
696C4⋊C4—81no—
697C4⋊C4—81no—
698C4⋊C4—81no—
699C4⋊C4—82no—
700C4⋊C4—82no—
701C22⋊C4—24no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—44no—
705C22⋊C4—42no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—44no—
712C22⋊C4—81no—
713C22⋊C4—82no—
714C22⋊C4—82no—
715C22⋊C4—82no—
716C42—22no—
717C42—22no—
718C42—21no—
719C42—21no—
720C42—22no—
721C42—22no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—44no—
727C42—42no—
728C42—42no—
729C42—42no—
730C42—44no—
731C42—42no—
732C42—82no—
733C42H(5,𝔽2)12yes—
734C42H(5,𝔽2)12yes—
735C23—22no—
736C23—21no—
737C23—22no—
738C23—21no—
739C23—22no—
740C23—21no—
741C23—22no—
742C23—21no—
743C23—22no—
744C23—21no—
745C23—22no—
746C23—21no—
747C23C2×#13512yes—
748C23C2×#13714yes—
749C23C23×D411yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—22no—
755Q8—22no—
756Q8—48no—
757Q8—44no—
758Q8—41no—
759Q8—41no—
760Q8—41no—
761Q8—41no—
762Q8—41no—
763Q8—41no—
764Q8—84no—
765D4—28no—
766D4—48no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—28no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—82no—
834C2×C4—84no—
835C2×C4—84no—
836C2×C4#53412yes—
837C2×C4#53412yes—
838C2×C4C2×#13512yes—
839C2×C4C2×#13512yes—
840C2×C4C2×#13712yes—
841C2×C4C22×#4111yescharacteristic
842C2×C4C2×H(5,𝔽2)11yescharacteristic
843C2×C4C2×H(5,𝔽2)11yescharacteristic
844C2×C4C2×2−1+411yescharacteristic
845C2×C4#58511yescharacteristic
846C2×C4#58511yescharacteristic
847C8—22no—
848C8—42no—
849C8—41no—
850C8—42no—
851C8—41no—
852C8—41no—
853C22—24no—
854C22—22no—
855C22—24no—
856C22—22no—
857C22—24no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22C2×#53411yescharacteristic
868C22D4×#4111yescharacteristic
869C22#348911yescharacteristic
870C22C22×#13511yescharacteristic
871C22C22×#13711yescharacteristic
872C22#358411yescharacteristic
873C22#358611yescharacteristic
874C4—22no—
875C4—22no—
876C4—42no—
877C4—42no—
878C4—41no—
879C4—42no—
880C4—41no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—81no—
885C4—82no—
886C4—81no—
887C4—81no—
888C4—81no—
889C4—82no—
890C4—81no—
891C4—82no—
892C4—82no—
893C4#319014yes—
894C4#350511yescharacteristic
895C4#352011yescharacteristic
896C4#354011yescharacteristic
897C4#354111yescharacteristic
898C2—44no—
899C2—42no—
900C2#3986011yescharacteristic
901C2C2×#319011yescharacteristic
902C2#6076611yescharacteristic
903C2#6143011yescharacteristic
904C2#6145711yescharacteristic
905C2#6210111yescharacteristic
906C2#6213911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32954C2semidirect
4. #32265C2semidirect
5. #32008C2semidirect
6. #31267C2semidirect
7. #30411C2semidirect
8. #30174C2semidirect
9. #29417C2semidirect
10. #29158C2semidirect
11. #28228C2semidirect
12. #28142C2semidirect
13. #27877C2semidirect
14. #27628C2semidirect
15. #25341C2semidirect
16. #25341C2semidirect
17. #25063C2semidirect
18. #24997C2semidirect
19. #24332C2semidirect
20. #24332C2semidirect
22. #22183C2semidirect
23. C4×#451C2semidirect
356. C2×Q16#41semidirect

Maximal subgroups

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

subgroupindex
#365052
#349522
#329542
#322652
#320082
#312672
#304112
#301742
#294172
#291582
#282282
#281422
#278772
#276282
#253412
#250632
#249972
#243322
#224692
#221832
C4×#4512