Finite Group Databasebeta

← #6396681

Subgroups — #6396681

Order 512.

1752 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3236C211yesmaximal, characteristic
2#34239C211yesmaximal, characteristic
3#34214C211yesmaximal, characteristic
4#23078C212yesmaximal, complemented
5#23074C212yesmaximal, complemented
6#22980C212yesmaximal, complemented
7#22976C212yesmaximal, complemented
8#22934C212yesmaximal
9#22932C212yesmaximal
10#22922C212yesmaximal
11#22920C212yesmaximal
12#22251C211yesmaximal, characteristic, complemented
13#22250C211yesmaximal, characteristic, complemented
14#22225C211yesmaximal, characteristic, complemented
15#22225C211yesmaximal, characteristic, complemented
16#21987C211yesmaximal, characteristic
17#21731C211yesmaximal, characteristic, complemented
18C4×#501C211yesmaximal, characteristic, complemented
19#21657C211yesmaximal, characteristic, complemented
20C4×#491C211yesmaximal, characteristic, complemented
21#21407C211yesmaximal, characteristic
22C2×#1992C211yesmaximal, characteristic
23#20479C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C22×#125C2211yescharacteristic
26#3236C4116yescomplemented
27C2×#501C2211yescharacteristic
28C2×#501C2211yescharacteristic
29C2×#491C2211yescharacteristic
30C2×#491C2211yescharacteristic
31C2×#484C2212yes—
32C2×#483C2212yes—
33C2×#479C2212yes—
34C2×#479C2212yes—
35C2×#432C2211yescharacteristic
36C22×#97C2211yescharacteristic
37#2371—21no—
38#2371—21no—
39#2370C2211yescharacteristic
40#2370C2211yescharacteristic
41#2370C2211yescharacteristic
42#2370C2211yescharacteristic
43#2360—21no—
44#2360—21no—
45#2360C2212yes—
46#2360C2212yes—
47#2355—21no—
48#2355C2212yes—
49Q8×C4⋊C4—21no—
50Q8×C4⋊C4C2212yes—
51#2345C2211yescharacteristic
52#2345C2211yescharacteristic
53#2344—21no—
54#2344—21no—
55#2344C2211yescharacteristic
56#2344C2211yescharacteristic
57#2336—21no—
58#2336—21no—
59#2330—21no—
60#2330—21no—
61#2317—21no—
62#2313—21no—
63C4×C4⋊Q8C2211yescharacteristic
64C4×C4⋊Q8C2211yescharacteristic
65C4×C4⋊Q8C2211yescharacteristic
66C4×C4⋊Q8C2211yescharacteristic
67C4×#125C2211yescharacteristic
68C4×#125C2211yescharacteristic
69C4×#125C2211yescharacteristic
70C4×#125C2211yescharacteristic
71C2×#384C2211yescharacteristic
72#2283C2211yescharacteristic
73#2274—21no—
74#2274—21no—
75C4×#117C2211yescharacteristic
76#1993C2211yescharacteristic
77#1993C2211yescharacteristic
78#1992C2212yes—
79#1992C2212yes—
80#1992C2211yescharacteristic
81#1992C2211yescharacteristic
82#1992C2211yescharacteristic
83#1992C2211yescharacteristic
84#1960C2211yescharacteristic
85#1960C2211yescharacteristic
86#1948C2212yes—
87#1947C2212yes—
88#1944C2212yes—
89#1943C2212yes—
90#1942C2212yes—
91#1941C2212yes—
92#1935C2212yes—
93#1935C2212yes—
94#1933C2212yes—
95#1933C2212yes—
96#1928C2212yes—
97#1928C2212yes—
98#1927C2212yes—
99#1927C2212yes—
100#1921C2212yes—
101#1921C2212yes—
102#1920C2212yes—
103#1920C2212yes—
104#1919C2212yes—
105#1919C2212yes—
106#1918C2212yes—
107#1918C2212yes—
108#1892C2212yes—
109#1892C2212yes—
110#1865C2212yes—
111#1865C2212yes—
112#1863C2212yes—
113#1863C2212yes—
114#1853C2212yes—
115#1852C2212yes—
116#1847C2211yescharacteristic
117#1847C2211yescharacteristic
118#1836C2211yescharacteristic
119#1836C2211yescharacteristic
120#1776C2212yes—
121#1776C2212yes—
122C4×#107C2212yes—
123C4×#106C2212yes—
124#1771C2212yes—
125#1771C2212yes—
126#1763C2212yes—
127#1763C2212yes—
128#1763C2212yes—
129#1763C2212yes—
130C4×#103C2212yes—
131C4×#103C2212yes—
132#1752C2212yes—
133C8×C22⋊C4C2212yes—
134#1745C2211yescharacteristic
135#1745C2211yescharacteristic
136C2×#340C2212yes—
137C2×#340C2212yes—
138C4×#97C2211yescharacteristic
139C4×#97C2211yescharacteristic
140C23×C8C2312yes—
141#533—24no—
142#533C2×C418yes—
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×#125—21no—
146C2×#125—21no—
147C2×#125—21no—
148C2×#125—24no—
149C2×#125C2×C418yes—
150C2×#125C2311yescharacteristic
151C2×#125C2311yescharacteristic
152C2×#125C2311yescharacteristic
153C2×#125C2311yescharacteristic
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8C2312yes—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8—21no—
159C2×C4×Q8C2312yes—
160C2×C4×Q8C2312yes—
161C2×C4×Q8C2312yes—
162C2×#117—21no—
163C2×#117—21no—
164C2×#117—21no—
165C2×#117D411yescharacteristic
166C2×#117D411yescharacteristic
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4—21no—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C42C2311yescharacteristic
175#501C2×C418yescomplemented
176#501C2×C418yescomplemented
177#491C2×C418yescomplemented
178#491C2×C418yescomplemented
179#484C2×C4116yes—
180#483C2×C4116yes—
181#479C2×C4116yescomplemented
182#479C2×C4116yescomplemented
183#432C2×C418yes—
184C2×#107C2312yes—
185C2×#107C2312yes—
186C2×#107C2312yes—
187C2×#107C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×C4⋊C8C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#103C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×C22⋊C8C2312yes—
202C2×#97—24no—
203C2×#97C2311yescharacteristic
204C2×#97C2311yescharacteristic
205C2×#97C2312yes—
206C2×#97C2312yes—
207C2×#97C2312yes—
208C2×#97C2311yescharacteristic
209C2×#97C2311yescharacteristic
210C2×C4×C8C2312yes—
211C2×C4×C8C2312yes—
212#391—21no—
213#391—21no—
214#391C2312yes—
215#391C2312yes—
216#389—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389—21no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—22no—
227#389—22no—
228#389—22no—
229#389—22no—
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2311yescharacteristic
233#389C2311yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2312yes—
239#389C2312yes—
240#387—21no—
241#387—21no—
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—22no—
257#387—22no—
258#387—22no—
259#387—22no—
260#387—21no—
261#387—21no—
262#387—21no—
263#387—21no—
264#387—21no—
265#387—21no—
266#387—21no—
267#387—21no—
268#385—22no—
269#385—22no—
270#384—22no—
271#384—21no—
272#384—21no—
273#384C2311yescharacteristic
274#384C2311yescharacteristic
275#384C2312yes—
276#383—21no—
277#382—22no—
278#382C2311yescharacteristic
279#382C2311yescharacteristic
280#381—21no—
281#381—21no—
282#381—21no—
283#380—21no—
284#380—21no—
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⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4—21no—
307C4×C4⋊C4D411yescharacteristic
308C4×C4⋊C4D411yescharacteristic
309C4×C4⋊C4C2311yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2311yescharacteristic
315C4×C4⋊C4C2311yescharacteristic
316C4×C4⋊C4C2311yescharacteristic
317C4×C4⋊C4C2312yes—
318C4×C4⋊C4C2312yes—
319C4×C4⋊C4C2311yescharacteristic
320C4×C4⋊C4C2311yescharacteristic
321C4×C4⋊C4C2311yescharacteristic
322C4×C4⋊C4C2311yescharacteristic
323C4×C22⋊C4—21no—
324C4×C22⋊C4—21no—
325C4×C22⋊C4—21no—
326C4×C22⋊C4—22no—
327C4×C22⋊C4—22no—
328C4×C22⋊C4D411yescharacteristic
329C4×C22⋊C4D411yescharacteristic
330C4×C22⋊C4C2311yescharacteristic
331C4×C22⋊C4C2311yescharacteristic
332#376—21no—
333#376D411yescharacteristic
334#376D411yescharacteristic
335C43C2311yescharacteristic
336C43C2311yescharacteristic
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#340C2312yes—
346#340C2312yes—
347#340C2312yes—
348#340C2312yes—
349#340C2312yes—
350#340C2312yes—
351#340C2312yes—
352#340C2312yes—
353#336C2312yes—
354#336C2312yes—
355#336C2312yes—
356#336C2312yes—
357C22×Q8—21no—
358C22×Q8C2412yes—
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—22no—
362C23×C4C2×D411yescharacteristic
363C23×C4C2×D411yescharacteristic
364C23×C4C2411yescharacteristic
365C22×C8—24no—
366C22×C8—24no—
367C22×C8—42no—
368C22×C8C2412yes—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C22×C8C2412yes—
372C4⋊Q8—22no—
373C4⋊Q8—22no—
374C4⋊Q8C22×C414yes—
375C4⋊Q8C22×C414yes—
376#125—28no—
377#125—28no—
378#125—28no—
379#125—22no—
380#125—22no—
381#125—22no—
382#125—22no—
383#125C22×C414yes—
384#125C22×C414yes—
385#125C22×C414yes—
386#125C22×C414yes—
387C22⋊Q8—28no—
388C22⋊Q8—24no—
389C22⋊Q8C22×C418yes—
390C4×Q8—28no—
391C4×Q8—24no—
392C4×Q8—42no—
393C4×Q8—42no—
394C4×Q8—42no—
395C4×Q8—42no—
396C4×Q8—82no—
397C4×Q8—82no—
398C4×Q8C22×C418yes—
399#117—28no—
400#117—24no—
401#117—42no—
402#117—44no—
403#117—44no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—28no—
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—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—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—44no—
445C2×C4⋊C4—82no—
446C2×C4⋊C4C22×C414yes—
447C2×C4⋊C4C22×C414yes—
448C2×C4⋊C4C2×D411yescharacteristic
449C2×C4⋊C4C2×D411yescharacteristic
450C2×C4⋊C4C2×D411yescharacteristic
451C2×C4⋊C4C2×D411yescharacteristic
452C2×C4⋊C4C2412yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2411yescharacteristic
459C2×C4⋊C4C2411yescharacteristic
460C2×C4⋊C4C2411yescharacteristic
461C2×C4⋊C4C2411yescharacteristic
462C2×C4⋊C4C2412yes—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4C2×D411yescharacteristic
467C2×C22⋊C4C2×D411yescharacteristic
468C2×C22⋊C4C2×D411yescharacteristic
469C2×C22⋊C4C2×D411yescharacteristic
470C2×C42—22no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42C22×C414yes—
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×C42C2×D411yescharacteristic
495C2×C42C2×D411yescharacteristic
496C2×C42#4114yes—
497C2×C42C2411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501C2×C42C2411yescharacteristic
502C2×C42C2411yescharacteristic
503#107—42no—
504#107—42no—
505#107C22×C418yes—
506#107C22×C418yes—
507#106—42no—
508#106—42no—
509#106C22×C418yes—
510#106C22×C418yes—
511C4⋊C8C22×C418yes—
512#103—24no—
513#103—24no—
514#103—42no—
515#103—42no—
516#103C22×C418yes—
517#103C22×C418yes—
518#103C22×C418yes—
519#103C22×C418yes—
520C22⋊C8C22×C418yes—
521#97—24no—
522#97—24no—
523#97—22no—
524#97—22no—
525#97—42no—
526#97C22×C414yes—
527#97C22×C414yes—
528C4×C8—24no—
529C4×C8—42no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—22no—
549#95—22no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—22no—
561#95—22no—
562#95C2×D411yescharacteristic
563#95C2×D411yescharacteristic
564#95C2×D411yescharacteristic
565#95C2×D411yescharacteristic
566#95C2×D411yescharacteristic
567#95C2×D411yescharacteristic
568#95C2×D411yescharacteristic
569#95C2×D411yescharacteristic
570C24C22×D411yescharacteristic
571C2×Q8—24no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—42no—
578C2×Q8—42no—
579C2×Q8C23×C414yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4C4×D414yes—
608C22×C4C4×D414yes—
609C22×C4C23×C412yes—
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×C4C22×D411yescharacteristic
623C22×C4C2×#4112yes—
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—48no—
635C2×C8C23×C414yes—
636C2×C8C23×C414yes—
637C2×C82−1+414yes—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—41no—
669C4⋊C4—41no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4C23×C412yes—
690C4⋊C4C23×C412yes—
691C4⋊C4C23×C412yes—
692C4⋊C4C23×C412yes—
693C4⋊C4C23×C414yes—
694C22⋊C4—28no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4#13714yes—
701C42—28no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—41no—
709C42—41no—
710C42—41no—
711C42—41no—
712C42—41no—
713C42—41no—
714C42—42no—
715C42—42no—
716C42—42no—
717C42—42no—
718C42—81no—
719C42—81no—
720C42—81no—
721C42—81no—
722C42—81no—
723C42—81no—
724C42—82no—
725C42—82no—
726C42—82no—
727C42—82no—
728C42C4×D414yes—
729C42C4×D414yes—
730C42C23×C412yes—
731C42C23×C412yes—
732C42C2×#4112yes—
733C42C2×#4112yes—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23C2×C4×D412yes—
739C23C2×#13712yes—
740C23#57512yes—
741C23C23×D411yescharacteristic
742Q8—24no—
743Q8—24no—
744Q8—48no—
745Q8—42no—
746Q8—42no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—28no—
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—24no—
763C2×C4—24no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
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—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—48no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
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—84no—
821C2×C4—164no—
822C2×C4C2×C4×D412yes—
823C2×C4C2×C4×D412yes—
824C2×C4C2×C4×D412yes—
825C2×C4C2×C4×D412yes—
826C2×C4C2×C4×D412yes—
827C2×C4C2×#13712yes—
828C2×C4C2×#13712yes—
829C2×C4C24×C411yescharacteristic
830C2×C4C22×#4111yescharacteristic
831C2×C4C2×2−1+412yes—
832C2×C4#58512yes—
833C8—24no—
834C8—24no—
835C8—24no—
836C8—42no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22C4×#13714yes—
844C22C22×C4×D411yescharacteristic
845C22#349911yescharacteristic
846C22#350011yescharacteristic
847C22C22×#13711yescharacteristic
848C22C2×#57511yescharacteristic
849C22#358511yescharacteristic
850C22#358611yescharacteristic
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—22no—
857C4—22no—
858C4—42no—
859C4—42no—
860C4—44no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—44no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—82no—
875C4—82no—
876C4C4×2−1+412yes—
877C4#349512yes—
878C2—24no—
879C2#3427611yescharacteristic
880C2C2×C4×#13711yescharacteristic
881C2#6017011yescharacteristic
882C2#6250411yescharacteristic
883C2#6250511yescharacteristic
884C2#6257711yescharacteristic
885C2#6257811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C2×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
4. #23078C2semidirect
5. #23074C2semidirect
6. #22980C2semidirect
7. #22976C2semidirect
12. #22251C2semidirect
13. #22250C2semidirect
14. #22225C2semidirect
15. #22225C2semidirect
17. #21731C2semidirect
18. C4×#501C2semidirect
19. #21657C2semidirect
20. C4×#491C2semidirect
26. #3236C4semidirect
175. #501C2×C4semidirect
176. #501C2×C4semidirect
177. #491C2×C4semidirect
178. #491C2×C4semidirect
181. #479C2×C4semidirect
182. #479C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#32362
#342392
#342142
#230782
#230742
#229802
#229762
#229342
#229322
#229222
#229202
#222512
#222502
#222252
#219872
#217312
C4×#5012
#216572
C4×#4912
#214072
C2×#19922
#204792