Finite Group Databasebeta

← #6502549

Subgroups — #6502549

Order 512.

1698 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2451C211yesmaximal, characteristic
2#34235C211yesmaximal, characteristic
3#28124C211yesmaximal, characteristic
4#28124C211yesmaximal, characteristic
5#27616C211yesmaximal, characteristic
6#27589C211yesmaximal, characteristic
7#27448C212yesmaximal, complemented
8#27437C212yesmaximal, complemented
9#27017C212yesmaximal, complemented
10#27000C212yesmaximal, complemented
11#26911C212yesmaximal, complemented
12#26894C212yesmaximal, complemented
13#26393C212yesmaximal, complemented
14#26369C212yesmaximal, complemented
15#24302C211yesmaximal, characteristic
16#24301C211yesmaximal, characteristic
17#24063C211yesmaximal, characteristic
18#23934C211yesmaximal, characteristic
19#22084C211yesmaximal, characteristic
20#22078C211yesmaximal, characteristic
21#21914C211yesmaximal, characteristic
22#21455C211yesmaximal, characteristic
23C4×#451C211yesmaximal, characteristic
24C2×#533C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C2×#483C2211yescharacteristic
28C2×#483C2211yescharacteristic
29C2×#477C2212yes—
30C2×#475C2212yes—
31C2×#451C2211yescharacteristic
32C2×#451C2211yescharacteristic
33C2×#441C2212yes—
34C2×C4×Q16C2212yes—
35#2451—21no—
36#2451—21no—
37#2451—21no—
38#2451—21no—
39#2451C2212yes—
40#2451C2212yes—
41#2451C2212yes—
42#2451C2212yes—
43C2×#398—21no—
44C2×#395—21no—
45#2365C2211yescharacteristic
46#2365C2211yescharacteristic
47#2365C2211yescharacteristic
48#2365C2211yescharacteristic
49#2360—21no—
50#2360—21no—
51#2356C2211yescharacteristic
52#2356C2211yescharacteristic
53#2351C2211yescharacteristic
54#2351C2211yescharacteristic
55#2343—21no—
56#2343—21no—
57#2336—21no—
58#2336—21no—
59#2320—21no—
60C4×C22⋊Q8C2211yescharacteristic
61C4×C22⋊Q8C2211yescharacteristic
62C4×C22⋊Q8C2211yescharacteristic
63C4×C22⋊Q8C2211yescharacteristic
64C2×#391—21no—
65C2×#391C2211yescharacteristic
66C2×#391C2211yescharacteristic
67C2×#389C2211yescharacteristic
68C2×#389C2211yescharacteristic
69C2×#387—21no—
70#2283C2211yescharacteristic
71#2276—21no—
72C2×C4×C4⋊C4C2211yescharacteristic
73#2101C2212yes—
74#2097C2212yes—
75#2085C2212yes—
76#2074C2212yes—
77#2066C2212yes—
78#2066C2212yes—
79#2058C2212yes—
80#2058C2212yes—
81#2057C2212yes—
82#2056C2212yes—
83#2056C2212yes—
84#2043C2212yes—
85#2024C2212yes—
86#2024C2212yes—
87#2024C2212yes—
88#2016C2212yes—
89#1988C2212yes—
90#1987C2212yes—
91#1944C2212yes—
92#1941C2212yes—
93#1935C2212yes—
94#1933C2212yes—
95#1928C2212yes—
96#1927C2212yes—
97#1927C2212yes—
98#1927C2212yes—
99#1921C2212yes—
100#1920C2212yes—
101#1920C2212yes—
102#1919C2212yes—
103#1917C2212yes—
104#1917C2212yes—
105#1916C2212yes—
106#1916C2212yes—
107#1878C2212yes—
108#1878C2212yes—
109#1878C2212yes—
110#1878C2212yes—
111#1878C2212yes—
112#1878C2212yes—
113#1872C2211yescharacteristic
114#1872C2211yescharacteristic
115#1872C2211yescharacteristic
116#1872C2211yescharacteristic
117#1865C2212yes—
118#1865C2212yes—
119#1865C2212yes—
120#1865C2212yes—
121#1863C2212yes—
122#1863C2212yes—
123#1853C2211yescharacteristic
124#1853C2211yescharacteristic
125#1852C2211yescharacteristic
126#1852C2211yescharacteristic
127#1823C2211yescharacteristic
128#1823C2211yescharacteristic
129#1817C2211yescharacteristic
130#1817C2211yescharacteristic
131#1797C2211yescharacteristic
132#1797C2211yescharacteristic
133#1787C2211yescharacteristic
134#1787C2211yescharacteristic
135#1763C2212yes—
136C4×#103C2212yes—
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8—21no—
140C23×Q8C2311yescharacteristic
141C22×Q16C2312yes—
142C22×Q16C2312yes—
143#533—24no—
144#533—24no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—44no—
148C2×C4⋊Q8C2311yescharacteristic
149C2×C4⋊Q8C2311yescharacteristic
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2312yes—
152C2×#125—21no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8C2311yescharacteristic
155C2×C22⋊Q8C2311yescharacteristic
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8—21no—
159C2×C4×Q8—21no—
160C2×C4×Q8—21no—
161C2×C4×Q8—44no—
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×Q8C2312yes—
165C2×C4×Q8C2312yes—
166C2×C4×Q8C2311yescharacteristic
167C2×C4×Q8C2311yescharacteristic
168C2×C4×Q8C2311yescharacteristic
169C2×C4×Q8C2311yescharacteristic
170C2×#117—21no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4D411yescharacteristic
176C22×C4⋊C4D411yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C42—21no—
181C22×C42C2311yescharacteristic
182C22×C42C2311yescharacteristic
183C22×C42C2311yescharacteristic
184#483—24no—
185#483—24no—
186#477—44no—
187#475—44no—
188#451—24no—
189#451—24no—
190#441—44no—
191C4×Q16—44no—
192C2×#107C2312yes—
193C2×#107C2312yes—
194C2×#106C2312yes—
195C2×#106C2312yes—
196C2×#106C2312yes—
197C2×#106C2312yes—
198C2×C4⋊C8C2312yes—
199C2×C4⋊C8C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#103C2312yes—
212C2×C22⋊C8C2311yescharacteristic
213C2×C22⋊C8C2311yescharacteristic
214C2×C22⋊C8C2311yescharacteristic
215C2×C22⋊C8C2311yescharacteristic
216C2×#97C2312yes—
217C2×C4×C8C2312yes—
218#398—22no—
219#398—22no—
220#398—22no—
221#398—22no—
222#395—22no—
223#395—22no—
224#395—22no—
225#395—22no—
226#391—21no—
227#391—21no—
228#391—21no—
229#391—21no—
230#391—21no—
231#391—21no—
232#391—22no—
233#391—22no—
234#391—22no—
235#391—22no—
236#391C2311yescharacteristic
237#391C2311yescharacteristic
238#391C2312yes—
239#391C2312yes—
240#391C2312yes—
241#391C2311yescharacteristic
242#391C2311yescharacteristic
243#391C2312yes—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389—21no—
253#389—21no—
254#389C2311yescharacteristic
255#389C2311yescharacteristic
256#389C2312yes—
257#389C2312yes—
258#389C2311yescharacteristic
259#389C2311yescharacteristic
260#389C2312yes—
261#389C2312yes—
262#387—21no—
263#387—21no—
264#387—21no—
265#387—21no—
266#387—22no—
267#387—22no—
268#387—22no—
269#387—22no—
270#387—21no—
271#387—21no—
272#387—21no—
273#387—21no—
274#387—21no—
275#387—21no—
276#387—21no—
277#387—21no—
278#387—21no—
279#387—21no—
280#387—21no—
281#387—21no—
282#385—21no—
283#385—21no—
284#385—21no—
285#385—21no—
286#383—21no—
287#383—21no—
288#383—21no—
289#382—21no—
290#382—21no—
291#382C2311yescharacteristic
292#382C2311yescharacteristic
293#381—21no—
294#380C2311yescharacteristic
295#380C2311yescharacteristic
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⋊C4D411yescharacteristic
305C4×C4⋊C4D411yescharacteristic
306C4×C4⋊C4D411yescharacteristic
307C4×C4⋊C4D411yescharacteristic
308C4×C4⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
318C4×C22⋊C4—21no—
319C4×C22⋊C4—21no—
320C4×C22⋊C4—21no—
321C4×C22⋊C4—21no—
322C4×C22⋊C4—21no—
323#376—21no—
324#376—21no—
325#376—21no—
326C2×#95—21no—
327C2×#95—21no—
328C2×#95—21no—
329C2×#95—21no—
330C2×#95—21no—
331C2×#95—21no—
332C2×#95D411yescharacteristic
333C2×#95D411yescharacteristic
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#340C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351#336C2312yes—
352#336C2312yes—
353#336C2312yes—
354C22×Q8—24no—
355C22×Q8—21no—
356C22×Q8—21no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—22no—
361C22×Q8—42no—
362C22×Q8—44no—
363C22×Q8—44no—
364C22×Q8—82no—
365C22×Q8C2411yescharacteristic
366C22×Q8C2411yescharacteristic
367C22×Q8C2412yes—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4—21no—
372C23×C4C2×D411yescharacteristic
373C23×C4C2×D411yescharacteristic
374C23×C4C2×D411yescharacteristic
375C23×C4C2×D411yescharacteristic
376C23×C4C2×D411yescharacteristic
377C23×C4C2×D411yescharacteristic
378C23×C4C2411yescharacteristic
379C2×Q16—24no—
380C2×Q16—24no—
381C2×Q16—24no—
382C2×Q16—24no—
383C2×Q16—42no—
384C2×Q16—42no—
385C22×C8C2412yes—
386C22×C8C2412yes—
387C22×C8C2412yes—
388C22×C8C2412yes—
389C4⋊Q8—22no—
390C4⋊Q8—22no—
391C4⋊Q8—22no—
392C4⋊Q8—22no—
393C4⋊Q8—24no—
394C4⋊Q8—24no—
395C4⋊Q8—42no—
396C4⋊Q8—42no—
397C4⋊Q8—44no—
398C4⋊Q8—44no—
399#125—28no—
400C22⋊Q8—28no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8#4114yes—
404C22⋊Q8#4114yes—
405C4×Q8—28no—
406C4×Q8—22no—
407C4×Q8—22no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×Q8—24no—
411C4×Q8—24no—
412C4×Q8—42no—
413C4×Q8—42no—
414C4×Q8—42no—
415C4×Q8—42no—
416C4×Q8—42no—
417C4×Q8—42no—
418C4×Q8—44no—
419C4×Q8—44no—
420C4×Q8—44no—
421C4×Q8—44no—
422#117—28no—
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—21no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—44no—
456C2×C4⋊C4—44no—
457C2×C4⋊C4—82no—
458C2×C4⋊C4—82no—
459C2×C4⋊C4C2×D411yescharacteristic
460C2×C4⋊C4C2×D411yescharacteristic
461C2×C4⋊C4C2×D411yescharacteristic
462C2×C4⋊C4C2×D411yescharacteristic
463C2×C4⋊C4C2×D411yescharacteristic
464C2×C4⋊C4C2×D411yescharacteristic
465C2×C4⋊C4C2×D411yescharacteristic
466C2×C4⋊C4C2×D411yescharacteristic
467C2×C4⋊C4C2412yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2411yescharacteristic
470C2×C4⋊C4C2411yescharacteristic
471C2×C4⋊C4C2411yescharacteristic
472C2×C4⋊C4C2411yescharacteristic
473C2×C4⋊C4C2411yescharacteristic
474C2×C4⋊C4C2411yescharacteristic
475C2×C4⋊C4C2412yes—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—42no—
497C2×C42—42no—
498C2×C42—44no—
499C2×C42C2×D411yescharacteristic
500C2×C42C2×D411yescharacteristic
501C2×C42C2×D411yescharacteristic
502C2×C42C2×D411yescharacteristic
503C2×C42C2×D411yescharacteristic
504C2×C42C2×D411yescharacteristic
505C2×C42C2411yescharacteristic
506C2×C42C2411yescharacteristic
507C2×C42C2411yescharacteristic
508C2×C42C2411yescharacteristic
509C2×C42C2411yescharacteristic
510C2×C42C2411yescharacteristic
511#107—24no—
512#107—42no—
513#106—24no—
514#106—24no—
515#106—24no—
516#106—42no—
517C4⋊C8—42no—
518C4⋊C8—42no—
519#103—24no—
520#103—24no—
521#103—24no—
522#103—24no—
523#103—24no—
524#103—24no—
525#103—24no—
526#103—24no—
527#103—42no—
528#103—42no—
529#103—42no—
530#103—42no—
531C22⋊C8—22no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535#97—42no—
536C4×C8—42no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—21no—
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—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95C2×D411yescharacteristic
574#95C2×D411yescharacteristic
575#95C2×D411yescharacteristic
576#95C2×D411yescharacteristic
577#95C2×D411yescharacteristic
578#95C2×D411yescharacteristic
579#95C2×D411yescharacteristic
580#95C2×D411yescharacteristic
581C24C22×D411yescharacteristic
582C2×Q8—24no—
583C2×Q8—24no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—44no—
596C2×Q8—44no—
597C2×Q8—48no—
598C2×Q8—48no—
599C2×Q8—42no—
600C2×Q8—42no—
601C2×Q8—44no—
602C2×Q8—42no—
603C2×Q8—42no—
604C2×Q8—44no—
605C2×Q8—82no—
606C2×Q8—82no—
607C2×Q8—816no—
608C2×Q8C2×#4112yes—
609C2×Q8C2×#4112yes—
610C2×Q82−1+414yes—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4C22×D411yescharacteristic
656C22×C4C22×D411yescharacteristic
657C22×C4C22×D411yescharacteristic
658C22×C4C22×D411yescharacteristic
659C22×C4C22×D411yescharacteristic
660C22×C4C22×D411yescharacteristic
661C22×C4C22×D411yescharacteristic
662C22×C4C22×D411yescharacteristic
663C22×C4C22×D411yescharacteristic
664C22×C4C22×D411yescharacteristic
665C22×C4C22×D411yescharacteristic
666C22×C4C22×D411yescharacteristic
667C22×C4C22×D411yescharacteristic
668C22×C4C2×#4112yes—
669C22×C4C2×#4112yes—
670C22×C4C2511yescharacteristic
671Q16—48no—
672Q16—48no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—22no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—24no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—41no—
710C4⋊C4—41no—
711C4⋊C4—44no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—44no—
715C4⋊C4—42no—
716C4⋊C4—42no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—82no—
722C4⋊C4—82no—
723C4⋊C4—82no—
724C4⋊C4—82no—
725C4⋊C4—81no—
726C4⋊C4—81no—
727C4⋊C4—81no—
728C4⋊C4—81no—
729C4⋊C4#13714yes—
730C4⋊C4C2×#4112yes—
731C4⋊C4C2×#4112yes—
732C4⋊C4H(5,𝔽2)14yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C42—24no—
738C42—24no—
739C42—22no—
740C42—22no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—22no—
746C42—22no—
747C42—22no—
748C42—22no—
749C42—41no—
750C42—41no—
751C42—41no—
752C42—41no—
753C42—44no—
754C42—44no—
755C42—42no—
756C42—42no—
757C42—42no—
758C42—42no—
759C42—42no—
760C42—42no—
761C42—81no—
762C42—81no—
763C42—81no—
764C42—81no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23#52512yes—
770C23#57712yes—
771C23#57812yes—
772C23C23×D411yescharacteristic
773Q8—24no—
774Q8—24no—
775Q8—24no—
776Q8—24no—
777Q8—48no—
778Q8—48no—
779Q8—42no—
780Q8—42no—
781Q8—42no—
782Q8—42no—
783Q8—88no—
784Q8—88no—
785C2×C4—21no—
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—24no—
796C2×C4—24no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—48no—
832C2×C4—48no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—42no—
864C2×C4—82no—
865C2×C4—84no—
866C2×C4—84no—
867C2×C4#52512yes—
868C2×C4C2×#13712yes—
869C2×C4C2×#13712yes—
870C2×C4C2×#13712yes—
871C2×C4#57512yes—
872C2×C4C22×#4111yescharacteristic
873C2×C4C22×#4111yescharacteristic
874C2×C4C2×H(5,𝔽2)12yes—
875C2×C4C2×2−1+412yes—
876C8—42no—
877C8—42no—
878C8—42no—
879C8—42no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22#312114yes—
887C22C2×#52511yescharacteristic
888C22#348411yescharacteristic
889C22#348611yescharacteristic
890C22C22×#13711yescharacteristic
891C22C2×#57511yescharacteristic
892C22C2×#57711yescharacteristic
893C22C2×#57811yescharacteristic
894C4—22no—
895C4—22no—
896C4—22no—
897C4—22no—
898C4—22no—
899C4—44no—
900C4—42no—
901C4—42no—
902C4—41no—
903C4—41no—
904C4—41no—
905C4—42no—
906C4—42no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—44no—
911C4—41no—
912C4—41no—
913C4—82no—
914C4—81no—
915C4—81no—
916C4—81no—
917C4—82no—
918C4—81no—
919C4#352012yes—
920C4#352012yes—
921C2—24no—
922C2#3535711yescharacteristic
923C2C2×#312111yescharacteristic
924C2#6056211yescharacteristic
925C2#6160111yescharacteristic
926C2#6160211yescharacteristic
927C2#6183811yescharacteristic
928C2#6184211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
7. #27448C2semidirect
8. #27437C2semidirect
9. #27017C2semidirect
10. #27000C2semidirect
11. #26911C2semidirect
12. #26894C2semidirect
13. #26393C2semidirect
14. #26369C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24512
#342352
#281242
#276162
#275892
#274482
#274372
#270172
#270002
#269112
#268942
#263932
#263692
#243022
#243012
#240632
#239342
#220842
#220782
#219142
#214552
C4×#4512