Finite Group Databasebeta

← #6446237

Subgroups — #6446237

Order 512.

1616 conjugacy classes of subgroups.

The subgroup lattice has 929 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2584C211yesmaximal, characteristic
2Q8×#117C211yesmaximal, characteristic
3#26291C212yesmaximal, complemented
4#26290C212yesmaximal, complemented
5#26289C212yesmaximal, complemented
6#26288C212yesmaximal, complemented
7#26287C212yesmaximal, complemented
8#26286C212yesmaximal, complemented
9#26285C212yesmaximal, complemented
10#26284C212yesmaximal, complemented
11#23747C211yesmaximal, characteristic
12#23747C211yesmaximal, characteristic
13#23657C211yesmaximal, characteristic
14#23657C211yesmaximal, characteristic
15#21325C211yesmaximal, characteristic
16#21314C211yesmaximal, characteristic
17#21303C211yesmaximal, characteristic
18#21170C211yesmaximal, characteristic
19#21034C211yesmaximal, characteristic
20#21034C211yesmaximal, characteristic
21#21034C211yesmaximal, characteristic
22#21034C211yesmaximal, characteristic
23C4×#428C211yesmaximal, characteristic
24C22×#125C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C2×#428C2211yescharacteristic
27C2×#428C2211yescharacteristic
28C2×#428C2211yescharacteristic
29C2×#428C2211yescharacteristic
30C2×#423C2211yescharacteristic
31C2×C4×M16C2211yescharacteristic
32#2584—21no—
33#2584—21no—
34#2584—21no—
35#2584—21no—
36#2584C2212yes—
37#2584C2212yes—
38#2584C2212yes—
39#2584C2212yes—
40C2×#398—21no—
41C2×#395—21no—
42#2355C2211yescharacteristic
43#2355C2211yescharacteristic
44#2355C2211yescharacteristic
45#2355C2211yescharacteristic
46#2355C2211yescharacteristic
47#2355C2211yescharacteristic
48Q8×C4⋊C4C2211yescharacteristic
49Q8×C4⋊C4C2211yescharacteristic
50#2345—21no—
51#2345—21no—
52#2345—21no—
53Q8×C22⋊C4—21no—
54#2295—21no—
55#2295—21no—
56#2295—21no—
57C2×#389—21no—
58C2×#389—21no—
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#389C2211yescharacteristic
63#2285C2211yescharacteristic
64#2285C2211yescharacteristic
65#2285C2211yescharacteristic
66C42×Q8—21no—
67C4×#117C2211yescharacteristic
68C4×#117C2211yescharacteristic
69C4×#117C2211yescharacteristic
70C2×C4×C4⋊C4C2211yescharacteristic
71#2101C2212yes—
72#2101C2212yes—
73#2101C2212yes—
74#2101C2212yes—
75#2100C2212yes—
76#2100C2212yes—
77#2099C2212yes—
78#2099C2212yes—
79#2085C2212yes—
80#2085C2212yes—
81#2085C2212yes—
82#2085C2212yes—
83#2084C2212yes—
84#2084C2212yes—
85#2083C2212yes—
86#2083C2212yes—
87#1992C2212yes—
88#1992C2212yes—
89#1991C2212yes—
90#1991C2212yes—
91#1989C2212yes—
92#1989C2212yes—
93#1989C2212yes—
94#1989C2212yes—
95#1985C2212yes—
96#1985C2212yes—
97#1984C2212yes—
98#1984C2212yes—
99#1949C2212yes—
100#1949C2212yes—
101#1948C2212yes—
102#1947C2212yes—
103#1921C2212yes—
104#1921C2212yes—
105#1921C2212yes—
106#1921C2212yes—
107#1920C2212yes—
108#1920C2212yes—
109#1920C2212yes—
110#1920C2212yes—
111#1919C2212yes—
112#1919C2212yes—
113#1919C2212yes—
114#1919C2212yes—
115#1918C2212yes—
116#1918C2212yes—
117#1918C2212yes—
118#1918C2212yes—
119#1776C2212yes—
120#1776C2212yes—
121C4×#107C2212yes—
122C4×#106C2212yes—
123#1736C2211yescharacteristic
124#1736C2211yescharacteristic
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1736C2211yescharacteristic
128#1736C2211yescharacteristic
129#1736C2211yescharacteristic
130#1736C2211yescharacteristic
131#1736C2211yescharacteristic
132#1736C2211yescharacteristic
133#1736C2211yescharacteristic
134#1736C2211yescharacteristic
135#1728C2211yescharacteristic
136#1728C2211yescharacteristic
137#1728C2211yescharacteristic
138#1728C2211yescharacteristic
139C23×Q8D411yescharacteristic
140C22×M16C2311yescharacteristic
141C22×M16C2311yescharacteristic
142C22×M16C2311yescharacteristic
143C22×M16C2311yescharacteristic
144C2×#125—21no—
145C2×#125—21no—
146C2×#125—24no—
147C2×#125—24no—
148C2×#125C2312yes—
149C2×#125C2312yes—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8—24no—
153C2×C4×Q8—24no—
154C2×C4×Q8D411yescharacteristic
155C2×C4×Q8D411yescharacteristic
156C2×C4×Q8D411yescharacteristic
157C2×C4×Q8D411yescharacteristic
158C2×C4×Q8C2311yescharacteristic
159C2×C4×Q8C2311yescharacteristic
160C2×C4×Q8C2311yescharacteristic
161C2×C4×Q8C2311yescharacteristic
162C2×#117C2311yescharacteristic
163C2×#117C2311yescharacteristic
164C2×#117C2311yescharacteristic
165C2×#117C2311yescharacteristic
166C22×C4⋊C4—21no—
167C22×C4⋊C4—21no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4—21no—
170C22×C4⋊C4—21no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4D411yescharacteristic
173C22×C4⋊C4D411yescharacteristic
174C22×C4⋊C4D411yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C42—21no—
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182C22×C42C2311yescharacteristic
183#428—24no—
184#428—24no—
185#428—24no—
186#428Q818yescomplemented
187C2×#107C2312yes—
188C2×#107C2312yes—
189C2×#107C2312yes—
190C2×#107C2312yes—
191C2×#106C2312yes—
192C2×#106C2312yes—
193C2×#106C2312yes—
194C2×#106C2312yes—
195#423—24no—
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2312yes—
198C4×M16—24no—
199C2×#97C2312yes—
200C2×C4×C8C2312yes—
201#398—22no—
202#398—22no—
203#398—22no—
204#398—22no—
205#395—22no—
206#395—22no—
207#395—22no—
208#395—22no—
209#391—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#389—22no—
216#389—22no—
217#389—22no—
218#389—22no—
219#389—22no—
220#389—22no—
221#389—22no—
222#389—22no—
223#389—21no—
224#389—21no—
225#389—21no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389C2312yes—
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
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—21no—
257#384C2311yescharacteristic
258#384C2311yescharacteristic
259#384C2311yescharacteristic
260#384C2311yescharacteristic
261#384C2311yescharacteristic
262#384C2311yescharacteristic
263#382C2311yescharacteristic
264#382C2311yescharacteristic
265#382C2311yescharacteristic
266#382C2311yescharacteristic
267#382C2311yescharacteristic
268#382C2311yescharacteristic
269#380—21no—
270#380—21no—
271#380—21no—
272#380—21no—
273#380—21no—
274#380—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—21no—
289C4×C4⋊C4C2312yes—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2311yescharacteristic
300C4×C4⋊C4C2311yescharacteristic
301C4×C4⋊C4C2311yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C22⋊C4—21no—
304C4×C22⋊C4—21no—
305C4×C22⋊C4—21no—
306C4×C22⋊C4—21no—
307C4×C22⋊C4—21no—
308C4×C22⋊C4—21no—
309#376—21no—
310#376—21no—
311#376—21no—
312C2×#95—21no—
313C2×#95—21no—
314C2×#95—21no—
315C2×#95—21no—
316C2×#95—21no—
317C43—21no—
318C43—21no—
319C43—21no—
320#340C2312yes—
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
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#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351#336C2312yes—
352C22×Q8—24no—
353C22×Q8—42no—
354C22×Q8—42no—
355C22×Q8C2×D411yescharacteristic
356C22×Q8C2×D411yescharacteristic
357C22×Q8C2×D411yescharacteristic
358C22×Q8C2×D411yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4C2×D411yescharacteristic
364C23×C4C2×D411yescharacteristic
365C23×C4C2×D411yescharacteristic
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2411yescharacteristic
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—22no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—22no—
381C2×M16C2×Q814yes—
382C22×C8C2412yes—
383C22×C8C2412yes—
384C22×C8C2412yes—
385C22×C8C2412yes—
386#125—24no—
387#125—24no—
388#125—24no—
389#125—24no—
390#125—44no—
391#125—44no—
392C4×Q8—24no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—24no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—44no—
405C4×Q8—44no—
406#117—22no—
407#117—22no—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—22no—
412#117—22no—
413#117C2×Q814yes—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
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—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—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—44no—
452C2×C4⋊C4—44no—
453C2×C4⋊C4—44no—
454C2×C4⋊C4—44no—
455C2×C4⋊C4—82no—
456C2×C4⋊C4—82no—
457C2×C4⋊C4C2×D411yescharacteristic
458C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
468C2×C4⋊C4C2×D411yescharacteristic
469C2×C4⋊C4C2×Q814yes—
470C2×C4⋊C4#4114yes—
471C2×C4⋊C4C2412yes—
472C2×C4⋊C4C2412yes—
473C2×C4⋊C4C2411yescharacteristic
474C2×C4⋊C4C2411yescharacteristic
475C2×C4⋊C4C2411yescharacteristic
476C2×C4⋊C4C2411yescharacteristic
477C2×C4⋊C4C2411yescharacteristic
478C2×C4⋊C4C2411yescharacteristic
479C2×C4⋊C4C2412yes—
480C2×C4⋊C4C2411yescharacteristic
481C2×C4⋊C4C2411yescharacteristic
482C2×C4⋊C4C2412yes—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—82no—
510C2×C42C2×D411yescharacteristic
511C2×C42C2×D411yescharacteristic
512C2×C42C2×D411yescharacteristic
513C2×C42C2×D411yescharacteristic
514C2×C42C2×D411yescharacteristic
515C2×C42C2×D411yescharacteristic
516C2×C42#4114yes—
517C2×C42#4114yes—
518C2×C42C2411yescharacteristic
519C2×C42C2411yescharacteristic
520C2×C42C2411yescharacteristic
521C2×C42C2411yescharacteristic
522C2×C42C2411yescharacteristic
523C2×C42C2411yescharacteristic
524#107—24no—
525#107—24no—
526#107—24no—
527#107C2×Q818yescomplemented
528#106—24no—
529#106—24no—
530#106—24no—
531#106C2×Q818yescomplemented
532C4⋊C8—24no—
533C4⋊C8—24no—
534#97—24no—
535C4×C8—24no—
536#95—22no—
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—21no—
547#95—21no—
548#95—21no—
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—
570C24C22×D411yescharacteristic
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—41no—
580C2×Q8—41no—
581C2×Q8—41no—
582C2×Q8—41no—
583C2×Q8—416no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4#12314yes—
625C22×C4#12314yes—
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C22×D411yescharacteristic
631C22×C4C22×D411yescharacteristic
632C22×C4C22×D411yescharacteristic
633C22×C4C22×D411yescharacteristic
634C22×C4C22×D411yescharacteristic
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×Q812yes—
640C22×C4C2×#4112yes—
641C22×C4C2×#4112yes—
642C22×C4C2×#4112yes—
643C22×C42−1+412yes—
644C22×C42−1+412yes—
645C22×C4C2511yescharacteristic
646M16—28no—
647M16—44no—
648M16—44no—
649M16—44no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8C22×Q814yes—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—42no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4—42no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C4⋊C4—44no—
708C4⋊C4—44no—
709C4⋊C4—44no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—81no—
713C4⋊C4—81no—
714C4⋊C4—81no—
715C4⋊C4—81no—
716C4⋊C4—81no—
717C4⋊C4—81no—
718C4⋊C4—82no—
719C4⋊C4—82no—
720C4⋊C4—82no—
721C4⋊C4—82no—
722C4⋊C4C22×Q812yes—
723C4⋊C4C22×Q814yes—
724C4⋊C4C22×Q812yes—
725C4⋊C4C2×#4114yes—
726C22⋊C4—24no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C42—22no—
731C42—22no—
732C42—22no—
733C42—22no—
734C42—24no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42—42no—
744C42—42no—
745C42—42no—
746C42—42no—
747C42—42no—
748C42—42no—
749C42—42no—
750C42—42no—
751C42—42no—
752C42—81no—
753C42—81no—
754C42—81no—
755C42—81no—
756C42—81no—
757C42—81no—
758C42—82no—
759C42—82no—
760C42#12314yes—
761C42#12314yes—
762C42C2×#4112yes—
763C42C2×#4112yes—
764C42C2×#4112yes—
765C42C2×#4112yes—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23C2×#12312yes—
771C23#54812yes—
772C23D4×Q812yes—
773C23C23×D411yescharacteristic
774Q8—28no—
775Q8—44no—
776Q8—44no—
777Q8—44no—
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—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—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—48no—
817C2×C4—48no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—42no—
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—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
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—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—82no—
851C2×C4—82no—
852C2×C4—84no—
853C2×C4—84no—
854C2×C4C2×#12312yes—
855C2×C4C2×#12312yes—
856C2×C4C2×#12312yes—
857C2×C4C2×#12312yes—
858C2×C4C2×#12312yes—
859C2×C4#53314yes—
860C2×C4#54114yes—
861C2×C4#54812yes—
862C2×C4D4×Q812yes—
863C2×C4#55614yes—
864C2×C4#55714yes—
865C2×C4#57512yes—
866C2×C4#57512yes—
867C2×C4C23×Q811yescharacteristic
868C2×C4C22×#4111yescharacteristic
869C2×C4C22×#4111yescharacteristic
870C2×C4C22×#4111yescharacteristic
871C2×C4C2×2−1+411yescharacteristic
872C2×C4C2×2−1+411yescharacteristic
873C8—24no—
874C8—42no—
875C8—42no—
876C8—42no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22#244614yes—
884C22C22×#12311yescharacteristic
885C22C2×#54811yescharacteristic
886C22C2×D4×Q811yescharacteristic
887C22C2×#57511yescharacteristic
888C22C2×#57511yescharacteristic
889C22#358511yescharacteristic
890C22#358611yescharacteristic
891C4—22no—
892C4—22no—
893C4—22no—
894C4—22no—
895C4—22no—
896C4—22no—
897C4—41no—
898C4—41no—
899C4—41no—
900C4—41no—
901C4—41no—
902C4—41no—
903C4—44no—
904C4—42no—
905C4—44no—
906C4—42no—
907C4—82no—
908C4—82no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4—81no—
915C4#244614yes—
916C4C2×#53311yescharacteristic
917C4C2×#54111yescharacteristic
918C4C2×#55611yescharacteristic
919C4C2×#55711yescharacteristic
920C2—24no—
921C2C2×#244611yescharacteristic
922C2#6051111yescharacteristic
923C2#6052011yescharacteristic
924C2#6131811yescharacteristic
925C2#6132011yescharacteristic
926C2#6136711yescharacteristic
927C2#6136911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #26291C2semidirect
4. #26290C2semidirect
5. #26289C2semidirect
6. #26288C2semidirect
7. #26287C2semidirect
8. #26286C2semidirect
9. #26285C2semidirect
10. #26284C2semidirect
186. #428Q8semidirect
527. #107C2×Q8semidirect
531. #106C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25842
Q8×#1172
#262912
#262902
#262892
#262882
#262872
#262862
#262852
#262842
#237472
#236572
#213252
#213142
#213032
#211702
#210342
C4×#4282