Finite Group Databasebeta

← #6454272

Subgroups — #6454272

Order 512.

2518 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
1C2×#3103C211yesmaximal, characteristic, complemented
2C22×#431C211yesmaximal, characteristic, complemented
3#36624C211yesmaximal, characteristic
4C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
5#24838C212yesmaximal, complemented
6#24753C212yesmaximal, complemented
7#24703C212yesmaximal, complemented
8#24653C212yesmaximal, complemented
9#24603C212yesmaximal, complemented
10#24553C212yesmaximal, complemented
11#24503C212yesmaximal, complemented
12#24381C212yesmaximal, complemented
13#23700C214yesmaximal, complemented
14C4×#465C214yesmaximal, complemented
15#21386C211yesmaximal, characteristic, complemented
16#21359C211yesmaximal, characteristic, complemented
17#20734C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525—21no—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#3103—28no—
24C2×#481C2212yes—
25C2×#475C2212yescomplemented
26C2×#465C2214yes—
27C2×#460C2212yescomplemented
28C2×#448C2212yes—
29C2×C4×SD16C2214yescomplemented
30C2×#431—28no—
31C2×#431C2212yes—
32C2×#431C2212yes—
33C2×#431C2211yescharacteristic
34C2×#431C2212yes—
35C2×#431C2211yescharacteristic
36C22×C4⋊C8C2212yes—
37C22×C22⋊C8C2212yes—
38C22×C4×C8C2212yes—
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2856C2211yescharacteristic
42#2856C2211yescharacteristic
43#2854—21no—
44#2854C2212yes—
45#2850—21no—
46#2850—21no—
47#2847—21no—
48#2847C2212yes—
49C4×C22⋊Q8—21no—
50C4×C22⋊Q8—21no—
51C4×C22⋊Q8—21no—
52C4×C22⋊Q8—21no—
53C4×C22⋊Q8C2212yes—
54C4×C22⋊Q8C2212yes—
55C4×C22⋊Q8C2212yes—
56C4×C22⋊Q8C2212yes—
57C4×#121—21no—
58C4×#121—21no—
59C4×#121C2212yes—
60C4×#121C2212yes—
61#2297—21no—
62C2×#391C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#387—21no—
65C2×#385—21no—
66#2285C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×C4×C4⋊C4—21no—
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4—21no—
71#2088C2214yescomplemented
72#2077C2214yes—
73#2066C2214yescomplemented
74#2065C2214yescomplemented
75#2055C2214yescomplemented
76#2035C2214yes—
77#2034C2214yes—
78#2000C2214yes—
79#1988C2212yescomplemented
80#1982C2212yescomplemented
81#1968C2214yescomplemented
82#1948C2212yescomplemented
83#1948C2212yescomplemented
84#1941C2214yescomplemented
85#1934C2214yescomplemented
86#1933C2214yescomplemented
87#1893C2214yes—
88#1892C2214yes—
89#1874C2212yes—
90#1874C2212yes—
91#1853C2212yes—
92#1853C2212yes—
93#1824C2212yes—
94#1807C2214yes—
95#1803C2212yescomplemented
96#1803C2212yescomplemented
97#1787C2212yes—
98C4×#106C2214yescomplemented
99C4×#103C2214yescomplemented
100C4×#102C2214yescomplemented
101C22×#41—21no—
102C23×Q8C2311yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4C2311yescharacteristic
106C22×SD16C2314yes—
107C23×C8C2314yes—
108#532—24no—
109#532—24no—
110C2×C4⋊Q8C2311yescharacteristic
111C2×#127C2311yescharacteristic
112C2×#124—21no—
113#525—48no—
114C2×#123—22no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—21no—
119C2×C22⋊Q8—21no—
120C2×C22⋊Q8C2312yes—
121C2×C22⋊Q8C2312yes—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121—21no—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#121C2312yes—
130C2×#120—22no—
131C2×C4×Q8—21no—
132C2×C4×Q8—21no—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8C2312yes—
136C2×C4×Q8C2312yes—
137C2×C4×D4—22no—
138C2×C4×D4—22no—
139C2×C4×D4—21no—
140C2×C4×D4C2312yes—
141C2×#117—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C42—24no—
151C22×C42—24no—
152C22×C42—21no—
153C22×C42—21no—
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#481—28no—
167#475—28no—
168#465—216no—
169#460—28no—
170#448—28no—
171C4×SD16—216no—
172#431—24no—
173#431—28no—
174#431—28no—
175#431—28no—
176#431D418yescomplemented
177C2×#106C2314yes—
178C2×#106C2314yes—
179C2×#106C2314yes—
180C2×C4⋊C8—28no—
181C2×C4⋊C8C2314yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×C22⋊C8—28no—
191C2×C22⋊C8C2314yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C4×C8—28no—
195C2×C4×C8C2314yes—
196C2×C4×C8C2312yes—
197C2×C4×C8C2312yes—
198#391—21no—
199#391—21no—
200#391—21no—
201#391—21no—
202#391C2312yes—
203#391C2312yes—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390C2312yes—
209#390C2312yes—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389C2312yes—
215#389C2312yes—
216#389C2312yes—
217#389C2312yes—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#387—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#385—22no—
233#385—22no—
234#385—22no—
235#385—22no—
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#382—21no—
239#380—21no—
240#380—21no—
241#380—21no—
242#380—21no—
243#380—21no—
244#380C2312yes—
245#380C2312yes—
246#380C2312yes—
247#380C2312yes—
248#380C2312yes—
249C4×C4⋊C4—22no—
250C4×C4⋊C4—22no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4—22no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4C2312yes—
257C4×C4⋊C4C2312yes—
258C4×C4⋊C4C2312yes—
259C4×C22⋊C4—22no—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—22no—
263C4×C22⋊C4—22no—
264C4×C22⋊C4—22no—
265C2×#95—21no—
266C2×#95—21no—
267C2×#95—21no—
268C2×#95—21no—
269C2×#95—21no—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276C25C2×D411yescharacteristic
277C2×#41—44no—
278C2×#41—44no—
279C2×#41—44no—
280C22×Q8—24no—
281C22×Q8—21no—
282C22×Q8—21no—
283C22×Q8—22no—
284C22×Q8—22no—
285C22×Q8—42no—
286C22×Q8C2412yes—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4C2412yes—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—24no—
298C23×C4—22no—
299C23×C4—24no—
300C23×C4—22no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—22no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4SD1618yescomplemented
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C2×SD16—28no—
327C2×SD16—28no—
328C2×SD16—44no—
329C22×C8—28no—
330C22×C8—28no—
331C22×C8—44no—
332C22×C8C2414yes—
333C22×C8C2414yes—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336#127—22no—
337#127—22no—
338#124—44no—
339#123—48no—
340C22⋊Q8—28no—
341C22⋊Q8—28no—
342C22⋊Q8—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—44no—
346C22⋊Q8—44no—
347C22⋊Q8#4118yescomplemented
348#121—24no—
349#121—24no—
350#121—28no—
351#121—44no—
352#121—44no—
353#121—44no—
354#121—44no—
355#121—44no—
356#121—44no—
357#120—48no—
358C4×Q8—24no—
359C4×Q8—24no—
360C4×Q8—24no—
361C4×Q8—24no—
362C4×Q8—44no—
363C4×Q8—44no—
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—48no—
367C4×D4—48no—
368C4×D4—44no—
369#117—44no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2412yes—
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—44no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—44no—
438C2×C42—44no—
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D414yes—
452C2×C42#4114yes—
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457#106—28no—
458#106—28no—
459#106—44no—
460C4⋊C8—28no—
461C4⋊C8—24no—
462C4⋊C8C2×D418yes—
463#103—28no—
464#103—28no—
465#103—44no—
466#102—28no—
467#102—28no—
468#102—44no—
469C22⋊C8—24no—
470C22⋊C8—28no—
471C22⋊C8C2×D418yes—
472C4×C8—28no—
473C4×C8—24no—
474C4×C8C2×D418yes—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—41no—
497C24—41no—
498C24C2×SD1614yes—
499C24C22×D411yescharacteristic
500C24C22×D411yescharacteristic
501C24C22×D411yescharacteristic
502#41—816no—
503C2×Q8—24no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—48no—
510C2×Q8—48no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8C2×#4114yes—
517C2×D4—22no—
518C2×D4—24no—
519C2×D4—22no—
520C2×D4—24no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—232no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—416no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4#12114yes—
608C22×C4#12114yes—
609C22×C4C2×SD1614yes—
610C22×C4C2×SD1614yes—
611C22×C4C2×SD1614yes—
612C22×C4C2×SD1614yes—
613C22×C4C2×SD1614yes—
614C22×C4C2×SD1614yes—
615C22×C4#13514yes—
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C2×#4112yes—
629C22×C4C2×#4114yes—
630C22×C4C2511yescharacteristic
631SD16—416no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C2×C8—416no—
638C2×C8C22×D418yes—
639C4⋊C4—24no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—42no—
652C4⋊C4—44no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4C2×#4114yes—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—44no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C42—22no—
681C42—22no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—22no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—44no—
695C42—44no—
696C42—44no—
697C42—44no—
698C42—44no—
699C42#12114yes—
700C42#12114yes—
701C42C22×D412yes—
702C42C22×D412yes—
703C42C2×#4112yes—
704C42C2×#4112yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—28no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—28no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23C2×#12112yes—
734C23#52512yes—
735C23C22×SD1612yes—
736C23C22×SD1612yes—
737C23C22×SD1612yes—
738C23C2×#13512yes—
739C23#57512yes—
740C23C23×D411yescharacteristic
741Q8—24no—
742Q8—24no—
743Q8—48no—
744Q8—42no—
745Q8—42no—
746Q8—84no—
747D4—44no—
748D4—44no—
749D4—84no—
750D4—88no—
751D4—88no—
752D4—88no—
753D4—84no—
754C2×C4—28no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—28no—
763C2×C4—21no—
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—24no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—48no—
795C2×C4—48no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
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—84no—
818C2×C4—84no—
819C2×C4—88no—
820C2×C4#465116yescomplemented
821C2×C4C2×#12112yes—
822C2×C4C2×#12112yes—
823C2×C4C2×#12112yes—
824C2×C4C2×#12112yes—
825C2×C4C2×#12112yes—
826C2×C4#52512yes—
827C2×C4C22×SD1612yes—
828C2×C4C22×SD1612yes—
829C2×C4C22×SD1612yes—
830C2×C4C22×SD1612yes—
831C2×C4C2×#13512yes—
832C2×C4C2×#13512yes—
833C2×C4#57512yes—
834C2×C4C23×D411yescharacteristic
835C2×C4C22×#4112yes—
836C2×C4C22×#4111yescharacteristic
837C2×C4#58512yes—
838C8—28no—
839C8—44no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—416no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22C2×#46514yes—
868C22#310314yescomplemented
869C22C22×#12111yescharacteristic
870C22C2×#52511yescharacteristic
871C22#344911yescharacteristic
872C22C23×SD1611yescharacteristic
873C22C22×#13511yescharacteristic
874C22C2×#57511yescharacteristic
875C22C2×#57511yescharacteristic
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—22no—
883C4—41no—
884C4—44no—
885C4—41no—
886C4—44no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4C2×#46514yes—
893C4C2×#46514yes—
894C4D4×#4112yes—
895C4#347512yes—
896C2—24no—
897C2—24no—
898C2—42no—
899C2—162no—
900C2#3473711yescharacteristic
901C2C22×#46511yescharacteristic
902C2#6044411yescharacteristic
903C2C2×#310311yescharacteristic
904C2#6053611yescharacteristic
905C2#6094111yescharacteristic
906C2#6094211yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3103C2semidirect
2. C22×#431C2semidirect
4. C2×C4×C22⋊Q8C2semidirect
5. #24838C2semidirect
6. #24753C2semidirect
7. #24703C2semidirect
8. #24653C2semidirect
9. #24603C2semidirect
10. #24553C2semidirect
11. #24503C2semidirect
12. #24381C2semidirect
13. #23700C2semidirect
14. C4×#465C2semidirect
15. #21386C2semidirect
16. #21359C2semidirect
17. #20734C2semidirect
25. C2×#475C22semidirect
27. C2×#460C22semidirect
29. C2×C4×SD16C22semidirect
71. #2088C22semidirect
73. #2066C22semidirect
74. #2065C22semidirect
75. #2055C22semidirect
79. #1988C22semidirect
80. #1982C22semidirect
81. #1968C22semidirect
82. #1948C22semidirect
83. #1948C22semidirect
84. #1941C22semidirect
85. #1934C22semidirect
86. #1933C22semidirect
95. #1803C22semidirect
96. #1803C22semidirect
98. C4×#106C22semidirect
99. C4×#103C22semidirect
100. C4×#102C22semidirect
176. #431D4semidirect
307. C23×C4SD16semidirect
347. C22⋊Q8#41semidirect
820. C2×C4#465semidirect
868. C22#3103semidirect

Maximal subgroups

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

subgroupindex
C2×#31032
C22×#4312
#366242
C2×C4×C22⋊Q82
#248382
#247532
#247032
#246532
#246032
#245532
#245032
#243812
#237002
C4×#4652
#213862
#213592
#207342