Finite Group Databasebeta

← #6679725

Subgroups — #6679725

Order 512.

1674 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39351C211yesmaximal, characteristic
2Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
3#32903C211yesmaximal, characteristic
4#31804C212yesmaximal, complemented
5#31740C212yesmaximal, complemented
6#31520C212yesmaximal, complemented
7#31352C212yesmaximal, complemented
8#29938C211yesmaximal, characteristic, complemented
9#29843C211yesmaximal, characteristic
10#27815C211yesmaximal, characteristic, complemented
11#27554C212yesmaximal, complemented
12#27226C212yesmaximal, complemented
13#26042C211yesmaximal, characteristic, complemented
14#25932C211yesmaximal, characteristic, complemented
15#25322C211yesmaximal, characteristic, complemented
16#25295C211yesmaximal, characteristic, complemented
17#25060C211yesmaximal, characteristic, complemented
18#24898C212yesmaximal, complemented
19#24813C212yesmaximal, complemented
20#22997C211yesmaximal, characteristic, complemented
21Q8×#103C211yesmaximal, characteristic, complemented
22#22098C211yesmaximal, characteristic, complemented
23#20734C211yesmaximal, characteristic, complemented
24C2×Q82C2211yescharacteristic
25C2×#542—21no—
26C22×C4×Q8C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#475C2212yes—
29C2×#460C2211yescharacteristic
30C2×#460C2211yescharacteristic
31C2×#448C2212yes—
32C2×C8×Q8C2211yescharacteristic
33C2×C4×SD16C2212yes—
34C2×#431C2211yescharacteristic
35#2857—21no—
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2723—22no—
39#2672—22no—
40#2624—21no—
41#2582—21no—
42#2582C2211yescharacteristic
43#2567—21no—
44#2567C2211yescharacteristic
45#2551C2211yescharacteristic
46#2548C2211yescharacteristic
47#2542C2212yes—
48#2512C2212yes—
49#2491C2212yes—
50#2452—21no—
51#2451—22no—
52#2451C2212yes—
53#2448—21no—
54#2440—22no—
55#2440C2212yes—
56#2422C2212yes—
57#2366C2211yescharacteristic
58Q8×C4⋊C4C2211yescharacteristic
59Q8×C4⋊C4C2212yes—
60Q8×C4⋊C4C2211yescharacteristic
61Q8×C22⋊C4C2212yes—
62C4×C22⋊Q8—21no—
63C4×C22⋊Q8C2211yescharacteristic
64#2285C2211yescharacteristic
65#2100C2212yes—
66#2099C2212yes—
67#2096C2212yes—
68#2088C2212yes—
69#2084C2212yes—
70#2084C2212yes—
71#2077C2212yes—
72#2077C2212yes—
73#2071C2212yes—
74#2065C2212yes—
75#2065C2212yes—
76#2065C2212yes—
77#2058C2212yes—
78#2055C2212yes—
79#2055C2212yes—
80#2034C2212yes—
81#2034C2212yes—
82#2024C2212yes—
83#2023C2212yes—
84#2023C2212yes—
85#1990C2212yes—
86#1990C2211yescharacteristic
87#1990C2212yes—
88#1987C2212yes—
89#1987C2211yescharacteristic
90#1987C2211yescharacteristic
91#1984C2211yescharacteristic
92#1968C2212yes—
93#1957C2211yescharacteristic
94#1948C2211yescharacteristic
95#1948C2211yescharacteristic
96#1939C2212yes—
97#1939C2211yescharacteristic
98#1934C2212yes—
99#1934C2212yes—
100#1933C2212yes—
101#1927C2212yes—
102#1923C2212yes—
103#1923C2212yes—
104#1920C2212yes—
105#1916C2212yes—
106#1880C2212yes—
107#1880C2212yes—
108#1880C2212yes—
109#1880C2212yes—
110#1880C2212yes—
111#1877C2212yes—
112#1874C2212yes—
113#1865C2212yes—
114#1864C2212yes—
115#1844C2211yescharacteristic
116#1824C2211yescharacteristic
117#1824C2211yescharacteristic
118#1803C2211yescharacteristic
119#1803C2211yescharacteristic
120#1803C2212yes—
121#1803C2211yescharacteristic
122#1803C2211yescharacteristic
123#1803C2211yescharacteristic
124#1803C2211yescharacteristic
125#1802C2212yes—
126#1797C2211yescharacteristic
127#1787C2211yescharacteristic
128#1787C2211yescharacteristic
129C8×C4⋊C4C2211yescharacteristic
130C4×#103C2211yescharacteristic
131C4×#103C2212yes—
132C4×#103C2211yescharacteristic
133C4×#103C2211yescharacteristic
134C4×#103C2211yescharacteristic
135C23×Q8C2311yescharacteristic
136C22×SD16C2312yes—
137C22×SD16C2312yes—
138Q82—24no—
139Q82—42no—
140#542—48no—
141C2×C4⋊Q8—21no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—22no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2312yes—
146C2×C4⋊Q8C2312yes—
147C2×#127C2311yescharacteristic
148C2×#126—22no—
149C2×#124—21no—
150C2×#124—22no—
151C2×#123—22no—
152C2×C22⋊Q8—21no—
153C2×C22⋊Q8—22no—
154C2×C22⋊Q8—22no—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8D411yescharacteristic
157C2×#121—21no—
158C2×#121—21no—
159C2×#121C2312yes—
160C2×C4×Q8—21no—
161C2×C4×Q8—21no—
162C2×C4×Q8—21no—
163C2×C4×Q8—21no—
164C2×C4×Q8—24no—
165C2×C4×Q8—42no—
166C2×C4×Q8C2311yescharacteristic
167C2×C4×Q8C2312yes—
168C2×C4×Q8C2311yescharacteristic
169C2×C4×Q8C2311yescharacteristic
170C2×C4×Q8C2312yes—
171C2×C4×Q8C2311yescharacteristic
172C2×C4×Q8C2311yescharacteristic
173C2×C4×D4—21no—
174C2×C4×D4C2312yes—
175C2×#117—21no—
176C22×C4⋊C4—21no—
177C22×C4⋊C4C2311yescharacteristic
178C22×C42—21no—
179C22×C42C2311yescharacteristic
180#486—42no—
181#475—44no—
182#460—24no—
183#460—42no—
184#448—44no—
185C8×Q8—42no—
186C4×SD16—44no—
187#431—42no—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×C4⋊C8C2311yescharacteristic
193C2×C4⋊C8C2311yescharacteristic
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×#103C2311yescharacteristic
199C2×#103C2312yes—
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2311yescharacteristic
204C2×#103C2311yescharacteristic
205C2×#103C2311yescharacteristic
206C2×#103C2312yes—
207C2×#103C2311yescharacteristic
208C2×#102C2312yes—
209C2×#102C2312yes—
210C2×#102C2312yes—
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2311yescharacteristic
216C2×C22⋊C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2312yes—
220C2×C4×C8C2312yes—
221#399—22no—
222#399—22no—
223#398—22no—
224#398—22no—
225#398—22no—
226#397—22no—
227#397—22no—
228#396—22no—
229#395—22no—
230#395—22no—
231#395—22no—
232#395—22no—
233#394—22no—
234#394—22no—
235#394—22no—
236#393—22no—
237#391—21no—
238#391—21no—
239#391—22no—
240#391—22no—
241#391—22no—
242#391D411yescharacteristic
243#391C2312yes—
244#391C2312yes—
245#390—21no—
246#390—21no—
247#390—21no—
248#390—21no—
249#390C2312yes—
250#390C2312yes—
251#390C2312yes—
252#390C2312yes—
253#389—21no—
254#389—21no—
255#389—21no—
256#389—21no—
257#389—22no—
258#389—21no—
259#389—21no—
260#389—22no—
261#389—22no—
262#389—22no—
263#389D411yescharacteristic
264#389C2312yes—
265#389C2312yes—
266#389C2312yes—
267#389C2312yes—
268#388—22no—
269#388—22no—
270#387—22no—
271#387D412yes—
272#386—22no—
273#385—22no—
274#385—22no—
275#385D412yes—
276#384—22no—
277#384—21no—
278#384C2312yes—
279#384C2311yescharacteristic
280#384C2311yescharacteristic
281#384C2311yescharacteristic
282#384C2312yes—
283#384C2311yescharacteristic
284#382—21no—
285#380—21no—
286#380—21no—
287#380—22no—
288#380D411yescharacteristic
289#380C2311yescharacteristic
290#380C2311yescharacteristic
291#380C2312yes—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—22no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2312yes—
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2312yes—
300C4×C22⋊C4—22no—
301C4×C22⋊C4C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2311yescharacteristic
305#340C2312yes—
306#340C2311yescharacteristic
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2311yescharacteristic
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2312yes—
323#336C2312yes—
324#336C2312yes—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—21no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—21no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—41no—
334C22×Q8—41no—
335C22×Q8C2×D411yescharacteristic
336C22×Q8C2411yescharacteristic
337C22×Q8C2411yescharacteristic
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4C2412yes—
342C23×C4—21no—
343C23×C4—21no—
344C23×C4—22no—
345C23×C4C2×D411yescharacteristic
346C23×C4C2×D411yescharacteristic
347C23×C4C2411yescharacteristic
348C2×SD16—24no—
349C2×SD16—24no—
350C2×SD16—24no—
351C2×SD16—24no—
352C2×SD16—42no—
353C2×SD16—42no—
354C22×C8C2412yes—
355C22×C8C2412yes—
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C4⋊Q8—24no—
361C4⋊Q8—22no—
362C4⋊Q8—22no—
363C4⋊Q8—42no—
364C4⋊Q8—42no—
365C4⋊Q8—42no—
366C4⋊Q8—44no—
367C4⋊Q8—48no—
368C4⋊Q8—44no—
369#127—22no—
370#127—22no—
371#126—48no—
372#124—44no—
373#124—48no—
374#123—48no—
375C22⋊Q8—48no—
376C22⋊Q8—84no—
377C22⋊Q8—82no—
378C22⋊Q8—84no—
379C22⋊Q8SD1618yescomplemented
380#121—44no—
381#121—42no—
382#121—42no—
383#121—82no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—24no—
389C4×Q8—24no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—44no—
394C4×Q8—41no—
395C4×Q8—41no—
396C4×Q8—42no—
397C4×Q8—42no—
398C4×Q8—44no—
399C4×Q8—44no—
400C4×Q8—44no—
401C4×Q8#4114yes—
402C4×D4—42no—
403C4×D4—42no—
404C4×D4—44no—
405#117—44no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
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—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—44no—
435C2×C4⋊C4C2×D411yescharacteristic
436C2×C4⋊C4C2×D412yes—
437C2×C4⋊C4C2×D411yescharacteristic
438C2×C4⋊C4C2×D412yes—
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D412yes—
441C2×C4⋊C4C2411yescharacteristic
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4C2×D412yes—
464C2×C22⋊C4C2×D412yes—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—22no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—44no—
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2412yes—
480C2×C42C2412yes—
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483#106—42no—
484#106—42no—
485#106—42no—
486#106—42no—
487C4⋊C8—22no—
488C4⋊C8—22no—
489C4⋊C8—41no—
490C4⋊C8—41no—
491C4⋊C8—42no—
492C4⋊C8—42no—
493#103—22no—
494#103—24no—
495#103—22no—
496#103—22no—
497#103—22no—
498#103—22no—
499#103—22no—
500#103—41no—
501#103—41no—
502#103—42no—
503#102—24no—
504#102—42no—
505#102—42no—
506#102—42no—
507#102—42no—
508#102—42no—
509C22⋊C8—41no—
510C22⋊C8—41no—
511C22⋊C8—42no—
512C4×C8—22no—
513C4×C8—22no—
514C4×C8—42no—
515C4×C8—42no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—22no—
523#95—21no—
524#95—21no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95C2×D412yes—
531#95C2×D412yes—
532#95C2×D412yes—
533#95C2×D412yes—
534#95C2×D412yes—
535C24—22no—
536C24C22×D411yescharacteristic
537C2×Q8—24no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—42no—
549C2×Q8—42no—
550C2×Q8—44no—
551C2×Q8—44no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—42no—
556C2×Q8—44no—
557C2×Q8—82no—
558C2×Q8—81no—
559C2×Q8—82no—
560C2×Q8—82no—
561C2×Q8—81no—
562C2×Q8—82no—
563C2×Q8C2×SD1614yes—
564C2×Q8C2×#4112yes—
565C2×Q8H(5,𝔽2)12yes—
566C2×Q82−1+412yes—
567C2×Q82−1+412yes—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4—82no—
582C2×D4—82no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—44no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—81no—
614C22×C4C2×SD1614yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C2511yescharacteristic
625SD16—48no—
626SD16—84no—
627C2×C8—22no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—21no—
644C2×C8—21no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4—82no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—82no—
692C4⋊C4C2×SD1614yes—
693C4⋊C4C2×SD1618yes—
694C4⋊C4C2×#4112yes—
695C22⋊C4—42no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—82no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C22⋊C4C2×SD1618yes—
710C42—22no—
711C42—22no—
712C42—24no—
713C42—21no—
714C42—22no—
715C42—22no—
716C42—22no—
717C42—21no—
718C42—22no—
719C42—42no—
720C42—42no—
721C42—44no—
722C42—44no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—44no—
727C42C2×#4112yes—
728C42H(5,𝔽2)12yes—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23C22×SD1612yes—
743C23C23×D411yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—22no—
747Q8—28no—
748Q8—22no—
749Q8—22no—
750Q8—48no—
751Q8—41no—
752Q8—41no—
753Q8—162no—
754Q8—164no—
755Q8—164no—
756Q8#54214yescomplemented
757D4—42no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—84no—
762D4—162no—
763D4—164no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—28no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—82no—
824C2×C4—84no—
825C2×C4—164no—
826C2×C4#54612yes—
827C2×C4#54612yes—
828C2×C4C22×SD1614yes—
829C2×C4C22×SD1612yes—
830C2×C4C22×SD1614yes—
831C2×C4C22×SD1612yes—
832C2×C4#57812yes—
833C2×C4C22×#4111yescharacteristic
834C2×C4C2×H(5,𝔽2)11yescharacteristic
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4C2×2−1+411yescharacteristic
837C2×C4C2×2−1+411yescharacteristic
838C2×C4#58511yescharacteristic
839C8—42no—
840C8—41no—
841C8—41no—
842C8—42no—
843C8—41no—
844C8—41no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22C2×#54611yescharacteristic
860C22#348611yescharacteristic
861C22#348811yescharacteristic
862C22C23×SD1611yescharacteristic
863C22C2×#57811yescharacteristic
864C22#358511yescharacteristic
865C22#358511yescharacteristic
866C4—24no—
867C4—22no—
868C4—24no—
869C4—22no—
870C4—24no—
871C4—41no—
872C4—42no—
873C4—42no—
874C4—41no—
875C4—42no—
876C4—42no—
877C4—82no—
878C4—81no—
879C4—81no—
880C4—81no—
881C4—82no—
882C4—81no—
883C4—82no—
884C4—81no—
885C4#329814yes—
886C4C2×#54211yescharacteristic
887C4#349511yescharacteristic
888C4#353611yescharacteristic
889C4#354111yescharacteristic
890C2—42no—
891C2—162no—
892C2#3766511yescharacteristic
893C2C2×#329811yescharacteristic
894C2#6117911yescharacteristic
895C2#6182011yescharacteristic
896C2#6185411yescharacteristic
897C2#6195111yescharacteristic
898C2#6204611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2856C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. Q8×C22⋊Q8C2semidirect
4. #31804C2semidirect
5. #31740C2semidirect
6. #31520C2semidirect
7. #31352C2semidirect
8. #29938C2semidirect
10. #27815C2semidirect
11. #27554C2semidirect
12. #27226C2semidirect
13. #26042C2semidirect
14. #25932C2semidirect
15. #25322C2semidirect
16. #25295C2semidirect
17. #25060C2semidirect
18. #24898C2semidirect
19. #24813C2semidirect
20. #22997C2semidirect
21. Q8×#103C2semidirect
22. #22098C2semidirect
23. #20734C2semidirect
379. C22⋊Q8SD16semidirect
756. Q8#542semidirect

Maximal subgroups

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

subgroupindex
#393512
Q8×C22⋊Q82
#329032
#318042
#317402
#315202
#313522
#299382
#298432
#278152
#275542
#272262
#260422
#259322
#253222
#252952
#250602
#248982
#248132
#229972
Q8×#1032
#220982
#207342