Finite Group Databasebeta

← #72318871

Subgroups — #72318871

Order 1024.

1061 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#495861C211yesmaximal, characteristic
2C2×#12065C211yesmaximal, characteristic, complemented
3C22×#1368C211yesmaximal, characteristic, complemented
4#229109C211yesmaximal, characteristic
5#229108C211yesmaximal, characteristic, complemented
6#140749C211yesmaximal, characteristic, complemented
7#140353C211yesmaximal, characteristic, complemented
8#140121C211yesmaximal, characteristic, complemented
9#140120C211yesmaximal, characteristic, complemented
10#136613C211yesmaximal, characteristic
11#136611C211yesmaximal, characteristic, complemented
12#135909C211yesmaximal, characteristic, complemented
13#135908C211yesmaximal, characteristic, complemented
14#129165C211yesmaximal, characteristic, complemented
15#128255C211yesmaximal, characteristic, complemented
16C2×#2217C411yescharacteristic
17C2×#2175C2211yescharacteristic
18C22×#346C2211yescharacteristic
19#22985—21no—
20#22952—21no—
21C4×#467C2211yescharacteristic
22C4×#466C2211yescharacteristic
23C2×#1580C2211yescharacteristic
24C2×#1579C2211yescharacteristic
25C22×#334C2211yescharacteristic
26C22×#334C2211yescharacteristic
27#13238C411yescharacteristic
28#13167C411yescharacteristic
29#13150C411yescharacteristic
30#13149C411yescharacteristic
31#13060C411yescharacteristic
32#13059C411yescharacteristic
33#12834C411yescharacteristic
34#12674C2211yescharacteristic
35#12638C2211yescharacteristic
36#12637C2211yescharacteristic
37#12599C2211yescharacteristic
38#12065—24no—
39C2×#1368—24no—
40C2×#1368C2211yescharacteristic
41C2×#1368C2211yescharacteristic
42C2×#1368C2211yescharacteristic
43C2×#1368C2211yescharacteristic
44C2×#1334C2211yescharacteristic
45C2×#1334C2211yescharacteristic
46C2×#1333C2211yescharacteristic
47C2×#1333C2211yescharacteristic
48C2×#1313C2211yescharacteristic
49C2×#1313C2211yescharacteristic
50#9659C2211yescharacteristic
51#9658C2211yescharacteristic
52#9595C2211yescharacteristic
53#9595C2211yescharacteristic
54#9543—21no—
55#9542—21no—
56#8939—21no—
57#8937—21no—
58#8846—21no—
59#8845—21no—
60#8284C2211yescharacteristic
61#8284C2211yescharacteristic
62#8144C2211yescharacteristic
63#7178C2211yescharacteristic
64#7178C2211yescharacteristic
65#7178C2211yescharacteristic
66#7178C2211yescharacteristic
67#7137C2211yescharacteristic
68#7137C2211yescharacteristic
69C22×SD32C2×C411yescharacteristic
70C23×C16C2×C411yescharacteristic
71C23×C16C2×C411yescharacteristic
72C2×#467C2×C411yescharacteristic
73C2×#466C2×C411yescharacteristic
74C2×C8×Q8—21no—
75C2×C4×Q16C2311yescharacteristic
76C2×C4×D8C2311yescharacteristic
77C2×C8×D4—21no—
78C2×C8×D4—41no—
79C22×C4⋊C8—21no—
80C22×C4⋊C8—21no—
81C22×C4×C8C2311yescharacteristic
82C4×C22⋊Q8—21no—
83C4×#121—21no—
84#2217C818yescomplemented
85#2175—22no—
86#2175—22no—
87C2×#367C2×C411yescharacteristic
88C2×#366C2×C411yescharacteristic
89C2×#366C2×C411yescharacteristic
90C2×#358C2×C411yescharacteristic
91C2×#358C2×C411yescharacteristic
92C2×#358C2×C411yescharacteristic
93C2×#357C2×C411yescharacteristic
94C2×#357C2×C411yescharacteristic
95C2×#357C2×C411yescharacteristic
96C2×C22⋊C16—21no—
97C2×#346—22no—
98C2×#346—22no—
99C2×#346C2×C411yescharacteristic
100C2×#346C2×C411yescharacteristic
101C2×#346C2311yescharacteristic
102C2×#346C2311yescharacteristic
103C2×#346C2311yescharacteristic
104C2×#346C2311yescharacteristic
105#1984—21no—
106#1970C2×C411yescharacteristic
107#1969C2×C411yescharacteristic
108#1954—21no—
109#1942C2×C411yescharacteristic
110#1942C2×C411yescharacteristic
111#1939—21no—
112#1939—21no—
113#1939—41no—
114#1934—21no—
115#1933—21no—
116#1923—41no—
117#1916—41no—
118#1893—21no—
119#1892—21no—
120#1869—41no—
121#1850—41no—
122#1850—41no—
123#1808C2×C411yescharacteristic
124#1808C2×C411yescharacteristic
125C4×#107C2311yescharacteristic
126C4×#107C2311yescharacteristic
127C8×C4⋊C4—21no—
128C8×C4⋊C4—21no—
129C4×#103—21no—
130C4×#102—21no—
131C8×C22⋊C4—41no—
132C4×C22⋊C8D411yescharacteristic
133C4×C22⋊C8D411yescharacteristic
134#1580—22no—
135#1580—41no—
136#1579—22no—
137#1579—41no—
138C2×#334—22no—
139C2×#334—22no—
140C2×#334—21no—
141C2×#334—21no—
142C2×#334—41no—
143C2×#334—41no—
144C2×#334C2311yescharacteristic
145C2×#334C2311yescharacteristic
146C2×#334C2311yescharacteristic
147C2×#334C2311yescharacteristic
148C2×Q8⋊C8—21no—
149C2×Q8⋊C8—21no—
150C2×D4⋊C8—21no—
151C2×D4⋊C8—21no—
152C2×#322C2311yescharacteristic
153C2×#322C2311yescharacteristic
154#1380C2×C411yescharacteristic
155#1380C2×C411yescharacteristic
156#1380C2×C411yescharacteristic
157#1380C2×C411yescharacteristic
158#1380C2×C411yescharacteristic
159#1380C2×C411yescharacteristic
160#1374—21no—
161#1368—22no—
162#1368—22no—
163#1368—22no—
164#1368D414yescomplemented
165#1334—22no—
166#1334—41no—
167#1333—22no—
168#1333—41no—
169#1313—22no—
170#1313—22no—
171#1279—21no—
172#1279—21no—
173#1279—21no—
174#1279—21no—
175#1273D411yescharacteristic
176#1273D411yescharacteristic
177C22×Q16C22×C411yescharacteristic
178C22×D8C22×C411yescharacteristic
179C23×C8—41no—
180C23×C8—41no—
181C23×C8—41no—
182C23×C8C22×C411yescharacteristic
183C23×C8#4111yescharacteristic
184C2×C22⋊Q8—21no—
185C2×#121—21no—
186C2×C4×Q8—21no—
187C2×C4×D4—21no—
188C2×C4×D4—41no—
189C22×C42C2×D411yescharacteristic
190C2×SD32—22no—
191C2×SD32—22no—
192C2×SD32C2×C814yescomplemented
193C22×C16—22no—
194C22×C16—22no—
195C22×C16—22no—
196C22×C16—22no—
197C22×C16—21no—
198C22×C16—21no—
199C22×C16—41no—
200C22×C16C2×C814yescomplemented
201C22×C16C22×C411yescharacteristic
202C22×C16C22×C411yescharacteristic
203C22×C16C22×C411yescharacteristic
204C22×C16C22×C411yescharacteristic
205#467—22no—
206#467C2×C814yescomplemented
207#466—22no—
208#466C2×C814yes—
209C8×Q8—42no—
210C8×Q8—81no—
211C4×Q16—21no—
212C4×Q16—21no—
213C4×Q16—21no—
214C4×Q16—21no—
215C4×D8—21no—
216C4×D8—21no—
217C4×D8—21no—
218C4×D8—21no—
219C8×D4—42no—
220C8×D4—81no—
221C8×D4—84no—
222C2×#107C22×C411yescharacteristic
223C2×#107C22×C411yescharacteristic
224C2×#107C22×C411yescharacteristic
225C2×#107C22×C411yescharacteristic
226C2×#107C22×C411yescharacteristic
227C2×#107C22×C411yescharacteristic
228C2×C4⋊C8—21no—
229C2×C4⋊C8—21no—
230C2×C4⋊C8—21no—
231C2×C4⋊C8—21no—
232C2×C4⋊C8—42no—
233C2×C4⋊C8—42no—
234C2×C4⋊C8—41no—
235C2×C4⋊C8—41no—
236C2×C4⋊C8—41no—
237C2×C4⋊C8—41no—
238C2×C4⋊C8—41no—
239C2×C4⋊C8—81no—
240C2×C4⋊C8—81no—
241C2×#103—21no—
242C2×#103—21no—
243C2×#103—21no—
244C2×#102—21no—
245C2×#102—21no—
246C2×#102—21no—
247C2×C22⋊C8—21no—
248C2×C22⋊C8—21no—
249C2×C22⋊C8—41no—
250C2×C22⋊C8—41no—
251C2×C22⋊C8—41no—
252C2×C4×C8—21no—
253C2×C4×C8—21no—
254C2×C4×C8—21no—
255C2×C4×C8—21no—
256C2×C4×C8—41no—
257C2×C4×C8—41no—
258C2×C4×C8—41no—
259C2×C4×C8C22×C411yescharacteristic
260C2×C4×C8C2×D411yescharacteristic
261C2×C4×C8C2×D411yescharacteristic
262C2×C4×C8C2×D411yescharacteristic
263C2×C4×C8C2×D411yescharacteristic
264C2×C4×C8C2×D411yescharacteristic
265C2×C4×C8#4111yescharacteristic
266C2×C4×C8C2411yescharacteristic
267#391—21no—
268#390—21no—
269#389—21no—
270#389—21no—
271#388—41no—
272#387—41no—
273#386—41no—
274#385—41no—
275#380—21no—
276#380—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—41no—
280C4×C22⋊C4—41no—
281C4×C22⋊C4—41no—
282#367C2×C814yescomplemented
283#366—22no—
284#366—22no—
285#358—22no—
286#358—41no—
287#358C2×C814yescomplemented
288#357—22no—
289#357—41no—
290#357C2×C814yescomplemented
291C22⋊C16—42no—
292#346—22no—
293#346—22no—
294#346—21no—
295#346—21no—
296#346—21no—
297#346—21no—
298#346—21no—
299#346—21no—
300#346C2×D412yes—
301#346#4112yes—
302#340—21no—
303#340—21no—
304#340—21no—
305#340—21no—
306#340—21no—
307#340—21no—
308#336—21no—
309#336—21no—
310#336—41no—
311#336—41no—
312#336—41no—
313#336—41no—
314#336—41no—
315#336—41no—
316#334—21no—
317#334—21no—
318#334—21no—
319#334—21no—
320#334—21no—
321#334—21no—
322#334—42no—
323#334—42no—
324#334C2×D412yes—
325#334C2×D412yes—
326Q8⋊C8—42no—
327Q8⋊C8—81no—
328D4⋊C8—42no—
329D4⋊C8—81no—
330#322—21no—
331#322—21no—
332#322—21no—
333#322—21no—
334C22×Q8—21no—
335C22×D4—21no—
336C22×D4—41no—
337C23×C4—41no—
338C23×C4C4×D411yescharacteristic
339C23×C4AGL(1,ℤ/8)11yescharacteristic
340C23×C4AGL(1,ℤ/8)11yescharacteristic
341C2×Q16—21no—
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16C22×C812yes—
347C2×D8—21no—
348C2×D8—21no—
349C2×D8—21no—
350C2×D8—21no—
351C2×D8—21no—
352C2×D8C22×C812yes—
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—22no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—41no—
365C22×C8—41no—
366C22×C8—41no—
367C22×C8—41no—
368C22×C8—41no—
369C22×C8—82no—
370C22×C8—82no—
371C22×C8—82no—
372C22×C8—82no—
373C22×C8—82no—
374C22×C8—82no—
375C22×C8—161no—
376C22×C8—161no—
377C22×C8—161no—
378C22×C8C4×D411yescharacteristic
379C22×C8C4×D411yescharacteristic
380C22×C8C22×C812yes—
381C22×C8#13112yes—
382C22×C8C23×C411yescharacteristic
383C22×C8C2×#4111yescharacteristic
384C22⋊Q8—24no—
385C22⋊Q8—42no—
386#121—24no—
387#121—42no—
388C4×Q8—41no—
389C4×Q8—41no—
390C4×Q8—41no—
391C4×Q8—41no—
392C4×D4—41no—
393C4×D4—41no—
394C4×D4—41no—
395C4×D4—41no—
396C4×D4—82no—
397C4×D4—82no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—41no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4—41no—
407C2×C4⋊C4—41no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—41no—
411C2×C22⋊C4—41no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4—41no—
414C2×C22⋊C4—41no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—41no—
420C2×C42—41no—
421C2×C42—41no—
422C2×C42C4×D411yescharacteristic
423C2×C42AGL(1,ℤ/8)11yescharacteristic
424C2×C42AGL(1,ℤ/8)11yescharacteristic
425C2×C42C22×D411yescharacteristic
426SD32—28no—
427C2×C16—21no—
428C2×C16—21no—
429C2×C16—21no—
430C2×C16—21no—
431C2×C16—28no—
432C2×C16—21no—
433C2×C16—21no—
434C2×C16—21no—
435C2×C16—44no—
436C2×C16—41no—
437C2×C16—41no—
438C2×C16—41no—
439C2×C16—41no—
440C2×C16—41no—
441C2×C16—41no—
442C2×C16C4×D412yes—
443C2×C16C4×D412yes—
444C2×C16C22×C812yes—
445C2×C16C22×C812yes—
446C2×C16#13112yes—
447#107—21no—
448#107—21no—
449#107—21no—
450#107—21no—
451#107—21no—
452#107—21no—
453#107—21no—
454#107—21no—
455#107—21no—
456#107—21no—
457#107C22×C812yes—
458#107C22×C812yes—
459C4⋊C8—22no—
460C4⋊C8—22no—
461C4⋊C8—41no—
462C4⋊C8—41no—
463C4⋊C8—41no—
464C4⋊C8—41no—
465C4⋊C8—41no—
466C4⋊C8—41no—
467C4⋊C8—82no—
468C4⋊C8—82no—
469C4⋊C8—82no—
470C4⋊C8—82no—
471C4⋊C8—161no—
472#103—24no—
473#103—41no—
474#103—41no—
475#103—81no—
476#102—24no—
477#102—41no—
478#102—41no—
479#102—81no—
480C22⋊C8—42no—
481C22⋊C8—42no—
482C22⋊C8—82no—
483C22⋊C8—82no—
484C22⋊C8—161no—
485C4×C8—21no—
486C4×C8—21no—
487C4×C8—21no—
488C4×C8—21no—
489C4×C8—21no—
490C4×C8—21no—
491C4×C8—21no—
492C4×C8—21no—
493C4×C8—21no—
494C4×C8—21no—
495C4×C8—21no—
496C4×C8—21no—
497C4×C8—21no—
498C4×C8—21no—
499C4×C8—82no—
500C4×C8—82no—
501C4×C8—161no—
502C4×C8C22×D411yescharacteristic
503C4×C8C2×#4111yescharacteristic
504C4×C8H(5,𝔽2)11yescharacteristic
505C4×C82−1+411yescharacteristic
506#95—41no—
507#95—41no—
508#95—41no—
509#95—41no—
510#95—41no—
511#95—41no—
512#95—41no—
513#95—41no—
514C24—41no—
515C24#44211yescharacteristic
516C2×Q8—22no—
517C2×Q8—41no—
518C2×Q8—41no—
519C2×Q8—41no—
520C2×Q8—41no—
521C2×Q8—41no—
522C2×D4—22no—
523C2×D4—44no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—82no—
530C2×D4—82no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4C8×D412yes—
557C22×C4#44211yescharacteristic
558C22×C4#44211yescharacteristic
559C22×C4#44211yescharacteristic
560C22×C4#44412yes—
561C22×C4C2×C4×D411yescharacteristic
562C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
563C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
564Q16—22no—
565Q16—22no—
566Q16—41no—
567Q16—41no—
568D8—22no—
569D8—22no—
570D8—41no—
571D8—41no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—42no—
584C2×C8—42no—
585C2×C8—41no—
586C2×C8—41no—
587C2×C8—41no—
588C2×C8—41no—
589C2×C8—41no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8—41no—
595C2×C8—41no—
596C2×C8—41no—
597C2×C8—42no—
598C2×C8—42no—
599C2×C8—81no—
600C2×C8—81no—
601C2×C8—81no—
602C2×C8—81no—
603C2×C8—81no—
604C2×C8—81no—
605C2×C8—81no—
606C2×C8—81no—
607C2×C8—81no—
608C2×C8—81no—
609C2×C8—164no—
610C2×C8—164no—
611C2×C8—164no—
612C2×C8C8×D412yes—
613C2×C8C2×C4×D411yescharacteristic
614C2×C8#52011yescharacteristic
615C2×C8#54811yescharacteristic
616C2×C8#55311yescharacteristic
617C2×C8C23×C811yescharacteristic
618C2×C8C2×#13111yescharacteristic
619C2×C8C2×#13111yescharacteristic
620C2×C8#56811yescharacteristic
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—44no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—41no—
629C4⋊C4—41no—
630C4⋊C4—41no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—82no—
635C4⋊C4—81no—
636C4⋊C4—81no—
637C4⋊C4—161no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—82no—
641C22⋊C4—82no—
642C22⋊C4—82no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—161no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—81no—
653C42—81no—
654C42—81no—
655C42—81no—
656C42—81no—
657C42—81no—
658C42D4211yescharacteristic
659C42#54711yescharacteristic
660C42#57711yescharacteristic
661C42#57711yescharacteristic
662C16—22no—
663C16—22no—
664C16—41no—
665C16—81no—
666C16—81no—
667C16C8×D414yescomplemented
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—42no—
673C23—81no—
674C23—81no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—81no—
679C23#158012yes—
680C23#218012yes—
681C23AGL(1,ℤ/16)12yes—
682C23C2×#44211yescharacteristic
683Q8—42no—
684Q8—42no—
685Q8—81no—
686Q8—81no—
687D4—42no—
688D4—42no—
689D4—88no—
690D4—81no—
691D4—81no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—161no—
734C2×C4—161no—
735C2×C4—161no—
736C2×C4—161no—
737C2×C4#158012yes—
738C2×C4#236111yescharacteristic
739C2×C4C2×C8×D411yescharacteristic
740C2×C4#293511yescharacteristic
741C2×C4#295211yescharacteristic
742C2×C4C2×#44411yescharacteristic
743C2×C4#295711yescharacteristic
744C2×C4#326511yescharacteristic
745C2×C4#326511yescharacteristic
746C2×C4#334511yescharacteristic
747C2×C4#334511yescharacteristic
748C8—22no—
749C8—21no—
750C8—21no—
751C8—41no—
752C8—81no—
753C8—81no—
754C8—81no—
755C8—81no—
756C8—82no—
757C8—82no—
758C8—161no—
759C8—161no—
760C8C2×C8×D411yescharacteristic
761C8#293311yescharacteristic
762C8#298811yescharacteristic
763C8#299411yescharacteristic
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—161no—
774C22—161no—
775C22—161no—
776C22—161no—
777C22#1206514yescomplemented
778C22C2×#158011yescharacteristic
779C22#1807311yescharacteristic
780C22#2302911yescharacteristic
781C22C2×#218011yescharacteristic
782C22C2×AGL(1,ℤ/16)11yescharacteristic
783C22#3346911yescharacteristic
784C22#3346911yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—22no—
790C4—41no—
791C4—41no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—161no—
796C4—161no—
797C4—161no—
798C4—161no—
799C4#1785811yescharacteristic
800C4#1809311yescharacteristic
801C4#2298511yescharacteristic
802C4#2301911yescharacteristic
803C2—24no—
804C2—162no—
805C2#22910911yescharacteristic
806C2C2×#1206511yescharacteristic
807C2#48359711yescharacteristic
808C2#48413911yescharacteristic
809C2#48414011yescharacteristic
810C2#49837511yescharacteristic
811C2#49837611yescharacteristic
subgroupG/H
center, socleC23C2×#442
commutatorC2×C8C23×C8
Frattini, cosocleC2×C4×C8C24
prime radicalC2×#466C2×C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ #8144 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#12065C2semidirect
3. C22×#1368C2semidirect
5. #229108C2semidirect
6. #140749C2semidirect
7. #140353C2semidirect
8. #140121C2semidirect
9. #140120C2semidirect
11. #136611C2semidirect
12. #135909C2semidirect
13. #135908C2semidirect
14. #129165C2semidirect
15. #128255C2semidirect
84. #2217C8semidirect
164. #1368D4semidirect
192. C2×SD32C2×C8semidirect
200. C22×C16C2×C8semidirect
206. #467C2×C8semidirect
282. #367C2×C8semidirect
287. #358C2×C8semidirect
290. #357C2×C8semidirect
667. C16C8×D4semidirect
777. C22#12065semidirect

Maximal subgroups

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

subgroupindex
#4958612
C2×#120652
C22×#13682
#2291092
#2291082
#1407492
#1403532
#1401212
#1401202
#1366132
#1366112
#1359092
#1359082
#1291652
#1282552