Finite Group Databasebeta

← #25140401

Subgroups — #25140401

Order 11008.

1204 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583033C211yesmaximal, characteristic
2C2×#14582979C211yesmaximal, characteristic, complemented
3#19138089C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic43C211yesmaximal, characteristic, complemented
5#19136118C211yesmaximal, characteristic, complemented
6#19136026C211yesmaximal, characteristic, complemented
7#19135904C211yesmaximal, characteristic, complemented
8#19135785C211yesmaximal, characteristic, complemented
9#19135280C211yesmaximal, characteristic, complemented
10#19135204C211yesmaximal, characteristic, complemented
11#19134941C211yesmaximal, characteristic, complemented
12#19134940C211yesmaximal, characteristic, complemented
13#19134858C211yesmaximal, characteristic, complemented
14#19134603C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic, complemented
22C22×C22⋊Dic43—21no—
23#14583033—24no—
24#14582979—24no—
25C2×#13063258C2211yescharacteristic, complemented
26C2×#13063257C2211yescharacteristic, complemented
27C2×Dic43⋊C8C2211yescharacteristic, complemented
28C2×#13063247C2211yescharacteristic, complemented
29C2×#13063247C2211yescharacteristic, complemented
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic, complemented
34#14582826—21no—
35#14582815—21no—
36#14582802C2211yescharacteristic
37#14582802C2211yescharacteristic
38#14582800C2211yescharacteristic, complemented
39#14582798C2211yescharacteristic, complemented
40#14582779—21no—
41#14582779—21no—
42#14582775—21no—
43#14582764C2211yescharacteristic, complemented
44#14582761—21no—
45#14582759C2211yescharacteristic
46#14582755—21no—
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C23×D4×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C23×Dic43—21no—
64C23×Dic43—21no—
65C22×C4×D43—21no—
66C2×#10621882—22no—
67C2×#10621882—22no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—41no—
71C2×#10621882D414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063299—22no—
75#13063299—41no—
76D4×Dic43—22no—
77D4×Dic43—22no—
78D4×Dic43—41no—
79D4×Dic43—41no—
80#13063287—22no—
81#13063287—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—44no—
94C2×C22⋊Dic43D411yescharacteristic
95C2×C22⋊Dic43D411yescharacteristic
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063258—22no—
103#13063257—41no—
104Dic43⋊C8—41no—
105#13063247—22no—
106#13063247—41no—
107#13063246—22no—
108#13063246—22no—
109C22⋊(C43⋊C8)—22no—
110C8×Dic43—22no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C25×C43—21no—
118C22×D4×C43—22no—
119C22×D4×C43—22no—
120C22×D4×C43—22no—
121C22×D4×C43—22no—
122C22×D4×C43—21no—
123C22×D4×C43—41no—
124C22×D4×C43—41no—
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133#102×C43—22no—
134#102×C43—22no—
135#102×C43—22no—
136#102×C43—41no—
137C22⋊C8×C43—41no—
138#95×C43—21no—
139C24×C43—21no—
140C24×C43—24no—
141C24×C43—21no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C23×D43—21no—
150C2×D4×C43—24no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—44no—
162C2×D4×C43—44no—
163C2×D4×C43—44no—
164C2×D4×C43—44no—
165C2×D4×C43C2×D412yes—
166C2×D4×C43#4112yes—
167C2×D4×C43#4112yes—
168C2×D4×C43#4112yes—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—42no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—81no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—42no—
186C22×Dic43—42no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43—81no—
190C22×Dic43—81no—
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172—21no—
200C2×D172C2×D412yes—
201C2×C4×D43—42no—
202C2×C4×D43—42no—
203C2×C4×D43—81no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C22⋊C4×C43—81no—
215C22⋊Dic43—22no—
216C22⋊Dic43—22no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—81no—
223C22⋊Dic43—81no—
224#10621882—28no—
225#10621882—44no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—81no—
229(C2×D43)⋊C4—81no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—81no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C2×D412yes—
247C23×C43—21no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—22no—
257C23×C43—48no—
258C23×C43—48no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—84no—
270C23×C43—84no—
271C23×C43—84no—
272C23×C43—84no—
273C23×C43—84no—
274C23×C43#13512yes—
275C23×C43C22×D411yescharacteristic
276C22×D43—22no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—48no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43#12314yes—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C22⋊D43—84no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—84no—
333C2×Dic43—84no—
334C2×Dic43AGL(1,ℤ/8)12yes—
335D172—22no—
336D172—22no—
337D172—41no—
338D172—41no—
339C4×D43—84no—
340C8×C43—41no—
341C8×C43—41no—
342C43⋊C8—22no—
343C43⋊C8—41no—
344#24897—431nomaximal, Sylow
345C22×C43—22no—
346C22×C43—24no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—41no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—816no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43#52511yescharacteristic
368C22×C43D4211yescharacteristic
369C22×C43#54611yescharacteristic
370C22×C43C2×#13511yescharacteristic
371C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C43#57611yescharacteristic
373C22×C43#57611yescharacteristic
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—81no—
378C2×D43—81no—
379C2×D43—81no—
380C2×D43—81no—
381C4×C43—41no—
382C4×C43—81no—
383C4×C43—81no—
384C4×C43C2×#12311yescharacteristic
385C4×C43#53811yescharacteristic
386C4×C43#54611yescharacteristic
387C4×C43#55111yescharacteristic
388Dic43—22no—
389Dic43—41no—
390Dic43—41no—
391Dic43—41no—
392Dic43—81no—
393Dic43—81no—
394Dic43—81no—
395C2×#447—431no—
396C2×C4×D8—431no—
397#2420—431no—
398D4×C22⋊C4—431no—
399#2092—431no—
400#2076—431no—
401#2054—431no—
402#2034—431no—
403#1934—431no—
404#1923—431no—
405#1879—431no—
406#1879—431no—
407#1864—431no—
408#1804—431no—
409#1786D4311yescharacteristic, complemented
410C2×C43—42no—
411C2×C43—44no—
412C2×C43—82no—
413C2×C43#241811yescharacteristic
414C2×C43#310511yescharacteristic
415C2×C43#312211yescharacteristic
416C2×C43#326411yescharacteristic
417C2×C43#328011yescharacteristic
418C2×C43#329711yescharacteristic
419C2×C43#332511yescharacteristic
420D43—82no—
421C23×D4C2×D4311yescharacteristic
422C22×D8—431no—
423C22×D8—431no—
424C2×#121—431no—
425C2×C4×D4—431no—
426C2×C4×D4—431no—
427C2×C4×D4—431no—
428C22×C22⋊C4—861no—
429#447—864no—
430C4×D8—864no—
431C2×#107—431no—
432C2×#106—431no—
433C2×C4⋊C8—431no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102C2×D4311yescharacteristic
439C2×#102C2×D4311yescharacteristic
440C2×#102C2×D4311yescharacteristic
441C2×#102C2×D4311yescharacteristic
442C2×C22⋊C8—431no—
443C2×C22⋊C8C2×D4311yescharacteristic
444C2×C4×C8—431no—
445#397—861no—
446#394—861no—
447#390—431no—
448#390—431no—
449#390—431no—
450#389—431no—
451#386—861no—
452#386—861no—
453#386—861no—
454#382—431no—
455#381—861no—
456#380—431no—
457#380C2×D4311yescharacteristic
458#379—861no—
459C4×C22⋊C4—431no—
460#340—431no—
461#340—431no—
462#340—431no—
463#340—431no—
464#336—431no—
465#336—431no—
466C43#2489711yescharacteristic, complemented, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4—431no—
476C22×D4—861no—
477C22×D4C22×D4311yescharacteristic
478C22×D4C22×D4311yescharacteristic
479C23×C4—861no—
480C23×C4—861no—
481C23×C4—861no—
482C23×C4C22×D4311yescharacteristic
483C2×D8—434no—
484C2×D8—862no—
485C2×D8—862no—
486C2×D8—862no—
487C2×D8—862no—
488C2×D8—1721no—
489C22×C8—431no—
490C22×C8—431no—
491C22×C8C22×D4311yescharacteristic
492C22×C8C22×D4311yescharacteristic
493#121—862no—
494#121—1721no—
495C4×D4—862no—
496C4×D4—862no—
497C4×D4—862no—
498C4×D4—1721no—
499C4×D4—1721no—
500C4×D4—1721no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—1724no—
522C2×C42—431no—
523C2×C42—431no—
524#107—862no—
525#106—1721no—
526C4⋊C8—1721no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—41no—
531#102—862no—
532#102—862no—
533#102—862no—
534#102—1721no—
535C22⋊C8—41no—
536C22⋊C8—862no—
537C4×C8—862no—
538#95—21no—
539#95—431no—
540#95—431no—
541#95—861no—
542#95—861no—
543#95—861no—
544#95—861no—
545C24—21no—
546C24—24no—
547C24—21no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24—861no—
555C24D4×D4311yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—432no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—861no—
575C2×D4—861no—
576C2×D4—861no—
577C2×D4—3441no—
578C2×D4—1722no—
579C2×D4—1722no—
580C2×D4#1062189812yes—
581C2×D4D4×D4312yes—
582C2×D4#1062190012yes—
583C2×D4#1062190012yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—431no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—431no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—3441no—
600C22×C4—3441no—
601C22×C4—3441no—
602C22×C4—1722no—
603C22×C4—1722no—
604C22×C4—1722no—
605C22×C4—1722no—
606C22×C4—1722no—
607C22×C4—1722no—
608C22×C4D4×D4311yescharacteristic
609C22×C4C23×D4311yescharacteristic
610D8—868no—
611D8—1724no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—432no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—3441no—
635C22⋊C4—81no—
636C22⋊C4—862no—
637C22⋊C4—862no—
638C22⋊C4—3441no—
639C22⋊C4—3441no—
640C22⋊C4—3441no—
641C22⋊C4—3441no—
642C22⋊C4—1722no—
643C22⋊C4—1722no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C22⋊C4—1722no—
649C42—861no—
650C42—861no—
651C42—861no—
652C42—861no—
653C23—21no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—21no—
660C23—22no—
661C23—21no—
662C23—22no—
663C23—48no—
664C23—48no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—862no—
681C23—1721no—
682C23—1721no—
683C23—1721no—
684C23—1721no—
685C23—1721no—
686C23—1721no—
687C23#1306334612yes—
688C23C2×D4×D4311yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—41no—
696D4—41no—
697D4—862no—
698D4—862no—
699D4—3444no—
700D4—1721no—
701D4—1721no—
702D4#1306330714yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—432no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—3444no—
729C2×C4—3444no—
730C2×C4—3444no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4C2×#1062190011yescharacteristic
742C2×C4C2×#1062190011yescharacteristic
743C2×C4C2×#1062189811yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337011yescharacteristic
746C8—41no—
747C8—41no—
748C8—862no—
749C8—1721no—
750C22—24no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—816no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—3441no—
773C22—3441no—
774C22—3441no—
775C22—3441no—
776C22—1722no—
777C22—1722no—
778C22—1722no—
779C22#1458340511yescharacteristic
780C22#1458353111yescharacteristic
781C22#1458353911yescharacteristic
782C22C2×#1306334611yescharacteristic
783C22AGL(1,ℤ/8)×D4311yescharacteristic
784C22#1458370011yescharacteristic
785C22#1458370311yescharacteristic
786C4—41no—
787C4—81no—
788C4—81no—
789C4—862no—
790C4—3441no—
791C4—3441no—
792C4—3441no—
793C4—1721no—
794C4—1721no—
795C4—1721no—
796C4C2×#1306330711yescharacteristic
797C4#1458348411yescharacteristic
798C4#1458353611yescharacteristic
799C4#1458357511yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—3442no—
804C2#1913806111yescharacteristic
805C2#1914464311yescharacteristic
806C2#1914483211yescharacteristic
807C2#1914607311yescharacteristic
808C2#1914627311yescharacteristic
809C2#1914644111yescharacteristic
810C2#1914683311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
hypercenter#1786D43
hypocenterC43#24897
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#14582979C2semidirect
3. #19138089C2semidirect
4. D4×C22⋊Dic43C2semidirect
5. #19136118C2semidirect
6. #19136026C2semidirect
7. #19135904C2semidirect
8. #19135785C2semidirect
9. #19135280C2semidirect
10. #19135204C2semidirect
11. #19134941C2semidirect
12. #19134940C2semidirect
13. #19134858C2semidirect
14. #19134603C2semidirect
15. C43×#1786C2semidirect
21. C2×#13063287C22semidirect
25. C2×#13063258C22semidirect
26. C2×#13063257C22semidirect
27. C2×Dic43⋊C8C22semidirect
28. C2×#13063247C22semidirect
29. C2×#13063247C22semidirect
33. C2×C8×Dic43C22semidirect
38. #14582800C22semidirect
39. #14582798C22semidirect
43. #14582764C22semidirect
48. #14582662C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
409. #1786D43semidirect
466. C43#24897semidirect

Maximal subgroups

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

subgroupindex
C2×#145830332
C2×#145829792
#191380892
D4×C22⋊Dic432
#191361182
#191360262
#191359042
#191357852
#191352802
#191352042
#191349412
#191349402
#191348582
#191346032
C43×#17862
#2489743