Finite Group Databasebeta

← #25140394

Subgroups — #25140394

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×#14583032C211yesmaximal, characteristic
2C2×C4×#10621882C211yesmaximal, characteristic, complemented
3C22⋊C4×D172C211yesmaximal, characteristic, complemented
4#19136119C211yesmaximal, characteristic, complemented
5#19136026C211yesmaximal, characteristic, complemented
6#19135905C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135277C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134855C211yesmaximal, characteristic, complemented
13#19134602C211yesmaximal, characteristic, complemented
14#19134525C211yesmaximal, characteristic, complemented
15C43×#2420C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C22⋊C4×D43—21no—
22#14583032—24no—
23C4×#10621882—24no—
24C2×#13063258C2211yescharacteristic, complemented
25C2×#13063256C2211yescharacteristic, complemented
26C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
27C2×#13063246C2211yescharacteristic, complemented
28C2×#13063246C2211yescharacteristic, complemented
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic, complemented
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582777—21no—
41#14582777—21no—
42#14582759C2211yescharacteristic
43#14582754—21no—
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C2×#121×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic, complemented
52C43×#397—21no—
53C43×#394—21no—
54C43×#390C2211yescharacteristic, complemented
55C43×#389C2211yescharacteristic, complemented
56C43×#386—21no—
57C43×#382C2211yescharacteristic, complemented
58C43×#381—21no—
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43C2211yescharacteristic
61C24×D43—21no—
62C22×D172—21no—
63C22×D172—22no—
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—41no—
68C22×D172—41no—
69C22×D172C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C2×#10621882—22no—
74C2×#10621882—22no—
75C2×#10621882—22no—
76C2×#10621882—22no—
77C2×#10621882—41no—
78C2×#10621882D414yes—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C4×D172—22no—
84C4×D172—22no—
85C4×D172—41no—
86C4×D172—41no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C22⋊Dic43—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C22⋊C4×D43—44no—
97#13063258—22no—
98#13063256—41no—
99C4⋊(C43⋊C8)—41no—
100#13063246—22no—
101#13063246—41no—
102#13063245—22no—
103#13063245—22no—
104#13063245—22no—
105#13063245—22no—
106#13063245—22no—
107#13063245—41no—
108C22⋊(C43⋊C8)—22no—
109C22⋊(C43⋊C8)—41no—
110C4×C43⋊C8—22no—
111C43⋊#95—21no—
112C22×D4×C43—21no—
113C22×D4×C43C2311yescharacteristic
114C23×C4×C43—21no—
115C23×C4×C43C2311yescharacteristic
116#121×C43—22no—
117#121×C43—41no—
118C4×D4×C43—22no—
119C4×D4×C43—41no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43D411yescharacteristic
138#95×C43D411yescharacteristic
139C24×C43—21no—
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142C23×D43—21no—
143C23×D43—24no—
144C23×D43—42no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43—42no—
148C23×D43—81no—
149C23×D43—81no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—42no—
156C2×D4×C43—42no—
157C2×D4×C43—81no—
158C2×D4×C43C2×D412yes—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—42no—
169C22×C4×C43—42no—
170C22×C4×C43—81no—
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C22×Dic43—21no—
178C22×Dic43—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—24no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—42no—
189C2×D172—42no—
190C2×D172—44no—
191C2×D172—44no—
192C2×D172—44no—
193C2×D172—44no—
194C2×D172C2×D412yes—
195C2×D172#4112yes—
196C2×D172#4112yes—
197C2×D172#4112yes—
198C2×C4×D43—42no—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43—42no—
202C2×C4×D43—81no—
203C2×C4×D43—81no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—81no—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—81no—
216C22⋊C4×C43—81no—
217C22⋊C4×C43—81no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—21no—
221C42×C43—21no—
222C22⋊Dic43—42no—
223#10621882—28no—
224#10621882—44no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—42no—
229(C2×D43)⋊C4—81no—
230(C2×D43)⋊C4—81no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—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—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—22no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43#13512yes—
261C23×C43C22×D411yescharacteristic
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—22no—
265C22×D43—22no—
266C22×D43—48no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—48no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—84no—
279C22×D43—84no—
280C22×D43—84no—
281C22×D43—84no—
282C22×D43—84no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—41no—
286D4×C43—41no—
287D4×C43—84no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—84no—
316C2×C4×C43AGL(1,ℤ/8)12yes—
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C2×C4×C43C2×#4111yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329D172—22no—
330D172—22no—
331D172—22no—
332D172—22no—
333D172—22no—
334D172—48no—
335D172—41no—
336D172—41no—
337D172#12314yes—
338C4×D43—84no—
339C4×D43—84no—
340C43⋊C8—22no—
341C43⋊C8—41no—
342C43⋊C8—41no—
343C43⋊C8—41no—
344#24897—431nomaximal, Sylow
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43#52511yescharacteristic
360C22×C43D4211yescharacteristic
361C22×C43#54611yescharacteristic
362C22×C43C2×#13511yescharacteristic
363C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C43#57611yescharacteristic
365C22×C43#57611yescharacteristic
366C2×D43—24no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—816no—
377C2×D43—81no—
378C2×D43—81no—
379C2×D43—81no—
380C2×D43—81no—
381C4×C43—22no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43—81no—
387C4×C43—81no—
388C4×C43—81no—
389C4×C43C2×#12311yescharacteristic
390C4×C43#53811yescharacteristic
391C4×C43#54611yescharacteristic
392C4×C43#55111yescharacteristic
393Dic43—81no—
394Dic43—81no—
395C2×#447—431no—
396C2×C4×D8—431no—
397#2420D4311yescharacteristic, complemented
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#1786—431no—
410C2×C43—42no—
411C2×C43—82no—
412C2×C43#241811yescharacteristic
413C2×C43#310511yescharacteristic
414C2×C43#312211yescharacteristic
415C2×C43#326411yescharacteristic
416C2×C43#328011yescharacteristic
417C2×C43#329711yescharacteristic
418C2×C43#332511yescharacteristic
419D43—44no—
420D43—82no—
421C23×D4—431no—
422C22×D8—431no—
423C22×D8—431no—
424C2×#121C2×D4311yescharacteristic
425C2×C4×D4—431no—
426C2×C4×D4—431no—
427C2×C4×D4C2×D4311yescharacteristic, complemented
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×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×#102—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C4×C8—431no—
445#397—21no—
446#394—21no—
447#390—431no—
448#390—431no—
449#390C2×D4311yescharacteristic, complemented
450#389C2×D4311yescharacteristic, complemented
451#386—21no—
452#386—861no—
453#386—861no—
454#382C2×D4311yescharacteristic, complemented
455#381—21no—
456#380—431no—
457#380C2×D4311yescharacteristic
458#379—861no—
459C4×C22⋊C4C2×D4311yescharacteristic
460#340—431no—
461#340—431no—
462#340—431no—
463#340—431no—
464#336—431no—
465#336—431no—
466C43#2489711yescharacteristic, complemented, Sylow
467C25—861no—
468C22×D4—21no—
469C22×D4—431no—
470C22×D4—431no—
471C22×D4—862no—
472C22×D4—862no—
473C22×D4—862no—
474C22×D4—862no—
475C22×D4—861no—
476C22×D4—1721no—
477C22×D4—1721no—
478C22×D4C22×D4311yescharacteristic
479C23×C4—21no—
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×C8—431no—
492C22×C8—431no—
493#121—22no—
494#121—41no—
495C4×D4—22no—
496C4×D4—41no—
497C4×D4—862no—
498C4×D4—862no—
499C4×D4—1721no—
500C4×D4—1721no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
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—1724no—
520C2×C22⋊C4C22⋊D4311yescharacteristic
521C2×C22⋊C4C22⋊D4311yescharacteristic
522C2×C42C22×D4311yescharacteristic
523C2×C42C22×D4311yescharacteristic
524#107—862no—
525#106—1721no—
526C4⋊C8—1721no—
527#102—862no—
528#102—862no—
529#102—862no—
530#102—862no—
531#102—862no—
532#102—862no—
533#102—1721no—
534#102—1721no—
535C22⋊C8—862no—
536C22⋊C8—1721no—
537C4×C8—862no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—861no—
543#95C22⋊D4311yescharacteristic
544#95C22⋊D4311yescharacteristic
545C24—21no—
546C24—864no—
547C24—861no—
548C24—861no—
549C24—3441no—
550C24—3441no—
551C24—1722no—
552C24—1722no—
553C24—1722no—
554C24—1722no—
555C24C2×C22⋊D4311yescharacteristic
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—81no—
564C2×D4—432no—
565C2×D4—432no—
566C2×D4—432no—
567C2×D4—432no—
568C2×D4—864no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—861no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—861no—
575C2×D4—861no—
576C2×D4—861no—
577C2×D4—1722no—
578C2×D4—1722no—
579C2×D4—1724no—
580C2×D4—1724no—
581C2×D4—1724no—
582C2×D4—1724no—
583C2×D4D4×D4312yes—
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—21no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—3441no—
599C22×C4—3441no—
600C22×C4—1722no—
601C22×C4—1722no—
602C22×C4—1722no—
603C22×C4—1722no—
604C22×C4C2×C22⋊D4311yescharacteristic
605C22×C4C2×C22⋊D4311yescharacteristic
606C22×C4C2×C22⋊D4311yescharacteristic
607C22×C4C2×C22⋊D4311yescharacteristic
608C22×C4C2×C22⋊D4311yescharacteristic
609C22×C4C23×D4311yescharacteristic
610D8—868no—
611D8—1724no—
612C2×C8—432no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
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—21no—
629C4⋊C4—21no—
630C4⋊C4—81no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—3441no—
643C22⋊C4—3441no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C22⋊C4—1722no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—862no—
667C23—862no—
668C23—862no—
669C23—862no—
670C23—3444no—
671C23—3444no—
672C23—3444no—
673C23—3444no—
674C23—3444no—
675C23—1728no—
676C23—1728no—
677C23—1721no—
678C23—1721no—
679C23—1721no—
680C23—1721no—
681C23—1721no—
682C23—1721no—
683C23—1721no—
684C23—1721no—
685C23—1721no—
686C23—1721no—
687C23#1306334512yes—
688C23C22×C22⋊D4311yescharacteristic
689D4—22no—
690D4—22no—
691D4—41no—
692D4—41no—
693D4—84no—
694D4—434no—
695D4—862no—
696D4—862no—
697D4—862no—
698D4—862no—
699D4—862no—
700D4—1728no—
701D4—1721no—
702D4—1721no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—3444no—
732C2×C4—3444no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4#1306335012yes—
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4#41×D4311yescharacteristic
742C2×C4#41×D4311yescharacteristic
743C2×C4#41×D4311yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337111yescharacteristic
746C8—862no—
747C8—1721no—
748C8—1721no—
749C8—1721no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—864no—
765C22—34416no—
766C22—3441no—
767C22—3441no—
768C22—3441no—
769C22—3441no—
770C22—1722no—
771C22—1722no—
772C22—1722no—
773C22—1722no—
774C22—1722no—
775C22—1722no—
776C22—1722no—
777C22—1722no—
778C22—1722no—
779C22#1458340611yescharacteristic
780C22D4×C22⋊D4311yescharacteristic
781C22#1458353711yescharacteristic
782C22C2×#1306334511yescharacteristic
783C22C2×#1306335011yescharacteristic
784C22#1458370211yescharacteristic
785C22#1458370211yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—3441no—
795C4—3441no—
796C4#123×D4311yescharacteristic
797C4#1458348511yescharacteristic
798C4#1458354111yescharacteristic
799C4#1458357711yescharacteristic
800C2—42no—
801C2—82no—
802C2—3442no—
803C2—1724no—
804C2#1913805411yescharacteristic
805C2#1914463811yescharacteristic
806C2#1914483311yescharacteristic
807C2#1914607611yescharacteristic
808C2#1914627611yescharacteristic
809C2#1914643911yescharacteristic
810C2#1914683111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2420C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
hypercenter#2420D43
hypocenterC43#24897
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2420

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621882C2semidirect
3. C22⋊C4×D172C2semidirect
4. #19136119C2semidirect
5. #19136026C2semidirect
6. #19135905C2semidirect
7. #19135781C2semidirect
8. #19135277C2semidirect
9. #19135203C2semidirect
10. #19134946C2semidirect
11. #19134943C2semidirect
12. #19134855C2semidirect
13. #19134602C2semidirect
14. #19134525C2semidirect
15. C43×#2420C2semidirect
24. C2×#13063258C22semidirect
25. C2×#13063256C22semidirect
26. C2×C4⋊(C43⋊C8)C22semidirect
27. C2×#13063246C22semidirect
28. C2×#13063246C22semidirect
37. C2×C4×C43⋊C8C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
51. C2×C4×D4×C43C22semidirect
54. C43×#390C22semidirect
55. C43×#389C22semidirect
57. C43×#382C22semidirect
397. #2420D43semidirect
427. C2×C4×D4C2×D43semidirect
449. #390C2×D43semidirect
450. #389C2×D43semidirect
454. #382C2×D43semidirect
466. C43#24897semidirect

Maximal subgroups

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

subgroupindex
C2×#145830322
C2×C4×#106218822
C22⋊C4×D1722
#191361192
#191360262
#191359052
#191357812
#191352772
#191352032
#191349462
#191349432
#191348552
#191346022
#191345252
C43×#24202
#2489743