Finite Group Databasebeta

← #25140397

Subgroups — #25140397

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×C4×#10621882C211yesmaximal, characteristic, complemented
3#19138087C211yesmaximal, characteristic, complemented
4#19136116C211yesmaximal, characteristic, complemented
5#19136026C211yesmaximal, characteristic, complemented
6#19135905C211yesmaximal, characteristic, complemented
7#19135784C211yesmaximal, characteristic, complemented
8#19135281C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134856C211yesmaximal, characteristic, complemented
13#19134605C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic, complemented
20#14583033—24no—
21C4×#10621882—24no—
22C2×#13063258C2211yescharacteristic, complemented
23C2×#13063256C2211yescharacteristic, complemented
24C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic, complemented
32C2×#13063245C2211yescharacteristic, complemented
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic, complemented
36#14582828—21no—
37#14582814—21no—
38#14582801C2211yescharacteristic, complemented
39#14582797C2211yescharacteristic, complemented
40#14582775—21no—
41#14582765C2211yescharacteristic, complemented
42#14582761—21no—
43#14582759C2211yescharacteristic
44#14582661C2211yescharacteristic, complemented
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50C23×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C22×C22⋊C4×C43—21no—
54C43×#390C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#386—21no—
57C43×#386—21no—
58C43×#380C2211yescharacteristic
59C43×#379—21no—
60C4×C22⋊C4×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C22×C4×D43—21no—
64C2×#10621882—22no—
65C2×#10621882—22no—
66C2×#10621882—22no—
67C2×#10621882—22no—
68C2×#10621882—41no—
69C2×#10621882D414yes—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063299—22no—
75#13063299—41no—
76C4×D172—22no—
77C4×D172—41no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87#13063258—22no—
88#13063256—41no—
89C4⋊(C43⋊C8)—41no—
90#13063246—22no—
91#13063246—22no—
92#13063246—22no—
93#13063246—22no—
94#13063246—22no—
95#13063246—41no—
96#13063245—22no—
97#13063245—41no—
98C22⋊(C43⋊C8)—22no—
99C22⋊(C43⋊C8)—41no—
100C4×C43⋊C8—22no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C25×C43—21no—
106C22×D4×C43—22no—
107C22×D4×C43—22no—
108C22×D4×C43—22no—
109C22×D4×C43—22no—
110C22×D4×C43—21no—
111C22×D4×C43—41no—
112C22×D4×C43—41no—
113C22×D4×C43C2311yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C23×C4×C43—21no—
116C23×C4×C43—21no—
117C23×C4×C43C2311yescharacteristic
118C4×D4×C43—22no—
119C4×D4×C43—22no—
120C4×D4×C43—41no—
121C4×D4×C43—41no—
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×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—44no—
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#95×C43—21no—
137#95×C43D411yescharacteristic
138#95×C43D411yescharacteristic
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×C43—42no—
178C22×C4×C43—42no—
179C22×C4×C43—42no—
180C22×C4×C43—42no—
181C22×C4×C43—81no—
182C22×C4×C43—81no—
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—42no—
190C2×C22⋊D43—42no—
191C2×C22⋊D43—81no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
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—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C22⋊C4×C43—22no—
209C22⋊C4×C43—22no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—42no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—81no—
216C22⋊C4×C43—81no—
217C42×C43—21no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—21no—
221C22⋊Dic43—81no—
222#10621882—28no—
223#10621882—44no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—81no—
227(C2×D43)⋊C4—81no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234Dic43⋊C4—81no—
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—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—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—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
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—41no—
316C2×C4×C43—84no—
317C2×C4×C43—84no—
318C2×C4×C43AGL(1,ℤ/8)12yes—
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43H(5,𝔽2)11yescharacteristic
324C2×C4×C43H(5,𝔽2)11yescharacteristic
325C22⋊D43—84no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335D172—22no—
336D172—22no—
337D172—41no—
338D172—41no—
339C4×D43—84no—
340C43⋊C8—22no—
341C43⋊C8—41no—
342C43⋊C8—41no—
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—22no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43—81no—
387C4×C43—81no—
388C4×C43C2×#12311yescharacteristic
389C4×C43#53811yescharacteristic
390C4×C43#54611yescharacteristic
391C4×C43#55111yescharacteristic
392Dic43—81no—
393Dic43—81no—
394Dic43—81no—
395C2×#447—431no—
396C2×C4×D8—431no—
397#2420—431no—
398D4×C22⋊C4D4311yescharacteristic, complemented
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—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×D4C2×D4311yescharacteristic
427C2×C4×D4C2×D4311yescharacteristic
428C22×C22⋊C4—21no—
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—861no—
446#394—861no—
447#390—431no—
448#390C2×D4311yescharacteristic
449#390C2×D4311yescharacteristic
450#389—431no—
451#386—21no—
452#386—21no—
453#386—861no—
454#382—431no—
455#381—861no—
456#380—431no—
457#380C2×D4311yescharacteristic
458#379—21no—
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—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—21no—
480C23×C4—21no—
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—862no—
494#121—1721no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—41no—
498C4×D4—41no—
499C4×D4—862no—
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—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—44no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
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—861no—
540#95—861no—
541#95—861no—
542#95—861no—
543#95C22⋊D4311yescharacteristic
544#95C22⋊D4311yescharacteristic
545C24—21no—
546C24—24no—
547C24—21no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24—861no—
555C24C2×C22⋊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×D4#1062189812yes—
582C2×D4D4×D4312yes—
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—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—81no—
597C22×C4—81no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—3441no—
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—861no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—3441no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—3441no—
645C22⋊C4—3441no—
646C22⋊C4—3441no—
647C22⋊C4—1722no—
648C22⋊C4—1722no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
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#1306334512yes—
688C23C22×C22⋊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—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—84no—
728C2×C4—84no—
729C2×C4—3444no—
730C2×C4—1721no—
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#1306335112yes—
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4C2×#1062190011yescharacteristic
742C2×C4C2×#1062189811yescharacteristic
743C2×C4C2×#1062189811yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337011yescharacteristic
746C8—862no—
747C8—1721no—
748C8—1721no—
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#1458341011yescharacteristic
780C22D4×C22⋊D4311yescharacteristic
781C22#1458354311yescharacteristic
782C22C2×#1306334511yescharacteristic
783C22C2×#1306335111yescharacteristic
784C22#1458370211yescharacteristic
785C22#1458370211yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—3441no—
794C4—3441no—
795C4—3441no—
796C4C2×#1306330711yescharacteristic
797C4#1458348711yescharacteristic
798C4#1458353911yescharacteristic
799C4#1458357511yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—3442no—
804C2#1913805711yescharacteristic
805C2#1914464211yescharacteristic
806C2#1914483811yescharacteristic
807C2#1914607111yescharacteristic
808C2#1914627611yescharacteristic
809C2#1914644511yescharacteristic
810C2#1914683711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
hypercenterD4×C22⋊C4D43
hypocenterC43#24897
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621882C2semidirect
3. #19138087C2semidirect
4. #19136116C2semidirect
5. #19136026C2semidirect
6. #19135905C2semidirect
7. #19135784C2semidirect
8. #19135281C2semidirect
9. #19135203C2semidirect
10. #19134946C2semidirect
11. #19134943C2semidirect
12. #19134856C2semidirect
13. #19134605C2semidirect
14. #19134526C2semidirect
15. D4×C22⋊C4×C43C2semidirect
19. C2×C4×D172C22semidirect
22. C2×#13063258C22semidirect
23. C2×#13063256C22semidirect
24. C2×C4⋊(C43⋊C8)C22semidirect
31. C2×#13063245C22semidirect
32. C2×#13063245C22semidirect
35. C2×C4×C43⋊C8C22semidirect
38. #14582801C22semidirect
39. #14582797C22semidirect
41. #14582765C22semidirect
44. #14582661C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582654C22semidirect
49. #14582654C22semidirect
398. D4×C22⋊C4D43semidirect
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×C4×#106218822
#191380872
#191361162
#191360262
#191359052
#191357842
#191352812
#191352032
#191349462
#191349432
#191348562
#191346052
#191345262
D4×C22⋊C4×C432
#2489743