Finite Group Databasebeta

← #25140334

Subgroups — #25140334

Order 11008.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 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#19136124C211yesmaximal, characteristic, complemented
5#19136021C211yesmaximal, characteristic, complemented
6#19135905C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135277C211yesmaximal, characteristic, complemented
9#19135203C211yesmaximal, characteristic, complemented
10#19134946C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134841C211yesmaximal, characteristic, complemented
13#19134592C211yesmaximal, characteristic, complemented
14#19134525C211yesmaximal, characteristic, complemented
15C43×#2422C211yesmaximal, 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×#13063258C2211yescharacteristic, 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×#123×C43—21no—
51C2×#121×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic, complemented
53C43×#397—21no—
54C43×#394—21no—
55C43×#390C2211yescharacteristic, complemented
56C43×#389C2211yescharacteristic, complemented
57C43×#385—21no—
58C43×#384C2211yescharacteristic, complemented
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#13063258—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#123×C43—44no—
117#121×C43—22no—
118#121×C43—41no—
119C4×D4×C43—22no—
120C4×D4×C43—41no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#95×C43—21no—
137#95×C43—21no—
138#95×C43D411yescharacteristic
139#95×C43D411yescharacteristic
140C24×C43—21no—
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C23×D43—21no—
144C23×D43—24no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43—42no—
148C23×D43—42no—
149C23×D43—81no—
150C23×D43—81no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43—81no—
159C2×D4×C43C2×D412yes—
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—21no—
169C22×C4×C43—42no—
170C22×C4×C43—42no—
171C22×C4×C43—81no—
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2411yescharacteristic
178C22×Dic43—21no—
179C22×Dic43—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—24no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—42no—
190C2×D172—42no—
191C2×D172—44no—
192C2×D172—44no—
193C2×D172—44no—
194C2×D172—44no—
195C2×D172C2×D412yes—
196C2×D172#4112yes—
197C2×D172#4112yes—
198C2×D172#4112yes—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43—42no—
202C2×C4×D43—42no—
203C2×C4×D43—81no—
204C2×C4×D43—81no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43—81no—
214C22⋊C4×C43—41no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—42no—
219C22⋊C4×C43—42no—
220C22⋊C4×C43D814yescomplemented
221C42×C43—21no—
222C42×C43—21no—
223C42×C43—21no—
224C42×C43—21no—
225C22⋊Dic43—42no—
226#10621882—28no—
227#10621882—44no—
228(C2×D43)⋊C4—42no—
229(C2×D43)⋊C4—42no—
230(C2×D43)⋊C4—42no—
231(C2×D43)⋊C4—42no—
232(C2×D43)⋊C4—81no—
233(C2×D43)⋊C4—81no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—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⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8C2×D412yes—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—22no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43C2×D812yes—
264C23×C43C22×D411yescharacteristic
265C22×D43—22no—
266C22×D43—22no—
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—48no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—48no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—84no—
282C22×D43—84no—
283C22×D43—84no—
284C22×D43—84no—
285C22×D43—84no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—84no—
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—21no—
303C2×C4×C43—21no—
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—41no—
316C2×C4×C43—41no—
317C2×C4×C43—84no—
318C2×C4×C43C2×D812yes—
319C2×C4×C43C2×D812yes—
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C2×C4×C43H(5,𝔽2)11yescharacteristic
325C2×C4×C43H(5,𝔽2)11yescharacteristic
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332D172—22no—
333D172—22no—
334D172—22no—
335D172—22no—
336D172—22no—
337D172—48no—
338D172—41no—
339D172—41no—
340D172#12314yescomplemented
341C4×D43—84no—
342C4×D43—84no—
343C43⋊C8—22no—
344C43⋊C8—41no—
345C43⋊C8—41no—
346C43⋊C8—41no—
347#24893—431nomaximal, Sylow
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43#52511yescharacteristic
363C22×C43D4211yescharacteristic
364C22×C43#54611yescharacteristic
365C22×C43C22×D811yescharacteristic
366C22×C43#57511yescharacteristic
367C22×C43#57611yescharacteristic
368C22×C43#57711yescharacteristic
369C2×D43—24no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—816no—
380C2×D43—81no—
381C2×D43—81no—
382C2×D43—81no—
383C2×D43—81no—
384C4×C43—22no—
385C4×C43—22no—
386C4×C43—41no—
387C4×C43—41no—
388C4×C43—41no—
389C4×C43—81no—
390C4×C43—81no—
391C4×C43—81no—
392C4×C43C2×#12311yescharacteristic
393C4×C43#53811yescharacteristic
394C4×C43#54611yescharacteristic
395C4×C43#55111yescharacteristic
396Dic43—81no—
397Dic43—81no—
398C2×#447—431no—
399C2×C4×D8—431no—
400#2422D4311yescharacteristic, complemented
401D4×C22⋊C4—431no—
402#2093—431no—
403#2075—431no—
404#2054—431no—
405#2033—431no—
406#1934—431no—
407#1923—431no—
408#1879—431no—
409#1879—431no—
410#1862—431no—
411#1802—431no—
412#1786—431no—
413C2×C43—42no—
414C2×C43—82no—
415C2×C43#241811yescharacteristic
416C2×C43#310011yescharacteristic
417C2×C43#311811yescharacteristic
418C2×C43#326711yescharacteristic
419C2×C43D4×D811yescharacteristic
420C2×C43#329411yescharacteristic
421C2×C43#332211yescharacteristic
422D43—44no—
423D43—82no—
424C23×D4—431no—
425C22×D8—431no—
426C22×D8—431no—
427C2×#123—21no—
428C2×#121C2×D4311yescharacteristic
429C2×C4×D4—431no—
430C2×C4×D4—431no—
431C2×C4×D4C2×D4311yescharacteristic, complemented
432C22×C22⋊C4—861no—
433#447—864no—
434C4×D8—864no—
435C2×#107—431no—
436C2×#107—431no—
437C2×C4⋊C8—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—431no—
443C2×#102—431no—
444C2×#102—431no—
445C2×#102—431no—
446C2×C22⋊C8—431no—
447C2×C22⋊C8—431no—
448C2×C4×C8—431no—
449#397—21no—
450#394—21no—
451#390—431no—
452#390—431no—
453#390C2×D4311yescharacteristic, complemented
454#389C2×D4311yescharacteristic, complemented
455#386—861no—
456#386—861no—
457#385—21no—
458#384C2×D4311yescharacteristic, complemented
459#380—431no—
460#380C2×D4311yescharacteristic
461#379—861no—
462C4×C22⋊C4C2×D4311yescharacteristic
463#340—431no—
464#340—431no—
465#340—431no—
466#340—431no—
467#336—431no—
468#336—431no—
469C43#2489311yescharacteristic, complemented, Sylow
470C25—861no—
471C22×D4—21no—
472C22×D4—431no—
473C22×D4—431no—
474C22×D4—862no—
475C22×D4—862no—
476C22×D4—862no—
477C22×D4—862no—
478C22×D4—861no—
479C22×D4—1721no—
480C22×D4—1721no—
481C22×D4C22×D4311yescharacteristic
482C23×C4—21no—
483C23×C4—861no—
484C23×C4—861no—
485C23×C4C22×D4311yescharacteristic
486C2×D8—434no—
487C2×D8—862no—
488C2×D8—862no—
489C2×D8—862no—
490C2×D8—862no—
491C2×D8—1721no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8—431no—
495C22×C8—431no—
496#123—44no—
497#121—22no—
498#121—41no—
499C4×D4—22no—
500C4×D4—41no—
501C4×D4—862no—
502C4×D4—862no—
503C4×D4—1721no—
504C4×D4—1721no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4C22×D4311yescharacteristic
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—1724no—
526C2×C22⋊C4C22⋊D4311yescharacteristic
527C2×C22⋊C4C22⋊D4311yescharacteristic
528C2×C42C22×D4311yescharacteristic
529C2×C42C22×D4311yescharacteristic
530#107—862no—
531#107—1721no—
532C4⋊C8—1721no—
533#102—862no—
534#102—862no—
535#102—862no—
536#102—862no—
537#102—862no—
538#102—862no—
539#102—1721no—
540#102—1721no—
541C22⋊C8—862no—
542C22⋊C8—1721no—
543C4×C8—862no—
544#95—21no—
545#95—21no—
546#95—861no—
547#95C22⋊D4311yescharacteristic
548#95C22⋊D4311yescharacteristic
549C24—21no—
550C24—864no—
551C24—861no—
552C24—861no—
553C24—3441no—
554C24—3441no—
555C24—1722no—
556C24—1722no—
557C24—1722no—
558C24—1722no—
559C24C2×C22⋊D4311yescharacteristic
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—432no—
569C2×D4—432no—
570C2×D4—432no—
571C2×D4—432no—
572C2×D4—864no—
573C2×D4—861no—
574C2×D4—861no—
575C2×D4—861no—
576C2×D4—861no—
577C2×D4—861no—
578C2×D4—861no—
579C2×D4—861no—
580C2×D4—861no—
581C2×D4—1722no—
582C2×D4—1722no—
583C2×D4—1724no—
584C2×D4—1724no—
585C2×D4—1724no—
586C2×D4—1724no—
587C2×D4D4×D4312yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—81no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—3441no—
603C22×C4—3441no—
604C22×C4—1722no—
605C22×C4—1722no—
606C22×C4—1722no—
607C22×C4—1722no—
608C22×C4C2×C22⋊D4311yescharacteristic
609C22×C4C2×C22⋊D4311yescharacteristic
610C22×C4C2×C22⋊D4311yescharacteristic
611C22×C4C2×C22⋊D4311yescharacteristic
612C22×C4C2×C22⋊D4311yescharacteristic
613C22×C4C23×D4311yescharacteristic
614D8—868no—
615D8—1724no—
616C2×C8—432no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—81no—
637C4⋊C4—861no—
638C4⋊C4—861no—
639C4⋊C4—861no—
640C4⋊C4—861no—
641C22⋊C4—41no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—3441no—
648C22⋊C4—3441no—
649C22⋊C4—1722no—
650C22⋊C4—1722no—
651C22⋊C4—1722no—
652C22⋊C4—1722no—
653C22⋊C4—1722no—
654C22⋊C4#1062188214yescomplemented
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—862no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—3444no—
677C23—3444no—
678C23—3444no—
679C23—3444no—
680C23—3444no—
681C23—1728no—
682C23—1728no—
683C23—1721no—
684C23—1721no—
685C23—1721no—
686C23—1721no—
687C23—1721no—
688C23—1721no—
689C23—1721no—
690C23—1721no—
691C23—1721no—
692C23—1721no—
693C23C2×#1062188212yes—
694C23C22×C22⋊D4311yescharacteristic
695D4—22no—
696D4—22no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—434no—
701D4—862no—
702D4—862no—
703D4—862no—
704D4—862no—
705D4—862no—
706D4—1728no—
707D4—1721no—
708D4—1721no—
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—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
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—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—84no—
736C2×C4—3444no—
737C2×C4—3444no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4C2×#1062188212yes—
745C2×C4C2×#1062188212yes—
746C2×C4C2×D4×D4311yescharacteristic
747C2×C4#41×D4311yescharacteristic
748C2×C4#41×D4311yescharacteristic
749C2×C4#41×D4311yescharacteristic
750C2×C4#1306337011yescharacteristic
751C2×C4#1306337111yescharacteristic
752C8—862no—
753C8—1721no—
754C8—1721no—
755C8—1721no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—864no—
771C22—34416no—
772C22—3441no—
773C22—3441no—
774C22—3441no—
775C22—3441no—
776C22—1722no—
777C22—1722no—
778C22—1722no—
779C22—1722no—
780C22—1722no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22#1458340611yescharacteristic
786C22D4×C22⋊D4311yescharacteristic
787C22#1458353711yescharacteristic
788C22C22×#1062188211yescharacteristic
789C22#1458369711yescharacteristic
790C22#1458370211yescharacteristic
791C22#1458370711yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—3441no—
801C4—3441no—
802C4#123×D4311yescharacteristic
803C4#1458348511yescharacteristic
804C4#1458354111yescharacteristic
805C4#1458357711yescharacteristic
806C2—42no—
807C2—82no—
808C2—3442no—
809C2—1724no—
810C2#1913805411yescharacteristic
811C2#1914459111yescharacteristic
812C2#1914477311yescharacteristic
813C2#1914612111yescharacteristic
814C2D4×#1062188211yescharacteristic
815C2#1914640211yescharacteristic
816C2#1914679011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2422C2
socleC23×C43C22×D4
prime radicalC2×#14583032C2
hypercenter#2422D43
hypocenterC43#24893
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2422

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621882C2semidirect
3. C22⋊C4×D172C2semidirect
4. #19136124C2semidirect
5. #19136021C2semidirect
6. #19135905C2semidirect
7. #19135774C2semidirect
8. #19135277C2semidirect
9. #19135203C2semidirect
10. #19134946C2semidirect
11. #19134943C2semidirect
12. #19134841C2semidirect
13. #19134592C2semidirect
14. #19134525C2semidirect
15. C43×#2422C2semidirect
24. C2×#13063258C22semidirect
25. C2×#13063258C22semidirect
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
52. C2×C4×D4×C43C22semidirect
55. C43×#390C22semidirect
56. C43×#389C22semidirect
58. C43×#384C22semidirect
220. C22⋊C4×C43D8semidirect
340. D172#123semidirect
400. #2422D43semidirect
431. C2×C4×D4C2×D43semidirect
453. #390C2×D43semidirect
454. #389C2×D43semidirect
458. #384C2×D43semidirect
469. C43#24893semidirect
654. C22⋊C4#10621882semidirect

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
#191361242
#191360212
#191359052
#191357742
#191352772
#191352032
#191349462
#191349432
#191348412
#191345922
#191345252
C43×#24222
#2489343