Finite Group Databasebeta

← #25148670

Subgroups — #25148670

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583196C211yesmaximal, characteristic
2C2×#14583030C211yesmaximal, characteristic, complemented
3#19139513C211yesmaximal, characteristic
4#19136096C211yesmaximal, characteristic, complemented
5#19136086C211yesmaximal, characteristic, complemented
6#19135966C211yesmaximal, characteristic
7#19135966C211yesmaximal, characteristic
8#19135565C211yesmaximal, characteristic, complemented
9#19135358C211yesmaximal, characteristic, complemented
10#19135335C211yesmaximal, characteristic, complemented
11#19135320C211yesmaximal, characteristic, complemented
12#19135291C211yesmaximal, characteristic
13#19135277C211yesmaximal, characteristic
14#19134423C211yesmaximal, characteristic
15C43×#2584C211yesmaximal, characteristic, complemented
16C2×#13063301—21no—
17C2×C4×D172C2211yescharacteristic
18#14583196—24no—
19#14583030—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063236C2211yescharacteristic
32C2×#13063236C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582821—21no—
35#14582821—21no—
36#14582801C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582769C2211yescharacteristic
41#14582756—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C2×#125×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C43×#398—21no—
53C43×#395—21no—
54C43×#389—21no—
55C43×#389—21no—
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063301—44no—
68C4×D172—22no—
69C4×D172—22no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82#13063258—22no—
83#13063256—22no—
84#13063256—22no—
85#13063256—22no—
86C4⋊(C43⋊C8)—22no—
87C4⋊(C43⋊C8)—22no—
88C4⋊(C43⋊C8)D414yes—
89#13063245—22no—
90#13063245—22no—
91#13063245—22no—
92#13063245Q814yescomplemented
93#13063236—22no—
94#13063236—22no—
95C4×C43⋊C8—22no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C22×Q8×C43D411yescharacteristic
99#125×C43—22no—
100#125×C43—22no—
101C4×Q8×C43—22no—
102C4×Q8×C43—22no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C42×C43—21no—
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119C2×C42×C43C2311yescharacteristic
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125C23×D43—21no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—41no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172C2×Q812yes—
149C2×C4×D43—42no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43—42no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43—81no—
166C4⋊C4×C43—81no—
167C4⋊C4×C43C2×Q812yes—
168C4⋊C4×C43#4112yes—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—81no—
174C42×C43C2×D412yes—
175C42×C43#4112yes—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—81no—
180(C2×D43)⋊C4—81no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—42no—
188C4⋊Dic43—81no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C2×D412yes—
201C2×C43⋊C8C2×D412yes—
202C2×C43⋊C8C2×Q812yes—
203C23×C43C22×D411yescharacteristic
204C22×D43—22no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211Q8×C43—44no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43#12112yes—
240C2×C4×C43#12112yes—
241C2×C4×C43AGL(1,ℤ/8)12yes—
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×Q811yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257D172—22no—
258D172—22no—
259D172—41no—
260D172—41no—
261C4×D43—84no—
262C43⋊C8—22no—
263C43⋊C8—22no—
264C43⋊C8—22no—
265C43⋊C8—41no—
266#25486—431nomaximal, Sylow
267C22×C43C2×#12111yescharacteristic
268C22×C43#54811yescharacteristic
269C22×C43D4×Q811yescharacteristic
270C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C43#57511yescharacteristic
272C22×C43#57711yescharacteristic
273C22×C43#57711yescharacteristic
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C4×C43—22no—
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—42no—
285C4×C43—42no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—81no—
290C4×C43—81no—
291C4×C43#53311yescharacteristic
292C4×C43#54111yescharacteristic
293C4×C43#54711yescharacteristic
294C4×C43D4×Q811yescharacteristic
295Dic43—81no—
296Dic43—81no—
297Dic43—81no—
298C2×#478—431no—
299C2×#446—431no—
300#2584D4311yescharacteristic, complemented
301#2538—431no—
302#2088—431no—
303#2086—431no—
304#2065—431no—
305#2065—431no—
306#1992—431no—
307#1948—431no—
308#1944—431no—
309#1941—431no—
310#1936—431no—
311#1934—431no—
312#1762—431no—
313C2×C43#242911yescharacteristic
314C2×C43#305511yescharacteristic
315C2×C43#306011yescharacteristic
316C2×C43#336811yescharacteristic
317C2×C43#337611yescharacteristic
318C2×C43#338411yescharacteristic
319C2×C43#338811yescharacteristic
320D43—82no—
321C2×#125C2×D4311yescharacteristic
322C2×C22⋊Q8—861no—
323C2×C4×Q8C2×D4311yescharacteristic
324C2×C4×D4—431no—
325#478—864no—
326#446—864no—
327C2×#107—431no—
328C2×#106—431no—
329C2×#106—431no—
330C2×#106—431no—
331C2×C4⋊C8—431no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8—431no—
334C2×#102—431no—
335C2×#102—431no—
336C2×#102—431no—
337C2×#102—431no—
338C2×#97—431no—
339C2×#97—431no—
340C2×C4×C8—431no—
341#398—21no—
342#396—861no—
343#396—861no—
344#395—21no—
345#390—431no—
346#390—431no—
347#389—21no—
348#389—21no—
349#389—431no—
350#389—431no—
351#389C2×D4311yescharacteristic
352#389C2×D4311yescharacteristic
353#389C2×D4311yescharacteristic
354#389C2×D4311yescharacteristic
355#384—431no—
356#380—861no—
357C4×C4⋊C4C2×D4311yescharacteristic
358#340—431no—
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366C43#2548611yescharacteristic, complemented, Sylow
367C22×Q8C22⋊D4311yescharacteristic
368C22×D4—431no—
369C23×C4—861no—
370C22×C8—431no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—431no—
374#125—22no—
375#125—22no—
376C22⋊Q8—1724no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×D4—862no—
380C4×D4—862no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—861no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4C22⋊D4311yescharacteristic
395C2×C4⋊C4C22⋊D4311yescharacteristic
396C2×C4⋊C4C22⋊D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C22⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—21no—
407C2×C42C22×D4311yescharacteristic
408C2×C42C22×D4311yescharacteristic
409C2×C42C22×D4311yescharacteristic
410#107—862no—
411#106—862no—
412#106—862no—
413#106—862no—
414C4⋊C8—434no—
415C4⋊C8—862no—
416C4⋊C8—862no—
417#102—434no—
418#102—862no—
419#102—862no—
420#102—862no—
421#97—862no—
422#97—862no—
423C4×C8—862no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—861no—
430#95—861no—
431C24—861no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—41no—
435C2×D4—432no—
436C2×D4—861no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—1722no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4C2×C22⋊D4311yescharacteristic
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458C2×C8—432no—
459C2×C8—432no—
460C2×C8—432no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—3441no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4Q8×D4312yes—
496C4⋊C4#1062190212yes—
497C22⋊C4—3441no—
498C22⋊C4—3441no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C22⋊C4—1722no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—81no—
507C42D4×D4312yes—
508C42#1062190012yes—
509C23—862no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23C22×C22⋊D4311yescharacteristic
517Q8—44no—
518D4—862no—
519D4—862no—
520D4—1721no—
521D4—1721no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—3444no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4#1306329712yes—
560C2×C4#1306329712yes—
561C2×C4#1306335012yes—
562C2×C4C2×D4×D4311yescharacteristic
563C2×C4C2×Q8×D4311yescharacteristic
564C2×C4C2×#1062190011yescharacteristic
565C2×C4C2×#1062190211yescharacteristic
566C2×C4#1306337311yescharacteristic
567C2×C4#1306337311yescharacteristic
568C8—862no—
569C8—862no—
570C8—862no—
571C8—1721no—
572C22—3441no—
573C22—3441no—
574C22—3441no—
575C22—3441no—
576C22—1722no—
577C22—1722no—
578C22—1722no—
579C22C2×#1306329711yescharacteristic
580C22#1458356011yescharacteristic
581C22Q8×C22⋊D4311yescharacteristic
582C22C2×#1306335011yescharacteristic
583C22#1458369711yescharacteristic
584C22#1458370711yescharacteristic
585C22#1458371011yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—3441no—
597C4—3441no—
598C4—3441no—
599C4#1458345411yescharacteristic
600C4#1458351011yescharacteristic
601C4#1458355211yescharacteristic
602C4#1458356411yescharacteristic
603C2—3442no—
604C2#1913819711yescharacteristic
605C2#1914421611yescharacteristic
606C2#1914425411yescharacteristic
607C2#1914732411yescharacteristic
608C2#1914742211yescharacteristic
609C2#1914749411yescharacteristic
610C2#1914753411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2584C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2584D43
hypocenterC43#25486
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2584

Complements

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

NH ≅ G/Ntype
2. C2×#14583030C2semidirect
4. #19136096C2semidirect
5. #19136086C2semidirect
8. #19135565C2semidirect
9. #19135358C2semidirect
10. #19135335C2semidirect
11. #19135320C2semidirect
15. C43×#2584C2semidirect
92. #13063245Q8semidirect
300. #2584D43semidirect
366. C43#25486semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
C2×#145830302
#191395132
#191360962
#191360862
#191359662
#191355652
#191353582
#191353352
#191353202
#191352912
#191352772
#191344232
C43×#25842
#2548643