Finite Group Databasebeta

← #25148375

Subgroups — #25148375

Order 11008.

812 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583309C211yesmaximal, characteristic, complemented
2C2×#14583196C211yesmaximal, characteristic
3#19139544C211yesmaximal, characteristic
4#19136071C211yesmaximal, characteristic, complemented
5#19136066C211yesmaximal, characteristic, complemented
6#19135980C211yesmaximal, characteristic
7#19135966C211yesmaximal, characteristic
8#19135543C211yesmaximal, characteristic, complemented
9#19135358C211yesmaximal, characteristic, complemented
10#19135353C211yesmaximal, characteristic, complemented
11#19135319C211yesmaximal, characteristic, complemented
12#19135222C211yesmaximal, characteristic
13#19135215C211yesmaximal, characteristic
14#19134423C211yesmaximal, characteristic
15C43×#2370C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×#13063305—21no—
18C2×#13063305—21no—
19C2×C4×D172C2211yescharacteristic
20#14583309—24no—
21#14583196—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063236C2211yescharacteristic
36#14582836—21no—
37#14582836—21no—
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582769C2211yescharacteristic
41#14582769C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×#125×C43C2211yescharacteristic
51C43×#389—21no—
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#387—21no—
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×Dic86—21no—
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063325—22no—
69#13063325—22no—
70#13063305—44no—
71#13063305—44no—
72C4×D172—22no—
73C4×D172—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×(C2×D43)⋊C4—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#13063258—22no—
89#13063258—22no—
90#13063256—22no—
91#13063256—22no—
92#13063256—22no—
93C4⋊(C43⋊C8)—22no—
94C4⋊(C43⋊C8)—22no—
95C4⋊(C43⋊C8)—22no—
96#13063245—22no—
97#13063245—22no—
98#13063245—22no—
99#13063245Q814yescomplemented
100#13063236—22no—
101#125×C43—22no—
102#125×C43D414yes—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43D411yescharacteristic
125#95×C43D411yescharacteristic
126C23×D43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2411yescharacteristic
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172C2×Q812yes—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×Dic86—42no—
151C2×Dic86—42no—
152C2×Dic86—42no—
153C4⋊C4×C43—24no—
154C4⋊C4×C43—24no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43—81no—
164C4⋊C4×C43C2×D412yes—
165C4⋊C4×C43C2×D412yes—
166C4⋊C4×C43C2×Q812yes—
167C42×C43—21no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—42no—
172C42×C43—81no—
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—42no—
180(C2×D43)⋊C4—42no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—42no—
188C4⋊Dic43—42no—
189C4⋊Dic43—42no—
190C4⋊Dic43—42no—
191C4⋊Dic43—42no—
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⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×Q812yes—
203C2×C43⋊C8#4112yes—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
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—22no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
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#12112yes—
239C2×C4×C43#12112yes—
240C2×C4×C43AGL(1,ℤ/8)12yes—
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—
262Dic86—84no—
263C43⋊C8—22no—
264C43⋊C8—22no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#25465—431nomaximal, Sylow
268C22×C43C2×#12111yescharacteristic
269C22×C43#54711yescharacteristic
270C22×C43D4×Q811yescharacteristic
271C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57811yescharacteristic
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—22no—
286C4×C43—41no—
287C4×C43—41no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—42no—
291C4×C43—81no—
292C4×C43#53311yescharacteristic
293C4×C43#54111yescharacteristic
294C4×C43#54811yescharacteristic
295C4×C43D4×Q811yescharacteristic
296Dic43—81no—
297Dic43—81no—
298Dic43—81no—
299C2×#501—431no—
300C2×#478—431no—
301#2542—431no—
302#2370D4311yescharacteristic, complemented
303#2084—431no—
304#2083—431no—
305#2067—431no—
306#2065—431no—
307#1987—431no—
308#1948—431no—
309#1947—431no—
310#1940—431no—
311#1926—431no—
312#1925—431no—
313#1762—431no—
314C2×C43#242911yescharacteristic
315C2×C43#303811yescharacteristic
316C2×C43#304611yescharacteristic
317C2×C43#334311yescharacteristic
318C2×C43#334511yescharacteristic
319C2×C43#338411yescharacteristic
320C2×C43#338611yescharacteristic
321D43—82no—
322C2×C4⋊Q8—431no—
323C2×#125C2×D4311yescharacteristic
324C2×C22⋊Q8—861no—
325C2×C22⋊Q8—861no—
326C2×C4×D4—431no—
327#501—864no—
328#478—864no—
329C2×#107—431no—
330C2×#107—431no—
331C2×#107—431no—
332C2×#106—431no—
333C2×#106—431no—
334C2×#106—431no—
335C2×C4⋊C8—431no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8—431no—
338C2×#102—431no—
339C2×#102—431no—
340C2×#102—431no—
341C2×#102—431no—
342C2×#97—431no—
343#399—861no—
344#399—861no—
345#390—431no—
346#390—431no—
347#389—21no—
348#389C2×D4311yescharacteristic
349#389C2×D4311yescharacteristic
350#387—21no—
351#387—21no—
352#384—431no—
353#384—431no—
354C4×C4⋊C4—21no—
355C4×C4⋊C4C2×D4311yescharacteristic
356C4×C4⋊C4C2×D4311yescharacteristic
357C4×C4⋊C4C2×D4311yescharacteristic
358C4×C4⋊C4C2×D4311yescharacteristic
359#340—431no—
360#340—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#336—431no—
366#336—431no—
367C43#2546511yescharacteristic, complemented, Sylow
368C22×Q8—861no—
369C22×D4—431no—
370C23×C4—861no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8—431no—
374C22×C8—431no—
375C4⋊Q8—862no—
376C4⋊Q8—862no—
377#125—22no—
378#125D17214yes—
379C22⋊Q8—1724no—
380C22⋊Q8—1724no—
381C4×D4—862no—
382C4×D4—862no—
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⋊C4—861no—
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×C42—21no—
408C2×C42—21no—
409C2×C42C22×D4311yescharacteristic
410C2×C42C22×D4311yescharacteristic
411C2×C42C22×D4311yescharacteristic
412#107—862no—
413#107—862no—
414#107—862no—
415#106—862no—
416#106—862no—
417#106—862no—
418C4⋊C8—862no—
419C4⋊C8—862no—
420C4⋊C8—862no—
421#102—434no—
422#102—862no—
423#102—862no—
424#102—862no—
425#97—862no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95C22⋊D4311yescharacteristic
432#95C22⋊D4311yescharacteristic
433C24—861no—
434C2×Q8—1722no—
435C2×Q8—1722no—
436C2×Q8—1722no—
437C2×D4—432no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—1722no—
451C22×C4—1722no—
452C22×C4—1722no—
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460C2×C8—432no—
461C2×C8—432no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—81no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—1722no—
490C4⋊C4—1722no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4C2×D17212yes—
495C4⋊C4C2×D17212yes—
496C4⋊C4Q8×D4312yes—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C22⋊C4—1722no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—81no—
508C42—81no—
509C42C2×D17212yes—
510C42#1062189812yes—
511C23—862no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23C22×C22⋊D4311yescharacteristic
519Q8—3444no—
520D4—862no—
521D4—862no—
522D4—1721no—
523D4—1721no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
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—41no—
550C2×C4—3444no—
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—1721no—
560C2×C4#1306329912yes—
561C2×C4#1306329912yes—
562C2×C4#1306335012yes—
563C2×C4#1306335012yes—
564C2×C4C22×D17211yescharacteristic
565C2×C4C2×Q8×D4311yescharacteristic
566C2×C4#41×D4311yescharacteristic
567C2×C4C2×#1062189811yescharacteristic
568C2×C4#1306337211yescharacteristic
569C2×C4#1306337311yescharacteristic
570C8—862no—
571C8—862no—
572C8—1721no—
573C8—1721no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22—1722no—
579C22—1722no—
580C22—1722no—
581C22C2×#1306329911yescharacteristic
582C22#1458354811yescharacteristic
583C22Q8×C22⋊D4311yescharacteristic
584C22C2×#1306335011yescharacteristic
585C22C2×#1306335011yescharacteristic
586C22#1458371011yescharacteristic
587C22#1458371411yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—22no—
592C4—41no—
593C4—41no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4—81no—
598C4—3441no—
599C4—3441no—
600C4—3441no—
601C4#1458345311yescharacteristic
602C4#1458350711yescharacteristic
603C4#1458356111yescharacteristic
604C4Q8×D17211yescharacteristic
605C2—3442no—
606C2#1913818811yescharacteristic
607C2#1914407511yescharacteristic
608C2#1914414511yescharacteristic
609C2#1914703511yescharacteristic
610C2#1914705911yescharacteristic
611C2#1914749411yescharacteristic
612C2#1914751211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2370C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2370D43
hypocenterC43#25465
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
1. C2×#14583309C2semidirect
4. #19136071C2semidirect
5. #19136066C2semidirect
8. #19135543C2semidirect
9. #19135358C2semidirect
10. #19135353C2semidirect
11. #19135319C2semidirect
15. C43×#2370C2semidirect
99. #13063245Q8semidirect
302. #2370D43semidirect
367. C43#25465semidirect

Maximal subgroups

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

subgroupindex
C2×#145833092
C2×#145831962
#191395442
#191360712
#191360662
#191359802
#191359662
#191355432
#191353582
#191353532
#191353192
#191352222
#191352152
#191344232
C43×#23702
#2546543