Finite Group Databasebeta

← #25148387

Subgroups — #25148387

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×#14583196C211yesmaximal, characteristic
2#19139549C211yesmaximal, characteristic
3#19137695C211yesmaximal, characteristic, complemented
4#19136074C211yesmaximal, characteristic, complemented
5#19136069C211yesmaximal, characteristic, complemented
6#19135978C211yesmaximal, characteristic
7#19135964C211yesmaximal, characteristic
8#19135544C211yesmaximal, characteristic, complemented
9#19135355C211yesmaximal, characteristic, complemented
10#19135350C211yesmaximal, characteristic, complemented
11#19135318C211yesmaximal, characteristic, complemented
12#19135221C211yesmaximal, characteristic
13#19135214C211yesmaximal, characteristic
14#19134421C211yesmaximal, characteristic
15C2×C43×#501C211yesmaximal, characteristic, complemented
16C2×#13063301—21no—
17C2×#13063301—21no—
18C2×C4×D172C2211yescharacteristic
19#14583196—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29#14582834—21no—
30#14582834—21no—
31#14582800C2211yescharacteristic
32#14582800C2211yescharacteristic
33#14582798—21no—
34#14582798C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582785—21no—
37#14582785—21no—
38#14582768C2211yescharacteristic
39#14582768C2211yescharacteristic
40C4⋊C4×Dic43—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4⋊Q8×C43C2211yescharacteristic
54C2×#125×C43C2211yescharacteristic
55C43×#501—24no—
56C2×#107×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#106×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063301—44no—
66#13063301—44no—
67C4×D172—22no—
68C4×D172—22no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063258—22no—
91#13063256—22no—
92C4⋊(C43⋊C8)—22no—
93Dic43⋊C8—22no—
94Dic43⋊C8—22no—
95#13063247—22no—
96#13063247Q814yescomplemented
97#13063245—22no—
98#13063245—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×Q8×C43—21no—
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C4⋊Q8×C43—22no—
110C4⋊Q8×C43—22no—
111#125×C43—22no—
112#125×C43D414yes—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#107×C43—22no—
122#107×C43—22no—
123#106×C43—22no—
124#106×C43—22no—
125#97×C43—22no—
126C23×D43—21no—
127C2×Q8×C43—42no—
128C2×Q8×C43—42no—
129C2×Q8×C43—42no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172C2×Q812yes—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43C2×Q812yes—
158C2×C8×C43#4112yes—
159C4⋊C4×C43—24no—
160C4⋊C4×C43—24no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43C2×D412yes—
169C4⋊C4×C43C2×D412yes—
170C42×C43C2×D412yes—
171C42×C43#4112yes—
172(C2×D43)⋊C4—42no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177C4⋊Dic43—21no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—42no—
185C4⋊Dic43—81no—
186C4⋊Dic43C2×Q812yes—
187Dic43⋊C4—42no—
188Dic43⋊C4—42no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—42no—
196C4×Dic43—81no—
197C4×Dic43—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212Q8×C43—84no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43#12112yes—
230C2×C4×C43#12112yes—
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×Q811yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C432−1+411yescharacteristic
236C2×C4×C432−1+411yescharacteristic
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
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×Dic43AGL(1,ℤ/8)12yes—
257C2×Dic43AGL(1,ℤ/8)12yes—
258D172—22no—
259D172—22no—
260D172—41no—
261D172—41no—
262C4×D43—84no—
263C8×C43—22no—
264C8×C43—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—42no—
285C4×C43—42no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43#53311yescharacteristic
289C4×C43#54111yescharacteristic
290C4×C43#54811yescharacteristic
291C4×C43D4×Q811yescharacteristic
292Dic43—22no—
293Dic43—22no—
294Dic43—41no—
295Dic43—41no—
296Dic43—42no—
297Dic43—81no—
298Dic43—81no—
299C2×#501D4311yescharacteristic, complemented
300C2×#478—431no—
301#2542—431no—
302#2370—431no—
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⋊Q8C2×D4311yescharacteristic
323C2×#125C2×D4311yescharacteristic
324C2×C22⋊Q8—861no—
325C2×C22⋊Q8—861no—
326C2×C4×D4—431no—
327#501—24no—
328#478—864no—
329C2×#107—431no—
330C2×#107C2×D4311yescharacteristic
331C2×#107C2×D4311yescharacteristic
332C2×#106—431no—
333C2×#106C2×D4311yescharacteristic
334C2×#106C2×D4311yescharacteristic
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×#97C2×D4311yescharacteristic
343#399—861no—
344#399—861no—
345#390—431no—
346#390—431no—
347#389—431no—
348#389—431no—
349#389—861no—
350#387—861no—
351#387—861no—
352#384—431no—
353#384—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—861no—
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—21no—
369C22×D4—431no—
370C23×C4—861no—
371C22×C8—431no—
372C22×C8—431no—
373C22×C8C22×D4311yescharacteristic
374C22×C8C22×D4311yescharacteristic
375C4⋊Q8—22no—
376C4⋊Q8—22no—
377#125—22no—
378#125C22⋊D4314yes—
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—431no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—861no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
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—431no—
407C2×C42—431no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42C22×D4311yescharacteristic
412#107—22no—
413#107—22no—
414#107—862no—
415#106—22no—
416#106—22no—
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—22no—
426#95—431no—
427#95—431no—
428#95—861no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433C24—861no—
434C2×Q8—42no—
435C2×Q8—42no—
436C2×Q8—42no—
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—431no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—431no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—861no—
454C22×C4—1722no—
455C22×C4—1722no—
456C22×C4—1722no—
457C22×C4D4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4C23×D4311yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8Q8×D4312yes—
471C2×C8#1062190212yes—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—432no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—3441no—
490C4⋊C4—1722no—
491C4⋊C4—1722no—
492C4⋊C4—1722no—
493C4⋊C4—1722no—
494C4⋊C4—1722no—
495C4⋊C4C2×C22⋊D4312yes—
496C4⋊C4C2×C22⋊D4312yes—
497C22⋊C4—1722no—
498C22⋊C4—1722no—
499C22⋊C4—1722no—
500C22⋊C4—1722no—
501C22⋊C4—1722no—
502C42—861no—
503C42—861no—
504C42—861no—
505C42—861no—
506C42—3441no—
507C42—3441no—
508C42—1722no—
509C42#1062190012yes—
510C42C2×C22⋊D4312yes—
511C23—862no—
512C23—1721no—
513C23—1721no—
514C23—1721no—
515C23—1721no—
516C23—1721no—
517C23—1721no—
518C23C2×D4×D4311yescharacteristic
519Q8—84no—
520D4—862no—
521D4—862no—
522D4—1721no—
523D4—1721no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—432no—
541C2×C4—432no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—862no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—3444no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4#1306329712yes—
563C2×C4#1306329712yes—
564C2×C4C22×C22⋊D4311yescharacteristic
565C2×C4C2×Q8×D4311yescharacteristic
566C2×C4C2×#1062190011yescharacteristic
567C2×C4C2×#1062190211yescharacteristic
568C2×C4#1306337311yescharacteristic
569C2×C4#1306337311yescharacteristic
570C8—22no—
571C8—22no—
572C8—1721no—
573C8—1721no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22—1722no—
579C22—1722no—
580C22—1722no—
581C22C2×#1306329711yescharacteristic
582C22#1458355211yescharacteristic
583C22#1458356411yescharacteristic
584C22AGL(1,ℤ/8)×D4311yescharacteristic
585C22AGL(1,ℤ/8)×D4311yescharacteristic
586C22#1458370811yescharacteristic
587C22#1458371511yescharacteristic
588C4—22no—
589C4—22no—
590C4—42no—
591C4—42no—
592C4—81no—
593C4—81no—
594C4—862no—
595C4—862no—
596C4—3441no—
597C4—3441no—
598C4—1721no—
599C4—1721no—
600C4—1722no—
601C4#1458345411yescharacteristic
602C4#1458351011yescharacteristic
603C4#1458356011yescharacteristic
604C4Q8×C22⋊D4311yescharacteristic
605C2—3442no—
606C2#1913819711yescharacteristic
607C2#1914407311yescharacteristic
608C2#1914414911yescharacteristic
609C2#1914703411yescharacteristic
610C2#1914706411yescharacteristic
611C2#1914749111yescharacteristic
612C2#1914751311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#501C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenterC2×#501D43
hypocenterC43#25465
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #19137695C2semidirect
4. #19136074C2semidirect
5. #19136069C2semidirect
8. #19135544C2semidirect
9. #19135355C2semidirect
10. #19135350C2semidirect
11. #19135318C2semidirect
15. C2×C43×#501C2semidirect
96. #13063247Q8semidirect
299. C2×#501D43semidirect
367. C43#25465semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
#191395492
#191376952
#191360742
#191360692
#191359782
#191359642
#191355442
#191353552
#191353502
#191353182
#191352212
#191352142
#191344212
C2×C43×#5012
#2546543