Finite Group Databasebeta

← #25196335

Subgroups — #25196335

Order 11008.

742 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
1#19142954C211yesmaximal, characteristic, complemented
2#19137134C211yesmaximal, characteristic
3#19136162C211yesmaximal, characteristic, complemented
4#19135837C211yesmaximal, characteristic
5#19135836C211yesmaximal, characteristic
6#19135293C211yesmaximal, characteristic
7#19135290C211yesmaximal, characteristic
8#19135286C211yesmaximal, characteristic, complemented
9#19135283C211yesmaximal, characteristic, complemented
10#19134599C211yesmaximal, characteristic, complemented
11#19134599C211yesmaximal, characteristic, complemented
12#19134594C211yesmaximal, characteristic
13#19134594C211yesmaximal, characteristic
14#19134447C211yesmaximal, characteristic, complemented
15C43×#2101C211yesmaximal, characteristic, complemented
16C2×#13063315—21no—
17C2×#13063313C2211yescharacteristic
18C2×#13063290C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32#14582804C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582796—21no—
37#14582795C2211yescharacteristic
38#14582794—21no—
39#14582788—21no—
40#14582788—21no—
41#14582768C2211yescharacteristic
42#14582768C2211yescharacteristic
43#14582763—21no—
44#14582746—21no—
45#14582746—21no—
46C42×Dic43C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#382C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063315—44no—
65#13063313—22no—
66#13063313—22no—
67#13063290—22no—
68#13063290—22no—
69#13063287—22no—
70#13063287—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93Dic43⋊C8—22no—
94Dic43⋊C8—22no—
95#13063250—22no—
96#13063250—41no—
97#13063248—22no—
98#13063248—41no—
99#13063247—22no—
100#13063247—41no—
101#13063245—22no—
102#13063245—41no—
103#13063235—41no—
104#13063235—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121C23×D43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172#4112yes—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144C2×C4×D43—42no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86#4112yes—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—42no—
166C42×C43—21no—
167C42×C43—21no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—42no—
171(C2×D43)⋊C4—42no—
172(C2×D43)⋊C4—42no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—42no—
178Dic43⋊C4—42no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184Dic43⋊C4—42no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—22no—
188C4×Dic43—22no—
189C4×Dic43—41no—
190C4×Dic43—41no—
191C4×Dic43—42no—
192C4×Dic43#4112yes—
193C4×Dic43#4112yes—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C23×C43C22×D411yescharacteristic
201C22×D43—22no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C2×C4×C432−1+411yescharacteristic
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—22no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43#12412yes—
250C2×Dic43#12412yes—
251C2×Dic43AGL(1,ℤ/8)12yes—
252C2×Dic43#13712yes—
253D172—22no—
254D172—22no—
255D172—41no—
256D172—41no—
257C4×D43—84no—
258Dic86—22no—
259Dic86—22no—
260Dic86—41no—
261Dic86—41no—
262C8×C43—41no—
263C8×C43—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266#29131—431nomaximal, Sylow
267C22×C43#52511yescharacteristic
268C22×C43C2×#12411yescharacteristic
269C22×C43#53711yescharacteristic
270C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C43C2×#13711yescharacteristic
272C22×C43#57511yescharacteristic
273C22×C43#57511yescharacteristic
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43#55211yescharacteristic
288C4×C43#55211yescharacteristic
289C4×C43#55311yescharacteristic
290C4×C43#55311yescharacteristic
291Dic43—22no—
292Dic43—42no—
293Dic43—41no—
294Dic43—41no—
295Dic43—81no—
296Dic43—81no—
297Dic43#48914yes—
298#2859—431no—
299C4×#124—431no—
300#2101—431no—
301#2101D4311yescharacteristic, complemented
302#2042—431no—
303#2042—431no—
304#1936—431no—
305#1936—431no—
306#1935—431no—
307#1935—431no—
308#1803—431no—
309#1803—431no—
310#1802—431no—
311#1802—431no—
312#1767—431no—
313C2×C43#256211yescharacteristic
314C2×C43#311511yescharacteristic
315C2×C43#311611yescharacteristic
316C2×C43C2×#48911yescharacteristic
317C2×C43#314211yescharacteristic
318C2×C43#325111yescharacteristic
319C2×C43#325211yescharacteristic
320D43—82no—
321C2×#125—861no—
322C2×#124—431no—
323C2×C4×Q8—431no—
324C2×C4×D4—431no—
325C2×C4⋊C8—431no—
326C2×C4⋊C8—431no—
327C2×#103—431no—
328C2×#103—431no—
329C2×#103—431no—
330C2×#103—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×#102—431no—
334C2×#102—431no—
335C2×#97—431no—
336C2×#97—431no—
337#391—431no—
338#390—431no—
339#389—431no—
340#389—431no—
341#389—431no—
342#389—861no—
343#389—861no—
344#389C2×D4311yescharacteristic
345#388—861no—
346#388—861no—
347#384—431no—
348#384—431no—
349#382—861no—
350#382C2×D4311yescharacteristic
351C4×C22⋊C4—861no—
352C4×C22⋊C4—861no—
353C43—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340C2×D4311yescharacteristic
359#340C2×D4311yescharacteristic
360#340C2×D4311yescharacteristic
361#340C2×D4311yescharacteristic
362#336—431no—
363#336C2×D4311yescharacteristic
364C43#2913111yescharacteristic, complemented, Sylow
365C22×Q8—431no—
366C22×D4—431no—
367C23×C4—861no—
368C22×C8—431no—
369C22×C8—431no—
370C22×C8C22×D4311yescharacteristic
371C22×C8C22×D4311yescharacteristic
372#125—1724no—
373#124—862no—
374#124—862no—
375C4×Q8—862no—
376C4×Q8—862no—
377C4×D4—862no—
378C4×D4—862no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C4⋊C4C22×D4311yescharacteristic
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—861no—
399C2×C42—431no—
400C2×C42—431no—
401C2×C42—431no—
402C2×C42—431no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—861no—
406C2×C42C22×D4311yescharacteristic
407C4⋊C8—862no—
408C4⋊C8—862no—
409#103—862no—
410#103—862no—
411#103—1721no—
412#103—1721no—
413#102—862no—
414#102—862no—
415#102—1721no—
416#102—1721no—
417#97—1721no—
418#97—1721no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427C24—861no—
428C2×Q8—432no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×D4—432no—
435C2×D4—861no—
436C2×D4—861no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—1722no—
452C22×C4—1722no—
453C22×C4—1722no—
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4C23×D4311yescharacteristic
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4—1722no—
488C4⋊C4—1722no—
489C4⋊C4—1722no—
490C22⋊C4—864no—
491C22⋊C4—864no—
492C22⋊C4—1722no—
493C22⋊C4—1722no—
494C22⋊C4—1722no—
495C42—21no—
496C42—21no—
497C42—432no—
498C42—432no—
499C42—862no—
500C42—862no—
501C42—861no—
502C42—861no—
503C42—1721no—
504C42—1721no—
505C42—1722no—
506C23—862no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23C2×D4×D4311yescharacteristic
514Q8—862no—
515Q8—862no—
516Q8—1721no—
517Q8—1721no—
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—41no—
529C2×C4—41no—
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—432no—
543C2×C4—432no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—862no—
547C2×C4—861no—
548C2×C4—861no—
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#41×D4311yescharacteristic
563C2×C4#41×D4311yescharacteristic
564C2×C4#41×D4311yescharacteristic
565C2×C4#41×D4311yescharacteristic
566C2×C4#1306337111yescharacteristic
567C2×C4#1306337311yescharacteristic
568C8—41no—
569C8—41no—
570C8—1721no—
571C8—1721no—
572C22—3441no—
573C22—3441no—
574C22—3441no—
575C22—3441no—
576C22—1722no—
577C22—1722no—
578C22—1722no—
579C22#1458340711yescharacteristic
580C22#124×D4311yescharacteristic
581C22#1458347911yescharacteristic
582C22AGL(1,ℤ/8)×D4311yescharacteristic
583C22#137×D4311yescharacteristic
584C22#1458369611yescharacteristic
585C22#1458369611yescharacteristic
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—434no—
593C4—862no—
594C4—3441no—
595C4—3441no—
596C4—1722no—
597C4—1721no—
598C4—1721no—
599C4#1458358111yescharacteristic
600C4#1458358111yescharacteristic
601C4#1458360011yescharacteristic
602C4#1458360011yescharacteristic
603C2—3442no—
604C2#1913975711yescharacteristic
605C2#1914474111yescharacteristic
606C2#1914475211yescharacteristic
607C2#489×D4311yescharacteristic
608C2#1914499211yescharacteristic
609C2#1914595611yescharacteristic
610C2#1914596711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2101C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2101D43
hypocenterC43#29131
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
1. #19142954C2semidirect
3. #19136162C2semidirect
8. #19135286C2semidirect
9. #19135283C2semidirect
10. #19134599C2semidirect
11. #19134599C2semidirect
14. #19134447C2semidirect
15. C43×#2101C2semidirect
301. #2101D43semidirect
364. C43#29131semidirect

Maximal subgroups

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

subgroupindex
#191429542
#191371342
#191361622
#191358372
#191358362
#191352932
#191352902
#191352862
#191352832
#191345992
#191345942
#191344472
C43×#21012
#2913143