Finite Group Databasebeta

← #25154766

Subgroups — #25154766

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139616C211yesmaximal, characteristic, complemented
2#19137566C211yesmaximal, characteristic
3#19135982C211yesmaximal, characteristic
4#19135968C211yesmaximal, characteristic
5#19135742C211yesmaximal, characteristic
6#19135732C211yesmaximal, characteristic
7#19135550C211yesmaximal, characteristic, complemented
8#19135546C211yesmaximal, characteristic, complemented
9#19135365C211yesmaximal, characteristic, complemented
10#19135188C211yesmaximal, characteristic, complemented
11#19135181C211yesmaximal, characteristic, complemented
12#19134726C211yesmaximal, characteristic, complemented
13#19134606C211yesmaximal, characteristic
14C4×#13063247C211yesmaximal, characteristic
15C43×#1939C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063247C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25#14582832—21no—
26#14582819—21no—
27#14582803—21no—
28#14582801C2211yescharacteristic
29#14582801C2211yescharacteristic
30#14582797C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582796—21no—
33#14582789—21no—
34#14582789—21no—
35#14582765C2211yescharacteristic
36#14582765C2211yescharacteristic
37#14582761—21no—
38C4×C4⋊Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41#14582746—21no—
42#14582662C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C2×C4⋊C8×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62#13063325—22no—
63#13063325—41no—
64#13063317—22no—
65#13063317—41no—
66C4×D172—22no—
67C4×D172Q814yescomplemented
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
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—
88#13063259—22no—
89#13063257—22no—
90#13063247—22no—
91#13063247—22no—
92#13063247—41no—
93#13063247—41no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×C8×C43C2311yescharacteristic
104C22×C8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C2×C4⋊C4×C43D411yescharacteristic
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111C2×C42×C43C2311yescharacteristic
112C4⋊C8×C43—22no—
113C4⋊C8×C43—41no—
114C4⋊C8×C43—41no—
115C4×C8×C43—22no—
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118C23×D43—21no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C22×Dic43—21no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172C2×Q812yes—
139C2×C4×D43—24no—
140C2×C4×D43—81no—
141C2×C4×D43—81no—
142C2×Dic86—42no—
143C2×Dic86—42no—
144C2×Dic86—81no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
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—22no—
158C4⋊C4×C43—41no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43—21no—
163C42×C43C2×Q812yes—
164C42×C43#4112yes—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—42no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—81no—
169(C2×D43)⋊C4—81no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—42no—
182C4⋊Dic43C2×Q812yes—
183C4⋊Dic43#4112yes—
184C4⋊Dic43#4112yes—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188Dic43⋊C4—81no—
189C4×Dic43—81no—
190C4×Dic43—81no—
191C4×Dic43—81no—
192C23×C43C22×D411yescharacteristic
193C22×D43—22no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
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—21no—
215C2×C4×C43C22⋊Q812yes—
216C2×C4×C43C22⋊Q812yes—
217C2×C4×C43#13512yes—
218C2×C4×C43C22×Q811yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43H(5,𝔽2)11yescharacteristic
223C2×C4×C432−1+411yescharacteristic
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245D172—22no—
246D172—22no—
247D172—41no—
248D172—41no—
249C4×D43—84no—
250Dic86—84no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255#26028—431nomaximal, Sylow
256C22×C43C2×C22⋊Q811yescharacteristic
257C22×C43#54611yescharacteristic
258C22×C43#54811yescharacteristic
259C22×C43C2×#13511yescharacteristic
260C22×C43#57511yescharacteristic
261C22×C43#57611yescharacteristic
262C22×C43#57711yescharacteristic
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—42no—
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—22no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43#53311yescharacteristic
277C4×C43#54411yescharacteristic
278C4×C43#55511yescharacteristic
279C4×C43#55611yescharacteristic
280Dic43—42no—
281Dic43—42no—
282Dic43—42no—
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286Dic43—81no—
287#2550—431no—
288#2357—431no—
289#2067—431no—
290#2065—431no—
291#2025—431no—
292#2023—431no—
293#1989—431no—
294#1988—431no—
295#1949—431no—
296#1939D4311yescharacteristic, complemented
297#1921—431no—
298#1920—431no—
299#1835—431no—
300#1804—431no—
301C4×#102—431no—
302C2×C43#243911yescharacteristic
303C2×C43#307611yescharacteristic
304C2×C43#308111yescharacteristic
305C2×C43#329711yescharacteristic
306C2×C43#332611yescharacteristic
307C2×C43#336511yescharacteristic
308C2×C43#337011yescharacteristic
309D43—82no—
310C2×C4⋊Q8—431no—
311C2×#125—431no—
312C2×C4×D4—431no—
313C2×#107—431no—
314C2×#106—431no—
315C2×C4⋊C8C2×D4311yescharacteristic
316C2×C4⋊C8C2×D4311yescharacteristic
317C2×C4⋊C8C2×D4311yescharacteristic
318C2×#102—431no—
319C2×#102—431no—
320C2×#102—431no—
321C2×#102—431no—
322C2×C4×C8C2×D4311yescharacteristic
323#398—861no—
324#395—861no—
325#391—861no—
326#390—431no—
327#390—431no—
328#389—431no—
329#389—431no—
330#389—861no—
331#388—861no—
332#388—861no—
333#382—431no—
334#382—431no—
335#381—861no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4—431no—
338C4×C4⋊C4—431no—
339C4×C4⋊C4C2×D4311yescharacteristic
340C4×C22⋊C4—861no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#336C2×D4311yescharacteristic
352#336C2×D4311yescharacteristic
353C43#2602811yescharacteristic, complemented, Sylow
354C22×Q8—861no—
355C22×D4—431no—
356C23×C4—861no—
357C22×C8C22×D4311yescharacteristic
358C22×C8C22×D4311yescharacteristic
359C22×C8C22×D4311yescharacteristic
360C22×C8C22×D4311yescharacteristic
361C4⋊Q8—862no—
362C4⋊Q8—1721no—
363#125—862no—
364#125—1721no—
365C4×D4—434no—
366C4×D4—862no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4D17211yescharacteristic
380C2×C4⋊C4D17211yescharacteristic
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C42—861no—
387C2×C42—861no—
388C2×C42—861no—
389C2×C42C22×D4311yescharacteristic
390C2×C42C22×D4311yescharacteristic
391C2×C42C22×D4311yescharacteristic
392#107—862no—
393#106—862no—
394C4⋊C8—22no—
395C4⋊C8—41no—
396C4⋊C8—41no—
397#102—862no—
398#102—862no—
399#102—1721no—
400#102—1721no—
401C4×C8—22no—
402#95—861no—
403#95—861no—
404#95—861no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95D17211yescharacteristic
412#95D17211yescharacteristic
413C24—861no—
414C2×Q8—3441no—
415C2×Q8—1722no—
416C2×Q8—1722no—
417C2×D4—432no—
418C2×D4—861no—
419C2×D4—861no—
420C2×D4—861no—
421C2×D4—861no—
422C2×D4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—864no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—3441no—
432C22×C4—3441no—
433C22×C4C2×D17211yescharacteristic
434C22×C4C2×D17211yescharacteristic
435C22×C4C2×D17211yescharacteristic
436C22×C4C2×D17211yescharacteristic
437C22×C4C2×D17211yescharacteristic
438C22×C4C2×D17211yescharacteristic
439C22×C4C23×D4311yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C4⋊C4—22no—
453C4⋊C4—41no—
454C4⋊C4—432no—
455C4⋊C4—432no—
456C4⋊C4—432no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—3441no—
469C4⋊C4—1722no—
470C4⋊C4—1722no—
471C4⋊C4—1722no—
472C4⋊C4—1722no—
473C22⋊C4—864no—
474C22⋊C4—3441no—
475C22⋊C4—3441no—
476C22⋊C4—1722no—
477C22⋊C4—1722no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—3441no—
483C42—3441no—
484C42—3441no—
485C42#1062190012yes—
486C42Q8×D4312yes—
487C23—862no—
488C23—1721no—
489C23—1721no—
490C23—1721no—
491C23—1721no—
492C23—1721no—
493C23—1721no—
494C23C22×D17211yescharacteristic
495Q8—3444no—
496D4—862no—
497D4—862no—
498D4—1721no—
499D4—1721no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—3444no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4#1306330512yes—
538C2×C4#1306330512yes—
539C2×C4#1306334712yes—
540C2×C4C2×Q8×D4311yescharacteristic
541C2×C4#41×D4311yescharacteristic
542C2×C4#41×D4311yescharacteristic
543C2×C4C2×#1062190011yescharacteristic
544C2×C4#1306337011yescharacteristic
545C2×C4#1306337311yescharacteristic
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—3441no—
551C22—3441no—
552C22—3441no—
553C22—3441no—
554C22—1722no—
555C22—1722no—
556C22—1722no—
557C22C2×#1306330511yescharacteristic
558C22#1458354411yescharacteristic
559C22#1458356111yescharacteristic
560C22C2×#1306334711yescharacteristic
561C22#1458369911yescharacteristic
562C22#1458370411yescharacteristic
563C22#1458371111yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—3441no—
571C4—3441no—
572C4—3441no—
573C4—3441no—
574C4—1722no—
575C4—1722no—
576C4—1722no—
577C4#1458345511yescharacteristic
578C4#1458352611yescharacteristic
579C4#1458361311yescharacteristic
580C4#1458362011yescharacteristic
581C2—3442no—
582C2#1913828411yescharacteristic
583C2#1914438511yescharacteristic
584C2#1914442711yescharacteristic
585C2#1914644711yescharacteristic
586C2#1914685011yescharacteristic
587C2#1914729311yescharacteristic
588C2#1914735011yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1939C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1939D43
hypocenterC43#26028
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. #19139616C2semidirect
7. #19135550C2semidirect
8. #19135546C2semidirect
9. #19135365C2semidirect
10. #19135188C2semidirect
11. #19135181C2semidirect
12. #19134726C2semidirect
15. C43×#1939C2semidirect
67. C4×D172Q8semidirect
296. #1939D43semidirect
353. C43#26028semidirect

Maximal subgroups

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

subgroupindex
#191396162
#191375662
#191359822
#191359682
#191357422
#191357322
#191355502
#191355462
#191353652
#191351882
#191351812
#191347262
#191346062
C4×#130632472
C43×#19392
#2602843