Finite Group Databasebeta

← #25154792

Subgroups — #25154792

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#19135983C211yesmaximal, characteristic
3#19135969C211yesmaximal, characteristic
4#19135741C211yesmaximal, characteristic
5#19135731C211yesmaximal, characteristic
6#19135552C211yesmaximal, characteristic, complemented
7#19135543C211yesmaximal, characteristic, complemented
8#19135361C211yesmaximal, characteristic, complemented
9#19135314C211yesmaximal, characteristic, complemented
10#19135173C211yesmaximal, characteristic, complemented
11#19135166C211yesmaximal, characteristic, complemented
12#19134725C211yesmaximal, characteristic, complemented
13#19134605C211yesmaximal, characteristic
14C4×#13063246C211yesmaximal, characteristic
15C43×#2357C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28#14582832—21no—
29#14582819—21no—
30#14582803—21no—
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582796—21no—
34#14582765C2211yescharacteristic
35C4×C4⋊Dic43C2211yescharacteristic
36#14582661C2211yescharacteristic
37#14582661C2211yescharacteristic
38#14582661C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C4×D4×C43C2211yescharacteristic
49C43×#390C2211yescharacteristic
50C43×#390C2211yescharacteristic
51C43×#388—21no—
52C43×#388—21no—
53C43×#382C2211yescharacteristic
54C43×#381—21no—
55C4×C4⋊C4×C43C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C4×C22⋊C4×C43—21no—
59C22×Dic86—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063325—22no—
65#13063325—41no—
66#13063317—22no—
67#13063317—41no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C4×Dic43—21no—
78#13063258—22no—
79#13063256—22no—
80C4⋊(C43⋊C8)—22no—
81C4⋊(C43⋊C8)—41no—
82C4⋊(C43⋊C8)—41no—
83#13063246—22no—
84#13063246—22no—
85#13063246—41no—
86#13063246—41no—
87C4×C43⋊C8—22no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C22×D4×C43C2311yescharacteristic
94C23×C4×C43—21no—
95C4×D4×C43—22no—
96C4×D4×C43Q814yescomplemented
97C2×C4⋊C4×C43D411yescharacteristic
98C2×C4⋊C4×C43D411yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C42×C43—21no—
108C2×C42×C43—21no—
109C2×C42×C43C2311yescharacteristic
110C2×C42×C43C2311yescharacteristic
111C2×C42×C43C2311yescharacteristic
112#95×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
116#95×C43D411yescharacteristic
117#95×C43D411yescharacteristic
118C24×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43C2×Q812yes—
125C22×C4×C43—24no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—81no—
130C22×C4×C43—81no—
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—
141C22×Dic43—21no—
142C2×Dic86—42no—
143C2×Dic86—42no—
144C2×Dic86—81no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—41no—
152C4⋊C4×C43C2×Q812yes—
153C22⋊C4×C43—24no—
154C22⋊C4×C43—42no—
155C22⋊C4×C43—42no—
156C22⋊C4×C43—81no—
157C22⋊C4×C43—81no—
158C42×C43—21no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43—81no—
163C42×C43—81no—
164C42×C43C2×Q812yes—
165C42×C43#4112yes—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—42no—
173C4⋊Dic43#4112yes—
174C4⋊Dic43#4112yes—
175Dic43⋊C4—42no—
176Dic43⋊C4—42no—
177Dic43⋊C4—42no—
178Dic43⋊C4—81no—
179C4×Dic43—81no—
180C2×C43⋊C8—21no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—21no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C23×C43—22no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C22×D411yescharacteristic
200D4×C43—22no—
201D4×C43—22no—
202D4×C43—41no—
203D4×C43—41no—
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—22no—
211C2×C4×C43—21no—
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—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—84no—
229C2×C4×C43C22⋊Q812yes—
230C2×C4×C43C22⋊Q812yes—
231C2×C4×C43#13512yes—
232C2×C4×C43C22×Q811yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—41no—
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—41no—
250Dic86—84no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#26030—431nomaximal, Sylow
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43C2×C22⋊Q811yescharacteristic
264C22×C43#54611yescharacteristic
265C22×C43#54811yescharacteristic
266C22×C43C2×#13511yescharacteristic
267C22×C43#57511yescharacteristic
268C22×C43#57611yescharacteristic
269C22×C43#57711yescharacteristic
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—22no—
273C4×C43—42no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43#53311yescharacteristic
280C4×C43#54411yescharacteristic
281C4×C43#55511yescharacteristic
282C4×C43#55611yescharacteristic
283Dic43—42no—
284Dic43—42no—
285Dic43—81no—
286Dic43—81no—
287#2550—431no—
288#2357D4311yescharacteristic
289#2067—431no—
290#2065—431no—
291#2025—431no—
292#2023—431no—
293#1989—431no—
294#1987—431no—
295#1949—431no—
296#1939—431no—
297#1919—431no—
298#1918—431no—
299#1835—431no—
300#1804—431no—
301C4×#102—431no—
302C2×C43—82no—
303C2×C43#243911yescharacteristic
304C2×C43#307611yescharacteristic
305C2×C43#308111yescharacteristic
306C2×C43#330111yescharacteristic
307C2×C43#332211yescharacteristic
308C2×C43#336111yescharacteristic
309C2×C43#337111yescharacteristic
310C2×C4⋊Q8—431no—
311C2×#125—431no—
312C2×C4×D4C2×D4311yescharacteristic
313C2×#107—431no—
314C2×#106—431no—
315C2×C4⋊C8—431no—
316C2×C4⋊C8—431no—
317C2×C4⋊C8—431no—
318C2×#102—431no—
319C2×#102—431no—
320C2×#102—431no—
321C2×#102—431no—
322C2×C4×C8—431no—
323#398—861no—
324#395—861no—
325#391—861no—
326#390C2×D4311yescharacteristic
327#390C2×D4311yescharacteristic
328#389—431no—
329#389—431no—
330#389—861no—
331#388—21no—
332#388—21no—
333#382—431no—
334#382C2×D4311yescharacteristic
335#381—21no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4C2×D4311yescharacteristic
338C4×C4⋊C4C2×D4311yescharacteristic
339C4×C4⋊C4C2×D4311yescharacteristic
340C4×C22⋊C4—21no—
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#336—431no—
352#336—431no—
353C43#2603011yescharacteristic, complemented, Sylow
354C22×Q8—861no—
355C22×D4C22×D4311yescharacteristic
356C23×C4—21no—
357C22×C8—431no—
358C22×C8—431no—
359C22×C8—431no—
360C22×C8—431no—
361C4⋊Q8—862no—
362C4⋊Q8—1721no—
363#125—862no—
364#125—1721no—
365C4×D4—22no—
366C4×D4Dic8614yescomplemented
367C2×C4⋊C4—431no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4C22⋊D4311yescharacteristic
377C2×C4⋊C4C22⋊D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—861no—
389C2×C42C22×D4311yescharacteristic
390C2×C42C22×D4311yescharacteristic
391C2×C42C22×D4311yescharacteristic
392#107—862no—
393#106—862no—
394C4⋊C8—862no—
395C4⋊C8—1721no—
396C4⋊C8—1721no—
397#102—862no—
398#102—862no—
399#102—1721no—
400#102—1721no—
401C4×C8—862no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95C22⋊D4311yescharacteristic
412#95C22⋊D4311yescharacteristic
413C24—21no—
414C2×Q8—3441no—
415C2×Q8—1722no—
416C2×Q8—1722no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×Dic8612yes—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4C2×C22⋊D4311yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C2×C22⋊D4311yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439C22×C4C23×D4311yescharacteristic
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—432no—
460C4⋊C4—432no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—3441no—
468C4⋊C4—1722no—
469C4⋊C4—1722no—
470C4⋊C4—1722no—
471C4⋊C4—1722no—
472C4⋊C4C2×Dic8612yes—
473C22⋊C4—24no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—81no—
483C42—81no—
484C42—3441no—
485C42C2×Dic8612yes—
486C42#1062189812yes—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C22×C22⋊D4311yescharacteristic
495Q8—3444no—
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
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—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—84no—
525C2×C4—862no—
526C2×C4—862no—
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#1306330412yes—
538C2×C4#1306330412yes—
539C2×C4#1306334512yes—
540C2×C4C22×Dic8611yescharacteristic
541C2×C4#41×D4311yescharacteristic
542C2×C4#41×D4311yescharacteristic
543C2×C4C2×#1062189811yescharacteristic
544C2×C4#1306337111yescharacteristic
545C2×C4#1306337211yescharacteristic
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C8—1721no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#1306330411yescharacteristic
558C22#1458353711yescharacteristic
559C22#1458355611yescharacteristic
560C22C2×#1306334511yescharacteristic
561C22#1458369711yescharacteristic
562C22#1458370211yescharacteristic
563C22#1458371011yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—42no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—3441no—
574C4—3441no—
575C4—1722no—
576C4—1722no—
577C4#1458345211yescharacteristic
578C4#1458352711yescharacteristic
579C4#1458361211yescharacteristic
580C4#1458361711yescharacteristic
581C2—82no—
582C2#1913828011yescharacteristic
583C2#1914438311yescharacteristic
584C2#1914442611yescharacteristic
585C2#1914649111yescharacteristic
586C2#1914679011yescharacteristic
587C2#1914725111yescharacteristic
588C2#1914735711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2357C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2357D43
hypocenterC43#26030
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2357

Complements

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

NH ≅ G/Ntype
1. #19139616C2semidirect
6. #19135552C2semidirect
7. #19135543C2semidirect
8. #19135361C2semidirect
9. #19135314C2semidirect
10. #19135173C2semidirect
11. #19135166C2semidirect
12. #19134725C2semidirect
96. C4×D4×C43Q8semidirect
353. C43#26030semidirect
366. C4×D4Dic86semidirect

Maximal subgroups

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

subgroupindex
#191396162
#191359832
#191359692
#191357412
#191357312
#191355522
#191355432
#191353612
#191353142
#191351732
#191351662
#191347252
#191346052
C4×#130632462
C43×#23572
#2603043