Finite Group Databasebeta

← #24988088

Subgroups — #24988088

Order 11008.

1082 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
1C2×#14583450C211yesmaximal, characteristic
2#19134572C211yesmaximal, characteristic, complemented
3#19134572C211yesmaximal, characteristic, complemented
4C2×#14582645C211yesmaximal, characteristic, complemented
5C2×#14582642C211yesmaximal, characteristic, complemented
6C2×#14582642C211yesmaximal, characteristic, complemented
7C2×C43×#332C211yesmaximal, characteristic, complemented
8C22×#10621902—21no—
9#14583450—22no—
10#14583450—22no—
11#14583450—22no—
12#14583450—22no—
13C2×#13063322C2211yescharacteristic
14C2×#13063314—21no—
15C2×#13063300—21no—
16C2×#13063300C412yes—
17C2×#13063287—21no—
18C2×#13063287C412yes—
19C2×C42×D43C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×(C2×D43)⋊C8—21no—
23C2×(C2×D43)⋊C8—21no—
24#14582653—21no—
25#14582653—21no—
26#14582645—22no—
27#14582642—22no—
28#14582642—22no—
29C2×C4⋊Q8×C43C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×C4⋊C8×C43C2211yescharacteristic
32C43×#332—22no—
33C2×#10621902—24no—
34C2×#10621902—24no—
35C2×#10621902—42no—
36C2×#10621902—42no—
37C2×#10621902—42no—
38C2×#10621902—42no—
39C22×D172—22no—
40C22×D172—21no—
41C22×D172—21no—
42C22×D172C2×C412yes—
43C22×C4×D43—22no—
44C22×C4×D43C2×C411yescharacteristic
45C22×C4×D43D411yescharacteristic
46C22×C4×D43D411yescharacteristic
47C22×C43⋊C8—21no—
48C22×C43⋊C8—21no—
49#13063322—21no—
50#13063322—21no—
51#13063322D412yes—
52#13063322D412yes—
53#13063314—24no—
54#13063314—24no—
55#13063300—24no—
56#13063300—24no—
57#13063300—24no—
58#13063300—24no—
59#13063287—24no—
60#13063287—24no—
61#13063287—24no—
62#13063287—24no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—22no—
65C2×C4×Dic43C2×C411yescharacteristic
66C2×C4×Dic43D411yescharacteristic
67C2×C4×Dic43D411yescharacteristic
68C42×D43—21no—
69C42×D43—21no—
70C42×D43—21no—
71C42×D43—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)—21no—
74C4⋊(C43⋊C8)—21no—
75C4⋊(C43⋊C8)—21no—
76(C2×D43)⋊C8—42no—
77(C2×D43)⋊C8—42no—
78C22×Q8×C43—21no—
79C22×C8×C43—21no—
80C22×C8×C43—21no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43—21no—
83C4⋊Q8×C43D412yes—
84C4⋊Q8×C43D412yes—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43C2×C412yes—
87C2×C42×C43C2311yescharacteristic
88C4⋊C8×C43—21no—
89C4⋊C8×C43—21no—
90C4⋊C8×C43—21no—
91C4⋊C8×C43—21no—
92C23×D43—22no—
93C23×D43C22⋊C411yescharacteristic
94C2×Q8×C43—22no—
95C2×Q8×C43—22no—
96C2×Q8×C43—41no—
97C2×Q8×C43—41no—
98C2×Q8×C43—41no—
99C2×Q8×C43—41no—
100C22×C4×C43—22no—
101C22×C4×C43C22×C411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×Dic43C22⋊C411yescharacteristic
105C22×Dic43C22⋊C411yescharacteristic
106C22×Dic43C22⋊C411yescharacteristic
107#10621902—48no—
108#10621902—48no—
109#10621902—48no—
110#10621902—48no—
111C2×D172—28no—
112C2×D172—22no—
113C2×D172—22no—
114C2×D172—22no—
115C2×D172—22no—
116C2×D172—22no—
117C2×D172—44no—
118C2×D172—41no—
119C2×D172—41no—
120C2×D172—41no—
121C2×D172—41no—
122C2×D172—41no—
123C2×D172—41no—
124C2×D172—41no—
125C2×D172—41no—
126C2×D172—44no—
127C2×D172—42no—
128C2×D172—42no—
129C2×D172C22⋊C414yes—
130C2×C4×D43—21no—
131C2×C4×D43—21no—
132C2×C4×D43—21no—
133C2×C4×D43—21no—
134C2×C4×D43—28no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—21no—
143C2×C4×D43—41no—
144C2×C4×D43—41no—
145C2×C4×D43—44no—
146C2×C4×D43—44no—
147C2×C4×D43D812yes—
148C2×C4×D43SD1612yes—
149C2×C8×C43—41no—
150C2×C8×C43—41no—
151C2×C8×C43—41no—
152C2×C8×C43—41no—
153C2×C8×C43—41no—
154C2×C8×C43—41no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43C22⋊C414yes—
159C42×C43C2×D411yescharacteristic
160C42×C43C2×D411yescharacteristic
161C42×C43C2×D411yescharacteristic
162C42×C43C2×D411yescharacteristic
163(C2×D43)⋊C4—28no—
164(C2×D43)⋊C4—28no—
165C4×Dic43—21no—
166C4×Dic43—21no—
167C4×Dic43—21no—
168C4×Dic43—21no—
169C4×Dic43—21no—
170C4×Dic43—21no—
171C2×C43⋊C8—41no—
172C2×C43⋊C8—41no—
173C2×C43⋊C8—41no—
174C2×C43⋊C8—41no—
175C2×C43⋊C8—41no—
176C2×C43⋊C8—41no—
177C23×C43C2×C22⋊C411yescharacteristic
178C22×D43—21no—
179C22×D43—21no—
180C22×D43—21no—
181C22×D43—21no—
182C22×D43—21no—
183C22×D43—21no—
184C22×D43—24no—
185C22×D43—42no—
186C22×D43—42no—
187C22×D43—42no—
188C22×D43—42no—
189C22×D43—42no—
190C22×D43—42no—
191C22×D43#10212yes—
192Q8×C43—42no—
193Q8×C43—42no—
194Q8×C43—42no—
195Q8×C43—42no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—24no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43C2×C22⋊C411yescharacteristic
202C2×C4×C43C2×C22⋊C411yescharacteristic
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43#12011yescharacteristic
205C2×C4×C43#12011yescharacteristic
206C2×C4×C43#12011yescharacteristic
207C2×C4×C43C2×D811yescharacteristic
208C2×C4×C43C2×SD1611yescharacteristic
209C2×C4×C43#13511yescharacteristic
210C2×C4×C43#13511yescharacteristic
211C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
213C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
214C2×C4×C43#13711yescharacteristic
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43#10212yes—
224D172—44no—
225D172—44no—
226D172—416no—
227D172—42no—
228D172—42no—
229D172—42no—
230D172—42no—
231D172—42no—
232D172—42no—
233D172—42no—
234D172—42no—
235C4×D43—22no—
236C4×D43—22no—
237C4×D43—22no—
238C4×D43—22no—
239C4×D43—416no—
240C4×D43—42no—
241C4×D43—42no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—41no—
245C4×D43—41no—
246C8×C43—81no—
247C8×C43—81no—
248C43⋊C8—81no—
249C43⋊C8—81no—
250#8341—431nomaximal, Sylow
251C22×C43#37911yescharacteristic
252C22×C43#41311yescharacteristic
253C22×C43#41311yescharacteristic
254C22×C43C2×#10211yescharacteristic
255C22×C43#41611yescharacteristic
256C22×C43#41711yescharacteristic
257C22×C43#41811yescharacteristic
258C2×D43—22no—
259C2×D43—22no—
260C2×D43—22no—
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—44no—
266C2×D43—44no—
267C2×D43—44no—
268C2×D43—82no—
269C2×D43—82no—
270C2×D43—82no—
271C2×D43—82no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—44no—
275C4×C43#44711yescharacteristic
276C4×C43#44711yescharacteristic
277C4×C43#44911yescharacteristic
278C4×C43#44911yescharacteristic
279C4×C43#45011yescharacteristic
280C4×C43#45011yescharacteristic
281C4×C43#45211yescharacteristic
282C4×C43#45211yescharacteristic
283Dic43—22no—
284Dic43—41no—
285Dic43—41no—
286C2×#532—431no—
287#1797—431no—
288#1797—431no—
289C2×#332—431no—
290C2×#332D4311yescharacteristic, complemented
291C2×#331—431no—
292C2×#331—431no—
293C2×C43#154011yescharacteristic
294C2×C43#154711yescharacteristic
295C2×C43#155311yescharacteristic
296C2×C43#155711yescharacteristic
297C2×C43#178511yescharacteristic
298C2×C43#178611yescharacteristic
299C2×C43#178811yescharacteristic
300D43—42no—
301D43—84no—
302C22×#41—861no—
303#532—862no—
304#532—862no—
305#532—862no—
306#532—862no—
307C2×C4⋊Q8C2×D4311yescharacteristic
308C2×#127—431no—
309C2×#124—861no—
310C2×#121—432no—
311C2×#121—861no—
312C2×C4×D4—432no—
313C2×C4×D4—861no—
314C22×C42—431no—
315C2×C4⋊C8—431no—
316C2×C4⋊C8—431no—
317C2×C4⋊C8C2×D4311yescharacteristic
318C2×C4⋊C8C2×D4311yescharacteristic
319C2×C22⋊C8—861no—
320C2×C22⋊C8—861no—
321#336—861no—
322#336—861no—
323#332—22no—
324#332—862no—
325#331—862no—
326#331—862no—
327C43#834111yescharacteristic, complemented, Sylow
328C2×#41—864no—
329C2×#41—864no—
330C2×#41—1722no—
331C2×#41—1722no—
332C2×#41—1722no—
333C2×#41—1722no—
334C22×Q8—21no—
335C22×D4—432no—
336C22×D4—862no—
337C22×D4—861no—
338C22×D4—861no—
339C23×C4—431no—
340C23×C4—431no—
341C23×C4—431no—
342C23×C4—862no—
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—861no—
346C22×C8—861no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8D17212yes—
350C4⋊Q8C22⋊D4312yes—
351#127—432no—
352#127—432no—
353#127—861no—
354#127—861no—
355#124—864no—
356#124—864no—
357#121—864no—
358#121—864no—
359#121—864no—
360#121—864no—
361C4×D4—864no—
362C4×D4—864no—
363C4×D4—864no—
364C4×D4—864no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4C4×D4312yes—
367C2×C22⋊C4—862no—
368C2×C22⋊C4—862no—
369C2×C42—431no—
370C2×C42—431no—
371C2×C42—431no—
372C2×C42—861no—
373C2×C42—861no—
374C2×C42—861no—
375C2×C42—861no—
376C2×C42C22×D4311yescharacteristic
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—861no—
382C4⋊C8—861no—
383C4⋊C8—861no—
384C4⋊C8—861no—
385C22⋊C8—1722no—
386C22⋊C8—1722no—
387C24—431no—
388C24—862no—
389#41—1728no—
390#41—1728no—
391#41—1728no—
392#41—1728no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×D4—434no—
400C2×D4—868no—
401C2×D4—862no—
402C2×D4—862no—
403C2×D4—862no—
404C2×D4—862no—
405C2×D4—862no—
406C2×D4—1722no—
407C2×D4—1722no—
408C2×D4—1724no—
409C2×D4—1724no—
410C2×D4—1721no—
411C2×D4—1721no—
412C2×D4—1721no—
413C2×D4—1721no—
414C2×D4—1721no—
415C2×D4—1721no—
416C2×D4—1721no—
417C2×D4—1721no—
418C22×C4—22no—
419C22×C4—431no—
420C22×C4—432no—
421C22×C4—432no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—868no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—1721no—
438C22×C4—1721no—
439C22×C4—1724no—
440C22×C4—1724no—
441C22×C4C2×C4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4D4×D4311yescharacteristic
444C2×C8—41no—
445C2×C8—41no—
446C2×C8—41no—
447C2×C8—41no—
448C2×C8—41no—
449C2×C8—41no—
450C2×C8—1721no—
451C2×C8—1721no—
452C2×C8—1721no—
453C2×C8—1721no—
454C2×C8—1721no—
455C2×C8—1721no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4(C2×D43)⋊C414yes—
460C22⋊C4—868no—
461C22⋊C4—868no—
462C42—861no—
463C42—861no—
464C42—861no—
465C42—861no—
466C42—861no—
467C42—861no—
468C42C2×D17211yescharacteristic
469C42D4×D4311yescharacteristic
470C42D4×D4311yescharacteristic
471C42C2×C22⋊D4311yescharacteristic
472C23—432no—
473C23—861no—
474C23—861no—
475C23—861no—
476C23—861no—
477C23—861no—
478C23—861no—
479C23—864no—
480C23—1722no—
481C23—1722no—
482C23—1722no—
483C23—1722no—
484C23—1722no—
485C23—1722no—
486C23C22⋊C4×D4311yescharacteristic
487Q8—42no—
488Q8—42no—
489Q8—42no—
490Q8—42no—
491D4—1724no—
492D4—1724no—
493D4—17216no—
494D4—1722no—
495D4—1722no—
496D4—1722no—
497D4—1722no—
498D4—1722no—
499D4—1722no—
500D4—1722no—
501D4—1722no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—24no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—432no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—862no—
511C2×C4—862no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—1722no—
521C2×C4—1722no—
522C2×C4—17216no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4C22⋊C4×D4311yescharacteristic
528C2×C4C2×(C2×D43)⋊C411yescharacteristic
529C2×C4#1306329311yescharacteristic
530C2×C4#1306329311yescharacteristic
531C2×C4#1306329511yescharacteristic
532C2×C4#1306329511yescharacteristic
533C2×C4D8×D4311yescharacteristic
534C2×C4SD16×D4311yescharacteristic
535C2×C4#1306334611yescharacteristic
536C2×C4#1306334811yescharacteristic
537C2×C4#1306334911yescharacteristic
538C2×C4#1306335211yescharacteristic
539C2×C4#1306335211yescharacteristic
540C2×C4#1306335711yescharacteristic
541C8—81no—
542C8—81no—
543C8—3441no—
544C8—3441no—
545C22—862no—
546C22—862no—
547C22—862no—
548C22—3442no—
549C22—3442no—
550C22—3442no—
551C22—3442no—
552C22—1724no—
553C22—1724no—
554C22—1724no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22—1721no—
559C22#1458275411yescharacteristic
560C22#1458288211yescharacteristic
561C22#1458288211yescharacteristic
562C22#102×D4311yescharacteristic
563C22#1458289411yescharacteristic
564C22#1458289911yescharacteristic
565C22#1458290211yescharacteristic
566C4—21no—
567C4—21no—
568C4—44no—
569C4—862no—
570C4—1721no—
571C4—1721no—
572C4#1458303111yescharacteristic
573C4#1458303411yescharacteristic
574C4#1458304311yescharacteristic
575C4#1458304711yescharacteristic
576C4#1458304811yescharacteristic
577C4#1458305111yescharacteristic
578C4#1458306011yescharacteristic
579C4#1458306411yescharacteristic
580C2—3444no—
581C2—1722no—
582C2#1913324311yescharacteristic
583C2#1913327111yescharacteristic
584C2#1913329911yescharacteristic
585C2#1913331611yescharacteristic
586C2#1913452211yescharacteristic
587C2#1913452411yescharacteristic
588C2#1913453411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#14583450C2
cosocleC2×C42×C43C23
hypercenterC2×#332D43
hypocenterC43#8341
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #19134572C2semidirect
3. #19134572C2semidirect
4. C2×#14582645C2semidirect
5. C2×#14582642C2semidirect
6. C2×#14582642C2semidirect
7. C2×C43×#332C2semidirect
290. C2×#332D43semidirect
327. C43#8341semidirect

Maximal subgroups

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

subgroupindex
C2×#145834502
#191345722
C2×#145826452
C2×#145826422
C2×C43×#3322
#834143