Finite Group Databasebeta

← #25124173

Subgroups — #25124173

Order 11008.

1482 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583477C211yesmaximal, characteristic
2C22×#13063256C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic, complemented
4C2×#14582893C211yesmaximal, characteristic, complemented
5C2×#14582866C211yesmaximal, characteristic, complemented
6#19135791C214yesmaximal, complemented
7#19135784C214yesmaximal, complemented
8#19134316C211yesmaximal, characteristic, complemented
9C43×#2311C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12C23×C43⋊C8C2211yescharacteristic
13#14583477—24no—
14#14583477—24no—
15C2×#13063304C2212yes—
16C2×#13063301—21no—
17C2×#13063299C2212yes—
18C2×#13063297—22no—
19C2×#13063296—21no—
20C22×C4⋊Dic43C2211yescharacteristic
21C2×#13063256—24no—
22C2×#13063256C2214yes—
23#14582898—24no—
24#14582893—24no—
25C2×#13063248C2212yes—
26C2×#13063248C2212yes—
27C2×#13063245C2212yes—
28C2×#13063245C2212yes—
29#14582866—24no—
30C2×C22⋊(C43⋊C8)C2214yes—
31#14582661C2214yes—
32C22×#41×C43C2211yescharacteristic
33C2×#117×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2211yescharacteristic
35C43×#391—21no—
36C43×#390—21no—
37C43×#386—22no—
38C43×#380C2214yes—
39C2×#10621898—22no—
40C2×#10621898—22no—
41C2×#10621898—22no—
42C2×#10621898—22no—
43C2×#10621898—22no—
44C2×#10621898D414yes—
45C22×Dic86C2311yescharacteristic
46C22×D172C2311yescharacteristic
47C22×C22⋊D43—21no—
48C22×C22⋊D43—22no—
49C23×Dic43—21no—
50C22×C4×D43—21no—
51C2×#10621877—22no—
52C2×#10621877—22no—
53C2×#10621877—22no—
54C22×C43⋊C8—22no—
55C22×C43⋊C8—22no—
56C22×C43⋊C8D414yescomplemented
57C22×C43⋊C8C2312yes—
58C22×C43⋊C8C2312yes—
59#13063304—24no—
60#13063304—24no—
61#13063301—28no—
62#13063299—24no—
63#13063299—24no—
64#13063297—216no—
65#13063296—28no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—22no—
68C2×C4⋊Dic43D414yes—
69C2×C4⋊Dic43C2312yes—
70C2×Dic43⋊C4—22no—
71C2×C22⋊Dic43—22no—
72C2×(C2×D43)⋊C4—22no—
73#13063256—28no—
74#13063248—24no—
75#13063248—24no—
76#13063245—24no—
77#13063245—24no—
78C22⋊(C43⋊C8)—28no—
79C2×#41×C43—22no—
80C2×#41×C43—22no—
81C2×#41×C43—22no—
82C2×#41×C43—22no—
83C2×#41×C43—22no—
84C2×#41×C43—22no—
85C22×Q8×C43D411yescharacteristic
86C22×D4×C43D411yescharacteristic
87C22×D4×C43D412yes—
88C23×C4×C43—21no—
89C23×C4×C43C2312yes—
90C23×C4×C43C2311yescharacteristic
91#117×C43—22no—
92#117×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43C2312yes—
97C2×C4⋊C4×C43C2312yes—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—24no—
100C2×C42×C43—21no—
101#95×C43—24no—
102C24×C43C2×D412yes—
103C24×C43C2×D411yescharacteristic
104C23×D43—21no—
105#41×C43—44no—
106#41×C43—44no—
107#41×C43—44no—
108#41×C43—44no—
109C2×Q8×C43—22no—
110C2×Q8×C43—22no—
111C2×Q8×C43—22no—
112C2×D4×C43—22no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—24no—
116C2×D4×C43—24no—
117C2×D4×C43—24no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—42no—
127C22×C4×C43—82no—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43#4112yes—
134C22×C4×C43#4112yes—
135C22×C4×C43#4112yes—
136C22×C4×C43C2411yescharacteristic
137C2×C22⋊D43—28no—
138C2×C22⋊D43—24no—
139C2×C22⋊D43—42no—
140C2×C22⋊D43—42no—
141C2×C22⋊D43—84no—
142C22×Dic43—24no—
143C22×Dic43—22no—
144C22×Dic43—21no—
145C22×Dic43—82no—
146#10621898—28no—
147#10621898—28no—
148#10621898—44no—
149#10621898—44no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C2×D412yes—
156C2×C4×D43—24no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D412yes—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—42no—
170C22⋊C4×C43—42no—
171C22⋊C4×C43—84no—
172C42×C43—42no—
173C22⋊Dic43—28no—
174(C2×D43)⋊C4—28no—
175C4⋊Dic43—24no—
176C4⋊Dic43—22no—
177C4⋊Dic43C2×D414yes—
178Dic43⋊C4—28no—
179#10621877—44no—
180C2×C43⋊C8—28no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8C2×D414yes—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—24no—
193C23×C43—24no—
194C23×C43#12012yes—
195C23×C43#12112yes—
196C23×C43#12312yes—
197C23×C43C22×D411yescharacteristic
198C22×D43—22no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—42no—
202C22×D43—42no—
203Q8×C43—44no—
204D4×C43—48no—
205D4×C43—44no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—44no—
217C2×C4×C43—42no—
218C2×C4×C43—84no—
219C2×C4×C43#12012yes—
220C2×C4×C43#12112yes—
221C2×C4×C43#12114yes—
222C2×C4×C43#12114yes—
223C2×C4×C43#12314yes—
224C2×C4×C43#12312yes—
225C2×C4×C43#12414yes—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—48no—
233C22⋊D43—88no—
234C2×Dic43—22no—
235C2×Dic43—24no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—44no—
239C2×Dic43—84no—
240D172—22no—
241D172—22no—
242D172—41no—
243D172—41no—
244C4×D43—48no—
245Dic86—22no—
246Dic86—22no—
247Dic86—41no—
248Dic86—41no—
249C43⋊C8—24no—
250C43⋊C8—42no—
251#23489—431nomaximal, Sylow
252C22×C43—24no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—24no—
256C22×C43—44no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—44no—
261C22×C43#39414yes—
262C22×C43C2×#12011yescharacteristic
263C22×C43C2×#12111yescharacteristic
264C22×C43C2×#12311yescharacteristic
265C22×C43#57712yes—
266C22×C43#57712yes—
267C2×D43—42no—
268C2×D43—42no—
269C2×D43—42no—
270C2×D43—82no—
271C2×D43—82no—
272C4×C43—42no—
273C4×C43—82no—
274C4×C43—82no—
275C4×C43#39414yes—
276C4×C43C2×#12111yescharacteristic
277C4×C43C2×#12111yescharacteristic
278C4×C43C2×#12311yescharacteristic
279C4×C43C2×#12411yescharacteristic
280Dic43—42no—
281Dic43—44no—
282C2×#537—431no—
283C22×#106—431no—
284C2×#417—431no—
285C2×#416—431no—
286C2×#408—431no—
287#2311D4311yescharacteristic, complemented
288#2035—434no—
289#2034—434no—
290#1736—431no—
291C2×C43—24no—
292C2×C43—82no—
293C2×C43C2×#39411yescharacteristic
294C2×C43#300911yescharacteristic
295C2×C43#301011yescharacteristic
296C2×C43#306012yes—
297C2×C43#309912yes—
298D43—82no—
299C22×#41—431no—
300C22×#41C2×D4311yescharacteristic
301C22×M16—431no—
302C23×C8—431no—
303#537—864no—
304#537—864no—
305C2×C22⋊Q8—432no—
306C2×C22⋊Q8—861no—
307C2×#121—432no—
308C2×#121—861no—
309C2×#121—862no—
310C2×#117C2×D4311yescharacteristic
311C22×C4⋊C4—431no—
312C22×C4⋊C4C2×D4311yescharacteristic
313C2×#106—434no—
314C2×#106—864no—
315#417—864no—
316#416—864no—
317C2×#103—432no—
318C2×#103—432no—
319C2×#102—432no—
320C2×#102—432no—
321#408—864no—
322C2×C22⋊C8—434no—
323#391—21no—
324#390—21no—
325#386—22no—
326#380C2×D4314yes—
327#340—434no—
328C43#2348911yescharacteristic, complemented, Sylow
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—434no—
336C2×#41—862no—
337C2×#41—862no—
338C2×#41—862no—
339C2×#41—862no—
340C2×#41—862no—
341C22×Q8—431no—
342C22×Q8C22⋊D4311yescharacteristic
343C22×D4—431no—
344C22×D4—862no—
345C22×D4—861no—
346C22×D4C22⋊D4312yes—
347C22×D4C22⋊D4311yescharacteristic
348C23×C4—21no—
349C23×C4—861no—
350C23×C4—861no—
351C23×C4C22×D4312yes—
352C23×C4C22×D4311yescharacteristic
353C2×M16—862no—
354C2×M16—862no—
355C2×M16—862no—
356C22×C8—434no—
357C22×C8—432no—
358C22×C8—432no—
359C22×C8—862no—
360C22×C8—862no—
361C22⋊Q8—864no—
362C22⋊Q8—864no—
363C22⋊Q8—868no—
364#121—864no—
365#121—864no—
366#121—868no—
367#121—8616no—
368#117—22no—
369#117—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—434no—
374C2×C4⋊C4—432no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4C22×D4312yes—
379C2×C4⋊C4C22×D4312yes—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—862no—
383C2×C22⋊C4—862no—
384C2×C42—21no—
385#106—868no—
386#103—864no—
387#103—864no—
388#102—864no—
389#102—864no—
390C22⋊C8—868no—
391#95—24no—
392C24—861no—
393C24C2×C22⋊D4312yes—
394C24C2×C22⋊D4311yescharacteristic
395#41—44no—
396#41—44no—
397#41—44no—
398#41—44no—
399#41—868no—
400#41—868no—
401#41—1724no—
402#41—1724no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—432no—
407C2×Q8—861no—
408C2×Q8—861no—
409C2×Q8—861no—
410C2×Q8—861no—
411C2×Q8—861no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—432no—
419C2×D4—868no—
420C2×D4—864no—
421C2×D4—861no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—861no—
426C2×D4—3444no—
427C2×D4—1722no—
428C2×D4—1722no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—42no—
438C22×C4—82no—
439C22×C4—864no—
440C22×C4—862no—
441C22×C4—861no—
442C22×C4—864no—
443C22×C4—3442no—
444C22×C4—1722no—
445C22×C4—1722no—
446C22×C4#1062189812yes—
447C22×C4#1062189812yes—
448C22×C4D4×D4312yes—
449C22×C4D4×D4312yes—
450C22×C4D4×D4312yes—
451C22×C4#1062190012yes—
452C22×C4C2×C22⋊D4312yes—
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C23×D4311yescharacteristic
455M16—1724no—
456C2×C8—434no—
457C2×C8—868no—
458C2×C8—862no—
459C2×C8—862no—
460C2×C8—862no—
461C2×C8—862no—
462C2×C8—862no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4—434no—
469C4⋊C4—868no—
470C4⋊C4—864no—
471C4⋊C4—862no—
472C22⋊C4—42no—
473C22⋊C4—84no—
474C22⋊C4—868no—
475C22⋊C4—868no—
476C42—42no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—24no—
483C23—24no—
484C23—862no—
485C23—1721no—
486C23—1721no—
487C23—1722no—
488C23—1722no—
489C23#1306329312yes—
490C23#1306329712yes—
491C23#1306330812yes—
492C23C22×C22⋊D4311yescharacteristic
493Q8—44no—
494Q8—862no—
495Q8—862no—
496Q8—1721no—
497Q8—1721no—
498D4—48no—
499D4—44no—
500D4—862no—
501D4—862no—
502D4—3448no—
503D4—1728no—
504D4—1721no—
505D4—1721no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—84no—
519C2×C4—864no—
520C2×C4—862no—
521C2×C4—3444no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1724no—
525C2×C4—1728no—
526C2×C4#1306329312yes—
527C2×C4#1306329712yes—
528C2×C4#1306329814yes—
529C2×C4#1306329814yes—
530C2×C4#1306330714yes—
531C2×C4#1306330812yes—
532C2×C4#1306331114yes—
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4C2×D4×D4311yescharacteristic
536C2×C4C2×#1062190011yescharacteristic
537C2×C4C2×#1062189811yescharacteristic
538C2×C4C2×#1062189811yescharacteristic
539C8—864no—
540C8—1722no—
541C22—24no—
542C22—24no—
543C22—22no—
544C22—22no—
545C22—42no—
546C22—44no—
547C22—44no—
548C22—42no—
549C22—42no—
550C22—3442no—
551C22—3442no—
552C22—1722no—
553C22—1722no—
554C22—1722no—
555C22#1458281414yes—
556C22C2×#1306329311yescharacteristic
557C22C2×#1306329711yescharacteristic
558C22C2×#1306330811yescharacteristic
559C22#1458370712yes—
560C22#1458371012yes—
561C4—42no—
562C4—82no—
563C4—82no—
564C4—1722no—
565C4—1724no—
566C4#1458281414yes—
567C4C2×#1306329811yescharacteristic
568C4C2×#1306329811yescharacteristic
569C4C2×#1306330711yescharacteristic
570C4C2×#1306331111yescharacteristic
571C2—24no—
572C2—82no—
573C2—3442no—
574C2C2×#1458281411yescharacteristic
575C2#1914387011yescharacteristic
576C2#1914387911yescharacteristic
577C2#1914425412yes—
578C2#1914458412yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2311C2
socleC23×C43C22×D4
prime radicalC2×#14583477C2
hypercenter#2311D43
hypocenterC43#23489
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C22×#13063256C2semidirect
3. C2×#14582898C2semidirect
4. C2×#14582893C2semidirect
5. C2×#14582866C2semidirect
6. #19135791C2semidirect
7. #19135784C2semidirect
8. #19134316C2semidirect
9. C43×#2311C2semidirect
56. C22×C43⋊C8D4semidirect
287. #2311D43semidirect
328. C43#23489semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
C22×#130632562
C2×#145828982
C2×#145828932
C2×#145828662
#191357912
#191357842
#191343162
C43×#23112
#2348943