Finite Group Databasebeta

← #25125276

Subgroups — #25125276

Order 11008.

1102 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582942C211yesmaximal, characteristic, complemented
2C2×#14582926C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic
4C2×#14582893C211yesmaximal, characteristic
5#19137183C211yesmaximal, characteristic
6#19135987C212yesmaximal, complemented
7#19135980C212yesmaximal, complemented
8#19135973C212yesmaximal, complemented
9#19135966C212yesmaximal, complemented
10C2×#14582661C211yesmaximal, characteristic, complemented
11C43×#2317C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C23×C43⋊C8C2211yescharacteristic
15C22×C4⋊Dic43C2211yescharacteristic
16#14582942—24no—
17C2×#13063258C2212yes—
18C2×#13063256C2212yes—
19#14582926—24no—
20C2×C4⋊(C43⋊C8)C2212yes—
21C2×C4⋊(C43⋊C8)C2212yes—
22#14582898—24no—
23#14582893—24no—
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2212yes—
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2212yes—
30#14582805C2212yes—
31#14582801C2212yes—
32#14582776—22no—
33#14582756—21no—
34#14582756—21no—
35#14582661C2212yes—
36#14582661C2212yes—
37C2×#117×C43C2211yescharacteristic
38C2×#117×C43C2211yescharacteristic
39C22×C4⋊C4×C43C2211yescharacteristic
40C43×#389C2212yes—
41C43×#389C2212yes—
42C43×#385—22no—
43C43×#384—21no—
44C43×#382—21no—
45C2×#10621898—22no—
46C2×#10621898—22no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898Q814yes—
51C22×Dic86C2311yescharacteristic
52C22×D172C2311yescharacteristic
53C22×C22⋊D43—21no—
54C23×Dic43—21no—
55C22×C4×D43—21no—
56C2×#10621877—22no—
57C2×#10621877—22no—
58C2×#10621877D414yes—
59C22×C43⋊C8—22no—
60C22×C43⋊C8—22no—
61C22×C43⋊C8—22no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2312yes—
65C2×C4⋊Dic43—22no—
66C2×C4⋊Dic43—22no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2312yes—
69C2×(C2×D43)⋊C4—22no—
70C2×(C2×D43)⋊C4—22no—
71#13063258—24no—
72#13063256—24no—
73C4⋊(C43⋊C8)—24no—
74C4⋊(C43⋊C8)—24no—
75#13063248—22no—
76#13063248—22no—
77#13063248—24no—
78#13063245—22no—
79#13063245—22no—
80#13063245—24no—
81C43⋊#95—22no—
82C43⋊#95—22no—
83C23×C4×C43—21no—
84C23×C4×C43C2311yescharacteristic
85#117×C43—22no—
86#117×C43—22no—
87#117×C43—22no—
88#117×C43D414yes—
89C2×C4⋊C4×C43—22no—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—21no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43D411yescharacteristic
95C2×C4⋊C4×C43D411yescharacteristic
96C2×C4⋊C4×C43C2312yes—
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43D412yes—
101C2×C42×C43—21no—
102C2×C42×C43C2312yes—
103#95×C43—22no—
104#95×C43—22no—
105C24×C43C2×D411yescharacteristic
106C23×D43—21no—
107C22×C4×C43—21no—
108C22×C4×C43—21no—
109C22×C4×C43—22no—
110C22×C4×C43—42no—
111C22×C4×C43—81no—
112C22×C4×C43—81no—
113C22×C4×C43C2×D412yes—
114C22×C4×C43C2×D412yes—
115C22×C4×C43C2×D412yes—
116C22×C4×C43C2×D412yes—
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×Q812yes—
119C22×C4×C43#4112yes—
120C22×C4×C43#4112yes—
121C22×C4×C43#4112yes—
122C22×C4×C43C2411yescharacteristic
123C2×C22⋊D43—24no—
124C2×C22⋊D43—42no—
125C2×C22⋊D43—42no—
126C22×Dic43—21no—
127C22×Dic43—22no—
128C22×Dic43—42no—
129C22×Dic43—81no—
130C22×Dic43—81no—
131#10621898—28no—
132#10621898—28no—
133#10621898—44no—
134#10621898—44no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172C2×Q812yes—
141C2×C4×D43—24no—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86C2×Q812yes—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43—82no—
158C4⋊C4×C43—82no—
159C4⋊C4×C43C2×D412yes—
160C4⋊C4×C43C2×D412yes—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—24no—
163C42×C43—24no—
164C42×C43—22no—
165C42×C43—22no—
166(C2×D43)⋊C4—82no—
167(C2×D43)⋊C4—82no—
168C4⋊Dic43—22no—
169C4⋊Dic43—22no—
170C4⋊Dic43—42no—
171#10621877—28no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—21no—
175C2×C43⋊C8—21no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8—21no—
180C2×C43⋊C8—44no—
181C2×C43⋊C8C2×D414yes—
182C23×C43—21no—
183C23×C43—21no—
184C23×C43—21no—
185C23×C43—21no—
186C23×C43#12112yes—
187C23×C43#12112yes—
188C23×C43C22⋊Q812yes—
189C23×C43C22×D411yescharacteristic
190C22×D43—22no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—84no—
213C2×C4×C43#12112yes—
214C2×C4×C43#12112yes—
215C2×C4×C43#12114yes—
216C2×C4×C43C22⋊Q812yes—
217C2×C4×C43C22⋊Q814yes—
218C2×C4×C43C22⋊Q814yes—
219C2×C4×C43#12614yes—
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C22×Q811yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—48no—
227C2×Dic43—22no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—84no—
234D172—22no—
235D172—22no—
236D172—41no—
237D172—41no—
238C4×D43—48no—
239Dic86—22no—
240Dic86—22no—
241Dic86—41no—
242Dic86—41no—
243C43⋊C8—24no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246#23616—431nomaximal, Sylow
247C22×C43—22no—
248C22×C43—22no—
249C22×C43—22no—
250C22×C43—22no—
251C22×C43—22no—
252C22×C43—22no—
253C22×C43#39614yes—
254C22×C43C2×#12111yescharacteristic
255C22×C43C2×#12111yescharacteristic
256C22×C43C2×C22⋊Q811yescharacteristic
257C22×C43#57611yescharacteristic
258C22×C43#57711yescharacteristic
259C22×C43#57711yescharacteristic
260C22×C43#57811yescharacteristic
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43—42no—
271C4×C43—42no—
272C4×C43—82no—
273C4×C43#39614yes—
274C4×C43C2×#12111yescharacteristic
275C4×C43C2×C22⋊Q811yescharacteristic
276C4×C43C2×C22⋊Q811yescharacteristic
277C4×C43C2×#12611yescharacteristic
278Dic43—42no—
279Dic43—82no—
280C2×#428—431no—
281C2×#424—431no—
282C2×#417—431no—
283C2×#416—431no—
284#2317D4311yescharacteristic, complemented
285#2311—431no—
286#2068—432no—
287#2067—432no—
288#2066—432no—
289#2065—432no—
290C2×#340—431no—
291C2×C43—24no—
292C2×C43C2×#39611yescharacteristic
293C2×C43#304511yescharacteristic
294C2×C43#304611yescharacteristic
295C2×C43#306211yescharacteristic
296C2×C43#306311yescharacteristic
297C2×C43#308311yescharacteristic
298C2×C43#308411yescharacteristic
299D43—82no—
300C22×#41—431no—
301C22×M16—431no—
302C23×C8—431no—
303C2×#117C2×D4311yescharacteristic
304C2×#117C2×D4311yescharacteristic
305C22×C4⋊C4—431no—
306C22×C4⋊C4C2×D4311yescharacteristic
307#428—864no—
308C2×#107—432no—
309C2×#106—432no—
310#424—864no—
311C2×C4⋊C8—432no—
312C2×C4⋊C8—432no—
313#417—864no—
314#416—864no—
315C2×#103—431no—
316C2×#103—432no—
317C2×#103—431no—
318C2×#102—431no—
319C2×#102—432no—
320C2×#102—431no—
321#391—432no—
322#390—432no—
323#389C2×D4312yes—
324#389C2×D4312yes—
325#386—862no—
326#385—22no—
327#384—21no—
328#382—21no—
329#380—861no—
330#380—861no—
331#340—432no—
332#340—432no—
333C43#2361611yescharacteristic, complemented, Sylow
334C2×#41—434no—
335C2×#41—862no—
336C2×#41—862no—
337C2×#41—862no—
338C2×#41—862no—
339C2×#41—862no—
340C22×Q8—431no—
341C22×D4—431no—
342C22×D4—861no—
343C23×C4—21no—
344C23×C4—861no—
345C23×C4—861no—
346C23×C4C22×D4311yescharacteristic
347C2×M16—434no—
348C2×M16—862no—
349C2×M16—862no—
350C22×C8—432no—
351C22×C8—431no—
352C22×C8—431no—
353C22×C8—862no—
354C22×C8—862no—
355C22×C8—862no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117D17214yes—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—432no—
366C2×C4⋊C4—862no—
367C2×C4⋊C4—862no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4C22⋊D4311yescharacteristic
370C2×C4⋊C4C22⋊D4311yescharacteristic
371C2×C4⋊C4C22×D4312yes—
372C2×C4⋊C4C22×D4311yescharacteristic
373C2×C4⋊C4C22×D4311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—862no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4C22⋊D4312yes—
378C2×C42—21no—
379C2×C42C22×D4312yes—
380#107—864no—
381#106—864no—
382C4⋊C8—864no—
383C4⋊C8—864no—
384#103—864no—
385#103—862no—
386#103—862no—
387#102—864no—
388#102—862no—
389#102—862no—
390#95—22no—
391#95—22no—
392#95—862no—
393#95—862no—
394C24—861no—
395C24C2×C22⋊D4311yescharacteristic
396#41—868no—
397#41—868no—
398#41—1724no—
399#41—1724no—
400C2×Q8—432no—
401C2×Q8—861no—
402C2×Q8—861no—
403C2×Q8—861no—
404C2×Q8—861no—
405C2×Q8—861no—
406C2×D4—432no—
407C2×D4—864no—
408C2×D4—861no—
409C2×D4—861no—
410C2×D4—861no—
411C2×D4—861no—
412C2×D4—861no—
413C2×D4—1722no—
414C2×D4—1722no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—42no—
419C22×C4—81no—
420C22×C4—81no—
421C22×C4—861no—
422C22×C4—864no—
423C22×C4—862no—
424C22×C4—3441no—
425C22×C4—3441no—
426C22×C4—1722no—
427C22×C4—1722no—
428C22×C4—1722no—
429C22×C4C2×D17212yes—
430C22×C4#1062189812yes—
431C22×C4D4×D4312yes—
432C22×C4#1062190012yes—
433C22×C4Q8×D4312yes—
434C22×C4#1062190212yes—
435C22×C4C2×C22⋊D4312yes—
436C22×C4C2×C22⋊D4312yes—
437C22×C4C2×C22⋊D4311yescharacteristic
438C22×C4C23×D4311yescharacteristic
439M16—868no—
440C2×C8—434no—
441C2×C8—862no—
442C2×C8—862no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—1724no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—42no—
457C4⋊C4—82no—
458C4⋊C4—82no—
459C4⋊C4—862no—
460C4⋊C4—862no—
461C4⋊C4—1722no—
462C4⋊C4C2×D17212yes—
463C4⋊C4C2×D17212yes—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—3442no—
467C22⋊C4—3442no—
468C42—24no—
469C42—22no—
470C42—22no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—862no—
476C23—1721no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23—1721no—
482C23#1306329712yes—
483C23#1306329912yes—
484C23#1306330112yes—
485C23C22×C22⋊D4311yescharacteristic
486Q8—862no—
487Q8—862no—
488Q8—1721no—
489Q8—1721no—
490D4—862no—
491D4—862no—
492D4—1728no—
493D4—1721no—
494D4—1721no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—84no—
511C2×C4—862no—
512C2×C4—3444no—
513C2×C4—1722no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1728no—
519C2×C4#1306329712yes—
520C2×C4#1306329912yes—
521C2×C4#1306330014yes—
522C2×C4#1306330112yes—
523C2×C4#1306330314yes—
524C2×C4#1306330514yes—
525C2×C4#1306332014yes—
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×D17211yescharacteristic
528C2×C4C2×Q8×D4311yescharacteristic
529C2×C4C2×#1062190011yescharacteristic
530C2×C4C2×#1062189811yescharacteristic
531C2×C4C2×#1062190211yescharacteristic
532C8—864no—
533C8—1721no—
534C8—1721no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—3441no—
542C22—3441no—
543C22—3441no—
544C22—3441no—
545C22—1722no—
546C22—1722no—
547C22—1722no—
548C22#1458282114yes—
549C22C2×#1306329711yescharacteristic
550C22C2×#1306329911yescharacteristic
551C22C2×#1306330111yescharacteristic
552C22#1458370211yescharacteristic
553C22#1458370711yescharacteristic
554C22#1458371011yescharacteristic
555C22#1458371411yescharacteristic
556C4—42no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—82no—
561C4—3442no—
562C4—1722no—
563C4#1458282114yes—
564C4C2×#1306330011yescharacteristic
565C4C2×#1306330311yescharacteristic
566C4C2×#1306330511yescharacteristic
567C4C2×#1306332011yescharacteristic
568C2—24no—
569C2—3442no—
570C2C2×#1458282111yescharacteristic
571C2#1914413411yescharacteristic
572C2#1914414511yescharacteristic
573C2#1914427111yescharacteristic
574C2#1914428211yescharacteristic
575C2#1914444211yescharacteristic
576C2#1914445311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2317C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenter#2317D43
hypocenterC43#23616
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
1. C2×#14582942C2semidirect
2. C2×#14582926C2semidirect
6. #19135987C2semidirect
7. #19135980C2semidirect
8. #19135973C2semidirect
9. #19135966C2semidirect
10. C2×#14582661C2semidirect
11. C43×#2317C2semidirect
284. #2317D43semidirect
333. C43#23616semidirect

Maximal subgroups

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

subgroupindex
C2×#145829422
C2×#145829262
C2×#145828982
C2×#145828932
#191371832
#191359872
#191359802
#191359732
#191359662
C2×#145826612
C43×#23172
#2361643