Finite Group Databasebeta

← #24992131

Subgroups — #24992131

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143617C211yesmaximal, characteristic, complemented
2#19137255C211yesmaximal, characteristic
3#19132911C211yesmaximal, characteristic, complemented
4C2×#14582622C211yesmaximal, characteristic, complemented
5C2×#14582622C211yesmaximal, characteristic, complemented
6#19132443C211yesmaximal, characteristic, complemented
7C43×#1282C211yesmaximal, characteristic, complemented
8C2×#13063295C411yescharacteristic
9C2×C4×C22⋊D43C2211yescharacteristic
10C22×(C2×D43)⋊C4C2211yescharacteristic
11C8×C22⋊D43—22no—
12(C22⋊D43)⋊C8—22no—
13#14582949—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16C22⋊C8×D43—21no—
17#14582801—21no—
18#14582791—21no—
19#14582790—21no—
20#14582777—21no—
21#14582776C411yescharacteristic
22#14582774C411yescharacteristic
23#14582754C411yescharacteristic
24#14582624—21no—
25#14582622—21no—
26#14582622—22no—
27#14582622—22no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C24×D43C2×C411yescharacteristic
32C22×D172—21no—
33C22×C22⋊D43C2×C411yescharacteristic
34C23×Dic43C2×C411yescharacteristic
35C22×C4×D43D411yescharacteristic
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38C2×C8×D43—22no—
39#13063295—22no—
40#13063295C814yescomplemented
41C4×C22⋊D43—21no—
42C4×C22⋊D43—21no—
43C4×C22⋊D43—21no—
44C4×C22⋊D43—21no—
45C2×C4⋊Dic43—21no—
46C2×Dic43⋊C4D411yescharacteristic
47C2×C22⋊Dic43C2×C411yescharacteristic
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4—21no—
56C2×(C2×D43)⋊C4—21no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4D411yescharacteristic
59C2×C4×Dic43D411yescharacteristic
60Dic43⋊C8—22no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)—21no—
63C22⋊(C43⋊C8)—21no—
64C22⋊(C43⋊C8)D412yescomplemented
65(C2×D43)⋊C8—22no—
66C8×Dic43—22no—
67C43⋊#95—21no—
68C43⋊#95—21no—
69C23×C4×C43C2311yescharacteristic
70C22×C8×C43—21no—
71C22×C8×C43—21no—
72C2×C22⋊C4×C43C2×C411yescharacteristic
73C2×C22⋊C4×C43C2×C411yescharacteristic
74C2×C42×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43D412yescomplemented
79#95×C43—21no—
80C24×C43C22×C411yescharacteristic
81C23×D43—21no—
82C23×D43—21no—
83C23×D43—21no—
84C23×D43—21no—
85C23×D43—21no—
86C23×D43—21no—
87C23×D43—81no—
88C23×D43—81no—
89C23×D43C22⋊C411yescharacteristic
90C23×D43C2×C812yescomplemented
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—81no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—21no—
101C2×C22⋊D43—21no—
102C2×C22⋊D43—21no—
103C2×C22⋊D43—21no—
104C2×C22⋊D43C2×C812yes—
105C2×C22⋊D43M1612yes—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—21no—
109C22×Dic43—81no—
110C22×Dic43C22⋊C411yescharacteristic
111C22×Dic43C22⋊C411yescharacteristic
112C22×Dic43C22⋊C411yescharacteristic
113C2×D172—24no—
114C2×D172—81no—
115C2×D172—81no—
116C2×C4×D43—21no—
117C2×C4×D43—21no—
118C2×C4×D43—81no—
119C2×C8×C43—22no—
120C2×C8×C43—41no—
121C2×C8×C43—81no—
122C2×C8×C43—81no—
123C22⋊C4×C43—21no—
124C22⋊C4×C43—21no—
125C22⋊C4×C43—21no—
126C22⋊C4×C43C2×C812yescomplemented
127C42×C43—81no—
128C22⋊Dic43—21no—
129C22⋊Dic43—21no—
130(C2×D43)⋊C4—21no—
131(C2×D43)⋊C4—21no—
132(C2×D43)⋊C4—24no—
133(C2×D43)⋊C4—41no—
134(C2×D43)⋊C4—41no—
135(C2×D43)⋊C4—41no—
136(C2×D43)⋊C4—41no—
137(C2×D43)⋊C4—81no—
138(C2×D43)⋊C4—81no—
139(C2×D43)⋊C4—81no—
140C4⋊Dic43—81no—
141Dic43⋊C4—21no—
142Dic43⋊C4—21no—
143C4×Dic43—21no—
144C4×Dic43—21no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—81no—
148C2×C43⋊C8—81no—
149C8×D43—82no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43C2×C22⋊C411yescharacteristic
153C23×C43C4×D411yescharacteristic
154C23×C43C4×D411yescharacteristic
155C23×C43C22×C811yescharacteristic
156C23×C43C2×M1611yescharacteristic
157C23×C43#13111yescharacteristic
158C23×C43#13111yescharacteristic
159C22×D43—21no—
160C22×D43—21no—
161C22×D43—22no—
162C22×D43—22no—
163C22×D43—22no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171C22×D43—41no—
172C22×D43—41no—
173C22×D43—41no—
174C22×D43—82no—
175C22×D43—82no—
176C22×D43—81no—
177C22×D43—81no—
178C22×D43—81no—
179C22×D43—81no—
180C22×D43—82no—
181C22×D43—82no—
182C22×D43C22⋊C812yes—
183C2×C4×C43—22no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43#12011yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#12311yescharacteristic
199C22⋊D43—22no—
200C22⋊D43—22no—
201C22⋊D43—22no—
202C22⋊D43—22no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—81no—
213C2×Dic43—81no—
214C2×Dic43C22⋊C812yes—
215D172—84no—
216C4×D43—42no—
217C4×D43—81no—
218C8×C43—42no—
219C8×C43—81no—
220C43⋊C8—42no—
221C43⋊C8—81no—
222#9107—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—41no—
230C22×C43—41no—
231C22×C43—41no—
232C22×C43—41no—
233C22×C43#38611yescharacteristic
234C22×C43C2×C22⋊C811yescharacteristic
235C22×C43#40811yescharacteristic
236C22×C43C8×D411yescharacteristic
237C22×C43C8×D411yescharacteristic
238C22×C43#43511yescharacteristic
239C22×C43#43511yescharacteristic
240C2×D43—22no—
241C2×D43—41no—
242C2×D43—41no—
243C2×D43—42no—
244C2×D43—42no—
245C2×D43—42no—
246C2×D43—42no—
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—81no—
250C2×D43—82no—
251C2×D43—82no—
252C2×D43—81no—
253C2×D43—81no—
254C2×D43—82no—
255C2×D43—82no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—42no—
261C4×C43—81no—
262Dic43—22no—
263Dic43—41no—
264Dic43—41no—
265Dic43—81no—
266#2972—431no—
267#2321—431no—
268#1459—431no—
269C2×#323—431no—
270C2×#323—431no—
271#1282—431no—
272#1282D4311yescharacteristic, complemented
273C2×C43—21no—
274C2×C43—21no—
275C2×C43—21no—
276C2×C43—21no—
277C2×C43—21no—
278C2×C43—21no—
279C2×C43#186911yescharacteristic
280C2×C43#191311yescharacteristic
281C2×C43#191411yescharacteristic
282D43—42no—
283D43—82no—
284C2×#120—431no—
285C2×C4×D4—431no—
286C22×C22⋊C4—431no—
287C8×D4—862no—
288C8×D4—862no—
289#431—861no—
290C2×C22⋊C8—431no—
291C2×C22⋊C8—431no—
292C2×C22⋊C8—861no—
293C2×C22⋊C8C2×D4311yescharacteristic
294C2×C22⋊C8C2×D4311yescharacteristic
295#390—861no—
296#388—861no—
297#388—861no—
298#386—431no—
299#386—861no—
300#385—431no—
301#379—431no—
302C4×C22⋊C4C2×D4311yescharacteristic
303#324—861no—
304#323—862no—
305#323—861no—
306#323—862no—
307C43#910711yescharacteristic, complemented, Sylow
308C25—431no—
309C22×D4—431no—
310C22×D4—861no—
311C23×C4—431no—
312C23×C4—431no—
313C23×C4C22×D4311yescharacteristic
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—862no—
317C22×C8—861no—
318C22×C8—861no—
319#120—434no—
320#120—862no—
321C4×D4—861no—
322C4×D4—861no—
323C4×D4—861no—
324C4×D4—861no—
325C2×C4⋊C4—431no—
326C2×C4⋊C4—861no—
327C2×C22⋊C4—431no—
328C2×C22⋊C4—431no—
329C2×C22⋊C4—861no—
330C2×C22⋊C4—861no—
331C2×C22⋊C4—861no—
332C2×C22⋊C4—861no—
333C2×C22⋊C4—861no—
334C2×C22⋊C4—861no—
335C2×C22⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4C4×D4311yescharacteristic
340C2×C22⋊C4C4×D4311yescharacteristic
341C2×C42—21no—
342C2×C42—431no—
343C4⋊C8—862no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—432no—
348C22⋊C8—862no—
349C22⋊C8—861no—
350C22⋊C8—861no—
351C22⋊C8—861no—
352C22⋊C8D17212yescomplemented
353C4×C8—862no—
354#95—21no—
355#95—861no—
356#95—861no—
357C24—431no—
358C24—432no—
359C24—861no—
360C24—861no—
361C24—861no—
362C24—861no—
363C24—861no—
364C24—861no—
365C24—3441no—
366C24—3441no—
367C24C2×C4×D4311yescharacteristic
368C2×D4—432no—
369C2×D4—432no—
370C2×D4—864no—
371C2×D4—861no—
372C2×D4—861no—
373C2×D4—861no—
374C2×D4—861no—
375C2×D4—3441no—
376C2×D4—3441no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—81no—
380C22×C4—431no—
381C22×C4—431no—
382C22×C4—431no—
383C22×C4—861no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4—3441no—
389C22×C4—3441no—
390C22×C4C2×D17211yescharacteristic
391C22×C4#1062189811yescharacteristic
392C22×C4D4×D4311yescharacteristic
393C22×C4D4×D4311yescharacteristic
394C22×C4D4×D4311yescharacteristic
395C22×C4#1062190211yescharacteristic
396C2×C8—22no—
397C2×C8—41no—
398C2×C8—81no—
399C2×C8—81no—
400C2×C8—862no—
401C2×C8—3442no—
402C2×C8—3441no—
403C2×C8—3441no—
404C2×C8—1721no—
405C4⋊C4—861no—
406C4⋊C4—861no—
407C4⋊C4—3441no—
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—864no—
412C22⋊C4—861no—
413C22⋊C4—861no—
414C22⋊C4—861no—
415C22⋊C4—861no—
416C22⋊C4—3441no—
417C22⋊C4—3441no—
418C22⋊C4—3441no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C22⋊C4—1721no—
422C22⋊C4—1721no—
423C22⋊C4C8×D4312yescomplemented
424C42—81no—
425C42—861no—
426C42—861no—
427C23—41no—
428C23—41no—
429C23—432no—
430C23—861no—
431C23—861no—
432C23—862no—
433C23—862no—
434C23—862no—
435C23—3441no—
436C23—3441no—
437C23—3441no—
438C23—3441no—
439C23—3442no—
440C23—3442no—
441C23—3442no—
442C23—3442no—
443C23—1721no—
444C23—1721no—
445C23—1721no—
446C23—1721no—
447C23—1721no—
448C23—1721no—
449C23—1721no—
450C23—1721no—
451C23—1721no—
452C23—1721no—
453C23C22⋊C4×D4311yescharacteristic
454C23#1306328711yescharacteristic
455C23C4×D17211yescharacteristic
456C23C2×C8×D4311yescharacteristic
457C23M16×D4311yescharacteristic
458C23#1306333111yescharacteristic
459C23#1306333311yescharacteristic
460D4—862no—
461D4—862no—
462D4—862no—
463D4—862no—
464D4—3444no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—432no—
478C2×C4—861no—
479C2×C4—861no—
480C2×C4—861no—
481C2×C4—861no—
482C2×C4—3441no—
483C2×C4—3441no—
484C2×C4—3441no—
485C2×C4—1722no—
486C2×C4—1721no—
487C2×C4—1721no—
488C2×C4—1721no—
489C2×C4—1721no—
490C2×C4—1721no—
491C2×C4#1306329511yescharacteristic
492C2×C4#1306329811yescharacteristic
493C2×C4#1306330011yescharacteristic
494C2×C4#1306331011yescharacteristic
495C8—42no—
496C8—81no—
497C8—3441no—
498C8—1722no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—862no—
510C22—3442no—
511C22—3442no—
512C22—3442no—
513C22—3442no—
514C22—3441no—
515C22—3441no—
516C22—3441no—
517C22—3441no—
518C22—3441no—
519C22—1722no—
520C22—1722no—
521C22—1722no—
522C22—1722no—
523C22—1721no—
524C22—1721no—
525C22#1458277711yescharacteristic
526C22C22⋊C8×D4311yescharacteristic
527C22#1458286411yescharacteristic
528C22#1458296411yescharacteristic
529C22C8×D17211yescharacteristic
530C22#1458296911yescharacteristic
531C22#1458297211yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—21no—
536C4—42no—
537C4—81no—
538C4—862no—
539C4—3441no—
540C4—1721no—
541C4—1721no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—3442no—
549C2—1722no—
550C2#1913488611yescharacteristic
551C2#1913513611yescharacteristic
552C2#1913514111yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC43×#1282C2
socleC22×C43#386
prime radicalC2×#13063295C4
cosocleC23×C4×C43C23
hypercenter#1282D43
hypocenterC43#9107
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
1. #19143617C2semidirect
3. #19132911C2semidirect
4. C2×#14582622C2semidirect
5. C2×#14582622C2semidirect
6. #19132443C2semidirect
7. C43×#1282C2semidirect
40. #13063295C8semidirect
64. C22⋊(C43⋊C8)D4semidirect
78. C22⋊C8×C43D4semidirect
90. C23×D43C2×C8semidirect
126. C22⋊C4×C43C2×C8semidirect
272. #1282D43semidirect
307. C43#9107semidirect
352. C22⋊C8D172semidirect
423. C22⋊C4C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191436172
#191372552
#191329112
C2×#145826222
#191324432
C43×#12822
#910743