Finite Group Databasebeta

← #24992129

Subgroups — #24992129

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#19137253C211yesmaximal, characteristic
3#19132911C211yesmaximal, characteristic, complemented
4C2×#14582623C211yesmaximal, characteristic, complemented
5#19132442C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C2×C43×#323C211yesmaximal, characteristic, complemented
8C2×#13063294C411yescharacteristic
9C2×C4×C22⋊D43C2211yescharacteristic
10C8×C22⋊D43—22no—
11(C22⋊D43)⋊C8—22no—
12#14582949—21no—
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C22⋊C8×D43—21no—
16#14582799—21no—
17#14582793—21no—
18#14582787—21no—
19#14582778C411yescharacteristic
20#14582775—21no—
21#14582772C411yescharacteristic
22#14582755C411yescharacteristic
23C4×C22⋊Dic43C2211yescharacteristic
24#14582624—21no—
25#14582623—22no—
26#14582622—21no—
27C22×C22⋊C4×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#323—22no—
31C22×C22⋊D43—21no—
32C22×C22⋊D43C2×C411yescharacteristic
33C22×C4×D43D411yescharacteristic
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36C2×C8×D43—22no—
37#13063294—22no—
38#13063294C814yescomplemented
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43—21no—
42C4×C22⋊D43—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4D411yescharacteristic
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43C2×C411yescharacteristic
49C2×C22⋊Dic43C2×C411yescharacteristic
50C2×C22⋊Dic43C2×C411yescharacteristic
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4D411yescharacteristic
53C2×C4×Dic43—21no—
54C2×C4×Dic43D411yescharacteristic
55Dic43⋊C8—22no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)D412yescomplemented
60(C2×D43)⋊C8—22no—
61C8×Dic43—22no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C25×C43C2×C411yescharacteristic
66C23×C4×C43C2×C411yescharacteristic
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43—21no—
69C22×C8×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43D412yescomplemented
80C24×C43—21no—
81C24×C43—21no—
82C24×C43—21no—
83C24×C43—21no—
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—81no—
87C24×C43—81no—
88C24×C43C2×C812yescomplemented
89C24×C43C22×C411yescharacteristic
90C23×D43C22⋊C411yescharacteristic
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—81no—
95C22×C4×C43—81no—
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C22×C4×C43#4111yescharacteristic
102C2×C22⋊D43—21no—
103C2×C22⋊D43—21no—
104C2×C22⋊D43—21no—
105C2×C22⋊D43—21no—
106C2×C22⋊D43—24no—
107C2×C22⋊D43—81no—
108C2×C22⋊D43—81no—
109C2×C22⋊D43C2×C812yes—
110C2×C22⋊D43M1612yes—
111C22×Dic43—21no—
112C22×Dic43—21no—
113C22×Dic43C22⋊C411yescharacteristic
114C22×Dic43C22⋊C411yescharacteristic
115C22×Dic43C22⋊C411yescharacteristic
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—41no—
124C22⋊C4×C43—41no—
125C22⋊C4×C43—41no—
126C22⋊C4×C43—41no—
127C22⋊Dic43—24no—
128C22⋊Dic43—21no—
129C22⋊Dic43—21no—
130C22⋊Dic43—21no—
131C22⋊Dic43—21no—
132C22⋊Dic43—21no—
133C22⋊Dic43—81no—
134C22⋊Dic43—81no—
135C22⋊Dic43C2×C812yescomplemented
136(C2×D43)⋊C4—21no—
137(C2×D43)⋊C4—21no—
138(C2×D43)⋊C4—81no—
139Dic43⋊C4—21no—
140Dic43⋊C4—21no—
141Dic43⋊C4—81no—
142C4×Dic43—21no—
143C4×Dic43—21no—
144C4×Dic43—81no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—81no—
148C2×C43⋊C8—81no—
149C8×D43—82no—
150C23×C43—22no—
151C23×C43—22no—
152C23×C43—22no—
153C23×C43—41no—
154C23×C43—41no—
155C23×C43—41no—
156C23×C43—41no—
157C23×C43—41no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43—41no—
161C23×C43—41no—
162C23×C43—41no—
163C23×C43—81no—
164C23×C43—81no—
165C23×C43—81no—
166C23×C43—81no—
167C23×C43—82no—
168C23×C43—82no—
169C23×C43—82no—
170C23×C43—82no—
171C23×C43C2×C22⋊C411yescharacteristic
172C23×C43C4×D411yescharacteristic
173C23×C43C4×D411yescharacteristic
174C23×C43C22×C811yescharacteristic
175C23×C43C2×M1611yescharacteristic
176C23×C43#13111yescharacteristic
177C23×C43#13111yescharacteristic
178C22×D43—21no—
179C22×D43—21no—
180C22×D43—41no—
181C22×D43—41no—
182C22×D43C22⋊C812yes—
183C2×C4×C43—41no—
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—81no—
193C2×C4×C43—81no—
194C2×C4×C43#12011yescharacteristic
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12311yescharacteristic
198C22⋊D43—22no—
199C22⋊D43—22no—
200C22⋊D43—22no—
201C22⋊D43—22no—
202C22⋊D43—84no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—22no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43C22⋊C812yes—
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—42no—
234C22×C43—42no—
235C22×C43—42no—
236C22×C43—82no—
237C22×C43—82no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43—82no—
241C22×C43—82no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43#38611yescharacteristic
245C22×C43C2×C22⋊C811yescharacteristic
246C22×C43#40811yescharacteristic
247C22×C43C8×D411yescharacteristic
248C22×C43C8×D411yescharacteristic
249C22×C43#43511yescharacteristic
250C22×C43#43511yescharacteristic
251C2×D43—22no—
252C2×D43—41no—
253C2×D43—41no—
254C2×D43—42no—
255C2×D43—81no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—81no—
261Dic43—22no—
262Dic43—42no—
263Dic43—41no—
264Dic43—41no—
265Dic43—81no—
266#2972—431no—
267#2321—431no—
268#1459—431no—
269C2×#323—431no—
270C2×#323D4311yescharacteristic, complemented
271#1282—431no—
272#1282—431no—
273C2×C43—21no—
274C2×C43—21no—
275C2×C43—21no—
276C2×C43—21no—
277C2×C43—21no—
278C2×C43—21no—
279C2×C43—82no—
280C2×C43#186911yescharacteristic
281C2×C43#191311yescharacteristic
282C2×C43#191411yescharacteristic
283D43—42no—
284C2×#120—431no—
285C2×C4×D4—431no—
286C22×C22⋊C4C2×D4311yescharacteristic
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⋊C4—431no—
303#324—861no—
304#323—22no—
305#323—861no—
306#323—862no—
307C43#910711yescharacteristic, complemented, Sylow
308C25C4×D4311yescharacteristic
309C22×D4—431no—
310C22×D4—861no—
311C23×C4—431no—
312C23×C4C4×D4311yescharacteristic
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—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—431no—
334C2×C22⋊C4—431no—
335C2×C22⋊C4—431no—
336C2×C22⋊C4—431no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—861no—
340C2×C22⋊C4—861no—
341C2×C42—431no—
342C2×C42—861no—
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⋊C8C22⋊D4312yescomplemented
353C4×C8—862no—
354#95—861no—
355#95—861no—
356#95—861no—
357C24—21no—
358C24—21no—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—81no—
364C24—81no—
365C24—431no—
366C24C8×D4312yescomplemented
367C24C2×C4×D4311yescharacteristic
368C2×D4—432no—
369C2×D4—432no—
370C2×D4—861no—
371C2×D4—861no—
372C2×D4—861no—
373C2×D4—861no—
374C2×D4—864no—
375C2×D4—3441no—
376C2×D4—3441no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—81no—
381C22×C4—81no—
382C22×C4—431no—
383C22×C4—431no—
384C22×C4—431no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4—861no—
389C22×C4—3441no—
390C22×C4#1062189811yescharacteristic
391C22×C4D4×D4311yescharacteristic
392C22×C4D4×D4311yescharacteristic
393C22×C4D4×D4311yescharacteristic
394C22×C4#1062190011yescharacteristic
395C22×C4C2×C22⋊D4311yescharacteristic
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—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—432no—
413C22⋊C4—864no—
414C22⋊C4—861no—
415C22⋊C4—861no—
416C22⋊C4—861no—
417C22⋊C4—861no—
418C22⋊C4—861no—
419C22⋊C4—861no—
420C22⋊C4—861no—
421C22⋊C4—3441no—
422C22⋊C4—3441no—
423C22⋊C4—3441no—
424C42—861no—
425C42—861no—
426C42—3441no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23—81no—
444C23—82no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—432no—
449C23—861no—
450C23—861no—
451C23—1721no—
452C23—1721no—
453C23C22⋊C4×D4311yescharacteristic
454C23(C22⋊D43)⋊C411yescharacteristic
455C23C4×C22⋊D4311yescharacteristic
456C23C2×C8×D4311yescharacteristic
457C23M16×D4311yescharacteristic
458C23#1306333111yescharacteristic
459C23#1306333311yescharacteristic
460D4—862no—
461D4—862no—
462D4—862no—
463D4—862no—
464D4—3444no—
465C2×C4—41no—
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—81no—
475C2×C4—81no—
476C2×C4—432no—
477C2×C4—861no—
478C2×C4—861no—
479C2×C4—862no—
480C2×C4—861no—
481C2×C4—861no—
482C2×C4—3441no—
483C2×C4—1722no—
484C2×C4—1721no—
485C2×C4—1721no—
486C2×C4—1721no—
487C2×C4—1721no—
488C2×C4—1721no—
489C2×C4—1721no—
490C2×C4—1721no—
491C2×C4#1306329311yescharacteristic
492C2×C4#1306329611yescharacteristic
493C2×C4#1306329811yescharacteristic
494C2×C4#1306330711yescharacteristic
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—42no—
510C22—42no—
511C22—42no—
512C22—82no—
513C22—82no—
514C22—81no—
515C22—81no—
516C22—82no—
517C22—82no—
518C22—81no—
519C22—81no—
520C22—862no—
521C22—3441no—
522C22—1722no—
523C22—1721no—
524C22—1721no—
525C22#1458277511yescharacteristic
526C22C22⋊C8×D4311yescharacteristic
527C22#1458286411yescharacteristic
528C22(C22⋊D43)⋊C811yescharacteristic
529C22C8×C22⋊D4311yescharacteristic
530C22#1458296811yescharacteristic
531C22#1458297311yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—21no—
536C4—81no—
537C4—862no—
538C4—3441no—
539C4—1722no—
540C4—1721no—
541C4—1721no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—82no—
549C2—1722no—
550C2#1913488411yescharacteristic
551C2#1913513411yescharacteristic
552C2#1913513911yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC2×C43×#323C2
socleC22×C43#386
prime radicalC2×#13063294C4
cosocleC23×C4×C43C23
hypercenterC2×#323D43
hypocenterC43#9107
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
1. #19143617C2semidirect
3. #19132911C2semidirect
4. C2×#14582623C2semidirect
5. #19132442C2semidirect
6. #19132441C2semidirect
7. C2×C43×#323C2semidirect
38. #13063294C8semidirect
59. C22⋊(C43⋊C8)D4semidirect
79. C22⋊C8×C43D4semidirect
88. C24×C43C2×C8semidirect
135. C22⋊Dic43C2×C8semidirect
270. C2×#323D43semidirect
307. C43#9107semidirect
352. C22⋊C8C22⋊D43semidirect
366. C24C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191436172
#191372532
#191329112
C2×#145826232
#191324422
#191324412
C2×C43×#3232
#910743