Finite Group Databasebeta

← #24993079

Subgroups — #24993079

Order 11008.

504 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145356C211yesmaximal, characteristic
2#19133099C211yesmaximal, characteristic, complemented
3C2×#14582634C211yesmaximal, characteristic, complemented
4#19132954C211yesmaximal, characteristic, complemented
5#19132483C211yesmaximal, characteristic, complemented
6#19132437C211yesmaximal, characteristic, complemented
7C43×#2977C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583232C411yescharacteristic, complemented
10#14583223—21no—
11#14583215C411yescharacteristic, complemented
12#14583133—21no—
13#14583130—21no—
14#14583049C411yescharacteristic, complemented
15#14583044—21no—
16#14583032C411yescharacteristic, complemented
17#14582863C2211yescharacteristic
18C2×C22⋊(C43⋊C8)C2211yescharacteristic
19C2×C43⋊#95C2211yescharacteristic
20#14582636—21no—
21#14582634—21no—
22#14582634—21no—
23#14582633—21no—
24#14582622—21no—
25#14582622—21no—
26C43×#525C2211yescharacteristic
27C43×#435—21no—
28C43×#435—21no—
29C8×D4×C43—21no—
30C8×D4×C43—21no—
31C43×#433—21no—
32C43×#408—21no—
33C2×C22⋊C8×C43C2211yescharacteristic
34C2×C22⋊C8×C43C2211yescharacteristic
35C22×D172C2×C411yescharacteristic
36C22×C22⋊D43—21no—
37C23×Dic43—21no—
38C2×#10621884—21no—
39C2×#10621882—21no—
40C2×#10621877—21no—
41C22×C43⋊C8—21no—
42#13063299—21no—
43#13063299—21no—
44#13063299—21no—
45#13063299—21no—
46C2×C4⋊Dic43C2×C411yescharacteristic
47C2×(C2×D43)⋊C4—21no—
48#13063258—21no—
49#13063256—21no—
50#13063249—21no—
51#13063246—21no—
52#13063245—21no—
53#13063245—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)C2×C411yescharacteristic
58C22⋊(C43⋊C8)C2×C411yescharacteristic
59C43⋊#95—21no—
60C43⋊#95—21no—
61C2×#41×C43D411yescharacteristic
62C23×C4×C43C2311yescharacteristic
63C2×M16×C43—21no—
64C22×C8×C43—21no—
65C22×C8×C43—21no—
66C22×C8×C43—21no—
67#123×C43—21no—
68C22⋊Q8×C43C2×C411yescharacteristic
69C22⋊Q8×C43D411yescharacteristic
70#121×C43C2×C411yescharacteristic
71#121×C43D411yescharacteristic
72#120×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43—21no—
75#117×C43D411yescharacteristic
76C4⋊C8×C43—21no—
77C4⋊C8×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43—21no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43—21no—
82C22⋊C8×C43D411yescharacteristic
83C22⋊C8×C43D411yescharacteristic
84C22⋊C8×C43D411yescharacteristic
85C22⋊C8×C43D411yescharacteristic
86#97×C43—21no—
87C4×C8×C43—21no—
88C24×C43#4111yescharacteristic
89C23×D43—21no—
90#41×C43—81no—
91C2×Q8×C43C22⋊C411yescharacteristic
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43C22⋊C411yescharacteristic
96C22×C4×C43—21no—
97C22×C4×C43—81no—
98C22×C4×C43C22×C411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C2×C22⋊D43—41no—
105C2×C22⋊D43—41no—
106C2×C22⋊D43—81no—
107C2×C22⋊D43—81no—
108C22×Dic43—22no—
109C22×Dic43—21no—
110C22×Dic43—41no—
111C22×Dic43—41no—
112C22×Dic43—81no—
113C22×Dic43—81no—
114C2×D172—21no—
115C2×D172—21no—
116C2×D172—81no—
117M16×C43—81no—
118C2×C8×C43—21no—
119C2×C8×C43—21no—
120C2×C8×C43—21no—
121C2×C8×C43—21no—
122C2×C8×C43—81no—
123C2×C8×C43—81no—
124C2×C8×C43—81no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43C22⋊C411yescharacteristic
128C4⋊C4×C43C22⋊C411yescharacteristic
129C22⋊C4×C43—21no—
130C22⋊C4×C43—21no—
131C22⋊C4×C43—21no—
132C22⋊C4×C43—21no—
133C22⋊C4×C43—21no—
134C42×C43—21no—
135#10621884—81no—
136#10621882—81no—
137(C2×D43)⋊C4—41no—
138(C2×D43)⋊C4—41no—
139C4⋊Dic43—21no—
140C4⋊Dic43—21no—
141#10621877—81no—
142C2×C43⋊C8—21no—
143C2×C43⋊C8—21no—
144C2×C43⋊C8—41no—
145C2×C43⋊C8—81no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—41no—
152C23×C43C4×D411yescharacteristic
153C23×C43#12111yescharacteristic
154C23×C43#12311yescharacteristic
155C22×D43—41no—
156C22×D43—41no—
157C22×D43—41no—
158C22×D43—81no—
159C22×D43—81no—
160Q8×C43—41no—
161D4×C43—41no—
162D4×C43—41no—
163D4×C43—41no—
164D4×C43—41no—
165D4×C43—41no—
166D4×C43—81no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43C2×C22⋊C411yescharacteristic
179C2×C4×C43C4×D411yescharacteristic
180C2×C4×C43#12011yescharacteristic
181C2×C4×C43#12111yescharacteristic
182C22⋊D43—82no—
183C22⋊D43—81no—
184C22⋊D43—81no—
185C2×Dic43—42no—
186C2×Dic43—41no—
187C2×Dic43—81no—
188C2×Dic43—82no—
189C2×Dic43—81no—
190C2×Dic43—81no—
191C2×Dic43—82no—
192D172—41no—
193D172—41no—
194D172—81no—
195C8×C43—41no—
196C8×C43—41no—
197C8×C43—41no—
198C8×C43—41no—
199C43⋊C8—41no—
200C43⋊C8—41no—
201C43⋊C8—81no—
202#9264—431nomaximal, Sylow
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—41no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—41no—
216C22×C43—41no—
217C22×C43#38611yescharacteristic
218C22×C43#44311yescharacteristic
219C22×C43#44411yescharacteristic
220C22×C43#47111yescharacteristic
221C22×C43#47211yescharacteristic
222C2×D43—81no—
223C2×D43—81no—
224C2×D43—81no—
225C2×D43—161no—
226C2×D43—161no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—41no—
232C4×C43—41no—
233C4×C43—41no—
234Dic43—82no—
235Dic43—81no—
236#3188—431no—
237#2977D4311yescharacteristic, complemented
238#1504—431no—
239C2×#327—431no—
240#1471—431no—
241#1298—431no—
242#1280—431no—
243C2×C43—21no—
244C2×C43—21no—
245C2×C43—21no—
246C2×C43—21no—
247C2×C43—41no—
248C2×C43—81no—
249C2×C43#187611yescharacteristic
250C2×C43#190711yescharacteristic
251C2×C43#191311yescharacteristic
252D43—161no—
253#525C2×D4311yescharacteristic
254C2×#121—431no—
255#484—431no—
256#482—861no—
257#481—431no—
258#466—861no—
259#465—861no—
260#450—431no—
261#449—861no—
262#447—431no—
263#435—21no—
264#435—21no—
265C8×D4—21no—
266C8×D4—21no—
267#433—21no—
268#408—21no—
269#407—431no—
270C2×C22⋊C8—431no—
271C2×C22⋊C8C2×D4311yescharacteristic
272C2×C22⋊C8C2×D4311yescharacteristic
273C2×#95—431no—
274#328—861no—
275#327—861no—
276#327—861no—
277#327—861no—
278#323—861no—
279#323—861no—
280C43#926411yescharacteristic, complemented, Sylow
281C2×#41C22⋊D4311yescharacteristic
282C22×D4—431no—
283C22×D4—861no—
284C23×C4—861no—
285C23×C4C22×D4311yescharacteristic
286C2×SD16—861no—
287C2×D8—861no—
288C2×M16—21no—
289C2×M16—861no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—861no—
294#123—21no—
295C22⋊Q8C4×D4311yescharacteristic
296C22⋊Q8D17211yescharacteristic
297#121—861no—
298#121—861no—
299#121—861no—
300#121—861no—
301#121C4×D4311yescharacteristic
302#121D17211yescharacteristic
303#120—21no—
304C4×D4—21no—
305C4×D4—21no—
306#117C22⋊D4311yescharacteristic
307C2×C4⋊C4—431no—
308C2×C22⋊C4—861no—
309#107—861no—
310#106—861no—
311C4⋊C8—21no—
312C4⋊C8—21no—
313#103—861no—
314#102—861no—
315#102—861no—
316#102—861no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—431no—
322C22⋊C8—431no—
323C22⋊C8—861no—
324C22⋊C8—861no—
325C22⋊C8—861no—
326C22⋊C8C22⋊D4311yescharacteristic
327C22⋊C8C22⋊D4311yescharacteristic
328C22⋊C8C22⋊D4311yescharacteristic
329C22⋊C8C22⋊D4311yescharacteristic
330#97—21no—
331C4×C8—21no—
332#95—861no—
333#95—861no—
334C24—861no—
335C24#1062189811yescharacteristic
336#41—81no—
337C2×Q8(C2×D43)⋊C411yescharacteristic
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—861no—
342C2×D4—861no—
343C2×D4—3441no—
344C2×D4—3441no—
345C2×D4—3441no—
346C2×D4—1721no—
347C2×D4—1721no—
348C2×D4(C2×D43)⋊C411yescharacteristic
349C22×C4—21no—
350C22×C4—81no—
351C22×C4—862no—
352C22×C4—861no—
353C22×C4—3441no—
354C22×C4—3441no—
355C22×C4—1721no—
356C22×C4—1721no—
357C22×C4C2×C4×D4311yescharacteristic
358C22×C4C2×D17211yescharacteristic
359C22×C4#1062189811yescharacteristic
360C22×C4C2×C22⋊D4311yescharacteristic
361C22×C4C2×C22⋊D4311yescharacteristic
362C22×C4C2×C22⋊D4311yescharacteristic
363SD16—3441no—
364D8—3441no—
365M16—81no—
366M16—3441no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—81no—
372C2×C8—81no—
373C2×C8—81no—
374C2×C8—861no—
375C2×C8—861no—
376C2×C8—3441no—
377C2×C8—1721no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—861no—
381C4⋊C4—861no—
382C4⋊C4(C2×D43)⋊C411yescharacteristic
383C4⋊C4(C2×D43)⋊C411yescharacteristic
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C42—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—3441no—
399C23—3441no—
400C23—1721no—
401C23—1721no—
402C23—1721no—
403C23C4×C22⋊D4311yescharacteristic
404C23#1306329911yescharacteristic
405C23#1306330811yescharacteristic
406Q8—41no—
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—81no—
413D4—3441no—
414D4—3442no—
415D4—3441no—
416D4—3441no—
417D4—1721no—
418D4—1721no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—3441no—
431C2×C4—3442no—
432C2×C4—3441no—
433C2×C4—3441no—
434C2×C4—3442no—
435C2×C4—1722no—
436C2×C4—1721no—
437C2×C4C2×(C2×D43)⋊C411yescharacteristic
438C2×C4C4×C22⋊D4311yescharacteristic
439C2×C4#1306329411yescharacteristic
440C2×C4#1306329911yescharacteristic
441C8—41no—
442C8—41no—
443C8—41no—
444C8—41no—
445C8—3441no—
446C8—1721no—
447C8—1721no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—3441no—
463C22—3441no—
464C22—3441no—
465C22—6881no—
466C22—6881no—
467C22#1458277811yescharacteristic
468C22#1458301411yescharacteristic
469C22#1458301911yescharacteristic
470C22#1458316211yescharacteristic
471C22#1458316911yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—3442no—
480C4—3441no—
481C2—21no—
482C2—21no—
483C2—21no—
484C2—21no—
485C2—41no—
486C2—81no—
487C2—6881no—
488C2#1913492211yescharacteristic
489C2#1913510311yescharacteristic
490C2#1913513711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2977C2
socleC22×C43#386
prime radical#19145356C2
cosocleC23×C4×C43C23
hypercenter#2977D43
hypocenterC43#9264
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2977

Complements

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

NH ≅ G/Ntype
2. #19133099C2semidirect
3. C2×#14582634C2semidirect
4. #19132954C2semidirect
5. #19132483C2semidirect
6. #19132437C2semidirect
7. C43×#2977C2semidirect
9. #14583232C4semidirect
11. #14583215C4semidirect
14. #14583049C4semidirect
16. #14583032C4semidirect
237. #2977D43semidirect
280. C43#9264semidirect

Maximal subgroups

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

subgroupindex
#191453562
#191330992
C2×#145826342
#191329542
#191324832
#191324372
C43×#29772
#926443