Finite Group Databasebeta

← #24991454

Subgroups — #24991454

Order 11008.

578 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144595C211yesmaximal, characteristic
2D4×#10621877C211yesmaximal, characteristic, complemented
3#19135513C211yesmaximal, characteristic, complemented
4#19133047C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C4×#102×C43C211yesmaximal, characteristic, complemented
8C22×#10621877—21no—
9#14583449C2211yescharacteristic
10#14583212—21no—
11#14583179C411yescharacteristic, complemented
12#14583179C411yescharacteristic, complemented
13#14583094C411yescharacteristic, complemented
14#14583094C411yescharacteristic, complemented
15#14583033—21no—
16C4×#10621882—21no—
17C4×#10621882—21no—
18#14582977—21no—
19#14582971—22no—
20D4×C43⋊C8—21no—
21#14582952C2211yescharacteristic
22#14582923C2211yescharacteristic
23C2×#13063253—21no—
24C2×#13063253—21no—
25#14582863—21no—
26C4×#10621877C2211yescharacteristic
27#14582628—22no—
28C2×C4×D4×C43C2211yescharacteristic
29C2×#102×C43—21no—
30C2×C4×C8×C43C2211yescharacteristic
31C4×C4⋊C4×C43C2211yescharacteristic
32C43×#340—21no—
33C2×#10621898—21no—
34C2×#10621882—21no—
35C2×#10621882—21no—
36C2×#10621877—22no—
37C2×#10621877—21no—
38C2×#10621877—42no—
39C2×#10621877—42no—
40C2×#10621877D411yescharacteristic
41C2×#10621877D411yescharacteristic
42C22×C43⋊C8—22no—
43#13063325C2×C411yescharacteristic
44#13063322C2×C411yescharacteristic
45#13063313—21no—
46#13063299—21no—
47#13063299—21no—
48C4×D172—21no—
49C4×D172—21no—
50#13063258—21no—
51#13063258—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)C2×C411yescharacteristic
54C4⋊(C43⋊C8)C2×C411yescharacteristic
55C4⋊(C43⋊C8)D412yes—
56#13063253—42no—
57#13063253—42no—
58#13063246—21no—
59#13063246—21no—
60#13063245—21no—
61#13063245—21no—
62C22⋊(C43⋊C8)—22no—
63C22⋊(C43⋊C8)—22no—
64C22⋊(C43⋊C8)—21no—
65#13063236—21no—
66C4×C43⋊C8—21no—
67C4×C43⋊C8—21no—
68C22×D4×C43D411yescharacteristic
69C23×C4×C43—21no—
70C22×C8×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43C2×C411yescharacteristic
74C4×D4×C43C2×C411yescharacteristic
75C4×D4×C43D411yescharacteristic
76C4×D4×C43D411yescharacteristic
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43D411yescharacteristic
79C2×C22⋊C4×C43—21no—
80C2×C42×C43—21no—
81C2×C42×C43C2311yescharacteristic
82#102×C43—24no—
83C4×C8×C43—21no—
84C4×C8×C43—21no—
85#95×C43—21no—
86C24×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43—22no—
89C2×D4×C43—41no—
90C2×D4×C43C22⋊C411yescharacteristic
91C2×D4×C43C22⋊C411yescharacteristic
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C2×C22⋊D43—41no—
106#10621898—41no—
107#10621898—41no—
108#10621898—41no—
109#10621898—41no—
110C2×D172—21no—
111C2×D172—21no—
112C2×D172—21no—
113C2×C4×D43—41no—
114C2×Dic86—21no—
115C2×C8×C43—22no—
116C2×C8×C43—41no—
117C2×C8×C43—41no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—22no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43C22⋊C411yescharacteristic
122C4⋊C4×C43C22⋊C411yescharacteristic
123C22⋊C4×C43—21no—
124C22⋊C4×C43—21no—
125C22⋊C4×C43—21no—
126C22⋊C4×C43—21no—
127C42×C43—41no—
128C42×C43—41no—
129C42×C43C22×C411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43C2×D411yescharacteristic
132C42×C43#4111yescharacteristic
133#10621882—42no—
134#10621882—42no—
135(C2×D43)⋊C4—41no—
136(C2×D43)⋊C4—41no—
137C4⋊Dic43—21no—
138C4⋊Dic43—21no—
139#10621877—21no—
140#10621877—21no—
141#10621877—21no—
142#10621877—44no—
143#10621877—41no—
144#10621877—41no—
145#10621877D812yescomplemented
146C2×C43⋊C8—21no—
147C2×C43⋊C8—21no—
148C2×C43⋊C8—21no—
149C2×C43⋊C8—21no—
150C2×C43⋊C8—22no—
151C2×C43⋊C8—44no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43—42no—
155C23×C43—41no—
156C23×C43—41no—
157C23×C43—81no—
158C23×C43#12111yescharacteristic
159C22×D43—41no—
160D4×C43—21no—
161D4×C43—21no—
162D4×C43—21no—
163D4×C43—42no—
164D4×C43#10412yescomplemented
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—41no—
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×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—42no—
181C2×C4×C43—81no—
182C2×C4×C43—81no—
183C2×C4×C43C2×C22⋊C411yescharacteristic
184C2×C4×C43C4×D411yescharacteristic
185C2×C4×C43C4×D411yescharacteristic
186C2×C4×C43#12011yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43#12311yescharacteristic
189C2×C4×C43C2×D811yescharacteristic
190C2×C4×C43#13511yescharacteristic
191C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
193C22⋊D43—81no—
194C22⋊D43—81no—
195C2×Dic43—41no—
196D172—42no—
197D172—41no—
198D172—41no—
199D172—41no—
200D172—41no—
201C4×D43—81no—
202C4×D43—81no—
203Dic86—41no—
204Dic86—41no—
205C8×C43—42no—
206C43⋊C8—22no—
207C43⋊C8—41no—
208C43⋊C8—41no—
209C43⋊C8—42no—
210C43⋊C8—41no—
211#8991—431nomaximal, Sylow
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—22no—
215C22×C43—41no—
216C22×C43—41no—
217C22×C43—41no—
218C22×C43—41no—
219C22×C43—41no—
220C22×C43—82no—
221C22×C43—82no—
222C22×C43#38611yescharacteristic
223C22×C43#45911yescharacteristic
224C22×C43#46311yescharacteristic
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—81no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—41no—
232C4×C43—41no—
233C4×C43—82no—
234C4×C43C2×#10411yescharacteristic
235C4×C43#42111yescharacteristic
236C4×C43C4×D811yescharacteristic
237C4×C43#44211yescharacteristic
238C4×C43#44711yescharacteristic
239C4×C43#44911yescharacteristic
240Dic43—81no—
241#3100—431no—
242D4×M16—431no—
243#1980—431no—
244C4×#102D4311yescharacteristic, complemented
245#1492—431no—
246#1303—431no—
247#1278—431no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—42no—
251C2×C43—81no—
252C2×C43#187111yescharacteristic
253C2×C43#187911yescharacteristic
254C2×C43#188111yescharacteristic
255D43—161no—
256C22×M16—861no—
257#532—431no—
258C2×C4×D4C2×D4311yescharacteristic
259#480—861no—
260#474—431no—
261#474—431no—
262#459—431no—
263#459—431no—
264#447—861no—
265C4×D8—861no—
266C4×D8—861no—
267#436—861no—
268#435—862no—
269C8×D4—861no—
270#431—431no—
271#423—431no—
272C2×#104—861no—
273C2×#104—861no—
274C2×#102—21no—
275#407—861no—
276C4×M16—431no—
277C2×C4×C8C2×D4311yescharacteristic
278C4×C4⋊C4C2×D4311yescharacteristic
279#340—21no—
280D4⋊C8—862no—
281C43#899111yescharacteristic, complemented, Sylow
282C2×#41—861no—
283C22×D4C22⋊D4311yescharacteristic
284C23×C4—21no—
285C2×D8—861no—
286C2×D8—861no—
287C2×M16—431no—
288C2×M16—431no—
289C2×M16—862no—
290C2×M16—861no—
291C2×M16—1722no—
292C2×M16—1722no—
293C22×C8—21no—
294C22×C8—862no—
295C4⋊Q8—431no—
296#127—431no—
297#124—861no—
298#121—861no—
299#121—861no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—861no—
303C4×D4—861no—
304C4×D4C4×D4311yescharacteristic
305C4×D4C4×D4311yescharacteristic
306C4×D4D17211yescharacteristic
307C4×D4D17211yescharacteristic
308C2×C4⋊C4—21no—
309C2×C4⋊C4C22⋊D4311yescharacteristic
310C2×C22⋊C4—21no—
311C2×C42—21no—
312C2×C42C22×D4311yescharacteristic
313#107—861no—
314#107—861no—
315C4⋊C8—431no—
316C4⋊C8—431no—
317C4⋊C8—432no—
318C4⋊C8—861no—
319#104—1722no—
320#104—1722no—
321#102—24no—
322#102—861no—
323#102—861no—
324#102—861no—
325#102—861no—
326C22⋊C8—862no—
327C22⋊C8—862no—
328C22⋊C8—861no—
329#97—861no—
330C4×C8—21no—
331C4×C8—21no—
332C4×C8—861no—
333C4×C8—861no—
334#95—21no—
335C24—21no—
336#41—1721no—
337#41—1721no—
338#41—1721no—
339#41—1721no—
340C2×Q8—861no—
341C2×D4—22no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—861no—
345C2×D4—861no—
346C2×D4—861no—
347C2×D4—1721no—
348C2×D4(C2×D43)⋊C411yescharacteristic
349C2×D4(C2×D43)⋊C411yescharacteristic
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—1721no—
361C22×C4D4×D4311yescharacteristic
362C22×C4#1062190011yescharacteristic
363C22×C4C2×C22⋊D4311yescharacteristic
364D8—1722no—
365D8—1722no—
366M16—432no—
367M16—861no—
368M16—861no—
369M16—861no—
370M16—1724no—
371M16—1721no—
372M16—1721no—
373C2×C8—22no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—861no—
377C2×C8—861no—
378C2×C8—861no—
379C2×C8—861no—
380C2×C8—862no—
381C2×C8—1724no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—41no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C4⋊C4(C2×D43)⋊C411yescharacteristic
388C4⋊C4(C2×D43)⋊C411yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—1721no—
394C22⋊C4—1721no—
395C42—41no—
396C42—41no—
397C42C2×C4×D4311yescharacteristic
398C42C2×D17211yescharacteristic
399C42D4×D4311yescharacteristic
400C42#1062190011yescharacteristic
401C23—21no—
402C23—21no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—81no—
407C23—1721no—
408C23#1306329711yescharacteristic
409Q8—1721no—
410Q8—1721no—
411D4—21no—
412D4—21no—
413D4—21no—
414D4—42no—
415D4—3441no—
416D4—3441no—
417D4—1722no—
418D4—1721no—
419D4—1721no—
420D4—1721no—
421D4—1721no—
422D4#1306325312yescomplemented
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—3441no—
442C2×C4—3441no—
443C2×C4—1721no—
444C2×C4C2×(C2×D43)⋊C411yescharacteristic
445C2×C4(C22⋊D43)⋊C411yescharacteristic
446C2×C4(C22⋊D43)⋊C411yescharacteristic
447C2×C4#1306329511yescharacteristic
448C2×C4#1306329711yescharacteristic
449C2×C4#1306330911yescharacteristic
450C2×C4D8×D4311yescharacteristic
451C2×C4#1306334611yescharacteristic
452C2×C4#1306334911yescharacteristic
453C2×C4#1306335211yescharacteristic
454C8—42no—
455C8—862no—
456C8—1721no—
457C8—1721no—
458C8—1721no—
459C8—1722no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—82no—
469C22—82no—
470C22—3441no—
471C22—3441no—
472C22—3441no—
473C22#1458277611yescharacteristic
474C22#1458309211yescharacteristic
475C22#1458311611yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—41no—
480C4—41no—
481C4—82no—
482C4—3441no—
483C4C2×#1306325311yescharacteristic
484C4#1458291711yescharacteristic
485C4#1458297911yescharacteristic
486C4#1458300811yescharacteristic
487C4#1458303411yescharacteristic
488C4#1458304511yescharacteristic
489C2—21no—
490C2—21no—
491C2—42no—
492C2—81no—
493C2—6881no—
494C2#1913489511yescharacteristic
495C2#1913494111yescharacteristic
496C2#1913495511yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC4×#102×C43C2
socleC22×C43#386
prime radical#19144595C2
cosocleC2×C42×C43C23
hypercenterC4×#102D43
hypocenterC43#8991
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. D4×#10621877C2semidirect
3. #19135513C2semidirect
4. #19133047C2semidirect
5. #19132498C2semidirect
6. #19132432C2semidirect
7. C4×#102×C43C2semidirect
11. #14583179C4semidirect
12. #14583179C4semidirect
13. #14583094C4semidirect
14. #14583094C4semidirect
145. #10621877D8semidirect
164. D4×C43#104semidirect
244. C4×#102D43semidirect
281. C43#8991semidirect
422. D4#13063253semidirect

Maximal subgroups

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

subgroupindex
#191445952
D4×#106218772
#191355132
#191330472
#191324982
#191324322
C4×#102×C432
#899143