Finite Group Databasebeta

← #24993002

Subgroups — #24993002

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583094C211yesmaximal, characteristic
2#19135435C211yesmaximal, characteristic, complemented
3#19133264C211yesmaximal, characteristic, complemented
4#19133020C211yesmaximal, characteristic, complemented
5#19132469C211yesmaximal, characteristic, complemented
6#19132446C211yesmaximal, characteristic, complemented
7D4×M16×C43C211yesmaximal, characteristic, complemented
8C22×#10621882C412yes—
9C2×#13063322C2211yescharacteristic
10#14583094—21no—
11#14583094—21no—
12#14583094—21no—
13#14583094—21no—
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×#13063245C412yes—
18C2×#13063241—21no—
19C2×#13063241—21no—
20#14582642—22no—
21D4⋊(C43⋊C8)—21no—
22D4⋊(C43⋊C8)—21no—
23C22×M16×C43—21no—
24C2×C4×D4×C43C2211yescharacteristic
25C43×#436—21no—
26C43×#435—22no—
27C8×D4×C43—21no—
28C43×#423C2211yescharacteristic
29C43×#407—21no—
30C4×M16×C43C2211yescharacteristic
31C22×D172—21no—
32C22×D172—21no—
33C22×D172C2×C412yes—
34C2×#10621882—22no—
35C2×#10621882—22no—
36C2×#10621882—44no—
37C2×#10621877—21no—
38C22×C43⋊C8C2×C412yes—
39#13063322—21no—
40#13063322—21no—
41#13063322—21no—
42#13063322—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48#13063245—22no—
49#13063245—22no—
50#13063241—42no—
51#13063241—42no—
52C22⋊(C43⋊C8)—21no—
53C4×C43⋊C8—21no—
54C22×D4×C43C2×C411yescharacteristic
55C23×C4×C43—21no—
56C2×M16×C43—22no—
57C2×M16×C43—21no—
58C2×M16×C43—42no—
59C2×M16×C43—42no—
60C2×M16×C43D411yescharacteristic
61C2×M16×C43D411yescharacteristic
62C22×C8×C43—22no—
63C4×D4×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43D411yescharacteristic
66C4×D4×C43D411yescharacteristic
67C4×D4×C43D411yescharacteristic
68C4×D4×C43D411yescharacteristic
69C2×C4⋊C4×C43C2×C411yescharacteristic
70C2×C22⋊C4×C43—21no—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—21no—
73C4⋊C8×C43D412yes—
74C22⋊C8×C43—22no—
75C22⋊C8×C43—22no—
76#97×C43—21no—
77C4×C8×C43—21no—
78C24×C43—21no—
79C23×D43—22no—
80C2×D4×C43—21no—
81C2×D4×C43—22no—
82C2×D4×C43—41no—
83C2×D4×C43C22⋊C411yescharacteristic
84C2×D4×C43C22⋊C411yescharacteristic
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43C22×C411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C2×D172—22no—
98C2×D172—22no—
99C2×D172—41no—
100C2×D172—41no—
101C2×D172—41no—
102C2×D172—41no—
103C2×D172—41no—
104C2×D172—41no—
105C2×D172—41no—
106C2×D172—41no—
107C2×D172—42no—
108C2×D172—42no—
109C2×D172—82no—
110M16×C43—21no—
111M16×C43—21no—
112M16×C43—21no—
113M16×C43—44no—
114M16×C43—41no—
115M16×C43—41no—
116M16×C43D812yescomplemented
117C2×C8×C43—21no—
118C2×C8×C43—21no—
119C2×C8×C43—22no—
120C2×C8×C43—44no—
121C4⋊C4×C43—21no—
122C4⋊C4×C43C22⋊C411yescharacteristic
123C4⋊C4×C43C22⋊C411yescharacteristic
124C22⋊C4×C43—21no—
125C22⋊C4×C43—21no—
126C22⋊C4×C43—21no—
127C22⋊C4×C43—21no—
128C42×C43C2×D411yescharacteristic
129C42×C43C2×D411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43#4111yescharacteristic
132#10621882—44no—
133#10621882—44no—
134#10621877—41no—
135#10621877—41no—
136C2×C43⋊C8—22no—
137C2×C43⋊C8—42no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8—41no—
140C23×C43—21no—
141C23×C43—21no—
142C23×C43—42no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—81no—
146C23×C43C4×D411yescharacteristic
147C22×D43—42no—
148C22×D43—42no—
149C22×D43—42no—
150C22×D43—82no—
151C22×D43—82no—
152D4×C43—21no—
153D4×C43—21no—
154D4×C43—21no—
155D4×C43—42no—
156D4×C43#10012yescomplemented
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43C2×C22⋊C411yescharacteristic
173C2×C4×C43C4×D411yescharacteristic
174C2×C4×C43#12011yescharacteristic
175C2×C4×C43#12111yescharacteristic
176C2×C4×C43#12111yescharacteristic
177C2×C4×C43#12311yescharacteristic
178C2×C4×C43C2×D811yescharacteristic
179C2×C4×C43#13511yescharacteristic
180C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
182D172—42no—
183D172—42no—
184D172—82no—
185D172—82no—
186D172—82no—
187D172—81no—
188D172—81no—
189D172—81no—
190D172—81no—
191C8×C43—22no—
192C8×C43—42no—
193C8×C43—41no—
194C43⋊C8—42no—
195C43⋊C8—81no—
196C43⋊C8—81no—
197#9253—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—22no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—82no—
207C22×C43—82no—
208C22×C43#38611yescharacteristic
209C22×C43C4×D811yescharacteristic
210C22×C43#44211yescharacteristic
211C2×D43—82no—
212C2×D43—82no—
213C2×D43—82no—
214C2×D43—162no—
215C2×D43—162no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—41no—
220C4×C43—41no—
221C4×C43C2×#10011yescharacteristic
222C4×C43#41311yescharacteristic
223C4×C43#44711yescharacteristic
224C4×C43#44911yescharacteristic
225C4×C43#45911yescharacteristic
226C4×C43#46311yescharacteristic
227C2×#459—431no—
228D4×M16D4311yescharacteristic, complemented
229#1965—431no—
230#1545—431no—
231#1486—431no—
232#1292—431no—
233#1283—431no—
234C2×C43—21no—
235C2×C43—21no—
236C2×C43—42no—
237C2×C43—81no—
238C2×C43#187911yescharacteristic
239C2×C43#190011yescharacteristic
240C2×C43#190311yescharacteristic
241D43—162no—
242C22×D8—432no—
243C22×M16—21no—
244C2×#127—431no—
245C2×C4×D4C2×D4311yescharacteristic
246#459—861no—
247#459—861no—
248#459—861no—
249#459—861no—
250#436—21no—
251#435—22no—
252C8×D4—21no—
253#431—431no—
254#423—431no—
255#423C2×D4311yescharacteristic
256C2×C4⋊C8—431no—
257C2×#102—432no—
258C2×#100—861no—
259C2×#100—861no—
260#407—21no—
261C4×M16C2×D4311yescharacteristic
262#331—862no—
263D4⋊C8—861no—
264D4⋊C8—861no—
265C43#925311yescharacteristic, complemented, Sylow
266C22×D4—432no—
267C22×D4—861no—
268C22×D4—861no—
269C22×D4C4×D4311yescharacteristic
270C23×C4—21no—
271C2×D8—862no—
272C2×D8—862no—
273C2×D8—1724no—
274C2×M16—22no—
275C2×M16—21no—
276C2×M16—42no—
277C2×M16—42no—
278C2×M16—861no—
279C2×M16C22⋊D4311yescharacteristic
280C2×M16C22⋊D4311yescharacteristic
281C22×C8—22no—
282C22×C8—432no—
283#127—861no—
284#127—861no—
285#127—861no—
286#127—861no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4D17211yescharacteristic
290C4×D4D17211yescharacteristic
291C4×D4C22⋊D4311yescharacteristic
292C4×D4C22⋊D4311yescharacteristic
293C2×C4⋊C4C4×D4311yescharacteristic
294C2×C22⋊C4—21no—
295C2×C42C22×D4311yescharacteristic
296C4⋊C8—21no—
297C4⋊C8—861no—
298C4⋊C8—861no—
299C4⋊C8—861no—
300C4⋊C8—861no—
301C4⋊C8—861no—
302C4⋊C8C22⋊D4312yes—
303#102—862no—
304#102—862no—
305#100—1722no—
306#100—1722no—
307C22⋊C8—22no—
308C22⋊C8—22no—
309C22⋊C8—861no—
310#97—21no—
311C4×C8—21no—
312C4×C8—861no—
313C24—21no—
314C24—862no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—862no—
319C2×D4—862no—
320C2×D4—3442no—
321C2×D4—1722no—
322C2×D4—1722no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1721no—
326C2×D4—1721no—
327C2×D4—1721no—
328C2×D4—1721no—
329C2×D4—1721no—
330C2×D4—1721no—
331C2×D4(C2×D43)⋊C411yescharacteristic
332C2×D4(C2×D43)⋊C411yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4C2×C4×D4311yescharacteristic
343C22×C4#1062189811yescharacteristic
344C22×C4C2×C22⋊D4311yescharacteristic
345D8—1724no—
346D8—1724no—
347M16—21no—
348M16—21no—
349M16—21no—
350M16—44no—
351M16—41no—
352M16—41no—
353M16—1721no—
354M16—1721no—
355M16#1062188212yescomplemented
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—44no—
360C2×C8—862no—
361C2×C8—1721no—
362C2×C8—1721no—
363C2×C8—1722no—
364C4⋊C4—21no—
365C4⋊C4(C2×D43)⋊C411yescharacteristic
366C4⋊C4(C2×D43)⋊C411yescharacteristic
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C42C2×D17211yescharacteristic
372C42#1062189811yescharacteristic
373C42C2×C22⋊D4311yescharacteristic
374C42C2×C22⋊D4311yescharacteristic
375C23—21no—
376C23—21no—
377C23—42no—
378C23—41no—
379C23—41no—
380C23—81no—
381C23—3442no—
382C23—3442no—
383C23—1722no—
384C23—1722no—
385C23—1722no—
386C23C4×C22⋊D4311yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4—3442no—
392D4—3442no—
393D4—3442no—
394D4—3441no—
395D4—3441no—
396D4—3441no—
397D4—3441no—
398D4—1722no—
399D4—1722no—
400D4#1306324112yescomplemented
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4C2×(C2×D43)⋊C411yescharacteristic
417C2×C4C4×C22⋊D4311yescharacteristic
418C2×C4#1306329411yescharacteristic
419C2×C4#1306329911yescharacteristic
420C2×C4#1306329911yescharacteristic
421C2×C4#1306330811yescharacteristic
422C2×C4C2×#1062188211yescharacteristic
423C2×C4#1306334511yescharacteristic
424C2×C4#1306335011yescharacteristic
425C2×C4#1306335111yescharacteristic
426C8—22no—
427C8—41no—
428C8—42no—
429C8—3441no—
430C8—3441no—
431C8—1722no—
432C22—21no—
433C22—21no—
434C22—22no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—82no—
441C22—82no—
442C22—3442no—
443C22—3442no—
444C22—3442no—
445C22—6882no—
446C22—6882no—
447C22#1458277811yescharacteristic
448C22C4×#1062188211yescharacteristic
449C22#1458300911yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—41no—
454C4—41no—
455C4C2×#1306324111yescharacteristic
456C4#1458288111yescharacteristic
457C4#1458303311yescharacteristic
458C4#1458304411yescharacteristic
459C4#1458309411yescharacteristic
460C4#1458311411yescharacteristic
461C2—21no—
462C2—21no—
463C2—42no—
464C2—81no—
465C2—6882no—
466C2#1913494311yescharacteristic
467C2#1913505811yescharacteristic
468C2#1913507511yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingD4×M16×C43C2
socleC22×C43#386
prime radicalC2×#14583094C2
cosocleC2×C42×C43C23
hypercenterD4×M16D43
hypocenterC43#9253
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. #19135435C2semidirect
3. #19133264C2semidirect
4. #19133020C2semidirect
5. #19132469C2semidirect
6. #19132446C2semidirect
7. D4×M16×C43C2semidirect
116. M16×C43D8semidirect
156. D4×C43#100semidirect
228. D4×M16D43semidirect
265. C43#9253semidirect
355. M16#10621882semidirect
400. D4#13063241semidirect

Maximal subgroups

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

subgroupindex
C2×#145830942
#191354352
#191332642
#191330202
#191324692
#191324462
D4×M16×C432
#925343