Finite Group Databasebeta

← #24993396

Subgroups — #24993396

Order 11008.

518 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143636C211yesmaximal, characteristic, complemented
2#19134605C211yesmaximal, characteristic, complemented
3#19133155C211yesmaximal, characteristic, complemented
4#19132994C211yesmaximal, characteristic, complemented
5#19132490C211yesmaximal, characteristic, complemented
6#19132455C211yesmaximal, characteristic, complemented
7C43×#3036C211yesmaximal, characteristic
8#14582977—22no—
9#14582977—22no—
10#14582952C2211yescharacteristic
11#14582952C2211yescharacteristic
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×#13063246—21no—
14#14582863—22no—
15#14582765C2211yescharacteristic
16#14582661—21no—
17#14582633—22no—
18D4⋊(C43⋊C8)—22no—
19C2×AGL(1,ℤ/8)×C43—21no—
20C43×#532C2211yescharacteristic
21C2×C4×D4×C43C2211yescharacteristic
22C43×#463—22no—
23C43×#461C412yescomplemented
24C43×#459C412yescomplemented
25C43×#423C2211yescharacteristic
26C43×#417—21no—
27C2×#10621877—24no—
28C22×C43⋊C8—21no—
29C2×C4⋊Dic43—21no—
30C4⋊(C43⋊C8)—21no—
31C4⋊(C43⋊C8)—21no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34#13063246—42no—
35C22⋊(C43⋊C8)—24no—
36C22⋊(C43⋊C8)—21no—
37C22⋊(C43⋊C8)D412yes—
38C4×C43⋊C8—21no—
39C4×C43⋊C8D412yes—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C2×#41×C43—21no—
43C22×D4×C43D411yescharacteristic
44C23×C4×C43—21no—
45AGL(1,ℤ/8)×C43—42no—
46AGL(1,ℤ/8)×C43—42no—
47C2×SD16×C43—22no—
48C2×D8×C43—22no—
49C2×M16×C43—21no—
50C4⋊Q8×C43C2×C411yescharacteristic
51#127×C43C2×C411yescharacteristic
52#124×C43—21no—
53#121×C43—21no—
54#121×C43—21no—
55C4×D4×C43—21no—
56C4×D4×C43—21no—
57C4×D4×C43—21no—
58C4×D4×C43—21no—
59C4×D4×C43C2×C412yes—
60C4×D4×C43D412yes—
61C2×C4⋊C4×C43D411yescharacteristic
62C2×C22⋊C4×C43—21no—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43—21no—
65C4⋊C8×C43C2×C412yes—
66#103×C43—22no—
67#102×C43—22no—
68C24×C43—21no—
69#41×C43—41no—
70#41×C43—41no—
71#41×C43—41no—
72#41×C43—41no—
73C2×Q8×C43—21no—
74C2×D4×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—41no—
83C2×D4×C43C22⋊C412yes—
84C22×C4×C43—22no—
85C22×C4×C43—22no—
86C22×C4×C43—21no—
87C22×C4×C43—41no—
88C22×C4×C43—82no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C22×Dic43—41no—
93SD16×C43—44no—
94D8×C43—44no—
95M16×C43—41no—
96M16×C43—41no—
97C2×C8×C43—22no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43C22⋊C412yes—
102C22⋊C4×C43—22no—
103C22⋊C4×C43—22no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—41no—
106C42×C43C22×C411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43#4111yescharacteristic
110C4⋊Dic43—41no—
111C4⋊Dic43—41no—
112#10621877—84no—
113C2×C43⋊C8—22no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C23×C43—22no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—81no—
123C23×C43—81no—
124C23×C43#12111yescharacteristic
125Q8×C43—41no—
126Q8×C43—41no—
127D4×C43—22no—
128D4×C43—22no—
129D4×C43—42no—
130D4×C43—41no—
131D4×C43—41no—
132D4×C43—41no—
133D4×C43—41no—
134D4×C43—81no—
135D4×C43—81no—
136D4×C43—81no—
137C2×C4×C43—22no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—44no—
141C2×C4×C43—41no—
142C2×C4×C43—82no—
143C2×C4×C43—81no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43C2×C22⋊C411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12311yescharacteristic
152C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C43#13711yescharacteristic
156C2×Dic43—81no—
157C2×Dic43—81no—
158C2×Dic43—81no—
159C8×C43—42no—
160C43⋊C8—42no—
161C43⋊C8—42no—
162C43⋊C8—81no—
163#9309—431nomaximal, Sylow
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—42no—
167C22×C43—42no—
168C22×C43—42no—
169C22×C43—82no—
170C22×C43—82no—
171C22×C43—81no—
172C22×C43—81no—
173C22×C43—81no—
174C22×C43#38611yescharacteristic
175C22×C43#46811yescharacteristic
176C22×C43#46911yescharacteristic
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—42no—
182C4×C43—81no—
183C4×C43#41711yescharacteristic
184C4×C43#41811yescharacteristic
185C4×C43#46811yescharacteristic
186C4×C43#46911yescharacteristic
187Dic43—161no—
188#3036D4311yescharacteristic
189#2975—431no—
190#1804—431no—
191#1517—431no—
192#1480—431no—
193#1301—431no—
194#1286—431no—
195C2×C43—21no—
196C2×C43—21no—
197C2×C43—82no—
198C2×C43—161no—
199C2×C43#188111yescharacteristic
200C2×C43#189511yescharacteristic
201C2×C43#190411yescharacteristic
202C2×AGL(1,ℤ/8)—21no—
203#532C2×D4311yescharacteristic
204C2×C4×D4C2×D4311yescharacteristic
205#463—22no—
206#461Dic4312yescomplemented
207#459Dic4312yescomplemented
208#436—862no—
209#436—862no—
210#431—431no—
211#431—431no—
212#423C2×D4311yescharacteristic
213C2×C4⋊C8—431no—
214#417—21no—
215C2×#102—861no—
216#407—862no—
217#382—431no—
218#340—861no—
219#327—862no—
220D4⋊C8—862no—
221C43#930911yescharacteristic, complemented, Sylow
222C2×#41—21no—
223C22×D4C22⋊D4311yescharacteristic
224C23×C4—21no—
225AGL(1,ℤ/8)—42no—
226AGL(1,ℤ/8)—42no—
227C2×SD16—22no—
228C2×D8—22no—
229C2×M16—21no—
230C2×M16—864no—
231C22×C8—861no—
232C4⋊Q8C2×Dic4311yescharacteristic
233#127C2×Dic4311yescharacteristic
234#124—21no—
235#121—21no—
236#121—21no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4C2×Dic4312yes—
242C4×D4C22⋊D4312yes—
243C2×C4⋊C4—861no—
244C2×C4⋊C4C22⋊D4311yescharacteristic
245C2×C22⋊C4—21no—
246C2×C42C22×D4311yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—861no—
249C4⋊C8—861no—
250C4⋊C8—861no—
251C4⋊C8—861no—
252C4⋊C8C2×Dic4312yes—
253#103—22no—
254#102—22no—
255#102—1722no—
256C22⋊C8—432no—
257C22⋊C8—864no—
258C22⋊C8—861no—
259C4×C8—432no—
260C4×C8—861no—
261#95—861no—
262#95—861no—
263C24—21no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4C22⋊Dic4312yes—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—82no—
284C22×C4—1721no—
285C22×C4D4×D4311yescharacteristic
286C22×C4#1062190011yescharacteristic
287C22×C4C2×C22⋊D4311yescharacteristic
288SD16—44no—
289D8—44no—
290M16—41no—
291M16—41no—
292M16—3444no—
293C2×C8—22no—
294C2×C8—862no—
295C2×C8—862no—
296C2×C8—1721no—
297C2×C8—1721no—
298C2×C8—1721no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—1721no—
303C4⋊C4—1721no—
304C4⋊C4C22⋊Dic4312yes—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42D4×D4311yescharacteristic
310C42#1062190011yescharacteristic
311C42C22×Dic4311yescharacteristic
312C42C2×C22⋊D4311yescharacteristic
313C23—22no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—81no—
318C23—81no—
319C23#1306329711yescharacteristic
320Q8—41no—
321Q8—41no—
322D4—22no—
323D4—22no—
324D4—42no—
325D4—41no—
326D4—41no—
327D4—41no—
328D4—41no—
329D4—81no—
330D4—81no—
331D4—81no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—41no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—3441no—
342C2×C4—3441no—
343C2×C4—3441no—
344C2×C4C2×C22⋊Dic4311yescharacteristic
345C2×C4D4×Dic4311yescharacteristic
346C2×C4D4×Dic4311yescharacteristic
347C2×C4#1306329311yescharacteristic
348C2×C4#1306329711yescharacteristic
349C2×C4#1306330611yescharacteristic
350C2×C4#1306335011yescharacteristic
351C2×C4#1306335111yescharacteristic
352C2×C4#1306335111yescharacteristic
353C2×C4#1306335511yescharacteristic
354C8—42no—
355C8—3441no—
356C8—1722no—
357C8—1722no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22—82no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22#1458277911yescharacteristic
369C22#1458314311yescharacteristic
370C22#1458315011yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—6881no—
378C4#1458290011yescharacteristic
379C4#1458290411yescharacteristic
380C4#1458314311yescharacteristic
381C4#1458315011yescharacteristic
382C2—21no—
383C2—21no—
384C2—82no—
385C2—161no—
386C2#1913495911yescharacteristic
387C2#1913503411yescharacteristic
388C2#1913508411yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3036C2
socleC22×C43#386
cosocleC2×C42×C43C23
hypercenter#3036D43
hypocenterC43#9309
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #19143636C2semidirect
2. #19134605C2semidirect
3. #19133155C2semidirect
4. #19132994C2semidirect
5. #19132490C2semidirect
6. #19132455C2semidirect
23. C43×#461C4semidirect
24. C43×#459C4semidirect
206. #461Dic43semidirect
207. #459Dic43semidirect
221. C43#9309semidirect

Maximal subgroups

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

subgroupindex
#191436362
#191346052
#191331552
#191329942
#191324902
#191324552
C43×#30362
#930943