Finite Group Databasebeta

← #25013724

Subgroups — #25013724

Order 11008.

494 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583334C211yesmaximal, characteristic
2C2×#14582706C211yesmaximal, characteristic, complemented
3C2×#14582699C211yesmaximal, characteristic, complemented
4#19135505C211yesmaximal, characteristic, complemented
5#19132703C211yesmaximal, characteristic, complemented
6#19132684C211yesmaximal, characteristic, complemented
7C43×#2951C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9#14583334—22no—
10#14583334C414yescomplemented
11C2×#13063268—21no—
12C2×#13063266—21no—
13C2×#13063265C2211yescharacteristic
14C22×C43⋊C16C2211yescharacteristic
15C2×#13063261C2211yescharacteristic
16#14582903—21no—
17C2×#13063241—21no—
18#14582706—22no—
19#14582699—22no—
20C2×#135×C43C2211yescharacteristic
21C43×#520—21no—
22C43×#440—22no—
23C4×Q16×C43—21no—
24C4×D8×C43—21no—
25C2×#107×C43C2211yescharacteristic
26C43×#417—21no—
27C43×#405C2211yescharacteristic
28C22×D172—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344C2×C412yescomplemented
35C2×#10621877—21no—
36#13063268—24no—
37#13063266—24no—
38#13063265—21no—
39#13063265C2×C412yescomplemented
40C2×C43⋊C16—21no—
41C2×C43⋊C16—21no—
42C2×C43⋊C16—21no—
43C2×C43⋊C16—21no—
44#13063261—21no—
45#13063261—21no—
46#13063245—41no—
47#13063245—41no—
48#13063241—42no—
49C2×#41×C43—21no—
50#135×C43—21no—
51#135×C43—21no—
52#135×C43C2×C412yes—
53#135×C43D412yes—
54C2×Q16×C43D411yescharacteristic
55C2×SD16×C43—21no—
56C2×D8×C43D411yescharacteristic
57C2×M16×C43D411yescharacteristic
58C22×C8×C43C2311yescharacteristic
59C4×Q8×C43—22no—
60C4×D4×C43—22no—
61C4×D4×C43—42no—
62#117×C43—41no—
63#117×C43D411yescharacteristic
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—41no—
66#107×C43—21no—
67#107×C43D412yes—
68#103×C43—22no—
69#102×C43—22no—
70#97×C43—21no—
71C4×C8×C43—21no—
72C23×D43—41no—
73#41×C43—22no—
74#41×C43—22no—
75#41×C43—41no—
76#41×C43—41no—
77C2×Q8×C43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—41no—
80C22×C4×C43—42no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43C2×D411yescharacteristic
84C2×D172—22no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90Q16×C43—21no—
91Q16×C43C22⋊C412yes—
92SD16×C43—22no—
93SD16×C43—22no—
94D8×C43—21no—
95D8×C43C22⋊C412yes—
96M16×C43—21no—
97M16×C43—21no—
98C2×C8×C43—21no—
99C2×C8×C43C22×C411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43C2×D411yescharacteristic
103C2×C8×C43#4111yescharacteristic
104C2×C8×C43#4111yescharacteristic
105C4⋊C4×C43—22no—
106C4⋊C4×C43—42no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43D811yescharacteristic
109C4⋊C4×C43D811yescharacteristic
110C22⋊C4×C43—21no—
111C22⋊C4×C43—42no—
112C42×C43—21no—
113C42×C43—42no—
114#10621877—41no—
115#10621877—41no—
116C2×C43⋊C8—41no—
117D344—22no—
118D344—22no—
119D344—41no—
120D344—41no—
121C43⋊C16—22no—
122C43⋊C16—41no—
123C23×C43—41no—
124C23×C43AGL(1,ℤ/8)11yescharacteristic
125C22×D43—42no—
126C22×D43—81no—
127C22×D43—81no—
128C22×D43—161no—
129C22×D43—161no—
130Q8×C43—22no—
131Q8×C43—41no—
132D4×C43—22no—
133D4×C43—42no—
134D4×C43—42no—
135D4×C43—41no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—162no—
143C2×C4×C43—161no—
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43C2×D811yescharacteristic
148C2×C4×C43#13511yescharacteristic
149C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
150D172—42no—
151D172—42no—
152D172—81no—
153D172—81no—
154C8×C43—41no—
155C8×C43C2×C22⋊C411yescharacteristic
156C8×C43C4×D411yescharacteristic
157C8×C43#12111yescharacteristic
158C8×C43#12311yescharacteristic
159C43⋊C8—81no—
160#13022—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—42no—
164C22×C43—81no—
165C22×C43—81no—
166C22×C43#44211yescharacteristic
167C22×C43#44711yescharacteristic
168C22×C43#46311yescharacteristic
169C2×D43—82no—
170C2×D43—162no—
171C2×D43—161no—
172C2×D43—161no—
173C2×D43—162no—
174C4×C43—42no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—82no—
178C4×C43#38611yescharacteristic
179C4×C43C4×D811yescharacteristic
180C4×C43#44911yescharacteristic
181C4×C43#45911yescharacteristic
182C2×#509—431no—
183#2951D4311yescharacteristic, complemented
184C2×#359—431no—
185C2×#357—431no—
186#1978—431no—
187#1387—431no—
188#1379—431no—
189C2×C43—21no—
190C2×C43—21no—
191C2×C43—82no—
192C2×C43#187911yescharacteristic
193C2×C43#219211yescharacteristic
194C2×C43#219311yescharacteristic
195D43—162no—
196C2×#135C2×D4311yescharacteristic
197C22×D8—431no—
198#520—21no—
199#509—434no—
200#509—862no—
201C2×SD32—861no—
202C2×D16—861no—
203C2×M32—431no—
204C22×C16—431no—
205#440—22no—
206C4×Q16—21no—
207C4×D8—21no—
208C2×#108—431no—
209C2×#107C2×D4311yescharacteristic
210#418—861no—
211#417—21no—
212C2×#100—861no—
213#405C2×D4311yescharacteristic
214#359—862no—
215#357—862no—
216C43#1302211yescharacteristic, complemented, Sylow
217C2×#41—21no—
218C22×D4—861no—
219#135—21no—
220#135—21no—
221#135C4×D4312yes—
222#135D17212yes—
223C2×Q16C22⋊D4311yescharacteristic
224C2×SD16—21no—
225C2×D8—432no—
226C2×D8—861no—
227C2×D8—861no—
228C2×D8—861no—
229C2×D8—861no—
230C2×D8—861no—
231C2×D8C22⋊D4311yescharacteristic
232C2×M16—861no—
233C2×M16C22⋊D4311yescharacteristic
234C22×C8C22×D4311yescharacteristic
235C4×Q8—22no—
236C4×D4—22no—
237C4×D4—42no—
238#117—41no—
239#117C22⋊D4311yescharacteristic
240C2×C4⋊C4—21no—
241C2×C4⋊C4—41no—
242SD32—864no—
243D16—864no—
244M32—432no—
245M32—861no—
246C2×C16—861no—
247C2×C16—861no—
248C2×C16—861no—
249C2×C16—861no—
250#108—861no—
251#108—861no—
252#107—21no—
253#107C22⋊D4312yes—
254#103—22no—
255#102—22no—
256#102—1721no—
257#102—1721no—
258#100—1722no—
259#97—21no—
260C4×C8—21no—
261C24—1721no—
262#41—22no—
263#41—22no—
264#41—41no—
265#41—41no—
266C2×Q8—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—862no—
270C2×D4—1721no—
271C2×D4—1721no—
272C2×D4—1721no—
273C2×D4—1721no—
274C2×D4—1721no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×C22⋊D4311yescharacteristic
279Q16—21no—
280Q16(C2×D43)⋊C412yes—
281SD16—22no—
282SD16—22no—
283D8—21no—
284D8—862no—
285D8—862no—
286D8—1721no—
287D8—1721no—
288D8(C2×D43)⋊C412yes—
289M16—21no—
290M16—21no—
291M16—1721no—
292M16—1721no—
293C2×C8—21no—
294C2×C8—1721no—
295C2×C8C2×C4×D4311yescharacteristic
296C2×C8C2×D17211yescharacteristic
297C2×C8#1062189811yescharacteristic
298C2×C8#1062189811yescharacteristic
299C2×C8C2×C22⋊D4311yescharacteristic
300C2×C8C2×C22⋊D4311yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—42no—
303C4⋊C4—41no—
304C4⋊C4#1062188211yescharacteristic
305C4⋊C4#1062188211yescharacteristic
306C22⋊C4—21no—
307C22⋊C4—42no—
308C42—21no—
309C42—42no—
310C16—862no—
311C16—1721no—
312C23—41no—
313C23—3441no—
314C23—3441no—
315C23—1722no—
316C23—6881no—
317C23—6881no—
318C23#1306335111yescharacteristic
319Q8—22no—
320Q8—41no—
321D4—22no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—3441no—
326D4—3441no—
327D4—1722no—
328D4—1722no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—162no—
336C2×C4—161no—
337C2×C4C4×C22⋊D4311yescharacteristic
338C2×C4#1306329411yescharacteristic
339C2×C4#1306329911yescharacteristic
340C2×C4C2×#1062188211yescharacteristic
341C2×C4#1306334511yescharacteristic
342C2×C4#1306335011yescharacteristic
343C8—41no—
344C8—3441no—
345C8C2×(C2×D43)⋊C411yescharacteristic
346C8C4×C22⋊D4311yescharacteristic
347C8#1306329911yescharacteristic
348C8#1306330811yescharacteristic
349C22—21no—
350C22—21no—
351C22—42no—
352C22—81no—
353C22—81no—
354C22—3442no—
355C22—6882no—
356C22—6882no—
357C22—6881no—
358C22—6881no—
359C22#1458300911yescharacteristic
360C22#1458303311yescharacteristic
361C22#1458311411yescharacteristic
362C4—41no—
363C4—41no—
364C4—42no—
365C4—82no—
366C4#1458277811yescharacteristic
367C4C4×#1062188211yescharacteristic
368C4#1458304411yescharacteristic
369C4#1458309411yescharacteristic
370C2—21no—
371C2—21no—
372C2—82no—
373C2—6882no—
374C2#1913494311yescharacteristic
375C2#1913655211yescharacteristic
376C2#1913655911yescharacteristic
subgroupG/H
centerC22#14583033
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2951C2
socleC22×C43#447
prime radicalC2×#14583334C2
cosocleC22×C8×C43C23
hypercenter#2951D43
hypocenterC43#13022
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
2. C2×#14582706C2semidirect
3. C2×#14582699C2semidirect
4. #19135505C2semidirect
5. #19132703C2semidirect
6. #19132684C2semidirect
7. C43×#2951C2semidirect
10. #14583334C4semidirect
34. C2×D344C2×C4semidirect
39. #13063265C2×C4semidirect
183. #2951D43semidirect
216. C43#13022semidirect

Maximal subgroups

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

subgroupindex
C2×#145833342
C2×#145827062
C2×#145826992
#191355052
#191327032
#191326842
C43×#29512
#1302243