Finite Group Databasebeta

← #25006828

Subgroups — #25006828

Order 11008.

504 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144176C211yesmaximal, characteristic
2#19136206C211yesmaximal, characteristic, complemented
3#19132606C212yesmaximal, complemented
4#19132603C212yesmaximal, complemented
5C2×C43×#340C211yesmaximal, characteristic, complemented
6C2×#13063347C411yescharacteristic, complemented
7#14583410—21no—
8C2×#13063265—21no—
9#14583140C411yescharacteristic, complemented
10#14583140C2211yescharacteristic
11#14583135C411yescharacteristic, complemented
12#14583135C2211yescharacteristic
13#14583128—21no—
14#14583128—21no—
15#14582937C411yescharacteristic, complemented
16#14582896—21no—
17C22⋊(C43⋊C16)—21no—
18C22⋊(C43⋊C16)C2212yes—
19C23×C8×C43C2211yescharacteristic
20C22×C4⋊C4×C43—21no—
21C43×#340—21no—
22C43×#340C2212yes—
23C2×#10621898—21no—
24#13063347—42no—
25C2×Dic172C2×C411yescharacteristic, complemented
26C2×#10621873—21no—
27C2×D344C2×C411yescharacteristic, complemented
28#13063308—41no—
29#13063304—21no—
30#13063304—21no—
31#13063299—21no—
32#13063299—21no—
33#13063294—41no—
34C4×C22⋊D43—41no—
35C4×C22⋊D43—41no—
36#13063284—21no—
37#13063265—42no—
38C2×C43⋊C16—22no—
39#13063259C2×C411yescharacteristic, complemented
40#13063259C2×C411yescharacteristic, complemented
41#13063257—21no—
42#13063250—21no—
43#13063250—21no—
44#13063247—21no—
45#13063247—21no—
46C23×C4×C43—41no—
47C23×C4×C43D411yescharacteristic
48C22×C8×C43—42no—
49C22×C8×C43C2×C411yescharacteristic
50C22×C8×C43C2×C411yescharacteristic
51C22×C8×C43D411yescharacteristic
52C22×C8×C43D411yescharacteristic
53C22×C8×C43D411yescharacteristic
54C22×C8×C43C2311yescharacteristic
55C2×C4⋊C4×C43—24no—
56C2×C4⋊C4×C43—22no—
57C2×C4⋊C4×C43—42no—
58C2×C4⋊C4×C43—41no—
59C24×C43D811yescharacteristic
60C22×C4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—44no—
63C22×C4×C43—42no—
64C22×C4×C43—82no—
65C22×C4×C43—82no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43D811yescharacteristic
69C22×C4×C43SD1611yescharacteristic
70C22×C4×C43SD1611yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—41no—
73C2×C22⋊D43—41no—
74C2×C22⋊D43—41no—
75#10621898—42no—
76#10621898—42no—
77C2×D172—21no—
78C2×C4×D43—41no—
79C2×Dic86—21no—
80C2×C8×C43—22no—
81C2×C8×C43—22no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43C22⋊C411yescharacteristic
87C2×C8×C43C22⋊C411yescharacteristic
88C2×C8×C43C22×C411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C4⋊C4×C43—24no—
91C4⋊C4×C43—44no—
92C4⋊C4×C43—42no—
93C22⋊Dic43—41no—
94C22⋊Dic43—41no—
95C22⋊Dic43—41no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—41no—
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102C4×Dic43—41no—
103Dic172—41no—
104D344—41no—
105#10621873—42no—
106C43⋊C16—42no—
107C23×C43—22no—
108C23×C43—22no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43#10211yescharacteristic
112C23×C43#10211yescharacteristic
113C23×C43C2×D811yescharacteristic
114C22×D43—41no—
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—44no—
123C2×C4×C43—88no—
124C2×C4×C43—82no—
125C2×C4×C43—82no—
126C2×C4×C43#9912yes—
127C2×C4×C43#10211yescharacteristic
128C2×C4×C43#10211yescharacteristic
129C2×C4×C43#10412yes—
130C2×C4×C43C2×C22⋊C411yescharacteristic
131C2×C4×C43C2×SD1611yescharacteristic
132C22⋊D43—82no—
133C22⋊D43—82no—
134C22⋊D43—81no—
135C22⋊D43—81no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139D172—41no—
140D172—41no—
141C4×D43—82no—
142Dic86—41no—
143Dic86—41no—
144C8×C43—21no—
145C8×C43—21no—
146C8×C43—21no—
147C8×C43—21no—
148#11704—431nomaximal, Sylow
149C22×C43—24no—
150C22×C43—24no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43#32712yes—
158C22×C43#36012yes—
159C22×C43C2×#10211yescharacteristic
160C22×C43#50911yescharacteristic
161C22×C43#51011yescharacteristic
162C2×D43—81no—
163C2×D43—81no—
164C2×D43—81no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—84no—
168C4×C43#32712yes—
169C4×C43C2×#9911yescharacteristic
170C4×C43C2×#10411yescharacteristic
171Dic43—81no—
172Dic43—81no—
173Dic43—81no—
174#3050—431no—
175#2112—431no—
176C2×#340D4311yescharacteristic, complemented
177#1348—432no—
178#1347—432no—
179C2×C43—21no—
180C2×C43—22no—
181C2×C43—22no—
182C2×C43—21no—
183C2×C43C2×#32711yescharacteristic
184C2×C43#213911yescharacteristic
185C2×C43C2×#36011yescharacteristic
186D43—161no—
187C2×#135—431no—
188C23×C8C2×D4311yescharacteristic
189#525—861no—
190C22×C4⋊C4—21no—
191C2×M32—861no—
192#467—431no—
193#467—431no—
194#466—431no—
195#466—431no—
196#465—861no—
197#465—861no—
198#427—431no—
199#416—861no—
200C22⋊C16—432no—
201C22⋊C16—861no—
202#340—21no—
203#340C2×D4312yes—
204C43#1170411yescharacteristic, complemented, Sylow
205C2×#41—861no—
206C23×C4—41no—
207C23×C4C22⋊D4311yescharacteristic
208#135—1722no—
209C2×Q16—431no—
210C2×SD16—861no—
211C2×D8—431no—
212C22×C8—42no—
213C22×C8C4×D4311yescharacteristic
214C22×C8C4×D4311yescharacteristic
215C22×C8D17211yescharacteristic
216C22×C8D17211yescharacteristic
217C22×C8C22⋊D4311yescharacteristic
218C22×C8C22×D4311yescharacteristic
219#123—1721no—
220C22⋊Q8—861no—
221C22⋊Q8—861no—
222#121—861no—
223#121—861no—
224#120—1721no—
225C4×D4—1721no—
226C4×D4—1721no—
227#117—861no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—42no—
231C2×C4⋊C4—41no—
232M32—1722no—
233C2×C16—862no—
234#107—431no—
235#107—431no—
236#106—861no—
237#103—861no—
238#103—861no—
239#102—861no—
240#102—861no—
241C24#1062188211yescharacteristic
242#41—1722no—
243#41—1722no—
244C2×Q8—861no—
245C2×D4—861no—
246C2×D4—1721no—
247C2×D4—1721no—
248C2×D4—1721no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—82no—
254C22×C4—82no—
255C22×C4—1721no—
256C22×C4(C2×D43)⋊C411yescharacteristic
257C22×C4(C2×D43)⋊C411yescharacteristic
258C22×C4#1062188211yescharacteristic
259C22×C4#1062188411yescharacteristic
260C22×C4#1062188411yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262Q16—1721no—
263SD16—1722no—
264D8—1721no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8(C2×D43)⋊C411yescharacteristic
272C2×C8(C2×D43)⋊C411yescharacteristic
273C2×C8C2×C4×D4311yescharacteristic
274C2×C8C2×D17211yescharacteristic
275C4⋊C4—24no—
276C4⋊C4—42no—
277C4⋊C4—44no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C22⋊C4—1721no—
283C22⋊C4—1721no—
284C22⋊C4—1721no—
285C22⋊C4—1721no—
286C22⋊C4—1721no—
287C42—1721no—
288C16—1722no—
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—1721no—
294C23#1306324511yescharacteristic
295C23#1306324511yescharacteristic
296C23C2×#1062188211yescharacteristic
297Q8—1721no—
298Q8—1721no—
299D4—3441no—
300D4—3441no—
301D4—3442no—
302D4—3442no—
303D4—1721no—
304D4—1721no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—44no—
313C2×C4—88no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—3442no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4#1306323912yes—
321C2×C4#1306324511yescharacteristic
322C2×C4#1306324511yescharacteristic
323C2×C4#1306325312yes—
324C2×C4C2×(C2×D43)⋊C411yescharacteristic
325C2×C4C2×#1062188411yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—24no—
331C22—24no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—3441no—
339C22—3441no—
340C22—3441no—
341C22#1458263212yes—
342C22#1458270812yes—
343C22C2×#1306324511yescharacteristic
344C22#1458333511yescharacteristic
345C22#1458334011yescharacteristic
346C4—21no—
347C4—21no—
348C4—84no—
349C4—3441no—
350C4—3441no—
351C4—3441no—
352C4#1458263212yes—
353C4C2×#1306323911yescharacteristic
354C4C2×#1306325311yescharacteristic
355C2—21no—
356C2—21no—
357C2—22no—
358C2—22no—
359C2—6881no—
360C2C2×#1458263211yescharacteristic
361C2#1913630511yescharacteristic
362C2C2×#1458270811yescharacteristic
subgroupG/H
centerC22C2×#13063245
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#340C2
socleC22×C43C2×#102
prime radical#19144176C2
cosocleC22×C8×C43C23
hypercenterC2×#340D43
hypocenterC43#11704
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. #19136206C2semidirect
3. #19132606C2semidirect
4. #19132603C2semidirect
5. C2×C43×#340C2semidirect
6. C2×#13063347C4semidirect
9. #14583140C4semidirect
11. #14583135C4semidirect
15. #14582937C4semidirect
25. C2×Dic172C2×C4semidirect
27. C2×D344C2×C4semidirect
39. #13063259C2×C4semidirect
40. #13063259C2×C4semidirect
176. C2×#340D43semidirect
204. C43#11704semidirect

Maximal subgroups

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

subgroupindex
#191441762
#191362062
#191326062
#191326032
C2×C43×#3402
#1170443