Finite Group Databasebeta

← #25013987

Subgroups — #25013987

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063265C211yesmaximal, characteristic, complemented
2#19144176C211yesmaximal, characteristic
3C2×#14582708C212yesmaximal, complemented
4#19132702C212yesmaximal, complemented
5C43×#1807C211yesmaximal, characteristic, complemented
6C2×#13063347C2211yescharacteristic
7#14583410—21no—
8C2×#13063265—24no—
9C2×#13063265—21no—
10C2×#13063265C2212yes—
11C22×C43⋊C16—21no—
12#14583140C411yescharacteristic, complemented
13#14583140C411yescharacteristic, complemented
14#14583135C411yescharacteristic, complemented
15#14583135C411yescharacteristic, complemented
16#14583128—21no—
17#14583128—21no—
18#14582937C2211yescharacteristic
19#14582896—21no—
20#14582708—24no—
21C23×C8×C43C2211yescharacteristic
22C2×#106×C43C2212yes—
23C43×#380—21no—
24C43×#340—21no—
25C2×#10621898—21no—
26#13063347—22no—
27#13063347—22no—
28C2×Dic172C2×C411yescharacteristic
29C2×#10621873—21no—
30C2×D344C2×C411yescharacteristic
31#13063308—41no—
32#13063304—21no—
33#13063304—21no—
34#13063299—21no—
35#13063299—21no—
36#13063294—41no—
37C4×C22⋊D43—41no—
38C4×C22⋊D43—41no—
39#13063284—21no—
40#13063265—24no—
41#13063265—22no—
42#13063265D414yescomplemented
43C2×C43⋊C16—24no—
44C2×C43⋊C16—22no—
45#13063259C2×C411yescharacteristic
46#13063259C2×C411yescharacteristic
47#13063257—21no—
48#13063250—21no—
49#13063250—21no—
50#13063247—21no—
51#13063247—21no—
52C23×C4×C43D411yescharacteristic
53C22×C8×C43—22no—
54C22×C8×C43—22no—
55C22×C8×C43C2×C411yescharacteristic
56C22×C8×C43C2×C411yescharacteristic
57C22×C8×C43D411yescharacteristic
58C22×C8×C43D411yescharacteristic
59C22×C8×C43D411yescharacteristic
60C22×C8×C43C2311yescharacteristic
61C2×C4⋊C4×C43—22no—
62C2×C22⋊C4×C43—41no—
63#106×C43—22no—
64#106×C43—22no—
65#95×C43—41no—
66C24×C43D811yescharacteristic
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—42no—
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43D811yescharacteristic
73C22×C4×C43SD1611yescharacteristic
74C22×C4×C43SD1611yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—41no—
77C2×C22⋊D43—41no—
78C2×C22⋊D43—41no—
79#10621898—42no—
80#10621898—42no—
81C2×D172—21no—
82C2×C4×D43—41no—
83C2×Dic86—21no—
84C2×C8×C43—22no—
85C2×C8×C43—22no—
86C2×C8×C43—22no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—21no—
90C2×C8×C43—21no—
91C2×C8×C43C22⋊C411yescharacteristic
92C2×C8×C43C22⋊C411yescharacteristic
93C2×C8×C43C22×C411yescharacteristic
94C2×C8×C43C2×D411yescharacteristic
95C2×C8×C43C2×D412yes—
96C2×C8×C43#4112yes—
97C4⋊C4×C43—42no—
98C4⋊C4×C43—42no—
99C22⋊C4×C43—82no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102C22⋊Dic43—41no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109C4×Dic43—41no—
110Dic172—22no—
111D344—22no—
112#10621873—41no—
113#10621873—41no—
114C43⋊C16—24no—
115C23×C43—22no—
116C23×C43—22no—
117C23×C43—41no—
118C23×C43#10211yescharacteristic
119C23×C43#10211yescharacteristic
120C23×C43C2×D811yescharacteristic
121C22×D43—41no—
122C2×C4×C43—22no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—82no—
130C2×C4×C43—82no—
131C2×C4×C43—82no—
132C2×C4×C43#10211yescharacteristic
133C2×C4×C43#10211yescharacteristic
134C2×C4×C43C2×C22⋊C411yescharacteristic
135C2×C4×C43#12112yes—
136C2×C4×C43C2×SD1611yescharacteristic
137C2×C4×C43#13512yes—
138C22⋊D43—82no—
139C22⋊D43—82no—
140C22⋊D43—82no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144D172—41no—
145D172—41no—
146C4×D43—82no—
147Dic86—41no—
148Dic86—41no—
149C8×C43—21no—
150C8×C43—21no—
151C8×C43C4×D412yes—
152C8×C43#12011yescharacteristic
153C8×C43#12311yescharacteristic
154#13065—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—44no—
163C22×C43#36012yescomplemented
164C22×C43C2×#10211yescharacteristic
165C22×C43#46612yes—
166C2×D43—81no—
167C2×D43—81no—
168C2×D43—81no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—162no—
172C4×C43#38611yescharacteristic
173C4×C43#41611yescharacteristic
174C4×C43#46512yes—
175Dic43—81no—
176Dic43—81no—
177Dic43—81no—
178C22×M32—431no—
179#3050—431no—
180C2×#360—432no—
181#1807D4311yescharacteristic, complemented
182#1386—432no—
183C2×C43—22no—
184C2×C43—22no—
185C2×C43—41no—
186C2×C43#189311yescharacteristic
187C2×C43C2×#36011yescharacteristic
188C2×C43#214511yescharacteristic
189D43—161no—
190C2×#135—431no—
191C23×C8C2×D4311yescharacteristic
192#525—861no—
193C2×M32—432no—
194C2×M32—864no—
195C2×M32—861no—
196C22×C16—861no—
197#467—431no—
198#467—431no—
199#466—431no—
200#466—431no—
201#465—861no—
202#465—861no—
203#427—431no—
204C2×#106C2×D4312yes—
205#416—861no—
206#380—21no—
207#360—864no—
208#340—21no—
209C43#1306511yescharacteristic, complemented, Sylow
210C2×#41—861no—
211C23×C4C22⋊D4311yescharacteristic
212#135—862no—
213#135—862no—
214C2×Q16—431no—
215C2×SD16—861no—
216C2×D8—431no—
217C22×C8—22no—
218C22×C8—22no—
219C22×C8C4×D4311yescharacteristic
220C22×C8C4×D4311yescharacteristic
221C22×C8D17211yescharacteristic
222C22×C8D17211yescharacteristic
223C22×C8C22⋊D4311yescharacteristic
224C22×C8C22×D4311yescharacteristic
225#123—1721no—
226C22⋊Q8—861no—
227C22⋊Q8—861no—
228#121—861no—
229#121—861no—
230#120—1721no—
231C4×D4—1721no—
232C4×D4—1721no—
233#117—861no—
234C2×C4⋊C4—22no—
235C2×C22⋊C4—41no—
236M32—434no—
237M32—864no—
238M32—862no—
239C2×C16—864no—
240C2×C16—862no—
241#107—431no—
242#107—431no—
243#106—22no—
244#106—22no—
245#106—861no—
246#103—861no—
247#103—861no—
248#102—861no—
249#102—861no—
250#95—41no—
251C24#1062188211yescharacteristic
252#41—1722no—
253#41—1722no—
254C2×Q8—861no—
255C2×D4—861no—
256C2×D4—1721no—
257C2×D4—1721no—
258C2×D4—1721no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—42no—
262C22×C4—1721no—
263C22×C4(C2×D43)⋊C411yescharacteristic
264C22×C4(C2×D43)⋊C411yescharacteristic
265C22×C4#1062188211yescharacteristic
266C22×C4#1062188411yescharacteristic
267C22×C4#1062188411yescharacteristic
268C22×C4C2×C22⋊D4311yescharacteristic
269Q16—862no—
270SD16—1721no—
271SD16—1721no—
272D8—862no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8(C2×D43)⋊C411yescharacteristic
281C2×C8(C2×D43)⋊C411yescharacteristic
282C2×C8C2×C4×D4311yescharacteristic
283C2×C8C2×D17211yescharacteristic
284C2×C8D4×D4312yes—
285C2×C8#1062190012yes—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C4⋊C4—1721no—
291C4⋊C4—1721no—
292C22⋊C4—82no—
293C22⋊C4—1721no—
294C22⋊C4—1721no—
295C22⋊C4—1721no—
296C22⋊C4—1721no—
297C22⋊C4—1721no—
298C42—1721no—
299C16—864no—
300C23—22no—
301C23—22no—
302C23—41no—
303C23—1721no—
304C23#1306324511yescharacteristic
305C23#1306324511yescharacteristic
306C23C2×#1062188211yescharacteristic
307Q8—1721no—
308Q8—1721no—
309D4—3442no—
310D4—3442no—
311D4—3442no—
312D4—1721no—
313D4—1721no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4—3442no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4#1306324511yescharacteristic
329C2×C4#1306324511yescharacteristic
330C2×C4C2×(C2×D43)⋊C411yescharacteristic
331C2×C4#1306329712yes—
332C2×C4C2×#1062188411yescharacteristic
333C2×C4#1306334512yes—
334C8—21no—
335C8—21no—
336C8(C22⋊D43)⋊C412yes—
337C8#1306329511yescharacteristic
338C8#1306330911yescharacteristic
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—44no—
347C22—3441no—
348C22—3441no—
349C22—3441no—
350C22#1458270812yescomplemented
351C22C2×#1306324511yescharacteristic
352C22#1458313312yes—
353C4—21no—
354C4—21no—
355C4—162no—
356C4—3441no—
357C4—3441no—
358C4—3441no—
359C4#1458277611yescharacteristic
360C4#1458289311yescharacteristic
361C4#1458313012yes—
362C2—22no—
363C2—22no—
364C2—41no—
365C2—6881no—
366C2#1913502111yescharacteristic
367C2C2×#1458270811yescharacteristic
368C2#1913633011yescharacteristic
subgroupG/H
centerC22C2×#13063245
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1807C2
socleC22×C43C2×#102
prime radical#19144176C2
cosocleC22×C8×C43C23
hypercenter#1807D43
hypocenterC43#13065
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #1807

Complements

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

NH ≅ G/Ntype
1. C22×#13063265C2semidirect
3. C2×#14582708C2semidirect
4. #19132702C2semidirect
5. C43×#1807C2semidirect
12. #14583140C4semidirect
13. #14583140C4semidirect
14. #14583135C4semidirect
15. #14583135C4semidirect
42. #13063265D4semidirect
163. C22×C43#360semidirect
181. #1807D43semidirect
209. C43#13065semidirect
350. C22#14582708semidirect

Maximal subgroups

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

subgroupindex
C22×#130632652
#191441762
C2×#145827082
#191327022
C43×#18072
#1306543