Finite Group Databasebeta

← #25018075

Subgroups — #25018075

Order 11008.

2154 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D43)⋊C4C213yesmaximal
2C2×#14582744C211yesmaximal, characteristic, complemented
3C2×#95×D43C211yesmaximal, characteristic
4#19132822C213yesmaximal, complemented
5#19132819C213yesmaximal, complemented
6(C2×D43)⋊#95C213yesmaximal
7C4×#95×C43C211yesmaximal, characteristic, complemented
8C23×C4×D43C2213yes—
9C22×(C2×D43)⋊C4C2213yes—
10C22×(C2×D43)⋊C4C2211yescharacteristic
11C22×C4×Dic43C2213yes—
12C4×(C2×D43)⋊C4C4124yescomplemented
13#14582744—24no—
14C2×C43⋊#95C2213yes—
15C2×C43⋊#95C2213yes—
16C2×C43⋊#95C2216yes—
17C2×C43⋊#95C2213yes—
18C2×C43⋊#95C2213yes—
19#95×D43—24no—
20C22×C42×C43C2213yes—
21C2×#95×C43C2213yes—
22C2×#95×C43C2211yescharacteristic
23C24×D43C2311yescharacteristic
24C23×Dic43C2313yes—
25C23×Dic43C2313yes—
26C23×Dic43C2311yescharacteristic
27C22×C4×D43—212no—
28C22×C4×D43—26no—
29C22×C4×D43—26no—
30C22×C4×D43—46no—
31C22×C4×D43C2×C4112yes—
32C2×(C2×D43)⋊C4—26no—
33C2×(C2×D43)⋊C4—26no—
34C2×(C2×D43)⋊C4C2×C4112yes—
35C2×(C2×D43)⋊C4C2×C4112yes—
36C2×C4×Dic43—26no—
37C2×C4×Dic43—26no—
38C2×C4×Dic43C2×C4112yescomplemented
39C43⋊#95—26no—
40C43⋊#95—26no—
41C43⋊#95—46no—
42C43⋊#95C2×C4112yescomplemented
43C43⋊#95C2×C4112yescomplemented
44C23×C4×C43C2313yes—
45C23×C4×C43C2311yescharacteristic
46C23×C4×C43C2313yes—
47C2×C42×C43—46no—
48C2×C42×C43C2×C4112yescomplemented
49#95×C43—26no—
50#95×C43D414yes—
51C24×C43C2411yescharacteristic
52C23×D43—21no—
53C23×D43—23no—
54C23×D43—23no—
55C23×D43—21no—
56C23×D43C22×C416yes—
57C23×D43#4112yes—
58C23×D43#4116yes—
59C22×C4×C43—26no—
60C22×C4×C43—26no—
61C22×C4×C43—23no—
62C22×C4×C43—23no—
63C22×C4×C43—23no—
64C22×C4×C43—26no—
65C22×C4×C43—26no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C416yes—
68C22×C4×C43C22×C416yes—
69C22×C4×C43C22×C416yes—
70C22×C4×C43C2×D416yes—
71C22×C4×C43#4116yes—
72C22×Dic43—21no—
73C22×Dic43—23no—
74C22×Dic43—23no—
75C22×Dic43—23no—
76C22×Dic43—23no—
77C22×Dic43—23no—
78C22×Dic43—23no—
79C22×Dic43—26no—
80C22×Dic43—23no—
81C22×Dic43—23no—
82C22×Dic43—26no—
83C22×Dic43—23no—
84C22×Dic43C22×C416yes—
85C22×Dic43C22×C416yes—
86C22×Dic43C22×C416yes—
87C2×C4×D43—224no—
88C2×C4×D43—224no—
89C2×C4×D43—412no—
90C2×C4×D43—424no—
91C2×C4×D43—424no—
92C42×C43—412no—
93(C2×D43)⋊C4—224no—
94(C2×D43)⋊C4C42116yes—
95C4×Dic43—224no—
96C23×C43C23×C413yes—
97C23×C43C22×D411yescharacteristic
98C23×C43C2×#4113yes—
99C23×C43C2×#4111yescharacteristic
100C23×C43C2×#4113yes—
101C23×C43H(5,𝔽2)13yes—
102C23×C432−1+411yescharacteristic
103C22×D43—26no—
104C22×D43—26no—
105C22×D43—26no—
106C22×D43—26no—
107C22×D43—26no—
108C22×D43—22no—
109C22×D43—212no—
110C22×D43—26no—
111C22×D43—26no—
112C22×D43C2×C4214yes—
113C22×D43#117112yes—
114C22×D43#117112yes—
115C2×C4×C43—26no—
116C2×C4×C43—26no—
117C2×C4×C43—26no—
118C2×C4×C43—26no—
119C2×C4×C43—212no—
120C2×C4×C43—212no—
121C2×C4×C43—26no—
122C2×C4×C43—26no—
123C2×C4×C43—26no—
124C2×C4×C43—46no—
125C2×C4×C43—46no—
126C2×C4×C43C2×C4214yes—
127C2×C4×C43C4×D4112yes—
128C2×Dic43—26no—
129C2×Dic43—26no—
130C2×Dic43—26no—
131C2×Dic43—26no—
132C2×Dic43—26no—
133C2×Dic43—26no—
134C2×Dic43—26no—
135C2×Dic43—26no—
136C2×Dic43—46no—
137C2×Dic43—43no—
138C2×Dic43—43no—
139C2×Dic43—46no—
140C2×Dic43—43no—
141C2×Dic43—43no—
142C2×Dic43C2×C4214yes—
143C4×D43—448no—
144#13809—431nomaximal, Sylow
145C22×C43C22×C4211yescharacteristic
146C22×C43C2×#11713yes—
147C22×C43C2×#11713yes—
148C22×C43C2×C4×D413yes—
149C22×C43C4×#4113yes—
150C22×C43#51813yes—
151C22×C43#52013yes—
152C22×C43#54613yes—
153C22×C43#54811yescharacteristic
154C22×C43#55116yes—
155C22×C43#55213yes—
156C22×C43#55313yes—
157C2×D43—212no—
158C2×D43—212no—
159C2×D43—212no—
160C2×D43—212no—
161C2×D43—24no—
162C2×D43—24no—
163C2×D43#37618yescomplemented
164C4×C43—212no—
165C4×C43—24no—
166C4×C43—46no—
167Dic43—24no—
168Dic43—46no—
169Dic43—46no—
170C2×C4×C22⋊C4—433no—
171C2×#376—431no—
172C22×#95—431no—
173#1434—433no—
174#1434—433no—
175C22⋊#95—433no—
176C4×#95D4311yescharacteristic, complemented
177C2×C43C2×#37611yescharacteristic
178C2×C43C42×D411yescharacteristic
179C2×C43#227511yescharacteristic
180C2×C43#234213yes—
181C2×C43#234313yes—
182C2×C43#235213yes—
183C2×C43#235313yes—
184D43—28no—
185C24×C4—433no—
186C22×C22⋊C4—431no—
187C22×C22⋊C4—433no—
188C22×C42—433no—
189C22×C42C2×D4313yes—
190C4×C22⋊C4—4324no—
191#376—864no—
192C2×#95—433no—
193C2×#95—433no—
194C2×#95—433no—
195C2×#95—433no—
196C2×#95—436no—
197C2×#95—864no—
198C2×#95C2×D4313yes—
199C2×#95C2×D4311yescharacteristic
200C43#1380911yescharacteristic, complemented, Sylow
201C25—431no—
202C23×C4—431no—
203C23×C4—433no—
204C23×C4—433no—
205C23×C4—4312no—
206C23×C4—8612no—
207C23×C4—866no—
208C23×C4—866no—
209C23×C4—1726no—
210C23×C4C22×D4313yes—
211C23×C4C22×D4311yescharacteristic
212C23×C4C22×D4313yes—
213C2×C22⋊C4—4312no—
214C2×C22⋊C4—4312no—
215C2×C22⋊C4—866no—
216C2×C22⋊C4—866no—
217C2×C42—46no—
218C2×C42—4312no—
219C2×C42—866no—
220C2×C42—866no—
221C2×C42C4×D43112yescomplemented
222#95—26no—
223#95—4312no—
224#95—4312no—
225#95—866no—
226#95—866no—
227#95—1726no—
228#95D17214yes—
229C24—436no—
230C24—432no—
231C24—436no—
232C24—861no—
233C24—863no—
234C24—863no—
235C24—861no—
236C24C23×D4311yescharacteristic
237C22×C4—26no—
238C22×C4—23no—
239C22×C4—26no—
240C22×C4—21no—
241C22×C4—23no—
242C22×C4—23no—
243C22×C4—26no—
244C22×C4—26no—
245C22×C4—436no—
246C22×C4—436no—
247C22×C4—436no—
248C22×C4—8624no—
249C22×C4—861no—
250C22×C4—863no—
251C22×C4—863no—
252C22×C4—863no—
253C22×C4—863no—
254C22×C4—863no—
255C22×C4—866no—
256C22×C4—863no—
257C22×C4—863no—
258C22×C4—863no—
259C22×C4—866no—
260C22×C4—863no—
261C22×C4—8624no—
262C22×C4—17212no—
263C22×C4—17224no—
264C22×C4—17224no—
265C22×C4C2×C4×D4316yes—
266C22×C4C2×C4×D4316yes—
267C22×C4C2×C4×D4316yes—
268C22×C4C2×D17216yes—
269C22×C4#1062189816yes—
270C22⋊C4—4316no—
271C22⋊C4—8624no—
272C42—412no—
273C42—8624no—
274C23—434no—
275C23—4312no—
276C23—4312no—
277C23—862no—
278C23—8612no—
279C23—866no—
280C23—866no—
281C23—866no—
282C23—866no—
283C23—866no—
284C23—866no—
285C23—866no—
286C23C22×C4×D4313yes—
287C23C22×D17211yescharacteristic
288C23#41×D4311yescharacteristic
289C23#41×D4313yes—
290C23C2×#1062189813yes—
291C23#1306337013yes—
292C23#1306337311yescharacteristic
293C2×C4—212no—
294C2×C4—26no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—212no—
299C2×C4—26no—
300C2×C4—26no—
301C2×C4—26no—
302C2×C4—46no—
303C2×C4—46no—
304C2×C4—434no—
305C2×C4—866no—
306C2×C4—866no—
307C2×C4—866no—
308C2×C4—866no—
309C2×C4—866no—
310C2×C4—866no—
311C2×C4—866no—
312C2×C4—866no—
313C2×C4—17248no—
314C2×C4—1723no—
315C2×C4—1726no—
316C2×C4—1723no—
317C2×C4—1723no—
318C2×C4—1726no—
319C2×C4—1723no—
320C2×C4C42×D4314yes—
321C2×C4C4×D172112yes—
322C22—438no—
323C22—8612no—
324C22—8612no—
325C22—864no—
326C22—8612no—
327C22—864no—
328C22—8612no—
329C22C2×C42×D4311yescharacteristic
330C22#117×D4313yes—
331C22#117×D4313yes—
332C22C2×C4×D17213yes—
333C22C4×#1062189813yes—
334C22#1458337213yes—
335C22#1458338013yes—
336C22#1458354413yes—
337C22#1458356111yescharacteristic
338C22#1458357816yes—
339C22#1458359013yes—
340C22#1458359913yes—
341C4—212no—
342C4—24no—
343C4—46no—
344C4—864no—
345C4—1726no—
346C4—1726no—
347C2—868no—
348C2#376×D4311yescharacteristic
349C2C42×D17211yescharacteristic
350C2#1913695311yescharacteristic
351C2#1913744713yes—
352C2#1913745813yes—
353C2#1913752713yes—
354C2#1913753813yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC4×#95×C43C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC4×#95D43
hypocenterC43#13809
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582744C2semidirect
4. #19132822C2semidirect
5. #19132819C2semidirect
7. C4×#95×C43C2semidirect
12. C4×(C2×D43)⋊C4C4semidirect
38. C2×C4×Dic43C2×C4semidirect
42. C43⋊#95C2×C4semidirect
43. C43⋊#95C2×C4semidirect
48. C2×C42×C43C2×C4semidirect
163. C2×D43#376semidirect
176. C4×#95D43semidirect
200. C43#13809semidirect
221. C2×C42C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D43)⋊C42
C2×#145827442
C2×#95×D432
#191328222
#191328192
(C2×D43)⋊#952
C4×#95×C432
#1380943