Finite Group Databasebeta

← #25023608

Subgroups — #25023608

Order 11008.

1590 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582836C211yesmaximal, characteristic
2C2×#14582797C213yesmaximal, complemented
3C2×#14582790C213yesmaximal
4#19132862C213yesmaximal, complemented
5#19132860C211yesmaximal, characteristic, complemented
6#19132841C213yesmaximal
7C4×#95×C43C211yesmaximal, characteristic, complemented
8C22×C4⋊Dic43C2213yes—
9C22×C4⋊Dic43C2213yes—
10C22×Dic43⋊C4C2213yes—
11C22×(C2×D43)⋊C4C2211yescharacteristic
12C22×(C2×D43)⋊C4C2213yes—
13C22×(C2×D43)⋊C4C2213yes—
14#14582836C418yescomplemented
15#14582797—212no—
16#14582790—212no—
17C2×C43⋊#95C2213yes—
18C2×C43⋊#95C2213yes—
19C2×C43⋊#95C2216yes—
20C22×C42×C43C2213yes—
21C2×#95×C43C2213yes—
22C2×#95×C43C2211yescharacteristic
23C24×D43C2311yescharacteristic
24C23×Dic43C2313yes—
25C23×Dic43C2311yescharacteristic
26C23×Dic43C2313yes—
27C2×C4⋊Dic43—26no—
28C2×C4⋊Dic43—26no—
29C2×C4⋊Dic43—26no—
30C2×C4⋊Dic43—46no—
31C2×C4⋊Dic43C2×C4112yes—
32C2×Dic43⋊C4—26no—
33C2×Dic43⋊C4—212no—
34C2×(C2×D43)⋊C4—26no—
35C2×(C2×D43)⋊C4—26no—
36C2×(C2×D43)⋊C4—26no—
37C2×(C2×D43)⋊C4—26no—
38C2×(C2×D43)⋊C4—46no—
39C2×(C2×D43)⋊C4C2×C4112yes—
40C43⋊#95—26no—
41C43⋊#95—26no—
42C43⋊#95—212no—
43C23×C4×C43C2313yes—
44C23×C4×C43C2313yes—
45C23×C4×C43C2311yescharacteristic
46C2×C42×C43—46no—
47C2×C42×C43D4112yes—
48#95×C43—26no—
49#95×C43C2×C414yes—
50C24×C43C2411yescharacteristic
51C23×D43—23no—
52C23×D43—23no—
53C23×D43—23no—
54C23×D43—21no—
55C23×D43—21no—
56C23×D43—23no—
57C23×D43C22×C412yes—
58C22×C4×C43—26no—
59C22×C4×C43—23no—
60C22×C4×C43—26no—
61C22×C4×C43—26no—
62C22×C4×C43—26no—
63C22×C4×C43—21no—
64C22×C4×C43—23no—
65C22×C4×C43—23no—
66C22×C4×C43C22×C416yes—
67C22×C4×C43C2×D416yes—
68C22×C4×C43C2×D416yes—
69C22×C4×C43C2×D416yes—
70C22×C4×C43#4116yes—
71C22×Dic43—23no—
72C22×Dic43—26no—
73C22×Dic43—23no—
74C22×Dic43—23no—
75C22×Dic43—26no—
76C22×Dic43—23no—
77C22×Dic43—26no—
78C22×Dic43—26no—
79C22×Dic43—23no—
80C22×Dic43—21no—
81C22×Dic43—23no—
82C22×Dic43—23no—
83C22×Dic43C22×C416yes—
84C42×C43—412no—
85(C2×D43)⋊C4—224no—
86(C2×D43)⋊C4—412no—
87(C2×D43)⋊C4—44no—
88C4⋊Dic43—224no—
89C4⋊Dic43—412no—
90Dic43⋊C4—412no—
91C23×C43C23×C411yescharacteristic
92C23×C43C22×D413yes—
93C23×C43C2×#4113yes—
94C23×C43H(5,𝔽2)13yes—
95C23×C432−1+411yescharacteristic
96C23×C432−1+413yes—
97C23×C432−1+411yescharacteristic
98C22×D43—26no—
99C22×D43—22no—
100C22×D43—26no—
101C22×D43—41no—
102C22×D43—43no—
103C22×D43—43no—
104C22×D43—43no—
105C22×D43—43no—
106C22×D43—43no—
107C22×D43—46no—
108C22×D43—43no—
109C22×D43—43no—
110C2×C4×C43—212no—
111C2×C4×C43—26no—
112C2×C4×C43—26no—
113C2×C4×C43—26no—
114C2×C4×C43—26no—
115C2×C4×C43—212no—
116C2×C4×C43—26no—
117C2×C4×C43—26no—
118C2×C4×C43—26no—
119C2×C4×C43—46no—
120C2×C4×C43—46no—
121C2×C4×C43C4×D4112yes—
122C2×C4×C43#12714yes—
123C2×Dic43—212no—
124C2×Dic43—26no—
125C2×Dic43—43no—
126C2×Dic43—43no—
127C2×Dic43—46no—
128C2×Dic43—43no—
129C2×Dic43—41no—
130C2×Dic43—46no—
131C2×Dic43—43no—
132C2×Dic43—43no—
133C2×Dic43—43no—
134C2×Dic43—43no—
135C2×Dic43—46no—
136#14322—431nomaximal, Sylow
137C22×C43C2×C4×D413yes—
138C22×C43#51911yescharacteristic
139C22×C43#52013yes—
140C22×C43C2×#12711yescharacteristic
141C22×C43#53213yes—
142C22×C43#53413yes—
143C22×C43#53613yes—
144C22×C43#53613yes—
145C22×C43#53713yes—
146C22×C43#53916yes—
147C22×C43#54113yes—
148C22×C43#54213yes—
149C2×D43—42no—
150C2×D43—46no—
151C2×D43—46no—
152C2×D43—81no—
153C2×D43—81no—
154C2×D43—83no—
155C2×D43—83no—
156C4×C43—212no—
157C4×C43—24no—
158C4×C43—46no—
159Dic43—46no—
160Dic43—83no—
161Dic43—81no—
162C2×#399—431no—
163C2×#389—433no—
164C2×#388—433no—
165#1445—433no—
166#1444—431no—
167#1439—433no—
168C4×#95D4311yescharacteristic, complemented
169C2×C43C4×#12711yescharacteristic
170C2×C43#232213yes—
171C2×C43#232313yes—
172C2×C43#265611yescharacteristic
173C2×C43#265811yescharacteristic
174C2×C43#266313yes—
175C2×C43#266413yes—
176D43—82no—
177C22×C4⋊C4—433no—
178C22×C4⋊C4—433no—
179C22×C4⋊C4—433no—
180C22×C22⋊C4—433no—
181C22×C22⋊C4—431no—
182C22×C22⋊C4—433no—
183C22×C42C2×D4313yes—
184#399—438no—
185#389—8612no—
186#388—8612no—
187C2×#95—436no—
188C2×#95—433no—
189C2×#95—433no—
190C2×#95C2×D4313yes—
191C2×#95C2×D4311yescharacteristic
192C43#1432211yescharacteristic, complemented, Sylow
193C25—431no—
194C23×C4—433no—
195C23×C4—433no—
196C23×C4—431no—
197C23×C4C22×D4313yes—
198C23×C4C22×D4313yes—
199C23×C4C22×D4311yescharacteristic
200C2×C4⋊C4—4312no—
201C2×C4⋊C4—866no—
202C2×C4⋊C4—866no—
203C2×C4⋊C4—866no—
204C2×C4⋊C4—8612no—
205C2×C4⋊C4—866no—
206C2×C4⋊C4—1726no—
207C2×C22⋊C4—4312no—
208C2×C22⋊C4—866no—
209C2×C22⋊C4—866no—
210C2×C22⋊C4—866no—
211C2×C22⋊C4—866no—
212C2×C22⋊C4—1726no—
213C2×C42—46no—
214C2×C42D172112yes—
215#95—26no—
216#95—866no—
217#95—866no—
218#95—8612no—
219#95C4×D4314yes—
220C24—432no—
221C24—863no—
222C24—863no—
223C24—863no—
224C24—861no—
225C24—863no—
226C24—861no—
227C24C23×D4311yescharacteristic
228C22×C4—23no—
229C22×C4—26no—
230C22×C4—26no—
231C22×C4—21no—
232C22×C4—26no—
233C22×C4—26no—
234C22×C4—23no—
235C22×C4—23no—
236C22×C4—436no—
237C22×C4—863no—
238C22×C4—866no—
239C22×C4—863no—
240C22×C4—866no—
241C22×C4—863no—
242C22×C4—863no—
243C22×C4—866no—
244C22×C4—866no—
245C22×C4—863no—
246C22×C4—861no—
247C22×C4—863no—
248C22×C4—863no—
249C22×C4C2×C4×D4316yes—
250C22×C4C2×D17216yes—
251C22×C4C2×D17216yes—
252C22×C4C2×D17216yes—
253C22×C4#1062189816yes—
254C4⋊C4—8624no—
255C4⋊C4—17212no—
256C4⋊C4—17212no—
257C22⋊C4—8624no—
258C22⋊C4—17212no—
259C22⋊C4—1724no—
260C42—412no—
261C23—866no—
262C23—862no—
263C23—866no—
264C23—1721no—
265C23—1723no—
266C23—1723no—
267C23—1723no—
268C23—1723no—
269C23—1723no—
270C23—1726no—
271C23—1723no—
272C23—1723no—
273C23C22×C4×D4311yescharacteristic
274C23C22×D17213yes—
275C23C2×#1062189813yes—
276C23#1306337013yes—
277C23#1306337211yescharacteristic
278C23#1306337213yes—
279C23#1306337311yescharacteristic
280C2×C4—212no—
281C2×C4—26no—
282C2×C4—26no—
283C2×C4—26no—
284C2×C4—26no—
285C2×C4—212no—
286C2×C4—26no—
287C2×C4—26no—
288C2×C4—26no—
289C2×C4—46no—
290C2×C4—46no—
291C2×C4—866no—
292C2×C4—8612no—
293C2×C4—1721no—
294C2×C4—1723no—
295C2×C4—1723no—
296C2×C4—1726no—
297C2×C4—1723no—
298C2×C4—1723no—
299C2×C4—1723no—
300C2×C4—1726no—
301C2×C4—1723no—
302C2×C4—1723no—
303C2×C4—1726no—
304C2×C4C4×D172112yes—
305C2×C4#1306332214yes—
306C22—3441no—
307C22—3441no—
308C22—3443no—
309C22—3443no—
310C22—1722no—
311C22—1726no—
312C22—1726no—
313C22C2×C4×D17213yes—
314C22#1458337511yescharacteristic
315C22#1458337813yes—
316C22C2×#1306332211yescharacteristic
317C22#1458344913yes—
318C22#1458346113yes—
319C22#1458347513yes—
320C22#1458347513yes—
321C22#1458348013yes—
322C22#1458349116yes—
323C22#1458350713yes—
324C22#1458351413yes—
325C4—24no—
326C4—212no—
327C4—46no—
328C4—3443no—
329C4—3441no—
330C4—1726no—
331C2—3442no—
332C2C4×#1306332211yescharacteristic
333C2#1913726613yes—
334C2#1913727813yes—
335C2#1914069711yescharacteristic
336C2#1914070511yescharacteristic
337C2#1914074313yes—
338C2#1914075413yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC4×#95×C43C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenterC4×#95D43
hypocenterC43#14322
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×#14582797C2semidirect
4. #19132862C2semidirect
5. #19132860C2semidirect
7. C4×#95×C43C2semidirect
14. #14582836C4semidirect
168. C4×#95D43semidirect
192. C43#14322semidirect

Maximal subgroups

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

subgroupindex
C2×#145828362
C2×#145827972
C2×#145827902
#191328622
#191328602
#191328412
C4×#95×C432
#1432243