Finite Group Databasebeta

← #24984732

Subgroups — #24984732

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134663C211yesmaximal, characteristic
2#19134289C211yesmaximal, characteristic
3#19132418C214yesmaximal, complemented
4C2×C43×#389C211yesmaximal, characteristic
5C22×#10621877—21no—
6C2×C22⋊(C43⋊C8)—21no—
7#14582654—21no—
8#14582654—21no—
9#14582654C2212yes—
10#14582654C2212yes—
11C22×C4⋊C4×C43—21no—
12C22×C4⋊C4×C43C411yescharacteristic
13C22×C4⋊C4×C43C411yescharacteristic
14C22×C42×C43C2211yescharacteristic
15C43×#389—21no—
16C43×#389—21no—
17C43×#389C412yes—
18C43×#389C2212yes—
19C2×#95×C43—21no—
20C2×#10621877—24no—
21C2×#10621877—42no—
22C2×#10621877—42no—
23C22×C43⋊C8—22no—
24C22×C43⋊C8—22no—
25C22⋊(C43⋊C8)—42no—
26C23×C4×C43—21no—
27C23×C4×C43—21no—
28C23×C4×C43C2×C411yescharacteristic
29C23×C4×C43D411yescharacteristic
30C23×C4×C43D411yescharacteristic
31C2×C4⋊C4×C43—21no—
32C2×C4⋊C4×C43—24no—
33C2×C4⋊C4×C43—22no—
34C2×C4⋊C4×C43—21no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—42no—
37C2×C4⋊C4×C43—44no—
38C2×C4⋊C4×C43C2×C412yes—
39C2×C4⋊C4×C43C2×C412yes—
40C2×C42×C43—42no—
41C2×C42×C43C2×C411yescharacteristic
42C2×C42×C43D411yescharacteristic
43C2×C42×C43D411yescharacteristic
44C2×C42×C43C2311yescharacteristic
45#95×C43—22no—
46#95×C43—22no—
47C24×C43C22⋊C411yescharacteristic
48C22×C4×C43—22no—
49C22×C4×C43—22no—
50C22×C4×C43—24no—
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—41no—
59C22×C4×C43—42no—
60C22×C4×C43—42no—
61C22×C4×C43—42no—
62C22×C4×C43—42no—
63C22×C4×C43—42no—
64C22×C4×C43C22⋊C411yescharacteristic
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43SD1612yes—
68C22×C4×C43Q1612yes—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C4⋊C4×C43—24no—
73C4⋊C4×C43—22no—
74C4⋊C4×C43—42no—
75C4⋊C4×C43—42no—
76C4⋊C4×C43—44no—
77C4⋊C4×C43—44no—
78C4⋊C4×C43M1614yescomplemented
79C42×C43—41no—
80C42×C43—41no—
81C42×C43—41no—
82C42×C43—41no—
83#10621877—48no—
84C2×C43⋊C8—24no—
85C2×C43⋊C8—42no—
86C2×C43⋊C8—42no—
87C2×C43⋊C8—42no—
88C2×C43⋊C8—42no—
89C2×C43⋊C8—42no—
90C23×C43—21no—
91C23×C43—21no—
92C23×C43—21no—
93C23×C43—21no—
94C23×C43#9912yes—
95C23×C43#10312yes—
96C23×C43#10412yes—
97C23×C43C2×C22⋊C411yescharacteristic
98C2×C4×C43—28no—
99C2×C4×C43—24no—
100C2×C4×C43—24no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—24no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—44no—
116C2×C4×C43—48no—
117C2×C4×C43—42no—
118C2×C4×C43—42no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—84no—
123C2×C4×C43#10112yes—
124C2×C4×C43#10312yes—
125C2×C4×C43C2×M1612yes—
126C2×C4×C43C2×SD1611yescharacteristic
127C2×C4×C43C2×Q1611yescharacteristic
128C2×C4×C43AGL(1,ℤ/8)12yes—
129C43⋊C8—44no—
130C43⋊C8—82no—
131#7607—431nomaximal, Sylow
132C22×C43—22no—
133C22×C43—22no—
134C22×C43—22no—
135C22×C43—22no—
136C22×C43—22no—
137C22×C43—22no—
138C22×C43#32814yes—
139C22×C43#40711yescharacteristic
140C22×C43C2×#9911yescharacteristic
141C22×C43C2×#10111yescharacteristic
142C22×C43C2×#10311yescharacteristic
143C22×C43#41811yescharacteristic
144C22×C43C2×#10411yescharacteristic
145C22×C43#42111yescharacteristic
146C4×C43—22no—
147C4×C43—22no—
148C4×C43—21no—
149C4×C43—22no—
150C4×C43—21no—
151C4×C43—22no—
152C4×C43—44no—
153C4×C43—41no—
154C4×C43—82no—
155C2×#389D4311yescharacteristic
156#1817—431no—
157#1728—431no—
158#1271—434no—
159C2×C43—24no—
160C2×C43#146311yescharacteristic
161C2×C43#148711yescharacteristic
162C2×C43#149011yescharacteristic
163C2×C43C2×#32811yescharacteristic
164C2×C43#151011yescharacteristic
165C2×C43#152811yescharacteristic
166C2×C43#154911yescharacteristic
167C22×M16—861no—
168C22×C4⋊C4—21no—
169C22×C4⋊C4Dic4311yescharacteristic
170C22×C4⋊C4Dic4311yescharacteristic
171C22×C42C2×D4311yescharacteristic
172C2×C22⋊C8—861no—
173#389—21no—
174#389—21no—
175#389Dic4312yes—
176#389C2×D4312yes—
177C2×#95—21no—
178#336—432no—
179#336—432no—
180#336—861no—
181#336—861no—
182C43#760711yescharacteristic, complemented, Sylow
183C23×C4—21no—
184C23×C4—21no—
185C23×C4C2×Dic4311yescharacteristic
186C23×C4C22⋊D4311yescharacteristic
187C23×C4C22⋊D4311yescharacteristic
188C2×M16—864no—
189C2×M16—1722no—
190C2×M16—1722no—
191C22×C8—862no—
192C22×C8—862no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—44no—
200C2×C4⋊C4C2×Dic4312yes—
201C2×C4⋊C4C2×Dic4312yes—
202C2×C42—42no—
203C2×C42C2×Dic4311yescharacteristic
204C2×C42C22⋊D4311yescharacteristic
205C2×C42C22⋊D4311yescharacteristic
206C2×C42C22×D4311yescharacteristic
207C22⋊C8—1722no—
208#95—22no—
209#95—22no—
210C24C22⋊Dic4311yescharacteristic
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—41no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4#1062188412yes—
228C22×C4#1062188512yes—
229C22×C4C22⋊Dic4311yescharacteristic
230C22×C4C22⋊Dic4311yescharacteristic
231C22×C4C22⋊Dic4311yescharacteristic
232C22×C4C22×Dic4311yescharacteristic
233C22×C4C2×C22⋊D4311yescharacteristic
234C22×C4C2×C22⋊D4311yescharacteristic
235M16—1728no—
236C2×C8—864no—
237C2×C8—1722no—
238C2×C8—1722no—
239C2×C8—1722no—
240C2×C8—1722no—
241C2×C8—1722no—
242C4⋊C4—24no—
243C4⋊C4—22no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—44no—
247C4⋊C4—44no—
248C4⋊C4#1062187714yescomplemented
249C42—41no—
250C42—41no—
251C42—41no—
252C42—41no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#1306324012yes—
258C23#1306324912yes—
259C23#1306325212yes—
260C23C2×C22⋊Dic4311yescharacteristic
261C2×C4—28no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—44no—
279C2×C4—48no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—84no—
286C2×C4#1306324412yes—
287C2×C4#1306324912yes—
288C2×C4C2×#1062187712yes—
289C2×C4C2×#1062188411yescharacteristic
290C2×C4C2×#1062188511yescharacteristic
291C2×C4#1306335112yes—
292C8—3442no—
293C8—1724no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22#1458263614yes—
301C22#1458286311yescharacteristic
302C22C2×#1306324011yescharacteristic
303C22C2×#1306324411yescharacteristic
304C22C2×#1306324911yescharacteristic
305C22#1458290411yescharacteristic
306C22C2×#1306325211yescharacteristic
307C22#1458291611yescharacteristic
308C4—21no—
309C4—22no—
310C4—21no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—44no—
315C4—41no—
316C4—82no—
317C2—24no—
318C2#1913292511yescharacteristic
319C2#1913302411yescharacteristic
320C2#1913303811yescharacteristic
321C2C2×#1458263611yescharacteristic
322C2#1913312411yescharacteristic
323C2#1913319711yescharacteristic
324C2#1913328011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#389C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×#389D43
hypocenterC43#7607
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #19132418C2semidirect
78. C4⋊C4×C43M16semidirect
182. C43#7607semidirect
248. C4⋊C4#10621877semidirect

Maximal subgroups

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

subgroupindex
#191346632
#191342892
#191324182
C2×C43×#3892
#760743