Finite Group Databasebeta

← #24985250

Subgroups — #24985250

Order 11008.

634 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#19134663C211yesmaximal, characteristic, complemented
2#19134575C211yesmaximal, characteristic, complemented
3#19132416C214yesmaximal, complemented
4C43×#2856C211yesmaximal, characteristic
5C2×C4⋊(C43⋊C8)—21no—
6C2×C22⋊(C43⋊C8)—21no—
7C2×C22⋊(C43⋊C8)—21no—
8#14582654—21no—
9#14582654C2212yes—
10#14582654C2212yes—
11C2×#127×C43C411yescharacteristic
12C2×#121×C43—21no—
13C2×#121×C43—21no—
14C2×#121×C43C412yes—
15C22×C42×C43C2211yescharacteristic
16C43×#390—21no—
17C43×#390—21no—
18C43×#390C2212yes—
19C43×#384C411yescharacteristic
20C22×C43⋊C8—22no—
21C22×C43⋊C8—22no—
22C4⋊(C43⋊C8)—42no—
23C22⋊(C43⋊C8)—42no—
24C22⋊(C43⋊C8)—42no—
25C22×D4×C43—22no—
26C22×D4×C43—21no—
27C22×D4×C43—21no—
28C22×D4×C43C2×C412yes—
29C23×C4×C43C2×C411yescharacteristic
30C23×C4×C43D411yescharacteristic
31C23×C4×C43D411yescharacteristic
32#127×C43—42no—
33#121×C43—44no—
34#121×C43—42no—
35#121×C43—42no—
36#121×C43—44no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43C2×C412yes—
40C2×C22⋊C4×C43—22no—
41C2×C22⋊C4×C43—22no—
42C2×C22⋊C4×C43—22no—
43C2×C42×C43—42no—
44C2×C42×C43C2×C411yescharacteristic
45C2×C42×C43D411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C2×C42×C43C2311yescharacteristic
48C24×C43—22no—
49C24×C43C22⋊C411yescharacteristic
50C2×D4×C43—24no—
51C2×D4×C43—44no—
52C2×D4×C43—44no—
53C2×D4×C43—42no—
54C2×D4×C43—42no—
55C2×D4×C43—42no—
56C2×D4×C43—42no—
57C2×D4×C43—42no—
58C2×D4×C43—42no—
59C2×D4×C43—44no—
60C2×D4×C43—42no—
61C2×D4×C43—42no—
62C22×C4×C43—22no—
63C22×C4×C43—22no—
64C22×C4×C43—22no—
65C22×C4×C43—22no—
66C22×C4×C43—22no—
67C22×C4×C43—41no—
68C22×C4×C43—41no—
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43D812yes—
75C22×C4×C43SD1612yes—
76C22×C4×C43C22×C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C4⋊C4×C43—42no—
80C4⋊C4×C43—42no—
81C4⋊C4×C43—42no—
82C22⋊C4×C43—44no—
83C22⋊C4×C43—42no—
84C22⋊C4×C43—42no—
85C22⋊C4×C43—44no—
86C42×C43—22no—
87C42×C43—22no—
88C42×C43—41no—
89C42×C43—41no—
90C2×C43⋊C8—42no—
91C2×C43⋊C8—42no—
92C2×C43⋊C8—42no—
93C2×C43⋊C8—42no—
94C2×C43⋊C8—42no—
95C2×C43⋊C8—42no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—42no—
103C23×C43—42no—
104C23×C43—42no—
105C23×C43—42no—
106C23×C43—42no—
107C23×C43—42no—
108C23×C43—42no—
109C23×C43#10212yes—
110C23×C43C2×C22⋊C411yescharacteristic
111D4×C43—84no—
112D4×C43—84no—
113D4×C43—84no—
114D4×C43—88no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43—44no—
130C2×C4×C43—44no—
131C2×C4×C43—42no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43#9912yes—
135C2×C4×C43#10012yes—
136C2×C4×C43#10212yes—
137C2×C4×C43#13112yes—
138C2×C4×C43C2×D811yescharacteristic
139C2×C4×C43C2×SD1611yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)12yes—
141C43⋊C8—82no—
142C43⋊C8—82no—
143#7724—431nomaximal, Sylow
144C22×C43—22no—
145C22×C43—22no—
146C22×C43—22no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—82no—
152C22×C43—82no—
153C22×C43—82no—
154C22×C43—82no—
155C22×C43—82no—
156C22×C43—82no—
157C22×C43—82no—
158C22×C43#40811yescharacteristic
159C22×C43C2×#9911yescharacteristic
160C22×C43C2×#10011yescharacteristic
161C22×C43C2×#10211yescharacteristic
162C22×C43#41811yescharacteristic
163C22×C43#42111yescharacteristic
164C22×C43#42111yescharacteristic
165C4×C43—22no—
166C4×C43—22no—
167C4×C43—22no—
168C4×C43—22no—
169C4×C43—21no—
170C4×C43—22no—
171C4×C43—21no—
172C4×C43—82no—
173#2856D4311yescharacteristic
174#1817—431no—
175#1797—431no—
176#1270—434no—
177C2×C43—42no—
178C2×C43—162no—
179C2×C43#147111yescharacteristic
180C2×C43#148011yescharacteristic
181C2×C43#149611yescharacteristic
182C2×C43#151011yescharacteristic
183C2×C43#151911yescharacteristic
184C2×C43#153611yescharacteristic
185C2×C43#154511yescharacteristic
186C2×#127Dic4311yescharacteristic
187C2×#121—21no—
188C2×#121—21no—
189C2×#121Dic4312yes—
190C22×C42C2×D4311yescharacteristic
191C2×C4⋊C8—861no—
192C2×C22⋊C8—861no—
193C2×C22⋊C8—861no—
194#390—21no—
195#390—21no—
196#390C2×D4312yes—
197#384Dic4311yescharacteristic
198#336—432no—
199#336—432no—
200#336—861no—
201C43#772411yescharacteristic, complemented, Sylow
202C22×D4—22no—
203C22×D4—21no—
204C22×D4—21no—
205C22×D4C2×Dic4312yes—
206C23×C4C2×Dic4311yescharacteristic
207C23×C4C22⋊D4311yescharacteristic
208C23×C4C22⋊D4311yescharacteristic
209C22×C8—862no—
210C22×C8—862no—
211#127—42no—
212#121—44no—
213#121—42no—
214#121—42no—
215#121—44no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×Dic4312yes—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C42—42no—
223C2×C42C2×Dic4311yescharacteristic
224C2×C42C22⋊D4311yescharacteristic
225C2×C42C22⋊D4311yescharacteristic
226C2×C42C22×D4311yescharacteristic
227C4⋊C8—1722no—
228C22⋊C8—1722no—
229C22⋊C8—1722no—
230C24—22no—
231C24C22⋊Dic4311yescharacteristic
232C2×D4—24no—
233C2×D4—42no—
234C2×D4—42no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4—44no—
240C2×D4—44no—
241C2×D4—44no—
242C2×D4—42no—
243C2×D4—42no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4#1062188212yes—
254C22×C4#1062188312yes—
255C22×C4C22⋊Dic4311yescharacteristic
256C22×C4C22⋊Dic4311yescharacteristic
257C22×C4C22⋊Dic4311yescharacteristic
258C22×C4C22×Dic4311yescharacteristic
259C22×C4C2×C22⋊D4311yescharacteristic
260C22×C4C2×C22⋊D4311yescharacteristic
261C2×C8—1722no—
262C2×C8—1722no—
263C2×C8—1722no—
264C2×C8—1722no—
265C2×C8—1722no—
266C2×C8—1722no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C22⋊C4—44no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—44no—
274C42—22no—
275C42—22no—
276C42—41no—
277C42—41no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—42no—
285C23—42no—
286C23—42no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23#1306324612yes—
292C23C2×C22⋊Dic4311yescharacteristic
293D4—84no—
294D4—84no—
295D4—84no—
296D4—88no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4#1306324012yes—
317C2×C4#1306324212yes—
318C2×C4#1306324612yes—
319C2×C4#1306333212yes—
320C2×C4C2×#1062188211yescharacteristic
321C2×C4C2×#1062188311yescharacteristic
322C2×C4#1306335112yes—
323C8—3442no—
324C8—3442no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—82no—
333C22—82no—
334C22—82no—
335C22—82no—
336C22—82no—
337C22—82no—
338C22—82no—
339C22#1458286611yescharacteristic
340C22C2×#1306324011yescharacteristic
341C22C2×#1306324211yescharacteristic
342C22C2×#1306324611yescharacteristic
343C22#1458290411yescharacteristic
344C22#1458291611yescharacteristic
345C22#1458291611yescharacteristic
346C4—22no—
347C4—22no—
348C4—22no—
349C4—22no—
350C4—21no—
351C4—22no—
352C4—21no—
353C4—82no—
354C2—42no—
355C2—162no—
356C2#1913295511yescharacteristic
357C2#1913299411yescharacteristic
358C2#1913306411yescharacteristic
359C2#1913312411yescharacteristic
360C2#1913316311yescharacteristic
361C2#1913323011yescharacteristic
362C2#1913326311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2856C2
socleC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#2856D43
hypocenterC43#7724
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. #19134663C2semidirect
2. #19134575C2semidirect
3. #19132416C2semidirect
201. C43#7724semidirect

Maximal subgroups

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

subgroupindex
#191346632
#191345752
#191324162
C43×#28562
#772443