Finite Group Databasebeta

← #24995733

Subgroups — #24995733

Order 11008.

624 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134575C211yesmaximal, characteristic
2C2×#14582636C214yesmaximal
3#19132822C211yesmaximal, characteristic
4C43×#2857C211yesmaximal, characteristic
5C2×C4⋊(C43⋊C8)—21no—
6C2×C22⋊(C43⋊C8)C2212yes—
7C2×C43⋊#95—21no—
8C2×C43⋊#95—21no—
9C2×C43⋊#95C2212yes—
10#14582654—21no—
11#14582636—28no—
12C2×C4⋊Q8×C43C411yescharacteristic, complemented
13C2×C22⋊Q8×C43C2212yes—
14C22×C42×C43C2211yescharacteristic
15C43×#391C412yescomplemented
16C43×#389—21no—
17C43×#389—21no—
18C43×#384C411yescharacteristic, complemented
19C43×#380—21no—
20C43×#380—21no—
21C23×Dic43—22no—
22C22×C43⋊C8—22no—
23C4⋊(C43⋊C8)—42no—
24C22⋊(C43⋊C8)—24no—
25C43⋊#95—22no—
26C43⋊#95—42no—
27C43⋊#95—42no—
28C43⋊#95D414yes—
29C22×Q8×C43C2×C412yes—
30C23×C4×C43D411yescharacteristic
31C23×C4×C43D411yescharacteristic
32C23×C4×C43C2311yescharacteristic
33C4⋊Q8×C43—42no—
34C22⋊Q8×C43—24no—
35C22⋊Q8×C43—24no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43—21no—
38C2×C4⋊C4×C43—21no—
39C2×C4⋊C4×C43—21no—
40C2×C4⋊C4×C43—22no—
41C2×C4⋊C4×C43C2×C412yes—
42C2×C22⋊C4×C43—22no—
43C2×C42×C43—42no—
44C2×C42×C43C2×C411yescharacteristic
45C2×C42×C43C2×C411yescharacteristic
46C2×C42×C43D411yescharacteristic
47C2×C42×C43D411yescharacteristic
48#95×C43—22no—
49#95×C43—22no—
50C24×C43C2×D411yescharacteristic
51C2×Q8×C43—24no—
52C2×Q8×C43—42no—
53C2×Q8×C43—42no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—22no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43—41no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43C22⋊C411yescharacteristic
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×D412yes—
72C22×C4×C43#4112yes—
73C22×Dic43—24no—
74C22×Dic43—42no—
75C22×Dic43—42no—
76C22×Dic43—42no—
77C22×Dic43—42no—
78C22×Dic43—42no—
79C22×Dic43—42no—
80C4⋊C4×C43—24no—
81C4⋊C4×C43—42no—
82C4⋊C4×C43—42no—
83C4⋊C4×C43—42no—
84C4⋊C4×C43—42no—
85C4⋊C4×C43—42no—
86C4⋊C4×C43—42no—
87C22⋊C4×C43—44no—
88C42×C43—22no—
89C42×C43—22no—
90C42×C43—41no—
91C42×C43—41no—
92C2×C43⋊C8—42no—
93C2×C43⋊C8—42no—
94C2×C43⋊C8—42no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43C2×C22⋊C411yescharacteristic
100C23×C43#12112yes—
101C23×C43C2×SD1611yescharacteristic
102C23×C43C2×Q1611yescharacteristic
103C23×C43#13712yes—
104Q8×C43—84no—
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—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—42no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—42no—
122C2×C4×C43—44no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—42no—
129C2×C4×C43#9912yes—
130C2×C4×C43#10312yes—
131C2×C4×C43#10312yes—
132C2×C4×C43C4×D412yes—
133C2×C4×C43#12411yescharacteristic
134C2×C4×C43#12711yescharacteristic
135C2×Dic43—44no—
136C2×Dic43—44no—
137C2×Dic43—44no—
138C2×Dic43—82no—
139C2×Dic43—82no—
140C2×Dic43—82no—
141C2×Dic43—82no—
142C43⋊C8—82no—
143#9714—431nomaximal, Sylow
144C22×C43—22no—
145C22×C43—22no—
146C22×C43—22no—
147C22×C43—22no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43#39011yescharacteristic
153C22×C43C2×#9911yescharacteristic
154C22×C43#41011yescharacteristic
155C22×C43C2×#10311yescharacteristic
156C22×C43#41911yescharacteristic
157C22×C43#42111yescharacteristic
158C22×C43#42111yescharacteristic
159C22×C43#46112yes—
160C22×C43#46212yes—
161C4×C43—21no—
162C4×C43—22no—
163C4×C43—21no—
164C4×C43—22no—
165C4×C43—22no—
166C4×C43—22no—
167C4×C43—41no—
168C4×C43—82no—
169C4×C43—82no—
170Dic43—84no—
171#2857D4311yescharacteristic
172#1797—431no—
173C2×#328—434no—
174#1434—431no—
175C2×C43—22no—
176C2×C43—22no—
177C2×C43#151111yescharacteristic
178C2×C43#151511yescharacteristic
179C2×C43#151811yescharacteristic
180C2×C43#152011yescharacteristic
181C2×C43#196311yescharacteristic
182C2×C43#196411yescharacteristic
183C2×C43#198111yescharacteristic
184C2×C4⋊Q8Dic4311yescharacteristic, complemented
185C2×C22⋊Q8C2×D4312yes—
186C22×C42C2×D4311yescharacteristic
187C2×C4⋊C8—861no—
188C2×C22⋊C8—432no—
189#391Dic4312yescomplemented
190#389—21no—
191#389—21no—
192#384Dic4311yescharacteristic, complemented
193#380—21no—
194#380—21no—
195C2×#95—432no—
196C2×#95—861no—
197C2×#95—861no—
198#336—861no—
199#328—868no—
200C43#971411yescharacteristic, complemented, Sylow
201C22×Q8C2×Dic4312yes—
202C23×C4—862no—
203C23×C4C22⋊D4311yescharacteristic
204C23×C4C22⋊D4311yescharacteristic
205C23×C4C22×D4311yescharacteristic
206C22×C8—862no—
207C4⋊Q8—42no—
208C22⋊Q8—24no—
209C22⋊Q8—24no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4C2×Dic4312yes—
216C2×C22⋊C4—22no—
217C2×C42—42no—
218C2×C42C2×Dic4311yescharacteristic
219C2×C42C2×Dic4311yescharacteristic
220C2×C42C22⋊D4311yescharacteristic
221C2×C42C22⋊D4311yescharacteristic
222C4⋊C8—1722no—
223C22⋊C8—864no—
224#95—22no—
225#95—22no—
226#95—434no—
227#95—862no—
228#95—1722no—
229#95—1722no—
230C24C2×C22⋊D4311yescharacteristic
231C2×Q8—24no—
232C2×Q8—42no—
233C2×Q8—42no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—864no—
244C22×C4—1722no—
245C22×C4—1722no—
246C22×C4—1722no—
247C22×C4—1722no—
248C22×C4—1722no—
249C22×C4—1722no—
250C22×C4#1062188412yes—
251C22×C4#1062188512yes—
252C22×C4C22⋊Dic4311yescharacteristic
253C22×C4C22⋊Dic4311yescharacteristic
254C22×C4C22⋊Dic4311yescharacteristic
255C22×C4C22⋊Dic4311yescharacteristic
256C22×C4D4×D4312yes—
257C22×C4#1062190012yes—
258C22×C4C22×Dic4311yescharacteristic
259C22×C4C2×C22⋊D4311yescharacteristic
260C2×C8—1722no—
261C2×C8—1722no—
262C2×C8—1722no—
263C4⋊C4—24no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C22⋊C4—44no—
271C42—22no—
272C42—22no—
273C42—41no—
274C42—41no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23C2×C22⋊Dic4311yescharacteristic
280C23#1306329612yes—
281C23C2×#1062188411yescharacteristic
282C23C2×#1062188511yescharacteristic
283C23#1306335612yes—
284Q8—84no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—44no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—3442no—
310C2×C4—3442no—
311C2×C4—3442no—
312C2×C4—3442no—
313C2×C4—1724no—
314C2×C4—1724no—
315C2×C4—1724no—
316C2×C4#1306324012yes—
317C2×C4#1306324912yes—
318C2×C4#1306324912yes—
319C2×C4D4×Dic4312yes—
320C2×C4#1306331211yescharacteristic
321C2×C4#1306332111yescharacteristic
322C8—3442no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—22no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22#1458280211yescharacteristic
332C22C2×#1306324011yescharacteristic
333C22#1458287311yescharacteristic
334C22C2×#1306324911yescharacteristic
335C22#1458290811yescharacteristic
336C22#1458291611yescharacteristic
337C22#1458291611yescharacteristic
338C22#1458310112yes—
339C22#1458310612yes—
340C4—22no—
341C4—21no—
342C4—22no—
343C4—21no—
344C4—22no—
345C4—22no—
346C4—41no—
347C4—82no—
348C4—82no—
349C4—3444no—
350C2—22no—
351C2—22no—
352C2#1913312811yescharacteristic
353C2#1913314611yescharacteristic
354C2#1913315911yescharacteristic
355C2#1913316711yescharacteristic
356C2#1913542811yescharacteristic
357C2#1913543211yescharacteristic
358C2#1913551911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2857C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#2857D43
hypocenterC43#9714
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
12. C2×C4⋊Q8×C43C4semidirect
15. C43×#391C4semidirect
18. C43×#384C4semidirect
184. C2×C4⋊Q8Dic43semidirect
189. #391Dic43semidirect
192. #384Dic43semidirect
200. C43#9714semidirect

Maximal subgroups

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

subgroupindex
#191345752
C2×#145826362
#191328222
C43×#28572
#971443