Finite Group Databasebeta

← #24995574

Subgroups — #24995574

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142947C211yesmaximal, characteristic
2C4×C22⋊(C43⋊C8)C211yesmaximal, characteristic
3C2×#14582635C214yesmaximal
4C43×C4⋊#95C211yesmaximal, characteristic
5C2×#13063325C411yescharacteristic, complemented
6C2×#13063304C2212yes—
7C2×C22⋊(C43⋊C8)C2212yes—
8C2×C4×C43⋊C8—21no—
9#14582805C412yescomplemented
10#14582797—21no—
11#14582797—21no—
12#14582769C411yescharacteristic, complemented
13#14582759—21no—
14#14582759—21no—
15#14582654—21no—
16#14582635—28no—
17C22×C4⋊C4×C43—21no—
18C22×C42×C43C2211yescharacteristic
19C2×#95×C43—21no—
20C2×#95×C43C2212yes—
21C22×Dic86C2×C412yes—
22C22×C43⋊C8—22no—
23#13063325—42no—
24#13063304—24no—
25#13063304—24no—
26C2×C4⋊Dic43—21no—
27C2×C4⋊Dic43—21no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43C2×C412yes—
31C2×Dic43⋊C4—22no—
32C2×C22⋊Dic43—22no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)D414yes—
35C4×C43⋊C8—42no—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C23×C4×C43—22no—
39C23×C4×C43D411yescharacteristic
40C23×C4×C43D411yescharacteristic
41C23×C4×C43C2311yescharacteristic
42C2×C4⋊C4×C43—24no—
43C2×C4⋊C4×C43—42no—
44C2×C4⋊C4×C43—42no—
45C2×C42×C43—42no—
46C2×C42×C43C2×C411yescharacteristic
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43D411yescharacteristic
49C2×C42×C43D411yescharacteristic
50#95×C43—24no—
51#95×C43—42no—
52C24×C43C2×D411yescharacteristic
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—24no—
56C22×C4×C43—41no—
57C22×C4×C43—41no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43—42no—
61C22×C4×C43—42no—
62C22×C4×C43—42no—
63C22×C4×C43—42no—
64C22×C4×C43—42no—
65C22×C4×C43—42no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43SD1612yes—
71C22×C4×C43SD1612yes—
72C22×C4×C43Q1612yes—
73C22×C4×C43Q1612yes—
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D412yes—
77C22×C4×C43#4112yes—
78C22×Dic43—22no—
79C22×Dic43—22no—
80C2×Dic86—24no—
81C2×Dic86—42no—
82C2×Dic86—42no—
83C4⋊C4×C43—48no—
84C42×C43—22no—
85C42×C43—22no—
86C42×C43—41no—
87C42×C43—41no—
88C22⋊Dic43—42no—
89C22⋊Dic43—42no—
90C4⋊Dic43—24no—
91C4⋊Dic43—42no—
92C4⋊Dic43—42no—
93C4⋊Dic43—42no—
94C4⋊Dic43—42no—
95Dic43⋊C4—44no—
96C2×C43⋊C8—24no—
97C2×C43⋊C8—42no—
98C2×C43⋊C8—42no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43C2×C22⋊C411yescharacteristic
104C23×C43#12411yescharacteristic
105C23×C43#12711yescharacteristic
106C23×C43C2×SD1611yescharacteristic
107C23×C43C2×SD1611yescharacteristic
108C23×C43C2×Q1611yescharacteristic
109C23×C43C2×Q1611yescharacteristic
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—21no—
119C2×C4×C43—21no—
120C2×C4×C43—24no—
121C2×C4×C43—24no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43—42no—
126C2×C4×C43—44no—
127C2×C4×C43—44no—
128C2×C4×C43—44no—
129C2×C4×C43—82no—
130C2×C4×C43—82no—
131C2×C4×C43—82no—
132C2×C4×C43—82no—
133C2×C4×C43#9912yes—
134C2×C4×C43#10312yes—
135C2×C4×C43#10312yes—
136C2×C4×C43#10312yes—
137C2×C4×C43#10312yes—
138C2×C4×C43#10412yes—
139C2×C4×C43C4×D412yes—
140C2×C4×C43#12112yes—
141C2×Dic43—42no—
142C2×Dic43—42no—
143C2×Dic43—42no—
144C2×Dic43—42no—
145C2×Dic43—42no—
146C2×Dic43—42no—
147Dic86—84no—
148C43⋊C8—44no—
149#9679—431nomaximal, Sylow
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43#39011yescharacteristic
163C22×C43C2×#9911yescharacteristic
164C22×C43#41011yescharacteristic
165C22×C43C2×#10311yescharacteristic
166C22×C43C2×#10311yescharacteristic
167C22×C43C2×#10411yescharacteristic
168C22×C43#42111yescharacteristic
169C22×C43#48711yescharacteristic
170C22×C43#48711yescharacteristic
171C22×C43#49211yescharacteristic
172C22×C43#49411yescharacteristic
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—22no—
176C4×C43—22no—
177C4×C43—22no—
178C4×C43—84no—
179C4×C43#32814yescomplemented
180Dic43—82no—
181Dic43—82no—
182#2857—431no—
183C4×C22⋊C8—431no—
184C2×#328—434no—
185C4⋊#95D4311yescharacteristic
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—21no—
190C2×C43C2×#32811yescharacteristic
191C2×C43#150311yescharacteristic
192C2×C43#151811yescharacteristic
193C2×C43#152011yescharacteristic
194C2×C43#195611yescharacteristic
195C2×C43#196411yescharacteristic
196C2×C43#198011yescharacteristic
197C2×C4⋊Q8—431no—
198C2×C22⋊Q8—432no—
199C22×C4⋊C4—21no—
200C22×C42C2×D4311yescharacteristic
201C2×C22⋊C8—432no—
202C2×C4×C8—861no—
203#391—432no—
204#389—861no—
205#389—861no—
206#384—431no—
207#380—861no—
208#380—861no—
209C2×#95—21no—
210C2×#95C2×D4312yes—
211#336—861no—
212#328—868no—
213C43#967911yescharacteristic, complemented, Sylow
214C22×Q8—432no—
215C23×C4—22no—
216C23×C4C22⋊D4311yescharacteristic
217C23×C4C22⋊D4311yescharacteristic
218C23×C4C22×D4311yescharacteristic
219C22×C8—862no—
220C4⋊Q8—1722no—
221C22⋊Q8—864no—
222C22⋊Q8—864no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4—42no—
226C2×C4⋊C4—432no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—862no—
232C2×C22⋊C4—862no—
233C2×C42—42no—
234C2×C42C4×D4311yescharacteristic
235C2×C42C4×D4311yescharacteristic
236C2×C42D17211yescharacteristic
237C2×C42D17211yescharacteristic
238C22⋊C8—434no—
239C22⋊C8—862no—
240C4×C8—1722no—
241#95—24no—
242#95—42no—
243#95—862no—
244#95—862no—
245C24C2×C22⋊D4311yescharacteristic
246C2×Q8—864no—
247C2×Q8—1722no—
248C2×Q8—1722no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—862no—
263C22×C4—862no—
264C22×C4(C2×D43)⋊C411yescharacteristic
265C22×C4(C2×D43)⋊C411yescharacteristic
266C22×C4(C2×D43)⋊C411yescharacteristic
267C22×C4(C2×D43)⋊C411yescharacteristic
268C22×C4#1062188312yes—
269C22×C4#1062188312yes—
270C22×C4#1062188512yes—
271C22×C4#1062188512yes—
272C22×C4C2×C4×D4311yescharacteristic
273C22×C4C2×D17211yescharacteristic
274C22×C4D4×D4312yes—
275C22×C4#1062190212yes—
276C2×C8—864no—
277C2×C8—1722no—
278C2×C8—1722no—
279C4⋊C4—48no—
280C4⋊C4—864no—
281C4⋊C4—1722no—
282C4⋊C4—1722no—
283C4⋊C4—1722no—
284C4⋊C4—1722no—
285C4⋊C4—1724no—
286C22⋊C4—1722no—
287C22⋊C4—1722no—
288C42—22no—
289C42—22no—
290C42—41no—
291C42—41no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23C2×(C2×D43)⋊C411yescharacteristic
297C23#1306331411yescharacteristic
298C23#1306332111yescharacteristic
299C23C2×#1062188311yescharacteristic
300C23C2×#1062188311yescharacteristic
301C23C2×#1062188511yescharacteristic
302C23C2×#1062188511yescharacteristic
303Q8—3444no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—1722no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4—1722no—
332C2×C4—1722no—
333C2×C4#1306323912yes—
334C2×C4#1306324812yes—
335C2×C4#1306324812yes—
336C2×C4#1306324812yes—
337C2×C4#1306324812yes—
338C2×C4#1306325312yes—
339C2×C4#1306328712yes—
340C2×C4#1306330012yes—
341C8—1724no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22#1458280011yescharacteristic
355C22C2×#1306323911yescharacteristic
356C22#1458287211yescharacteristic
357C22C2×#1306324811yescharacteristic
358C22C2×#1306324811yescharacteristic
359C22C2×#1306325311yescharacteristic
360C22#1458291711yescharacteristic
361C22#1458325111yescharacteristic
362C22#1458325111yescharacteristic
363C22#1458327111yescharacteristic
364C22#1458327811yescharacteristic
365C4—22no—
366C4—22no—
367C4—22no—
368C4—22no—
369C4—22no—
370C4—84no—
371C4—3442no—
372C4—3442no—
373C4#1458263514yescomplemented
374C2—21no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2C2×#1458263511yescharacteristic
379C2#1913309311yescharacteristic
380C2#1913315811yescharacteristic
381C2#1913316611yescharacteristic
382C2#1913539611yescharacteristic
383C2#1913543011yescharacteristic
384C2#1913551311yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×C4⋊#95C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC4⋊#95D43
hypocenterC43#9679
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
5. C2×#13063325C4semidirect
9. #14582805C4semidirect
12. #14582769C4semidirect
179. C4×C43#328semidirect
213. C43#9679semidirect
373. C4#14582635semidirect

Maximal subgroups

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

subgroupindex
#191429472
C4×C22⋊(C43⋊C8)2
C2×#145826352
C43×C4⋊#952
#967943