Finite Group Databasebeta

← #24992137

Subgroups — #24992137

Order 11008.

586 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137260C211yesmaximal, characteristic
2#19132913C211yesmaximal, characteristic
3C2×#14582624C212yesmaximal, complemented
4#19132441C212yesmaximal, complemented
5C43×#2972C211yesmaximal, characteristic
6C2×#13063306C411yescharacteristic
7C22×Dic43⋊C4C2211yescharacteristic
8C2×C22⋊(C43⋊C8)C2212yes—
9#14582794—21no—
10#14582793—21no—
11#14582783—21no—
12#14582779C411yescharacteristic
13#14582772—21no—
14#14582771C411yescharacteristic
15#14582760C411yescharacteristic
16C4×C22⋊Dic43C2211yescharacteristic
17#14582625—21no—
18#14582624—24no—
19#14582623—21no—
20C2×C4×D4×C43C2211yescharacteristic
21C8×D4×C43—24no—
22C43×#431—21no—
23C2×C22⋊C8×C43—21no—
24C2×C22⋊C8×C43C2212yes—
25C23×Dic43C2×C411yescharacteristic
26C23×Dic43C2×C411yescharacteristic
27C22×C43⋊C8—22no—
28#13063306—22no—
29#13063306C814yescomplemented
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—22no—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—22no—
35C2×Dic43⋊C4—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43C2×C411yescharacteristic
39C2×C22⋊Dic43C2×C411yescharacteristic
40C2×C4×Dic43—21no—
41C22⋊(C43⋊C8)—22no—
42C22⋊(C43⋊C8)—22no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C22×D4×C43C2×C411yescharacteristic
49C23×C4×C43D411yescharacteristic
50C23×C4×C43C2311yescharacteristic
51C22×C8×C43—22no—
52C22×C8×C43—22no—
53C4×D4×C43—22no—
54C4×D4×C43—22no—
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C22⋊C4×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43D411yescharacteristic
58C2×C42×C43D411yescharacteristic
59C4⋊C8×C43—22no—
60C22⋊C8×C43—22no—
61C22⋊C8×C43—22no—
62C22⋊C8×C43D414yes—
63C4×C8×C43—22no—
64C24×C43C22⋊C411yescharacteristic
65C24×C43C22×C411yescharacteristic
66C2×D4×C43—22no—
67C2×D4×C43—22no—
68C2×D4×C43C2×C812yes—
69C2×D4×C43M1612yes—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—81no—
73C22×C4×C43—81no—
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D412yes—
80C22×C4×C43#4112yes—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—22no—
86C22×Dic43—22no—
87C22×Dic43—21no—
88C22×Dic43—22no—
89C22×Dic43—81no—
90C22×Dic43C2×C812yescomplemented
91C2×C8×C43—24no—
92C2×C8×C43—82no—
93C2×C8×C43—82no—
94C4⋊C4×C43—22no—
95C22⋊C4×C43—22no—
96C22⋊C4×C43—22no—
97C42×C43—21no—
98C42×C43—21no—
99C22⋊Dic43—24no—
100C22⋊Dic43—21no—
101C22⋊Dic43—22no—
102C22⋊Dic43—81no—
103C22⋊Dic43C2×C812yescomplemented
104Dic43⋊C4—24no—
105Dic43⋊C4—41no—
106Dic43⋊C4—42no—
107Dic43⋊C4—41no—
108Dic43⋊C4—81no—
109C4×Dic43—81no—
110C2×C43⋊C8—42no—
111C2×C43⋊C8—82no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43C22⋊C812yes—
119C23×C43C2×C22⋊C411yescharacteristic
120C23×C43C4×D412yes—
121C23×C43C22×C811yescharacteristic
122C23×C43C2×M1611yescharacteristic
123C23×C43#13112yes—
124D4×C43—24no—
125D4×C43—24no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—42no—
131C2×C4×C43—41no—
132C2×C4×C43—42no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—81no—
138C2×C4×C43C22⋊C812yes—
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43#12112yes—
141C2×C4×C43#12311yescharacteristic
142C2×Dic43—22no—
143C2×Dic43—22no—
144C2×Dic43—24no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—42no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—82no—
157C8×C43—44no—
158C43⋊C8—82no—
159#9108—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—22no—
162C22×C43—21no—
163C22×C43—22no—
164C22×C43—22no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—42no—
168C22×C43—42no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—81no—
172C22×C43#38611yescharacteristic
173C22×C43C2×C22⋊C811yescharacteristic
174C22×C43#40811yescharacteristic
175C22×C43C8×D412yes—
176C22×C43#43512yes—
177C4×C43—22no—
178C4×C43—22no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—41no—
182C4×C43—41no—
183Dic43—42no—
184Dic43—42no—
185Dic43—81no—
186Dic43—81no—
187#2972D4311yescharacteristic
188#2322—431no—
189#1459—431no—
190C2×#324—432no—
191#1282—432no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—22no—
195C2×C43—22no—
196C2×C43—42no—
197C2×C43#186911yescharacteristic
198C2×C43#191311yescharacteristic
199C2×C43#191511yescharacteristic
200C2×#123—431no—
201C2×C4×D4C2×D4311yescharacteristic
202C22×C4⋊C4—431no—
203C8×D4—24no—
204#431—21no—
205C2×C22⋊C8—21no—
206C2×C22⋊C8—432no—
207C2×C22⋊C8C2×D4312yes—
208#389—861no—
209#388—861no—
210#387—861no—
211#386—431no—
212#385—431no—
213#385—861no—
214#381—431no—
215C4×C22⋊C4—431no—
216#324—861no—
217#324—864no—
218#323—861no—
219C43#910811yescharacteristic, complemented, Sylow
220C22×D4C4×D4311yescharacteristic
221C23×C4—431no—
222C23×C4—431no—
223C23×C4C22⋊D4311yescharacteristic
224C23×C4C22×D4311yescharacteristic
225C22×C8—22no—
226C22×C8—22no—
227C22×C8—862no—
228#123—434no—
229#123—862no—
230C4×D4—22no—
231C4×D4—22no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—862no—
236C2×C4⋊C4—862no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4D17211yescharacteristic
239C2×C22⋊C4—431no—
240C2×C22⋊C4—431no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4C4×D4311yescharacteristic
244C2×C22⋊C4D17211yescharacteristic
245C2×C42—861no—
246C2×C42C22⋊D4311yescharacteristic
247C4⋊C8—22no—
248C22⋊C8—22no—
249C22⋊C8—22no—
250C22⋊C8—862no—
251C22⋊C8—862no—
252C22⋊C8C22⋊D4314yes—
253C4×C8—22no—
254#95—861no—
255#95—861no—
256#95—861no—
257#95—861no—
258#95—861no—
259C24(C2×D43)⋊C411yescharacteristic
260C24C2×C4×D4311yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4C8×D4312yes—
264C2×D4#1062187212yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—81no—
268C22×C4—81no—
269C22×C4—432no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—862no—
273C22×C4—861no—
274C22×C4—862no—
275C22×C4—862no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4—3441no—
279C22×C4(C2×D43)⋊C411yescharacteristic
280C22×C4(C2×D43)⋊C411yescharacteristic
281C22×C4(C2×D43)⋊C411yescharacteristic
282C22×C4C2×D17211yescharacteristic
283C22×C4#1062189812yes—
284C22×C4C2×C22⋊D4312yes—
285C22×C4C2×C22⋊D4311yescharacteristic
286C2×C8—24no—
287C2×C8—82no—
288C2×C8—82no—
289C2×C8—3442no—
290C2×C8—1722no—
291C4⋊C4—22no—
292C4⋊C4—864no—
293C4⋊C4—3441no—
294C4⋊C4—1721no—
295C4⋊C4—1722no—
296C4⋊C4—1721no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—432no—
300C22⋊C4—864no—
301C22⋊C4—861no—
302C22⋊C4—862no—
303C22⋊C4—3441no—
304C42—21no—
305C42—21no—
306C42—3441no—
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23(C2×D43)⋊C812yes—
314C23C2×(C2×D43)⋊C411yescharacteristic
315C23C4×C22⋊D4312yes—
316C23C2×C8×D4311yescharacteristic
317C23C2×#1062187211yescharacteristic
318C23#1306333112yes—
319D4—24no—
320D4—24no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—862no—
334C2×C4—862no—
335C2×C4—864no—
336C2×C4—3442no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1722no—
347C2×C4—1721no—
348C2×C4(C2×D43)⋊C812yes—
349C2×C4#1306329411yescharacteristic
350C2×C4#1306329912yes—
351C2×C4#1306330811yescharacteristic
352C8—44no—
353C8—3442no—
354C22—21no—
355C22—22no—
356C22—21no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22#1458277811yescharacteristic
367C22C2×(C2×D43)⋊C811yescharacteristic
368C22#1458286511yescharacteristic
369C22C8×C22⋊D4312yes—
370C22#1458297012yes—
371C4—21no—
372C4—22no—
373C4—21no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—3441no—
378C4—3441no—
379C4—1722no—
380C4—1722no—
381C2—21no—
382C2—21no—
383C2—22no—
384C2—22no—
385C2—42no—
386C2#1913488711yescharacteristic
387C2#1913513711yescharacteristic
388C2#1913514711yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC23×C43C22×C8
FrattiniC23×C4C22×D43
FittingC43×#2972C2
socleC22×C43#386
prime radicalC22×D4×C43C2×C4
cosocleC23×C4×C43C23
hypercenter#2972D43
hypocenterC43#9108
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2972

Complements

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

NH ≅ G/Ntype
3. C2×#14582624C2semidirect
4. #19132441C2semidirect
29. #13063306C8semidirect
90. C22×Dic43C2×C8semidirect
103. C22⋊Dic43C2×C8semidirect
219. C43#9108semidirect

Maximal subgroups

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

subgroupindex
#191372602
#191329132
C2×#145826242
#191324412
C43×#29722
#910843