Finite Group Databasebeta

← #24995840

Subgroups — #24995840

Order 11008.

654 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583275C211yesmaximal, characteristic
2#19135523C211yesmaximal, characteristic, complemented
3#19135521C211yesmaximal, characteristic, complemented
4#19134460C211yesmaximal, characteristic, complemented
5C2×#14582651C211yesmaximal, characteristic, complemented
6C2×#14582642C211yesmaximal, characteristic, complemented
7C2×C43×#331C211yesmaximal, characteristic, complemented
8C22×#10621882—21no—
9C22×#10621882—21no—
10C2×#13063322C2211yescharacteristic
11#14583275—22no—
12#14583275C414yescomplemented
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063247—22no—
15C2×#13063246—22no—
16C2×C4×C43⋊C8C2211yescharacteristic
17C2×C8×Dic43—21no—
18C4×C4⋊Dic43C2211yescharacteristic
19#14582653—21no—
20#14582651—22no—
21#14582642—22no—
22C2×#127×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C43×#331—22no—
26C22×D172—21no—
27C22×D172—21no—
28C22×D172—21no—
29C2×#10621882—24no—
30C2×#10621882—24no—
31C2×#10621882—42no—
32C2×#10621882—42no—
33C2×#10621882—42no—
34C2×#10621882—42no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8D411yescharacteristic
37C22×C43⋊C8D411yescharacteristic
38#13063322—21no—
39#13063322—21no—
40#13063322—21no—
41#13063322C2×C412yes—
42C2×C4⋊Dic43D412yes—
43C2×C4×Dic43—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)—21no—
46#13063247—44no—
47#13063246—44no—
48C4×C43⋊C8C2×C412yes—
49C4×C43⋊C8D412yes—
50C8×Dic43—42no—
51C43⋊#95—21no—
52C22×D4×C43—21no—
53C22×D4×C43—21no—
54C22×D4×C43—21no—
55C22×C8×C43—21no—
56C22×C8×C43—21no—
57#127×C43—21no—
58#127×C43—21no—
59#127×C43—21no—
60#127×C43C2×C412yes—
61C2×C42×C43C2311yescharacteristic
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43D412yes—
66C24×C43—41no—
67C23×D43—41no—
68C2×D4×C43—22no—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—42no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—42no—
78C2×D4×C43—41no—
79C2×D4×C43—41no—
80C2×D4×C43—82no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×Dic43—22no—
85C2×D172—22no—
86C2×D172—22no—
87C2×D172—22no—
88C2×D172—41no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—42no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—42no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—82no—
98C2×C8×C43—22no—
99C2×C8×C43—41no—
100C2×C8×C43—41no—
101C2×C8×C43—41no—
102C2×C8×C43—42no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43#4111yescharacteristic
107#10621882—48no—
108#10621882—48no—
109C4⋊Dic43—22no—
110C4⋊Dic43D814yescomplemented
111C4×Dic43—41no—
112C4×Dic43—41no—
113C2×C43⋊C8—21no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—42no—
117C2×C43⋊C8C22⋊C412yes—
118C2×C43⋊C8C22⋊C412yes—
119C2×C43⋊C8D812yes—
120C2×C43⋊C8SD1612yes—
121C23×C43—42no—
122C23×C43—81no—
123C23×C43—81no—
124C23×C43—82no—
125C23×C43—82no—
126C23×C43#12111yescharacteristic
127C22×D43—42no—
128C22×D43—81no—
129C22×D43—81no—
130C22×D43—82no—
131C22×D43—82no—
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—44no—
135D4×C43—82no—
136D4×C43—82no—
137D4×C43—81no—
138D4×C43—81no—
139D4×C43—81no—
140D4×C43—81no—
141C2×C4×C43—22no—
142C2×C4×C43C2×C22⋊C411yescharacteristic
143C2×C4×C43C4×D411yescharacteristic
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12411yescharacteristic
147C2×C4×C43#12711yescharacteristic
148C2×C4×C43C2×D811yescharacteristic
149C2×C4×C43C2×D812yes—
150C2×C4×C43C2×SD1611yescharacteristic
151C2×C4×C43#13512yes—
152C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×Dic43—24no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157D172—42no—
158D172—42no—
159D172—44no—
160D172—82no—
161D172—82no—
162D172—81no—
163D172—81no—
164D172—81no—
165D172—81no—
166C8×C43—42no—
167C8×C43—81no—
168C43⋊C8—22no—
169C43⋊C8—81no—
170C43⋊C8#10214yescomplemented
171#9734—431nomaximal, Sylow
172C22×C43—82no—
173C22×C43—82no—
174C22×C43—82no—
175C22×C43—162no—
176C22×C43—162no—
177C22×C43#39011yescharacteristic
178C22×C43#45911yescharacteristic
179C22×C43#46011yescharacteristic
180C22×C43#46612yes—
181C22×C43#47212yes—
182C2×D43—82no—
183C2×D43—82no—
184C2×D43—82no—
185C2×D43—162no—
186C2×D43—162no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43C2×#10211yescharacteristic
190C4×C43#41811yescharacteristic
191C4×C43C4×D812yes—
192C4×C43#45911yescharacteristic
193C4×C43#46011yescharacteristic
194C4×C43#49311yescharacteristic
195C4×C43#49511yescharacteristic
196Dic43—44no—
197C2×#493—431no—
198#1982—431no—
199#1982—431no—
200C8×C4⋊C4—431no—
201C2×#335—431no—
202C2×#331—431no—
203C2×#331D4311yescharacteristic, complemented
204C2×C43—162no—
205C2×C43#166712yes—
206C2×C43#166812yes—
207C2×C43#197011yescharacteristic
208C2×C43#197811yescharacteristic
209C2×C43#198211yescharacteristic
210D43—162no—
211C22×D8—861no—
212C22×D8—861no—
213C2×#127—431no—
214C2×#127C2×D4311yescharacteristic
215#493—434no—
216#493—862no—
217C2×C4⋊C8—431no—
218C2×C4⋊C8C2×D4311yescharacteristic
219C2×C4⋊C8C2×D4311yescharacteristic
220C2×#102—862no—
221C2×#102—862no—
222C2×C4×C8—431no—
223C2×C4×C8—861no—
224C4×C4⋊C4—431no—
225#336—861no—
226#335—862no—
227#331—22no—
228#331—862no—
229C43#973411yescharacteristic, complemented, Sylow
230C22×D4—21no—
231C22×D4—21no—
232C22×D4—21no—
233C22×D4—861no—
234C22×D4—861no—
235C22×D4—861no—
236C2×D8—864no—
237C2×D8—864no—
238C2×D8—1722no—
239C2×D8—1722no—
240C2×D8—1722no—
241C2×D8—1722no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—431no—
245C22×C8—431no—
246C22×C8—861no—
247#127—21no—
248#127—21no—
249#127—21no—
250#127—432no—
251#127—861no—
252#127—861no—
253#127—861no—
254#127C4×D4312yes—
255C2×C4⋊C4—432no—
256C2×C42—861no—
257C2×C42C22×D4311yescharacteristic
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—861no—
262C4⋊C8—861no—
263C4⋊C8C22⋊D4312yes—
264#102—1724no—
265#102—1724no—
266C4×C8—432no—
267C4×C8—432no—
268C4×C8—1722no—
269#95—861no—
270C24—41no—
271C24—1721no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—82no—
285C2×D4—862no—
286C2×D4—862no—
287C2×D4—862no—
288C2×D4—3442no—
289C2×D4—1721no—
290C2×D4—1721no—
291C2×D4—1721no—
292C2×D4—1722no—
293C2×D4—1721no—
294C2×D4—1721no—
295C2×D4—1722no—
296C2×D4—1721no—
297C2×D4—1721no—
298C22×C4—862no—
299C22×C4#1062189811yescharacteristic
300C22×C4D4×D4311yescharacteristic
301C22×C4D4×D4311yescharacteristic
302D8—1728no—
303D8—1728no—
304C2×C8—22no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—42no—
309C2×C8—432no—
310C2×C8—432no—
311C2×C8—432no—
312C2×C8—432no—
313C2×C8—861no—
314C2×C8—861no—
315C2×C8—1721no—
316C2×C8—1722no—
317C4⋊C4—434no—
318C4⋊C4—862no—
319C42—1721no—
320C42—1721no—
321C42C2×C4×D4311yescharacteristic
322C42D4×D4311yescharacteristic
323C42#1062190011yescharacteristic
324C42C2×C22⋊D4311yescharacteristic
325C23—42no—
326C23—81no—
327C23—81no—
328C23—82no—
329C23—82no—
330C23—3441no—
331C23—3441no—
332C23—3442no—
333C23—3442no—
334C23—1722no—
335C23#1306329811yescharacteristic
336D4—42no—
337D4—42no—
338D4—44no—
339D4—82no—
340D4—82no—
341D4—81no—
342D4—81no—
343D4—81no—
344D4—81no—
345D4—3442no—
346D4—3442no—
347D4—3441no—
348D4—3441no—
349D4—3441no—
350D4—3441no—
351D4—1722no—
352D4—1722no—
353D4—1724no—
354C2×C4—22no—
355C2×C4—864no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4C22⋊C4×D4311yescharacteristic
359C2×C4(C22⋊D43)⋊C411yescharacteristic
360C2×C4C4×C22⋊D4311yescharacteristic
361C2×C4#1306329711yescharacteristic
362C2×C4#1306331111yescharacteristic
363C2×C4#1306332111yescharacteristic
364C2×C4D8×D4311yescharacteristic
365C2×C4D8×D4312yes—
366C2×C4SD16×D4311yescharacteristic
367C2×C4#1306334612yes—
368C2×C4#1306334911yescharacteristic
369C2×C4#1306335211yescharacteristic
370C8—42no—
371C8—81no—
372C8—434no—
373C8—862no—
374C8—3441no—
375C22—82no—
376C22—82no—
377C22—82no—
378C22—162no—
379C22—162no—
380C22—3442no—
381C22—3442no—
382C22—3442no—
383C22—6882no—
384C22—6882no—
385C22#1458279911yescharacteristic
386C22#1458309311yescharacteristic
387C22#1458309811yescharacteristic
388C22#1458313412yes—
389C22#1458316812yes—
390C4—21no—
391C4—21no—
392C4—1724no—
393C4#102×D4311yescharacteristic
394C4#1458290211yescharacteristic
395C4#1458297912yes—
396C4#1458309211yescharacteristic
397C4#1458309711yescharacteristic
398C4#1458327411yescharacteristic
399C4#1458328011yescharacteristic
400C2—162no—
401C2—6882no—
402C2#1913394912yes—
403C2#1913395412yes—
404C2#1913545811yescharacteristic
405C2#1913550211yescharacteristic
406C2#1913552011yescharacteristic
subgroupG/H
centerC23#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#331C2
socleC23×C43#121
prime radicalC2×#14583275C2
cosocleC2×C42×C43C23
hypercenterC2×#331D43
hypocenterC43#9734
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #19135523C2semidirect
3. #19135521C2semidirect
4. #19134460C2semidirect
5. C2×#14582651C2semidirect
6. C2×#14582642C2semidirect
7. C2×C43×#331C2semidirect
12. #14583275C4semidirect
110. C4⋊Dic43D8semidirect
170. C43⋊C8#102semidirect
203. C2×#331D43semidirect
229. C43#9734semidirect

Maximal subgroups

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

subgroupindex
C2×#145832752
#191355232
#191355212
#191344602
C2×#145826512
C2×#145826422
C2×C43×#3312
#973443