Finite Group Databasebeta

← #24994979

Subgroups — #24994979

Order 11008.

454 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#19135522C211yesmaximal, characteristic
2#19135400C211yesmaximal, characteristic
3#19134464C211yesmaximal, characteristic, complemented
4C2×#14582642C211yesmaximal, characteristic
5#19132478C211yesmaximal, characteristic, complemented
6#19132429C211yesmaximal, characteristic, complemented
7C43×#1947C211yesmaximal, characteristic, complemented
8C2×#13063322C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063245—21no—
12C2×#13063245—21no—
13C2×#13063245—21no—
14C2×#13063245—21no—
15C2×#13063236—21no—
16C2×C4×C43⋊C8C2211yescharacteristic
17#14582654—21no—
18#14582642C414yescomplemented
19C2×#107×C43—21no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C43×#384C2211yescharacteristic
22C4×C4⋊C4×C43C2211yescharacteristic
23C43×#340—21no—
24C22×D172—21no—
25C22×D172—21no—
26C22×D172—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29C22×C43⋊C8D411yescharacteristic
30C22×C43⋊C8D411yescharacteristic
31#13063322—21no—
32#13063322—21no—
33#13063322—21no—
34#13063322C2×C412yes—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)C2×C412yes—
39#13063245—42no—
40#13063245—42no—
41#13063245—42no—
42#13063245—42no—
43#13063236—42no—
44C4×C43⋊C8—21no—
45C4×C43⋊C8—21no—
46C22×C8×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C42×C43—21no—
53C2×C42×C43C2311yescharacteristic
54#107×C43—42no—
55C4⋊C8×C43—21no—
56C4⋊C8×C43C2×C412yes—
57#95×C43—21no—
58C23×D43—41no—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—41no—
62C22×C4×C43C2×D411yescharacteristic
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43#4111yescharacteristic
65C2×D172—22no—
66C2×D172—22no—
67C2×D172—22no—
68C2×D172—41no—
69C2×D172—41no—
70C2×D172—41no—
71C2×D172—41no—
72C2×D172—41no—
73C2×D172—41no—
74C2×D172—41no—
75C2×D172—41no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—81no—
80C2×D172—81no—
81C2×C8×C43—22no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—81no—
93C42×C43—41no—
94C42×C43—41no—
95C42×C43C22×C411yescharacteristic
96C42×C43#4111yescharacteristic
97C42×C43#4111yescharacteristic
98C42×C43#4111yescharacteristic
99C2×C43⋊C8—21no—
100C2×C43⋊C8—21no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8D812yes—
111C23×C43#12111yescharacteristic
112C22×D43—42no—
113C22×D43—81no—
114C22×D43—81no—
115C22×D43—81no—
116C22×D43—81no—
117C22×D43—81no—
118C22×D43—81no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43#11711yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12311yescharacteristic
134C2×C4×C43#12411yescharacteristic
135C2×C4×C43#12611yescharacteristic
136C2×C4×C43C2×D811yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×C4×C43#13711yescharacteristic
144D172—42no—
145D172—42no—
146D172—42no—
147D172—42no—
148D172—82no—
149D172—82no—
150D172—81no—
151D172—81no—
152D172—81no—
153D172—81no—
154C8×C43—42no—
155C43⋊C8—22no—
156C43⋊C8—42no—
157C43⋊C8—41no—
158C43⋊C8—81no—
159#9571—431nomaximal, Sylow
160C22×C43#38811yescharacteristic
161C22×C43#45911yescharacteristic
162C22×C43#46411yescharacteristic
163C22×C43#46811yescharacteristic
164C22×C43#46911yescharacteristic
165C22×C43#47111yescharacteristic
166C22×C43#47211yescharacteristic
167C2×D43—82no—
168C2×D43—82no—
169C2×D43—82no—
170C2×D43—161no—
171C2×D43—161no—
172C2×D43—161no—
173C2×D43—161no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—81no—
177C4×C43—81no—
178C4×C43—161no—
179C4×C43C4×D811yescharacteristic
180C4×C43#44011yescharacteristic
181C4×C43#44011yescharacteristic
182C4×C43#44211yescharacteristic
183C4×C43#48011yescharacteristic
184C4×C43#48211yescharacteristic
185C4×C43#48911yescharacteristic
186C4×C43#49011yescharacteristic
187#1982—431no—
188#1957—431no—
189#1947D4311yescharacteristic, complemented
190#1770—431no—
191C2×#331—431no—
192#1296—431no—
193#1277—431no—
194C2×C43#168511yescharacteristic
195C2×C43#168711yescharacteristic
196C2×C43#169811yescharacteristic
197C2×C43#170211yescharacteristic
198C2×C43#192511yescharacteristic
199C2×C43#193111yescharacteristic
200C2×C43#193611yescharacteristic
201D43—162no—
202C2×#127—431no—
203C2×#107—21no—
204C2×C4⋊C8—431no—
205C2×C4⋊C8—431no—
206C2×C4⋊C8C2×D4311yescharacteristic
207C2×#102—861no—
208C2×#102—861no—
209C2×#102—861no—
210C2×#102—861no—
211C2×#97—861no—
212C2×C4×C8—431no—
213#384C2×D4311yescharacteristic
214C4×C4⋊C4C2×D4311yescharacteristic
215#340—21no—
216#336—861no—
217#331—434no—
218C43#957111yescharacteristic, complemented, Sylow
219C22×D4—861no—
220C22×D4—861no—
221C22×D4—861no—
222C22×C8—21no—
223C22×C8—431no—
224C22×C8—431no—
225C22×C8—861no—
226C22×C8—861no—
227#127—432no—
228#127—861no—
229#127—861no—
230#127—861no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C22⋊D4311yescharacteristic
235C2×C4⋊C4C22⋊D4311yescharacteristic
236C2×C42—21no—
237C2×C42C22×D4311yescharacteristic
238#107—42no—
239C4⋊C8—21no—
240C4⋊C8—432no—
241C4⋊C8—861no—
242C4⋊C8—861no—
243C4⋊C8—861no—
244C4⋊C8C4×D4312yes—
245#102—1722no—
246#102—1722no—
247#102—1722no—
248#102—1722no—
249#97—1722no—
250C4×C8—861no—
251C4×C8—861no—
252#95—21no—
253C24—1721no—
254C2×D4—862no—
255C2×D4—862no—
256C2×D4—862no—
257C2×D4—3441no—
258C2×D4—3441no—
259C2×D4—1721no—
260C2×D4—1721no—
261C2×D4—1721no—
262C2×D4—1721no—
263C2×D4—1721no—
264C2×D4—1721no—
265C2×D4—1721no—
266C2×D4—1721no—
267C2×D4—1721no—
268C2×D4—1721no—
269C2×D4—1721no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4D4×D4311yescharacteristic
274C22×C4#1062190011yescharacteristic
275C22×C4C2×C22⋊D4311yescharacteristic
276C2×C8—22no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—432no—
280C2×C8—861no—
281C2×C8—861no—
282C2×C8—862no—
283C2×C8—861no—
284C2×C8—861no—
285C2×C8—861no—
286C2×C8—1721no—
287C2×C8—1721no—
288C2×C8—1721no—
289C2×C8—1721no—
290C2×C8—1721no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—81no—
300C42—41no—
301C42—41no—
302C42C2×C4×D4311yescharacteristic
303C42#1062189811yescharacteristic
304C42#1062190211yescharacteristic
305C42#1062190211yescharacteristic
306C23—3441no—
307C23—3441no—
308C23—3441no—
309C23—3441no—
310C23—3441no—
311C23—3441no—
312C23—1722no—
313C23#1306329711yescharacteristic
314D4—3442no—
315D4—3442no—
316D4—3441no—
317D4—3441no—
318D4—3441no—
319D4—3441no—
320D4—1722no—
321D4—1722no—
322D4—1722no—
323D4—1722no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4#1306328311yescharacteristic
336C2×C4C4×C22⋊D4311yescharacteristic
337C2×C4#1306328711yescharacteristic
338C2×C4#1306331011yescharacteristic
339C2×C4#1306331411yescharacteristic
340C2×C4#1306332011yescharacteristic
341C2×C4D8×D4311yescharacteristic
342C2×C4#1306334811yescharacteristic
343C2×C4#1306334911yescharacteristic
344C2×C4#1306335011yescharacteristic
345C2×C4#1306335011yescharacteristic
346C2×C4#1306335111yescharacteristic
347C2×C4#1306335611yescharacteristic
348C2×C4#1306335711yescharacteristic
349C8—42no—
350C8—862no—
351C8—3441no—
352C8—1721no—
353C8—1722no—
354C22—3442no—
355C22—3442no—
356C22—3442no—
357C22—6881no—
358C22—6881no—
359C22—6881no—
360C22—6881no—
361C22#1458278911yescharacteristic
362C22#1458309211yescharacteristic
363C22#1458312311yescharacteristic
364C22#1458314711yescharacteristic
365C22#1458315011yescharacteristic
366C22#1458316411yescharacteristic
367C22#1458316711yescharacteristic
368C4—21no—
369C4—21no—
370C4—81no—
371C4—81no—
372C4—161no—
373C4#1458298111yescharacteristic
374C4#1458299711yescharacteristic
375C4#1458299811yescharacteristic
376C4#1458300911yescharacteristic
377C4#1458321411yescharacteristic
378C4#1458322611yescharacteristic
379C4#1458326111yescharacteristic
380C4#1458326511yescharacteristic
381C2—6882no—
382C2#1913406211yescharacteristic
383C2#1913407211yescharacteristic
384C2#1913413711yescharacteristic
385C2#1913416511yescharacteristic
386C2#1913521411yescharacteristic
387C2#1913525611yescharacteristic
388C2#1913529111yescharacteristic
subgroupG/H
centerC23#13063297
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1947C2
socleC23×C43#121
prime radicalC2×#13063322C22
cosocleC2×C42×C43C23
hypercenter#1947D43
hypocenterC43#9571
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
3. #19134464C2semidirect
5. #19132478C2semidirect
6. #19132429C2semidirect
7. C43×#1947C2semidirect
18. #14582642C4semidirect
189. #1947D43semidirect
218. C43#9571semidirect

Maximal subgroups

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

subgroupindex
#191355222
#191354002
#191344642
C2×#145826422
#191324782
#191324292
C43×#19472
#957143