Finite Group Databasebeta

← #25001139

Subgroups — #25001139

Order 11008.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135522C211yesmaximal, characteristic
2#19135400C211yesmaximal, characteristic
3#19135314C211yesmaximal, characteristic, complemented
4C2×#14582651C211yesmaximal, characteristic, complemented
5C2×#14582642C211yesmaximal, characteristic
6#19132478C211yesmaximal, characteristic, complemented
7C43×#1947C211yesmaximal, characteristic, complemented
8C2×#13063322C2211yescharacteristic
9C2×C4⋊(C43⋊C8)—21no—
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063245—21no—
13C2×#13063245—21no—
14C2×#13063245—21no—
15C2×#13063245—21no—
16C2×C4×C43⋊C8C2211yescharacteristic
17#14582654—21no—
18#14582651—22no—
19#14582642—22no—
20C2×#107×C43—21no—
21C2×C4⋊C8×C43C2211yescharacteristic
22C43×#384C2211yescharacteristic
23C4×C4⋊C4×C43C2211yescharacteristic
24C43×#340—21no—
25C22×D172—21no—
26C22×D172—21no—
27C22×D172—21no—
28C22×C43⋊C8—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8D411yescharacteristic
31C22×C43⋊C8D411yescharacteristic
32#13063322—21no—
33#13063322—21no—
34#13063322—21no—
35#13063322Q812yes—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—42no—
41#13063245—42no—
42#13063245—42no—
43#13063245—42no—
44#13063245—42no—
45C4×C43⋊C8—21no—
46C4×C43⋊C8—21no—
47C22×C8×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C42×C43—21no—
54C2×C42×C43C2311yescharacteristic
55#107×C43—42no—
56C4⋊C8×C43—21no—
57C4⋊C8×C43D412yes—
58#95×C43—21no—
59C23×D43—41no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—41no—
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43#4111yescharacteristic
66C2×D172—22no—
67C2×D172—22no—
68C2×D172—22no—
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—41no—
80C2×D172—81no—
81C2×D172—81no—
82C2×C8×C43—22no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
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—
93C4⋊C4×C43D812yes—
94C42×C43—41no—
95C42×C43—41no—
96C42×C43C2×D411yescharacteristic
97C42×C43C2×Q811yescharacteristic
98C42×C43#4111yescharacteristic
99C42×C43#4111yescharacteristic
100C2×C43⋊C8—21no—
101C2×C43⋊C8—21no—
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⋊C8—41no—
111C2×C43⋊C8D812yes—
112C23×C43#12111yescharacteristic
113C22×D43—42no—
114C22×D43—81no—
115C22×D43—81no—
116C22×D43—81no—
117C22×D43—81no—
118C22×D43—81no—
119C22×D43—81no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—22no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43#12111yescharacteristic
132C2×C4×C43#12111yescharacteristic
133C2×C4×C43C22⋊Q811yescharacteristic
134C2×C4×C43C22⋊Q811yescharacteristic
135C2×C4×C43C22⋊Q811yescharacteristic
136C2×C4×C43#12611yescharacteristic
137C2×C4×C43C2×D811yescharacteristic
138C2×C4×C43C2×D811yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C43#13711yescharacteristic
144C2×C4×C43#13711yescharacteristic
145D172—42no—
146D172—42no—
147D172—42no—
148D172—42no—
149D172—82no—
150D172—82no—
151D172—81no—
152D172—81no—
153D172—81no—
154D172—81no—
155C8×C43—42no—
156C43⋊C8—22no—
157C43⋊C8—41no—
158C43⋊C8—81no—
159C43⋊C8—81no—
160#10591—431nomaximal, Sylow
161C22×C43#39611yescharacteristic
162C22×C43#45911yescharacteristic
163C22×C43#46411yescharacteristic
164C22×C43#46611yescharacteristic
165C22×C43#46811yescharacteristic
166C22×C43#47111yescharacteristic
167C22×C43#47211yescharacteristic
168C2×D43—82no—
169C2×D43—82no—
170C2×D43—82no—
171C2×D43—161no—
172C2×D43—161no—
173C2×D43—161no—
174C2×D43—161no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—42no—
178C4×C43—81no—
179C4×C43—161no—
180C4×C43#45911yescharacteristic
181C4×C43#46411yescharacteristic
182C4×C43#46611yescharacteristic
183C4×C43#46811yescharacteristic
184C4×C43#47411yescharacteristic
185C4×C43#47411yescharacteristic
186C4×C43#47811yescharacteristic
187C4×C43#47811yescharacteristic
188#1982—431no—
189#1957—431no—
190#1947D4311yescharacteristic, complemented
191#1939—431no—
192C2×#335—431no—
193C2×#331—431no—
194#1296—431no—
195C2×C43#166711yescharacteristic
196C2×C43#168211yescharacteristic
197C2×C43#168511yescharacteristic
198C2×C43#169811yescharacteristic
199C2×C43#206311yescharacteristic
200C2×C43#206711yescharacteristic
201C2×C43#206711yescharacteristic
202D43—162no—
203C2×#127—431no—
204C2×#107—21no—
205C2×C4⋊C8—431no—
206C2×C4⋊C8—431no—
207C2×C4⋊C8—861no—
208C2×C4⋊C8C2×D4311yescharacteristic
209C2×#102—861no—
210C2×#102—861no—
211C2×#102—861no—
212C2×#102—861no—
213C2×C4×C8—431no—
214#384C2×D4311yescharacteristic
215C4×C4⋊C4C2×D4311yescharacteristic
216#340—21no—
217#336—861no—
218#335—862no—
219#331—862no—
220C43#1059111yescharacteristic, complemented, Sylow
221C22×D4—861no—
222C22×D4—861no—
223C22×D4—861no—
224C22×C8—21no—
225C22×C8—431no—
226C22×C8—431no—
227C22×C8—861no—
228C22×C8—861no—
229#127—432no—
230#127—861no—
231#127—861no—
232#127—861no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C22⋊D4311yescharacteristic
237C2×C4⋊C4C22⋊D4311yescharacteristic
238C2×C42—21no—
239C2×C42C22×D4311yescharacteristic
240#107—42no—
241C4⋊C8—21no—
242C4⋊C8—861no—
243C4⋊C8—861no—
244C4⋊C8—861no—
245C4⋊C8—861no—
246C4⋊C8—1722no—
247C4⋊C8D17212yes—
248#102—1722no—
249#102—1722no—
250#102—1722no—
251#102—1722no—
252C4×C8—861no—
253C4×C8—861no—
254#95—21no—
255C24—1721no—
256C2×D4—862no—
257C2×D4—862no—
258C2×D4—862no—
259C2×D4—3441no—
260C2×D4—3441no—
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—
270C2×D4—1721no—
271C2×D4—1721no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4D4×D4311yescharacteristic
276C22×C4#1062190011yescharacteristic
277C22×C4C2×C22⋊D4311yescharacteristic
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—432no—
282C2×C8—861no—
283C2×C8—861no—
284C2×C8—861no—
285C2×C8—861no—
286C2×C8—861no—
287C2×C8—1721no—
288C2×C8—1721no—
289C2×C8—1721no—
290C2×C8—1721no—
291C2×C8—1721no—
292C2×C8—1721no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C4⋊C4#1062188212yes—
302C42—41no—
303C42—41no—
304C42C2×D17211yescharacteristic
305C42#1062189811yescharacteristic
306C42Q8×D4311yescharacteristic
307C42#1062190211yescharacteristic
308C23—3441no—
309C23—3441no—
310C23—3441no—
311C23—3441no—
312C23—3441no—
313C23—3441no—
314C23—1722no—
315C23#1306329711yescharacteristic
316D4—3442no—
317D4—3442no—
318D4—3441no—
319D4—3441no—
320D4—3441no—
321D4—3441no—
322D4—1722no—
323D4—1722no—
324D4—1722no—
325D4—1722no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#1306329911yescharacteristic
338C2×C4#1306330011yescharacteristic
339C2×C4#1306330111yescharacteristic
340C2×C4#1306330311yescharacteristic
341C2×C4#1306330511yescharacteristic
342C2×C4#1306332011yescharacteristic
343C2×C4D8×D4311yescharacteristic
344C2×C4C2×#1062188211yescharacteristic
345C2×C4#1306334511yescharacteristic
346C2×C4#1306334811yescharacteristic
347C2×C4#1306334911yescharacteristic
348C2×C4#1306335011yescharacteristic
349C2×C4#1306335611yescharacteristic
350C2×C4#1306335711yescharacteristic
351C8—42no—
352C8—862no—
353C8—3441no—
354C8—3441no—
355C8—1721no—
356C22—3442no—
357C22—3442no—
358C22—3442no—
359C22—6881no—
360C22—6881no—
361C22—6881no—
362C22—6881no—
363C22#1458282111yescharacteristic
364C22#1458309211yescharacteristic
365C22#1458312311yescharacteristic
366C22#1458313311yescharacteristic
367C22#1458314711yescharacteristic
368C22#1458316411yescharacteristic
369C22#1458316711yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—161no—
375C4#1458309411yescharacteristic
376C4#1458312111yescharacteristic
377C4#1458313611yescharacteristic
378C4#1458314611yescharacteristic
379C4#1458317611yescharacteristic
380C4#1458317811yescharacteristic
381C4#1458319611yescharacteristic
382C4#1458320211yescharacteristic
383C2—6882no—
384C2#1913394811yescharacteristic
385C2#1913404111yescharacteristic
386C2#1913406211yescharacteristic
387C2#1913413711yescharacteristic
388C2#1913595211yescharacteristic
389C2#1913597811yescharacteristic
390C2#1913598011yescharacteristic
subgroupG/H
centerC23#13063297
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1947C2
socleC23×C43#121
prime radicalC2×#13063322C22
hypercenter#1947D43
hypocenterC43#10591
LCSG ▷ C2×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. #19135314C2semidirect
4. C2×#14582651C2semidirect
6. #19132478C2semidirect
7. C43×#1947C2semidirect
190. #1947D43semidirect
220. C43#10591semidirect

Maximal subgroups

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

subgroupindex
#191355222
#191354002
#191353142
C2×#145826512
C2×#145826422
#191324782
C43×#19472
#1059143