Finite Group Databasebeta

← #25000409

Subgroups — #25000409

Order 11008.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583099C211yesmaximal, characteristic
2#19135401C211yesmaximal, characteristic
3#19134600C211yesmaximal, characteristic, complemented
4C2×#14582650C211yesmaximal, characteristic, complemented
5C2×#14582642C211yesmaximal, characteristic
6#19132479C211yesmaximal, characteristic, complemented
7C43×#1984C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C2×#13063322C2211yescharacteristic
10#14583099—22no—
11#14583099—22no—
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063249—21no—
15C2×#13063247—21no—
16C2×#13063247—21no—
17C2×#13063245—21no—
18#14582769C2211yescharacteristic
19#14582661—21no—
20#14582650—22no—
21#14582642—22no—
22C2×C4×Q8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4×C8×C43C2211yescharacteristic
25C43×#336—21no—
26C43×#336—21no—
27C22×D172—21no—
28C22×D172—21no—
29C22×D172—21no—
30C2×#10621884—24no—
31C2×#10621884—42no—
32C2×#10621884—42no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35#13063322—21no—
36#13063322—21no—
37#13063322—21no—
38#13063322D412yes—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)D412yes—
46#13063249—42no—
47#13063247—42no—
48#13063247—42no—
49#13063245—24no—
50C22×Q8×C43D411yescharacteristic
51C22×C8×C43—21no—
52C22×C8×C43D411yescharacteristic
53C22×C8×C43D411yescharacteristic
54C4×Q8×C43—21no—
55C4×Q8×C43—21no—
56C4×Q8×C43—21no—
57C4×Q8×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43D411yescharacteristic
60C2×C42×C43—21no—
61C2×C42×C43C2311yescharacteristic
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C4×C8×C43—21no—
65C4×C8×C43—21no—
66C23×D43—41no—
67C2×Q8×C43—21no—
68C2×Q8×C43—21no—
69C2×Q8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43SD1612yes—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43#4111yescharacteristic
78C22×Dic43—41no—
79C2×D172—22no—
80C2×D172—22no—
81C2×D172—22no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×D172—41no—
93C2×D172—81no—
94C2×D172—81no—
95C2×C8×C43—21no—
96C2×C8×C43—21no—
97C2×C8×C43—21no—
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C2×C8×C43—41no—
101C2×C8×C43—41no—
102C2×C8×C43—41no—
103C2×C8×C43SD1612yescomplemented
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C42×C43—41no—
109C42×C43—41no—
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43#4111yescharacteristic
113C42×C43#4111yescharacteristic
114#10621884—48no—
115C4⋊Dic43—41no—
116C4⋊Dic43—41no—
117C4⋊Dic43—41no—
118C4⋊Dic43—41no—
119C4⋊Dic43—81no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C23×C43#12111yescharacteristic
127C22×D43—42no—
128C22×D43—81no—
129C22×D43—81no—
130C22×D43—81no—
131C22×D43—81no—
132C22×D43—81no—
133C22×D43—81no—
134Q8×C43—22no—
135Q8×C43—22no—
136Q8×C43—41no—
137Q8×C43—41no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—22no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12311yescharacteristic
150C2×C4×C43#12311yescharacteristic
151C2×C4×C43#12411yescharacteristic
152C2×C4×C43C2×SD1611yescharacteristic
153C2×C4×C43C2×SD1611yescharacteristic
154C2×C4×C43#13511yescharacteristic
155C2×C4×C43#13511yescharacteristic
156C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C43#13711yescharacteristic
160C2×Dic43—81no—
161C2×Dic43—81no—
162C2×Dic43—81no—
163D172—42no—
164D172—42no—
165D172—42no—
166D172—42no—
167D172—82no—
168D172—82no—
169D172—81no—
170D172—81no—
171D172—81no—
172D172—81no—
173C8×C43—22no—
174C8×C43—41no—
175C8×C43—81no—
176C43⋊C8—42no—
177C43⋊C8—81no—
178#10475—431nomaximal, Sylow
179C22×C43#39411yescharacteristic
180C22×C43#46011yescharacteristic
181C22×C43#46411yescharacteristic
182C22×C43#46511yescharacteristic
183C22×C43#46911yescharacteristic
184C22×C43#47111yescharacteristic
185C22×C43#47211yescharacteristic
186C2×D43—82no—
187C2×D43—82no—
188C2×D43—82no—
189C2×D43—161no—
190C2×D43—161no—
191C2×D43—161no—
192C2×D43—161no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—42no—
196C4×C43—81no—
197C4×C43#44911yescharacteristic
198C4×C43#45011yescharacteristic
199C4×C43#46111yescharacteristic
200C4×C43#46311yescharacteristic
201C4×C43#46511yescharacteristic
202C4×C43#46811yescharacteristic
203C4×C43#48111yescharacteristic
204C4×C43#48211yescharacteristic
205Dic43—161no—
206C2×#460—431no—
207#1984D4311yescharacteristic, complemented
208#1957—431no—
209#1803—431no—
210C2×#334—431no—
211C2×#331—431no—
212#1296—431no—
213C2×C43#166611yescharacteristic
214C2×C43#167811yescharacteristic
215C2×C43#168811yescharacteristic
216C2×C43#170211yescharacteristic
217C2×C43#203411yescharacteristic
218C2×C43#205111yescharacteristic
219C2×C43#205511yescharacteristic
220D43—162no—
221C22×SD16—861no—
222C2×#127—431no—
223C2×C4×Q8C2×D4311yescharacteristic
224#460—862no—
225#460—862no—
226C2×C4⋊C8—431no—
227C2×C4⋊C8—431no—
228C2×C4⋊C8C2×D4311yescharacteristic
229C2×#103—861no—
230C2×#102—861no—
231C2×#102—861no—
232C2×#102—861no—
233C2×C4×C8C2×D4311yescharacteristic
234#384—431no—
235#340—861no—
236#336—21no—
237#336—21no—
238#334—862no—
239#331—862no—
240C43#1047511yescharacteristic, complemented, Sylow
241C22×Q8D17211yescharacteristic
242C22×D4—861no—
243C22×D4—861no—
244C22×D4—861no—
245C2×SD16—864no—
246C2×SD16—1722no—
247C2×SD16—1722no—
248C22×C8—21no—
249C22×C8—861no—
250C22×C8—861no—
251C22×C8C22⋊D4311yescharacteristic
252C22×C8C22⋊D4311yescharacteristic
253#127—432no—
254#127—861no—
255#127—861no—
256#127—861no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4D17211yescharacteristic
266C2×C42—21no—
267C2×C42C22×D4311yescharacteristic
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—432no—
271C4⋊C8—861no—
272C4⋊C8—861no—
273C4⋊C8—861no—
274#103—1722no—
275#102—864no—
276#102—1722no—
277#102—1722no—
278C4×C8—21no—
279C4×C8—21no—
280C24—1721no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8#1062187312yes—
287C2×D4—862no—
288C2×D4—862no—
289C2×D4—862no—
290C2×D4—3441no—
291C2×D4—3441no—
292C2×D4—1721no—
293C2×D4—1721no—
294C2×D4—1721no—
295C2×D4—1721no—
296C2×D4—1721no—
297C2×D4—1721no—
298C2×D4—1721no—
299C2×D4—1721no—
300C2×D4—1721no—
301C2×D4—1721no—
302C2×D4—1721no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—1721no—
306C22×C4C2×D17211yescharacteristic
307C22×C4#1062189811yescharacteristic
308C22×C4C2×C22⋊D4311yescharacteristic
309SD16—1728no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—862no—
319C2×C8—1721no—
320C2×C8—1721no—
321C2×C8—1721no—
322C2×C8—1721no—
323C2×C8—1721no—
324C2×C8#1062188412yescomplemented
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—3441no—
330C4⋊C4—1721no—
331C4⋊C4—1721no—
332C4⋊C4—1721no—
333C4⋊C4—1721no—
334C42—41no—
335C42—41no—
336C42D4×D4311yescharacteristic
337C42D4×D4311yescharacteristic
338C42#1062190011yescharacteristic
339C42#1062190011yescharacteristic
340C23—3441no—
341C23—3441no—
342C23—3441no—
343C23—3441no—
344C23—3441no—
345C23—3441no—
346C23—1722no—
347C23#1306329911yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352D4—3442no—
353D4—3442no—
354D4—3441no—
355D4—3441no—
356D4—3441no—
357D4—3441no—
358D4—1722no—
359D4—1722no—
360D4—1722no—
361D4—1722no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—3441no—
371C2×C4—3441no—
372C2×C4—3441no—
373C2×C4#1306329511yescharacteristic
374C2×C4#1306329611yescharacteristic
375C2×C4#1306329711yescharacteristic
376C2×C4#1306330711yescharacteristic
377C2×C4#1306330911yescharacteristic
378C2×C4#1306331111yescharacteristic
379C2×C4C2×#1062188411yescharacteristic
380C2×C4C2×#1062187311yescharacteristic
381C2×C4#1306334511yescharacteristic
382C2×C4#1306334711yescharacteristic
383C2×C4#1306335011yescharacteristic
384C2×C4#1306335311yescharacteristic
385C2×C4#1306335311yescharacteristic
386C2×C4#1306335611yescharacteristic
387C8—22no—
388C8—41no—
389C8—81no—
390C8—3441no—
391C8—1722no—
392C22—3442no—
393C22—3442no—
394C22—3442no—
395C22—6881no—
396C22—6881no—
397C22—6881no—
398C22—6881no—
399C22#1458281511yescharacteristic
400C22#1458309911yescharacteristic
401C22#1458312111yescharacteristic
402C22#1458312811yescharacteristic
403C22#1458315211yescharacteristic
404C22#1458316211yescharacteristic
405C22#1458316911yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—6881no—
411C4#1458304611yescharacteristic
412C4#1458305211yescharacteristic
413C4#1458310111yescharacteristic
414C4#1458311111yescharacteristic
415C4#1458313011yescharacteristic
416C4#1458314711yescharacteristic
417C4#1458321811yescharacteristic
418C4#1458322411yescharacteristic
419C2—6882no—
420C2#1913394311yescharacteristic
421C2#1913401111yescharacteristic
422C2#1913407911yescharacteristic
423C2#1913416311yescharacteristic
424C2#1913578511yescharacteristic
425C2#1913588611yescharacteristic
426C2#1913591011yescharacteristic
subgroupG/H
centerC23#13063299
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1984C2
socleC23×C43#121
prime radicalC2×#13063322C22
hypercenter#1984D43
hypocenterC43#10475
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
3. #19134600C2semidirect
4. C2×#14582650C2semidirect
6. #19132479C2semidirect
7. C43×#1984C2semidirect
103. C2×C8×C43SD16semidirect
207. #1984D43semidirect
240. C43#10475semidirect
324. C2×C8#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145830992
#191354012
#191346002
C2×#145826502
C2×#145826422
#191324792
C43×#19842
#1047543