Finite Group Databasebeta

← #25000392

Subgroups — #25000392

Order 11008.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583091C211yesmaximal, characteristic
2#19135402C211yesmaximal, characteristic, complemented
3#19135388C211yesmaximal, characteristic, complemented
4#19134596C211yesmaximal, characteristic, complemented
5C2×#14582649C211yesmaximal, characteristic, complemented
6#19132479C211yesmaximal, characteristic, complemented
7C2×C43×#331C211yesmaximal, characteristic, complemented
8C22×#10621882—21no—
9C2×C4×D172C2211yescharacteristic
10#14583091—22no—
11#14583091—22no—
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×#13063247—21no—
14C2×#13063246—21no—
15C2×#13063246—21no—
16C2×#13063246—21no—
17C2×(C2×D43)⋊C8—21no—
18C2×(C2×D43)⋊C8—21no—
19C2×C4×C43⋊C8C2211yescharacteristic
20#14582769C2211yescharacteristic
21#14582662—21no—
22#14582649—22no—
23C2×#127×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C43×#331—22no—
27C22×D172D411yescharacteristic
28C22×C4×D43—21no—
29C2×#10621882—24no—
30C2×#10621882—42no—
31C2×#10621882—42no—
32C22×C43⋊C8—21no—
33C22×C43⋊C8D411yescharacteristic
34C22×C43⋊C8D411yescharacteristic
35C4×D172—21no—
36C4×D172—21no—
37C4×D172—21no—
38C4×D172—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×(C2×D43)⋊C4—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)D412yes—
46#13063247—42no—
47#13063246—24no—
48#13063246—42no—
49#13063246—42no—
50(C2×D43)⋊C8—42no—
51(C2×D43)⋊C8—42no—
52C4×C43⋊C8—21no—
53C4×C43⋊C8—21no—
54C22×D4×C43—21no—
55C22×D4×C43—21no—
56C22×D4×C43—21no—
57C22×C8×C43—21no—
58C22×C8×C43—21no—
59#127×C43—21no—
60#127×C43—21no—
61#127×C43—21no—
62#127×C43D412yes—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67C4⋊C8×C43—21no—
68C24×C43—41no—
69C23×D43—21no—
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—22no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C2×D4×C43—41no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C2×D4×C43—41no—
84C2×D4×C43—81no—
85C2×D4×C43—81no—
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×Dic43—21no—
90C22×Dic43—41no—
91C2×D172—21no—
92C2×D172—21no—
93C2×D172—21no—
94C2×D172—21no—
95C2×D172—21no—
96C2×D172SD1612yes—
97C2×C4×D43—41no—
98C2×C4×D43—41no—
99C2×C4×D43—41no—
100C2×C4×D43—41no—
101C2×C4×D43—41no—
102C2×C4×D43—41no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C2×C8×C43—41no—
108C2×C8×C43—41no—
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43#4111yescharacteristic
112C42×C43#4111yescharacteristic
113#10621882—48no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—41no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—41no—
119C4⋊Dic43—41no—
120C4⋊Dic43—41no—
121C4⋊Dic43—41no—
122C4⋊Dic43—81no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8D812yescomplemented
132C23×C43—42no—
133C23×C43—81no—
134C23×C43—81no—
135C23×C43—81no—
136C23×C43—81no—
137C23×C43—81no—
138C23×C43—81no—
139C23×C43#12111yescharacteristic
140C22×D43—22no—
141C22×D43—41no—
142C22×D43—41no—
143C22×D43—41no—
144C22×D43—41no—
145C22×D43—41no—
146C22×D43—41no—
147D4×C43—42no—
148D4×C43—42no—
149D4×C43—42no—
150D4×C43—42no—
151D4×C43—82no—
152D4×C43—82no—
153D4×C43—81no—
154D4×C43—81no—
155D4×C43—81no—
156D4×C43—81no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12311yescharacteristic
163C2×C4×C43#12311yescharacteristic
164C2×C4×C43#12411yescharacteristic
165C2×C4×C43C2×D811yescharacteristic
166C2×C4×C43C2×SD1611yescharacteristic
167C2×C4×C43#13511yescharacteristic
168C2×C4×C43#13511yescharacteristic
169C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—81no—
177C2×Dic43—81no—
178C2×Dic43—81no—
179D172—22no—
180D172—22no—
181D172—41no—
182D172—41no—
183C4×D43—81no—
184C4×D43—81no—
185C4×D43—81no—
186C4×D43—81no—
187C8×C43—81no—
188C8×C43—81no—
189C43⋊C8—22no—
190C43⋊C8—42no—
191C43⋊C8—41no—
192#10473—431nomaximal, Sylow
193C22×C43—82no—
194C22×C43—82no—
195C22×C43—82no—
196C22×C43—161no—
197C22×C43—161no—
198C22×C43—161no—
199C22×C43—161no—
200C22×C43#39411yescharacteristic
201C22×C43#45911yescharacteristic
202C22×C43#46311yescharacteristic
203C22×C43#46511yescharacteristic
204C22×C43#46911yescharacteristic
205C22×C43#47111yescharacteristic
206C22×C43#47211yescharacteristic
207C2×D43—42no—
208C2×D43—42no—
209C2×D43—42no—
210C2×D43—81no—
211C2×D43—81no—
212C2×D43—81no—
213C2×D43—81no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43#44911yescharacteristic
217C4×C43#45011yescharacteristic
218C4×C43#45911yescharacteristic
219C4×C43#46311yescharacteristic
220C4×C43#46611yescharacteristic
221C4×C43#46911yescharacteristic
222C4×C43#48111yescharacteristic
223C4×C43#48211yescharacteristic
224Dic43—81no—
225Dic43—161no—
226C2×#459—431no—
227#1957—431no—
228#1954—431no—
229#1802—431no—
230C2×#334—431no—
231C2×#331D4311yescharacteristic, complemented
232#1296—431no—
233C2×C43—162no—
234C2×C43#166511yescharacteristic
235C2×C43#167711yescharacteristic
236C2×C43#168711yescharacteristic
237C2×C43#170111yescharacteristic
238C2×C43#203411yescharacteristic
239C2×C43#205111yescharacteristic
240C2×C43#205411yescharacteristic
241D43—82no—
242C22×D8—861no—
243C2×#127C2×D4311yescharacteristic
244C2×C4×D4—431no—
245#459—862no—
246#459—862no—
247C2×C4⋊C8—431no—
248C2×C4⋊C8C2×D4311yescharacteristic
249C2×C4⋊C8C2×D4311yescharacteristic
250C2×#102—861no—
251C2×#102—861no—
252C2×#102—861no—
253C2×#102—861no—
254C2×C22⋊C8—861no—
255C2×C22⋊C8—861no—
256C2×C4×C8—431no—
257#384—431no—
258#340—861no—
259#334—862no—
260#331—22no—
261C43#1047311yescharacteristic, complemented, Sylow
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—431no—
266C23×C4—861no—
267C2×D8—864no—
268C2×D8—1722no—
269C2×D8—1722no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—431no—
273C22×C8—431no—
274C22×C8—861no—
275#127—21no—
276#127—21no—
277#127—21no—
278#127C22⋊D4312yes—
279C4×D4—861no—
280C4×D4—861no—
281C4×D4—861no—
282C4×D4—861no—
283C2×C4⋊C4—431no—
284C2×C4⋊C4—861no—
285C2×C4⋊C4—861no—
286C2×C4⋊C4—861no—
287C2×C22⋊C4—861no—
288C2×C42C22×D4311yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—432no—
294C4⋊C8—861no—
295#102—864no—
296#102—1722no—
297#102—1722no—
298#102—1722no—
299C22⋊C8—1722no—
300C22⋊C8—1722no—
301C4×C8—861no—
302C4×C8—861no—
303C24—41no—
304C24—861no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—81no—
320C2×D4—81no—
321C2×D4—432no—
322C2×D4—861no—
323C2×D4—861no—
324C2×D4—861no—
325C2×D4—861no—
326C2×D4—861no—
327C22×C4—861no—
328C22×C4—1721no—
329C22×C4—1721no—
330C22×C4—1721no—
331C22×C4—1721no—
332C22×C4—1721no—
333C22×C4—1721no—
334C22×C4—1721no—
335C22×C4#1062189811yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C22×C4D4×D4311yescharacteristic
338D8—1728no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—432no—
346C2×C8—861no—
347C2×C8—861no—
348C2×C8—862no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8—861no—
352C2×C8—1721no—
353C2×C8—1721no—
354C4⋊C4—861no—
355C4⋊C4—861no—
356C4⋊C4—3441no—
357C4⋊C4—1721no—
358C4⋊C4—1721no—
359C4⋊C4—1721no—
360C4⋊C4—1721no—
361C22⋊C4—1721no—
362C22⋊C4—1721no—
363C42#1062189811yescharacteristic
364C42D4×D4311yescharacteristic
365C42#1062190011yescharacteristic
366C42C2×C22⋊D4311yescharacteristic
367C23—42no—
368C23—81no—
369C23—81no—
370C23—81no—
371C23—81no—
372C23—81no—
373C23—81no—
374C23—862no—
375C23—1721no—
376C23—1721no—
377C23—1721no—
378C23—1721no—
379C23—1721no—
380C23—1721no—
381C23#1306329811yescharacteristic
382D4—42no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392D4—862no—
393D4—862no—
394D4—1721no—
395D4—1721no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—3441no—
399C2×C4—3441no—
400C2×C4—3441no—
401C2×C4—3441no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4#1306329311yescharacteristic
409C2×C4#1306329711yescharacteristic
410C2×C4#1306329811yescharacteristic
411C2×C4#1306330711yescharacteristic
412C2×C4#1306330811yescharacteristic
413C2×C4#1306331111yescharacteristic
414C2×C4D8×D4311yescharacteristic
415C2×C4SD16×D4311yescharacteristic
416C2×C4#1306334411yescharacteristic
417C2×C4#1306334611yescharacteristic
418C2×C4#1306334911yescharacteristic
419C2×C4#1306334911yescharacteristic
420C2×C4#1306335211yescharacteristic
421C2×C4#1306335211yescharacteristic
422C8—81no—
423C8—81no—
424C8—862no—
425C8—1722no—
426C8—1721no—
427C22—82no—
428C22—82no—
429C22—82no—
430C22—161no—
431C22—161no—
432C22—161no—
433C22—161no—
434C22—3441no—
435C22—3441no—
436C22—3441no—
437C22—3441no—
438C22—1722no—
439C22—1722no—
440C22—1722no—
441C22#1458281411yescharacteristic
442C22#1458309311yescharacteristic
443C22#1458311311yescharacteristic
444C22#1458312711yescharacteristic
445C22#1458315111yescharacteristic
446C22#1458316111yescharacteristic
447C22#1458316811yescharacteristic
448C4—21no—
449C4—21no—
450C4—3441no—
451C4—6881no—
452C4#1458304111yescharacteristic
453C4#1458304811yescharacteristic
454C4#1458309211yescharacteristic
455C4#1458311611yescharacteristic
456C4#1458313411yescharacteristic
457C4#1458315111yescharacteristic
458C4#1458321611yescharacteristic
459C4#1458322111yescharacteristic
460C2—162no—
461C2—3442no—
462C2#1913393511yescharacteristic
463C2#1913400311yescharacteristic
464C2#1913407311yescharacteristic
465C2#1913415511yescharacteristic
466C2#1913578211yescharacteristic
467C2#1913588711yescharacteristic
468C2#1913590411yescharacteristic
subgroupG/H
centerC23#13063298
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#331C2
socleC23×C43#121
prime radicalC2×#14583091C2
hypercenterC2×#331D43
hypocenterC43#10473
LCSG ▷ C2×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. #19135402C2semidirect
3. #19135388C2semidirect
4. #19134596C2semidirect
5. C2×#14582649C2semidirect
6. #19132479C2semidirect
7. C2×C43×#331C2semidirect
131. C2×C43⋊C8D8semidirect
231. C2×#331D43semidirect
261. C43#10473semidirect

Maximal subgroups

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

subgroupindex
C2×#145830912
#191354022
#191353882
#191345962
C2×#145826492
#191324792
C2×C43×#3312
#1047343