Finite Group Databasebeta

← #25000396

Subgroups — #25000396

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×#14583095C211yesmaximal, characteristic
2#19135401C211yesmaximal, characteristic, complemented
3#19135389C211yesmaximal, characteristic, complemented
4#19134596C211yesmaximal, characteristic, complemented
5C2×#14582642C211yesmaximal, characteristic, complemented
6#19132479C211yesmaximal, characteristic, complemented
7C2×C43×#334C211yesmaximal, characteristic, complemented
8C22×D344—21no—
9C2×#13063322C2211yescharacteristic
10C2×C4×D172C2211yescharacteristic
11#14583095—22no—
12#14583095—22no—
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063247—21no—
15C2×#13063247—21no—
16C2×#13063247—21no—
17C2×#13063247—21no—
18C2×(C2×D43)⋊C8—21no—
19C2×(C2×D43)⋊C8—21no—
20#14582769C2211yescharacteristic
21#14582662—21no—
22#14582642—22no—
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4×C8×C43C2211yescharacteristic
26C43×#334—22no—
27C22×D172—21no—
28C22×D172—21no—
29C22×D172—21no—
30C22×D172D411yescharacteristic
31C22×C4×D43—21no—
32C2×D344—24no—
33C2×D344—42no—
34C2×D344—42no—
35C22×C43⋊C8—21no—
36#13063322—21no—
37#13063322—21no—
38#13063322—21no—
39#13063322D412yes—
40C4×D172—21no—
41C4×D172—21no—
42C4×D172—21no—
43C4×D172—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43D411yescharacteristic
48C2×(C2×D43)⋊C4—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)—21no—
51#13063247—24no—
52#13063247—42no—
53#13063247—42no—
54#13063247—42no—
55(C2×D43)⋊C8—42no—
56(C2×D43)⋊C8—42no—
57C22×C8×C43—21no—
58C22×C8×C43—21no—
59C22×C8×C43D411yescharacteristic
60C22×C8×C43D411yescharacteristic
61C2×C42×C43C2311yescharacteristic
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43D412yes—
66C4×C8×C43—21no—
67C4×C8×C43—21no—
68C23×D43—21no—
69C23×D43—41no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43#4111yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—41no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172—21no—
80C2×D172—22no—
81C2×D172—22no—
82C2×D172—22no—
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—41no—
94C2×D172—81no—
95C2×D172—81no—
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—21no—
104C2×C8×C43—21no—
105C2×C8×C43—22no—
106C2×C8×C43—21no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—41no—
110C2×C8×C43—41no—
111C2×C8×C43—41no—
112C2×C8×C43—41no—
113C2×C8×C43—41no—
114C2×C8×C43D812yescomplemented
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43#4111yescharacteristic
118C42×C43#4111yescharacteristic
119(C2×D43)⋊C4—41no—
120(C2×D43)⋊C4—41no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123C4⋊Dic43—41no—
124C4⋊Dic43—41no—
125C4⋊Dic43—41no—
126C4⋊Dic43—41no—
127C4⋊Dic43—81no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131D344—48no—
132C23×C43#12111yescharacteristic
133C22×D43—22no—
134C22×D43—41no—
135C22×D43—41no—
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—42no—
141C22×D43—81no—
142C22×D43—81no—
143C22×D43—81no—
144C22×D43—81no—
145C22×D43—81no—
146C22×D43—81no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12311yescharacteristic
153C2×C4×C43#12311yescharacteristic
154C2×C4×C43#12411yescharacteristic
155C2×C4×C43C2×D811yescharacteristic
156C2×C4×C43C2×SD1611yescharacteristic
157C2×C4×C43#13511yescharacteristic
158C2×C4×C43#13511yescharacteristic
159C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—81no—
167C2×Dic43—81no—
168C2×Dic43—81no—
169D172—22no—
170D172—22no—
171D172—41no—
172D172—42no—
173D172—42no—
174D172—42no—
175D172—42no—
176D172—41no—
177D172—82no—
178D172—82no—
179D172—81no—
180D172—81no—
181D172—81no—
182D172—81no—
183C4×D43—81no—
184C4×D43—81no—
185C4×D43—81no—
186C4×D43—81no—
187C8×C43—22no—
188C8×C43—42no—
189C8×C43—41no—
190C8×C43—81no—
191C43⋊C8—81no—
192#10473—431nomaximal, Sylow
193C22×C43#39411yescharacteristic
194C22×C43#45911yescharacteristic
195C22×C43#46311yescharacteristic
196C22×C43#46511yescharacteristic
197C22×C43#46911yescharacteristic
198C22×C43#47111yescharacteristic
199C22×C43#47211yescharacteristic
200C2×D43—42no—
201C2×D43—42no—
202C2×D43—42no—
203C2×D43—81no—
204C2×D43—81no—
205C2×D43—81no—
206C2×D43—81no—
207C2×D43—82no—
208C2×D43—82no—
209C2×D43—82no—
210C2×D43—161no—
211C2×D43—161no—
212C2×D43—161no—
213C2×D43—161no—
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×#334D4311yescharacteristic, complemented
231C2×#331—431no—
232#1296—431no—
233C2×C43#166511yescharacteristic
234C2×C43#167711yescharacteristic
235C2×C43#168711yescharacteristic
236C2×C43#170111yescharacteristic
237C2×C43#203411yescharacteristic
238C2×C43#205111yescharacteristic
239C2×C43#205411yescharacteristic
240D43—82no—
241D43—162no—
242C22×D8—861no—
243C2×#127—431no—
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×C8C2×D4311yescharacteristic
257#384—431no—
258#340—861no—
259#334—22no—
260#331—862no—
261C43#1047311yescharacteristic, complemented, Sylow
262C22×D4—431no—
263C22×D4—861no—
264C22×D4—861no—
265C22×D4—861no—
266C23×C4—861no—
267C2×D8—864no—
268C2×D8—1722no—
269C2×D8—1722no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—861no—
273C22×C8D17211yescharacteristic
274C22×C8D17211yescharacteristic
275#127—432no—
276#127—861no—
277#127—861no—
278#127—861no—
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—861no—
293C4⋊C8—861no—
294C4⋊C8C22⋊D4312yes—
295#102—864no—
296#102—1722no—
297#102—1722no—
298#102—1722no—
299C22⋊C8—1722no—
300C22⋊C8—1722no—
301C4×C8—21no—
302C4×C8—21no—
303C24—861no—
304C24—1721no—
305C2×D4—432no—
306C2×D4—861no—
307C2×D4—862no—
308C2×D4—862no—
309C2×D4—861no—
310C2×D4—862no—
311C2×D4—861no—
312C2×D4—861no—
313C2×D4—861no—
314C2×D4—3441no—
315C2×D4—3441no—
316C2×D4—1721no—
317C2×D4—1721no—
318C2×D4—1721no—
319C2×D4—1721no—
320C2×D4—1721no—
321C2×D4—1721no—
322C2×D4—1721no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1721no—
326C2×D4—1721no—
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×C4C2×D17211yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C22×C4#1062190211yescharacteristic
338D8—1728no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—22no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—1721no—
351C2×C8—1721no—
352C2×C8—1721no—
353C2×C8D34412yescomplemented
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#1062190211yescharacteristic
366C42C2×C22⋊D4311yescharacteristic
367C23—862no—
368C23—3441no—
369C23—3441no—
370C23—3441no—
371C23—3441no—
372C23—3441no—
373C23—3441no—
374C23—1722no—
375C23—1721no—
376C23—1721no—
377C23—1721no—
378C23—1721no—
379C23—1721no—
380C23—1721no—
381C23#1306330011yescharacteristic
382D4—862no—
383D4—862no—
384D4—3442no—
385D4—3442no—
386D4—3441no—
387D4—3441no—
388D4—3441no—
389D4—3441no—
390D4—1722no—
391D4—1721no—
392D4—1722no—
393D4—1722no—
394D4—1722no—
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#1306329911yescharacteristic
410C2×C4#1306330011yescharacteristic
411C2×C4#1306331011yescharacteristic
412C2×C4#1306331011yescharacteristic
413C2×C4#1306331411yescharacteristic
414C2×C4C2×D34411yescharacteristic
415C2×C4SD16×D4311yescharacteristic
416C2×C4#1306334611yescharacteristic
417C2×C4#1306334711yescharacteristic
418C2×C4#1306335211yescharacteristic
419C2×C4#1306335211yescharacteristic
420C2×C4#1306335311yescharacteristic
421C2×C4#1306335311yescharacteristic
422C8—22no—
423C8—42no—
424C8—41no—
425C8—81no—
426C8—3441no—
427C22—3441no—
428C22—3441no—
429C22—3441no—
430C22—3441no—
431C22—3442no—
432C22—3442no—
433C22—3442no—
434C22—1722no—
435C22—1722no—
436C22—1722no—
437C22—6881no—
438C22—6881no—
439C22—6881no—
440C22—6881no—
441C22#1458281611yescharacteristic
442C22#1458309511yescharacteristic
443C22#1458311511yescharacteristic
444C22#1458312911yescharacteristic
445C22#1458315311yescharacteristic
446C22#1458316311yescharacteristic
447C22#1458317011yescharacteristic
448C4—21no—
449C4—21no—
450C4—3441no—
451C4—6881no—
452C4#1458304311yescharacteristic
453C4#1458304811yescharacteristic
454C4#1458309511yescharacteristic
455C4#1458311511yescharacteristic
456C4#1458313511yescharacteristic
457C4#1458315211yescharacteristic
458C4#1458321911yescharacteristic
459C4#1458322511yescharacteristic
460C2—3442no—
461C2—6882no—
462C2#1913393711yescharacteristic
463C2#1913400511yescharacteristic
464C2#1913407511yescharacteristic
465C2#1913415711yescharacteristic
466C2#1913578611yescharacteristic
467C2#1913588911yescharacteristic
468C2#1913590611yescharacteristic
subgroupG/H
centerC23#13063300
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#334C2
socleC23×C43#121
prime radicalC2×#14583095C2
hypercenterC2×#334D43
hypocenterC43#10473
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #19135401C2semidirect
3. #19135389C2semidirect
4. #19134596C2semidirect
5. C2×#14582642C2semidirect
6. #19132479C2semidirect
7. C2×C43×#334C2semidirect
114. C2×C8×C43D8semidirect
230. C2×#334D43semidirect
261. C43#10473semidirect
353. C2×C8D344semidirect

Maximal subgroups

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

subgroupindex
C2×#145830952
#191354012
#191353892
#191345962
C2×#145826422
#191324792
C2×C43×#3342
#1047343