Finite Group Databasebeta

← #24989044

Subgroups — #24989044

Order 11008.

736 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583653C211yesmaximal, characteristic
2#19135563C211yesmaximal, characteristic, complemented
3#19135409C211yesmaximal, characteristic
4C2×#14582641C211yesmaximal, characteristic, complemented
5C2×#14582640C211yesmaximal, characteristic, complemented
6C2×#14582638C211yesmaximal, characteristic
7C43×#1992C211yesmaximal, characteristic, complemented
8#14583653—22no—
9#14583653—22no—
10#14583653—22no—
11#14583653C414yescomplemented
12C2×#13063324—21no—
13C2×#13063320—21no—
14C2×#13063320—21no—
15C2×#13063317C2211yescharacteristic
16C2×#13063313C2211yescharacteristic
17C2×#13063310—21no—
18C2×#13063305—21no—
19C2×#13063303—21no—
20C2×#13063248—21no—
21C2×#13063245—21no—
22C2×#13063236C2211yescharacteristic
23C2×#13063236C2211yescharacteristic
24#14582661—21no—
25#14582661—21no—
26#14582641—22no—
27#14582640—22no—
28#14582638—22no—
29C2×#125×C43C2211yescharacteristic
30C2×#97×C43C2211yescharacteristic
31C43×#384C2211yescharacteristic
32C43×#340—21no—
33C43×#340—21no—
34C22×Dic86—21no—
35C22×Dic86D411yescharacteristic
36C22×D172D411yescharacteristic
37C22×C4×D43—21no—
38C22×C43⋊C8—21no—
39C22×C43⋊C8—21no—
40#13063324—24no—
41#13063324—24no—
42#13063320—24no—
43#13063320—24no—
44#13063320—24no—
45#13063320—24no—
46#13063317—21no—
47#13063317—21no—
48#13063317C2×C412yes—
49#13063317D412yes—
50#13063313—21no—
51#13063313—21no—
52#13063313C2×C412yes—
53#13063313D412yes—
54#13063310—24no—
55#13063310—24no—
56#13063305—24no—
57#13063305—24no—
58#13063303—24no—
59#13063303—24no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43D411yescharacteristic
62C2×C4⋊Dic43D411yescharacteristic
63C2×Dic43⋊C4—21no—
64C2×Dic43⋊C4—21no—
65C2×Dic43⋊C4—21no—
66C2×(C2×D43)⋊C4—21no—
67C2×(C2×D43)⋊C4—21no—
68C2×(C2×D43)⋊C4—21no—
69C2×(C2×D43)⋊C4—21no—
70C2×(C2×D43)⋊C4—21no—
71C2×C4×Dic43—21no—
72#13063248—42no—
73#13063245—42no—
74#13063236—21no—
75#13063236—21no—
76#13063236—21no—
77#13063236—21no—
78C22×C8×C43—21no—
79#125×C43—21no—
80#125×C43—21no—
81#125×C43C2×C412yes—
82#125×C43D412yes—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43D411yescharacteristic
89C2×C4⋊C4×C43D411yescharacteristic
90C2×C42×C43C2311yescharacteristic
91#97×C43—21no—
92#97×C43—21no—
93C23×D43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—41no—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—21no—
103C2×D172—21no—
104C2×D172—41no—
105C2×D172—41no—
106C2×D172C22⋊C412yes—
107C2×C4×D43—24no—
108C2×C4×D43—81no—
109C2×C4×D43—81no—
110C2×Dic86—24no—
111C2×Dic86—21no—
112C2×Dic86—41no—
113C2×Dic86—41no—
114C2×Dic86—81no—
115C2×Dic86—81no—
116C2×Dic86C22⋊C412yes—
117C2×C8×C43—22no—
118C2×C8×C43—41no—
119C2×C8×C43—41no—
120C4⋊C4×C43—22no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—22no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—42no—
127C4⋊C4×C43—42no—
128C4⋊C4×C43—41no—
129C4⋊C4×C43—41no—
130C4⋊C4×C43C22⋊C412yes—
131C4⋊C4×C43C22⋊C412yes—
132C42×C43C22×C411yescharacteristic
133C42×C43C2×D411yescharacteristic
134C42×C43C2×D411yescharacteristic
135C42×C43C2×D411yescharacteristic
136(C2×D43)⋊C4—24no—
137(C2×D43)⋊C4—24no—
138(C2×D43)⋊C4—24no—
139(C2×D43)⋊C4—22no—
140(C2×D43)⋊C4—22no—
141(C2×D43)⋊C4—22no—
142(C2×D43)⋊C4—22no—
143C4⋊Dic43—24no—
144C4⋊Dic43—21no—
145C4⋊Dic43—21no—
146C4⋊Dic43C22⋊C412yes—
147C4⋊Dic43C22⋊C412yes—
148Dic43⋊C4—24no—
149Dic43⋊C4—22no—
150Dic43⋊C4—22no—
151Dic43⋊C4—22no—
152Dic43⋊C4—22no—
153C4×Dic43—24no—
154C2×C43⋊C8—22no—
155C2×C43⋊C8—22no—
156C2×C43⋊C8—41no—
157C2×C43⋊C8—41no—
158C2×C43⋊C8—41no—
159C2×C43⋊C8—41no—
160C23×C43#12011yescharacteristic
161C22×D43—22no—
162C22×D43—41no—
163C22×D43—41no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—22no—
175C2×C4×C43—22no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—81no—
181C2×C4×C43—81no—
182C2×C4×C43—81no—
183C2×C4×C43C2×C22⋊C411yescharacteristic
184C2×C4×C43C2×C22⋊C411yescharacteristic
185C2×C4×C43C2×C22⋊C411yescharacteristic
186C2×C4×C43#12011yescharacteristic
187C2×C4×C43#12011yescharacteristic
188C2×C4×C43#12011yescharacteristic
189C2×Dic43—22no—
190C2×Dic43—22no—
191C2×Dic43—22no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198D172—42no—
199D172—81no—
200C4×D43—84no—
201Dic86—42no—
202Dic86—81no—
203Dic86—84no—
204C8×C43—42no—
205C43⋊C8—42no—
206C43⋊C8—42no—
207#8507—431nomaximal, Sylow
208C22×C43#37911yescharacteristic
209C22×C43#45311yescharacteristic
210C22×C43#45411yescharacteristic
211C22×C43#45411yescharacteristic
212C22×C43#45511yescharacteristic
213C22×C43#45611yescharacteristic
214C22×C43#45611yescharacteristic
215C2×D43—42no—
216C2×D43—42no—
217C2×D43—42no—
218C2×D43—81no—
219C2×D43—81no—
220C2×D43—81no—
221C2×D43—81no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—42no—
229C4×C43—42no—
230C4×C43—161no—
231Dic43—42no—
232Dic43—42no—
233Dic43—42no—
234C2×#563—431no—
235#1992—431no—
236#1992D4311yescharacteristic, complemented
237#1959—431no—
238C2×#330—431no—
239C2×#330—431no—
240C2×#329—431no—
241C2×C43#165711yescharacteristic
242C2×C43#166011yescharacteristic
243C2×C43#166411yescharacteristic
244C2×C43#166411yescharacteristic
245C2×C43#179211yescharacteristic
246C2×C43#179311yescharacteristic
247C2×C43#179311yescharacteristic
248D43—82no—
249#563—434no—
250#563—862no—
251#563—862no—
252#563—862no—
253C2×C4⋊Q8—861no—
254C2×#126—861no—
255C2×#126—861no—
256C2×#125—431no—
257C2×#125C2×D4311yescharacteristic
258C2×#124—431no—
259C2×#123—861no—
260C2×C22⋊Q8—861no—
261C2×C22⋊Q8—861no—
262C2×#103—861no—
263C2×#102—861no—
264C2×#97—431no—
265C2×#97—431no—
266C2×#97C2×D4311yescharacteristic
267#384C2×D4311yescharacteristic
268#340—21no—
269#340—21no—
270#340—861no—
271#340—861no—
272#330—862no—
273#330—862no—
274#329—862no—
275C43#850711yescharacteristic, complemented, Sylow
276C22×Q8—431no—
277C22×Q8—861no—
278C22×D4—431no—
279C23×C4—861no—
280C22×C8—21no—
281C22×C8—861no—
282C22×C8—861no—
283C4⋊Q8—864no—
284C4⋊Q8—864no—
285#126—864no—
286#126—864no—
287#126—864no—
288#126—864no—
289#125—21no—
290#125—21no—
291#125—432no—
292#125—432no—
293#125—861no—
294#125—861no—
295#125C4×D4312yes—
296#125D17212yes—
297#124—432no—
298#124—432no—
299#124—861no—
300#124—861no—
301#123—864no—
302#123—864no—
303C22⋊Q8—864no—
304C22⋊Q8—864no—
305C22⋊Q8—864no—
306C22⋊Q8—864no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—431no—
313C2×C4⋊C4—431no—
314C2×C4⋊C4—861no—
315C2×C4⋊C4—861no—
316C2×C4⋊C4—861no—
317C2×C4⋊C4—861no—
318C2×C4⋊C4C22⋊D4311yescharacteristic
319C2×C4⋊C4C22⋊D4311yescharacteristic
320C2×C22⋊C4—861no—
321C2×C22⋊C4—861no—
322C2×C22⋊C4—861no—
323C2×C22⋊C4—861no—
324C2×C22⋊C4—861no—
325C2×C42—861no—
326C2×C42C22×D4311yescharacteristic
327#103—1722no—
328#102—1722no—
329#97—21no—
330#97—21no—
331#97—861no—
332#97—861no—
333#97—861no—
334#97—861no—
335C24—861no—
336C2×Q8—432no—
337C2×Q8—864no—
338C2×Q8—861no—
339C2×Q8—3441no—
340C2×Q8—3441no—
341C2×Q8—1721no—
342C2×Q8—1721no—
343C2×D4—432no—
344C2×D4—861no—
345C2×D4—1721no—
346C2×D4—1721no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—864no—
351C22×C4—861no—
352C22×C4—861no—
353C22×C4—861no—
354C22×C4—3441no—
355C22×C4—3441no—
356C22×C4D4×D4311yescharacteristic
357C22×C4D4×D4311yescharacteristic
358C22×C4C2×C22⋊D4311yescharacteristic
359C2×C8—22no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—862no—
363C2×C8—862no—
364C2×C8—1721no—
365C2×C8—1721no—
366C2×C8—1721no—
367C2×C8—1721no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—432no—
379C4⋊C4—432no—
380C4⋊C4—864no—
381C4⋊C4—864no—
382C4⋊C4—862no—
383C4⋊C4—862no—
384C4⋊C4—862no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C4⋊C4—862no—
388C4⋊C4(C2×D43)⋊C412yes—
389C4⋊C4(C2×D43)⋊C412yes—
390C22⋊C4—864no—
391C22⋊C4—864no—
392C22⋊C4—864no—
393C22⋊C4—862no—
394C22⋊C4—862no—
395C22⋊C4—862no—
396C22⋊C4—862no—
397C42—864no—
398C42C2×C4×D4311yescharacteristic
399C42C2×D17211yescharacteristic
400C42D4×D4311yescharacteristic
401C42D4×D4311yescharacteristic
402C23—862no—
403C23—1721no—
404C23—1721no—
405C23—1721no—
406C23—1721no—
407C23—1721no—
408C23—1721no—
409C23#1306329311yescharacteristic
410Q8—3441no—
411Q8—3444no—
412Q8—1722no—
413D4—3441no—
414D4—1722no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—862no—
431C2×C4—862no—
432C2×C4—862no—
433C2×C4—3444no—
434C2×C4—1721no—
435C2×C4—1721no—
436C2×C4—1721no—
437C2×C4—1721no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4C22⋊C4×D4311yescharacteristic
441C2×C4C22⋊C4×D4311yescharacteristic
442C2×C4C2×(C2×D43)⋊C411yescharacteristic
443C2×C4#1306329311yescharacteristic
444C2×C4#1306329511yescharacteristic
445C2×C4#1306329511yescharacteristic
446C8—42no—
447C8—1722no—
448C8—1722no—
449C22—3441no—
450C22—3441no—
451C22—3441no—
452C22—3441no—
453C22—1722no—
454C22—1722no—
455C22—1722no—
456C22#1458275411yescharacteristic
457C22#1458306511yescharacteristic
458C22#1458307011yescharacteristic
459C22#1458307111yescharacteristic
460C22#1458307511yescharacteristic
461C22#1458308011yescharacteristic
462C22#1458308111yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—42no—
471C4—161no—
472C4—1722no—
473C4—1722no—
474C4—1722no—
475C2—3442no—
476C2#1913389211yescharacteristic
477C2#1913390511yescharacteristic
478C2#1913392611yescharacteristic
479C2#1913392711yescharacteristic
480C2#1913454711yescharacteristic
481C2#1913455211yescharacteristic
482C2#1913455311yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1992C2
socleC23×C43#120
prime radicalC22×D172D4
cosocleC2×C42×C43C23
hypercenter#1992D43
hypocenterC43#8507
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
2. #19135563C2semidirect
4. C2×#14582641C2semidirect
5. C2×#14582640C2semidirect
7. C43×#1992C2semidirect
11. #14583653C4semidirect
236. #1992D43semidirect
275. C43#8507semidirect

Maximal subgroups

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

subgroupindex
C2×#145836532
#191355632
#191354092
C2×#145826412
C2×#145826402
C2×#145826382
C43×#19922
#850743