Finite Group Databasebeta

← #24988545

Subgroups — #24988545

Order 11008.

750 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
1#19148411C211yesmaximal, characteristic
2#19134616C211yesmaximal, characteristic
3#19133283C211yesmaximal, characteristic, complemented
4#19133276C211yesmaximal, characteristic, complemented
5#19133093C211yesmaximal, characteristic, complemented
6#19132980C211yesmaximal, characteristic
7C43×#1981C211yesmaximal, characteristic, complemented
8#14583629C412yescomplemented
9#14583624—21no—
10#14583610C412yescomplemented
11#14583604—22no—
12#14583564—21no—
13Q8×C22⋊D43—22no—
14#14583530—21no—
15#14583526—22no—
16#14583456C2211yescharacteristic
17#14583454—21no—
18C4⋊Q8×D43—21no—
19#14583380—21no—
20C4×#10621898C2211yescharacteristic
21#14582952C2211yescharacteristic
22#14582923C2211yescharacteristic
23C2×#13063253—21no—
24#14582659—21no—
25#14582648—22no—
26#14582647—21no—
27#14582646—21no—
28#14582635—22no—
29#14582629—21no—
30#14582626—21no—
31C2×C4⋊Q8×C43C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic
33C2×#103×C43—22no—
34C4×C4⋊C4×C43C2211yescharacteristic
35C2×#10621898D411yescharacteristic
36C2×Q8×D43—22no—
37C2×#10621877—21no—
38#13063325D411yescharacteristic
39#13063325D411yescharacteristic
40#13063324—22no—
41#13063324—22no—
42#13063324—22no—
43#13063323—22no—
44#13063323—24no—
45#13063317—21no—
46#13063316—22no—
47#13063316—22no—
48#13063315—24no—
49#13063305—22no—
50#13063304—24no—
51#13063304—21no—
52#13063304D412yes—
53#13063303—24no—
54#13063301—22no—
55#13063301—24no—
56Q8×Dic43—22no—
57C4×Dic86—21no—
58C4×Dic86C2×C412yes—
59C4×Dic86C2×C411yescharacteristic
60C4×Dic86D411yescharacteristic
61#13063290—22no—
62#13063290—22no—
63C4×D172C2×C411yescharacteristic
64C4×D172D411yescharacteristic
65#13063287—22no—
66C4×C22⋊D43—24no—
67C4×C22⋊D43—21no—
68C4×C22⋊D43—21no—
69#13063284—21no—
70#13063284D411yescharacteristic
71#13063283—22no—
72#13063282—21no—
73C4⋊C4×D43—22no—
74C4⋊C4×D43—22no—
75C42×D43—21no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)—21no—
79#13063253—42no—
80C22⋊(C43⋊C8)—21no—
81C4×C43⋊C8—21no—
82C22×Q8×C43D412yes—
83C22×C8×C43—21no—
84C4⋊Q8×C43—21no—
85C4⋊Q8×C43—21no—
86C4⋊Q8×C43C2×C412yes—
87C4⋊Q8×C43D412yes—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—21no—
91C2×C42×C43—21no—
92C2×C42×C43C2311yescharacteristic
93C4⋊C8×C43—21no—
94C4⋊C8×C43—21no—
95#103×C43—44no—
96#95×C43—21no—
97C2×Q8×C43—22no—
98C2×Q8×C43—42no—
99C2×Q8×C43—42no—
100C2×Q8×C43C22⋊C414yes—
101C22×C4×C43—22no—
102C22×C4×C43—41no—
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C2×C22⋊D43—21no—
107Q8×D43—82no—
108Q8×D43—82no—
109#10621898—21no—
110#10621898—21no—
111#10621898SD1612yes—
112#10621898Q1612yes—
113C2×D172C22⋊C411yescharacteristic
114C2×C4×D43—21no—
115C2×C4×D43—21no—
116C2×C4×D43—21no—
117C2×C4×D43—24no—
118C2×Dic86—21no—
119C2×Dic86—24no—
120C2×Dic86C22⋊C411yescharacteristic
121C2×Dic86C22⋊C412yes—
122C2×C8×C43—42no—
123C2×C8×C43—41no—
124C4⋊C4×C43—22no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43—22no—
129C4⋊C4×C43—41no—
130C42×C43—41no—
131C42×C43—41no—
132C42×C43C22×C411yescharacteristic
133C42×C43C2×D411yescharacteristic
134C42×C43C2×D411yescharacteristic
135C42×C43C2×D411yescharacteristic
136C22⋊Dic43—22no—
137C22⋊Dic43—21no—
138(C2×D43)⋊C4—24no—
139(C2×D43)⋊C4—21no—
140(C2×D43)⋊C4—21no—
141C4⋊Dic43—24no—
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C4⋊Dic43—21no—
145C4⋊Dic43C22⋊C412yes—
146C4⋊Dic43C22⋊C411yescharacteristic
147C4⋊Dic43C22⋊C411yescharacteristic
148Dic43⋊C4—24no—
149Dic43⋊C4—24no—
150Dic43⋊C4—24no—
151Dic43⋊C4—21no—
152Dic43⋊C4—22no—
153Dic43⋊C4—21no—
154Dic43⋊C4—22no—
155C4×Dic43—24no—
156C4×Dic43—21no—
157C4×Dic43—22no—
158C4×Dic43—21no—
159C4×Dic43—21no—
160#10621877—41no—
161#10621877—41no—
162C2×C43⋊C8—41no—
163C2×C43⋊C8—41no—
164C23×C43#12011yescharacteristic
165C22×D43—21no—
166Q8×C43—44no—
167Q8×C43—42no—
168Q8×C43—42no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—24no—
172C2×C4×C43—41no—
173C2×C4×C43—42no—
174C2×C4×C43—82no—
175C2×C4×C43—81no—
176C2×C4×C43—81no—
177C2×C4×C43C2×C22⋊C411yescharacteristic
178C2×C4×C43C2×C22⋊C411yescharacteristic
179C2×C4×C43C2×C22⋊C411yescharacteristic
180C2×C4×C43#12011yescharacteristic
181C2×C4×C43#12011yescharacteristic
182C2×C4×C43#12011yescharacteristic
183C2×C4×C43C2×SD1611yescharacteristic
184C2×C4×C43C2×Q1611yescharacteristic
185C2×C4×C43#13711yescharacteristic
186C2×C4×C43#13711yescharacteristic
187C22⋊D43—22no—
188C22⋊D43—22no—
189C2×Dic43—21no—
190C2×Dic43—22no—
191C2×Dic43—21no—
192C2×Dic43—21no—
193C2×Dic43—22no—
194D172—21no—
195D172#10312yescomplemented
196C4×D43—22no—
197C4×D43—22no—
198C4×D43—42no—
199C4×D43—41no—
200C4×D43—41no—
201C4×D43—84no—
202Dic86—21no—
203Dic86—41no—
204Dic86—41no—
205Dic86—42no—
206Dic86—84no—
207Dic86#10312yescomplemented
208C8×C43—81no—
209C43⋊C8—81no—
210C43⋊C8—81no—
211#8425—431nomaximal, Sylow
212C22×C43—21no—
213C22×C43—21no—
214C22×C43#37911yescharacteristic
215C22×C43#44811yescharacteristic
216C22×C43#45111yescharacteristic
217C2×D43—22no—
218C2×D43—41no—
219C2×D43—41no—
220C4×C43—21no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—44no—
224C4×C43—82no—
225C4×C43C2×#10311yescharacteristic
226C4×C43#41911yescharacteristic
227C4×C43#44811yescharacteristic
228C4×C43#45111yescharacteristic
229C4×C43#45311yescharacteristic
230C4×C43#45511yescharacteristic
231Dic43—22no—
232Dic43—42no—
233Dic43—41no—
234Dic43—42no—
235Dic43—41no—
236#3503—431no—
237#1981D4311yescharacteristic, complemented
238#1806—431no—
239#1550—431no—
240#1548—431no—
241#1503—431no—
242#1477—431no—
243C2×C43—21no—
244C2×C43—21no—
245C2×C43#178711yescharacteristic
246C2×C43#179211yescharacteristic
247C2×C43#179611yescharacteristic
248D43—42no—
249Q82—432no—
250#557—861no—
251#554—432no—
252#554—862no—
253D4×Q8—861no—
254D4×Q8—862no—
255#544—861no—
256#544—862no—
257#533—431no—
258#533—861no—
259C2×C4⋊Q8—861no—
260C2×C4⋊Q8C2×D4311yescharacteristic
261#520—861no—
262C4×#41—431no—
263#431—431no—
264#423—431no—
265C2×C4⋊C8C2×D4311yescharacteristic
266C2×#104—861no—
267C2×#103—22no—
268C4×C4⋊C4C2×D4311yescharacteristic
269#339—861no—
270#333—861no—
271#333—862no—
272#332—861no—
273#328—862no—
274Q8⋊C8—861no—
275D4⋊C8—861no—
276C43#842511yescharacteristic, complemented, Sylow
277C2×#41—431no—
278C22×Q8—862no—
279C22×Q8C22⋊D4312yes—
280C2×M16—861no—
281C22×C8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—431no—
285C4⋊Q8—431no—
286C4⋊Q8—862no—
287C4⋊Q8—862no—
288C4⋊Q8—862no—
289C4⋊Q8—862no—
290C4⋊Q8—864no—
291C4⋊Q8C4×D4312yes—
292C4⋊Q8D17212yes—
293#125—862no—
294#125—862no—
295#125—864no—
296#125—861no—
297C22⋊Q8—432no—
298C22⋊Q8—862no—
299C22⋊Q8—864no—
300C22⋊Q8—864no—
301C22⋊Q8—862no—
302C22⋊Q8—864no—
303C22⋊Q8—861no—
304C4×Q8—431no—
305C4×Q8—432no—
306C4×Q8—431no—
307C4×Q8—862no—
308C4×Q8—862no—
309C4×Q8—862no—
310C4×Q8—861no—
311C4×D4—431no—
312C4×D4—431no—
313C4×D4—862no—
314C4×D4—864no—
315C4×D4—861no—
316C4×D4—861no—
317#117—431no—
318#117—862no—
319#117—861no—
320#117—861no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—862no—
325C2×C4⋊C4—862no—
326C2×C42—21no—
327C2×C42—861no—
328C2×C42C22×D4311yescharacteristic
329C4⋊C8—21no—
330C4⋊C8—21no—
331C4⋊C8—861no—
332C4⋊C8—861no—
333C4⋊C8—861no—
334#104—1722no—
335#103—44no—
336C22⋊C8—861no—
337C4×C8—861no—
338#95—21no—
339#41—432no—
340#41—432no—
341#41—861no—
342#41—861no—
343C2×Q8—22no—
344C2×Q8—42no—
345C2×Q8—42no—
346C2×Q8—431no—
347C2×Q8—432no—
348C2×Q8—864no—
349C2×Q8—861no—
350C2×Q8—3442no—
351C2×Q8—3442no—
352C2×Q8(C2×D43)⋊C414yes—
353C2×D4—431no—
354C2×D4—861no—
355C22×C4—22no—
356C22×C4—41no—
357C22×C4—864no—
358C22×C4—861no—
359C22×C4—861no—
360C22×C4—861no—
361C22×C4D4×D4311yescharacteristic
362C22×C4D4×D4311yescharacteristic
363C22×C4C2×C22⋊D4311yescharacteristic
364M16—1721no—
365M16—1721no—
366C2×C8—42no—
367C2×C8—41no—
368C2×C8—1721no—
369C2×C8—1721no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—41no—
376C4⋊C4—432no—
377C4⋊C4—431no—
378C4⋊C4—431no—
379C4⋊C4—864no—
380C4⋊C4—864no—
381C4⋊C4—864no—
382C4⋊C4—864no—
383C4⋊C4—861no—
384C4⋊C4—862no—
385C4⋊C4—861no—
386C4⋊C4—861no—
387C4⋊C4—861no—
388C4⋊C4—861no—
389C4⋊C4—862no—
390C22⋊C4—864no—
391C22⋊C4—861no—
392C22⋊C4—862no—
393C22⋊C4—861no—
394C22⋊C4—861no—
395C42—41no—
396C42—41no—
397C42—864no—
398C42—861no—
399C42—862no—
400C42—861no—
401C42—861no—
402C42C2×C4×D4311yescharacteristic
403C42C2×D17211yescharacteristic
404C42D4×D4311yescharacteristic
405C42D4×D4311yescharacteristic
406C23—861no—
407C23#1306329311yescharacteristic
408Q8—44no—
409Q8—42no—
410Q8—42no—
411Q8—432no—
412Q8—861no—
413Q8—3444no—
414Q8—1722no—
415Q8—1721no—
416Q8—1721no—
417D4—432no—
418D4—862no—
419D4—862no—
420D4—861no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—24no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—82no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—861no—
430C2×C4—862no—
431C2×C4—862no—
432C2×C4—862no—
433C2×C4—861no—
434C2×C4—861no—
435C2×C4—862no—
436C2×C4—3444no—
437C2×C4—1722no—
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
446C2×C4SD16×D4311yescharacteristic
447C2×C4Q16×D4311yescharacteristic
448C2×C4#1306335411yescharacteristic
449C2×C4#1306335711yescharacteristic
450C8—81no—
451C8—3441no—
452C8—3441no—
453C22—21no—
454C22—21no—
455C22—862no—
456C22—1721no—
457C22—1721no—
458C22#1458275411yescharacteristic
459C22#1458303611yescharacteristic
460C22#1458305311yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—44no—
465C4—82no—
466C4—862no—
467C4—1722no—
468C4—1721no—
469C4—1721no—
470C4—1722no—
471C4#103×D4311yescharacteristic
472C4#1458290611yescharacteristic
473C4#1458303911yescharacteristic
474C4#1458305611yescharacteristic
475C4#1458306611yescharacteristic
476C4#1458307611yescharacteristic
477C2—21no—
478C2—21no—
479C2—1722no—
480C2#1913452811yescharacteristic
481C2#1913454811yescharacteristic
482C2#1913456711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1981C2
socleC22×C43#379
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1981D43
hypocenterC43#8425
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
3. #19133283C2semidirect
4. #19133276C2semidirect
5. #19133093C2semidirect
7. C43×#1981C2semidirect
8. #14583629C4semidirect
10. #14583610C4semidirect
195. D172#103semidirect
207. Dic86#103semidirect
237. #1981D43semidirect
276. C43#8425semidirect

Maximal subgroups

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

subgroupindex
#191484112
#191346162
#191332832
#191332762
#191330932
#191329802
C43×#19812
#842543