Finite Group Databasebeta

← #24988586

Subgroups — #24988586

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148460C211yesmaximal, characteristic
2#19133245C211yesmaximal, characteristic
3#19133158C211yesmaximal, characteristic, complemented
4#19133154C211yesmaximal, characteristic
5#19132997C211yesmaximal, characteristic, complemented
6#19132990C211yesmaximal, characteristic, complemented
7C43×#1805C211yesmaximal, characteristic, complemented
8#14583634—21no—
9#14583627—21no—
10#14583622C412yescomplemented
11#14583621—22no—
12#14583609C412yescomplemented
13#14583590—22no—
14#14583496—22no—
15#14583473—21no—
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583433—22no—
19#14583380—21no—
20#14582952C2211yescharacteristic
21#14582952C2211yescharacteristic
22#14582646—21no—
23#14582642—21no—
24#14582635—22no—
25#14582632—22no—
26Q8⋊(C43⋊C8)—22no—
27#14582629—22no—
28C2×C4×Q8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×#103×C43—21no—
31C43×#382C2211yescharacteristic
32C43×#340—21no—
33C2×#10621898—21no—
34#13063325C2×C411yescharacteristic
35#13063325C2×C411yescharacteristic
36#13063325D411yescharacteristic
37#13063323—22no—
38#13063322D411yescharacteristic
39#13063320—24no—
40#13063319—24no—
41#13063317—21no—
42#13063317—22no—
43#13063315—24no—
44#13063314—22no—
45#13063313—22no—
46#13063313—21no—
47#13063310—24no—
48#13063308—24no—
49#13063304—21no—
50#13063304D412yes—
51#13063303—24no—
52#13063301—22no—
53#13063301—22no—
54#13063299—21no—
55#13063299D412yes—
56C4×Dic86—21no—
57C4×Dic86—22no—
58C4×Dic86D412yes—
59#13063290—22no—
60C4×D172—22no—
61C4×D172—21no—
62C4×D172C2×C412yes—
63#13063287—22no—
64C4×C22⋊D43—24no—
65#13063284—21no—
66#13063283—22no—
67#13063282—24no—
68C4⋊C4×D43—22no—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)—21no—
71C22⋊(C43⋊C8)—21no—
72C22⋊(C43⋊C8)—21no—
73C4×C43⋊C8—21no—
74C4×C43⋊C8—21no—
75C22×Q8×C43D411yescharacteristic
76C22×C8×C43—21no—
77C4×Q8×C43—21no—
78C4×Q8×C43—21no—
79C4×Q8×C43C2×C412yes—
80C4×Q8×C43D412yes—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43D411yescharacteristic
84C2×C42×C43—21no—
85C2×C42×C43C2311yescharacteristic
86C4⋊C8×C43—21no—
87C4⋊C8×C43—21no—
88#103×C43—42no—
89#95×C43—21no—
90#95×C43—21no—
91C2×Q8×C43—21no—
92C2×Q8×C43—21no—
93C2×Q8×C43—21no—
94C2×Q8×C43—21no—
95C2×Q8×C43—21no—
96C2×Q8×C43C22⋊C412yes—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—41no—
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C2×C22⋊D43—22no—
104#10621898—41no—
105#10621898—41no—
106#10621898—41no—
107#10621898—41no—
108C2×D172—21no—
109C2×D172—21no—
110C2×D172C22⋊C412yes—
111C2×C4×D43—22no—
112C2×C4×D43—24no—
113C2×Dic86—21no—
114C2×Dic86—21no—
115C2×Dic86C22⋊C412yes—
116C2×C8×C43—41no—
117C2×C8×C43—41no—
118C2×C8×C43—41no—
119C4⋊C4×C43—22no—
120C4⋊C4×C43—22no—
121C4⋊C4×C43—21no—
122C4⋊C4×C43—41no—
123C4⋊C4×C43—41no—
124C4⋊C4×C43C22⋊C412yes—
125C42×C43—22no—
126C42×C43—22no—
127C42×C43C22×C411yescharacteristic
128C42×C43C2×D411yescharacteristic
129C42×C43C2×D411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C22⋊Dic43—22no—
132(C2×D43)⋊C4—24no—
133(C2×D43)⋊C4—24no—
134(C2×D43)⋊C4—24no—
135(C2×D43)⋊C4—22no—
136(C2×D43)⋊C4—22no—
137C4⋊Dic43—21no—
138C4⋊Dic43—21no—
139C4⋊Dic43—21no—
140C4⋊Dic43—21no—
141C4⋊Dic43C22⋊C412yes—
142C4⋊Dic43C22⋊C412yes—
143Dic43⋊C4—24no—
144Dic43⋊C4—24no—
145Dic43⋊C4—24no—
146Dic43⋊C4—22no—
147Dic43⋊C4—22no—
148C4×Dic43—24no—
149C4×Dic43—22no—
150C2×C43⋊C8—41no—
151C2×C43⋊C8—41no—
152C23×C43#12011yescharacteristic
153C22×D43—22no—
154Q8×C43—22no—
155Q8×C43—22no—
156Q8×C43—41no—
157Q8×C43—41no—
158C2×C4×C43—22no—
159C2×C4×C43—22no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—81no—
165C2×C4×C43—81no—
166C2×C4×C43—81no—
167C2×C4×C43—81no—
168C2×C4×C43C2×C22⋊C411yescharacteristic
169C2×C4×C43C2×C22⋊C411yescharacteristic
170C2×C4×C43C2×C22⋊C411yescharacteristic
171C2×C4×C43#12011yescharacteristic
172C2×C4×C43#12011yescharacteristic
173C2×C4×C43#12011yescharacteristic
174C2×C4×C43#13511yescharacteristic
175C2×C4×C43#13511yescharacteristic
176C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C43#13711yescharacteristic
178C22⋊D43—42no—
179C22⋊D43—42no—
180C2×Dic43—22no—
181C2×Dic43—22no—
182C2×Dic43—22no—
183D172—42no—
184D172—41no—
185D172—41no—
186D172—81no—
187C4×D43—42no—
188C4×D43—42no—
189C4×D43—84no—
190Dic86—42no—
191Dic86—41no—
192Dic86—41no—
193Dic86—42no—
194C8×C43—81no—
195C43⋊C8—81no—
196C43⋊C8—81no—
197#8431—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43#37911yescharacteristic
201C22×C43#44911yescharacteristic
202C22×C43#45211yescharacteristic
203C2×D43—42no—
204C2×D43—42no—
205C2×D43—42no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—42no—
211C4×C43—42no—
212C4×C43—161no—
213C4×C43#41611yescharacteristic
214C4×C43#41711yescharacteristic
215C4×C43#44911yescharacteristic
216C4×C43#45211yescharacteristic
217Dic43—42no—
218Dic43—42no—
219Dic43—42no—
220#3507—431no—
221#1805D4311yescharacteristic, complemented
222#1540—431no—
223#1518—431no—
224#1517—431no—
225#1481—431no—
226#1479—431no—
227C2×C43—21no—
228C2×C43—21no—
229C2×C43#178811yescharacteristic
230C2×C43#179411yescharacteristic
231C2×C43#179611yescharacteristic
232D43—82no—
233#559—861no—
234#557—861no—
235#556—432no—
236#556—862no—
237#554—432no—
238#552—862no—
239#539—862no—
240#536—861no—
241#533—431no—
242#532—431no—
243#529—862no—
244#520—861no—
245C2×C4×Q8C2×D4311yescharacteristic
246#431—431no—
247#431—431no—
248C2×C4⋊C8C2×D4311yescharacteristic
249C2×#103—21no—
250#382C2×D4311yescharacteristic
251#340—21no—
252#332—861no—
253#331—861no—
254#328—862no—
255#327—862no—
256Q8⋊C8—862no—
257Q8⋊C8—862no—
258C43#843111yescharacteristic, complemented, Sylow
259C2×#41—861no—
260C22×Q8C22⋊D4311yescharacteristic
261C22×C8—21no—
262C4⋊Q8—431no—
263C4⋊Q8—431no—
264C4⋊Q8—431no—
265C4⋊Q8—862no—
266#127—431no—
267#126—864no—
268#126—864no—
269#125—862no—
270#125—864no—
271#125—861no—
272#124—862no—
273#124—862no—
274#124—861no—
275#123—864no—
276#123—864no—
277C22⋊Q8—432no—
278C22⋊Q8—864no—
279C22⋊Q8—862no—
280C22⋊Q8—862no—
281C22⋊Q8—861no—
282#121—432no—
283#121—861no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×Q8—432no—
287C4×Q8—862no—
288C4×Q8—862no—
289C4×Q8—861no—
290C4×Q8C4×D4312yes—
291C4×Q8D17212yes—
292C4×D4—432no—
293C4×D4—862no—
294C4×D4—862no—
295C4×D4—864no—
296C4×D4—861no—
297#117—864no—
298#117—861no—
299#117—862no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—862no—
303C2×C4⋊C4C22⋊D4311yescharacteristic
304C2×C42—21no—
305C2×C42C22×D4311yescharacteristic
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8—861no—
309C4⋊C8—861no—
310#103—42no—
311C22⋊C8—861no—
312C22⋊C8—861no—
313C4×C8—861no—
314C4×C8—861no—
315#95—21no—
316#95—21no—
317#41—1721no—
318#41—1721no—
319#41—1721no—
320#41—1721no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—432no—
327C2×Q8—861no—
328C2×Q8—861no—
329C2×Q8(C2×D43)⋊C412yes—
330C2×D4—432no—
331C2×D4—862no—
332C2×D4—861no—
333C2×D4—861no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—41no—
337C22×C4—864no—
338C22×C4—862no—
339C22×C4D4×D4311yescharacteristic
340C22×C4D4×D4311yescharacteristic
341C22×C4C2×C22⋊D4311yescharacteristic
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—1721no—
346C2×C8—1721no—
347C4⋊C4—22no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—432no—
353C4⋊C4—432no—
354C4⋊C4—864no—
355C4⋊C4—864no—
356C4⋊C4—864no—
357C4⋊C4—861no—
358C4⋊C4—861no—
359C4⋊C4—861no—
360C4⋊C4—862no—
361C4⋊C4—861no—
362C4⋊C4—862no—
363C4⋊C4(C2×D43)⋊C412yes—
364C22⋊C4—864no—
365C22⋊C4—864no—
366C22⋊C4—864no—
367C22⋊C4—862no—
368C22⋊C4—862no—
369C22⋊C4—862no—
370C42—22no—
371C42—22no—
372C42—864no—
373C42—862no—
374C42C2×C4×D4311yescharacteristic
375C42C2×D17211yescharacteristic
376C42D4×D4311yescharacteristic
377C42D4×D4311yescharacteristic
378C23—862no—
379C23#1306329311yescharacteristic
380Q8—22no—
381Q8—22no—
382Q8—41no—
383Q8—41no—
384Q8—1722no—
385Q8—1722no—
386Q8—1721no—
387Q8—1721no—
388D4—3441no—
389D4—1722no—
390D4—1722no—
391D4—1722no—
392D4—1721no—
393D4—1721no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—862no—
405C2×C4—862no—
406C2×C4—862no—
407C2×C4—3444no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4C22⋊C4×D4311yescharacteristic
411C2×C4C22⋊C4×D4311yescharacteristic
412C2×C4C2×(C2×D43)⋊C411yescharacteristic
413C2×C4#1306329311yescharacteristic
414C2×C4#1306329511yescharacteristic
415C2×C4#1306329511yescharacteristic
416C2×C4#1306334511yescharacteristic
417C2×C4#1306334511yescharacteristic
418C2×C4#1306335111yescharacteristic
419C2×C4#1306335611yescharacteristic
420C8—81no—
421C8—3441no—
422C8—3441no—
423C22—21no—
424C22—21no—
425C22—1722no—
426C22—1722no—
427C22—1722no—
428C22#1458275411yescharacteristic
429C22#1458304211yescharacteristic
430C22#1458305911yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—161no—
438C4—1722no—
439C4—1722no—
440C4—1722no—
441C4#1458289311yescharacteristic
442C4#1458289811yescharacteristic
443C4#1458304211yescharacteristic
444C4#1458305911yescharacteristic
445C2—21no—
446C2—21no—
447C2—3442no—
448C2#1913453311yescharacteristic
449C2#1913456011yescharacteristic
450C2#1913456711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1805C2
socleC22×C43#379
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1805D43
hypocenterC43#8431
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
3. #19133158C2semidirect
5. #19132997C2semidirect
6. #19132990C2semidirect
7. C43×#1805C2semidirect
10. #14583622C4semidirect
12. #14583609C4semidirect
221. #1805D43semidirect
258. C43#8431semidirect

Maximal subgroups

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

subgroupindex
#191484602
#191332452
#191331582
#191331542
#191329972
#191329902
C43×#18052
#843143