Finite Group Databasebeta

← #24993487

Subgroups — #24993487

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143712C211yesmaximal, characteristic, complemented
2#19135523C211yesmaximal, characteristic, complemented
3#19134615C211yesmaximal, characteristic, complemented
4#19133263C211yesmaximal, characteristic, complemented
5#19132496C211yesmaximal, characteristic, complemented
6#19132469C211yesmaximal, characteristic, complemented
7C43×#3038C211yesmaximal, characteristic
8#14583030—21no—
9#14582977—21no—
10#14582971—22no—
11#14582956—21no—
12#14582952C2211yescharacteristic
13#14582923—21no—
14#14582923C2211yescharacteristic
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C2×#13063252—21no—
17C2×#13063246—22no—
18C4×C4⋊Dic43C2211yescharacteristic
19#14582658—21no—
20#14582643—21no—
21#14582643—21no—
22C2×AGL(1,ℤ/8)×C43—21no—
23C2×#127×C43C2211yescharacteristic
24C4×#41×C43C2211yescharacteristic
25C43×#460—21no—
26C43×#460C412yescomplemented
27C43×#459—21no—
28C43×#459C412yescomplemented
29C43×#423C2211yescharacteristic
30C43×#418—21no—
31C2×#10621877—22no—
32C2×#10621877—21no—
33C22×C43⋊C8D412yes—
34C2×C4⋊Dic43—21no—
35C2×C4×Dic43—21no—
36C4⋊(C43⋊C8)—22no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)D411yescharacteristic
42C4⋊(C43⋊C8)D411yescharacteristic
43#13063252—42no—
44#13063246—44no—
45C22⋊(C43⋊C8)—22no—
46C22⋊(C43⋊C8)—21no—
47#13063236—22no—
48C4×C43⋊C8—21no—
49C43⋊#95—21no—
50C2×#41×C43D411yescharacteristic
51C22×D4×C43—21no—
52C22×D4×C43—21no—
53C22×D4×C43—21no—
54AGL(1,ℤ/8)×C43—42no—
55AGL(1,ℤ/8)×C43—42no—
56C2×SD16×C43—22no—
57C2×D8×C43—22no—
58C2×M16×C43—21no—
59#127×C43—21no—
60#127×C43—21no—
61#127×C43—21no—
62#127×C43C2×C412yes—
63C4×Q8×C43C2×C411yescharacteristic
64C4×Q8×C43D411yescharacteristic
65C4×D4×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43C2×C411yescharacteristic
68C4×D4×C43D411yescharacteristic
69#117×C43—21no—
70#117×C43D411yescharacteristic
71C2×C42×C43—21no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—21no—
74C4⋊C8×C43C2×C412yes—
75#102×C43—22no—
76#102×C43—22no—
77C24×C43—41no—
78#41×C43—21no—
79#41×C43—21no—
80#41×C43—21no—
81#41×C43—21no—
82C2×Q8×C43C22⋊C411yescharacteristic
83C2×D4×C43—21no—
84C2×D4×C43—22no—
85C2×D4×C43—22no—
86C2×D4×C43—22no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—42no—
91C2×D4×C43—42no—
92C2×D4×C43—41no—
93C2×D4×C43—41no—
94C2×D4×C43—41no—
95C2×D4×C43—41no—
96C2×D4×C43—82no—
97C2×D4×C43C22⋊C411yescharacteristic
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×Dic43—41no—
105SD16×C43—44no—
106D8×C43—44no—
107M16×C43—41no—
108M16×C43—41no—
109C2×C8×C43—22no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43C22⋊C411yescharacteristic
113C4⋊C4×C43C22⋊C411yescharacteristic
114C22⋊C4×C43—21no—
115C22⋊C4×C43—21no—
116C22⋊C4×C43—21no—
117C42×C43—21no—
118C42×C43—21no—
119C42×C43—21no—
120C42×C43C22×C411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43#4111yescharacteristic
124C4⋊Dic43—22no—
125C4⋊Dic43—41no—
126C4×Dic43—41no—
127C4×Dic43—41no—
128#10621877—41no—
129#10621877—41no—
130#10621877—82no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—42no—
135C2×C43⋊C8—41no—
136C23×C43—21no—
137C23×C43—42no—
138C23×C43—82no—
139C23×C43—82no—
140C23×C43—81no—
141C23×C43—81no—
142C23×C43#12111yescharacteristic
143Q8×C43—21no—
144Q8×C43—21no—
145D4×C43—21no—
146D4×C43—21no—
147D4×C43—44no—
148D4×C43—41no—
149D4×C43—41no—
150D4×C43—42no—
151D4×C43—42no—
152D4×C43—82no—
153D4×C43—82no—
154D4×C43—81no—
155D4×C43—81no—
156D4×C43—81no—
157D4×C43—81no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—81no—
169C2×C4×C43C2×C22⋊C411yescharacteristic
170C2×C4×C43C4×D411yescharacteristic
171C2×C4×C43C4×D411yescharacteristic
172C2×C4×C43#12011yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12311yescharacteristic
175C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C43#13711yescharacteristic
179C2×Dic43—42no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182C8×C43—42no—
183C43⋊C8—42no—
184C43⋊C8—41no—
185C43⋊C8—41no—
186C43⋊C8—81no—
187#9322—431nomaximal, Sylow
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—82no—
194C22×C43—82no—
195C22×C43—82no—
196C22×C43—162no—
197C22×C43—162no—
198C22×C43#38611yescharacteristic
199C22×C43#46811yescharacteristic
200C22×C43#46911yescharacteristic
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—41no—
205C4×C43—41no—
206C4×C43—41no—
207C4×C43#41711yescharacteristic
208C4×C43#41811yescharacteristic
209C4×C43#45311yescharacteristic
210C4×C43#45411yescharacteristic
211C4×C43#46811yescharacteristic
212C4×C43#46911yescharacteristic
213Dic43—82no—
214#3038D4311yescharacteristic
215#2989—431no—
216#1982—431no—
217#1806—431no—
218#1545—431no—
219#1303—431no—
220#1292—431no—
221C2×C43—21no—
222C2×C43—21no—
223C2×C43—81no—
224C2×C43—162no—
225C2×C43#188311yescharacteristic
226C2×C43#189511yescharacteristic
227C2×C43#190311yescharacteristic
228C2×AGL(1,ℤ/8)—21no—
229C2×#127C2×D4311yescharacteristic
230C4×#41C2×D4311yescharacteristic
231#460—21no—
232#460Dic4312yescomplemented
233#459—21no—
234#459Dic4312yescomplemented
235#446—861no—
236#436—861no—
237#435—862no—
238#432—861no—
239#431—431no—
240#423—431no—
241#423—861no—
242#423C2×D4311yescharacteristic
243C2×C4⋊C8—431no—
244C2×#104—861no—
245#418—21no—
246C2×#102—862no—
247C4×C4⋊C4—431no—
248#339—861no—
249#331—861no—
250#331—861no—
251C43#932211yescharacteristic, complemented, Sylow
252C2×#41C22⋊D4311yescharacteristic
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—21no—
256AGL(1,ℤ/8)—42no—
257AGL(1,ℤ/8)—42no—
258C2×SD16—22no—
259C2×D8—22no—
260C2×M16—21no—
261C2×M16—862no—
262C2×M16—861no—
263C22×C8—432no—
264#127—21no—
265#127—21no—
266#127—21no—
267#127C2×Dic4312yes—
268C4×Q8C2×Dic4311yescharacteristic
269C4×Q8C22⋊D4311yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4C2×Dic4311yescharacteristic
273C4×D4C22⋊D4311yescharacteristic
274#117—21no—
275#117C22⋊D4311yescharacteristic
276C2×C4⋊C4—861no—
277C2×C42—21no—
278C2×C42—861no—
279C2×C42C22×D4311yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—431no—
282C4⋊C8—431no—
283C4⋊C8—862no—
284C4⋊C8—861no—
285C4⋊C8—861no—
286C4⋊C8—861no—
287C4⋊C8—861no—
288C4⋊C8C2×Dic4312yes—
289#104—1722no—
290#102—22no—
291#102—22no—
292#102—1724no—
293C22⋊C8—862no—
294C22⋊C8—861no—
295#97—862no—
296C4×C8—861no—
297#95—861no—
298C24—41no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—21no—
303C2×Q8C22⋊Dic4311yescharacteristic
304C2×D4—21no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—42no—
309C2×D4—42no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—82no—
318C2×D4C22⋊Dic4311yescharacteristic
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—1721no—
323C22×C4D4×D4311yescharacteristic
324C22×C4#1062190011yescharacteristic
325C22×C4C2×C22⋊D4311yescharacteristic
326SD16—44no—
327D8—44no—
328M16—41no—
329M16—41no—
330M16—3442no—
331M16—1721no—
332M16—1721no—
333C2×C8—22no—
334C2×C8—861no—
335C2×C8—861no—
336C2×C8—862no—
337C2×C8—1721no—
338C2×C8—1722no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—862no—
342C4⋊C4—1721no—
343C4⋊C4C22⋊Dic4311yescharacteristic
344C4⋊C4C22⋊Dic4311yescharacteristic
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C42—21no—
349C42—21no—
350C42—21no—
351C42—1721no—
352C42—1721no—
353C42D4×D4311yescharacteristic
354C42#1062190011yescharacteristic
355C42C22×Dic4311yescharacteristic
356C42C2×C22⋊D4311yescharacteristic
357C23—21no—
358C23—42no—
359C23—82no—
360C23—82no—
361C23—81no—
362C23—81no—
363C23#1306329711yescharacteristic
364Q8—21no—
365Q8—21no—
366D4—21no—
367D4—21no—
368D4—44no—
369D4—41no—
370D4—41no—
371D4—42no—
372D4—42no—
373D4—82no—
374D4—82no—
375D4—81no—
376D4—81no—
377D4—81no—
378D4—81no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—3441no—
391C2×C4—3441no—
392C2×C4—1722no—
393C2×C4C2×C22⋊Dic4311yescharacteristic
394C2×C4D4×Dic4311yescharacteristic
395C2×C4D4×Dic4311yescharacteristic
396C2×C4#1306329311yescharacteristic
397C2×C4#1306329711yescharacteristic
398C2×C4#1306330611yescharacteristic
399C2×C4#1306335011yescharacteristic
400C2×C4#1306335111yescharacteristic
401C2×C4#1306335111yescharacteristic
402C2×C4#1306335511yescharacteristic
403C8—42no—
404C8—3441no—
405C8—1722no—
406C8—1721no—
407C8—1721no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—82no—
414C22—82no—
415C22—82no—
416C22—162no—
417C22—162no—
418C22#1458277911yescharacteristic
419C22#1458314311yescharacteristic
420C22#1458315011yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—3442no—
428C4#1458290011yescharacteristic
429C4#1458290411yescharacteristic
430C4#1458306511yescharacteristic
431C4#1458307011yescharacteristic
432C4#1458314311yescharacteristic
433C4#1458315011yescharacteristic
434C2—21no—
435C2—21no—
436C2—81no—
437C2—162no—
438C2#1913497311yescharacteristic
439C2#1913503411yescharacteristic
440C2#1913507711yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3038C2
socleC22×C43#386
cosocleC2×C42×C43C23
hypercenter#3038D43
hypocenterC43#9322
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. #19143712C2semidirect
2. #19135523C2semidirect
3. #19134615C2semidirect
4. #19133263C2semidirect
5. #19132496C2semidirect
6. #19132469C2semidirect
26. C43×#460C4semidirect
28. C43×#459C4semidirect
232. #460Dic43semidirect
234. #459Dic43semidirect
251. C43#9322semidirect

Maximal subgroups

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

subgroupindex
#191437122
#191355232
#191346152
#191332632
#191324962
#191324692
C43×#30382
#932243