Finite Group Databasebeta

← #25253040

Subgroups — #25253040

Order 11008.

488 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#19145234C211yesmaximal, characteristic, complemented
2#19136742C211yesmaximal, characteristic, complemented
3#19136739C211yesmaximal, characteristic, complemented
4#19136737C211yesmaximal, characteristic, complemented
5#19136734C211yesmaximal, characteristic, complemented
6#19136701C211yesmaximal, characteristic, complemented
7#19136696C211yesmaximal, characteristic
8#19136693C211yesmaximal, characteristic, complemented
9#19136689C211yesmaximal, characteristic, complemented
10#19136657C211yesmaximal, characteristic, complemented
11#19136654C211yesmaximal, characteristic, complemented
12#19136650C211yesmaximal, characteristic, complemented
13#19136647C211yesmaximal, characteristic, complemented
14#19136354C211yesmaximal, characteristic, complemented
15C43×#3175C211yesmaximal, characteristic, complemented
16#14583520—21no—
17C2×#13063271C2211yescharacteristic
18C2×#13063269C2211yescharacteristic
19C2×#13063268C2211yescharacteristic
20C2×#13063266C2211yescharacteristic
21C2×#13063265C2211yescharacteristic
22C22×C43⋊C16C2211yescharacteristic
23#14583304C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583259—21no—
26#14583145—21no—
27#14583140C2211yescharacteristic
28#14583135C2211yescharacteristic
29#14583001—21no—
30C4×Dic172C2211yescharacteristic
31C4×D344C2211yescharacteristic
32#14582726C2211yescharacteristic
33#14582726C2211yescharacteristic
34#14582726C2211yescharacteristic
35#14582726C2211yescharacteristic
36C4⋊(C43⋊C16)C2211yescharacteristic
37C4⋊(C43⋊C16)C2211yescharacteristic
38C4⋊(C43⋊C16)C2211yescharacteristic
39C4⋊(C43⋊C16)C2211yescharacteristic
40#14582703C2211yescharacteristic
41#14582703C2211yescharacteristic
42#14582702C2211yescharacteristic
43#14582702C2211yescharacteristic
44#14582700C2211yescharacteristic
45#14582700C2211yescharacteristic
46#14582699C2211yescharacteristic
47#14582699C2211yescharacteristic
48C43×#542—21no—
49C43×#500C2211yescharacteristic
50C43×#495C2211yescharacteristic
51C43×#489—21no—
52C43×#468—21no—
53C43×#467C2211yescharacteristic
54C43×#466C2211yescharacteristic
55C43×#440—21no—
56C4×Q16×C43C2211yescharacteristic
57C4×D8×C43C2211yescharacteristic
58C43×#405C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621873—21no—
61C2×D344C2311yescharacteristic
62#13063325—21no—
63#13063320—41no—
64#13063313—21no—
65#13063311—41no—
66#13063307—41no—
67#13063304—21no—
68#13063303—41no—
69#13063299—21no—
70C4×Dic86—21no—
71C4×D172—21no—
72#13063271—41no—
73#13063269—41no—
74#13063268—41no—
75#13063266—41no—
76#13063265—41no—
77C2×C43⋊C16—41no—
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80C2×C43⋊C16C2311yescharacteristic
81C2×C43⋊C16C2311yescharacteristic
82#13063259—21no—
83#13063259C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063250—21no—
86#13063250—21no—
87#13063247—21no—
88#13063247—21no—
89C2×Q16×C43C2311yescharacteristic
90C2×SD16×C43—21no—
91C2×D8×C43C2311yescharacteristic
92C2×M16×C43D411yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C4⋊Q8×C43—21no—
95#126×C43—41no—
96#124×C43—21no—
97#124×C43—41no—
98#123×C43—41no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—41no—
101#121×C43—21no—
102C4×Q8×C43—21no—
103C4×D4×C43—21no—
104#117×C43D411yescharacteristic
105#107×C43—21no—
106#107×C43C2311yescharacteristic
107#107×C43C2311yescharacteristic
108#103×C43—21no—
109#103×C43—21no—
110#102×C43—21no—
111#102×C43—21no—
112#97×C43D411yescharacteristic
113#97×C43D411yescharacteristic
114C4×C8×C43C2311yescharacteristic
115C4×C8×C43C2311yescharacteristic
116C2×Q8×C43—21no—
117C2×Q8×C43—41no—
118C2×D4×C43—21no—
119C2×D4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43C2×D411yescharacteristic
122C2×C22⋊D43—41no—
123C2×D172—21no—
124C2×C4×D43—41no—
125C2×Dic86—21no—
126C2×Dic86—41no—
127Q16×C43—21no—
128Q16×C43—21no—
129SD16×C43—42no—
130D8×C43—21no—
131D8×C43—21no—
132M16×C43—41no—
133C2×C8×C43—21no—
134C2×C8×C43—21no—
135C2×C8×C43C2×D411yescharacteristic
136C2×C8×C43C2×D411yescharacteristic
137C2×C8×C43C2×D411yescharacteristic
138C2×C8×C43C2411yescharacteristic
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—41no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43D811yescharacteristic
145C4⋊C4×C43D811yescharacteristic
146C22⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43D811yescharacteristic
152C22⋊C4×C43D811yescharacteristic
153C42×C43—41no—
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C22⋊Dic43—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166C4×Dic43—41no—
167Dic172—21no—
168Dic172—21no—
169D344—21no—
170D344—21no—
171#10621873—42no—
172C43⋊C16—21no—
173C43⋊C16—21no—
174C43⋊C16—21no—
175C43⋊C16—21no—
176C23×C43—41no—
177C23×C43C2×D811yescharacteristic
178C22×D43—41no—
179Q8×C43—41no—
180Q8×C43—41no—
181Q8×C43—161no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—161no—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—161no—
191C2×C4×C43C2×D811yescharacteristic
192C2×C4×C43C2×D811yescharacteristic
193C2×C4×C43C2×D811yescharacteristic
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C2×D811yescharacteristic
196C2×C4×C43C22×D411yescharacteristic
197C22⋊D43—161no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201D172—41no—
202D172—41no—
203C4×D43—161no—
204Dic86—41no—
205Dic86—41no—
206Dic86—161no—
207C8×C43—21no—
208C8×C43—21no—
209C8×C43—21no—
210C8×C43H(5,𝔽2)11yescharacteristic
211C8×C432−1+411yescharacteristic
212#33829—431nomaximal, Sylow
213C22×C43—21no—
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—81no—
217C22×C43—81no—
218C22×C43—81no—
219C22×C43C22×D811yescharacteristic
220C2×D43—81no—
221C2×D43—81no—
222C2×D43—81no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—81no—
229C4×C43—81no—
230C4×C43—81no—
231C4×C43#53711yescharacteristic
232C4×C43#57511yescharacteristic
233Dic43—81no—
234Dic43—81no—
235Dic43—81no—
236#3175—431no—
237#3175D4311yescharacteristic, complemented
238#2226—431no—
239#2226—431no—
240#2225—431no—
241#2225—431no—
242#2219—431no—
243#2218—431no—
244#2217—431no—
245#2217—431no—
246#2211—431no—
247#2211—431no—
248#2210—431no—
249#2210—431no—
250#2151—431no—
251C2×C43—41no—
252C2×C43—161no—
253C2×C43#324511yescharacteristic
254C2×C43#341611yescharacteristic
255C2×C43#341611yescharacteristic
256D43—161no—
257#542—21no—
258#542—861no—
259C2×Q32—431no—
260C2×SD32—431no—
261C2×SD32—431no—
262C2×D16—431no—
263C2×M32—431no—
264C22×C16—431no—
265#500—431no—
266#500C2×D4311yescharacteristic
267#495—431no—
268#495C2×D4311yescharacteristic
269#489—21no—
270#489—861no—
271#468—21no—
272#468—861no—
273#467—431no—
274#467C2×D4311yescharacteristic
275#466—431no—
276#466C2×D4311yescharacteristic
277#440—21no—
278#440—861no—
279C4×Q16—431no—
280C4×Q16C2×D4311yescharacteristic
281C4×D8—431no—
282C4×D8C2×D4311yescharacteristic
283#405C2×D4311yescharacteristic
284#367—431no—
285#367—431no—
286#367—431no—
287#367—431no—
288C4⋊C16—431no—
289C4⋊C16—431no—
290C4⋊C16—431no—
291C4⋊C16—431no—
292#358—431no—
293#358—431no—
294#358—431no—
295#358—431no—
296#357—431no—
297#357—431no—
298#357—431no—
299#357—431no—
300C43#3382911yescharacteristic, complemented, Sylow
301C2×Q16—431no—
302C2×Q16C22×D4311yescharacteristic
303C2×SD16—21no—
304C2×SD16—861no—
305C2×D8—431no—
306C2×D8C22×D4311yescharacteristic
307C2×M16C22⋊D4311yescharacteristic
308C22×C8C22×D4311yescharacteristic
309C4⋊Q8—21no—
310C4⋊Q8—861no—
311#126—41no—
312#126—1721no—
313#124—21no—
314#124—41no—
315#124—861no—
316#124—1721no—
317#123—41no—
318#123—1721no—
319C22⋊Q8—21no—
320C22⋊Q8—41no—
321C22⋊Q8—861no—
322C22⋊Q8—1721no—
323#121—21no—
324#121—861no—
325C4×Q8—21no—
326C4×Q8—861no—
327C4×D4—21no—
328C4×D4—861no—
329#117C22⋊D4311yescharacteristic
330Q32—1721no—
331SD32—1721no—
332SD32—1721no—
333D16—1721no—
334M32—1721no—
335C2×C16—431no—
336C2×C16—431no—
337C2×C16—431no—
338C2×C16—431no—
339C2×C16—1721no—
340#107—21no—
341#107—431no—
342#107—431no—
343#107—861no—
344#107C22×D4311yescharacteristic
345#107C22×D4311yescharacteristic
346#103—21no—
347#103—21no—
348#103—861no—
349#103—861no—
350#102—21no—
351#102—21no—
352#102—861no—
353#102—861no—
354#97C22⋊D4311yescharacteristic
355#97C22⋊D4311yescharacteristic
356C4×C8C22×D4311yescharacteristic
357C4×C8C22×D4311yescharacteristic
358C2×Q8—21no—
359C2×Q8—41no—
360C2×Q8—861no—
361C2×Q8—1721no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4—861no—
365C2×D4—1721no—
366C22×C4—41no—
367C22×C4—1721no—
368C22×C4C2×C22⋊D4311yescharacteristic
369Q16—21no—
370Q16—21no—
371Q16—861no—
372Q16—861no—
373SD16—42no—
374SD16—1722no—
375D8—21no—
376D8—21no—
377D8—861no—
378D8—861no—
379M16—41no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8C2×C22⋊D4311yescharacteristic
383C2×C8C2×C22⋊D4311yescharacteristic
384C2×C8C2×C22⋊D4311yescharacteristic
385C2×C8C23×D4311yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—861no—
392C4⋊C4—861no—
393C4⋊C4—1721no—
394C4⋊C4—1721no—
395C4⋊C4—1721no—
396C4⋊C4#1062188211yescharacteristic
397C4⋊C4#1062188211yescharacteristic
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—1721no—
404C22⋊C4—1721no—
405C22⋊C4—1721no—
406C22⋊C4—1721no—
407C22⋊C4—1721no—
408C22⋊C4#1062188211yescharacteristic
409C22⋊C4#1062188211yescharacteristic
410C42—41no—
411C42—1721no—
412C42C2×C22⋊D4311yescharacteristic
413C42C2×C22⋊D4311yescharacteristic
414C16—861no—
415C16—861no—
416C16—861no—
417C16—861no—
418C23—41no—
419C23—1721no—
420C23C2×#1062188211yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—161no—
424Q8—1721no—
425Q8—1721no—
426Q8—6881no—
427D4—41no—
428D4—41no—
429D4—161no—
430D4—1721no—
431D4—1721no—
432D4—6881no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—161no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4—6881no—
443C2×C4C2×#1062188211yescharacteristic
444C2×C4C2×#1062188211yescharacteristic
445C2×C4C2×#1062188211yescharacteristic
446C2×C4C2×#1062188211yescharacteristic
447C2×C4C2×#1062188211yescharacteristic
448C2×C4C22×C22⋊D4311yescharacteristic
449C8—21no—
450C8—21no—
451C8—21no—
452C8#1306337111yescharacteristic
453C8#1306337211yescharacteristic
454C22—21no—
455C22—21no—
456C22—21no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—3441no—
461C22—3441no—
462C22—3441no—
463C22C22×#1062188211yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4—3441no—
473C4—3441no—
474C4—3441no—
475C4#1458347711yescharacteristic
476C4#1458369711yescharacteristic
477C2—41no—
478C2—161no—
479C2—6881no—
480C2#1914590211yescharacteristic
481C2#1914773911yescharacteristic
482C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3175C2
socleC22×C43C22×D8
prime radical#19136696C2
hypercenter#3175D43
hypocenterC43#33829
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #19145234C2semidirect
2. #19136742C2semidirect
3. #19136739C2semidirect
4. #19136737C2semidirect
5. #19136734C2semidirect
6. #19136701C2semidirect
8. #19136693C2semidirect
9. #19136689C2semidirect
10. #19136657C2semidirect
11. #19136654C2semidirect
12. #19136650C2semidirect
13. #19136647C2semidirect
14. #19136354C2semidirect
15. C43×#3175C2semidirect
237. #3175D43semidirect
300. C43#33829semidirect

Maximal subgroups

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

subgroupindex
#191452342
#191367422
#191367392
#191367372
#191367342
#191367012
#191366962
#191366932
#191366892
#191366572
#191366542
#191366502
#191366472
#191363542
C43×#31752
#3382943