Finite Group Databasebeta

← #25251750

Subgroups — #25251750

Order 11008.

532 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145234C211yesmaximal, characteristic
2#19136803C211yesmaximal, characteristic, complemented
3#19136786C211yesmaximal, characteristic
4#19136747C211yesmaximal, characteristic, complemented
5#19136737C211yesmaximal, characteristic, complemented
6#19136657C211yesmaximal, characteristic, complemented
7#19136657C211yesmaximal, characteristic, complemented
8#19136529C211yesmaximal, characteristic, complemented
9#19136512C211yesmaximal, characteristic
10#19136464C211yesmaximal, characteristic, complemented
11#19136457C211yesmaximal, characteristic, complemented
12C4×#13063271C211yesmaximal, characteristic, complemented
13C4×#13063268C211yesmaximal, characteristic, complemented
14#19136402C211yesmaximal, characteristic, complemented
15C43×#2950C211yesmaximal, characteristic, complemented
16#14583520—21no—
17C2×#13063271C2211yescharacteristic
18C2×#13063271C2211yescharacteristic
19C2×#13063268C2211yescharacteristic
20C2×#13063268C2211yescharacteristic
21#14583304C2211yescharacteristic
22#14583283C2211yescharacteristic
23#14583259—21no—
24#14583145—21no—
25#14583140C2211yescharacteristic
26#14583135C2211yescharacteristic
27#14583001—21no—
28C4×Dic172C2211yescharacteristic
29C4×D344C2211yescharacteristic
30#14582726C2211yescharacteristic
31#14582726C2211yescharacteristic
32#14582724C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35C4⋊(C43⋊C16)C2211yescharacteristic
36#14582703C2211yescharacteristic
37#14582703C2211yescharacteristic
38#14582703C2211yescharacteristic
39#14582703C2211yescharacteristic
40#14582702C2211yescharacteristic
41#14582702C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44C22⋊(C43⋊C16)C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46#14582675C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C22×Q16×C43C2211yescharacteristic
49C43×#519—21no—
50C43×#441—21no—
51C43×#441—21no—
52C4×Q16×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C4×Q16×C43C2211yescharacteristic
55C4×Q16×C43C2211yescharacteristic
56C43×#427C2211yescharacteristic
57C43×#419—21no—
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—22no—
73#13063271—22no—
74#13063268—22no—
75#13063268—22no—
76C2×C43⋊C16C2311yescharacteristic
77C2×C43⋊C16C2311yescharacteristic
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80#13063259—21no—
81#13063259C2311yescharacteristic
82#13063259C2311yescharacteristic
83#13063250—21no—
84#13063250—21no—
85#13063247—21no—
86#13063247—21no—
87C22×Q8×C43—21no—
88C2×Q16×C43—22no—
89C2×Q16×C43—22no—
90C2×Q16×C43—21no—
91C2×Q16×C43C2311yescharacteristic
92C2×Q16×C43C2311yescharacteristic
93C2×M16×C43D411yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43—41no—
100C4×Q8×C43—41no—
101#117×C43—21no—
102#117×C43—41no—
103#117×C43—41no—
104#117×C43D411yescharacteristic
105#107×C43C2311yescharacteristic
106#107×C43C2311yescharacteristic
107#106×C43—21no—
108#103×C43—21no—
109#103×C43—21no—
110#103×C43—21no—
111#103×C43—21no—
112#97×C43D411yescharacteristic
113#97×C43D411yescharacteristic
114C4×C8×C43C2311yescharacteristic
115C4×C8×C43C2311yescharacteristic
116C2×Q8×C43—24no—
117C2×Q8×C43—21no—
118C2×Q8×C43—21no—
119C2×Q8×C43—42no—
120C2×Q8×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43C2×D411yescharacteristic
123C2×C22⋊D43—41no—
124C2×D172—21no—
125C2×C4×D43—41no—
126C2×Dic86—21no—
127C2×Dic86—41no—
128Q16×C43—24no—
129Q16×C43—21no—
130Q16×C43—21no—
131Q16×C43#4112yes—
132Q16×C43#4112yes—
133M16×C43—41no—
134C2×C8×C43—21no—
135C2×C8×C43—21no—
136C2×C8×C43C2×D411yescharacteristic
137C2×C8×C43C2×D411yescharacteristic
138C2×C8×C43C2×D411yescharacteristic
139C2×C8×C43C2411yescharacteristic
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43D811yescharacteristic
147C4⋊C4×C43D811yescharacteristic
148C22⋊C4×C43—41no—
149C22⋊C4×C43D811yescharacteristic
150C22⋊C4×C43D811yescharacteristic
151C42×C43—41no—
152C42×C43—41no—
153C42×C43—41no—
154C42×C43—41no—
155C42×C43—41no—
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C22⋊Dic43—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—41no—
166Dic43⋊C4—41no—
167Dic43⋊C4—41no—
168C4×Dic43—41no—
169Dic172—21no—
170Dic172—21no—
171D344—21no—
172D344—21no—
173#10621873—42no—
174C43⋊C16—21no—
175C43⋊C16—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43C2×D811yescharacteristic
179C22×D43—41no—
180Q8×C43—22no—
181Q8×C43—22no—
182Q8×C43—44no—
183Q8×C43—41no—
184Q8×C43—41no—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—44no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43C2×D811yescharacteristic
193C2×C4×C43C2×D811yescharacteristic
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C2×D811yescharacteristic
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C22⋊D43—161no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202D172—41no—
203D172—41no—
204C4×D43—161no—
205Dic86—41no—
206Dic86—41no—
207Dic86—161no—
208C8×C43—21no—
209C8×C43—21no—
210C8×C43—21no—
211C8×C43C2×#4111yescharacteristic
212C8×C43C2×#4111yescharacteristic
213#33681—431nomaximal, Sylow
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—21no—
217C22×C43C22×D811yescharacteristic
218C2×D43—81no—
219C2×D43—81no—
220C2×D43—81no—
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—42no—
227C4×C43—42no—
228C4×C43—81no—
229C4×C43—81no—
230C4×C43#52511yescharacteristic
231C4×C43#57511yescharacteristic
232Dic43—81no—
233Dic43—81no—
234Dic43—81no—
235#3175—431no—
236#2950D4311yescharacteristic, complemented
237#2237—431no—
238#2234—431no—
239#2227—431no—
240#2225—431no—
241#2211—431no—
242#2211—431no—
243#2188—431no—
244#2185—431no—
245#2176—431no—
246#2175—431no—
247C4×Q32—431no—
248C4×SD32—431no—
249#2164—431no—
250C2×C43—41no—
251C2×C43#310011yescharacteristic
252C2×C43#341611yescharacteristic
253C2×C43#341711yescharacteristic
254D43—161no—
255C22×Q16C2×D4311yescharacteristic
256#542—861no—
257#519—21no—
258C2×Q32—431no—
259C2×Q32—431no—
260C2×SD32—431no—
261C2×SD32—431no—
262#500—431no—
263#495—431no—
264#489—861no—
265#468—861no—
266#467—431no—
267#466—431no—
268#441—21no—
269#441—21no—
270#440—861no—
271C4×Q16—431no—
272C4×Q16C2×D4311yescharacteristic
273C4×Q16C2×D4311yescharacteristic
274C4×Q16C2×D4311yescharacteristic
275C4×Q16C2×D4311yescharacteristic
276C4×D8—431no—
277#427C2×D4311yescharacteristic
278#419—21no—
279#405C2×D4311yescharacteristic
280#367—431no—
281#367—431no—
282#366—431no—
283#366—431no—
284C4⋊C16—431no—
285C4⋊C16—431no—
286#358—431no—
287#358—431no—
288#358—431no—
289#358—431no—
290#358—431no—
291#358—431no—
292#357—431no—
293#357—431no—
294C22⋊C16—431no—
295C22⋊C16—431no—
296#346—431no—
297C4×C16—431no—
298C43#3368111yescharacteristic, complemented, Sylow
299C22×Q8—21no—
300C2×Q16—22no—
301C2×Q16—22no—
302C2×Q16—21no—
303C2×Q16—431no—
304C2×Q16C22×D4311yescharacteristic
305C2×Q16C22×D4311yescharacteristic
306C2×SD16—861no—
307C2×D8—431no—
308C2×M16C22⋊D4311yescharacteristic
309C22×C8C22×D4311yescharacteristic
310C4⋊Q8—861no—
311#126—1721no—
312#124—861no—
313#124—1721no—
314#123—1721no—
315C22⋊Q8—861no—
316C22⋊Q8—1721no—
317#121—861no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—41no—
323C4×Q8—41no—
324C4×Q8—861no—
325C4×D4—861no—
326#117—21no—
327#117—41no—
328#117—41no—
329#117C22⋊D4311yescharacteristic
330Q32—862no—
331Q32—862no—
332SD32—862no—
333SD32—862no—
334C2×C16—431no—
335C2×C16—431no—
336C2×C16—431no—
337C2×C16—431no—
338#107—431no—
339#107—431no—
340#107—861no—
341#107C22×D4311yescharacteristic
342#107C22×D4311yescharacteristic
343#106—21no—
344#103—21no—
345#103—21no—
346#103—21no—
347#103—21no—
348#103—861no—
349#103—861no—
350#102—861no—
351#102—861no—
352#97C22⋊D4311yescharacteristic
353#97C22⋊D4311yescharacteristic
354C4×C8C22×D4311yescharacteristic
355C4×C8C22×D4311yescharacteristic
356C2×Q8—24no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—42no—
360C2×Q8—41no—
361C2×Q8—861no—
362C2×Q8—1721no—
363C2×D4—861no—
364C2×D4—1721no—
365C22×C4—41no—
366C22×C4—1721no—
367C22×C4C2×C22⋊D4311yescharacteristic
368Q16—24no—
369Q16—21no—
370Q16—21no—
371Q16—861no—
372Q16—861no—
373Q16#1062189812yes—
374Q16#1062189812yes—
375SD16—1722no—
376D8—861no—
377D8—861no—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×C22⋊D4311yescharacteristic
382C2×C8C2×C22⋊D4311yescharacteristic
383C2×C8C2×C22⋊D4311yescharacteristic
384C2×C8C23×D4311yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
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—1721no—
400C22⋊C4—1721no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C22⋊C4—1721no—
404C22⋊C4#1062188211yescharacteristic
405C22⋊C4#1062188211yescharacteristic
406C42—41no—
407C42—41no—
408C42—41no—
409C42—41no—
410C42—41no—
411C42—1721no—
412C42C2×C22⋊D4311yescharacteristic
413C42C2×C22⋊D4311yescharacteristic
414C16—861no—
415C16—861no—
416C16—861no—
417C16—861no—
418C23—1721no—
419C23C2×#1062188211yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—44no—
423Q8—41no—
424Q8—41no—
425Q8—1721no—
426Q8—1721no—
427Q8—6881no—
428D4—1721no—
429D4—1721no—
430D4—6881no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—6881no—
442C2×C4C2×#1062188211yescharacteristic
443C2×C4C2×#1062188211yescharacteristic
444C2×C4C2×#1062188211yescharacteristic
445C2×C4C2×#1062188211yescharacteristic
446C2×C4C2×#1062188211yescharacteristic
447C2×C4C22×C22⋊D4311yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8C2×#1062189811yescharacteristic
452C8C2×#1062189811yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—3441no—
457C22—3441no—
458C22—3441no—
459C22C22×#1062188211yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—3441no—
470C4—3441no—
471C4—3441no—
472C4#1458341011yescharacteristic
473C4#1458369711yescharacteristic
474C2—41no—
475C2—6881no—
476C2#1914459511yescharacteristic
477C2#1914773911yescharacteristic
478C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2950C2
socleC22×C43C22×D8
prime radical#14583135C22
hypercenter#2950D43
hypocenterC43#33681
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2950

Complements

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

NH ≅ G/Ntype
2. #19136803C2semidirect
4. #19136747C2semidirect
5. #19136737C2semidirect
6. #19136657C2semidirect
7. #19136657C2semidirect
8. #19136529C2semidirect
10. #19136464C2semidirect
11. #19136457C2semidirect
12. C4×#13063271C2semidirect
13. C4×#13063268C2semidirect
14. #19136402C2semidirect
15. C43×#2950C2semidirect
236. #2950D43semidirect
298. C43#33681semidirect

Maximal subgroups

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

subgroupindex
#191452342
#191368032
#191367862
#191367472
#191367372
#191366572
#191365292
#191365122
#191364642
#191364572
C4×#130632712
C4×#130632682
#191364022
C43×#29502
#3368143