Finite Group Databasebeta

← #25251735

Subgroups — #25251735

Order 11008.

534 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#19145254C211yesmaximal, characteristic, complemented
2#19136797C211yesmaximal, characteristic, complemented
3#19136792C211yesmaximal, characteristic, complemented
4#19136759C211yesmaximal, characteristic, complemented
5#19136752C211yesmaximal, characteristic, complemented
6#19136645C211yesmaximal, characteristic, complemented
7#19136640C211yesmaximal, characteristic, complemented
8#19136535C211yesmaximal, characteristic
9#19136535C211yesmaximal, characteristic
10#19136464C211yesmaximal, characteristic, complemented
11#19136459C211yesmaximal, characteristic, complemented
12C4×#13063271C211yesmaximal, characteristic, complemented
13C4×#13063269C211yesmaximal, characteristic, complemented
14#19136402C211yesmaximal, characteristic, complemented
15C43×#2951C211yesmaximal, characteristic
16#14583511—21no—
17C2×#13063271C2211yescharacteristic
18C2×#13063271C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20C2×#13063269C2211yescharacteristic
21#14583301C2211yescharacteristic
22#14583279C2211yescharacteristic
23#14583268—21no—
24#14583157—21no—
25#14583140C2211yescharacteristic
26#14583140C2211yescharacteristic
27#14583007—21no—
28C4×Dic172C2211yescharacteristic
29C4×Dic172C2211yescharacteristic
30#14582726C2211yescharacteristic
31#14582726C2211yescharacteristic
32#14582724C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35C4⋊(C43⋊C16)C2211yescharacteristic
36#14582703C2211yescharacteristic
37#14582703C2211yescharacteristic
38#14582702C2211yescharacteristic
39#14582702C2211yescharacteristic
40#14582702C2211yescharacteristic
41#14582702C2211yescharacteristic
42#14582700C2211yescharacteristic
43#14582700C2211yescharacteristic
44C22⋊(C43⋊C16)C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46#14582675C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C2×#135×C43C2211yescharacteristic
49C43×#520—21no—
50C43×#440—21no—
51C43×#440—21no—
52C4×Q16×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C4×D8×C43C2211yescharacteristic
55C4×D8×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C43×#417—21no—
58C43×#405C2211yescharacteristic
59C2×Dic172—21no—
60C2×Dic172C2311yescharacteristic
61C2×Dic172C2311yescharacteristic
62#13063325—21no—
63#13063318—41no—
64#13063318—41no—
65#13063317—21no—
66#13063315—41no—
67#13063315—41no—
68#13063304—21no—
69#13063304—21no—
70C4×Dic86—21no—
71C4×Dic86—21no—
72#13063271—22no—
73#13063271—22no—
74#13063269—22no—
75#13063269—22no—
76C2×C43⋊C16C2311yescharacteristic
77C2×C43⋊C16C2311yescharacteristic
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80#13063259C2311yescharacteristic
81#13063259C2311yescharacteristic
82#13063257—21no—
83#13063250—21no—
84#13063250—21no—
85#13063250—21no—
86#13063250—21no—
87C2×#41×C43—21no—
88#135×C43—22no—
89#135×C43—22no—
90C2×Q16×C43C2311yescharacteristic
91C2×SD16×C43—21no—
92C2×D8×C43C2311yescharacteristic
93C2×M16×C43D411yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—41no—
100C4×D4×C43—41no—
101#117×C43—41no—
102#117×C43D411yescharacteristic
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—41no—
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
116#41×C43—24no—
117#41×C43—42no—
118C2×Q8×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43C2×D411yescharacteristic
126C2×Dic86—21no—
127C2×Dic86—21no—
128Q16×C43—21no—
129Q16×C43#4112yes—
130SD16×C43—24no—
131D8×C43—21no—
132D8×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×C43D811yescharacteristic
146C4⋊C4×C43D811yescharacteristic
147C22⋊C4×C43—41no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43D811yescharacteristic
150C22⋊C4×C43D811yescharacteristic
151C42×C43—41no—
152C42×C43—41no—
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C22⋊Dic43—41no—
156C22⋊Dic43—41no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—41no—
160C4⋊Dic43—41no—
161Dic43⋊C4—41no—
162Dic43⋊C4—41no—
163Dic43⋊C4—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167C4×Dic43—41no—
168C4×Dic43—41no—
169Dic172—21no—
170Dic172—21no—
171Dic172—21no—
172Dic172—21no—
173Dic172—42no—
174C43⋊C16—21no—
175C43⋊C16—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—41no—
179C23×C43C2×D811yescharacteristic
180Q8×C43—22no—
181Q8×C43—41no—
182D4×C43—22no—
183D4×C43—44no—
184D4×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—161no—
192C2×C4×C43—161no—
193C2×C4×C43—161no—
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C2×D811yescharacteristic
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C2×D811yescharacteristic
198C2×C4×C43C2×D811yescharacteristic
199C2×C4×C43C22×D411yescharacteristic
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—41no—
203C2×Dic43—41no—
204Dic86—41no—
205Dic86—41no—
206Dic86—41no—
207Dic86—41no—
208C8×C43—21no—
209C8×C43—21no—
210C8×C43—21no—
211C8×C43C2×#4111yescharacteristic
212C8×C43C2×#4111yescharacteristic
213#33680—431nomaximal, Sylow
214C22×C43—21no—
215C22×C43—21no—
216C22×C43—21no—
217C22×C43—42no—
218C22×C43—81no—
219C22×C43—81no—
220C22×C43C22×D811yescharacteristic
221C4×C43—21no—
222C4×C43—21no—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—42no—
227C4×C43—81no—
228C4×C43—81no—
229C4×C43#52511yescharacteristic
230C4×C43#57511yescharacteristic
231Dic43—81no—
232Dic43—81no—
233Dic43—81no—
234Dic43—81no—
235#3177—431no—
236#2951D4311yescharacteristic
237#2236—431no—
238#2235—431no—
239#2229—431no—
240#2228—431no—
241#2209—431no—
242#2208—431no—
243#2189—431no—
244#2189—431no—
245#2176—431no—
246#2175—431no—
247C4×Q32—431no—
248C4×SD32—431no—
249#2164—431no—
250C2×C43—41no—
251C2×C43—82no—
252C2×C43#310011yescharacteristic
253C2×C43#341611yescharacteristic
254C2×C43#341711yescharacteristic
255C2×#135C2×D4311yescharacteristic
256#541—861no—
257#520—21no—
258C2×Q32—431no—
259C2×Q32—431no—
260C2×SD32—431no—
261C2×SD32—431no—
262#499—431no—
263#494—431no—
264#491—861no—
265#470—861no—
266#467—431no—
267#467—431no—
268#441—861no—
269#440—21no—
270#440—21no—
271C4×Q16—431no—
272C4×Q16—431no—
273C4×Q16C2×D4311yescharacteristic
274C4×Q16C2×D4311yescharacteristic
275C4×D8C2×D4311yescharacteristic
276C4×D8C2×D4311yescharacteristic
277C2×#107C2×D4311yescharacteristic
278#417—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#3368011yescharacteristic, complemented, Sylow
299C2×#41—21no—
300#135—22no—
301#135—22no—
302C2×Q16—431no—
303C2×Q16—431no—
304C2×Q16—861no—
305C2×Q16C22×D4311yescharacteristic
306C2×SD16—21no—
307C2×D8C22×D4311yescharacteristic
308C2×M16C22⋊D4311yescharacteristic
309C22×C8C22×D4311yescharacteristic
310C4⋊Q8—861no—
311#126—1721no—
312#126—1721no—
313#125—861no—
314#125—1721no—
315#125—1721no—
316C22⋊Q8—861no—
317C22⋊Q8—861no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—861no—
321C4×Q8—861no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—41no—
325C4×D4—41no—
326#117—41no—
327#117C22⋊D4311yescharacteristic
328C2×C4⋊C4—21no—
329C2×C4⋊C4—41no—
330Q32—862no—
331Q32—862no—
332SD32—862no—
333SD32—862no—
334C2×C16—431no—
335C2×C16—431no—
336C2×C16—431no—
337C2×C16—431no—
338#107—21no—
339#107—431no—
340#107—431no—
341#107C22×D4311yescharacteristic
342#107C22×D4311yescharacteristic
343#106—861no—
344#103—21no—
345#103—21no—
346#103—861no—
347#103—861no—
348#103—861no—
349#103—861no—
350#102—21no—
351#102—21no—
352#97C22⋊D4311yescharacteristic
353#97C22⋊D4311yescharacteristic
354C4×C8C22×D4311yescharacteristic
355C4×C8C22×D4311yescharacteristic
356#41—24no—
357#41—42no—
358C2×Q8—21no—
359C2×Q8—861no—
360C2×Q8—861no—
361C2×D4—21no—
362C2×D4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4C2×C22⋊D4311yescharacteristic
368Q16—21no—
369Q16—861no—
370Q16—861no—
371Q16—861no—
372Q16—861no—
373Q16—1722no—
374Q16#1062189812yes—
375SD16—24no—
376D8—21no—
377D8#1062189812yes—
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—861no—
391C4⋊C4—861no—
392C4⋊C4—1721no—
393C4⋊C4—1721no—
394C4⋊C4—1721no—
395C4⋊C4—1721no—
396C4⋊C4—1721no—
397C4⋊C4—1721no—
398C4⋊C4—1721no—
399C4⋊C4—1721no—
400C4⋊C4#1062188211yescharacteristic
401C4⋊C4#1062188211yescharacteristic
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—1721no—
405C22⋊C4—1721no—
406C22⋊C4#1062188211yescharacteristic
407C22⋊C4#1062188211yescharacteristic
408C42—41no—
409C42—41no—
410C42—1721no—
411C42—1721no—
412C42C2×C22⋊D4311yescharacteristic
413C42C2×C22⋊D4311yescharacteristic
414C16—861no—
415C16—861no—
416C16—861no—
417C16—861no—
418C23—41no—
419C23C2×#1062188211yescharacteristic
420Q8—22no—
421Q8—41no—
422Q8—1721no—
423Q8—1721no—
424Q8—1721no—
425Q8—1721no—
426D4—22no—
427D4—44no—
428D4—41no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—44no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—161no—
436C2×C4—161no—
437C2×C4—161no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
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—42no—
457C22—81no—
458C22—81no—
459C22C22×#1062188211yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—81no—
467C4—81no—
468C4—3441no—
469C4—3441no—
470C4—3441no—
471C4—3441no—
472C4#1458341011yescharacteristic
473C4#1458369711yescharacteristic
474C2—41no—
475C2—82no—
476C2#1914459511yescharacteristic
477C2#1914774211yescharacteristic
478C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2951C2
socleC22×C43C22×D8
prime radicalC2×#135×C43C22
hypercenter#2951D43
hypocenterC43#33680
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #19145254C2semidirect
2. #19136797C2semidirect
3. #19136792C2semidirect
4. #19136759C2semidirect
5. #19136752C2semidirect
6. #19136645C2semidirect
7. #19136640C2semidirect
10. #19136464C2semidirect
11. #19136459C2semidirect
12. C4×#13063271C2semidirect
13. C4×#13063269C2semidirect
14. #19136402C2semidirect
298. C43#33680semidirect

Maximal subgroups

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

subgroupindex
#191452542
#191367972
#191367922
#191367592
#191367522
#191366452
#191366402
#191365352
#191364642
#191364592
C4×#130632712
C4×#130632692
#191364022
C43×#29512
#3368043