Finite Group Databasebeta

← #25254682

Subgroups — #25254682

Order 11008.

504 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147584C211yesmaximal, characteristic, complemented
2#19136867C211yesmaximal, characteristic, complemented
3#19136864C211yesmaximal, characteristic, complemented
4#19136854C211yesmaximal, characteristic
5#19136657C211yesmaximal, characteristic, complemented
6#19136654C211yesmaximal, characteristic, complemented
7#19136650C211yesmaximal, characteristic
8#19136647C211yesmaximal, characteristic
9#19136645C211yesmaximal, characteristic, complemented
10#19136642C211yesmaximal, characteristic, complemented
11#19136504C211yesmaximal, characteristic, complemented
12#19136459C211yesmaximal, characteristic, complemented
13#19136457C211yesmaximal, characteristic, complemented
14C4×#13063271C211yesmaximal, characteristic, complemented
15C43×#3393C211yesmaximal, characteristic, complemented
16#14583622—21no—
17C2×#13063271C2211yescharacteristic
18C2×#13063271C2211yescharacteristic
19C2×#13063271C2211yescharacteristic
20C2×#13063271C2211yescharacteristic
21C2×#13063269C2211yescharacteristic
22C2×#13063269C2211yescharacteristic
23C2×#13063268C2211yescharacteristic
24C2×#13063268C2211yescharacteristic
25C2×#13063266C2211yescharacteristic
26#14583283C2211yescharacteristic
27#14583283C2211yescharacteristic
28#14583279C2211yescharacteristic
29#14583122—21no—
30#14583122—21no—
31#14583105—21no—
32C4×Dic172C2211yescharacteristic
33C4×Dic172C2211yescharacteristic
34C4×D344C2211yescharacteristic
35#14582724C2211yescharacteristic
36C4⋊(C43⋊C16)C2211yescharacteristic
37C4⋊(C43⋊C16)C2211yescharacteristic
38C4⋊(C43⋊C16)C2211yescharacteristic
39#14582703C2211yescharacteristic
40#14582703C2211yescharacteristic
41#14582702C2211yescharacteristic
42#14582702C2211yescharacteristic
43#14582700C2211yescharacteristic
44#14582699C2211yescharacteristic
45#14582675C2211yescharacteristic
46#14582675C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C43×#556—21no—
49C43×#495C2211yescharacteristic
50C43×#495C2211yescharacteristic
51C43×#494C2211yescharacteristic
52C43×#464—21no—
53C43×#464—21no—
54C43×#461—21no—
55C8×Q8×C43C2211yescharacteristic
56C4×Q16×C43C2211yescharacteristic
57C4×Q16×C43C2211yescharacteristic
58C4×D8×C43C2211yescharacteristic
59C2×Dic172—21no—
60C2×Dic172C2311yescharacteristic
61C2×Dic172C2311yescharacteristic
62C2×#10621873—21no—
63C2×#10621873—21no—
64C2×D344C2311yescharacteristic
65#13063325—21no—
66#13063320—41no—
67#13063320—41no—
68#13063313—21no—
69#13063313—21no—
70#13063301—41no—
71C4×Dic86—21no—
72C4×Dic86—21no—
73C4×D172—21no—
74#13063283—41no—
75#13063271—22no—
76#13063271—41no—
77#13063271—41no—
78#13063271—41no—
79#13063269—22no—
80#13063269—41no—
81#13063268—22no—
82#13063268—41no—
83#13063266—41no—
84C2×C43⋊C16C2311yescharacteristic
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063250—21no—
90#13063250—21no—
91#13063247—21no—
92C2×Q16×C43—21no—
93C2×Q16×C43C2311yescharacteristic
94C2×Q16×C43C2311yescharacteristic
95C2×SD16×C43—21no—
96C2×SD16×C43—21no—
97C2×D8×C43C2311yescharacteristic
98C4⋊Q8×C43—21no—
99#126×C43—41no—
100#126×C43—41no—
101#124×C43—21no—
102#124×C43—21no—
103C22⋊Q8×C43—41no—
104C4×Q8×C43—21no—
105C4×Q8×C43—21no—
106C4×Q8×C43D411yescharacteristic
107C4×D4×C43—21no—
108#117×C43—41no—
109#107×C43C2311yescharacteristic
110C4⋊C8×C43D411yescharacteristic
111C4⋊C8×C43D411yescharacteristic
112C4⋊C8×C43D411yescharacteristic
113#103×C43—21no—
114#103×C43—21no—
115#102×C43—21no—
116C4×C8×C43C2311yescharacteristic
117C4×C8×C43C2311yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C2×Q8×C43—21no—
120C2×Q8×C43—21no—
121C2×Q8×C43D811yescharacteristic
122C2×D4×C43—21no—
123C22×C4×C43—41no—
124C2×D172—21no—
125C2×C4×D43—41no—
126C2×Dic86—21no—
127C2×Dic86—21no—
128Q16×C43—21no—
129Q16×C43—21no—
130Q16×C43—21no—
131Q16×C43—21no—
132Q16×C43—81no—
133SD16×C43—81no—
134SD16×C43—81no—
135D8×C43—21no—
136D8×C43—21no—
137C2×C8×C43C2×D411yescharacteristic
138C2×C8×C43C2×D411yescharacteristic
139C2×C8×C43C2×D411yescharacteristic
140C2×C8×C43C2411yescharacteristic
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
148C4⋊C4×C43D811yescharacteristic
149C22⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C22⋊C4×C43—41no—
154C42×C43—41no—
155C42×C43—41no—
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C42×C43C2×D411yescharacteristic
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163(C2×D43)⋊C4—41no—
164C4⋊Dic43—21no—
165C4⋊Dic43—41no—
166C4⋊Dic43—41no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169C4×Dic43—41no—
170C4×Dic43—41no—
171Dic172—21no—
172Dic172—21no—
173Dic172—21no—
174Dic172—21no—
175Dic172—81no—
176D344—21no—
177D344—21no—
178#10621873—81no—
179#10621873—81no—
180C43⋊C16—21no—
181C43⋊C16—21no—
182C43⋊C16—21no—
183C43⋊C16#4112yes—
184C23×C43—41no—
185C22×D43—41no—
186Q8×C43—41no—
187Q8×C43—41no—
188Q8×C43—41no—
189Q8×C43—41no—
190Q8×C43—41no—
191D4×C43—41no—
192D4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—82no—
197C2×C4×C43C2×D811yescharacteristic
198C2×C4×C43C2×D811yescharacteristic
199C2×C4×C43C2×D811yescharacteristic
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C2×D811yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207D172—41no—
208D172—41no—
209C4×D43—82no—
210Dic86—41no—
211Dic86—41no—
212Dic86—41no—
213Dic86—41no—
214C8×C43—21no—
215C8×C43—21no—
216C8×C43—21no—
217C8×C43C2×#4111yescharacteristic
218C8×C43H(5,𝔽2)11yescharacteristic
219#33969—431nomaximal, Sylow
220C22×C43—81no—
221C22×C43—81no—
222C22×C43—81no—
223C22×C43C22×D811yescharacteristic
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—81no—
234C4×C43—81no—
235C4×C43—81no—
236C4×C43#55011yescharacteristic
237C4×C43#57611yescharacteristic
238Dic43—81no—
239Dic43—81no—
240Dic43—81no—
241#3393—431no—
242#3393D4311yescharacteristic, complemented
243#2251—431no—
244#2251—431no—
245#2249—431no—
246#2211—431no—
247#2211—431no—
248#2210—431no—
249#2210—431no—
250#2209—431no—
251#2209—431no—
252#2183—431no—
253#2175—431no—
254#2175—431no—
255C4×Q32—431no—
256C2×C43—161no—
257C2×C43#339111yescharacteristic
258C2×C43#341411yescharacteristic
259C2×C43#341711yescharacteristic
260D43—161no—
261#556—21no—
262#556—861no—
263C2×Q32—431no—
264C2×Q32—431no—
265C2×Q32—431no—
266C2×Q32—431no—
267C2×SD32—431no—
268C2×SD32—431no—
269C2×SD32—431no—
270C2×SD32—431no—
271C2×D16—431no—
272#495—431no—
273#495—431no—
274#495C2×D4311yescharacteristic
275#495C2×D4311yescharacteristic
276#494—431no—
277#494C2×D4311yescharacteristic
278#464—21no—
279#464—21no—
280#464—861no—
281#464—861no—
282#461—21no—
283#461—861no—
284C8×Q8C2×D4311yescharacteristic
285C4×Q16—431no—
286C4×Q16—431no—
287C4×Q16C2×D4311yescharacteristic
288C4×Q16C2×D4311yescharacteristic
289C4×D8—431no—
290C4×D8C2×D4311yescharacteristic
291#366—431no—
292C4⋊C16—431no—
293C4⋊C16—431no—
294C4⋊C16—431no—
295#358—431no—
296#358—431no—
297#358—431no—
298#358—431no—
299#357—431no—
300#357—431no—
301#346—431no—
302#346—431no—
303C4×C16—431no—
304C43#3396911yescharacteristic, complemented, Sylow
305C2×Q16—21no—
306C2×Q16—431no—
307C2×Q16—431no—
308C2×Q16—861no—
309C2×Q16C22×D4311yescharacteristic
310C2×Q16C22×D4311yescharacteristic
311C2×SD16—21no—
312C2×SD16—21no—
313C2×SD16—861no—
314C2×SD16—861no—
315C2×D8—431no—
316C2×D8C22×D4311yescharacteristic
317C4⋊Q8—21no—
318C4⋊Q8—861no—
319#126—41no—
320#126—41no—
321#126—1721no—
322#126—1721no—
323#124—21no—
324#124—21no—
325#124—861no—
326#124—861no—
327C22⋊Q8—41no—
328C22⋊Q8—1721no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8—861no—
332C4×Q8—861no—
333C4×Q8C22⋊D4311yescharacteristic
334C4×D4—21no—
335C4×D4—861no—
336#117—41no—
337#117—1721no—
338Q32—862no—
339Q32—1721no—
340Q32—1721no—
341Q32—1721no—
342SD32—862no—
343SD32—862no—
344SD32—1721no—
345SD32—1721no—
346D16—1721no—
347C2×C16—431no—
348C2×C16—431no—
349C2×C16—431no—
350C2×C16—431no—
351#107—431no—
352#107C22×D4311yescharacteristic
353C4⋊C8C22⋊D4311yescharacteristic
354C4⋊C8C22⋊D4311yescharacteristic
355C4⋊C8C22⋊D4311yescharacteristic
356#103—21no—
357#103—21no—
358#103—861no—
359#103—861no—
360#102—21no—
361#102—861no—
362C4×C8C22×D4311yescharacteristic
363C4×C8C22×D4311yescharacteristic
364C4×C8C22×D4311yescharacteristic
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—861no—
368C2×Q8—861no—
369C2×Q8#1062188211yescharacteristic
370C2×D4—21no—
371C2×D4—861no—
372C22×C4—41no—
373C22×C4—1721no—
374Q16—21no—
375Q16—21no—
376Q16—21no—
377Q16—21no—
378Q16—81no—
379Q16—861no—
380Q16—861no—
381Q16—861no—
382Q16—861no—
383Q16—3441no—
384SD16—81no—
385SD16—81no—
386SD16—3441no—
387SD16—3441no—
388D8—21no—
389D8—21no—
390D8—861no—
391D8—861no—
392C2×C8C2×C22⋊D4311yescharacteristic
393C2×C8C2×C22⋊D4311yescharacteristic
394C2×C8C2×C22⋊D4311yescharacteristic
395C2×C8C23×D4311yescharacteristic
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—861no—
402C4⋊C4—1721no—
403C4⋊C4—1721no—
404C4⋊C4—1721no—
405C4⋊C4—1721no—
406C4⋊C4#1062188211yescharacteristic
407C4⋊C4#1062188211yescharacteristic
408C4⋊C4#1062188211yescharacteristic
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C22⋊C4—1721no—
417C22⋊C4—1721no—
418C22⋊C4—1721no—
419C42—41no—
420C42—41no—
421C42—1721no—
422C42—1721no—
423C42C2×C22⋊D4311yescharacteristic
424C42C2×C22⋊D4311yescharacteristic
425C42C2×C22⋊D4311yescharacteristic
426C16—432no—
427C16—861no—
428C16—861no—
429C16—861no—
430C23—41no—
431C23—1721no—
432Q8—41no—
433Q8—41no—
434Q8—41no—
435Q8—41no—
436Q8—41no—
437Q8—1721no—
438Q8—1721no—
439Q8—1721no—
440Q8—1721no—
441D4—41no—
442D4—41no—
443D4—1721no—
444D4—1721no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—82no—
449C2×C4—3442no—
450C2×C4—1721no—
451C2×C4—1721no—
452C2×C4—1721no—
453C2×C4C2×#1062188211yescharacteristic
454C2×C4C2×#1062188211yescharacteristic
455C2×C4C2×#1062188211yescharacteristic
456C2×C4C2×#1062188211yescharacteristic
457C2×C4C2×#1062188211yescharacteristic
458C2×C4C2×#1062188211yescharacteristic
459C2×C4C22×C22⋊D4311yescharacteristic
460C8—21no—
461C8—21no—
462C8—21no—
463C8#41×D4311yescharacteristic
464C8#1306337111yescharacteristic
465C22—81no—
466C22—81no—
467C22—81no—
468C22—3441no—
469C22—3441no—
470C22—3441no—
471C22C22×#1062188211yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—3441no—
482C4—3441no—
483C4—3441no—
484C4#1458356811yescharacteristic
485C4#1458370211yescharacteristic
486C2—161no—
487C2—6881no—
488C2#1914756711yescharacteristic
489C2#1914772911yescharacteristic
490C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3393C2
socleC22×C43C22×D8
prime radicalC2×#13063266C22
hypercenter#3393D43
hypocenterC43#33969
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. #19147584C2semidirect
2. #19136867C2semidirect
3. #19136864C2semidirect
5. #19136657C2semidirect
6. #19136654C2semidirect
9. #19136645C2semidirect
10. #19136642C2semidirect
11. #19136504C2semidirect
12. #19136459C2semidirect
13. #19136457C2semidirect
14. C4×#13063271C2semidirect
15. C43×#3393C2semidirect
242. #3393D43semidirect
304. C43#33969semidirect

Maximal subgroups

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

subgroupindex
#191475842
#191368672
#191368642
#191368542
#191366572
#191366542
#191366502
#191366472
#191366452
#191366422
#191365042
#191364592
#191364572
C4×#130632712
C43×#33932
#3396943