Finite Group Databasebeta

← #25254673

Subgroups — #25254673

Order 11008.

516 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147608C211yesmaximal, characteristic, complemented
2#19136864C211yesmaximal, characteristic, complemented
3#19136862C211yesmaximal, characteristic
4#19136854C211yesmaximal, characteristic, complemented
5#19136657C211yesmaximal, characteristic, complemented
6#19136654C211yesmaximal, characteristic, complemented
7#19136650C211yesmaximal, characteristic, complemented
8#19136647C211yesmaximal, characteristic, complemented
9#19136637C211yesmaximal, characteristic, complemented
10#19136635C211yesmaximal, characteristic, complemented
11#19136504C211yesmaximal, characteristic, complemented
12#19136469C211yesmaximal, characteristic, complemented
13#19136464C211yesmaximal, characteristic, complemented
14C4×#13063268C211yesmaximal, characteristic, complemented
15C43×#3393C211yesmaximal, characteristic, complemented
16#14583634—21no—
17C2×#13063271C2211yescharacteristic
18C2×#13063271C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20C2×#13063268C2211yescharacteristic
21C2×#13063268C2211yescharacteristic
22C2×#13063268C2211yescharacteristic
23C2×#13063268C2211yescharacteristic
24C2×#13063266C2211yescharacteristic
25C2×#13063266C2211yescharacteristic
26#14583283C2211yescharacteristic
27#14583283C2211yescharacteristic
28#14583276C2211yescharacteristic
29#14583115—21no—
30#14583115—21no—
31#14583100—21no—
32C4×Dic172C2211yescharacteristic
33C4×D344C2211yescharacteristic
34C4×D344C2211yescharacteristic
35#14582726C2211yescharacteristic
36C4⋊(C43⋊C16)C2211yescharacteristic
37C4⋊(C43⋊C16)C2211yescharacteristic
38C4⋊(C43⋊C16)C2211yescharacteristic
39#14582703C2211yescharacteristic
40#14582703C2211yescharacteristic
41#14582702C2211yescharacteristic
42#14582700C2211yescharacteristic
43#14582699C2211yescharacteristic
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×Dic172C2311yescharacteristic
60C2×#10621873—21no—
61C2×#10621873—21no—
62C2×D344—21no—
63C2×D344C2311yescharacteristic
64C2×D344C2311yescharacteristic
65#13063322—21no—
66#13063314—41no—
67#13063313—21no—
68#13063313—21no—
69#13063310—41no—
70#13063310—41no—
71C4×Dic86—21no—
72C4×D172—21no—
73C4×D172—21no—
74#13063287—41no—
75#13063271—22no—
76#13063271—41no—
77#13063269—41no—
78#13063268—22no—
79#13063268—41no—
80#13063268—41no—
81#13063268—41no—
82#13063266—22no—
83#13063266—41no—
84C2×C43⋊C16C2311yescharacteristic
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063250—21no—
90#13063247—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×D172—21no—
126C2×D172—41no—
127C2×D172—41no—
128C2×C4×D43—41no—
129C2×C4×D43—41no—
130C2×Dic86—21no—
131Q16×C43—21no—
132Q16×C43—21no—
133Q16×C43—21no—
134Q16×C43—21no—
135Q16×C43—81no—
136SD16×C43—81no—
137SD16×C43—81no—
138D8×C43—21no—
139D8×C43—21no—
140C2×C8×C43C2×D411yescharacteristic
141C2×C8×C43C2×D411yescharacteristic
142C2×C8×C43C2×D411yescharacteristic
143C2×C8×C43C2411yescharacteristic
144C4⋊C4×C43—21no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43—41no—
147C4⋊C4×C43—41no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43D811yescharacteristic
150C4⋊C4×C43D811yescharacteristic
151C4⋊C4×C43D811yescharacteristic
152C22⋊C4×C43—41no—
153C22⋊C4×C43—41no—
154C22⋊C4×C43—41no—
155C22⋊C4×C43—41no—
156C22⋊C4×C43—41no—
157C42×C43—41no—
158C42×C43—41no—
159C42×C43C2×D411yescharacteristic
160C42×C43C2×D411yescharacteristic
161C42×C43C2×D411yescharacteristic
162(C2×D43)⋊C4—41no—
163(C2×D43)⋊C4—41no—
164(C2×D43)⋊C4—41no—
165(C2×D43)⋊C4—41no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—41no—
168C4⋊Dic43—21no—
169Dic43⋊C4—41no—
170C4×Dic43—41no—
171Dic172—21no—
172Dic172—21no—
173D344—21no—
174D344—21no—
175D344—21no—
176D344—21no—
177D344—81no—
178#10621873—81no—
179#10621873—81no—
180C43⋊C16—21no—
181C43⋊C16—21no—
182C43⋊C16—21no—
183C43⋊C16#4112yes—
184C23×C43—41no—
185C22×D43—41no—
186C22×D43—41no—
187Q8×C43—41no—
188Q8×C43—41no—
189Q8×C43—41no—
190Q8×C43—41no—
191Q8×C43—41no—
192D4×C43—41no—
193D4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—82no—
198C2×C4×C43C2×D811yescharacteristic
199C2×C4×C43C2×D811yescharacteristic
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C2×D811yescharacteristic
203C2×C4×C43C2×D811yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C2×Dic43—41no—
206C2×Dic43—41no—
207D172—41no—
208D172—41no—
209D172—41no—
210D172—41no—
211D172—82no—
212D172—161no—
213C4×D43—161no—
214C4×D43—161no—
215Dic86—41no—
216Dic86—41no—
217C8×C43—21no—
218C8×C43—21no—
219C8×C43—21no—
220C8×C43C2×#4111yescharacteristic
221C8×C43H(5,𝔽2)11yescharacteristic
222#33968—431nomaximal, Sylow
223C22×C43—81no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43C22×D811yescharacteristic
227C2×D43—81no—
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C2×D43—81no—
232C2×D43—81no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—81no—
240C4×C43—81no—
241C4×C43—81no—
242C4×C43#55011yescharacteristic
243C4×C43#57611yescharacteristic
244Dic43—81no—
245Dic43—81no—
246#3396—431no—
247#3393D4311yescharacteristic, complemented
248#2251—431no—
249#2250—431no—
250#2249—431no—
251#2211—431no—
252#2211—431no—
253#2210—431no—
254#2210—431no—
255#2208—431no—
256#2207—431no—
257#2183—431no—
258#2177—431no—
259#2176—431no—
260C4×SD32—431no—
261C2×C43—161no—
262C2×C43#339111yescharacteristic
263C2×C43#341411yescharacteristic
264C2×C43#341611yescharacteristic
265D43—161no—
266D43—161no—
267#559—861no—
268#556—21no—
269C2×Q32—431no—
270C2×Q32—431no—
271C2×SD32—431no—
272C2×SD32—431no—
273C2×SD32—431no—
274C2×SD32—431no—
275C2×SD32—431no—
276C2×D16—431no—
277C2×D16—431no—
278#495—431no—
279#495—431no—
280#495C2×D4311yescharacteristic
281#495C2×D4311yescharacteristic
282#494C2×D4311yescharacteristic
283#493—431no—
284#464—21no—
285#464—21no—
286#463—861no—
287#463—861no—
288#461—21no—
289#460—861no—
290C8×Q8C2×D4311yescharacteristic
291C4×Q16—431no—
292C4×Q16C2×D4311yescharacteristic
293C4×Q16C2×D4311yescharacteristic
294C4×D8—431no—
295C4×D8—431no—
296C4×D8C2×D4311yescharacteristic
297#367—431no—
298C4⋊C16—431no—
299C4⋊C16—431no—
300C4⋊C16—431no—
301#358—431no—
302#358—431no—
303#358—431no—
304#357—431no—
305#357—431no—
306#357—431no—
307#346—431no—
308#346—431no—
309C4×C16—431no—
310C43#3396811yescharacteristic, complemented, Sylow
311C2×Q16—21no—
312C2×Q16—431no—
313C2×Q16C22×D4311yescharacteristic
314C2×Q16C22×D4311yescharacteristic
315C2×SD16—21no—
316C2×SD16—21no—
317C2×SD16—861no—
318C2×SD16—861no—
319C2×D8—431no—
320C2×D8—431no—
321C2×D8—861no—
322C2×D8C22×D4311yescharacteristic
323C4⋊Q8—21no—
324#127—861no—
325#126—41no—
326#126—41no—
327#124—21no—
328#124—21no—
329#124—861no—
330#124—861no—
331#124—1721no—
332#123—1721no—
333#123—1721no—
334C22⋊Q8—41no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—861no—
338C4×Q8C22⋊D4311yescharacteristic
339C4×D4—21no—
340C4×D4—861no—
341C4×D4—861no—
342C4×D4—1721no—
343#117—41no—
344Q32—862no—
345Q32—1721no—
346SD32—862no—
347SD32—1721no—
348SD32—1721no—
349SD32—1721no—
350SD32—1721no—
351D16—862no—
352D16—1721no—
353C2×C16—431no—
354C2×C16—431no—
355C2×C16—431no—
356C2×C16—431no—
357#107—431no—
358#107C22×D4311yescharacteristic
359C4⋊C8C22⋊D4311yescharacteristic
360C4⋊C8C22⋊D4311yescharacteristic
361C4⋊C8C22⋊D4311yescharacteristic
362#103—21no—
363#103—21no—
364#103—861no—
365#102—21no—
366#102—861no—
367#102—861no—
368C4×C8C22×D4311yescharacteristic
369C4×C8C22×D4311yescharacteristic
370C4×C8C22×D4311yescharacteristic
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—861no—
374C2×Q8#1062188211yescharacteristic
375C2×D4—21no—
376C2×D4—861no—
377C2×D4—861no—
378C2×D4—1721no—
379C2×D4—1721no—
380C22×C4—41no—
381C22×C4—1721no—
382C22×C4—1721no—
383Q16—21no—
384Q16—21no—
385Q16—21no—
386Q16—21no—
387Q16—81no—
388Q16—861no—
389Q16—861no—
390SD16—81no—
391SD16—81no—
392SD16—3441no—
393SD16—3441no—
394D8—21no—
395D8—21no—
396D8—861no—
397D8—861no—
398D8—861no—
399D8—861no—
400D8—3441no—
401C2×C8C2×C22⋊D4311yescharacteristic
402C2×C8C2×C22⋊D4311yescharacteristic
403C2×C8C2×C22⋊D4311yescharacteristic
404C2×C8C23×D4311yescharacteristic
405C4⋊C4—21no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—861no—
411C4⋊C4—1721no—
412C4⋊C4#1062188211yescharacteristic
413C4⋊C4#1062188211yescharacteristic
414C4⋊C4#1062188211yescharacteristic
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—1721no—
421C22⋊C4—1721no—
422C22⋊C4—1721no—
423C22⋊C4—1721no—
424C22⋊C4—1721no—
425C22⋊C4—1721no—
426C42—41no—
427C42—41no—
428C42—1721no—
429C42C2×C22⋊D4311yescharacteristic
430C42C2×C22⋊D4311yescharacteristic
431C42C2×C22⋊D4311yescharacteristic
432C16—432no—
433C16—861no—
434C16—861no—
435C16—861no—
436C23—41no—
437C23—1721no—
438C23—1721no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—41no—
444Q8—1721no—
445Q8—1721no—
446D4—41no—
447D4—41no—
448D4—3442no—
449D4—1721no—
450D4—1721no—
451D4—1721no—
452D4—1721no—
453D4—6881no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—82no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—6881no—
461C2×C4—6881no—
462C2×C4C2×#1062188211yescharacteristic
463C2×C4C2×#1062188211yescharacteristic
464C2×C4C2×#1062188211yescharacteristic
465C2×C4C2×#1062188211yescharacteristic
466C2×C4C2×#1062188211yescharacteristic
467C2×C4C2×#1062188211yescharacteristic
468C2×C4C22×C22⋊D4311yescharacteristic
469C8—21no—
470C8—21no—
471C8—21no—
472C8#41×D4311yescharacteristic
473C8#1306337111yescharacteristic
474C22—81no—
475C22—81no—
476C22—81no—
477C22—3441no—
478C22—3441no—
479C22—3441no—
480C22—3441no—
481C22—3441no—
482C22—3441no—
483C22C22×#1062188211yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—81no—
491C4—81no—
492C4—81no—
493C4—3441no—
494C4—3441no—
495C4#1458356811yescharacteristic
496C4#1458370211yescharacteristic
497C2—161no—
498C2—6881no—
499C2—6881no—
500C2#1914756711yescharacteristic
501C2#1914772911yescharacteristic
502C2#1914773911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3393C2
socleC22×C43C22×D8
prime radical#19136862C2
hypercenter#3393D43
hypocenterC43#33968
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. #19147608C2semidirect
2. #19136864C2semidirect
4. #19136854C2semidirect
5. #19136657C2semidirect
6. #19136654C2semidirect
7. #19136650C2semidirect
8. #19136647C2semidirect
9. #19136637C2semidirect
10. #19136635C2semidirect
11. #19136504C2semidirect
12. #19136469C2semidirect
13. #19136464C2semidirect
14. C4×#13063268C2semidirect
15. C43×#3393C2semidirect
247. #3393D43semidirect
310. C43#33968semidirect

Maximal subgroups

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

subgroupindex
#191476082
#191368642
#191368622
#191368542
#191366572
#191366542
#191366502
#191366472
#191366372
#191366352
#191365042
#191364692
#191364642
C4×#130632682
C43×#33932
#3396843