Finite Group Databasebeta

← #25254213

Subgroups — #25254213

Order 11008.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146993C211yesmaximal, characteristic, complemented
2#19146992C211yesmaximal, characteristic, complemented
3#19136872C211yesmaximal, characteristic, complemented
4#19136787C211yesmaximal, characteristic, complemented
5#19136784C211yesmaximal, characteristic, complemented
6#19136777C211yesmaximal, characteristic, complemented
7#19136755C211yesmaximal, characteristic, complemented
8#19136754C211yesmaximal, characteristic, complemented
9#19136697C211yesmaximal, characteristic, complemented
10#19136696C211yesmaximal, characteristic, complemented
11#19136439C211yesmaximal, characteristic, complemented
12#19136424C211yesmaximal, characteristic, complemented
13#19136381C211yesmaximal, characteristic, complemented
14#19136380C211yesmaximal, characteristic, complemented
15C43×#2232C211yesmaximal, characteristic, complemented
16#14583597—21no—
17#14583596—21no—
18C2×#13063266C2211yescharacteristic
19C2×#13063265C2211yescharacteristic
20C2×#13063264C2211yescharacteristic
21#14583300C2211yescharacteristic
22#14583300C2211yescharacteristic
23#14583226—21no—
24#14583220—21no—
25#14583217—21no—
26#14583216—21no—
27#14583202—21no—
28#14583201—21no—
29#14583136C2211yescharacteristic
30#14583135C2211yescharacteristic
31#14583132C2211yescharacteristic
32D8×Dic43C2211yescharacteristic
33#14582981C2211yescharacteristic
34C8×C22⋊D43C2211yescharacteristic
35#14582937C2211yescharacteristic
36#14582936C2211yescharacteristic
37#107×D43C2211yescharacteristic
38#14582727C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582726C2211yescharacteristic
41#14582726C2211yescharacteristic
42#14582725C2211yescharacteristic
43#14582724C2211yescharacteristic
44#14582724C2211yescharacteristic
45Dic43⋊C16C2211yescharacteristic
46#14582701C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582700C2211yescharacteristic
49#14582699C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C43×#466C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C43×#366C2211yescharacteristic
55C43×#366C2211yescharacteristic
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic
59C2×D344C2311yescharacteristic
60C2×C8×D43C2311yescharacteristic
61#13063320—41no—
62#13063318—41no—
63#13063316—21no—
64#13063316—21no—
65#13063310—41no—
66#13063306—41no—
67#13063300—21no—
68#13063299—21no—
69#13063299—41no—
70#13063296—21no—
71#13063296—41no—
72D4×Dic43—21no—
73#13063287—21no—
74C4×C22⋊D43—41no—
75C4×C22⋊D43D411yescharacteristic
76(C22⋊D43)⋊C4—41no—
77#13063284—21no—
78#13063283—21no—
79C4⋊C4×D43—21no—
80#13063266—22no—
81#13063265—22no—
82#13063264—22no—
83C2×C43⋊C16C2311yescharacteristic
84C2×C43⋊C16C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063258—21no—
89#13063257—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93Dic43⋊C8D411yescharacteristic
94#13063247—21no—
95#13063246—21no—
96#13063246—21no—
97#13063245—21no—
98#13063245—21no—
99C22⋊(C43⋊C8)D411yescharacteristic
100(C2×D43)⋊C8D411yescharacteristic
101C8×Dic43C2311yescharacteristic
102C2×D8×C43C2311yescharacteristic
103C22×C8×C43C2311yescharacteristic
104#121×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C16×C43C2311yescharacteristic
107C2×C16×C43C2311yescharacteristic
108#107×C43—21no—
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#102×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43C2×D411yescharacteristic
117C2×C22⋊D43—41no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43D811yescharacteristic
120C22×Dic43—41no—
121C2×D172—21no—
122C2×D172—41no—
123C2×C4×D43—41no—
124C2×C4×D43—41no—
125C2×C4×D43C2×D411yescharacteristic
126D8×C43—21no—
127D8×C43—21no—
128C2×C8×C43—21no—
129C2×C8×C43—21no—
130C2×C8×C43C2×D411yescharacteristic
131C2×C8×C43C2411yescharacteristic
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—41no—
136C22⋊C4×C43—41no—
137C22⋊Dic43—41no—
138C22⋊Dic43—41no—
139C22⋊Dic43—41no—
140C22⋊Dic43D811yescharacteristic
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4D811yescharacteristic
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—41no—
150C4⋊Dic43—41no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4D811yescharacteristic
155C4×Dic43—41no—
156C4×Dic43—41no—
157C4×Dic43C2×D411yescharacteristic
158C2×C43⋊C8C2×D411yescharacteristic
159C2×C43⋊C8C2×D411yescharacteristic
160D344—21no—
161D344—21no—
162C8×D43—21no—
163C8×D43—21no—
164C16×C43—21no—
165C16×C43—21no—
166C43⋊C16—21no—
167C43⋊C16#4112yes—
168C23×C43—41no—
169C23×C43C2×D811yescharacteristic
170C22×D43—41no—
171C22×D43C2×D811yescharacteristic
172D4×C43—41no—
173D4×C43—41no—
174D4×C43—161no—
175C2×C4×C43—21no—
176C2×C4×C43—21no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—161no—
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C22⋊D43—41no—
184C22⋊D43—82no—
185C22⋊D43—82no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—161no—
190C2×Dic43C2×D811yescharacteristic
191C2×Dic43C2×D811yescharacteristic
192C2×Dic43C2×D811yescharacteristic
193D172—41no—
194D172—41no—
195D172—161no—
196C4×D43—21no—
197C4×D43—21no—
198C4×D43—161no—
199C4×D43—161no—
200C8×C43—21no—
201C8×C43C2×#4111yescharacteristic
202C8×C432−1+411yescharacteristic
203C43⋊C8—21no—
204C43⋊C8—21no—
205#33922—431nomaximal, Sylow
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—81no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43C22×D811yescharacteristic
213C2×D43—21no—
214C2×D43—21no—
215C2×D43—21no—
216C2×D43—81no—
217C2×D43—81no—
218C2×D43—81no—
219C4×C43—21no—
220C4×C43—81no—
221C4×C43—81no—
222C4×C43—81no—
223C4×C43#54711yescharacteristic
224C4×C43#57811yescharacteristic
225Dic43—21no—
226Dic43—21no—
227Dic43—21no—
228Dic43—81no—
229Dic43—81no—
230Dic43—81no—
231#3339—431no—
232#3339—431no—
233#2253—431no—
234#2234—431no—
235#2234—431no—
236#2232—431no—
237#2232D4311yescharacteristic, complemented
238#2228—431no—
239#2228—431no—
240#2218—431no—
241#2218—431no—
242C4×D16—431no—
243#2169—431no—
244#2159—431no—
245#2159—431no—
246C2×C43—41no—
247C2×C43—161no—
248C2×C43#333411yescharacteristic
249C2×C43#341411yescharacteristic
250C2×C43#341511yescharacteristic
251D43—41no—
252D43—161no—
253#553—861no—
254#553—861no—
255C2×D16—431no—
256C2×M32—431no—
257C2×M32—431no—
258#499—431no—
259#499—431no—
260#482—861no—
261#482—861no—
262#481—861no—
263#481—861no—
264#478—861no—
265#478—861no—
266#466—431no—
267#466—431no—
268#466—431no—
269#466C2×D4311yescharacteristic
270C4×D8—431no—
271C4×D8—431no—
272C8×D4—431no—
273#427—431no—
274#427—431no—
275C2×#107—431no—
276C2×#107C2×D4311yescharacteristic
277#367—431no—
278#367—431no—
279#367—431no—
280#367—431no—
281#366—431no—
282#366—431no—
283#366—431no—
284#366C2×D4311yescharacteristic
285#366C2×D4311yescharacteristic
286C4⋊C16—431no—
287#357—431no—
288#357—431no—
289#357—431no—
290#357—431no—
291#357C2×D4311yescharacteristic
292#357C2×D4311yescharacteristic
293C22⋊C16—431no—
294C22⋊C16C2×D4311yescharacteristic
295C4×C16—431no—
296C43#3392211yescharacteristic, complemented, Sylow
297C2×D8—431no—
298C2×D8C22×D4311yescharacteristic
299C22×C8—431no—
300C22×C8C22×D4311yescharacteristic
301#126—1721no—
302#126—1721no—
303#125—861no—
304#125—861no—
305#123—1721no—
306#123—1721no—
307#121—21no—
308#121—861no—
309#121—861no—
310#121—861no—
311#121—1721no—
312#121—1721no—
313C4×D4—431no—
314C4×D4—861no—
315C4×D4—861no—
316C4×D4—1721no—
317C4×D4—1721no—
318#117—861no—
319#117—861no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—861no—
322D16—862no—
323M32—862no—
324M32—862no—
325C2×C16—431no—
326C2×C16—431no—
327C2×C16C22×D4311yescharacteristic
328C2×C16C22×D4311yescharacteristic
329#107—21no—
330#107—431no—
331#107—431no—
332#107—431no—
333#107—861no—
334#107C22×D4311yescharacteristic
335#107C22×D4311yescharacteristic
336#107C22×D4311yescharacteristic
337#106—861no—
338#106—861no—
339#106—861no—
340#106—861no—
341C4⋊C8—431no—
342#102—21no—
343#102—861no—
344#102—861no—
345#102—861no—
346#102—861no—
347#102—861no—
348C22⋊C8—431no—
349C22⋊C8—431no—
350C4×C8—431no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—431no—
354C2×D4—861no—
355C2×D4—1721no—
356C2×D4—1721no—
357C2×D4—1721no—
358C22×C4—41no—
359C22×C4—431no—
360C22×C4—1721no—
361C22×C4—1721no—
362C22×C4—1721no—
363C22×C4D4×D4311yescharacteristic
364D8—21no—
365D8—21no—
366D8—861no—
367D8—861no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—431no—
371C2×C8—431no—
372C2×C8—861no—
373C2×C8—861no—
374C2×C8D4×D4311yescharacteristic
375C2×C8C23×D4311yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—431no—
381C4⋊C4—861no—
382C4⋊C4—861no—
383C4⋊C4—861no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C4⋊C4—1721no—
387C4⋊C4—1721no—
388C4⋊C4—1721no—
389C22⋊C4—41no—
390C22⋊C4—431no—
391C22⋊C4—431no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C22⋊C4—1721no—
395C22⋊C4—1721no—
396C22⋊C4—1721no—
397C22⋊C4—1721no—
398C22⋊C4—1721no—
399C42—431no—
400C42—1721no—
401C42—1721no—
402C16—21no—
403C16—21no—
404C16—432no—
405C16—861no—
406C23—41no—
407C23—431no—
408C23—1721no—
409C23D8×D4311yescharacteristic
410D4—41no—
411D4—41no—
412D4—161no—
413D4—3442no—
414D4—3442no—
415D4—1721no—
416D4—1721no—
417D4—1721no—
418D4—6881no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—161no—
425C2×C4—431no—
426C2×C4—431no—
427C2×C4—431no—
428C2×C4—861no—
429C2×C4—861no—
430C2×C4—1721no—
431C2×C4—1721no—
432C2×C4—1721no—
433C2×C4—6881no—
434C2×C4—6881no—
435C2×C4—6881no—
436C2×C4D8×D4311yescharacteristic
437C2×C4C2×D4×D4311yescharacteristic
438C8—21no—
439C8—861no—
440C8—861no—
441C8#41×D4311yescharacteristic
442C8#1306337211yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—861no—
450C22—861no—
451C22—861no—
452C22—3441no—
453C22—3441no—
454C22—3441no—
455C22C2×D8×D4311yescharacteristic
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—861no—
461C4—861no—
462C4—861no—
463C4—3441no—
464C4—3441no—
465C4—3441no—
466C4#1458354711yescharacteristic
467C4#1458371511yescharacteristic
468C2—41no—
469C2—161no—
470C2—1721no—
471C2—6881no—
472C2#1914693711yescharacteristic
473C2#1914773011yescharacteristic
474C2#1914773211yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2232C2
socleC22×C43C22×D8
hypercenter#2232D43
hypocenterC43#33922
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
1. #19146993C2semidirect
2. #19146992C2semidirect
3. #19136872C2semidirect
4. #19136787C2semidirect
5. #19136784C2semidirect
6. #19136777C2semidirect
7. #19136755C2semidirect
8. #19136754C2semidirect
9. #19136697C2semidirect
10. #19136696C2semidirect
11. #19136439C2semidirect
12. #19136424C2semidirect
13. #19136381C2semidirect
14. #19136380C2semidirect
15. C43×#2232C2semidirect
237. #2232D43semidirect
296. C43#33922semidirect

Maximal subgroups

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

subgroupindex
#191469932
#191469922
#191368722
#191367872
#191367842
#191367772
#191367552
#191367542
#191366972
#191366962
#191364392
#191364242
#191363812
#191363802
C43×#22322
#3392243