Finite Group Databasebeta

← #11866969

Subgroups — #11866969

Order 1152.

1341 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 1341 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×C3⋊D3C211yesmaximal, characteristic, complemented
2#10595081C212yesmaximal, complemented
3C2×#63797C211yesmaximal, characteristic, complemented
4C3×#5135C212yesmaximal, complemented
5#10591167C212yesmaximal, complemented
6#10590940C212yesmaximal, complemented
7#10590846C212yesmaximal, complemented
8#10590840C212yesmaximal, complemented
9#10590685C211yesmaximal, characteristic, complemented
10D3×#469—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×#3811—22no—
13C2×#3802C2212yes—
14C2×C32×M16C2211yescharacteristic, complemented
15C2×#3748C2211yescharacteristic, complemented
16M16×C3⋊D3—24no—
17C2×#3743C2211yescharacteristic, complemented
18C2×#3743C2211yescharacteristic, complemented
19C2×C8×C3⋊D3C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C3×#930C2214yescomplemented
22C2×C3×D24C2212yescomplemented
23#63980—22no—
24#63921—22no—
25#63916C2214yescomplemented
26#63912—22no—
27#63900C2212yes—
28C2×#3713C2212yescomplemented
29#63797—24no—
30C3×#821C2214yescomplemented
31C3×#817C2212yescomplemented
32#63574C2212yescomplemented
33#63562C2214yescomplemented
34C2×D3×D8—32no—
35C2×D3×M16—32no—
36C2×D3×M16—61no—
37D3×#121—34no—
38C3×#469—32no—
39#5159—32no—
40#5135D312yescomplemented
41#5039—34no—
42#4865—32no—
43D3×#106—32no—
44#4782—34no—
45D3×#102—34no—
46C23×C3⋊D3D411yescharacteristic
47C22×D32—22no—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3D411yescharacteristic
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3D411yescharacteristic
53C2×C4×C3⋊D3D411yescharacteristic
54C2×C4×C3⋊D3C2311yescharacteristic
55C2×C4×C3⋊D3C2311yescharacteristic
56C2×C3×#67—24no—
57C2×C3×D12C2314yes—
58#3811—48no—
59C2×#626—24no—
60C2×#625—22no—
61C2×#624—22no—
62#3802—24no—
63#3802—24no—
64C32×M16—22no—
65C2×C32×C8C2311yescharacteristic
66C2×C32×C8C2311yescharacteristic
67#3748—22no—
68C2×C3⋊(C3⋊C8)C2311yescharacteristic
69C2×C3⋊(C3⋊C8)C2311yescharacteristic
70#3743—22no—
71#3743—22no—
72C8×C3⋊D3—22no—
73C8×C3⋊D3D414yescomplemented
74C3×(C2×D3)⋊C4—24no—
75C3×C4⋊Dic3C2314yes—
76C3×D24—24no—
77#3724—22no—
78(C2×D3)⋊Dic3—24no—
79#3713—24no—
80C2×#469—91noSylow
81C2×D3×D4—34no—
82C2×D3×D4—64no—
83C22×C4×D3—32no—
84C22×C4×D3—61no—
85C2×C3×D8—32no—
86C2×C3×M16—21no—
87C2×C3×M16C2×D312yescomplemented
88C3×#121—34no—
89#939—64no—
90#938—34no—
91C2×#213—34no—
92#930C2×D314yescomplemented
93C2×#208—32no—
94C2×#208—61no—
95D3×D8—68no—
96D3×M16—68no—
97D3×M16—68no—
98C2×D24C2×D312yescomplemented
99C2×ΓL(1,𝔽25)—32no—
100C2×ΓL(1,𝔽25)—32no—
101C2×ΓL(1,𝔽25)—61no—
102C2×ΓL(1,𝔽25)—61no—
103C2×D3×C8—32no—
104C2×D3×C8—32no—
105C2×D3×C8—61no—
106C2×D3×C8—61no—
107#895—34no—
108D3×C4⋊C4—34no—
109#884—64no—
110D3×C22⋊C4—64no—
111C3×#106—32no—
112C3×#102—34no—
113#832—34no—
114#821C2×D314yescomplemented
115#817C2×D312yescomplemented
116#809—34no—
117#808—34no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—22no—
120C22×C3⋊D3—24no—
121C22×C3⋊D3C2×D411yescharacteristic
122C22×C3⋊D3C2×D411yescharacteristic
123C22×C3×D3—24no—
124C2×D32—44no—
125C2×D32—44no—
126C2×D32—44no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3C2×D411yescharacteristic
133C2×C3⋊Dic3C2×D411yescharacteristic
134C4×C3⋊D3—22no—
135C4×C3⋊D3—21no—
136C4×C3⋊D3—21no—
137C4×C3⋊D3—22no—
138C4×C3⋊D3C2×D412yes—
139C4×C3⋊D3#4112yes—
140C3×#67—48no—
141C2×C3×Dic3—24no—
142C3×D12—24no—
143C3×D12—24no—
144#626—48no—
145#625—44no—
146#624—44no—
147C32×C8—21no—
148C32×C8C2×D412yescomplemented
149C3⋊(C3⋊C8)—21no—
150C3⋊(C3⋊C8)C2×D412yescomplemented
151C22×D8—91no—
152C22×M16—91no—
153C2×#121—92no—
154#469—32no—
155#469—92no—
156#469—92no—
157#469—92no—
158C2×#106—91no—
159C2×#102—92no—
160C23×D3—32no—
161C23×D3—61no—
162C23×D3—64no—
163C2×C3×D4—34no—
164C2×C3×D4—64no—
165C22×C3×C4—21no—
166C22×C3×C4C22×D312yes—
167C2×#67—24no—
168C2×#67—64no—
169C2×#67—64no—
170C22×Dic3—32no—
171C22×Dic3—61no—
172D3×D4—68no—
173D3×D4—68no—
174D3×D4—1216no—
175C2×D12—64no—
176C2×D12C22×D314yes—
177C2×C4×D3—32no—
178C2×C4×D3—32no—
179C2×C4×D3—32no—
180C2×C4×D3—32no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—64no—
186C2×C4×D3—64no—
187C2×C4×D3—64no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C3×D8—64no—
191C3×M16—24no—
192C3×M16—24no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8C22×D312yes—
196C2×C3×C8C22×D312yes—
197C3×C4⋊C4—34no—
198C3×C22⋊C4—64no—
199#217—64no—
200#213—68no—
201(C2×D3)⋊C4—24no—
202(C2×D3)⋊C4—64no—
203C4⋊Dic3C22×D314yes—
204Dic3⋊C4—64no—
205#208—64no—
206#208—64no—
207C2×C3⋊C8—32no—
208C2×C3⋊C8—32no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211D24—24no—
212ΓL(1,𝔽25)—64no—
213ΓL(1,𝔽25)—64no—
214ΓL(1,𝔽25)—64no—
215ΓL(1,𝔽25)—64no—
216D3×C8—38no—
217D3×C8—64no—
218D3×C8—64no—
219D3×C8—64no—
220C22×C32—21no—
221C22×C32—22no—
222C22×C32C22×D411yescharacteristic
223C2×C3⋊D3—21no—
224C2×C3⋊D3—22no—
225C2×C3⋊D3—44no—
226C2×C3⋊D3#12112yes—
227C2×C3⋊D3AGL(1,ℤ/8)14yes—
228C2×C3×D3—44no—
229C2×C3×D3—44no—
230C2×C3×D3—44no—
231D32—88no—
232C32×C4—21no—
233C32×C4C22×D411yescharacteristic
234C32×C4C2×#4111yescharacteristic
235C3⋊Dic3—21no—
236C3⋊Dic3#12112yes—
237C3×Dic3—44no—
238C22×D4—92no—
239C22×D4—182no—
240C23×C4—91no—
241C2×D8—32no—
242C2×D8—92no—
243C2×D8—184no—
244C2×M16—91no—
245C2×M16—91no—
246C2×M16—91no—
247C2×M16—184no—
248C2×M16D3211yescharacteristic, complemented
249C22×C8—91no—
250C22×C8—91no—
251#121—34no—
252#121—94no—
253#121—182no—
254#121—182no—
255C2×C4⋊C4—92no—
256C2×C22⋊C4—182no—
257#106—32no—
258#106—92no—
259#102—34no—
260#102—94no—
261C23×C3—21no—
262C23×C3—64no—
263C23×C3D3×D412yes—
264C22×D3—24no—
265C22×D3—32no—
266C22×D3—32no—
267C22×D3—61no—
268C22×D3—61no—
269C22×D3—64no—
270C22×D3—68no—
271C22×D3—64no—
272C22×D3—124no—
273C22×D3—128no—
274C22×D3—128no—
275C22×D3—128no—
276C3×D4—64no—
277C3×D4—64no—
278C3×D4—128no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—64no—
286C2×C3×C4D3×D412yes—
287C2×C3×C4C23×D312yes—
288#67—48no—
289#67—128no—
290#67—128no—
291C2×Dic3—24no—
292C2×Dic3—32no—
293C2×Dic3—32no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—64no—
297C2×Dic3—64no—
298D12—24no—
299D12—24no—
300D12—128no—
301C4×D3—34no—
302C4×D3—34no—
303C4×D3—62no—
304C4×D3—62no—
305C4×D3—64no—
306C4×D3—64no—
307C4×D3—62no—
308C4×D3—64no—
309C4×D3—64no—
310C4×D3—62no—
311C4×D3—62no—
312C4×D3—62no—
313C4×D3—128no—
314C3×C8—22no—
315C3×C8—22no—
316C3×C8—22no—
317C3×C8D3×D414yescomplemented
318C3⋊C8—34no—
319C3⋊C8—62no—
320C3⋊C8—62no—
321C3⋊C8—62no—
322C2×C32—41no—
323C2×C32C2×#12111yescharacteristic
324C2×C32C2×AGL(1,ℤ/8)12yes—
325C3⋊D3—41no—
326C3⋊D3#46914yescomplemented
327C3×D3—84no—
328C24—91no—
329C24—182no—
330C2×D4—34no—
331C2×D4—64no—
332C2×D4—184no—
333C2×D4—184no—
334C2×D4—184no—
335C2×D4—182no—
336C2×D4—368no—
337C22×C4—91no—
338C22×C4—91no—
339C22×C4—91no—
340C22×C4—91no—
341C22×C4—91no—
342C22×C4—182no—
343C22×C4—182no—
344C22×C4—182no—
345C22×C4C2×D3211yescharacteristic
346D8—64no—
347D8—184no—
348M16—22no—
349M16—182no—
350M16—182no—
351M16—182no—
352C2×C8—91no—
353C2×C8—94no—
354C2×C8—91no—
355C2×C8—182no—
356C2×C8C2×D3211yescharacteristic
357C2×C8C2×D3211yescharacteristic
358C4⋊C4—34no—
359C4⋊C4—182no—
360C22⋊C4—64no—
361C22⋊C4—184no—
362C22×C3—22no—
363C22×C3—24no—
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—42no—
367C22×C3—124no—
368C22×C3—124no—
369C22×C3—124no—
370C22×C3C2×D3×D412yes—
371C2×D3—38no—
372C2×D3—34no—
373C2×D3—44no—
374C2×D3—44no—
375C2×D3—44no—
376C2×D3—62no—
377C2×D3—64no—
378C2×D3—62no—
379C2×D3—64no—
380C2×D3—62no—
381C2×D3—122no—
382C2×D3—128no—
383C2×D3—128no—
384C2×D3—2416no—
385C3×C4—22no—
386C3×C4—22no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—124no—
390C3×C4C2×D3×D412yes—
391C3×C4D3×#4112yes—
392Dic3—34no—
393Dic3—44no—
394Dic3—62no—
395Dic3—62no—
396Dic3—62no—
397C32C2×#46911yescharacteristic, complemented, Sylow
398C23—64no—
399C23—91no—
400C23—91no—
401C23—182no—
402C23—184no—
403C23—364no—
404C23—364no—
405C23—364no—
406C23#380211yescharacteristic
407D4—64no—
408D4—64no—
409D4—128no—
410D4—364no—
411D4—368no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—64no—
415C2×C4—91no—
416C2×C4—92no—
417C2×C4—92no—
418C2×C4—91no—
419C2×C4—182no—
420C2×C4—182no—
421C2×C4—182no—
422C2×C4—181no—
423C2×C4—181no—
424C2×C4—364no—
425C2×C4#380211yescharacteristic
426C2×C4C22×D3211yescharacteristic
427C8—21no—
428C8—92no—
429C8—181no—
430C8#381112yescomplemented
431C2×C3—21no—
432C2×C3—22no—
433C2×C3—42no—
434C2×C3—42no—
435C2×C3—244no—
436C2×C3D3×#12112yes—
437C2×C3D3×AGL(1,ℤ/8)14yes—
438D3—38no—
439D3—64no—
440D3—84no—
441D3—122no—
442D3—122no—
443C22—21no—
444C22—22no—
445C22—92no—
446C22—94no—
447C22—124no—
448C22—124no—
449C22—124no—
450C22—181no—
451C22—182no—
452C22—364no—
453C22—728no—
454C22C2×#380211yescharacteristic
455C4—21no—
456C4—92no—
457C4—124no—
458C4—181no—
459C4#6430611yescharacteristic
460C4C2×#381111yescharacteristic
461C3—21no—
462C3D3×#46912yescomplemented
463C2—41no—
464C2—94no—
465C2—244no—
466C2—361no—
467C2#1059471612yes—
468C2#1059508111yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32C2×#469
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×M16×C3⋊D3C2semidirect
2. #10595081C2semidirect
3. C2×#63797C2semidirect
4. C3×#5135C2semidirect
5. #10591167C2semidirect
6. #10590940C2semidirect
7. #10590846C2semidirect
8. #10590840C2semidirect
9. #10590685C2semidirect
14. C2×C32×M16C22semidirect
15. C2×#3748C22semidirect
17. C2×#3743C22semidirect
18. C2×#3743C22semidirect
21. C3×#930C22semidirect
22. C2×C3×D24C22semidirect
25. #63916C22semidirect
28. C2×#3713C22semidirect
30. C3×#821C22semidirect
31. C3×#817C22semidirect
32. #63574C22semidirect
33. #63562C22semidirect
40. #5135D3semidirect
73. C8×C3⋊D3D4semidirect
87. C2×C3×M16C2×D3semidirect
92. #930C2×D3semidirect
98. C2×D24C2×D3semidirect
114. #821C2×D3semidirect
115. #817C2×D3semidirect
148. C32×C8C2×D4semidirect
150. C3⋊(C3⋊C8)C2×D4semidirect
248. C2×M16D32semidirect
317. C3×C8D3×D4semidirect
326. C3⋊D3#469semidirect
397. C32C2×#469semidirect
430. C8#3811semidirect
462. C3D3×#469semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C3⋊D32
#105950812
C2×#637972
C3×#51352
#105911672
#105909402
#105908462
#105908402
#105906852
D3×#4693