Finite Group Databasebeta

← #11861137

Subgroups — #11861137

Order 1152.

1374 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#568C211yesmaximal, characteristic, complemented
2#10596293C211yesmaximal, characteristic
3#10596216C211yesmaximal, characteristic, complemented
4C2×#63664C211yesmaximal, characteristic, complemented
5#10592844C214yesmaximal, complemented
6#10592843C214yesmaximal, complemented
7C2×#63652C211yesmaximal, characteristic, complemented
8#10592823C211yesmaximal, characteristic, complemented
9M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
10#83811—34nomaximal
11C2×C32×#41C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C32×#131—22no—
14C32×#131C2214yescomplemented
15C2×C32×M16—22no—
16C2×C32×M16C2211yescharacteristic
17C2×C32×M16C2211yescharacteristic
18#64160C412yescomplemented
19#64159C2214yes—
20#64158C412yescomplemented
21#64151C412yescomplemented
22#64141C412yescomplemented
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26#64116—22no—
27M16×C3⋊D3—22no—
28#64110C2214yescomplemented
29#63664C2212yescomplemented
30#63664C2212yescomplemented
31#63652C2212yescomplemented
32#63652C2212yescomplemented
33#63649C2214yescomplemented
34#63642C2212yescomplemented
35C8×C3⋊Dic3C2212yescomplemented
36C3×#568D314yescomplemented
37#5822—34no—
38#5745—34no—
39C2×#837—34no—
40#5145—316no—
41#5144—316no—
42C2×#825—34no—
43#5124—34no—
44Dic3×M16—34no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41C2×C412yes—
48C32×#41C2312yes—
49C2×C32×Q8C2×C411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4C2×C411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C2×#638—21no—
55C22×C3⋊Dic3—21no—
56#3828—21no—
57#3828—21no—
58#3828C2×C412yes—
59#3828C2312yes—
60C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×#634C2×C411yescharacteristic
63C32×M16—21no—
64C32×M16—24no—
65C32×M16D412yes—
66C32×M16D412yes—
67C32×M16C2312yes—
68C2×C32×C8—21no—
69C2×C32×C8—24no—
70C2×C32×C8C2312yes—
71#3756C2×C414yescomplemented
72#3755C2×C414yescomplemented
73#3754C2×C414yescomplemented
74#3753C2×C414yescomplemented
75C4×C3⋊Dic3—21no—
76C4×C3⋊Dic3C2311yescharacteristic
77C4×C3⋊Dic3C2311yescharacteristic
78#3748—21no—
79#3748C2×C412yes—
80#3748C2×C412yes—
81#3748C2312yes—
82C2×C3⋊(C3⋊C8)—21no—
83C2×C3⋊(C3⋊C8)C2312yes—
84#3743—24no—
85C8×C3⋊D3—24no—
86#2956—91noSylow
87C2×C3×#41C2×D314yes—
88C2×#235—34no—
89C3×#131—28no—
90C3×#131C2×D3116yescomplemented
91C2×C3×M16—28no—
92C2×C3×M16C2×D314yes—
93C2×C3×M16C2×D314yes—
94#951—38no—
95#950—316no—
96#949—38no—
97#942—38no—
98#932—38no—
99C2×C4×Dic3—34no—
100C2×#208—34no—
101C2×#208—34no—
102#907—68no—
103D3×M16—68no—
104#901—316no—
105#837—38no—
106#837—38no—
107#825—38no—
108#825—38no—
109#822—316no—
110#815—38no—
111C8×Dic3—38no—
112C23×C32—21no—
113C23×C32#4111yescharacteristic
114C22×C3⋊D3—21no—
115C32×Q8—21no—
116C32×Q8C22×C412yes—
117C32×D4—22no—
118C32×D4—22no—
119C32×D4—21no—
120C32×D4C22×C412yes—
121C2×C32×C4—21no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4C2411yescharacteristic
130#638—22no—
131#638—22no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—42no—
136C4⋊(C3⋊D3)—21no—
137C4⋊(C3⋊D3)C22×C412yes—
138C4×C3⋊D3—22no—
139C4×C3⋊D3—22no—
140#634—21no—
141#634C22×C412yes—
142C32×C8—22no—
143C32×C8C2×D414yes—
144C3⋊(C3⋊C8)—22no—
145C3⋊(C3⋊C8)C22×C414yes—
146#575—91no—
147#568—91no—
148#568C3⋊D311yescharacteristic, complemented
149#444—94no—
150#443—94no—
151#430—91no—
152C2×#104—91no—
153C2×#104—91no—
154C4×M16—91no—
155C3×#41—24no—
156C3×#41—24no—
157C3×#41C4×D318yes—
158C3×#41C22×D318yes—
159C2×C3×Q8C4×D314yes—
160C2×C3×D4—24no—
161C2×C3×D4C4×D314yes—
162C22×C3×C4—24no—
163C22×C3×C4C22×D314yes—
164C2×#67—64no—
165C22×Dic3—64no—
166#235—38no—
167#235—38no—
168#235—64no—
169#235—64no—
170C2×D12—34no—
171C2×C4×D3—64no—
172C2×Dic6—34no—
173C3×M16—24no—
174C3×M16—216no—
175C3×M16#6718yes—
176C3×M16#6718yes—
177C3×M16C22×D318yes—
178C2×C3×C8—24no—
179C2×C3×C8—216no—
180C2×C3×C8C22×D318yes—
181#216—316no—
182#215—316no—
183#214—316no—
184#213—316no—
185C4×Dic3—34no—
186C4×Dic3—34no—
187C4×Dic3—64no—
188#208—38no—
189#208—38no—
190#208—38no—
191#208—64no—
192C2×C3⋊C8—38no—
193C2×C3⋊C8—64no—
194ΓL(1,𝔽25)—616no—
195D3×C8—616no—
196C22×C32—22no—
197C22×C32—41no—
198C22×C32—81no—
199C22×C32C4×D411yescharacteristic
200C22×C32C4×D411yescharacteristic
201C22×C32C2×#4111yescharacteristic
202C2×C3⋊D3—22no—
203C2×C3⋊D3—81no—
204C32×C4—22no—
205C32×C4C4×D411yescharacteristic
206C32×C4C4×D411yescharacteristic
207C32×C4C23×C411yescharacteristic
208C32×C4C22×D411yescharacteristic
209C3⋊Dic3—22no—
210C3⋊Dic3—22no—
211C3⋊Dic3—41no—
212C2×#41—91no—
213C2×#41C2×C3⋊D311yescharacteristic
214#137—92no—
215#137—92no—
216AGL(1,ℤ/8)—92no—
217AGL(1,ℤ/8)—92no—
218#135—94no—
219#131—22no—
220#131—94no—
221#131—182no—
222#131C2×C3⋊D314yescomplemented
223C2×M16—22no—
224C2×M16—91no—
225C2×M16—91no—
226C2×M16—182no—
227C2×M16C2×C3⋊D311yescharacteristic
228C2×M16C2×C3⋊D311yescharacteristic
229C2×C42—91no—
230#108—94no—
231#104—92no—
232#104—92no—
233#104—92no—
234#104—92no—
235#97—92no—
236C4×C8—92no—
237C23×C3—24no—
238C23×C3#23514yes—
239C22×D3—64no—
240C3×Q8—24no—
241C3×Q8C2×C4×D318yes—
242C3×D4—28no—
243C3×D4—28no—
244C3×D4—24no—
245C3×D4C2×C4×D318yes—
246C2×C3×C4—24no—
247C2×C3×C4—28no—
248C2×C3×C4—28no—
249C2×C3×C4C2×C4×D314yes—
250C2×C3×C4C2×C4×D314yes—
251C2×C3×C4#23514yes—
252C2×C3×C4C2×#6714yes—
253C2×C3×C4C2×#6714yes—
254C2×C3×C4C23×D314yes—
255#67—68no—
256#67—68no—
257C2×Dic3—64no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—128no—
261D12—38no—
262D12—64no—
263C4×D3—68no—
264C4×D3—68no—
265Dic6—38no—
266Dic6—64no—
267C3×C8—28no—
268C3×C8C2×#67116yes—
269C3⋊C8—316no—
270C3⋊C8—68no—
271C2×C32—21no—
272C2×C32—21no—
273C2×C32—21no—
274C2×C32—42no—
275C2×C32C2×C4×D411yescharacteristic
276C3⋊D3—42no—
277#41—21no—
278#41—21no—
279#41—92no—
280#41—92no—
281#41—181no—
282#41—181no—
283#41C4×C3⋊D312yes—
284#41C22×C3⋊D312yes—
285C2×Q8—91no—
286C2×Q8C4×C3⋊D311yescharacteristic
287C2×D4—21no—
288C2×D4—91no—
289C2×D4—181no—
290C2×D4C4×C3⋊D311yescharacteristic
291C22×C4—21no—
292C22×C4—181no—
293C22×C4—181no—
294C22×C4C22×C3⋊D311yescharacteristic
295Q16—94no—
296SD16—94no—
297SD16—94no—
298D8—94no—
299M16—21no—
300M16—24no—
301M16—92no—
302M16—92no—
303M16—92no—
304M16—181no—
305M16—184no—
306M16#63812yes—
307M16#63812yes—
308M16C22×C3⋊D312yes—
309C2×C8—21no—
310C2×C8—24no—
311C2×C8—92no—
312C2×C8—181no—
313C2×C8—184no—
314C2×C8C22×C3⋊D312yes—
315C42—91no—
316C42—91no—
317C42—181no—
318C22×C3—28no—
319C22×C3—44no—
320C22×C3—84no—
321C22×C3C4×#6714yes—
322C22×C3C4×#6714yes—
323C22×C3C2×#23514yes—
324C2×D3—68no—
325C2×D3—244no—
326C3×C4—28no—
327C3×C4C4×#6714yes—
328C3×C4C4×#6714yes—
329C3×C4C22×C4×D314yes—
330C3×C4C22×#6714yes—
331Dic3—68no—
332Dic3—68no—
333Dic3—124no—
334C32#295611yescharacteristic, complemented, Sylow
335C23—21no—
336C23—181no—
337C23#382811yescharacteristic
338Q8—21no—
339Q8—92no—
340Q8—181no—
341Q8C2×C4×C3⋊D312yes—
342D4—22no—
343D4—22no—
344D4—21no—
345D4—92no—
346D4—182no—
347D4—182no—
348D4—181no—
349D4C2×C4×C3⋊D312yes—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—181no—
358C2×C4—362no—
359C2×C4C2×C4×C3⋊D311yescharacteristic
360C2×C4C2×C4×C3⋊D311yescharacteristic
361C2×C4#382811yescharacteristic
362C2×C4C2×#63811yescharacteristic
363C2×C4C2×#63811yescharacteristic
364C2×C4C23×C3⋊D311yescharacteristic
365C8—22no—
366C8—94no—
367C8—182no—
368C8C2×#63814yes—
369C2×C3—24no—
370C2×C3—24no—
371C2×C3—24no—
372C2×C3—48no—
373C2×C3C2×C4×#6714yes—
374D3—128no—
375C22—22no—
376C22—41no—
377C22—81no—
378C22—182no—
379C22—721no—
380C22C4×#63811yescharacteristic
381C22C4×#63811yescharacteristic
382C22C2×#382811yescharacteristic
383C4—22no—
384C4—182no—
385C4—182no—
386C4—361no—
387C4C4×#63811yescharacteristic
388C4C4×#63811yescharacteristic
389C4C22×C4×C3⋊D311yescharacteristic
390C4C22×#63811yescharacteristic
391C3#8381114yescomplemented
392C2—21no—
393C2—21no—
394C2—21no—
395C2—42no—
396C2—362no—
397C2C2×C4×#63811yescharacteristic
subgroupG/H
centerC4C22×#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#568C2
socleC2×C32C2×C4×D4
prime radical#10596293C2
cosocleC2×C32×C4C24
hypercenter#568C3⋊D3
hypocenterC32#2956
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×M16 ◁ #568

Complements

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

NH ≅ G/Ntype
1. C32×#568C2semidirect
3. #10596216C2semidirect
4. C2×#63664C2semidirect
5. #10592844C2semidirect
6. #10592843C2semidirect
7. C2×#63652C2semidirect
8. #10592823C2semidirect
9. M16×C3⋊Dic3C2semidirect
14. C32×#131C22semidirect
18. #64160C4semidirect
20. #64158C4semidirect
21. #64151C4semidirect
22. #64141C4semidirect
28. #64110C22semidirect
29. #63664C22semidirect
30. #63664C22semidirect
31. #63652C22semidirect
32. #63652C22semidirect
33. #63649C22semidirect
34. #63642C22semidirect
35. C8×C3⋊Dic3C22semidirect
36. C3×#568D3semidirect
71. #3756C2×C4semidirect
72. #3755C2×C4semidirect
73. #3754C2×C4semidirect
74. #3753C2×C4semidirect
90. C3×#131C2×D3semidirect
148. #568C3⋊D3semidirect
222. #131C2×C3⋊D3semidirect
334. C32#2956semidirect
391. C3#83811semidirect

Maximal subgroups

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

subgroupindex
C32×#5682
#105962932
#105962162
C2×#636642
#105928442
#105928432
C2×#636522
#105928232
M16×C3⋊Dic32
#838113