Finite Group Databasebeta

← #11868151

Subgroups — #11868151

Order 1152.

1338 conjugacy classes of subgroups.

The subgroup lattice has 429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic, complemented
2#10596293C211yesmaximal, characteristic
3C2×#64151C211yesmaximal, characteristic, complemented
4#10596216C211yesmaximal, characteristic, complemented
5#10592936C211yesmaximal, characteristic, complemented
6C2×#63663C211yesmaximal, characteristic, complemented
7#10592891C214yesmaximal, complemented
8#10592876C214yesmaximal, complemented
9#10592824C211yesmaximal, characteristic, complemented
10#83998—34nomaximal
11C2×C32×#41C2211yescharacteristic
12C22×C32×Q8C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C32×#137—22no—
15C32×#137—22no—
16C2×C32×Q16C2212yescomplemented
17C2×C32×SD16C2212yescomplemented
18C2×C32×M16C2211yescharacteristic
19#64160—21no—
20#64159—22no—
21#64158—21no—
22C2×#3756—21no—
23#64151—22no—
24#64151C2214yes—
25#64151C2212yes—
26C2×#3755—21no—
27#64141C2212yes—
28C2×#3748C2211yescharacteristic
29C2×#3748C2211yescharacteristic
30C2×#3748C2211yescharacteristic
31#64116—22no—
32M16×C3⋊D3—22no—
33#64110C2214yes—
34#63663C2214yescomplemented
35#63663C2212yescomplemented
36#63660C2212yescomplemented
37#63646C2214yescomplemented
38C2×C3×#137D314yescomplemented
39#5822—34no—
40C2×#942—34no—
41#5745—34no—
42#5237—34no—
43C2×#836—34no—
44#5192—316no—
45#5177—316no—
46#5125—34no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—21no—
54C2×C32×Q8—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8C2312yes—
57C2×C32×Q8C2311yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4C2311yescharacteristic
60C22×C32×C4—21no—
61C22×C32×C4—21no—
62C22×C32×C4C2311yescharacteristic
63C2×#638—21no—
64#3828—21no—
65#3828—21no—
66#3828D412yes—
67#3828C2312yes—
68C2×C4⋊(C3⋊D3)D411yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634D411yescharacteristic
71C32×Q16—24no—
72C32×SD16—24no—
73C32×M16D412yes—
74C32×M16D412yes—
75C2×C32×C8C2312yes—
76#3756—24no—
77#3756—22no—
78#3755—24no—
79#3755—22no—
80#3754—22no—
81#3753—22no—
82#3748—21no—
83#3748—21no—
84#3748—21no—
85#3748C2312yes—
86#3748C2312yes—
87#3748C2312yes—
88C2×C3⋊(C3⋊C8)—21no—
89C2×C3⋊(C3⋊C8)—21no—
90C2×C3⋊(C3⋊C8)—21no—
91#3743—24no—
92C8×C3⋊D3—24no—
93#3069—91noSylow
94C2×C3×#41C2×D314yes—
95C22×C3×Q8C2×D314yes—
96C2×#235—34no—
97C3×#137—28no—
98C3×#137—28no—
99C2×C3×Q16C2×D318yescomplemented
100C2×C3×SD16C2×D318yescomplemented
101C2×C3×M16C2×D314yes—
102#951—64no—
103#950—68no—
104#949—64no—
105C2×#216—64no—
106#942—316no—
107#942—38no—
108#942—68no—
109C2×#215—64no—
110#932—38no—
111C2×#208—34no—
112C2×#208—34no—
113C2×#208—34no—
114#907—68no—
115D3×M16—68no—
116#901—316no—
117#836—316no—
118#836—38no—
119#833—38no—
120#819—316no—
121C23×C32—21no—
122C23×C32#4111yescharacteristic
123C22×C3⋊D3—21no—
124C32×Q8—22no—
125C32×Q8—21no—
126C32×Q8—22no—
127C32×Q8—21no—
128C32×Q8—41no—
129C32×Q8—41no—
130C32×D4—21no—
131C32×D4—21no—
132C32×D4—41no—
133C32×D4—41no—
134C2×C32×C4—21no—
135C2×C32×C4—22no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4C2411yescharacteristic
146#638—22no—
147#638—22no—
148C2×C3⋊Dic3—21no—
149C4⋊(C3⋊D3)—21no—
150C4⋊(C3⋊D3)C2×D412yes—
151C4×C3⋊D3—22no—
152C4×C3⋊D3—22no—
153#634—21no—
154#634C2×D412yes—
155C32×C8C2×D414yes—
156C3⋊(C3⋊C8)—22no—
157C3⋊(C3⋊C8)—22no—
158C3⋊(C3⋊C8)—22no—
159#575—91no—
160C2×#137—91no—
161C2×#137C3⋊D311yescharacteristic, complemented
162#568—91no—
163#473—94no—
164#471—94no—
165#430—91no—
166#413—91no—
167C2×#101—91no—
168C3×#41—24no—
169C3×#41—24no—
170C3×#41—24no—
171C3×#41—24no—
172C2×C3×Q8—24no—
173C2×C3×Q8—24no—
174C2×C3×Q8—24no—
175C2×C3×Q8—24no—
176C2×C3×Q8—24no—
177C2×C3×Q8C22×D318yes—
178C2×C3×Q8C22×D314yes—
179C2×C3×D4—24no—
180C2×C3×D4C22×D314yes—
181C22×C3×C4—24no—
182C22×C3×C4—24no—
183C22×C3×C4C22×D314yes—
184C2×#67—64no—
185#235—38no—
186#235—38no—
187#235—64no—
188#235—64no—
189C2×D12—34no—
190C2×C4×D3—64no—
191C2×Dic6—34no—
192C3×Q16—216no—
193C3×SD16—216no—
194C3×M16#6718yes—
195C3×M16#6718yes—
196C2×C3×C8C22×D318yes—
197#216—616no—
198#216—68no—
199#215—616no—
200#215—68no—
201#214—68no—
202#213—68no—
203#208—38no—
204#208—38no—
205#208—38no—
206#208—64no—
207#208—64no—
208#208—64no—
209C2×C3⋊C8—64no—
210C2×C3⋊C8—64no—
211C2×C3⋊C8—64no—
212ΓL(1,𝔽25)—616no—
213D3×C8—616no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—81no—
217C22×C32#12111yescharacteristic
218C22×C32#12111yescharacteristic
219C22×C32C2×#4111yescharacteristic
220C2×C3⋊D3—22no—
221C2×C3⋊D3—81no—
222C32×C4—41no—
223C32×C4—42no—
224C32×C4#12111yescharacteristic
225C32×C4#12111yescharacteristic
226C32×C4C22×D411yescharacteristic
227C32×C4C22×D411yescharacteristic
228C3⋊Dic3—22no—
229C2×#41—91no—
230C2×#41C2×C3⋊D311yescharacteristic
231C22×Q8C2×C3⋊D311yescharacteristic
232#137—22no—
233#137—22no—
234#137—94no—
235#137—92no—
236#137—182no—
237#137—181no—
238AGL(1,ℤ/8)—92no—
239AGL(1,ℤ/8)—181no—
240#135—182no—
241C2×Q16—181no—
242C2×Q16C2×C3⋊D312yescomplemented
243C2×SD16—181no—
244C2×SD16C2×C3⋊D312yescomplemented
245#131—94no—
246#131—182no—
247C2×M16—91no—
248C2×M16—91no—
249C2×M16—91no—
250C2×M16—182no—
251C2×M16C2×C3⋊D311yescharacteristic
252#108—94no—
253#101—94no—
254#101—92no—
255#100—92no—
256C23×C3—24no—
257C23×C3#23714yes—
258C22×D3—64no—
259C3×Q8—28no—
260C3×Q8—24no—
261C3×Q8—28no—
262C3×Q8—24no—
263C3×Q8—44no—
264C3×Q8—44no—
265C3×D4—24no—
266C3×D4—24no—
267C3×D4—44no—
268C3×D4—44no—
269C2×C3×C4—24no—
270C2×C3×C4—28no—
271C2×C3×C4—44no—
272C2×C3×C4—44no—
273C2×C3×C4—44no—
274C2×C3×C4—44no—
275C2×C3×C4D3×D414yes—
276C2×C3×C4D3×D414yes—
277C2×C3×C4#23714yes—
278C2×C3×C4C2×#6714yes—
279C2×C3×C4C2×#6714yes—
280C2×C3×C4C23×D314yes—
281#67—68no—
282#67—68no—
283C2×Dic3—64no—
284D12—38no—
285D12—64no—
286C4×D3—68no—
287C4×D3—68no—
288Dic6—38no—
289Dic6—64no—
290C3×C8C2×#67116yes—
291C3⋊C8—68no—
292C3⋊C8—68no—
293C3⋊C8—68no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32—81no—
298C2×C32C2×#12111yescharacteristic
299C3⋊D3—42no—
300#41—21no—
301#41—21no—
302#41—21no—
303#41—21no—
304#41—92no—
305#41—92no—
306#41—181no—
307#41—181no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—91no—
314C2×Q8C22×C3⋊D312yes—
315C2×Q8C22×C3⋊D311yescharacteristic
316C2×D4—21no—
317C2×D4—91no—
318C2×D4—181no—
319C2×D4C22×C3⋊D311yescharacteristic
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—181no—
323C22×C4C22×C3⋊D311yescharacteristic
324Q16—24no—
325Q16—184no—
326Q16—182no—
327SD16—24no—
328SD16—182no—
329SD16—184no—
330SD16—182no—
331D8—182no—
332M16—92no—
333M16—92no—
334M16—92no—
335M16—181no—
336M16—181no—
337M16—181no—
338M16—184no—
339M16#63812yes—
340M16#63812yes—
341C2×C8—181no—
342C2×C8—181no—
343C2×C8—181no—
344C2×C8—184no—
345C2×C8C22×C3⋊D312yes—
346C22×C3—44no—
347C22×C3—44no—
348C22×C3—84no—
349C22×C3#93814yes—
350C22×C3#93814yes—
351C22×C3C2×#23714yes—
352C2×D3—68no—
353C2×D3—244no—
354C3×C4—44no—
355C3×C4—48no—
356C3×C4#93814yes—
357C3×C4#93814yes—
358C3×C4C2×D3×D414yes—
359C3×C4C22×#6714yes—
360Dic3—68no—
361C32#306911yescharacteristic, complemented, Sylow
362C23—21no—
363C23—181no—
364C23#383011yescharacteristic
365Q8—22no—
366Q8—21no—
367Q8—22no—
368Q8—21no—
369Q8—41no—
370Q8—41no—
371Q8—92no—
372Q8—181no—
373D4—21no—
374D4—21no—
375D4—41no—
376D4—41no—
377D4—92no—
378D4—182no—
379D4—182no—
380D4—181no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—181no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4D4×C3⋊D311yescharacteristic
391C2×C4D4×C3⋊D311yescharacteristic
392C2×C4#383011yescharacteristic
393C2×C4C2×#63811yescharacteristic
394C2×C4C2×#63811yescharacteristic
395C2×C4C23×C3⋊D311yescharacteristic
396C8—182no—
397C8—182no—
398C8—182no—
399C8C2×#63814yes—
400C2×C3—24no—
401C2×C3—24no—
402C2×C3—24no—
403C2×C3—84no—
404C2×C3C2×#93814yes—
405D3—128no—
406C22—41no—
407C22—41no—
408C22—81no—
409C22—182no—
410C22—721no—
411C22#6414711yescharacteristic
412C22#6414711yescharacteristic
413C22C2×#383011yescharacteristic
414C4—41no—
415C4—42no—
416C4—182no—
417C4#6414711yescharacteristic
418C4#6414711yescharacteristic
419C4C2×D4×C3⋊D311yescharacteristic
420C4C22×#63811yescharacteristic
421C3#8399814yescomplemented
422C2—21no—
423C2—21no—
424C2—21no—
425C2—81no—
426C2—362no—
427C2C2×#6414711yescharacteristic
subgroupG/H
centerC2C2×#64147
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#137C2
socleC2×C32C2×#121
prime radical#10596293C2
hypercenterC2×#137C3⋊D3
hypocenterC32#3069
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C32×#137C2semidirect
3. C2×#64151C2semidirect
4. #10596216C2semidirect
5. #10592936C2semidirect
6. C2×#63663C2semidirect
7. #10592891C2semidirect
8. #10592876C2semidirect
9. #10592824C2semidirect
16. C2×C32×Q16C22semidirect
17. C2×C32×SD16C22semidirect
34. #63663C22semidirect
35. #63663C22semidirect
36. #63660C22semidirect
37. #63646C22semidirect
38. C2×C3×#137D3semidirect
99. C2×C3×Q16C2×D3semidirect
100. C2×C3×SD16C2×D3semidirect
161. C2×#137C3⋊D3semidirect
242. C2×Q16C2×C3⋊D3semidirect
244. C2×SD16C2×C3⋊D3semidirect
361. C32#3069semidirect
421. C3#83998semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
#105962932
C2×#641512
#105962162
#105929362
C2×#636632
#105928912
#105928762
#105928242
#839983