Finite Group Databasebeta

← #11870855

Subgroups — #11870855

Order 1152.

1362 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C32×#431C211yesmaximal, characteristic, complemented
4#10592546C212yesmaximal, complemented
5#10592543C212yesmaximal, complemented
6#10592434C211yesmaximal, characteristic, complemented
7#10592431C211yesmaximal, characteristic
8#10592430C211yesmaximal, characteristic, complemented
9#10592421C211yesmaximal, characteristic, complemented
10C4×#3745C212yesmaximal, complemented
11C4×#3744C212yesmaximal, complemented
12#79300—34nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C2×C32×C42C2211yescharacteristic
16#64139C2211yescharacteristic
17#64138—21no—
18C4×#638—21no—
19C2×#3752—21no—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21#64133C2211yescharacteristic
22C2×#3745C2212yes—
23C2×#3744C2212yes—
24#64085—21no—
25#64084C2211yescharacteristic, complemented
26C4×C4⋊(C3⋊D3)—21no—
27C4×C4⋊(C3⋊D3)—21no—
28C4×C4⋊(C3⋊D3)C2212yes—
29C4×C4⋊(C3⋊D3)C2212yes—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
31#64081—21no—
32#64079C2211yescharacteristic, complemented
33C4×#634C2211yescharacteristic, complemented
34C32×C4⋊C8C2212yescomplemented
35C32×C22⋊C8C2211yescharacteristic
36C32×C22⋊C8C2211yescharacteristic
37C32×C4×C8C2212yescomplemented
38#63648C2212yes—
39#63648C2212yes—
40#63648C2212yescomplemented
41#63645C2212yescomplemented
42#63644C2212yescomplemented
43#63643C2212yescomplemented
44#5479—34no—
45C2×C4×D12—34no—
46C3×#431D314yescomplemented
47#4847—38no—
48#4844—38no—
49#4735—34no—
50#4732—34no—
51#4731—34no—
52#4722—34no—
53C4×D24—38no—
54C4×#204—38no—
55C23×C3⋊D3—21no—
56C22×C32×C4D411yescharacteristic
57C22×C32×C4D411yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×#638—21no—
60C22×C3⋊Dic3—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—24no—
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—44no—
69C2×#634C2311yescharacteristic
70C2×C32×C8C2312yes—
71C2×C32×C8C2312yes—
72C32×C42D411yescharacteristic
73C32×C42D411yescharacteristic
74C32×C42C2311yescharacteristic
75C32×C42C2311yescharacteristic
76#3757—21no—
77#3752—21no—
78#3752—21no—
79#3752—22no—
80#3752—22no—
81#3752—21no—
82#3752—21no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4⋊(C3⋊Dic3)C2312yes—
87#3750—21no—
88#3750—21no—
89#3750—21no—
90#3750—21no—
91C4×C3⋊Dic3—21no—
92#3745—24no—
93#3744—24no—
94#3105—91noSylow
95C22×D12—34no—
96C22×C4×D3—64no—
97C2×C3×C42C2×D314yes—
98#930—34no—
99#929—64no—
100C4×#67—64no—
101C2×(C2×D3)⋊C4—64no—
102C2×C4⋊Dic3—34no—
103#924—34no—
104C2×D24—38no—
105C2×#204—38no—
106#876—64no—
107#875—34no—
108C4×D12—38no—
109C4×D12—38no—
110C4×D12—34no—
111C4×D12—64no—
112C4×D12—64no—
113#872—64no—
114#870—34no—
115C4×Dic6—34no—
116C3×C4⋊C8C2×D318yescomplemented
117C3×C22⋊C8C2×D314yes—
118C3×C22⋊C8C2×D314yes—
119C3×C4×C8C2×D318yescomplemented
120#821—38no—
121#821—38no—
122#821—38no—
123#818—38no—
124#817—38no—
125#816—38no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—24no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2411yescharacteristic
141#638—42no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—42no—
147C4⋊(C3⋊D3)—24no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)#4114yes—
151C4×C3⋊D3—44no—
152C4×C3⋊D3—42no—
153C4×C3⋊D3—44no—
154#634—22no—
155C32×C8—22no—
156C32×C8—22no—
157#529—91no—
158C2×C4×D4—91no—
159#484—91no—
160#481—91no—
161#478—92no—
162#463—92no—
163#450—91no—
164#447—91no—
165C4×SD16—92no—
166C4×D8—92no—
167#431C3⋊D311yescharacteristic, complemented
168C23×D3—64no—
169C22×C3×C4D1214yes—
170C22×C3×C4D1214yes—
171C22×C3×C4C22×D314yes—
172C2×#67—64no—
173C22×Dic3—64no—
174C2×D12—38no—
175C2×D12—34no—
176C2×D12—616no—
177C2×D12—64no—
178C2×C4×D3—64no—
179C2×C4×D3—68no—
180C2×C4×D3—68no—
181C2×C4×D3—1216no—
182C2×Dic6—34no—
183C2×C3×C8C22×D318yes—
184C2×C3×C8C22×D318yes—
185C3×C42D1214yes—
186C3×C42D1214yes—
187C3×C42C22×D314yes—
188C3×C42C22×D314yes—
189#217—64no—
190(C2×D3)⋊C4—64no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—68no—
193(C2×D3)⋊C4—68no—
194(C2×D3)⋊C4—64no—
195(C2×D3)⋊C4—64no—
196C4⋊Dic3—38no—
197C4⋊Dic3—34no—
198C4⋊Dic3—34no—
199C4⋊Dic3—64no—
200Dic3⋊C4—64no—
201Dic3⋊C4—64no—
202Dic3⋊C4—64no—
203Dic3⋊C4—64no—
204C4×Dic3—64no—
205D24—616no—
206#204—616no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32#13512yes—
210C22×C32C22×D411yescharacteristic
211C2×C3⋊D3—24no—
212C2×C3⋊D3—48no—
213C2×C3⋊D3—42no—
214C2×C3⋊D3—42no—
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4AGL(1,ℤ/8)12yes—
223C32×C4C2×#4112yes—
224C3⋊Dic3—41no—
225C3⋊Dic3—41no—
226C3⋊Dic3—42no—
227C3⋊Dic3—41no—
228C22×D4—91no—
229C23×C4—181no—
230C2×SD16—92no—
231C2×D8—92no—
232#126—181no—
233#125—91no—
234#124—91no—
235#123—181no—
236C22⋊Q8—91no—
237#121—91no—
238C4×Q8—91no—
239C4×D4—92no—
240C4×D4—92no—
241C4×D4—91no—
242C4×D4—181no—
243C4×D4—181no—
244C4×D4—181no—
245#117—181no—
246C2×C4⋊C4—91no—
247C2×C22⋊C4—181no—
248C2×C42C2×C3⋊D311yescharacteristic
249#107—92no—
250#106—92no—
251C4⋊C8C2×C3⋊D312yescomplemented
252#103—92no—
253#102—92no—
254#102—92no—
255#102—92no—
256C22⋊C8C2×C3⋊D311yescharacteristic
257C22⋊C8C2×C3⋊D311yescharacteristic
258C4×C8C2×C3⋊D312yescomplemented
259C23×C3C2×D1214yes—
260C22×D3—616no—
261C22×D3—68no—
262C22×D3—64no—
263C22×D3—128no—
264C22×D3—128no—
265C2×C3×C4—28no—
266C2×C3×C4—28no—
267C2×C3×C4—28no—
268C2×C3×C4C2×D1214yes—
269C2×C3×C4C2×D1214yes—
270C2×C3×C4C2×D1214yes—
271C2×C3×C4C2×D1214yes—
272C2×C3×C4C2×D1214yes—
273C2×C3×C4C23×D314yes—
274#67—128no—
275C2×Dic3—64no—
276C2×Dic3—64no—
277C2×Dic3—64no—
278C2×Dic3—68no—
279C2×Dic3—128no—
280D12—316no—
281D12—616no—
282D12—68no—
283D12—68no—
284C4×D3—1216no—
285C4×D3—128no—
286C4×D3—1216no—
287Dic6—68no—
288C3×C8—28no—
289C3×C8—28no—
290C2×C32—22no—
291C2×C32#52511yescharacteristic
292C2×C32C2×#13511yescharacteristic
293C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
294C3⋊D3—44no—
295C3⋊D3—81no—
296C24—181no—
297C2×Q8—91no—
298C2×D4—92no—
299C2×D4—91no—
300C2×D4—184no—
301C2×D4—181no—
302C2×D4—181no—
303C22×C4—181no—
304C22×C4—182no—
305C22×C4—181no—
306C22×C4—182no—
307C22×C4—364no—
308C22×C4C4⋊(C3⋊D3)11yescharacteristic
309C22×C4C4⋊(C3⋊D3)11yescharacteristic
310C22×C4C22×C3⋊D311yescharacteristic
311SD16—184no—
312D8—184no—
313C2×C8C22×C3⋊D312yes—
314C2×C8C22×C3⋊D312yes—
315C4⋊C4—91no—
316C4⋊C4—91no—
317C4⋊C4—92no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C22⋊C4—181no—
324C22⋊C4—182no—
325C22⋊C4—182no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C42—181no—
331C42C4⋊(C3⋊D3)11yescharacteristic
332C42C4⋊(C3⋊D3)11yescharacteristic
333C42C22×C3⋊D311yescharacteristic
334C42C22×C3⋊D311yescharacteristic
335C22×C3—24no—
336C22×C3—24no—
337C22×C3#90418yes—
338C22×C3C22×D1214yes—
339C2×D3—616no—
340C2×D3—1232no—
341C2×D3—128no—
342C2×D3—128no—
343C2×D3—124no—
344C2×D3—124no—
345C2×D3—124no—
346C3×C4—24no—
347C3×C4—24no—
348C3×C4—24no—
349C3×C4—24no—
350C3×C4#90818yes—
351C3×C4D3×#4118yes—
352Dic3—124no—
353Dic3—128no—
354Dic3—124no—
355Dic3—124no—
356C32#310511yescharacteristic, complemented, Sylow
357C23—184no—
358C23—182no—
359C23—181no—
360C23—362no—
361C23—362no—
362C23C2×C4⋊(C3⋊D3)11yescharacteristic
363Q8—182no—
364D4—94no—
365D4—184no—
366D4—182no—
367D4—182no—
368D4—362no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—181no—
373C2×C4—181no—
374C2×C4—181no—
375C2×C4—182no—
376C2×C4—364no—
377C2×C4—362no—
378C2×C4—364no—
379C2×C4—362no—
380C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
381C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
382C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
383C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
384C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
385C2×C4C23×C3⋊D311yescharacteristic
386C8—22no—
387C8—22no—
388C2×C3—28no—
389C2×C3#552414yes—
390C2×C3C2×#90414yes—
391C2×C3C2×#90814yes—
392D3—1216no—
393D3—244no—
394C22—21no—
395C22—21no—
396C22—184no—
397C22—368no—
398C22—362no—
399C22—362no—
400C22—361no—
401C22—361no—
402C22—361no—
403C22#6411312yes—
404C22C22×C4⋊(C3⋊D3)11yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—361no—
410C4—362no—
411C4—361no—
412C4—361no—
413C4#6411712yes—
414C4#41×C3⋊D312yes—
415C3#7930014yescomplemented
416C2—22no—
417C2—364no—
418C2—721no—
419C2#1059599511yescharacteristic
420C2C2×#6411311yescharacteristic
421C2C2×#6411711yescharacteristic
subgroupG/H
centerC2×C4C2×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#431C2
socleC22×C32C22×D4
prime radical#10592431C2
hypercenter#431C3⋊D3
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #10595950C2semidirect
2. C2×C4×C4⋊(C3⋊D3)C2semidirect
3. C32×#431C2semidirect
4. #10592546C2semidirect
5. #10592543C2semidirect
6. #10592434C2semidirect
8. #10592430C2semidirect
9. #10592421C2semidirect
10. C4×#3745C2semidirect
11. C4×#3744C2semidirect
25. #64084C22semidirect
30. C4×C4⋊(C3⋊D3)C22semidirect
32. #64079C22semidirect
33. C4×#634C22semidirect
34. C32×C4⋊C8C22semidirect
37. C32×C4×C8C22semidirect
40. #63648C22semidirect
41. #63645C22semidirect
42. #63644C22semidirect
43. #63643C22semidirect
46. C3×#431D3semidirect
116. C3×C4⋊C8C2×D3semidirect
119. C3×C4×C8C2×D3semidirect
167. #431C3⋊D3semidirect
251. C4⋊C8C2×C3⋊D3semidirect
258. C4×C8C2×C3⋊D3semidirect
356. C32#3105semidirect
415. C3#79300semidirect

Maximal subgroups

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

subgroupindex
#105959502
C2×C4×C4⋊(C3⋊D3)2
C32×#4312
#105925462
#105925432
#105924342
#105924312
#105924302
#105924212
C4×#37452
C4×#37442
#793003