Finite Group Databasebeta

← #11871323

Subgroups — #11871323

Order 1152.

1332 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C4×D4×C3⋊D3C211yesmaximal, characteristic
3C32×#461C211yesmaximal, characteristic, complemented
4#10592868C212yesmaximal
5#10592863C212yesmaximal, complemented
6#10592782C211yesmaximal, characteristic, complemented
7#10592706C211yesmaximal, characteristic, complemented
8#10592545C211yesmaximal, characteristic, complemented
9#10592534C211yesmaximal, characteristic, complemented
10#10592516C212yesmaximal, complemented
11#10592510C212yesmaximal, complemented
12#80410—34nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C2×C32×SD16C2212yes—
16C32×C4⋊Q8C2211yescharacteristic, complemented
17C32×C4×D4C2211yescharacteristic
18#64155C2212yes—
19Q8×C3⋊Dic3C2212yescomplemented
20C2×#3755C2212yes—
21D4×C3⋊Dic3C2211yescharacteristic
22C4×#638—21no—
23#64106—21no—
24#64102C2211yescharacteristic
25#64101—21no—
26C4⋊C4×C3⋊D3C2211yescharacteristic
27#64099—21no—
28#64096—21no—
29#64090—21no—
30C22⋊C4×C3⋊D3—21no—
31C4×C4⋊(C3⋊D3)C2211yescharacteristic
32C42×C3⋊D3C2211yescharacteristic
33#64078C2211yescharacteristic, complemented
34C32×C4⋊C8C2211yescharacteristic, complemented
35C32×#103C2212yescomplemented
36#63662C2212yescomplemented
37#63659C2212yes—
38#63648C2212yes—
39#63647C2212yes—
40#63645C2212yescomplemented
41#63642C2212yescomplemented
42#63634C2212yescomplemented
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
44#5728—34no—
45C4×D3×D4—34no—
46C3×#461D314yescomplemented
47#5169—38no—
48#5164—38no—
49#5083—34no—
50#5007—34no—
51#4846—34no—
52#4835—34no—
53#4817—38no—
54#4811—38no—
55C23×C3⋊D3—21no—
56C2×C32×Q8C2312yes—
57C2×C32×D4C2311yescharacteristic
58C22×C32×C4—21no—
59C2×#638—21no—
60C22×C3⋊Dic3—21no—
61D4×C3⋊D3—22no—
62D4×C3⋊D3—22no—
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—21no—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3—44no—
68C2×C4×C3⋊D3D411yescharacteristic
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×#634—21no—
72C32×SD16—24no—
73C2×C32×C8C2312yes—
74C32×C4⋊C4—21no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C22⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3757—21no—
80#3755—24no—
81#3752—22no—
82#3752—21no—
83#3752—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)—22no—
86C4⋊(C3⋊Dic3)C2312yes—
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88#3750—21no—
89#3750—22no—
90C4×C3⋊Dic3—22no—
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2312yes—
95#3110—91noSylow
96C2×D3×D4—34no—
97C22×C4×D3—64no—
98C2×C3×SD16C2×D318yes—
99C3×C4⋊Q8C2×D314yescomplemented
100C3×C4×D4C2×D314yes—
101#946—38no—
102Q8×Dic3—38no—
103C2×#215—38no—
104D4×Dic3—34no—
105C4×#67—64no—
106#897—64no—
107#893—34no—
108#892—64no—
109D3×C4⋊C4—34no—
110#890—64no—
111#887—64no—
112#67⋊C4—64no—
113D3×C22⋊C4—64no—
114C4×D12—34no—
115C42×D3—34no—
116#869—34no—
117C3×C4⋊C8C2×D314yescomplemented
118C3×#103C2×D318yescomplemented
119#835—38no—
120#832—38no—
121#821—38no—
122(C2×D3)⋊C8—38no—
123#818—38no—
124#815—38no—
125#807—38no—
126C4⋊(C3⋊C8)—34no—
127C23×C32—21no—
128C22×C3⋊D3—24no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C22×C3⋊D3C2×D411yescharacteristic
133C32×Q8—22no—
134C32×Q8—22no—
135C32×D4—21no—
136C32×D4#4112yes—
137C2×C32×C4—22no—
138C2×C32×C4—21no—
139C2×C32×C4—42no—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2411yescharacteristic
143#638—24no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—42no—
147C2×C3⋊Dic3C2×D411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D411yescharacteristic
150C4⋊(C3⋊D3)—21no—
151C4⋊(C3⋊D3)#4112yes—
152C4×C3⋊D3—22no—
153C4×C3⋊D3—22no—
154C4×C3⋊D3—21no—
155C4×C3⋊D3—21no—
156C4×C3⋊D3—42no—
157C4×C3⋊D3—42no—
158C4×C3⋊D3—42no—
159#634—42no—
160C32×C8—22no—
161C3⋊(C3⋊C8)—22no—
162#533—91no—
163C2×C4×D4—91no—
164#484—92no—
165#474—91no—
166#474—91no—
167#461—91no—
168#461C3⋊D311yescharacteristic, complemented
169#450—92no—
170#440—92no—
171#440—92no—
172#432—91no—
173C23×D3—64no—
174C2×C3×Q8C22×D318yes—
175C2×C3×D4C22×D314yes—
176C22×C3×C4—24no—
177C2×#67—64no—
178C22×Dic3—64no—
179D3×D4—68no—
180D3×D4—68no—
181C2×D12—34no—
182C2×C4×D3—34no—
183C2×C4×D3—34no—
184C2×C4×D3—34no—
185C2×C4×D3—64no—
186C2×C4×D3—64no—
187C2×C4×D3—64no—
188C2×C4×D3—1216no—
189C2×Dic6—64no—
190C3×SD16—216no—
191C2×C3×C8C22×D318yes—
192C3×C4⋊C4—24no—
193C3×C4⋊C4—24no—
194C3×C4⋊C4C22×D314yes—
195C3×C22⋊C4—24no—
196C3×C42C22×D314yes—
197#217—64no—
198#215—616no—
199(C2×D3)⋊C4—64no—
200(C2×D3)⋊C4—68no—
201(C2×D3)⋊C4—64no—
202C4⋊Dic3—38no—
203C4⋊Dic3—34no—
204C4⋊Dic3—68no—
205C4⋊Dic3—64no—
206Dic3⋊C4—64no—
207Dic3⋊C4—68no—
208C4×Dic3—34no—
209C4×Dic3—34no—
210C4×Dic3—34no—
211C4×Dic3—68no—
212C2×C3⋊C8—38no—
213C22×C32—22no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32C22×D411yescharacteristic
217C2×C3⋊D3—21no—
218C2×C3⋊D3—21no—
219C2×C3⋊D3—22no—
220C2×C3⋊D3—48no—
221C2×C3⋊D3—41no—
222C2×C3⋊D3—41no—
223C2×C3⋊D3#13712yes—
224C32×C4—21no—
225C32×C4—42no—
226C32×C4—41no—
227C32×C4AGL(1,ℤ/8)12yes—
228C32×C4C2×#4111yescharacteristic
229C32×C4C2×#4111yescharacteristic
230C3⋊Dic3—21no—
231C3⋊Dic3—21no—
232C3⋊Dic3—21no—
233C3⋊Dic3—42no—
234C3⋊Dic3—41no—
235C22×D4—91no—
236C23×C4—181no—
237C2×SD16—92no—
238C2×SD16C2×C3⋊D312yes—
239C4⋊Q8—91no—
240C4⋊Q8C2×C3⋊D311yescharacteristic, complemented
241#125—181no—
242C22⋊Q8—92no—
243C22⋊Q8—181no—
244C4×Q8—92no—
245C4×Q8—181no—
246C4×D4—91no—
247C4×D4—91no—
248C4×D4—91no—
249C4×D4—181no—
250C4×D4—181no—
251C4×D4C2×C3⋊D311yescharacteristic
252#117—181no—
253C2×C4⋊C4—91no—
254C2×C22⋊C4—181no—
255C2×C42—91no—
256#107—92no—
257#107—92no—
258C4⋊C8—91no—
259C4⋊C8C2×C3⋊D311yescharacteristic, complemented
260#103—92no—
261#103C2×C3⋊D312yescomplemented
262#102—92no—
263#102—92no—
264C22⋊C8—92no—
265#97—92no—
266C23×C3—24no—
267C22×D3—34no—
268C22×D3—616no—
269C22×D3—64no—
270C22×D3—128no—
271C22×D3—128no—
272C3×Q8—28no—
273C3×Q8—28no—
274C3×D4—24no—
275C3×D4#23718yes—
276C2×C3×C4—28no—
277C2×C3×C4—24no—
278C2×C3×C4—48no—
279C2×C3×C4D3×D414yes—
280C2×C3×C4D3×D414yes—
281C2×C3×C4C23×D314yes—
282#67—616no—
283C2×Dic3—34no—
284C2×Dic3—34no—
285C2×Dic3—34no—
286C2×Dic3—68no—
287C2×Dic3—64no—
288C2×Dic3—128no—
289D12—38no—
290D12—64no—
291C4×D3—68no—
292C4×D3—68no—
293C4×D3—64no—
294C4×D3—64no—
295C4×D3—128no—
296C4×D3—128no—
297C4×D3—128no—
298Dic6—128no—
299C3×C8—28no—
300C3⋊C8—68no—
301C2×C32—42no—
302C2×C32#52511yescharacteristic
303C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
304C2×C32C2×#13711yescharacteristic
305C3⋊D3—22no—
306C3⋊D3—42no—
307C24—181no—
308C2×Q8—181no—
309C2×Q8C22×C3⋊D312yes—
310C2×D4—91no—
311C2×D4—181no—
312C2×D4—182no—
313C2×D4—182no—
314C2×D4C22×C3⋊D311yescharacteristic
315C22×C4—21no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—91no—
319C22×C4—181no—
320C22×C4—181no—
321C22×C4—181no—
322C22×C4—181no—
323C22×C4—364no—
324SD16—24no—
325SD16—184no—
326C2×C8—92no—
327C2×C8C22×C3⋊D312yes—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—92no—
331C4⋊C4—91no—
332C4⋊C4—181no—
333C4⋊C4—182no—
334C4⋊C4—182no—
335C4⋊C4—181no—
336C4⋊C4C22×C3⋊D311yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—181no—
339C22⋊C4—182no—
340C22⋊C4—181no—
341C22⋊C4—181no—
342C42—91no—
343C42—91no—
344C42—91no—
345C42—182no—
346C42C22×C3⋊D311yescharacteristic
347C22×C3—28no—
348C22×C3—44no—
349C22×C3—44no—
350C22×C3C2×D3×D414yes—
351C2×D3—38no—
352C2×D3—64no—
353C2×D3—64no—
354C2×D3—68no—
355C2×D3—1232no—
356C2×D3—124no—
357C2×D3—124no—
358C3×C4—24no—
359C3×C4—44no—
360C3×C4—48no—
361C3×C4#91418yes—
362C3×C4C2×#23714yes—
363C3×C4D3×#4114yes—
364Dic3—64no—
365Dic3—64no—
366Dic3—64no—
367Dic3—128no—
368Dic3—124no—
369C32#311011yescharacteristic, complemented, Sylow
370C23—21no—
371C23—91no—
372C23—184no—
373C23—181no—
374C23—362no—
375C23—362no—
376Q8—22no—
377Q8—22no—
378Q8—362no—
379D4—21no—
380D4—92no—
381D4—184no—
382D4—181no—
383D4#383012yes—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—42no—
387C2×C4—91no—
388C2×C4—91no—
389C2×C4—91no—
390C2×C4—182no—
391C2×C4—181no—
392C2×C4—181no—
393C2×C4—182no—
394C2×C4—182no—
395C2×C4—181no—
396C2×C4—362no—
397C2×C4—362no—
398C2×C4—362no—
399C2×C4—362no—
400C2×C4D4×C3⋊D311yescharacteristic
401C2×C4D4×C3⋊D311yescharacteristic
402C2×C4C23×C3⋊D311yescharacteristic
403C8—22no—
404C8—182no—
405C2×C3—48no—
406C2×C3#560614yes—
407C2×C3C2×#91414yes—
408C2×C3D3×#13714yes—
409D3—68no—
410D3—128no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—92no—
415C22—181no—
416C22—181no—
417C22—182no—
418C22—368no—
419C22—361no—
420C22—361no—
421C22C2×D4×C3⋊D311yescharacteristic
422C4—21no—
423C4—41no—
424C4—42no—
425C4—181no—
426C4—181no—
427C4—181no—
428C4—361no—
429C4—362no—
430C4#6412312yes—
431C4C2×#383011yescharacteristic
432C4#41×C3⋊D311yescharacteristic
433C3#8041014yescomplemented
434C2—42no—
435C2—182no—
436C2—362no—
437C2#1059607711yescharacteristic
438C2C2×#6412311yescharacteristic
439C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#461C3⋊D3
hypocenterC32#3110
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
3. C32×#461C2semidirect
5. #10592863C2semidirect
6. #10592782C2semidirect
7. #10592706C2semidirect
8. #10592545C2semidirect
9. #10592534C2semidirect
10. #10592516C2semidirect
11. #10592510C2semidirect
16. C32×C4⋊Q8C22semidirect
19. Q8×C3⋊Dic3C22semidirect
33. #64078C22semidirect
34. C32×C4⋊C8C22semidirect
35. C32×#103C22semidirect
36. #63662C22semidirect
40. #63645C22semidirect
41. #63642C22semidirect
42. #63634C22semidirect
43. C4⋊(C3⋊(C3⋊C8))C22semidirect
46. C3×#461D3semidirect
99. C3×C4⋊Q8C2×D3semidirect
117. C3×C4⋊C8C2×D3semidirect
118. C3×#103C2×D3semidirect
168. #461C3⋊D3semidirect
240. C4⋊Q8C2×C3⋊D3semidirect
259. C4⋊C8C2×C3⋊D3semidirect
261. #103C2×C3⋊D3semidirect
369. C32#3110semidirect
433. C3#80410semidirect

Maximal subgroups

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

subgroupindex
#105961992
C4×D4×C3⋊D32
C32×#4612
#105928682
#105928632
#105927822
#105927062
#105925452
#105925342
#105925162
#105925102
#804103