Finite Group Databasebeta

← #11860261

Subgroups — #11860261

Order 1152.

1644 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64117C211yesmaximal, characteristic
2#10595993C211yesmaximal, characteristic, complemented
3C2×#64102C211yesmaximal, characteristic, complemented
4C32×#428C211yesmaximal, characteristic, complemented
5M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10592700C211yesmaximal, characteristic, complemented
7#10592665C211yesmaximal, characteristic, complemented
8#10592588C212yesmaximal, complemented
9#10592571C212yesmaximal, complemented
10#10592568C212yesmaximal, complemented
11#10592551C212yesmaximal, complemented
12#79199—34nomaximal
13C2×#3828C2211yescharacteristic
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C2×C32×M16C2211yescharacteristic
17C32×#117C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×#3752—21no—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22#64117C418yescomplemented
23C2×#3745C2212yes—
24C2×#3744C2212yes—
25#64102—21no—
26#64102—21no—
27#64102C2212yes—
28#64102C2212yes—
29#64102C2211yescharacteristic, complemented
30#64102C2211yescharacteristic, complemented
31#64096C2211yescharacteristic, complemented
32#64096C2211yescharacteristic, complemented
33#64090—21no—
34#64090—21no—
35#64081—21no—
36C42×C3⋊D3—21no—
37C32×#107C2212yescomplemented
38C32×#106C2212yescomplemented
39#63642C2212yescomplemented
40C8×C3⋊Dic3C2212yescomplemented
41#63637C2212yescomplemented
42#63636C2212yes—
43#63636C2212yes—
44#63636C2212yescomplemented
45C2×#908—34no—
46#5522—34no—
47C2×#893—34no—
48C3×#428D314yescomplemented
49Dic3×M16—34no—
50#5001—34no—
51#4966—34no—
52#4889—38no—
53#4872—38no—
54#4869—38no—
55#4852—38no—
56C23×C3⋊D3—21no—
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C2×#638—21no—
60C22×C3⋊Dic3D411yescharacteristic
61C22×C3⋊Dic3D411yescharacteristic
62#3828—22no—
63#3828C2×C414yescomplemented
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)C2×C414yescomplemented
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—44no—
75C2×#634C2311yescharacteristic
76C32×M16C2×C414yescomplemented
77C2×C32×C8C2312yes—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2311yescharacteristic
80C32×C4⋊C4C2311yescharacteristic
81C32×C4⋊C4C2312yes—
82C32×C22⋊C4—21no—
83C32×C42—21no—
84#3752—21no—
85#3752—21no—
86#3752—22no—
87#3752—22no—
88#3750—21no—
89#3750—21no—
90C4×C3⋊Dic3—21no—
91C4×C3⋊Dic3—21no—
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96#3748—22no—
97C2×C3⋊(C3⋊C8)C2312yes—
98#3745C2×C418yescomplemented
99#3744C2×C418yescomplemented
100C4×AGL(1,ℤ/8)—91noSylow
101C2×#235—34no—
102C22×D12—34no—
103C22×C4×D3—64no—
104C2×C3×M16C2×D314yes—
105C3×#117C2×D314yes—
106C2×C3×C4⋊C4C2×D314yes—
107C2×(C2×D3)⋊C4—64no—
108C2×C4×Dic3—34no—
109C2×#208—34no—
110#908—332no—
111C2×D24—38no—
112C2×#204—38no—
113#893—34no—
114#893—38no—
115#893—34no—
116#893—38no—
117#893—64no—
118#893—64no—
119#887—34no—
120#887—34no—
121#67⋊C4—64no—
122#67⋊C4—64no—
123#872—64no—
124C42×D3—64no—
125C3×#107C2×D318yescomplemented
126C3×#106C2×D318yescomplemented
127#815—38no—
128C8×Dic3—38no—
129#810—38no—
130#809—38no—
131#809—38no—
132#809—38no—
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—24no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—22no—
142C2×C32×C4—42no—
143C2×C32×C4C22×C412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147#638—24no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—41no—
151C2×C3⋊Dic3C2×D411yescharacteristic
152C2×C3⋊Dic3C2×D411yescharacteristic
153C2×C3⋊Dic3C2×D411yescharacteristic
154C2×C3⋊Dic3C2×D411yescharacteristic
155C4⋊(C3⋊D3)—24no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—21no—
158C4⋊(C3⋊D3)C22×C414yes—
159C4⋊(C3⋊D3)C22×C412yescomplemented
160C4×C3⋊D3—24no—
161C4×C3⋊D3—42no—
162C4×C3⋊D3—44no—
163C4×C3⋊D3—42no—
164C4×C3⋊D3—44no—
165#634—21no—
166#634C22×C412yescomplemented
167C32×C8C22×C414yescomplemented
168C3⋊(C3⋊C8)—22no—
169C2×AGL(1,ℤ/8)—91no—
170C4×#41—91no—
171C2×C4×D4—91no—
172#442—92no—
173#440—92no—
174C4×SD16—92no—
175C4×D8—92no—
176#428C3⋊D311yescharacteristic, complemented
177#418—91no—
178#417—91no—
179C4×M16—91no—
180C23×D3—64no—
181C22×C3×C4—24no—
182C22×C3×C4C22×D314yes—
183C2×#67—64no—
184C22×Dic3—34no—
185C22×Dic3—34no—
186#235—316no—
187#235—68no—
188C2×D12—316no—
189C2×D12—38no—
190C2×D12—34no—
191C2×D12—64no—
192C2×D12—68no—
193C2×C4×D3—64no—
194C2×C4×D3—64no—
195C2×C4×D3—64no—
196C2×C4×D3—68no—
197C2×C4×D3—68no—
198C2×C4×D3—1216no—
199C2×Dic6—34no—
200C3×M16C4×D3116yescomplemented
201C2×C3×C8C22×D318yes—
202C3×C4⋊C4—24no—
203C3×C4⋊C4C22×D314yes—
204C3×C4⋊C4C22×D314yes—
205C3×C4⋊C4C22×D318yes—
206C3×C22⋊C4—24no—
207C3×C42—24no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—68no—
211(C2×D3)⋊C4—68no—
212Dic3⋊C4—64no—
213Dic3⋊C4—64no—
214C4×Dic3—34no—
215C4×Dic3—34no—
216C4×Dic3—34no—
217C4×Dic3—34no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220#208—68no—
221C2×C3⋊C8—38no—
222D24—332no—
223#204—332no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32C4×D412yes—
227C22×C32C22×D411yescharacteristic
228C2×C3⋊D3—22no—
229C2×C3⋊D3—24no—
230C2×C3⋊D3—48no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—41no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—42no—
235C32×C4—42no—
236C32×C4—41no—
237C32×C4—41no—
238C32×C4C4×D412yes—
239C32×C4C23×C411yescharacteristic
240C32×C4C2×#4111yescharacteristic
241C3⋊Dic3—22no—
242C3⋊Dic3—21no—
243C3⋊Dic3—21no—
244C3⋊Dic3—21no—
245C3⋊Dic3AGL(1,ℤ/8)12yescomplemented
246C2×#41—91no—
247C22×D4—91no—
248C23×C4—181no—
249AGL(1,ℤ/8)—98no—
250C2×SD16—92no—
251C2×D8—92no—
252C2×M16—91no—
253C2×M16C2×C3⋊D311yescharacteristic
254C4×Q8—91no—
255C4×Q8—91no—
256C4×D4—92no—
257C4×D4—92no—
258C4×D4—91no—
259C4×D4—91no—
260C4×D4—181no—
261C4×D4—181no—
262C4×D4—181no—
263C4×D4—181no—
264#117—181no—
265#117C2×C3⋊D311yescharacteristic
266C2×C4⋊C4C2×C3⋊D311yescharacteristic
267C2×C22⋊C4—181no—
268C2×C42—91no—
269C2×C42—181no—
270#107C2×C3⋊D312yescomplemented
271#106C2×C3⋊D312yescomplemented
272#103—92no—
273#102—92no—
274#102—92no—
275#102—92no—
276#97—92no—
277C4×C8—92no—
278C23×C3D3×D414yes—
279C22×D3—616no—
280C22×D3—64no—
281C22×D3—68no—
282C22×D3—128no—
283C22×D3—128no—
284C2×C3×C4—24no—
285C2×C3×C4—24no—
286C2×C3×C4—28no—
287C2×C3×C4—48no—
288C2×C3×C4C2×C4×D318yes—
289C2×C3×C4D3×D414yes—
290C2×C3×C4#23918yes—
291C2×C3×C4C23×D314yes—
292#67—616no—
293C2×Dic3—34no—
294C2×Dic3—34no—
295C2×Dic3—34no—
296C2×Dic3—34no—
297C2×Dic3—68no—
298C2×Dic3—64no—
299C2×Dic3—124no—
300D12—316no—
301D12—38no—
302D12—616no—
303D12—68no—
304D12—64no—
305C4×D3—616no—
306C4×D3—128no—
307C4×D3—1216no—
308C4×D3—128no—
309C4×D3—1216no—
310Dic6—38no—
311Dic6—64no—
312C3×C8C2×C4×D3116yescomplemented
313C3⋊C8—68no—
314C2×C32—22no—
315C2×C32C2×C4×D411yescharacteristic
316C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
317C2×C32#57511yescharacteristic
318C3⋊D3—42no—
319C3⋊D3—44no—
320C24—181no—
321#41—94no—
322#41—182no—
323C2×Q8—91no—
324C2×D4—91no—
325C2×D4—92no—
326C2×D4—94no—
327C2×D4—181no—
328C2×D4—181no—
329C2×D4—182no—
330C22×C4—21no—
331C22×C4—91no—
332C22×C4—91no—
333C22×C4—181no—
334C22×C4—181no—
335C22×C4—182no—
336C22×C4—182no—
337C22×C4—181no—
338C22×C4—364no—
339C22×C4C22×C3⋊D311yescharacteristic
340SD16—98no—
341D8—98no—
342M16—182no—
343M16C4×C3⋊D314yescomplemented
344C2×C8—92no—
345C2×C8C22×C3⋊D312yes—
346C4⋊C4—21no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C4⋊C4C22×C3⋊D311yescharacteristic
350C4⋊C4C22×C3⋊D311yescharacteristic
351C4⋊C4C22×C3⋊D312yes—
352C22⋊C4—21no—
353C22⋊C4—182no—
354C22⋊C4—182no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C42—21no—
358C42—91no—
359C42—91no—
360C42—91no—
361C42—91no—
362C42—181no—
363C42—181no—
364C22×C3—24no—
365C22×C3—24no—
366C22×C3#89318yes—
367C22×C3C2×D3×D414yes—
368C2×D3—68no—
369C2×D3—616no—
370C2×D3—1232no—
371C2×D3—128no—
372C2×D3—124no—
373C2×D3—124no—
374C2×D3—128no—
375C3×C4—48no—
376C3×C4—44no—
377C3×C4—44no—
378C3×C4#89318yes—
379C3×C4C22×C4×D314yes—
380C3×C4C2×#23914yes—
381Dic3—38no—
382Dic3—68no—
383Dic3—64no—
384Dic3—64no—
385Dic3—64no—
386C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
387C23—184no—
388C23—181no—
389C23—182no—
390C23—362no—
391C23—362no—
392C23D4×C3⋊D311yescharacteristic
393Q8—92no—
394Q8—181no—
395D4—92no—
396D4—94no—
397D4—184no—
398D4—184no—
399D4—182no—
400D4—181no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—91no—
406C2×C4—91no—
407C2×C4—91no—
408C2×C4—91no—
409C2×C4—182no—
410C2×C4—181no—
411C2×C4—184no—
412C2×C4—364no—
413C2×C4—362no—
414C2×C4—364no—
415C2×C4—362no—
416C2×C4—361no—
417C2×C4C2×C4×C3⋊D312yes—
418C2×C4D4×C3⋊D311yescharacteristic
419C2×C4#383212yes—
420C2×C4C23×C3⋊D311yescharacteristic
421C8—182no—
422C8C2×C4×C3⋊D314yescomplemented
423C2×C3—28no—
424C2×C3C2×#89314yes—
425C2×C3D3×AGL(1,ℤ/8)14yes—
426C2×C3#577714yes—
427D3—1216no—
428D3—128no—
429C22—21no—
430C22—21no—
431C22—182no—
432C22—184no—
433C22—368no—
434C22—362no—
435C22—361no—
436C22—361no—
437C22—362no—
438C22#6410212yes—
439C22C2×D4×C3⋊D311yescharacteristic
440C4—42no—
441C4—41no—
442C4—41no—
443C4—92no—
444C4—182no—
445C4—181no—
446C4—181no—
447C4—181no—
448C4#6410212yes—
449C4C22×C4×C3⋊D311yescharacteristic
450C4C2×#383211yescharacteristic
451C3#7919914yescomplemented
452C2—22no—
453C2—364no—
454C2—362no—
455C2C2×#6410211yescharacteristic
456C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
457C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#428C2
socleC22×C32C22×D4
prime radicalC2×#64117C2
cosocleC2×C32×C4C24
hypercenter#428C3⋊D3
hypocenterC32C4×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #10595993C2semidirect
3. C2×#64102C2semidirect
4. C32×#428C2semidirect
5. M16×C3⋊Dic3C2semidirect
6. #10592700C2semidirect
7. #10592665C2semidirect
8. #10592588C2semidirect
9. #10592571C2semidirect
10. #10592568C2semidirect
11. #10592551C2semidirect
22. #64117C4semidirect
29. #64102C22semidirect
30. #64102C22semidirect
31. #64096C22semidirect
32. #64096C22semidirect
37. C32×#107C22semidirect
38. C32×#106C22semidirect
39. #63642C22semidirect
40. C8×C3⋊Dic3C22semidirect
41. #63637C22semidirect
44. #63636C22semidirect
48. C3×#428D3semidirect
63. #3828C2×C4semidirect
66. C2×C4⋊(C3⋊D3)C2×C4semidirect
76. C32×M16C2×C4semidirect
98. #3745C2×C4semidirect
99. #3744C2×C4semidirect
125. C3×#107C2×D3semidirect
126. C3×#106C2×D3semidirect
159. C4⋊(C3⋊D3)C22×C4semidirect
166. #634C22×C4semidirect
167. C32×C8C22×C4semidirect
176. #428C3⋊D3semidirect
200. C3×M16C4×D3semidirect
245. C3⋊Dic3AGL(1,ℤ/8)semidirect
270. #107C2×C3⋊D3semidirect
271. #106C2×C3⋊D3semidirect
312. C3×C8C2×C4×D3semidirect
343. M16C4×C3⋊D3semidirect
386. C32C4×AGL(1,ℤ/8)semidirect
422. C8C2×C4×C3⋊D3semidirect
451. C3#79199semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
#105959932
C2×#641022
C32×#4282
M16×C3⋊Dic32
#105927002
#105926652
#105925882
#105925712
#105925682
#105925512
#791993