Finite Group Databasebeta

← #11868373

Subgroups — #11868373

Order 1152.

961 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594605C211yesmaximal, characteristic
2#10594482C211yesmaximal, characteristic, complemented
3C3⋊D3×#107C211yesmaximal, characteristic, complemented
4C3×#4891C212yesmaximal, complemented
5#10590940C211yesmaximal, characteristic
6#10590767C212yesmaximal, complemented
7#10590658C211yesmaximal, characteristic, complemented
8#10590593C211yesmaximal, characteristic
9#10590575C211yesmaximal, characteristic, complemented
10#10590545C212yesmaximal, complemented
11#10590467C212yesmaximal, complemented
12D3×#478—32nomaximal
13C2×#3802C2211yescharacteristic
14C2×C4×D32—21no—
15C2×C8×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C3×#893C2212yes—
19C3×#890C2212yescomplemented
20#63921—21no—
21#63900—21no—
22#63900C2211yescharacteristic
23Dic3×D12C2212yes—
24#63883—21no—
25C4×#624C2211yescharacteristic
26#63879—22no—
27#63869C2212yescomplemented
28#63847—22no—
29C2×#3710C2211yescharacteristic
30C32×#107C2211yescharacteristic, complemented
31#63645C2211yescharacteristic, complemented
32#63634C2211yescharacteristic, complemented
33#63634C2211yescharacteristic, complemented
34C3×#821C2212yes—
35C3×Dic3⋊C8C2212yescomplemented
36C3×#809C2212yes—
37C3×#808C2212yescomplemented
38#63573C2212yescomplemented
39Dic3⋊(C3⋊C8)C2212yescomplemented
40#63563C2212yes—
41#63562C2212yes—
42D3×#125—32no—
43C4×D3×D4—32no—
44C3×#478—32no—
45#5066—32no—
46#5009—32no—
47#4891D312yescomplemented
48D3×#107—32no—
49D3×#107—61no—
50#4871—32no—
51D3×#106—32no—
52#4847—32no—
53D3×C4⋊C8—32no—
54D3×#102—32no—
55D3×#102—32no—
56#4766—32no—
57#4763—32no—
58C22×D32—21no—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3C2311yescharacteristic
62C2×C3×D12C2312yes—
63C2×C3×C4×D3—22no—
64C2×#625—21no—
65C2×#624—21no—
66C2×#624D411yescharacteristic
67C2×#624D411yescharacteristic
68C2×D3×Dic3—22no—
69#3802—22no—
70#3802Q814yes—
71C4×D32—44no—
72C2×C32×C8C2311yescharacteristic
73C32×C4⋊C4C2311yescharacteristic
74C32×C4⋊C4C2311yescharacteristic
75C4⋊(C3⋊Dic3)C2311yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77#3750—21no—
78#3750—21no—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C8×C3⋊D3—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3C2312yes—
86C2×C3×C3⋊C8C2312yes—
87#3724—21no—
88#3724—22no—
89Dic3⋊Dic3—22no—
90(C2×D3)⋊Dic3—22no—
91Dic32D412yes—
92#3710—22no—
93C2×#478—91noSylow
94C2×D3×D4—32no—
95C22×C4×D3—62no—
96C3×#125—32no—
97C3×C4×D4—32no—
98D4×Dic3—32no—
99C4×#67—62no—
100C2×D3×C8—32no—
101C2×D3×C8—32no—
102C2×D3×C8—61no—
103#893C2×D312yes—
104D3×C4⋊C4—32no—
105D3×C4⋊C4—32no—
106D3×C4⋊C4—32no—
107D3×C4⋊C4—61no—
108D3×C4⋊C4—61no—
109D3×C4⋊C4—62no—
110D3×C4⋊C4—62no—
111#890—32no—
112#890C2×D312yescomplemented
113#889—62no—
114#889—62no—
115#67⋊C4—62no—
116D3×C22⋊C4—62no—
117C4×D12—32no—
118C42×D3—32no—
119#870—32no—
120C3×#107—21no—
121C3×#107C2×D312yescomplemented
122C3×#106—32no—
123C3×C4⋊C8—32no—
124C3×#102—32no—
125C3×#102—32no—
126#832—32no—
127#832—32no—
128#821—32no—
129#821C2×D312yes—
130#818—32no—
131#818—61no—
132#817—32no—
133Dic3⋊C8—32no—
134Dic3⋊C8C2×D312yescomplemented
135#809—32no—
136#809C2×D312yes—
137#808—32no—
138#808C2×D312yescomplemented
139#807—32no—
140#807—32no—
141#807—61no—
142#807—61no—
143C4⋊(C3⋊C8)—32no—
144C22×C3⋊D3C2×D411yescharacteristic
145C22×C3×D3—22no—
146C2×D32—24no—
147C2×D32—42no—
148C2×D32—42no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4C2411yescharacteristic
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3C2×D411yescharacteristic
155C4×C3⋊D3—42no—
156C4×C3⋊D3—42no—
157C4×C3⋊D3C2×Q812yes—
158C4×C3⋊D3#4112yes—
159C2×C3×Dic3—22no—
160C2×C3×Dic3C2×D412yes—
161C2×C3×Dic3C2×D412yes—
162C3×D12—22no—
163C3×D12C2×Q814yes—
164C3×C4×D3—44no—
165#625—24no—
166#624—22no—
167#624—22no—
168#624—42no—
169D3×Dic3—44no—
170C32×C8—21no—
171C3⋊(C3⋊C8)—21no—
172C3×C3⋊C8—22no—
173C2×#125—91no—
174C2×C4×D4—91no—
175#478—32no—
176#478—92no—
177#478—92no—
178#478—92no—
179C2×#107—91no—
180C2×#106—91no—
181C2×C4⋊C8—91no—
182C2×#102—91no—
183C2×#102—91no—
184C23×D3—62no—
185C2×C3×D4—32no—
186C22×C3×C4—62no—
187C2×#67—62no—
188C22×Dic3—62no—
189D3×D4—38no—
190D3×D4—64no—
191C2×D12C22×D312yes—
192C2×C4×D3—22no—
193C2×C4×D3—32no—
194C2×C4×D3—32no—
195C2×C4×D3—32no—
196C2×C4×D3—61no—
197C2×C4×D3—62no—
198C2×C4×D3—62no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—121no—
202C2×C4×D3—121no—
203C2×C4×D3—128no—
204C2×C3×C8—21no—
205C2×C3×C8—32no—
206C2×C3×C8C22×D312yes—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—62no—
211C3×C4⋊C4—62no—
212C3×C4⋊C4C22×D312yes—
213C3×C4⋊C4C22×D312yes—
214C3×C22⋊C4—62no—
215C3×C42—32no—
216#217—62no—
217(C2×D3)⋊C4—22no—
218(C2×D3)⋊C4—62no—
219C4⋊Dic3—22no—
220C4⋊Dic3—32no—
221C4⋊Dic3—32no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—62no—
225C4⋊Dic3C22×D312yes—
226Dic3⋊C4—22no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233Dic3⋊C4—121no—
234Dic3⋊C4—121no—
235C4×Dic3—32no—
236C4×Dic3—32no—
237C4×Dic3C22×D312yes—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8C22×D312yes—
241D3×C8—64no—
242D3×C8—64no—
243D3×C8—64no—
244C22×C32C22×D411yescharacteristic
245C2×C3⋊D3C22⋊Q812yes—
246C2×C3⋊D3#13512yes—
247C2×C3⋊D3AGL(1,ℤ/8)12yes—
248C2×C3×D3—24no—
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251D32—48no—
252C32×C4—41no—
253C32×C4—41no—
254C32×C4C22×Q811yescharacteristic
255C32×C4C2×#4111yescharacteristic
256C3⋊Dic3—41no—
257C3⋊Dic3—41no—
258C3⋊Dic3C22⋊Q812yes—
259C3×Dic3—22no—
260C3×Dic3—22no—
261C3×Dic3—42no—
262C22×D4—91no—
263C23×C4—181no—
264C22×C8—91no—
265C22×C8—91no—
266#125—32no—
267#125—92no—
268#125—182no—
269C4×D4—32no—
270C4×D4—92no—
271C4×D4—182no—
272C2×C4⋊C4—91no—
273C2×C4⋊C4—91no—
274C2×C4⋊C4—91no—
275C2×C4⋊C4—181no—
276C2×C4⋊C4—181no—
277C2×C22⋊C4—181no—
278C2×C42—91no—
279#107—91no—
280#107—91no—
281#107—91no—
282#107D3211yescharacteristic, complemented
283#106—32no—
284#106—92no—
285C4⋊C8—32no—
286C4⋊C8—92no—
287#102—32no—
288#102—32no—
289#102—92no—
290#102—92no—
291C23×C3—62no—
292C22×D3—22no—
293C22×D3—32no—
294C22×D3—61no—
295C22×D3—68no—
296C22×D3—124no—
297C22×D3—124no—
298C3×D4—34no—
299C3×D4—62no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—32no—
304C2×C3×C4—32no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—62no—
308C2×C3×C4—124no—
309C2×C3×C4C23×D312yes—
310#67—68no—
311C2×Dic3—22no—
312C2×Dic3—32no—
313C2×Dic3—61no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—124no—
319C2×Dic3D3×D412yes—
320C2×Dic3D3×D412yes—
321D12—22no—
322D12D3×Q814yes—
323C4×D3—34no—
324C4×D3—34no—
325C4×D3—44no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—64no—
329C4×D3—64no—
330C4×D3—124no—
331C4×D3—124no—
332C4×D3—124no—
333C4×D3—124no—
334C4×D3—242no—
335C4×D3—242no—
336C3×C8—22no—
337C3×C8—22no—
338C3×C8—62no—
339C3⋊C8—22no—
340C3⋊C8—62no—
341C3⋊C8—62no—
342C2×C32C2×C22⋊Q811yescharacteristic
343C2×C32C2×#13511yescharacteristic
344C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
345C3⋊D3#47814yescomplemented
346C3×D3—44no—
347C24—181no—
348C2×D4—32no—
349C2×D4—94no—
350C2×D4—182no—
351C2×D4—181no—
352C22×C4—62no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4—91no—
356C22×C4—181no—
357C22×C4—181no—
358C22×C4—182no—
359C22×C4—181no—
360C22×C4—364no—
361C2×C8—32no—
362C2×C8—91no—
363C2×C8—182no—
364C2×C8—182no—
365C2×C8C2×D3211yescharacteristic
366C4⋊C4—32no—
367C4⋊C4—62no—
368C4⋊C4—62no—
369C4⋊C4—91no—
370C4⋊C4—91no—
371C4⋊C4—181no—
372C4⋊C4—181no—
373C4⋊C4—182no—
374C4⋊C4—182no—
375C4⋊C4—181no—
376C4⋊C4C2×D3211yescharacteristic
377C4⋊C4C2×D3211yescharacteristic
378C22⋊C4—62no—
379C22⋊C4—182no—
380C42—32no—
381C42—92no—
382C22×C3—21no—
383C22×C3—64no—
384C22×C3—122no—
385C22×C3—122no—
386C22×C3C2×D3×D412yes—
387C2×D3—24no—
388C2×D3—34no—
389C2×D3—34no—
390C2×D3—34no—
391C2×D3—42no—
392C2×D3—42no—
393C2×D3—62no—
394C2×D3—62no—
395C2×D3—62no—
396C2×D3—1216no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—42no—
400C3×C4—42no—
401C3×C4—62no—
402C3×C4—62no—
403C3×C4—81no—
404C3×C4—81no—
405C3×C4—122no—
406C3×C4C2×D3×Q812yes—
407C3×C4D3×#4112yes—
408Dic3—22no—
409Dic3—22no—
410Dic3—34no—
411Dic3—42no—
412Dic3—62no—
413Dic3—122no—
414Dic3—122no—
415Dic3—241no—
416Dic3—241no—
417C32C2×#47811yescharacteristic, complemented, Sylow
418C23—62no—
419C23—91no—
420C23—184no—
421C23—362no—
422C23—362no—
423D4—34no—
424D4—62no—
425D4—184no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—32no—
429C2×C4—32no—
430C2×C4—62no—
431C2×C4—91no—
432C2×C4—92no—
433C2×C4—92no—
434C2×C4—124no—
435C2×C4—182no—
436C2×C4—182no—
437C2×C4—181no—
438C2×C4—181no—
439C2×C4—362no—
440C2×C4—362no—
441C2×C4—364no—
442C2×C4—362no—
443C2×C4C22×D3211yescharacteristic
444C8—21no—
445C8—62no—
446C8—181no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—124no—
451C2×C3D3×C22⋊Q812yes—
452C2×C3D3×#13512yes—
453C2×C3D3×AGL(1,ℤ/8)12yes—
454D3—38no—
455D3—44no—
456D3—64no—
457C22—64no—
458C22—92no—
459C22—92no—
460C22—92no—
461C22—122no—
462C22—122no—
463C22—368no—
464C22D32×D411yescharacteristic
465C4—41no—
466C4—41no—
467C4—62no—
468C4—62no—
469C4—92no—
470C4—122no—
471C4—361no—
472C4—361no—
473C4#6430611yescharacteristic
474C4D32×Q811yescharacteristic
475C3—21no—
476C3D3×#47812yescomplemented
477C2—94no—
478C2—124no—
479C2#1059462411yescharacteristic
480C2#1059472611yescharacteristic
481C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenter#107D32
hypocenterC32C2×#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594482C2semidirect
3. C3⋊D3×#107C2semidirect
4. C3×#4891C2semidirect
6. #10590767C2semidirect
7. #10590658C2semidirect
9. #10590575C2semidirect
10. #10590545C2semidirect
11. #10590467C2semidirect
19. C3×#890C22semidirect
27. #63869C22semidirect
30. C32×#107C22semidirect
31. #63645C22semidirect
32. #63634C22semidirect
33. #63634C22semidirect
35. C3×Dic3⋊C8C22semidirect
37. C3×#808C22semidirect
38. #63573C22semidirect
39. Dic3⋊(C3⋊C8)C22semidirect
47. #4891D3semidirect
112. #890C2×D3semidirect
121. C3×#107C2×D3semidirect
134. Dic3⋊C8C2×D3semidirect
138. #808C2×D3semidirect
282. #107D32semidirect
345. C3⋊D3#478semidirect
417. C32C2×#478semidirect
476. C3D3×#478semidirect

Maximal subgroups

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

subgroupindex
#105946052
#105944822
C3⋊D3×#1072
C3×#48912
#105909402
#105907672
#105906582
#105905932
#105905752
#105905452
#105904672
D3×#4783