Finite Group Databasebeta

← #11885805

Subgroups — #11885805

Order 1152.

1578 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×D8C211yesmaximal, characteristic, complemented
2#10596277C212yesmaximal, complemented
3C2×#64121C211yesmaximal, characteristic, complemented
4#10592917C212yesmaximal, complemented
5#10592857C212yesmaximal, complemented
6#10592856C211yesmaximal, characteristic, complemented
7#10592854C211yesmaximal, characteristic, complemented
8#10592852C212yesmaximal, complemented
9D8×C3⋊Dic3C211yesmaximal, characteristic, complemented
10#10592815C211yesmaximal, characteristic, complemented
11C8×#638C211yesmaximal, characteristic, complemented
12#83839—34nomaximal
13C22×C32×D4C2212yes—
14C2×#3830C2212yescomplemented
15C2×C32×D8—24no—
16C2×C32×D8C2212yes—
17C2×C32×D8C2211yescharacteristic
18C2×C32×D8C2211yescharacteristic
19C22×C32×C8C2211yescharacteristic
20#64162—22no—
21C2×#3757—22no—
22#64148—22no—
23#64147C2212yescomplemented
24#64145C2212yescomplemented
25#64144—22no—
26D4×C3⋊Dic3C2212yescomplemented
27C2×#3754C2212yescomplemented
28C2×#3754C2212yescomplemented
29C4×#638C2211yescharacteristic
30#64133C2212yes—
31#64121—24no—
32C2×#3746C2211yescharacteristic, complemented
33C2×C8×C3⋊D3C2211yescharacteristic, complemented
34#63659C2212yescomplemented
35#63659C2212yescomplemented
36#63657C2211yescharacteristic
37#63647C2211yescharacteristic, complemented
38#63645C2211yescharacteristic, complemented
39#63643C2212yescomplemented
40#63641C2211yescharacteristic, complemented
41C8×C3⋊Dic3C2211yescharacteristic, complemented
42C22×C3×D8D314yescomplemented
43#5806—38no—
44C2×#912—34no—
45#5218—38no—
46#5158—38no—
47#5157—34no—
48#5155—34no—
49#5153—38no—
50Dic3×D8—34no—
51#5116—34no—
52C8×#67—34no—
53C24×C32—22no—
54C2×C32×D4—24no—
55C2×C32×D4—22no—
56C2×C32×D4—42no—
57C2×C32×D4C2312yes—
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×#638—22no—
61C2×#638—22no—
62C2×#638D411yescharacteristic
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3—22no—
65#3830—24no—
66#3830—42no—
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634C2312yes—
69C32×D8—24no—
70C32×D8—22no—
71C32×D8D414yescomplemented
72C2×C32×C8—22no—
73C2×C32×C8C2311yescharacteristic
74C2×C32×C8C2311yescharacteristic
75#3757—22no—
76#3757—22no—
77#3757—22no—
78#3757—22no—
79#3757—22no—
80#3757D411yescharacteristic
81#3754—24no—
82#3754—42no—
83#3752D411yescharacteristic
84C4⋊(C3⋊Dic3)C2312yes—
85#3750—22no—
86#3750D411yescharacteristic
87C4×C3⋊Dic3C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2311yescharacteristic
90#3746—22no—
91C8×C3⋊D3—22no—
92#3280—91noSylow
93C22×C3×D4C2×D318yes—
94C2×#237—38no—
95C2×C3×D8—216no—
96C2×C3×D8C2×D318yes—
97C2×C3×D8C2×D314yes—
98C2×C3×D8C2×D314yes—
99C22×C3×C8C2×D314yes—
100#953—68no—
101C2×#217—68no—
102#939—68no—
103#938—38no—
104#936—38no—
105#935—68no—
106D4×Dic3—38no—
107C2×#214—38no—
108C2×#214—38no—
109C4×#67—34no—
110#924—38no—
111#912—616no—
112C2×Dic12—34no—
113C2×D3×C8—34no—
114#832—38no—
115#832—38no—
116#830—34no—
117(C2×D3)⋊C8—34no—
118#818—34no—
119#816—38no—
120Dic3⋊C8—34no—
121C8×Dic3—34no—
122C23×C32—22no—
123C23×C32—22no—
124C23×C32—44no—
125C23×C32—44no—
126C23×C32—82no—
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3C2×D411yescharacteristic
129C32×D4—22no—
130C32×D4—22no—
131C32×D4—22no—
132C32×D4—44no—
133C32×D4C2×D414yes—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2411yescharacteristic
138#638—22no—
139#638—44no—
140#638—82no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—44no—
144C2×C3⋊Dic3—82no—
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C4×C3⋊D3—21no—
149C4×C3⋊D3—21no—
150#634—22no—
151#634—22no—
152C32×C8—21no—
153C32×C8C2×D412yes—
154C3⋊(C3⋊C8)—21no—
155C3⋊(C3⋊C8)—21no—
156C2×#135—91no—
157C22×D8C3⋊D311yescharacteristic, complemented
158#546—92no—
159#495—91no—
160#467—91no—
161#466—91no—
162#463—92no—
163#450—92no—
164#449—92no—
165C4×D8—91no—
166C8×D4—91no—
167C24×C3—28no—
168C2×C3×D4—216no—
169C2×C3×D4—28no—
170C2×C3×D4—48no—
171C2×C3×D4C22×D318yes—
172C2×C3×D4C22×D318yes—
173C22×C3×C4C22×D314yes—
174C2×#67—34no—
175C2×#67—68no—
176C2×#67—68no—
177C22×Dic3—68no—
178C22×Dic3—68no—
179#237—616no—
180#237—128no—
181C2×C4×D3—34no—
182C2×Dic6—38no—
183C3×D8—216no—
184C3×D8—28no—
185C3×D8#67116yescomplemented
186C2×C3×C8—28no—
187C2×C3×C8C22×D314yes—
188C2×C3×C8C22×D314yes—
189#217—34no—
190#217—68no—
191#217—68no—
192#217—68no—
193#217—68no—
194#217—68no—
195#214—616no—
196#214—128no—
197(C2×D3)⋊C4—34no—
198C4⋊Dic3—38no—
199Dic3⋊C4—34no—
200Dic3⋊C4—68no—
201C4×Dic3—34no—
202C2×C3⋊C8—34no—
203C2×C3⋊C8—34no—
204Dic12—68no—
205D3×C8—68no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32—24no—
209C22×C32—42no—
210C22×C32—42no—
211C22×C32—42no—
212C22×C32—42no—
213C22×C32—42no—
214C22×C32—88no—
215C22×C32#13512yescomplemented
216C22×C32C22×D411yescharacteristic
217C2×C3⋊D3—21no—
218C2×C3⋊D3—21no—
219C2×C3⋊D3—21no—
220C32×C4—21no—
221C32×C4C22×D411yescharacteristic
222C32×C4H(5,𝔽2)11yescharacteristic
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—21no—
226C3⋊Dic3—42no—
227C3⋊Dic3—42no—
228C2×#41—92no—
229C22×D4C2×C3⋊D312yes—
230#135—184no—
231C2×Q16—91no—
232C2×SD16—92no—
233C2×SD16—92no—
234C2×D8—24no—
235C2×D8C2×C3⋊D312yes—
236C2×D8C2×C3⋊D311yescharacteristic
237C2×D8C2×C3⋊D311yescharacteristic
238C22×C8—91no—
239C22×C8C2×C3⋊D311yescharacteristic
240#124—92no—
241#123—182no—
242C22⋊Q8—92no—
243#121—92no—
244#121—182no—
245#120—182no—
246C4×D4—91no—
247C4×D4—92no—
248C2×C22⋊C4—182no—
249#107—91no—
250C4⋊C8—91no—
251#103—92no—
252#102—92no—
253#102—92no—
254C22⋊C8—91no—
255C22⋊C8—91no—
256C4×C8—91no—
257C23×C3—28no—
258C23×C3—28no—
259C23×C3—416no—
260C23×C3—416no—
261C23×C3—88no—
262C23×C3D3×D414yes—
263C22×D3—34no—
264C3×D4—28no—
265C3×D4—28no—
266C3×D4—28no—
267C3×D4—416no—
268C3×D4C2×#67116yes—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4D3×D414yes—
272C2×C3×C4C23×D314yes—
273#67—68no—
274#67—1216no—
275#67—248no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—34no—
279C2×Dic3—68no—
280C2×Dic3—68no—
281C2×Dic3—1216no—
282C2×Dic3—248no—
283C4×D3—64no—
284C4×D3—64no—
285Dic6—68no—
286Dic6—68no—
287C3×C8—24no—
288C3×C8C2×#6718yes—
289C3⋊C8—64no—
290C3⋊C8—64no—
291C2×C32—22no—
292C2×C32—44no—
293C2×C32—82no—
294C2×C32D4211yescharacteristic
295C2×C32C2×#13511yescharacteristic
296C2×C32#57611yescharacteristic
297C3⋊D3—41no—
298C24—22no—
299#41—184no—
300#41—362no—
301C2×Q8—92no—
302C2×D4—24no—
303C2×D4—22no—
304C2×D4—42no—
305C2×D4—91no—
306C2×D4—182no—
307C2×D4—182no—
308C2×D4C22×C3⋊D312yes—
309C2×D4C22×C3⋊D312yes—
310C22×C4—91no—
311C22×C4—182no—
312C22×C4—182no—
313C22×C4C22×C3⋊D311yescharacteristic
314Q16—182no—
315SD16—184no—
316SD16—362no—
317D8—24no—
318D8—22no—
319D8#63814yescomplemented
320C2×C8—22no—
321C2×C8—91no—
322C2×C8—91no—
323C2×C8—182no—
324C2×C8C22×C3⋊D311yescharacteristic
325C2×C8C22×C3⋊D311yescharacteristic
326C4⋊C4—91no—
327C4⋊C4—92no—
328C4⋊C4—182no—
329C22⋊C4—91no—
330C22⋊C4—91no—
331C22⋊C4—182no—
332C22⋊C4—182no—
333C22⋊C4—182no—
334C22⋊C4—182no—
335C22⋊C4—182no—
336C42—91no—
337C22×C3—24no—
338C22×C3—24no—
339C22×C3—216no—
340C22×C3—48no—
341C22×C3—48no—
342C22×C3—48no—
343C22×C3—48no—
344C22×C3—48no—
345C22×C3—832no—
346C22×C3#91218yescomplemented
347C22×C3C2×D3×D414yes—
348C2×D3—64no—
349C2×D3—64no—
350C2×D3—64no—
351C3×C4—24no—
352C3×C4#100414yes—
353C3×C4C22×#6714yes—
354Dic3—64no—
355Dic3—64no—
356Dic3—64no—
357Dic3—128no—
358Dic3—128no—
359C32#328011yescharacteristic, complemented, Sylow
360C23—22no—
361C23—22no—
362C23—44no—
363C23—44no—
364C23—82no—
365C23—91no—
366C23D4×C3⋊D311yescharacteristic
367Q8—182no—
368Q8—182no—
369D4—22no—
370D4—22no—
371D4—22no—
372D4—44no—
373D4—182no—
374D4—364no—
375D4—722no—
376D4C2×#63814yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—91no—
380C2×C4—91no—
381C2×C4—91no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4—182no—
385C2×C4—182no—
386C2×C4—364no—
387C2×C4—722no—
388C2×C4D4×C3⋊D311yescharacteristic
389C2×C4C23×C3⋊D311yescharacteristic
390C8—21no—
391C8—181no—
392C8—181no—
393C8C2×#63812yes—
394C2×C3—28no—
395C2×C3—416no—
396C2×C3—88no—
397C2×C3C2×#91214yes—
398C2×C3#575714yes—
399C2×C3D4×#6714yes—
400D3—124no—
401C22—21no—
402C22—21no—
403C22—24no—
404C22—42no—
405C22—42no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—88no—
410C22—181no—
411C22—181no—
412C22—181no—
413C22#6412112yescomplemented
414C22C2×D4×C3⋊D311yescharacteristic
415C4—21no—
416C4—181no—
417C4—181no—
418C4—181no—
419C4—362no—
420C4—362no—
421C4#6436111yescharacteristic
422C4C22×#63811yescharacteristic
423C3#8383914yescomplemented
424C2—22no—
425C2—44no—
426C2—82no—
427C2—361no—
428C2C2×#6412111yescharacteristic
429C2#1059622811yescharacteristic
430C2D4×#63811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC22×C32×D8C2
socleC22×C32C22×D4
hypercenterC22×D8C3⋊D3
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×C32×D8C2semidirect
2. #10596277C2semidirect
3. C2×#64121C2semidirect
4. #10592917C2semidirect
5. #10592857C2semidirect
6. #10592856C2semidirect
7. #10592854C2semidirect
8. #10592852C2semidirect
9. D8×C3⋊Dic3C2semidirect
10. #10592815C2semidirect
11. C8×#638C2semidirect
14. C2×#3830C22semidirect
23. #64147C22semidirect
24. #64145C22semidirect
26. D4×C3⋊Dic3C22semidirect
27. C2×#3754C22semidirect
28. C2×#3754C22semidirect
32. C2×#3746C22semidirect
33. C2×C8×C3⋊D3C22semidirect
34. #63659C22semidirect
35. #63659C22semidirect
37. #63647C22semidirect
38. #63645C22semidirect
39. #63643C22semidirect
40. #63641C22semidirect
41. C8×C3⋊Dic3C22semidirect
42. C22×C3×D8D3semidirect
71. C32×D8D4semidirect
157. C22×D8C3⋊D3semidirect
185. C3×D8#67semidirect
215. C22×C32#135semidirect
319. D8#638semidirect
346. C22×C3#912semidirect
359. C32#3280semidirect
413. C22#64121semidirect
423. C3#83839semidirect

Maximal subgroups

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

subgroupindex
C22×C32×D82
#105962772
C2×#641212
#105929172
#105928572
#105928562
#105928542
#105928522
D8×C3⋊Dic32
#105928152
C8×#6382
#838393