Finite Group Databasebeta

← #11878671

Subgroups — #11878671

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic, complemented
2C2×C3×#874C211yesmaximal, characteristic, complemented
3#10592624C211yesmaximal, characteristic, complemented
4#10591160C214yesmaximal, complemented
5#10590352C212yesmaximal, complemented
6#10590347C214yesmaximal, complemented
7#10590277C212yesmaximal, complemented
8#83302—31nomaximal
9#83166—31nomaximal
10C2×C3×#235—21no—
11C22×C3×D12—21no—
12C22×C3×D12—21no—
13C22×C3×D12C2212yes—
14C2×C32×C42C2211yescharacteristic
15C3×#930—21no—
16C3×#930C2212yes—
17C3×#875—21no—
18C3×#874—21no—
19C3×#874—21no—
20C3×#874C2212yes—
21C3×#874C2212yes—
22C3×#874C2211yescharacteristic, complemented
23C3×C4×D12—21no—
24C3×C4×D12C2212yescomplemented
25C3×#869C2211yescharacteristic, complemented
26C2×#3713C2218yescomplemented
27#63657C2212yes—
28C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
29C4×C3⋊(C3⋊C8)C2212yescomplemented
30#63562C2218yescomplemented
31C3×#532—31no—
32C2×C3×#127—31no—
33#5477D311yescharacteristic, complemented
34C2×#874D311yescharacteristic, complemented
35#5217—34no—
36#5088—32no—
37#5073—32no—
38#5073—32no—
39#5072—34no—
40#5070—32no—
41#5036—34no—
42#5015—34no—
43#4925—31no—
44#4925—31no—
45#4925—61no—
46C23×C3×D3—22no—
47C22×C32×C4D411yescharacteristic
48C22×C32×C4D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C2×C3×#67—22no—
51C3×#235—44no—
52C2×C3×D12—21no—
53C2×C3×D12—22no—
54C2×C3×D12—22no—
55C2×C3×D12—22no—
56C2×C3×D12—22no—
57C2×C3×D12—22no—
58C2×C3×D12—21no—
59C2×C3×D12—44no—
60C2×C3×D12—44no—
61C2×C3×D12—44no—
62C2×C3×D12C2312yes—
63C2×C3×D12C2314yes—
64C2×C3×C4×D3—22no—
65C2×C3×Dic6—21no—
66C32×C42D411yescharacteristic
67C32×C42D411yescharacteristic
68C32×C42C2311yescharacteristic
69C32×C42C2311yescharacteristic
70C2×C3⋊(C3⋊C8)C2314yes—
71C3×(C2×D3)⋊C4—22no—
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75#3713—48no—
76#3205—91noSylow
77C2×C3×#41—61no—
78C22×C3×D4—32no—
79C22×C3×D4—61no—
80C22×C3×D4—61no—
81C2×#235—21no—
82C22×D12—21no—
83C22×D12—21no—
84C22×D12C2×D312yes—
85C3×C4⋊Q8—31no—
86C3×#127—32no—
87C3×#127—32no—
88C3×#127—31no—
89C3×#127—61no—
90C3×#127—61no—
91C3×#124—61no—
92C3×#121—32no—
93C3×#121—61no—
94C3×C4×D4—32no—
95C3×C4×D4—61no—
96C2×C3×C42—21no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C2×D311yescharacteristic
99C2×#213—38no—
100C2×#213—38no—
101#930—21no—
102#930C2×D312yes—
103#875—21no—
104#874—21no—
105#874—21no—
106#874C2×D312yes—
107#874C2×D312yes—
108#874C2×D311yescharacteristic, complemented
109C4×D12—21no—
110C4×D12C2×D312yescomplemented
111#869C2×D311yescharacteristic, complemented
112#832—38no—
113#830—32no—
114#830—32no—
115#830—62no—
116#809—38no—
117C4⋊(C3⋊C8)—32no—
118C4⋊(C3⋊C8)—32no—
119C4⋊(C3⋊C8)—62no—
120C4×C3⋊C8—32no—
121C4×C3⋊C8—32no—
122C4×C3⋊C8—62no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—24no—
125C22×C3×D3—22no—
126C22×C3×D3—44no—
127C22×C3×D3—44no—
128C22×C3×D3—44no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4D814yescomplemented
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2411yescharacteristic
138C3×#67—44no—
139C2×C3×Dic3—22no—
140C3×D12—24no—
141C3×D12—28no—
142C3×D12—44no—
143C3×D12—44no—
144C3×D12—44no—
145C3×D12—44no—
146C3×D12—42no—
147C3×D12—42no—
148C3×D12—44no—
149C3×C4×D3—44no—
150C3×Dic6—42no—
151C3⋊(C3⋊C8)—24no—
152#532—31no—
153C2×#127—31no—
154#493—92no—
155#486—92no—
156#459—94no—
157#447—94no—
158#431—91no—
159C24×C3—62no—
160C23×D3—22no—
161C3×#41—124no—
162C2×C3×Q8—61no—
163C2×C3×D4—34no—
164C2×C3×D4—32no—
165C2×C3×D4—62no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—62no—
169C2×C3×D4—62no—
170C2×C3×D4—62no—
171C2×C3×D4—62no—
172C2×C3×D4—62no—
173C2×C3×D4—124no—
174C2×C3×D4—124no—
175C2×C3×D4—124no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—62no—
180C22×C3×C4#6711yescharacteristic
181C22×C3×C4#6711yescharacteristic
182C22×C3×C4#6711yescharacteristic
183C22×C3×C4#6711yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C2×#67—22no—
187#235—44no—
188C2×D12—21no—
189C2×D12—22no—
190C2×D12—22no—
191C2×D12—22no—
192C2×D12—22no—
193C2×D12—22no—
194C2×D12—21no—
195C2×D12—44no—
196C2×D12—44no—
197C2×D12—44no—
198C2×D12C22×D314yes—
199C2×D12C22×D312yes—
200C2×C4×D3—22no—
201C2×Dic6—21no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—61no—
204C3×C22⋊C4—62no—
205C3×C22⋊C4—62no—
206C3×C42—21no—
207C3×C42—21no—
208C3×C42—21no—
209C3×C42—21no—
210C3×C42#6711yescharacteristic
211C3×C42#6711yescharacteristic
212C3×C42#6711yescharacteristic
213C3×C42#6711yescharacteristic
214C3×C42C22×D311yescharacteristic
215C3×C42C22×D311yescharacteristic
216C3×C42C22×D311yescharacteristic
217C3×C42C22×D311yescharacteristic
218#213—128no—
219#213—128no—
220(C2×D3)⋊C4—22no—
221(C2×D3)⋊C4—22no—
222C4⋊Dic3—21no—
223C4⋊Dic3C22×D312yes—
224C2×C3⋊C8—34no—
225C2×C3⋊C8—34no—
226C2×C3⋊C8—64no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32C2×D812yes—
230C22×C32C22×D411yescharacteristic
231C2×C3×D3—44no—
232C2×C3×D3—42no—
233C2×C3×D3—42no—
234C2×C3×D3—44no—
235C2×C3×D3—44no—
236C2×C3×D3—42no—
237C2×C3×D3—88no—
238C32×C4—21no—
239C32×C4—21no—
240C32×C4C2×D812yes—
241C32×C4C2×D812yes—
242C32×C4AGL(1,ℤ/8)12yes—
243C32×C4H(5,𝔽2)12yes—
244C3×Dic3—42no—
245C2×#41—61no—
246C22×D4—32no—
247C22×D4—61no—
248C22×D4—61no—
249C2×D8—98no—
250C4⋊Q8—31no—
251#127—32no—
252#127—32no—
253#127—31no—
254#127—61no—
255#127—61no—
256#124—61no—
257#121—32no—
258#121—61no—
259C4×D4—32no—
260C4×D4—61no—
261C2×C42D3211yescharacteristic
262C4⋊C8—92no—
263#102—98no—
264C22⋊C8—92no—
265C4×C8—92no—
266C23×C3—21no—
267C23×C3—62no—
268C23×C3—64no—
269C23×C3—124no—
270C23×C3—124no—
271C23×C3—124no—
272C23×C3C2×#6711yescharacteristic
273C23×C3C2×#6711yescharacteristic
274C22×D3—22no—
275C22×D3—24no—
276C22×D3—44no—
277C22×D3—44no—
278C22×D3—44no—
279C3×Q8—122no—
280C3×D4—64no—
281C3×D4—68no—
282C3×D4—124no—
283C3×D4—124no—
284C3×D4—124no—
285C3×D4—124no—
286C3×D4—124no—
287C3×D4—122no—
288C3×D4—122no—
289C3×D4—124no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—24no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—62no—
304C2×C3×C4—124no—
305C2×C3×C4#21314yescomplemented
306C2×C3×C4#21314yescomplemented
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314C2×C3×C4C2×#6711yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319#67—44no—
320C2×Dic3—22no—
321D12—28no—
322D12—24no—
323D12—44no—
324D12—44no—
325D12—44no—
326D12—44no—
327D12—42no—
328D12—44no—
329D12—42no—
330C4×D3—44no—
331Dic6—42no—
332C3⋊C8—64no—
333C3⋊C8—64no—
334C3⋊C8—124no—
335C2×C32—22no—
336C2×C32#53511yescharacteristic
337C2×C32C22×D811yescharacteristic
338C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
339C3×D3—82no—
340C3×D3—84no—
341C24—62no—
342#41—124no—
343C2×Q8—61no—
344C2×D4—34no—
345C2×D4—32no—
346C2×D4—62no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—62no—
350C2×D4—62no—
351C2×D4—62no—
352C2×D4—62no—
353C2×D4—62no—
354C2×D4—124no—
355C2×D4—124no—
356C2×D4—124no—
357C22×C4—62no—
358C22×C4#62511yescharacteristic
359C22×C4#62511yescharacteristic
360C22×C4C2×D3211yescharacteristic
361D8—368no—
362C2×C8—94no—
363C4⋊C4—32no—
364C4⋊C4—61no—
365C22⋊C4—62no—
366C22⋊C4—62no—
367C42#62511yescharacteristic
368C42#62511yescharacteristic
369C42C2×D3211yescharacteristic
370C42C2×D3211yescharacteristic
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—122no—
380C22×C3—124no—
381C22×C3—122no—
382C22×C3—122no—
383C22×C3—124no—
384C22×C3—124no—
385C22×C3—248no—
386C22×C3C2×#21312yes—
387C22×C3C2×#21312yes—
388C22×C3C22×#6711yescharacteristic
389C22×C3C22×#6711yescharacteristic
390C2×D3—42no—
391C2×D3—44no—
392C2×D3—44no—
393C2×D3—44no—
394C2×D3—42no—
395C2×D3—42no—
396C2×D3—88no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—22no—
402C3×C4—22no—
403C3×C4—22no—
404C3×C4—22no—
405C3×C4—41no—
406C3×C4—41no—
407C3×C4—122no—
408C3×C4C2×#21312yes—
409C3×C4C2×#21312yes—
410C3×C4C2×#21312yes—
411C3×C4C2×#21312yes—
412C3×C4#93212yes—
413C3×C4#94912yes—
414C3×C4#100412yes—
415C3×C4#100912yes—
416Dic3—42no—
417C32#320511yescharacteristic, complemented, Sylow
418C23—62no—
419C23—64no—
420C23—124no—
421C23—124no—
422C23—124no—
423C23C2×#62511yescharacteristic
424Q8—122no—
425D4—64no—
426D4—68no—
427D4—124no—
428D4—124no—
429D4—124no—
430D4—124no—
431D4—124no—
432D4—122no—
433D4—124no—
434D4—122no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—62no—
438C2×C4—124no—
439C2×C4#371314yescomplemented
440C2×C4C2×#62511yescharacteristic
441C2×C4C2×#62511yescharacteristic
442C2×C4C2×#62511yescharacteristic
443C2×C4C2×#62511yescharacteristic
444C2×C4C2×#62511yescharacteristic
445C2×C4C22×D3211yescharacteristic
446C8—184no—
447C2×C3—22no—
448C2×C3—22no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—42no—
453C2×C3—244no—
454C2×C3—242no—
455C2×C3C22×#21311yescharacteristic
456C2×C3C22×#21311yescharacteristic
457C2×C3C2×#93211yescharacteristic
458C2×C3#580511yescharacteristic
459C2×C3C2×#94911yescharacteristic
460C2×C3#583011yescharacteristic
461D3—82no—
462D3—84no—
463C22—21no—
464C22—21no—
465C22—122no—
466C22—124no—
467C22—124no—
468C22—122no—
469C22—124no—
470C22—122no—
471C22—248no—
472C22C2×#371312yes—
473C22C22×#62511yescharacteristic
474C4—21no—
475C4—21no—
476C4—122no—
477C4C2×#371312yes—
478C4C2×#371312yes—
479C4#6382312yes—
480C4#6430712yes—
481C3—21no—
482C3#8316611yescharacteristic, complemented
483C3#8330211yescharacteristic, complemented
484C2—22no—
485C2—244no—
486C2—242no—
487C2C22×#371311yescharacteristic
488C2C2×#6382311yescharacteristic
489C2#1059504011yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C3×#5477C2semidirect
2. C2×C3×#874C2semidirect
3. #10592624C2semidirect
4. #10591160C2semidirect
5. #10590352C2semidirect
6. #10590347C2semidirect
7. #10590277C2semidirect
22. C3×#874C22semidirect
24. C3×C4×D12C22semidirect
25. C3×#869C22semidirect
26. C2×#3713C22semidirect
28. C4⋊(C3⋊(C3⋊C8))C22semidirect
29. C4×C3⋊(C3⋊C8)C22semidirect
30. #63562C22semidirect
33. #5477D3semidirect
34. C2×#874D3semidirect
108. #874C2×D3semidirect
110. C4×D12C2×D3semidirect
111. #869C2×D3semidirect
131. C2×C32×C4D8semidirect
305. C2×C3×C4#213semidirect
306. C2×C3×C4#213semidirect
417. C32#3205semidirect
439. C2×C4#3713semidirect
482. C3#83166semidirect
483. C3#83302semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
C2×C3×#8742
#105926242
#105911602
#105903522
#105903472
#105902772
#833023
#831663