Finite Group Databasebeta

← #11775213

Subgroups — #11775213

Order 1152.

787 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2#10592906C211yesmaximal, characteristic, complemented
3C3×C4×#217C211yesmaximal, characteristic, complemented
4#10589149C214yesmaximal, complemented
5#71673—31nomaximal
6#69444—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×C3×#67—21no—
9C22×C3×D12C411yescharacteristic, complemented
10C2×#3748—21no—
11C2×C3×#217—21no—
12C3×#930—21no—
13C3×#930—21no—
14C3×#930C412yescomplemented
15C3×#930C2212yes—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C411yescharacteristic, complemented
18C2×C3×C4×Dic3—21no—
19#63657—21no—
20#63657C2212yescomplemented
21C3×C3⋊#95C2212yescomplemented
22C2×C3×#121—31no—
23C2×#930D311yescharacteristic
24C3×C4×C22⋊C4—31no—
25C4×#217D311yescharacteristic, complemented
26#5207—31no—
27#5207—31no—
28#5207—61no—
29#4537—34no—
30#4451—34no—
31C24×C32D411yescharacteristic
32C23×C3×D3—21no—
33C22×C32×C4—42no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67—22no—
41C2×C3×#67—22no—
42C2×C3×#67—44no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—22no—
45C2×C3×D12—21no—
46C2×C3×D12—42no—
47C2×C3×D12C2×C412yes—
48#3748—42no—
49C2×C3⋊(C3⋊C8)—22no—
50C3×#217—24no—
51C3×(C2×D3)⋊C4—22no—
52C3×(C2×D3)⋊C4—22no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3C2×C412yes—
55C3×C4×Dic3—42no—
56#1507—91noSylow
57C22×C3×D4—31no—
58C22×C3×D4—61no—
59C23×C3×C4—21no—
60C23×C3×C4C2×D311yescharacteristic
61C23×C3×C4C2×D311yescharacteristic
62C22×#67—21no—
63C22×D12Dic311yescharacteristic, complemented
64C3×#121—32no—
65C3×#121—32no—
66C3×#121—61no—
67C3×#121—61no—
68C2×C3×C4⋊C4—31no—
69C2×C3×C22⋊C4—61no—
70C2×C3×C22⋊C4—61no—
71C2×C3×C42—61no—
72C2×#217—21no—
73#930—21no—
74#930—21no—
75#930Dic312yescomplemented
76#930C2×D312yes—
77C2×(C2×D3)⋊C4—21no—
78C2×C4⋊Dic3Dic311yescharacteristic, complemented
79C2×C4×Dic3—21no—
80C2×#208—62no—
81C2×#208—61no—
82C2×#208—61no—
83C3×#95—32no—
84C3⋊#95C2×D312yescomplemented
85#830—32no—
86#830—32no—
87#830—62no—
88#830—62no—
89#830—61no—
90#830—61no—
91C23×C32—22no—
92C23×C32—22no—
93C23×C32—41no—
94C23×C32C22⋊C411yescharacteristic
95C23×C32C22⋊C411yescharacteristic
96C23×C32C2×D411yescharacteristic
97C22×C3×D3—22no—
98C22×C3×D3—42no—
99C22×C3×D3—42no—
100C22×C3×D3—42no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C3×#67—44no—
112C3×#67—44no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3—42no—
118C3×D12—42no—
119C3×D12—42no—
120C3⋊(C3⋊C8)—42no—
121C2×#121—31no—
122#407—91no—
123C4×C22⋊C4—31no—
124#327—94no—
125C24×C3—21no—
126C24×C3—61no—
127C24×C3#6711yescharacteristic
128C24×C3#6711yescharacteristic
129C23×D3—21no—
130C2×C3×D4—32no—
131C2×C3×D4—62no—
132C2×C3×D4—62no—
133C2×C3×D4—61no—
134C2×C3×D4—122no—
135C2×C3×D4—124no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—42no—
143C22×C3×C4—42no—
144C22×C3×C4—44no—
145C22×C3×C4—61no—
146C22×C3×C4—62no—
147C22×C3×C4C4×D311yescharacteristic
148C22×C3×C4C4×D311yescharacteristic
149C22×C3×C4D1211yescharacteristic
150C22×C3×C4D1211yescharacteristic
151C22×C3×C4C2×Dic311yescharacteristic
152C22×C3×C4C2×Dic311yescharacteristic
153C22×C3×C4#6711yescharacteristic
154C22×C3×C4#6711yescharacteristic
155C22×C3×C4#6711yescharacteristic
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C2×#67—22no—
160C2×#67—22no—
161C2×#67—44no—
162C22×Dic3—21no—
163C22×Dic3—22no—
164C2×D12—21no—
165C2×D12—42no—
166C2×D12C2×Dic312yes—
167C3×C4⋊C4—32no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—64no—
170C3×C22⋊C4—62no—
171C3×C22⋊C4—62no—
172C3×C42—122no—
173#217—24no—
174(C2×D3)⋊C4—22no—
175(C2×D3)⋊C4—22no—
176C4⋊Dic3—21no—
177C4⋊Dic3C2×Dic312yes—
178C4×Dic3—42no—
179#208—124no—
180#208—122no—
181#208—122no—
182C2×C3⋊C8—64no—
183C2×C3⋊C8—62no—
184C2×C3⋊C8—62no—
185C22×C32—21no—
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32—44no—
193C22×C32#10412yes—
194C22×C32C2×C22⋊C411yescharacteristic
195C22×C32AGL(1,ℤ/8)12yes—
196C2×C3×D3—42no—
197C2×C3×D3—42no—
198C2×C3×D3—42no—
199C2×C3×D3—84no—
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4#9912yes—
204C3×Dic3—44no—
205C3×Dic3—42no—
206C22×D4—31no—
207C22×D4—61no—
208C23×C4D3211yescharacteristic
209C2×M16—181no—
210#121—32no—
211#121—32no—
212#121—61no—
213#121—61no—
214C2×C4⋊C4—31no—
215C2×C22⋊C4—61no—
216C2×C22⋊C4—61no—
217C2×C42—61no—
218C22⋊C8—92no—
219C22⋊C8—181no—
220#95—32no—
221C23×C3—22no—
222C23×C3—22no—
223C23×C3—22no—
224C23×C3—22no—
225C23×C3—21no—
226C23×C3—21no—
227C23×C3—21no—
228C23×C3—42no—
229C23×C3—42no—
230C23×C3—41no—
231C23×C3—41no—
232C23×C3—42no—
233C23×C3—62no—
234C23×C3—122no—
235C23×C3—122no—
236C23×C3—122no—
237C23×C3(C2×D3)⋊C411yescharacteristic
238C23×C3(C2×D3)⋊C411yescharacteristic
239C23×C3#21711yescharacteristic
240C23×C3#21711yescharacteristic
241C23×C3C2×#6711yescharacteristic
242C23×C3C2×#6711yescharacteristic
243C22×D3—22no—
244C22×D3—42no—
245C22×D3—42no—
246C22×D3—42no—
247C3×D4—122no—
248C3×D4—124no—
249C3×D4—124no—
250C3×D4—122no—
251C2×C3×C4—24no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—41no—
270C2×C3×C4—42no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
273C2×C3×C4—64no—
274C2×C3×C4—62no—
275C2×C3×C4—122no—
276C2×C3×C4—122no—
277C2×C3×C4—122no—
278C2×C3×C4(C2×D3)⋊C411yescharacteristic
279C2×C3×C4(C2×D3)⋊C411yescharacteristic
280C2×C3×C4#21711yescharacteristic
281C2×C3×C4#21711yescharacteristic
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4C2×D1211yescharacteristic
284C2×C3×C4C22×Dic311yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286#67—44no—
287#67—44no—
288C2×Dic3—24no—
289C2×Dic3—22no—
290C2×Dic3—42no—
291C2×Dic3—42no—
292C2×Dic3—42no—
293D12—42no—
294D12—42no—
295C3⋊C8—124no—
296C3⋊C8—122no—
297C3⋊C8—122no—
298C2×C32—22no—
299C2×C32—22no—
300C2×C32—41no—
301C2×C32C2×#9911yescharacteristic
302C2×C32#41811yescharacteristic
303C2×C32C2×#10411yescharacteristic
304C3×D3—82no—
305C24—61no—
306C24#62511yescharacteristic
307C2×D4—32no—
308C2×D4—62no—
309C2×D4—62no—
310C2×D4—61no—
311C2×D4—122no—
312C2×D4—124no—
313C22×C4—42no—
314C22×C4—61no—
315C22×C4—62no—
316C22×C4D3×Dic311yescharacteristic
317C22×C4D3×Dic311yescharacteristic
318C22×C4#62511yescharacteristic
319C22×C4#62611yescharacteristic
320C22×C4#62611yescharacteristic
321C22×C4C2×D3211yescharacteristic
322M16—362no—
323C2×C8—182no—
324C4⋊C4—32no—
325C4⋊C4—61no—
326C22⋊C4—64no—
327C22⋊C4—62no—
328C22⋊C4—62no—
329C42—122no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—21no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—44no—
355C22×C3—44no—
356C22×C3—48no—
357C22×C3—122no—
358C22×C3—122no—
359C22×C3—122no—
360C22×C3—244no—
361C22×C3#80512yes—
362C22×C3#83712yes—
363C22×C3C2×(C2×D3)⋊C411yescharacteristic
364C22×C3#93212yes—
365C22×C3#94912yes—
366C22×C3C2×#21711yescharacteristic
367C2×D3—42no—
368C2×D3—42no—
369C2×D3—42no—
370C2×D3—84no—
371C3×C4—22no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—22no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—124no—
382C3×C4—122no—
383C3×C4#80612yes—
384C3×C4#83412yes—
385Dic3—44no—
386Dic3—42no—
387C32#150711yescharacteristic, complemented, Sylow
388C23—22no—
389C23—22no—
390C23—41no—
391C23—62no—
392C23—122no—
393C23—122no—
394C23—122no—
395C23(C2×D3)⋊Dic311yescharacteristic
396C23(C2×D3)⋊Dic311yescharacteristic
397C23C2×#62511yescharacteristic
398D4—122no—
399D4—124no—
400D4—124no—
401D4—122no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—64no—
409C2×C4—62no—
410C2×C4—122no—
411C2×C4—122no—
412C2×C4—122no—
413C2×C4(C2×D3)⋊Dic311yescharacteristic
414C2×C4(C2×D3)⋊Dic311yescharacteristic
415C2×C4C2×D3×Dic311yescharacteristic
416C2×C4C2×#62611yescharacteristic
417C8—362no—
418C2×C3—22no—
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—42no—
426C2×C3—42no—
427C2×C3—42no—
428C2×C3—41no—
429C2×C3—41no—
430C2×C3—242no—
431C2×C3C2×#80511yescharacteristic
432C2×C3C2×#80611yescharacteristic
433C2×C3#500111yescharacteristic
434C2×C3#521511yescharacteristic
435C2×C3C2×#83411yescharacteristic
436C2×C3C2×#83711yescharacteristic
437D3—82no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—44no—
446C22—122no—
447C22—122no—
448C22—122no—
449C22—244no—
450C22#6356912yes—
451C22#6382312yes—
452C22C2×(C2×D3)⋊Dic311yescharacteristic
453C4—21no—
454C4—21no—
455C4—21no—
456C4—124no—
457C4—122no—
458C4#6358012yes—
459C3—21no—
460C3#6944411yescharacteristic, complemented
461C3#7167311yescharacteristic, complemented
462C2—22no—
463C2—22no—
464C2—41no—
465C2—242no—
466C2#1059108511yescharacteristic
467C2C2×#6356911yescharacteristic
468C2C2×#6358011yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#930C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1507
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10592906C2semidirect
3. C3×C4×#217C2semidirect
4. #10589149C2semidirect
9. C22×C3×D12C4semidirect
14. C3×#930C4semidirect
17. C2×C3×C4⋊Dic3C4semidirect
20. #63657C22semidirect
21. C3×C3⋊#95C22semidirect
25. C4×#217D3semidirect
63. C22×D12Dic3semidirect
75. #930Dic3semidirect
78. C2×C4⋊Dic3Dic3semidirect
84. C3⋊#95C2×D3semidirect
387. C32#1507semidirect
460. C3#69444semidirect
461. C3#71673semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
#105929062
C3×C4×#2172
#105891492
#716733
#694443