Finite Group Databasebeta

← #11858837

Subgroups — #11858837

Order 1152.

1039 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×Dic3C211yesmaximal, characteristic
2M16×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#5126C211yesmaximal, characteristic
4C3×#5118C211yesmaximal, characteristic, complemented
5#10591115C211yesmaximal, characteristic, complemented
6#10591069C211yesmaximal, characteristic
7#10591060C211yesmaximal, characteristic, complemented
8#10590661C214yesmaximal, complemented
9#10590656C214yesmaximal, complemented
10#79038—31nomaximal
11#78619—31nomaximal
12C22×C3×C4×D3C2211yescharacteristic
13C22×D3×Dic3C412yes—
14C2×C32×M16C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×Dic32C412yes—
21C4×D3×Dic3C412yes—
22C4×D3×Dic3C412yes—
23C4×D3×Dic3C2212yes—
24C4×D3×Dic3C2212yes—
25#63642C2212yescomplemented
26C8×C3⋊Dic3C2212yescomplemented
27C3×(C2×D3)⋊C8C2214yes—
28C3×Dic3⋊C8C2214yescomplemented
29Dic3⋊(C3⋊C8)C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yes—
31#63555C2212yescomplemented
32#63553C2212yescomplemented
33C22×C4×Dic3—31no—
34C2×C42×D3—31no—
35C3×#423—31no—
36C3×#407—31no—
37#5207—31no—
38#5126—31no—
39#5126D311yescharacteristic
40#5118—31no—
41#5118D311yescharacteristic, complemented
42Dic3×M16—31no—
43Dic3×M16—31no—
44Dic3×M16—31no—
45Dic3×M16—31no—
46Dic3×M16—61no—
47#4924—31no—
48#4835—34no—
49#4833—34no—
50#4719—34no—
51#4718—34no—
52C23×C3×D3C2×C411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2×C412yes—
55C22×C3×Dic3C2×C412yes—
56C22×C3×Dic3C2×C411yescharacteristic
57C2×C3×C4×D3—22no—
58C2×C3×C4×D3—22no—
59C2×C3×C4×D3C2×C412yes—
60C2×C3×C4×D3C2312yes—
61C2×D3×Dic3—28no—
62C2×D3×Dic3C2×C412yes—
63C2×D3×Dic3C2×C412yes—
64C2×D3×Dic3C2×C412yes—
65C2×D3×Dic3C2×C412yes—
66C32×M16—22no—
67C2×C32×C8C2312yes—
68C4×C3⋊Dic3C2×C412yes—
69C4×C3⋊Dic3C2311yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71#3748—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×C4×Dic3C2×C411yescharacteristic
74C3×C4×Dic3C2×C411yescharacteristic
75C3×C4×Dic3C2312yes—
76C3×#208—22no—
77C3×#208—22no—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80Dic32C2×C412yes—
81Dic32C2×C412yes—
82Dic32C2×C412yes—
83Dic32C2×C412yes—
84#2920—91noSylow
85C23×C3×C4—31no—
86C23×Dic3—32no—
87C22×C4×D3—32no—
88C22×C4×D3C2×D311yescharacteristic
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94C2×C3×C42—31no—
95C2×C4×Dic3—31no—
96C2×C4×Dic3—31no—
97C2×C4×Dic3—32no—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3C2×D311yescharacteristic
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—61no—
108C2×#208C2×D311yescharacteristic
109C2×#208C2×D311yescharacteristic
110C42×D3—32no—
111C42×D3—32no—
112C42×D3—32no—
113C42×D3—32no—
114C3×C4⋊C8—34no—
115C3×C22⋊C8—34no—
116#830—34no—
117(C2×D3)⋊C8—34no—
118(C2×D3)⋊C8C2×D314yes—
119#815—32no—
120#815—32no—
121#815—32no—
122#815—32no—
123#815—62no—
124Dic3⋊C8—34no—
125Dic3⋊C8C2×D314yescomplemented
126C8×Dic3—32no—
127C8×Dic3—32no—
128C8×Dic3—32no—
129C8×Dic3—32no—
130C8×Dic3—62no—
131C4⋊(C3⋊C8)—34no—
132C23×C32C22×C411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—24no—
135C22×C3×D3C22×C412yes—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4#4112yes—
138C2×C32×C4#4112yes—
139C2×C32×C4C2411yescharacteristic
140C2×C3⋊Dic3—24no—
141C2×C3⋊Dic3C22×C412yes—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3C22×C412yes—
146C2×C3×Dic3C22×C412yes—
147C2×C3×Dic3C22×C412yes—
148C3×C4×D3—24no—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151D3×Dic3—24no—
152D3×Dic3—24no—
153D3×Dic3—24no—
154D3×Dic3M1618yescomplemented
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8—22no—
159C22×C42—91no—
160#432—94no—
161#431—94no—
162#423—31no—
163#423—91no—
164#407—31no—
165#407—91no—
166C4×M16—91no—
167C4×M16—91no—
168C24×C3—31no—
169C23×D3C4×D311yescharacteristic
170C22×C3×C4—21no—
171C22×C3×C4—31no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—62no—
176C22×C3×C4—62no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×Dic3—32no—
180C22×Dic3—32no—
181C22×Dic3—32no—
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—62no—
186C22×Dic3—68no—
187C22×Dic3C4×D311yescharacteristic
188C22×Dic3C4×D312yes—
189C2×C4×D3—22no—
190C2×C4×D3—22no—
191C2×C4×D3—32no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—32no—
195C2×C4×D3—68no—
196C2×C4×D3C4×D312yes—
197C2×C4×D3C22×D312yes—
198C3×M16—24no—
199C3×M16—22no—
200C3×M16—22no—
201C3×M16—62no—
202C3×M16—62no—
203C2×C3×C8—22no—
204C2×C3×C8—32no—
205C2×C3×C8—32no—
206C2×C3×C8C22×D312yes—
207C2×C3×C8C22×D312yes—
208C3×C42—31no—
209C3×C42—31no—
210C3×C42—32no—
211C4×Dic3—32no—
212C4×Dic3—32no—
213C4×Dic3—31no—
214C4×Dic3—31no—
215C4×Dic3—31no—
216C4×Dic3—31no—
217C4×Dic3—32no—
218C4×Dic3—32no—
219C4×Dic3—32no—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—62no—
228C4×Dic3C4×D311yescharacteristic
229C4×Dic3C4×D311yescharacteristic
230C4×Dic3C22×D312yes—
231#208—22no—
232#208—22no—
233#208—64no—
234#208—62no—
235#208—62no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—32no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8C22×D312yes—
240C2×C3⋊C8C22×D312yes—
241C22×C32—22no—
242C22×C32#11712yes—
243C22×C32C23×C411yescharacteristic
244C2×C3×D3—28no—
245C2×C3×D3—22no—
246C2×C3×D3—22no—
247C2×C3×D3C2×M1614yes—
248C32×C4#11712yes—
249C32×C4C2×#4111yescharacteristic
250C32×C4C2×#4111yescharacteristic
251C3⋊Dic3—22no—
252C3⋊Dic3C2×M1614yes—
253C3×Dic3—22no—
254C3×Dic3—22no—
255C3×Dic3C2×M1614yes—
256C23×C4—31no—
257C23×C4—92no—
258C2×M16—31no—
259C2×M16—31no—
260C2×M16—91no—
261C2×M16D3211yescharacteristic
262C2×C42—31no—
263C2×C42—92no—
264C2×C42—92no—
265C2×C42—92no—
266C2×C42—92no—
267C2×C42—92no—
268C2×C42—91no—
269C4⋊C8—34no—
270C4⋊C8—94no—
271C22⋊C8—34no—
272C22⋊C8—94no—
273#97—92no—
274#97—92no—
275C4×C8—92no—
276C4×C8—92no—
277C23×C3—21no—
278C23×C3—32no—
279C23×C3—64no—
280C23×C3—62no—
281C23×C3C2×C4×D311yescharacteristic
282C23×C3C2×C4×D311yescharacteristic
283C22×D3—22no—
284C22×D3—24no—
285C22×D3C2×C4×D312yes—
286C2×C3×C4—21no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—32no—
291C2×C3×C4—32no—
292C2×C3×C4—32no—
293C2×C3×C4—64no—
294C2×C3×C4—62no—
295C2×C3×C4—64no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4C2×C4×D311yescharacteristic
300C2×C3×C4#23712yes—
301C2×C3×C4#23712yes—
302C2×C3×C4#23712yes—
303C2×C3×C4#23912yes—
304C2×C3×C4C23×D311yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—24no—
308C2×Dic3—32no—
309C2×Dic3—32no—
310C2×Dic3—38no—
311C2×Dic3—32no—
312C2×Dic3—32no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—64no—
318C2×Dic3—64no—
319C2×Dic3—64no—
320C2×Dic3—124no—
321C2×Dic3C2×C4×D312yes—
322C2×Dic3C2×C4×D312yes—
323C2×Dic3C2×C4×D312yes—
324C4×D3—24no—
325C4×D3—22no—
326C4×D3—22no—
327C4×D3—38no—
328C4×D3—64no—
329C4×D3—64no—
330C4×D3—64no—
331C3×C8—24no—
332C3×C8—22no—
333C3×C8—22no—
334C3×C8—62no—
335C3×C8—62no—
336C3⋊C8—22no—
337C3⋊C8—22no—
338C3⋊C8—64no—
339C3⋊C8—62no—
340C3⋊C8—62no—
341C2×C32—22no—
342C2×C32C2×#11711yescharacteristic
343C2×C32C22×M1612yes—
344C3×D3—24no—
345C24—31no—
346C22×C4—32no—
347C22×C4—31no—
348C22×C4—32no—
349C22×C4—32no—
350C22×C4—62no—
351C22×C4—62no—
352C22×C4—92no—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—92no—
356C22×C4—92no—
357C22×C4—188no—
358C22×C4C2×D3211yescharacteristic
359M16—22no—
360M16—62no—
361M16—62no—
362M16—182no—
363C2×C8—32no—
364C2×C8—32no—
365C2×C8—92no—
366C2×C8C2×D3212yes—
367C42—32no—
368C42—31no—
369C42—31no—
370C42—92no—
371C42—92no—
372C42—92no—
373C42—92no—
374C42—91no—
375C42—91no—
376C42—92no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—22no—
381C22×C3—34no—
382C22×C3—42no—
383C22×C3—68no—
384C22×C3—62no—
385C22×C3—62no—
386C22×C3#87712yes—
387C22×C3#89212yes—
388C22×C3C22×C4×D311yescharacteristic
389C22×C3C22×C4×D311yescharacteristic
390C2×D3—28no—
391C2×D3—22no—
392C2×D3—22no—
393C2×D3D3×M1614yes—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—22no—
397C3×C4—34no—
398C3×C4—62no—
399C3×C4—62no—
400C3×C4#87712yes—
401C3×C4#89212yes—
402C3×C4C2×#23711yescharacteristic
403C3×C4C2×#23711yescharacteristic
404C3×C4C2×#23711yescharacteristic
405C3×C4C2×#23911yescharacteristic
406Dic3—22no—
407Dic3—22no—
408Dic3—34no—
409Dic3—34no—
410Dic3—64no—
411Dic3—62no—
412Dic3—62no—
413Dic3—122no—
414Dic3D3×M1614yes—
415C32#292011yescharacteristic, complemented, Sylow
416C23—32no—
417C23—64no—
418C23—62no—
419C23C4×D3211yescharacteristic
420C2×C4—32no—
421C2×C4—32no—
422C2×C4—32no—
423C2×C4—64no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—64no—
428C2×C4—98no—
429C2×C4—92no—
430C2×C4—92no—
431C2×C4—184no—
432C2×C4—184no—
433C2×C4—184no—
434C2×C4—184no—
435C2×C4#379612yes—
436C2×C4C4×D3211yescharacteristic
437C2×C4#380512yes—
438C2×C4C22×D3211yescharacteristic
439C8—22no—
440C8—62no—
441C8—62no—
442C8—182no—
443C2×C3—22no—
444C2×C3—22no—
445C2×C3—21no—
446C2×C3—22no—
447C2×C3—42no—
448C2×C3—64no—
449C2×C3C2×#87711yescharacteristic
450C2×C3C2×#89211yescharacteristic
451C2×C3C2×D3×M1612yes—
452C2×C3C2×D3×M1612yes—
453D3—24no—
454C22—22no—
455C22—34no—
456C22—68no—
457C22—62no—
458C22—62no—
459C22#6387812yes—
460C22C2×C4×D3211yescharacteristic
461C4—34no—
462C4—62no—
463C4—62no—
464C4—94no—
465C4—182no—
466C4#6387812yes—
467C4C2×#379611yescharacteristic
468C4C2×#380511yescharacteristic
469C3—21no—
470C3#7861911yescharacteristic, complemented
471C3#7903811yescharacteristic, complemented
472C2—22no—
473C2—64no—
474C2D32×M1612yes—
475C2C2×#6387811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2920
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. M16×C3⋊Dic3C2semidirect
4. C3×#5118C2semidirect
5. #10591115C2semidirect
7. #10591060C2semidirect
8. #10590661C2semidirect
9. #10590656C2semidirect
25. #63642C22semidirect
26. C8×C3⋊Dic3C22semidirect
28. C3×Dic3⋊C8C22semidirect
29. Dic3⋊(C3⋊C8)C22semidirect
31. #63555C22semidirect
32. #63553C22semidirect
41. #5118D3semidirect
125. Dic3⋊C8C2×D3semidirect
154. D3×Dic3M16semidirect
415. C32#2920semidirect
470. C3#78619semidirect
471. C3#79038semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×Dic32
M16×C3⋊Dic32
C3×#51262
C3×#51182
#105911152
#105910692
#105910602
#105906612
#105906562
#790383
#786193