Finite Group Databasebeta

← #11858838

Subgroups — #11858838

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×Dic3C211yesmaximal, characteristic
2#10592817C211yesmaximal, characteristic, complemented
3C3×#5126C211yesmaximal, characteristic
4C3×Dic3×M16C211yesmaximal, characteristic, complemented
5#10591120C211yesmaximal, characteristic, complemented
6#10591069C211yesmaximal, characteristic
7Dic3×#208C211yesmaximal, characteristic, complemented
8#10590660C214yesmaximal, complemented
9#10590655C214yesmaximal, complemented
10#78619—31nomaximal
11#78517—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#63641C2214yescomplemented
26C3×(C2×D3)⋊C8C2214yes—
27C3×#815C2212yescomplemented
28C3×C8×Dic3C2212yescomplemented
29#63572C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yes—
31#63554C2212yescomplemented
32Dic3×C3⋊C8C2212yescomplemented
33C22×C4×Dic3—31no—
34C2×C42×D3—31no—
35C3×#407—31no—
36C3×C4×M16—31no—
37#5207—31no—
38#5126—31no—
39#5126D311yescharacteristic
40#5118—31no—
41#5118—31no—
42#5118—31no—
43#5118—31no—
44#5118—61no—
45Dic3×M16—31no—
46Dic3×M16D311yescharacteristic, complemented
47C4×#208—31no—
48#4719—34no—
49#4718—34no—
50#4705—34no—
51#4685—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×C411yescharacteristic
69C4×C3⋊Dic3C2×C411yescharacteristic
70C4×C3⋊Dic3C2312yes—
71#3748—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×C4×Dic3C2×C412yes—
74C3×C4×Dic3C2311yescharacteristic
75C3×C4×Dic3C2311yescharacteristic
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×C22⋊C8—34no—
115C3×#97—32no—
116C3×C4×C8—32no—
117#830—34no—
118(C2×D3)⋊C8—34no—
119(C2×D3)⋊C8C2×D314yes—
120#815—32no—
121#815C2×D312yescomplemented
122Dic3⋊C8—34no—
123Dic3⋊C8—34no—
124Dic3⋊C8—34no—
125Dic3⋊C8—34no—
126Dic3⋊C8—64no—
127C8×Dic3—32no—
128C8×Dic3C2×D312yescomplemented
129#803—32no—
130C4×C3⋊C8—32no—
131C23×C32C22×C411yescharacteristic
132C22×C3×D3—22no—
133C22×C3×D3—24no—
134C22×C3×D3C22×C412yes—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4#4112yes—
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—24no—
140C2×C3⋊Dic3C22×C412yes—
141C2×C3⋊Dic3C22×C412yes—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3C22×C412yes—
145C2×C3×Dic3C22×C412yes—
146C2×C3×Dic3C22×C412yes—
147C3×C4×D3—24no—
148C3×C4×D3—22no—
149C3×C4×D3—22no—
150D3×Dic3—24no—
151D3×Dic3—24no—
152D3×Dic3—24no—
153D3×Dic3M1618yescomplemented
154C32×C8—22no—
155C3⋊(C3⋊C8)—22no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—22no—
158C22×C42—91no—
159#432—94no—
160#431—94no—
161#423—91no—
162#423—91no—
163#407—31no—
164#407—91no—
165C4×M16—31no—
166C4×M16—91no—
167C24×C3—31no—
168C23×D3C4×D311yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—32no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—62no—
175C22×C3×C4—62no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×Dic3—32no—
179C22×Dic3—32no—
180C22×Dic3—32no—
181C22×Dic3—32no—
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—62no—
185C22×Dic3—68no—
186C22×Dic3C4×D311yescharacteristic
187C22×Dic3C4×D312yes—
188C2×C4×D3—22no—
189C2×C4×D3—22no—
190C2×C4×D3—32no—
191C2×C4×D3—32no—
192C2×C4×D3—32no—
193C2×C4×D3—32no—
194C2×C4×D3—68no—
195C2×C4×D3C4×D312yes—
196C2×C4×D3C22×D312yes—
197C3×M16—22no—
198C3×M16—22no—
199C3×M16—42no—
200C3×M16—62no—
201C3×M16—62no—
202C2×C3×C8—22no—
203C2×C3×C8—32no—
204C2×C3×C8—32no—
205C2×C3×C8C22×D312yes—
206C2×C3×C8C22×D312yes—
207C3×C42—32no—
208C3×C42—31no—
209C3×C42—31no—
210C4×Dic3—31no—
211C4×Dic3—31no—
212C4×Dic3—31no—
213C4×Dic3—31no—
214C4×Dic3—32no—
215C4×Dic3—32no—
216C4×Dic3—32no—
217C4×Dic3—32no—
218C4×Dic3—32no—
219C4×Dic3—32no—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—62no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3C4×D312yes—
228C4×Dic3C22×D311yescharacteristic
229C4×Dic3C22×D311yescharacteristic
230#208—22no—
231#208—22no—
232#208—62no—
233#208—62no—
234#208—122no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8C22×D312yes—
239C2×C3⋊C8C22×D312yes—
240C22×C32—22no—
241C22×C32#11712yes—
242C22×C32C23×C411yescharacteristic
243C2×C3×D3—28no—
244C2×C3×D3—22no—
245C2×C3×D3—22no—
246C2×C3×D3C2×M1614yes—
247C32×C4#11712yes—
248C32×C4C2×#4111yescharacteristic
249C32×C4C2×#4111yescharacteristic
250C3⋊Dic3—22no—
251C3⋊Dic3C2×M1614yes—
252C3×Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3C2×M1614yes—
255C23×C4—31no—
256C23×C4—92no—
257C2×M16—31no—
258C2×M16—31no—
259C2×M16—91no—
260C2×M16D3211yescharacteristic
261C2×C42—31no—
262C2×C42—92no—
263C2×C42—92no—
264C2×C42—92no—
265C2×C42—92no—
266C2×C42—92no—
267C2×C42—91no—
268C4⋊C8—94no—
269C4⋊C8—94no—
270C22⋊C8—34no—
271C22⋊C8—94no—
272#97—32no—
273#97—92no—
274C4×C8—32no—
275C4×C8—92no—
276C23×C3—21no—
277C23×C3—32no—
278C23×C3—64no—
279C23×C3—62no—
280C23×C3C2×C4×D311yescharacteristic
281C23×C3C2×C4×D311yescharacteristic
282C22×D3—22no—
283C22×D3—24no—
284C22×D3C2×C4×D312yes—
285C2×C3×C4—21no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—32no—
290C2×C3×C4—32no—
291C2×C3×C4—32no—
292C2×C3×C4—64no—
293C2×C3×C4—62no—
294C2×C3×C4—64no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4#23512yes—
300C2×C3×C4#23512yes—
301C2×C3×C4#23712yes—
302C2×C3×C4#23712yes—
303C2×C3×C4C23×D311yescharacteristic
304C2×C3×C4C23×D311yescharacteristic
305C2×Dic3—22no—
306C2×Dic3—24no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—38no—
310C2×Dic3—32no—
311C2×Dic3—32no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—64no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—64no—
318C2×Dic3—64no—
319C2×Dic3—124no—
320C2×Dic3C2×C4×D312yes—
321C2×Dic3C2×C4×D312yes—
322C2×Dic3C2×C4×D312yes—
323C4×D3—24no—
324C4×D3—22no—
325C4×D3—22no—
326C4×D3—38no—
327C4×D3—64no—
328C4×D3—64no—
329C4×D3—64no—
330C3×C8—22no—
331C3×C8—22no—
332C3×C8—42no—
333C3×C8—62no—
334C3×C8—62no—
335C3⋊C8—22no—
336C3⋊C8—22no—
337C3⋊C8—62no—
338C3⋊C8—62no—
339C3⋊C8—122no—
340C2×C32—22no—
341C2×C32C2×#11711yescharacteristic
342C2×C32C22×M1612yes—
343C3×D3—24no—
344C24—31no—
345C22×C4—32no—
346C22×C4—31no—
347C22×C4—32no—
348C22×C4—32no—
349C22×C4—62no—
350C22×C4—62no—
351C22×C4—92no—
352C22×C4—92no—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—92no—
356C22×C4—188no—
357C22×C4C2×D3211yescharacteristic
358M16—22no—
359M16—62no—
360M16—62no—
361M16—182no—
362C2×C8—32no—
363C2×C8—32no—
364C2×C8—92no—
365C2×C8C2×D3212yes—
366C42—31no—
367C42—31no—
368C42—32no—
369C42—92no—
370C42—92no—
371C42—92no—
372C42—92no—
373C42—92no—
374C42—91no—
375C42—91no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—34no—
381C22×C3—42no—
382C22×C3—68no—
383C22×C3—62no—
384C22×C3—62no—
385C22×C3#87212yes—
386C22×C3#87712yes—
387C22×C3C22×C4×D311yescharacteristic
388C22×C3C22×C4×D311yescharacteristic
389C2×D3—28no—
390C2×D3—22no—
391C2×D3—22no—
392C2×D3D3×M1614yes—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—22no—
396C3×C4—34no—
397C3×C4—62no—
398C3×C4—62no—
399C3×C4#87212yes—
400C3×C4#87712yes—
401C3×C4C2×#23511yescharacteristic
402C3×C4C2×#23511yescharacteristic
403C3×C4C2×#23711yescharacteristic
404C3×C4C2×#23711yescharacteristic
405Dic3—22no—
406Dic3—22no—
407Dic3—34no—
408Dic3—34no—
409Dic3—64no—
410Dic3—62no—
411Dic3—62no—
412Dic3—122no—
413Dic3D3×M1614yes—
414C32#292011yescharacteristic, complemented, Sylow
415C23—32no—
416C23—64no—
417C23—62no—
418C23C4×D3211yescharacteristic
419C2×C4—32no—
420C2×C4—32no—
421C2×C4—32no—
422C2×C4—64no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—64no—
427C2×C4—98no—
428C2×C4—92no—
429C2×C4—92no—
430C2×C4—184no—
431C2×C4—184no—
432C2×C4—184no—
433C2×C4—184no—
434C2×C4#379512yes—
435C2×C4C4×D3211yescharacteristic
436C2×C4#380412yes—
437C2×C4C22×D3211yescharacteristic
438C8—22no—
439C8—62no—
440C8—62no—
441C8—182no—
442C2×C3—22no—
443C2×C3—22no—
444C2×C3—21no—
445C2×C3—22no—
446C2×C3—42no—
447C2×C3—64no—
448C2×C3C2×#87211yescharacteristic
449C2×C3C2×#87711yescharacteristic
450C2×C3C2×D3×M1612yes—
451C2×C3C2×D3×M1612yes—
452D3—24no—
453C22—22no—
454C22—34no—
455C22—68no—
456C22—62no—
457C22—62no—
458C22#6387712yes—
459C22C2×C4×D3211yescharacteristic
460C4—34no—
461C4—62no—
462C4—62no—
463C4—94no—
464C4—182no—
465C4#6387712yes—
466C4C2×#379511yescharacteristic
467C4C2×#380411yescharacteristic
468C3—21no—
469C3#7851711yescharacteristic, complemented
470C3#7861911yescharacteristic, complemented
471C2—22no—
472C2—64no—
473C2D32×M1612yes—
474C2C2×#6387711yescharacteristic
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. #10592817C2semidirect
4. C3×Dic3×M16C2semidirect
5. #10591120C2semidirect
7. Dic3×#208C2semidirect
8. #10590660C2semidirect
9. #10590655C2semidirect
25. #63641C22semidirect
27. C3×#815C22semidirect
28. C3×C8×Dic3C22semidirect
29. #63572C22semidirect
31. #63554C22semidirect
32. Dic3×C3⋊C8C22semidirect
46. Dic3×M16D3semidirect
121. #815C2×D3semidirect
128. C8×Dic3C2×D3semidirect
153. D3×Dic3M16semidirect
414. C32#2920semidirect
469. C3#78517semidirect
470. C3#78619semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×Dic32
#105928172
C3×#51262
C3×Dic3×M162
#105911202
#105910692
Dic3×#2082
#105906602
#105906552
#786193
#785173