Finite Group Databasebeta

← #11800789

Subgroups — #11800789

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C2×C4×#624C211yesmaximal, characteristic
3C2×#63874C211yesmaximal, characteristic
4C3×#4932C211yesmaximal, characteristic, complemented
5C3×C42×Dic3C211yesmaximal, characteristic, complemented
6#10591243C214yesmaximal, complemented
7C4×Dic32C211yesmaximal, characteristic, complemented
8#10591233C214yesmaximal
9#10591222C211yesmaximal, characteristic, complemented
10#73382—31nomaximal
11C4×#872—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×#624C2212yes—
14C2×C32×C42C2211yescharacteristic
15C2×#3752C2212yes—
16C2×#3750C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64081C418yescomplemented
19C2×C3×C4×Dic3C2214yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×#3724C2212yes—
25C2×#3722C2212yes—
26C2×Dic32C2214yes—
27C2×Dic32C2212yes—
28C4×#624C418yescomplemented
29#63874C418yescomplemented
30C3×C3⋊#95C2214yes—
31#63579C2214yes—
32C2×#872—31no—
33C2×#872—31no—
34C2×#872—31no—
35C2×#872—31no—
36C2×#872—61no—
37C2×C42×D3—31no—
38C2×C42×D3—31no—
39C3×#376—31no—
40C3×C43—31no—
41C4×(C2×D3)⋊C4—34no—
42#4932—31no—
43#4932—31no—
44#4932D311yescharacteristic, complemented
45C4×Dic3⋊C4—34no—
46C42×Dic3—31no—
47C42×Dic3—31no—
48C42×Dic3D311yescharacteristic, complemented
49#4666—34no—
50#4649—34no—
51C23×C3⋊D3C2311yescharacteristic
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C2×C4×C3⋊D3C2×C414yes—
57C2×C4×C3⋊D3C2×C414yes—
58C2×C4×C3⋊D3C2×C414yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C2×#624—28no—
64C2×#624C2×C418yes—
65C32×C42C2×C414yescomplemented
66#3752C2×C418yes—
67#3750C2×C418yescomplemented
68C4×C3⋊Dic3C2×C414yescomplemented
69C3×C4×Dic3—28no—
70C3×C4×Dic3C2×C414yes—
71C3×C4×Dic3C2×C414yes—
72C3×C4×Dic3C2×C414yescomplemented
73C3×C4×Dic3C2×C414yescomplemented
74#3724C2×C418yescomplemented
75#3722C2×C418yes—
76Dic32—28no—
77Dic32C2×C418yes—
78C4×#117—91noSylow
79C22×C4×D3—31no—
80C22×C4×D3—31no—
81C22×C4×D3—32no—
82C22×C4×D3—32no—
83C22×C4×D3—61no—
84C2×C3×C42—21no—
85C2×C3×C42—31no—
86C2×C3×C42—31no—
87C2×C3×C42—31no—
88C2×C3×C42—31no—
89C2×C3×C42—34no—
90C2×C3×C42C2×D311yescharacteristic
91C2×C3×C42C2×D311yescharacteristic
92C2×(C2×D3)⋊C4—32no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—62no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—32no—
100C2×Dic3⋊C4—32no—
101C2×Dic3⋊C4—62no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—31no—
104C2×C4×Dic3—32no—
105C2×C4×Dic3—32no—
106C2×C4×Dic3—34no—
107C2×C4×Dic3—34no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3C2×D314yes—
110C2×C4×Dic3C2×D311yescharacteristic
111C2×C4×Dic3C2×D311yescharacteristic
112C2×C4×Dic3C2×D311yescharacteristic
113C2×C4×Dic3C2×D311yescharacteristic
114#872—38no—
115#872—38no—
116#872—38no—
117#872—38no—
118#872—68no—
119C42×D3—38no—
120C42×D3—38no—
121C3×#95—34no—
122C3⋊#95—34no—
123C3⋊#95—34no—
124C3⋊#95C2×D314yes—
125C23×C32C2411yescharacteristic
126C22×C3⋊D3—24no—
127C22×C3⋊D3C22×C412yes—
128C22×C3⋊D3C22×C412yes—
129C22×C3⋊D3C22×C412yes—
130C2×C32×C4—24no—
131C2×C32×C4C22×C414yes—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C22×C412yes—
134C2×C32×C4C22×C412yes—
135C2×C3⋊Dic3—24no—
136C2×C3⋊Dic3C22×C414yes—
137C2×C3⋊Dic3C22×C412yes—
138C2×C3⋊Dic3C22×C412yes—
139C2×C3⋊Dic3C22×C412yes—
140C4×C3⋊D3C42116yescomplemented
141C2×C3×Dic3—24no—
142C2×C3×Dic3—24no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3C22×C414yes—
145C2×C3×Dic3C22×C414yes—
146C2×C3×Dic3C22×C414yes—
147C2×C3×Dic3C22×C414yes—
148C2×C3×Dic3#4118yes—
149#624—216no—
150C2×#117—91no—
151C2×#117—91no—
152C22×C42—91no—
153C4×C4⋊C4—94no—
154C4×C22⋊C4—94no—
155#376—31no—
156#376—91no—
157C43—31no—
158C43—91no—
159C23×D3—31no—
160C23×D3—31no—
161C23×D3—61no—
162C22×C3×C4—22no—
163C22×C3×C4—21no—
164C22×C3×C4—32no—
165C22×C3×C4—32no—
166C22×C3×C4—32no—
167C22×C3×C4—32no—
168C22×C3×C4C22×D312yes—
169C22×C3×C4C22×D312yes—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—32no—
175C22×Dic3—32no—
176C22×Dic3—61no—
177C22×Dic3—62no—
178C22×Dic3C22×D312yes—
179C22×Dic3C22×D312yes—
180C22×Dic3C22×D312yes—
181C22×Dic3C22×D312yes—
182C2×C4×D3—34no—
183C2×C4×D3—34no—
184C2×C4×D3—34no—
185C2×C4×D3—34no—
186C2×C4×D3—34no—
187C2×C4×D3—34no—
188C2×C4×D3—38no—
189C2×C4×D3—38no—
190C2×C4×D3—64no—
191C2×C4×D3—64no—
192C2×C4×D3—64no—
193C2×C4×D3—68no—
194C2×C4×D3—68no—
195C3×C42—24no—
196C3×C42—34no—
197C3×C42—34no—
198C3×C42—34no—
199C3×C42—34no—
200C3×C42—68no—
201C3×C42C4×D314yescomplemented
202C3×C42C4×D314yescomplemented
203(C2×D3)⋊C4—38no—
204(C2×D3)⋊C4—38no—
205(C2×D3)⋊C4—38no—
206(C2×D3)⋊C4—38no—
207(C2×D3)⋊C4—68no—
208Dic3⋊C4—38no—
209Dic3⋊C4—38no—
210Dic3⋊C4—38no—
211Dic3⋊C4—38no—
212Dic3⋊C4—68no—
213C4×Dic3—28no—
214C4×Dic3—34no—
215C4×Dic3—34no—
216C4×Dic3—38no—
217C4×Dic3—38no—
218C4×Dic3—64no—
219C4×Dic3—68no—
220C4×Dic3—68no—
221C4×Dic3C4×D314yes—
222C4×Dic3C4×D314yes—
223C4×Dic3C4×D314yescomplemented
224C4×Dic3C4×D314yescomplemented
225C22×C32C23×C411yescharacteristic
226C22×C32C23×C411yescharacteristic
227C22×C32C23×C411yescharacteristic
228C22×C32C2×#4114yes—
229C2×C3⋊D3—24no—
230C2×C3⋊D3—24no—
231C2×C3⋊D3—24no—
232C2×C3⋊D3C2×C4214yes—
233C32×C4—24no—
234C32×C4C2×C4214yes—
235C3⋊Dic3—24no—
236C3⋊Dic3C2×C4214yes—
237C3×Dic3—24no—
238C3×Dic3—24no—
239C3×Dic3—24no—
240C3×Dic3#11718yescomplemented
241C23×C4—92no—
242C23×C4—91no—
243#117—98no—
244#117—98no—
245C2×C4⋊C4—92no—
246C2×C4⋊C4—92no—
247C2×C22⋊C4—92no—
248C2×C22⋊C4—92no—
249C2×C42—31no—
250C2×C42—31no—
251C2×C42—31no—
252C2×C42—31no—
253C2×C42—34no—
254C2×C42—98no—
255C2×C42—92no—
256C2×C42—91no—
257C2×C42—94no—
258C2×C42D3211yescharacteristic
259#95—34no—
260#95—94no—
261C23×C3—21no—
262C23×C3C23×D311yescharacteristic
263C23×C3C23×D311yescharacteristic
264C22×D3—32no—
265C22×D3—32no—
266C22×D3—32no—
267C22×D3—32no—
268C22×D3—32no—
269C22×D3—32no—
270C22×D3—62no—
271C22×D3—62no—
272C22×D3—62no—
273C22×D3—64no—
274C22×D3—64no—
275C22×D3—124no—
276C2×C3×C4—24no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—24no—
282C2×C3×C4—34no—
283C2×C3×C4—38no—
284C2×C3×C4—34no—
285C2×C3×C4—34no—
286C2×C3×C4—34no—
287C2×C3×C4—44no—
288C2×C3×C4—64no—
289C2×C3×C4—64no—
290C2×C3×C4—64no—
291C2×C3×C4C2×C4×D312yes—
292C2×C3×C4C2×C4×D312yes—
293C2×C3×C4C2×C4×D312yes—
294C2×C3×C4C2×C4×D312yes—
295C2×C3×C4C2×C4×D314yes—
296C2×C3×C4C2×C4×D314yes—
297C2×C3×C4C2×C4×D312yes—
298C2×C3×C4C2×C4×D312yes—
299C2×Dic3—24no—
300C2×Dic3—24no—
301C2×Dic3—24no—
302C2×Dic3—32no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—32no—
308C2×Dic3—34no—
309C2×Dic3—34no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—64no—
314C2×Dic3—64no—
315C2×Dic3—64no—
316C2×Dic3—124no—
317C2×Dic3C2×C4×D314yes—
318C2×Dic3C2×C4×D314yes—
319C2×Dic3C2×C4×D314yes—
320C2×Dic3C2×C4×D314yes—
321C2×Dic3#23518yes—
322C4×D3—316no—
323C4×D3—316no—
324C4×D3—616no—
325C4×D3—616no—
326C4×D3—616no—
327C2×C32C22×C4211yescharacteristic
328C2×C32C2×#11712yes—
329C2×C32C4×#4112yes—
330C2×C32C4×#4112yes—
331C3⋊D3—24no—
332C24—91no—
333C22×C4—32no—
334C22×C4—32no—
335C22×C4—32no—
336C22×C4—32no—
337C22×C4—98no—
338C22×C4—91no—
339C22×C4—94no—
340C22×C4—94no—
341C22×C4—94no—
342C22×C4—92no—
343C22×C4—188no—
344C22×C4C2×D3212yes—
345C22×C4C2×D3211yescharacteristic
346C4⋊C4—98no—
347C4⋊C4—98no—
348C22⋊C4—98no—
349C22⋊C4—98no—
350C42—34no—
351C42—34no—
352C42—34no—
353C42—34no—
354C42—68no—
355C42—98no—
356C42—94no—
357C42—188no—
358C42#62414yescomplemented
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—24no—
362C22×C3—21no—
363C22×C3C22×C4×D311yescharacteristic
364C22×C3C22×C4×D311yescharacteristic
365C22×C3C22×C4×D311yescharacteristic
366C22×C3C22×C4×D311yescharacteristic
367C22×C3C22×C4×D311yescharacteristic
368C22×C3C22×C4×D311yescharacteristic
369C22×C3C2×#23514yes—
370C22×C3D3×#4114yes—
371C2×D3—34no—
372C2×D3—34no—
373C2×D3—64no—
374C2×D3—64no—
375C2×D3—64no—
376C2×D3—64no—
377C2×D3—64no—
378C2×D3—64no—
379C2×D3—64no—
380C2×D3—124no—
381C2×D3—124no—
382C2×D3—124no—
383C3×C4—24no—
384C3×C4—24no—
385C3×C4—24no—
386C3×C4—38no—
387C3×C4—44no—
388C3×C4—64no—
389C3×C4—64no—
390C3×C4—64no—
391C3×C4C42×D314yes—
392C3×C4C42×D314yes—
393Dic3—24no—
394Dic3—24no—
395Dic3—24no—
396Dic3—34no—
397Dic3—34no—
398Dic3—64no—
399Dic3—64no—
400Dic3—64no—
401Dic3—124no—
402Dic3#87218yescomplemented
403C32C4×#11711yescharacteristic, complemented, Sylow
404C23—92no—
405C23—92no—
406C23—92no—
407C23—184no—
408C23C22×D3211yescharacteristic
409C2×C4—24no—
410C2×C4—34no—
411C2×C4—38no—
412C2×C4—34no—
413C2×C4—34no—
414C2×C4—34no—
415C2×C4—64no—
416C2×C4—64no—
417C2×C4—64no—
418C2×C4—92no—
419C2×C4—92no—
420C2×C4—92no—
421C2×C4—916no—
422C2×C4—94no—
423C2×C4—1816no—
424C2×C4—184no—
425C2×C4C4×D3212yes—
426C2×C4C4×D3212yes—
427C2×C4C2×#62414yes—
428C2×C4C2×#62412yes—
429C2×C3—21no—
430C2×C3—22no—
431C2×C3—22no—
432C2×C3—22no—
433C2×C3C2×C42×D311yescharacteristic
434C2×C3C2×C42×D311yescharacteristic
435C2×C3C2×#87212yes—
436C2×C3C4×#23512yes—
437C2×C3C4×#23512yes—
438C2×C3D3×#11712yes—
439C2×C3#552212yes—
440C2×C3#552212yes—
441D3—64no—
442D3—64no—
443D3—124no—
444C22—94no—
445C22—184no—
446C22—184no—
447C22—184no—
448C22C2×C4×D3211yescharacteristic
449C22C2×C4×D3211yescharacteristic
450C22D3×#23514yes—
451C22C22×#62411yescharacteristic
452C4—24no—
453C4—38no—
454C4—64no—
455C4—64no—
456C4—64no—
457C4—94no—
458C4—184no—
459C4C4×#62414yes—
460C3—21no—
461C3C4×#87211yescharacteristic, complemented
462C3#7338211yescharacteristic, complemented
463C2—184no—
464C2#1059396512yes—
465C2D3×#87212yes—
466C2C2×C4×#62411yescharacteristic
467C2#1059495412yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32C4×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C3×#4932C2semidirect
5. C3×C42×Dic3C2semidirect
6. #10591243C2semidirect
7. C4×Dic32C2semidirect
9. #10591222C2semidirect
18. #64081C4semidirect
28. C4×#624C4semidirect
29. #63874C4semidirect
44. #4932D3semidirect
48. C42×Dic3D3semidirect
65. C32×C42C2×C4semidirect
67. #3750C2×C4semidirect
68. C4×C3⋊Dic3C2×C4semidirect
72. C3×C4×Dic3C2×C4semidirect
73. C3×C4×Dic3C2×C4semidirect
74. #3724C2×C4semidirect
140. C4×C3⋊D3C42semidirect
201. C3×C42C4×D3semidirect
202. C3×C42C4×D3semidirect
223. C4×Dic3C4×D3semidirect
224. C4×Dic3C4×D3semidirect
240. C3×Dic3#117semidirect
358. C42#624semidirect
402. Dic3#872semidirect
403. C32C4×#117semidirect
461. C3C4×#872semidirect
462. C3#73382semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C4×#6242
C2×#638742
C3×#49322
C3×C42×Dic32
#105912432
C4×Dic322
#105912332
#105912222
#733823
C4×#8723