Finite Group Databasebeta

← #11783113

Subgroups — #11783113

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C22×#3711C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic
4#10589390C211yesmaximal, characteristic, complemented
5C3×#4524C211yesmaximal, characteristic, complemented
6#10589155C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#71579—31nomaximal
9#68661—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C412yes—
15C2×C3×Dic3⋊C4C412yes—
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#872—22no—
20C3×#872—22no—
21C2×#3711—22no—
22C2×#3711—22no—
23C2×#3711C414yescomplemented
24C2×D3×C3⋊C8—22no—
25C2×D3×C3⋊C8—22no—
26C2×D3×C3⋊C8C414yescomplemented
27C2×C3×#117—31no—
28C22×#208—31no—
29C23×C3⋊C8—31no—
30C22×ΓL(1,𝔽25)—31no—
31C22×D3×C8—31no—
32C2×#872D311yescharacteristic
33C3×#336—31no—
34#4550—31no—
35#4550—31no—
36#4524—31no—
37#4524—31no—
38#4524—31no—
39#4524—31no—
40#4524—61no—
41#4524D311yescharacteristic, complemented
42C23×C3×D3C2×C411yescharacteristic
43C22×C32×C4C2×C412yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3×Dic3C2×C412yes—
46C22×C3×Dic3C2×C411yescharacteristic
47C2×C3×C4×D3C2×C412yes—
48C2×C3×C4×D3C2×C412yes—
49C2×C3×C4×D3D412yes—
50C2×C3×C4×D3D412yes—
51C2×C3×C4×D3D412yes—
52C2×C3×C4×D3Q812yes—
53C32×C42—21no—
54C32×C42—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)C2×C412yes—
60C2×C3⋊(C3⋊C8)C2×C412yes—
61C3×(C2×D3)⋊C4—24no—
62C3×Dic3⋊C4—24no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8C2×C412yes—
70C2×C3×C3⋊C8C2×C412yes—
71#3711—28no—
72D3×C3⋊C8—28no—
73#1729—91noSylow
74C23×C3×C4—31no—
75C22×C4×D3C2×D311yescharacteristic
76C22×C3×C8—31no—
77C22×C3×C8—31no—
78C3×#117—62no—
79C3×#117—62no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C22⋊C4—32no—
82C2×C3×C42—21no—
83C2×C3×C42—31no—
84C2×C3×C42C2×D311yescharacteristic
85C2×C3×C42C2×D311yescharacteristic
86C2×(C2×D3)⋊C4Dic312yes—
87C2×Dic3⋊C4Dic312yes—
88C2×C4×Dic3C2×D311yescharacteristic
89C2×#208—34no—
90C2×#208—62no—
91C2×#208—62no—
92C22×C3⋊C8—31no—
93C22×C3⋊C8—31no—
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—34no—
97C22×C3⋊C8—61no—
98C22×C3⋊C8—61no—
99C22×C3⋊C8—62no—
100C22×C3⋊C8—62no—
101C22×C3⋊C8C2×D311yescharacteristic
102C22×C3⋊C8C2×D311yescharacteristic
103C2×ΓL(1,𝔽25)—34no—
104C2×ΓL(1,𝔽25)—62no—
105C2×ΓL(1,𝔽25)—62no—
106C2×D3×C8—34no—
107C2×D3×C8—62no—
108C2×D3×C8—62no—
109#872—22no—
110#872—22no—
111C23×C32C22×C411yescharacteristic
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3C4212yes—
115C22×C3×D3C22⋊C412yes—
116C22×C3×D3C4⋊C412yes—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×Q811yescharacteristic
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3C4212yes—
130C2×C3×Dic3C22⋊C412yes—
131C2×C3×Dic3C4⋊C412yes—
132C3×C4×D3C22⋊C414yes—
133C3×C4×D3C22⋊C414yes—
134C3×C4×D3C4⋊C414yes—
135C3×C4×D3C4⋊C414yes—
136C3⋊(C3⋊C8)—22no—
137C3⋊(C3⋊C8)—22no—
138C3×C3⋊C8—22no—
139C3×C3⋊C8—22no—
140C22×M16—91no—
141C23×C8—91no—
142C2×#117—31no—
143#336—31no—
144#336—91no—
145#336—91no—
146#336—91no—
147C24×C3—31no—
148C23×D3C2×Dic311yescharacteristic
149C22×C3×C4—22no—
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—32no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4C4×D312yes—
160C22×C3×C4C2×Dic312yes—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3C2×Dic312yes—
164C22×Dic3C2×Dic311yescharacteristic
165C2×C4×D3Dic612yes—
166C2×C4×D3C4×D312yes—
167C2×C4×D3C4×D312yes—
168C2×C4×D3D1212yes—
169C2×C4×D3#6712yes—
170C2×C4×D3#6712yes—
171C2×C3×C8—32no—
172C2×C3×C8—32no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C3×C4⋊C4—64no—
178C3×C22⋊C4—64no—
179C3×C42—21no—
180C3×C42—21no—
181C3×C42—21no—
182C3×C42—21no—
183C3×C42—41no—
184C3×C42—41no—
185C3×C42—61no—
186C3×C42—61no—
187(C2×D3)⋊C4—24no—
188Dic3⋊C4—24no—
189C4×Dic3—21no—
190C4×Dic3—21no—
191#208—68no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—32no—
197C2×C3⋊C8—32no—
198C2×C3⋊C8—32no—
199C2×C3⋊C8—32no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—62no—
202C2×C3⋊C8—68no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—121no—
212C2×C3⋊C8—121no—
213C2×C3⋊C8—121no—
214C2×C3⋊C8—121no—
215C2×C3⋊C8C4×D312yes—
216C2×C3⋊C8C4×D312yes—
217ΓL(1,𝔽25)—68no—
218D3×C8—68no—
219C22×C32C2×C4211yescharacteristic
220C22×C32C2×C22⋊C411yescharacteristic
221C22×C32C2×C4⋊C411yescharacteristic
222C22×C32#13112yes—
223C22×C32#13112yes—
224C2×C3×D3—22no—
225C2×C3×D3—22no—
226C2×C3×D3—24no—
227C2×C3×D3—24no—
228C2×C3×D3#9514yes—
229C32×C4—42no—
230C32×C4C2×C22⋊C411yescharacteristic
231C32×C4C2×C22⋊C411yescharacteristic
232C32×C4C2×C4⋊C411yescharacteristic
233C32×C4C2×C4⋊C411yescharacteristic
234C3×Dic3—42no—
235C3×Dic3#9514yes—
236C23×C4—31no—
237C2×M16—94no—
238C2×M16—182no—
239C2×M16—182no—
240C22×C8—31no—
241C22×C8—31no—
242C22×C8—94no—
243C22×C8—91no—
244C22×C8—91no—
245C22×C8—182no—
246C22×C8—182no—
247#117—62no—
248#117—62no—
249C2×C4⋊C4—32no—
250C2×C22⋊C4—32no—
251C2×C42—31no—
252C2×C42D3211yescharacteristic
253C23×C3—21no—
254C23×C3—32no—
255C23×C3—32no—
256C23×C3—32no—
257C23×C3—62no—
258C23×C3—62no—
259C23×C3C2×C4×D311yescharacteristic
260C23×C3C22×Dic311yescharacteristic
261C22×D3—22no—
262C22×D3—22no—
263C22×D3C4×Dic312yes—
264C22×D3C4⋊Dic312yes—
265C22×D3#21712yes—
266C2×C3×C4—24no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—32no—
280C2×C3×C4—32no—
281C2×C3×C4—32no—
282C2×C3×C4—34no—
283C2×C3×C4—34no—
284C2×C3×C4—34no—
285C2×C3×C4—34no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4C2×Dic611yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×D1211yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×Q811yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3C4×Dic312yes—
307C2×Dic3C4⋊Dic312yes—
308C2×Dic3#21712yes—
309C4×D3Dic3⋊C414yes—
310C4×D3Dic3⋊C414yes—
311C4×D3(C2×D3)⋊C414yes—
312C4×D3(C2×D3)⋊C414yes—
313C3×C8—62no—
314C3×C8—62no—
315C3⋊C8—22no—
316C3⋊C8—22no—
317C3⋊C8—62no—
318C3⋊C8—62no—
319C3⋊C8—62no—
320C3⋊C8—62no—
321C3⋊C8—122no—
322C3⋊C8—122no—
323C2×C32C2×#9511yescharacteristic
324C2×C32#40511yescharacteristic
325C2×C32#40511yescharacteristic
326C2×C32#40812yes—
327C2×C32#42412yes—
328C3×D3—24no—
329C24—31no—
330C22×C4—31no—
331C22×C4—32no—
332C22×C4—32no—
333C22×C4—32no—
334C22×C4—32no—
335C22×C4—32no—
336C22×C4—32no—
337C22×C4—32no—
338C22×C4D3×Dic312yes—
339C22×C4C2×D3211yescharacteristic
340M16—188no—
341C2×C8—32no—
342C2×C8—32no—
343C2×C8—61no—
344C2×C8—61no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—92no—
348C2×C8—92no—
349C2×C8—188no—
350C2×C8—181no—
351C2×C8—181no—
352C2×C8—181no—
353C2×C8—181no—
354C4⋊C4—64no—
355C22⋊C4—64no—
356C42—21no—
357C42—21no—
358C42—61no—
359C42—61no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—34no—
366C22×C3—62no—
367C22×C3—62no—
368C22×C3—64no—
369C22×C3—64no—
370C22×C3C42×D311yescharacteristic
371C22×C3D3×C22⋊C411yescharacteristic
372C22×C3D3×C4⋊C411yescharacteristic
373C22×C3#90112yes—
374C22×C3#90712yes—
375C22×C3C2×C4×Dic311yescharacteristic
376C22×C3C2×C4⋊Dic311yescharacteristic
377C22×C3#94812yes—
378C22×C3#94812yes—
379C22×C3C2×#21711yescharacteristic
380C2×D3—24no—
381C2×D3—22no—
382C2×D3—22no—
383C2×D3—24no—
384C2×D3C3⋊#9514yes—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—34no—
390C3×C4—44no—
391C3×C4—42no—
392C3×C4—42no—
393C3×C4—122no—
394C3×C4D3×C22⋊C411yescharacteristic
395C3×C4D3×C22⋊C411yescharacteristic
396C3×C4D3×C4⋊C411yescharacteristic
397C3×C4D3×C4⋊C411yescharacteristic
398C3×C4C2×Dic3⋊C411yescharacteristic
399C3×C4C2×Dic3⋊C411yescharacteristic
400C3×C4C2×(C2×D3)⋊C411yescharacteristic
401C3×C4C2×(C2×D3)⋊C411yescharacteristic
402Dic3—42no—
403Dic3C3⋊#9514yes—
404C32#172911yescharacteristic, complemented, Sylow
405C23—32no—
406C23—32no—
407C23—32no—
408C23—62no—
409C23—62no—
410C23C2×D3×Dic311yescharacteristic
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—32no—
415C2×C4—32no—
416C2×C4—32no—
417C2×C4—34no—
418C2×C4—34no—
419C2×C4—34no—
420C2×C4—34no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4D3×Dic611yescharacteristic
425C2×C4C4×D3211yescharacteristic
426C2×C4C4×D3211yescharacteristic
427C2×C4D3×D1211yescharacteristic
428C2×C4D3×#6711yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C8—62no—
431C8—62no—
432C8—182no—
433C8—182no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—22no—
437C2×C3—21no—
438C2×C3—22no—
439C2×C3—64no—
440C2×C3D3×#9511yescharacteristic
441C2×C3#468911yescharacteristic
442C2×C3#470811yescharacteristic
443C2×C3#472712yes—
444C2×C3#483912yes—
445C2×C3#499711yescharacteristic
446C2×C3#499711yescharacteristic
447C2×C3#499912yes—
448C2×C3C2×C3⋊#9511yescharacteristic
449C2×C3#523412yes—
450D3—24no—
451C22—34no—
452C22—62no—
453C22—62no—
454C22—64no—
455C22—64no—
456C22#6381412yes—
457C22#6381512yes—
458C22C4×D3×Dic311yescharacteristic
459C22D3×C4⋊Dic311yescharacteristic
460C22D3×#21711yescharacteristic
461C4—34no—
462C4—42no—
463C4—122no—
464C4D3×Dic3⋊C411yescharacteristic
465C4D3×Dic3⋊C411yescharacteristic
466C4D3×(C2×D3)⋊C411yescharacteristic
467C4D3×(C2×D3)⋊C411yescharacteristic
468C3—21no—
469C3#6866111yescharacteristic, complemented
470C3#7157911yescharacteristic, complemented
471C2—64no—
472C2#1059031811yescharacteristic
473C2#1059031911yescharacteristic
474C2#1059032412yes—
475C2#1059114512yes—
476C2D3×C3⋊#9511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C2×C42
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1729
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10589390C2semidirect
5. C3×#4524C2semidirect
6. #10589155C2semidirect
7. #10589155C2semidirect
23. C2×#3711C4semidirect
26. C2×D3×C3⋊C8C4semidirect
41. #4524D3semidirect
404. C32#1729semidirect
469. C3#68661semidirect
470. C3#71579semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C22×#37112
C22×D3×C3⋊C82
#105893902
C3×#45242
#105891552
#715793
#686613