Finite Group Databasebeta

← #11783611

Subgroups — #11783611

Order 1152.

731 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
3C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
4C2×#63554C211yesmaximal, characteristic, complemented
5C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
6#10589390C211yesmaximal, characteristic, complemented
7C3×#4524C211yesmaximal, characteristic, complemented
8#71582—31nomaximal
9#68601—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—
21(C2×D3)⋊(C3⋊C8)C414yescomplemented
22(C2×D3)⋊(C3⋊C8)C414yescomplemented
23#63554—22no—
24Dic3×C3⋊C8—22no—
25C2×C3×#117—31no—
26C2×#872D311yescharacteristic
27C2×#830—31no—
28C2×#830—31no—
29C2×(C2×D3)⋊C8—31no—
30C2×(C2×D3)⋊C8—31no—
31C2×#815—31no—
32C2×C8×Dic3—31no—
33C2×#803—31no—
34C2×C4×C3⋊C8—31no—
35C3×#336—31no—
36#4524—31no—
37#4524—31no—
38#4524—61no—
39#4524D311yescharacteristic, complemented
40C23×C3×D3C2×C411yescharacteristic
41C22×C32×C4C2×C412yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3C2×C411yescharacteristic
44C22×C3×Dic3C2×C412yes—
45C2×C3×C4×D3—21no—
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3C2×C412yes—
50C2×C3×C4×D3C2×C412yes—
51C32×C42—21no—
52C32×C42—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)C2×C412yes—
58C2×C3⋊(C3⋊C8)C2×C412yes—
59C3×(C2×D3)⋊C4—24no—
60C3×Dic3⋊C4—24no—
61C3×C4×Dic3D412yes—
62C3×C4×Dic3D412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68C2×C3×C3⋊C8C2×C412yes—
69#1750—91noSylow
70C23×C3×C4—31no—
71C22×C4×D3C2×D311yescharacteristic
72C22×C3×C8—31no—
73C22×C3×C8—31no—
74C3×#117—62no—
75C3×#117—62no—
76C2×C3×C4⋊C4—32no—
77C2×C3×C22⋊C4—32no—
78C2×C3×C42—21no—
79C2×C3×C42—31no—
80C2×C3×C42C2×D311yescharacteristic
81C2×C3×C42C2×D311yescharacteristic
82C2×(C2×D3)⋊C4Dic312yes—
83C2×Dic3⋊C4Dic312yes—
84C2×C4×Dic3C2×D311yescharacteristic
85C22×C3⋊C8—31no—
86C22×C3⋊C8—31no—
87C22×C3⋊C8—31no—
88C22×C3⋊C8—31no—
89C22×C3⋊C8—61no—
90C22×C3⋊C8—61no—
91C22×C3⋊C8C2×D311yescharacteristic
92C22×C3⋊C8C2×D311yescharacteristic
93#872—22no—
94#872—22no—
95#830—34no—
96#830—34no—
97(C2×D3)⋊C8—34no—
98(C2×D3)⋊C8—34no—
99#815—62no—
100C8×Dic3—62no—
101#803—62no—
102C4×C3⋊C8—62no—
103C23×C32C22×C411yescharacteristic
104C22×C3×D3—21no—
105C22×C3×D3—21no—
106C22×C3×D3—22no—
107C22×C3×D3—22no—
108C22×C3×D3C4212yes—
109C2×C32×C4—22no—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3C4212yes—
123C2×C3×Dic3C22⋊C414yes—
124C3×C4×D3—22no—
125C3×C4×D3—22no—
126C3×C4×D3—22no—
127C3×C4×D3—22no—
128C3⋊(C3⋊C8)—22no—
129C3⋊(C3⋊C8)—22no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—22no—
132C2×#117—31no—
133C2×C22⋊C8—91no—
134C2×C22⋊C8—91no—
135C2×#97—91no—
136C2×C4×C8—91no—
137#336—31no—
138#336—91no—
139C24×C3—31no—
140C23×D3C2×Dic311yescharacteristic
141C22×C3×C4—22no—
142C22×C3×C4—21no—
143C22×C3×C4—32no—
144C22×C3×C4—31no—
145C22×C3×C4—32no—
146C22×C3×C4—32no—
147C22×C3×C4—61no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4—61no—
151C22×C3×C4C4×D312yes—
152C22×C3×C4C2×Dic312yes—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×Dic3C2×Dic311yescharacteristic
156C22×Dic3C2×Dic312yes—
157C2×C4×D3—21no—
158C2×C4×D3—21no—
159C2×C4×D3—21no—
160C2×C4×D3—21no—
161C2×C4×D3C4×D312yes—
162C2×C4×D3C4×D312yes—
163C2×C3×C8—32no—
164C2×C3×C8—32no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—64no—
170C3×C22⋊C4—64no—
171C3×C42—21no—
172C3×C42—21no—
173C3×C42—21no—
174C3×C42—21no—
175C3×C42—32no—
176C3×C42—32no—
177C3×C42—41no—
178C3×C42—41no—
179(C2×D3)⋊C4—24no—
180Dic3⋊C4—24no—
181C4×Dic3#6712yes—
182C4×Dic3#6712yes—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—32no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—32no—
190C2×C3⋊C8—32no—
191C2×C3⋊C8—62no—
192C2×C3⋊C8—62no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—121no—
202C2×C3⋊C8—121no—
203C2×C3⋊C8—121no—
204C2×C3⋊C8—121no—
205C2×C3⋊C8C4×D312yes—
206C2×C3⋊C8C4×D312yes—
207C22×C32C2×C4211yescharacteristic
208C22×C32C2×C22⋊C411yescharacteristic
209C22×C32#11711yescharacteristic
210C22×C32#13112yes—
211C22×C32#13112yes—
212C2×C3×D3—22no—
213C2×C3×D3—22no—
214C2×C3×D3—22no—
215C2×C3×D3—42no—
216C2×C3×D3—42no—
217C32×C4—42no—
218C32×C4C4×D411yescharacteristic
219C32×C4C4×D411yescharacteristic
220C32×C4C4×D411yescharacteristic
221C32×C4C4×D411yescharacteristic
222C3×Dic3—22no—
223C3×Dic3—24no—
224C23×C4—31no—
225C22×C8—31no—
226C22×C8—31no—
227C22×C8—91no—
228C22×C8—91no—
229#117—62no—
230#117—62no—
231C2×C4⋊C4—32no—
232C2×C22⋊C4—32no—
233C2×C42—31no—
234C2×C42D3211yescharacteristic
235C22⋊C8—94no—
236C22⋊C8—94no—
237#97—182no—
238C4×C8—182no—
239C23×C3—21no—
240C23×C3—32no—
241C23×C3—61no—
242C23×C3—61no—
243C23×C3—62no—
244C23×C3—62no—
245C23×C3C2×C4×D311yescharacteristic
246C23×C3C22×Dic311yescharacteristic
247C22×D3—21no—
248C22×D3—22no—
249C22×D3—22no—
250C22×D3—21no—
251C22×D3C4×Dic312yes—
252C2×C3×C4—24no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—32no—
266C2×C3×C4—34no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—62no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4#23511yescharacteristic
282C2×C3×C4#23511yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4#23711yescharacteristic
286C2×C3×C4#23911yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×Dic3—21no—
290C2×Dic3—22no—
291C2×Dic3—22no—
292C2×Dic3—21no—
293C2×Dic3C4×Dic312yes—
294C2×Dic3#21714yes—
295C4×D3—22no—
296C4×D3—22no—
297C4×D3—22no—
298C4×D3—22no—
299C3×C8—62no—
300C3×C8—62no—
301C3⋊C8—22no—
302C3⋊C8—22no—
303C3⋊C8—62no—
304C3⋊C8—62no—
305C3⋊C8—62no—
306C3⋊C8—62no—
307C3⋊C8—122no—
308C3⋊C8—122no—
309C2×C32C4×C22⋊C411yescharacteristic
310C2×C32#40511yescharacteristic
311C2×C32#40511yescharacteristic
312C2×C32#40812yes—
313C2×C32#43312yes—
314C3×D3—42no—
315C24—31no—
316C22×C4—32no—
317C22×C4—31no—
318C22×C4—32no—
319C22×C4—32no—
320C22×C4—61no—
321C22×C4—61no—
322C22×C4—61no—
323C22×C4—61no—
324C22×C4D3×Dic312yes—
325C22×C4C2×D3211yescharacteristic
326C2×C8—32no—
327C2×C8—32no—
328C2×C8—61no—
329C2×C8—61no—
330C2×C8—61no—
331C2×C8—61no—
332C2×C8—92no—
333C2×C8—92no—
334C2×C8—181no—
335C2×C8—181no—
336C2×C8—181no—
337C2×C8—181no—
338C4⋊C4—64no—
339C22⋊C4—64no—
340C42—21no—
341C42—21no—
342C42—32no—
343C42—32no—
344C22×C3—22no—
345C22×C3—22no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—62no—
350C22×C3—62no—
351C22×C3—62no—
352C22×C3—122no—
353C22×C3—122no—
354C22×C3C42×D311yescharacteristic
355C22×C3D3×C22⋊C411yescharacteristic
356C22×C3#89211yescharacteristic
357C22×C3#90112yes—
358C22×C3#90712yes—
359C22×C3C2×C4×Dic311yescharacteristic
360C22×C3#92611yescharacteristic
361C22×C3#94812yes—
362C22×C3#94812yes—
363C22×C3C2×#21711yescharacteristic
364C2×D3—22no—
365C2×D3—22no—
366C2×D3—22no—
367C2×D3—42no—
368C2×D3—42no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—44no—
374C3×C4—42no—
375C3×C4—42no—
376C3×C4—62no—
377C3×C4—64no—
378C3×C4#67⋊C411yescharacteristic
379C3×C4#67⋊C411yescharacteristic
380C3×C4#89311yescharacteristic
381C3×C4#89311yescharacteristic
382C3×C4C4×#6711yescharacteristic
383C3×C4C4×#6711yescharacteristic
384C3×C4C4×#6711yescharacteristic
385C3×C4C4×#6711yescharacteristic
386Dic3—22no—
387Dic3—24no—
388C32#175011yescharacteristic, complemented, Sylow
389C23—32no—
390C23—62no—
391C23—62no—
392C23—61no—
393C23—61no—
394C23C2×D3×Dic311yescharacteristic
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—32no—
399C2×C4—34no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—62no—
408C2×C4#379511yescharacteristic
409C2×C4#379911yescharacteristic
410C2×C4C4×D3211yescharacteristic
411C2×C4C4×D3211yescharacteristic
412C2×C4D3×#6711yescharacteristic
413C2×C4D3×#6711yescharacteristic
414C8—62no—
415C8—62no—
416C8—182no—
417C8—182no—
418C2×C3—21no—
419C2×C3—22no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—22no—
423C2×C3—122no—
424C2×C3#466611yescharacteristic
425C2×C3#468911yescharacteristic
426C2×C3#470811yescharacteristic
427C2×C3#472712yes—
428C2×C3#484012yes—
429C2×C3#499711yescharacteristic
430C2×C3#499711yescharacteristic
431C2×C3#500012yes—
432C2×C3C4×#21711yescharacteristic
433C2×C3#523412yes—
434D3—42no—
435C22—62no—
436C22—62no—
437C22—62no—
438C22—122no—
439C22—122no—
440C22#6381412yes—
441C22#6381512yes—
442C22#6384111yescharacteristic
443C22C4×D3×Dic311yescharacteristic
444C22D3×#21711yescharacteristic
445C4—42no—
446C4—62no—
447C4—64no—
448C4#6387911yescharacteristic
449C4#6387911yescharacteristic
450C4#6390411yescharacteristic
451C4#6390411yescharacteristic
452C3—21no—
453C3#6860111yescharacteristic, complemented
454C3#7158211yescharacteristic, complemented
455C2—122no—
456C2#1059025312yes—
457C2#1059031811yescharacteristic
458C2#1059031911yescharacteristic
459C2#1059114512yes—
460C2#1059123711yescharacteristic
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#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C2×#63554C2semidirect
5. C2×Dic3×C3⋊C8C2semidirect
6. #10589390C2semidirect
7. C3×#4524C2semidirect
21. (C2×D3)⋊(C3⋊C8)C4semidirect
22. (C2×D3)⋊(C3⋊C8)C4semidirect
39. #4524D3semidirect
388. C32#1750semidirect
453. C3#68601semidirect
454. C3#71582semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C2×(C2×D3)⋊(C3⋊C8)2
C2×#635542
C2×Dic3×C3⋊C82
#105893902
C3×#45242
#715823
#686013