Finite Group Databasebeta

← C3×#71983 #11783698

Subgroups — C3×#71983 #11783698

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×M16C211yesmaximal, characteristic
2C3×C4×#217C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×C3×#815C211yesmaximal, characteristic, complemented
5C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#1753—31nomaximal
9#71983C311yesmaximal, characteristic, direct product factor
10C23×C32×C4C2211yescharacteristic
11C2×C32×M16—22no—
12C2×C32×M16—22no—
13C2×C32×M16C414yescomplemented
14C22×C32×C8C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×C3×#217C412yes—
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×C3⋊#95C412yes—
22C3×#830C414yescomplemented
23C3×#815—22no—
24C3×C8×Dic3—22no—
25C22×C3×M16—21no—
26C22×C3×M16D311yescharacteristic
27C22×C3×M16C2×C311yescharacteristic
28C2×C3×C22⋊C8—31no—
29C2×C3×#97—31no—
30C2×C3×C4×C8—31no—
31C3×C4×C22⋊C4—31no—
32C4×#217C2×C311yescharacteristic
33C2×#830C2×C311yescharacteristic
34C2×#815C2×C311yescharacteristic, complemented
35C2×C8×Dic3C2×C311yescharacteristic, complemented
36C3×#336—31no—
37C3×#336—31no—
38#4550C2×C311yescharacteristic, complemented
39#4550C2×C311yescharacteristic, complemented
40C24×C32C2×C411yescharacteristic
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2×C411yescharacteristic
46C22×C32×C4C2×C412yes—
47C22×C32×C4C2×C412yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3C2×C412yes—
50C22×C3×Dic3C2×C412yes—
51C32×M16—28no—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8C2×C412yes—
55C2×C32×C8C2×C412yes—
56C2×C32×C8D412yes—
57C2×C32×C8D412yes—
58C3×#217—24no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C3×C4×Dic3—21no—
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#1753—31noSylow
70C23×C3×C4—21no—
71C23×C3×C4C2×D311yescharacteristic
72C23×C3×C4C22×C311yescharacteristic
73C2×C3×M16—24no—
74C2×C3×M16—24no—
75C2×C3×M16—22no—
76C2×C3×M16—22no—
77C2×C3×M16—22no—
78C2×C3×M16—22no—
79C2×C3×M16—24no—
80C2×C3×M16Dic314yescomplemented
81C2×C3×M16C3×C414yescomplemented
82C22×C3×C8—21no—
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8—31no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C22×C311yescharacteristic
89C22×C3×C8C22×C311yescharacteristic
90C2×C3×C22⋊C4—32no—
91C2×C3×C42—31no—
92C2×C3×C42—31no—
93C2×#217C3×C412yes—
94C2×C4×Dic3C22×C311yescharacteristic
95C2×C4×Dic3C22×C311yescharacteristic
96C22×C3⋊C8C22×C311yescharacteristic
97C22×C3⋊C8C22×C311yescharacteristic
98C3×C22⋊C8—34no—
99C3×#97—62no—
100C3×C4×C8—62no—
101C3×#95—32no—
102C3⋊#95C3×C412yes—
103#830C3×C414yescomplemented
104#815—22no—
105C8×Dic3—22no—
106C23×C32—21no—
107C23×C32—21no—
108C23×C32—22no—
109C23×C32—22no—
110C23×C32C4212yes—
111C23×C32C22×C411yescharacteristic
112C2×C32×C4—21no—
113C2×C32×C4—21no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4C4212yes—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3M1614yescomplemented
131C32×C8—22no—
132C32×C8C22⋊C414yescomplemented
133C3×C3⋊C8—22no—
134C3×C3⋊C8—22no—
135C22×M16C3×D311yescharacteristic
136C2×C22⋊C8—31no—
137C2×#97—31no—
138C2×C4×C8—31no—
139C4×C22⋊C4—31no—
140#336—31no—
141#336—31no—
142C24×C3—21no—
143C24×C3C4×D311yescharacteristic
144C24×C3C2×C3×C411yescharacteristic
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—32no—
162C22×C3×C4—32no—
163C22×C3×C4C4×D311yescharacteristic
164C22×C3×C4C4×D312yes—
165C22×C3×C4C2×Dic312yes—
166C22×C3×C4C2×C3×C411yescharacteristic
167C22×C3×C4C2×C3×C412yes—
168C22×C3×C4C2×C3×C412yes—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C23×C311yescharacteristic
171C22×Dic3C2×C3×C412yes—
172C22×Dic3C2×C3×C412yes—
173C3×M16—216no—
174C3×M16—28no—
175C3×M16—28no—
176C2×C3×C8—22no—
177C2×C3×C8—22no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—22no—
183C2×C3×C8—22no—
184C2×C3×C8—22no—
185C2×C3×C8—22no—
186C2×C3×C8—32no—
187C2×C3×C8—32no—
188C2×C3×C8—61no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C2×C3×C8C2×Dic312yes—
193C2×C3×C8C2×Dic312yes—
194C2×C3×C8#6712yes—
195C2×C3×C8#6712yes—
196C2×C3×C8C2×C3×C412yes—
197C2×C3×C8C2×C3×C412yes—
198C2×C3×C8C3×D412yes—
199C2×C3×C8C3×D412yes—
200C3×C22⋊C4—64no—
201C3×C42—61no—
202C3×C42—61no—
203C3×C42—61no—
204C3×C42—61no—
205#217—24no—
206C4×Dic3—21no—
207C4×Dic3—21no—
208C4×Dic3—21no—
209C4×Dic3—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8C2×C3×C412yes—
215C2×C3⋊C8C2×C3×C412yes—
216C22×C32—22no—
217C22×C32—22no—
218C22×C32—22no—
219C22×C32—42no—
220C22×C32—42no—
221C22×C32C2×C4211yescharacteristic
222C22×C32C4×D411yescharacteristic
223C22×C32C4×D411yescharacteristic
224C22×C32C2×M1612yes—
225C22×C32#13112yes—
226C32×C4—22no—
227C32×C4C2×C22⋊C411yescharacteristic
228C32×C4#11711yescharacteristic
229C32×C4C4×D411yescharacteristic
230C32×C4C4×D411yescharacteristic
231C3×Dic3—24no—
232C3×Dic3—42no—
233C23×C4C2×C3×D311yescharacteristic
234C2×M16—22no—
235C2×M16—22no—
236C2×M16C3×Dic314yescomplemented
237C22×C8—31no—
238C22×C8—31no—
239C22×C8C2×C3×D311yescharacteristic
240C22×C8C2×C3×D311yescharacteristic
241C2×C22⋊C4—32no—
242C2×C42—31no—
243C2×C42—31no—
244C22⋊C8—34no—
245#97—62no—
246C4×C8—62no—
247#95—32no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3—22no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—22no—
257C23×C3—22no—
258C23×C3—22no—
259C23×C3—21no—
260C23×C3—42no—
261C23×C3—42no—
262C23×C3C4×Dic312yes—
263C23×C3C3×C4212yes—
264C23×C3C2×C4×D311yescharacteristic
265C23×C3C22×C3×C411yescharacteristic
266C2×C3×C4—24no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—34no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4C4×Dic312yes—
298C2×C3×C4C3×C4212yes—
299C2×C3×C4C2×C4×D311yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4C22×Dic311yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×C3×C4C22×C3×C411yescharacteristic
306C2×C3×C4C22×C3×C411yescharacteristic
307C2×C3×C4C2×C3×D411yescharacteristic
308C2×C3×C4C2×C3×D411yescharacteristic
309C2×C3×C4C3×#4111yescharacteristic
310C2×C3×C4C3×#4111yescharacteristic
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3C3×M1614yescomplemented
317C3×C8—24no—
318C3×C8—22no—
319C3×C8—22no—
320C3×C8—24no—
321C3×C8—62no—
322C3×C8—62no—
323C3×C8#21714yescomplemented
324C3×C8C3×C22⋊C414yescomplemented
325C3⋊C8—22no—
326C3⋊C8—22no—
327C2×C32—42no—
328C2×C32C4×C22⋊C411yescharacteristic
329C2×C32C4×M1611yescharacteristic
330C2×C32#40511yescharacteristic
331C2×C32#43512yes—
332C2×C32#43612yes—
333C24C3×C4×D311yescharacteristic
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—32no—
339C22×C4—32no—
340C22×C4C3×C4×D311yescharacteristic
341C22×C4C3×C4×D312yes—
342C22×C4C2×C3×Dic312yes—
343C22×C4C22×C3×D311yescharacteristic
344M16—28no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—32no—
348C2×C8—32no—
349C2×C8—61no—
350C2×C8—61no—
351C2×C8—61no—
352C2×C8—61no—
353C2×C8C2×C3×Dic312yes—
354C2×C8C2×C3×Dic312yes—
355C2×C8C3×#6712yes—
356C2×C8C3×#6712yes—
357C22⋊C4—64no—
358C42—61no—
359C42—61no—
360C42—61no—
361C42—61no—
362C22×C3—24no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—44no—
377C22×C3—44no—
378C22×C3—42no—
379C22×C3—42no—
380C22×C3—42no—
381C22×C3—42no—
382C22×C3D3×M1612yes—
383C22×C3#90712yes—
384C22×C3C2×C4×Dic311yescharacteristic
385C22×C3C4×#6711yescharacteristic
386C22×C3C4×#6711yescharacteristic
387C22×C3C2×C3×C4211yescharacteristic
388C22×C3C3×C4×D411yescharacteristic
389C22×C3C3×C4×D411yescharacteristic
390C22×C3C2×C3×M1612yes—
391C22×C3C3×#13112yes—
392C3×C4—24no—
393C3×C4—22no—
394C3×C4—22no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—64no—
400C3×C4—122no—
401C3×C4#92611yescharacteristic
402C3×C4C4×#6711yescharacteristic
403C3×C4C4×#6711yescharacteristic
404C3×C4C2×#21711yescharacteristic
405C3×C4C2×C3×C22⋊C411yescharacteristic
406C3×C4C3×#11711yescharacteristic
407C3×C4C3×C4×D411yescharacteristic
408C3×C4C3×C4×D411yescharacteristic
409Dic3—24no—
410Dic3—42no—
411C32#175311yescharacteristic, complemented, Sylow
412C23—22no—
413C23—22no—
414C23—21no—
415C23—21no—
416C23C3×C4×Dic312yes—
417C23C2×C3×C4×D311yescharacteristic
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—34no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4C3×C4×Dic312yes—
431C2×C4C2×C3×C4×D311yescharacteristic
432C2×C4C3×#23511yescharacteristic
433C2×C4C3×#23511yescharacteristic
434C2×C4C22×C3×Dic311yescharacteristic
435C2×C4C2×C3×#6711yescharacteristic
436C2×C4C2×C3×#6711yescharacteristic
437C8—22no—
438C8—62no—
439C8—62no—
440C8C3×#21714yescomplemented
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—22no—
445C2×C3—22no—
446C2×C3—44no—
447C2×C3—42no—
448C2×C3—42no—
449C2×C3Dic3×M1611yescharacteristic
450C2×C3#512211yescharacteristic
451C2×C3#512712yes—
452C2×C3#512812yes—
453C2×C3C4×#21711yescharacteristic
454C2×C3C3×C4×C22⋊C411yescharacteristic
455C2×C3C3×C4×M1611yescharacteristic
456C2×C3C3×#40511yescharacteristic
457C2×C3C3×#43512yes—
458C2×C3C3×#43612yes—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—42no—
463C22—42no—
464C22C3×D3×M1612yes—
465C22C3×#90712yes—
466C22C2×C3×C4×Dic311yescharacteristic
467C22C3×C4×#6711yescharacteristic
468C22C3×C4×#6711yescharacteristic
469C4—22no—
470C4—64no—
471C4—122no—
472C4C3×#92611yescharacteristic
473C4C3×C4×#6711yescharacteristic
474C4C3×C4×#6711yescharacteristic
475C4C2×C3×#21711yescharacteristic
476C3—21no—
477C3#7198311yescharacteristic, direct product factor
478C3C3×#175311yescharacteristic, complemented
479C2—42no—
480C2C3×Dic3×M1611yescharacteristic
481C2C3×#512211yescharacteristic
482C2C3×#512712yes—
483C2C3×#512812yes—
484C2C3×C4×#21711yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC22×C32×M16C2
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC22×C3×M16D3
hypocenterC3C3×#1753
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C22×C3×M16

Complements

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

NH ≅ G/Ntype
4. C2×C3×#815C2semidirect
5. C2×C3×C8×Dic3C2semidirect
6. C3×#4550C2semidirect
7. C3×#4550C2semidirect
9. #71983C3direct (N × H)
13. C2×C32×M16C4semidirect
22. C3×#830C4semidirect
34. C2×#815C2×C3semidirect
35. C2×C8×Dic3C2×C3semidirect
38. #4550C2×C3semidirect
39. #4550C2×C3semidirect
80. C2×C3×M16Dic3semidirect
81. C2×C3×M16C3×C4semidirect
103. #830C3×C4semidirect
130. C2×C3×Dic3M16semidirect
132. C32×C8C22⋊C4semidirect
236. C2×M16C3×Dic3semidirect
316. C2×Dic3C3×M16semidirect
323. C3×C8#217semidirect
324. C3×C8C3×C22⋊C4semidirect
411. C32#1753semidirect
440. C8C3×#217semidirect
477. C3#71983direct (N × H)
478. C3C3×#1753semidirect

Maximal subgroups

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

subgroupindex
C22×C32×M162
C3×C4×#2172
C2×C3×#8302
C2×C3×#8152
C2×C3×C8×Dic32
C3×#45502
C3×#17533
#719833