Finite Group Databasebeta

← C3×#71975 #11787134

Subgroups — C3×#71975 #11787134

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×C8C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C8C212yesmaximal, complemented
5C3×#4550C212yesmaximal, complemented
6C3×#1869—31nomaximal
7#71975C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C22×C3×#67C411yescharacteristic
10C22×C3×C4×D3C2211yescharacteristic
11C22×C32×C8—22no—
12C22×C32×C8—24no—
13C22×C32×C8C2212yes—
14C2×C3×#217C411yescharacteristic
15C3×C4×#67—22no—
16C3×C4×#67—22no—
17C2×C3×(C2×D3)⋊C4C411yescharacteristic
18C2×C3×Dic3⋊C4C411yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2212yes—
21C3×#830—22no—
22C3×(C2×D3)⋊C8—24no—
23C23×C3×C8—21no—
24C23×C3×C8D311yescharacteristic, complemented
25C23×C3×C8C2×C311yescharacteristic, complemented
26C2×C3×C4×D4—31no—
27C2×C4×#67C2×C311yescharacteristic
28C2×C3×C22⋊C8—31no—
29C2×C3×C22⋊C8—32no—
30C2×#830C2×C311yescharacteristic, complemented
31C2×(C2×D3)⋊C8C2×C312yescomplemented
32C3×#336—32no—
33#4550C2×C312yescomplemented
34C24×C32C2×C411yescharacteristic
35C23×C3×D3C2×C411yescharacteristic
36C22×C32×C4—22no—
37C22×C32×C4—22no—
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4D412yes—
40C22×C32×C4D412yes—
41C22×C32×C4C2311yescharacteristic
42C2×C3×#67—22no—
43C2×C3×#67—22no—
44C2×C3×#67C814yescomplemented
45C22×C3×Dic3C2×C411yescharacteristic
46C22×C3×Dic3C2×C411yescharacteristic
47C22×C3×Dic3C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—22no—
51C2×C3×C4×D3—22no—
52C2×C32×C8—28no—
53C2×C32×C8—22no—
54C2×C32×C8—22no—
55C2×C32×C8D414yescomplemented
56C3×#217—22no—
57C3×(C2×D3)⋊C4—22no—
58C3×Dic3⋊C4—22no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C2×C3×C3⋊C8—22no—
62C2×C3×C3⋊C8—22no—
63C2×C3×C3⋊C8—22no—
64#1869—31noSylow
65C22×C3×D4—31no—
66C23×C3×C4—21no—
67C23×C3×C4—31no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C22×C311yescharacteristic
70C22×#67C3×C411yescharacteristic
71C22×C4×D3C22×C311yescharacteristic
72C22×C3×C8—24no—
73C22×C3×C8—28no—
74C22×C3×C8—22no—
75C22×C3×C8—22no—
76C22×C3×C8—24no—
77C22×C3×C8—24no—
78C22×C3×C8—22no—
79C22×C3×C8—32no—
80C22×C3×C8C2×D312yes—
81C22×C3×C8C22×C312yes—
82C3×C4×D4—62no—
83C3×C4×D4—62no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C22⋊C4—31no—
86C2×C3×C22⋊C4—31no—
87C2×C3×C42—31no—
88C2×#217C3×C411yescharacteristic
89C4×#67—22no—
90C4×#67—22no—
91C2×(C2×D3)⋊C4C3×C411yescharacteristic
92C2×Dic3⋊C4C3×C411yescharacteristic
93C2×C4×Dic3C22×C311yescharacteristic
94C22×C3⋊C8C22×C312yes—
95C3×C22⋊C8—62no—
96C3×C22⋊C8—64no—
97#830—22no—
98(C2×D3)⋊C8—24no—
99C23×C32—22no—
100C23×C32—22no—
101C23×C32C22⋊C412yes—
102C23×C32C2×C812yes—
103C23×C32M1612yes—
104C23×C32C22×C411yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—22no—
107C22×C3×D3—21no—
108C22×C3×D3—22no—
109C22×C3×D3C2×C812yescomplemented
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4—24no—
113C2×C32×C4—22no—
114C2×C32×C4C22⋊C412yes—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D412yes—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4112yes—
119C3×#67—28no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3C2×C812yescomplemented
127C3×C4×D3—41no—
128C3×C4×D3—42no—
129C3×C4×D3—41no—
130C32×C8—24no—
131C3×C3⋊C8—42no—
132C23×C8C3×D311yescharacteristic, complemented
133C2×C4×D4—31no—
134C2×C22⋊C8—31no—
135C2×C22⋊C8—32no—
136#336—32no—
137C24×C3—21no—
138C24×C3—31no—
139C24×C3C4×D311yescharacteristic
140C24×C3C2×C3×C411yescharacteristic
141C23×D3C2×C3×C411yescharacteristic
142C2×C3×D4—34no—
143C2×C3×D4—62no—
144C2×C3×D4—62no—
145C22×C3×C4—24no—
146C22×C3×C4—24no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—61no—
159C22×C3×C4—62no—
160C22×C3×C4—62no—
161C22×C3×C4—61no—
162C22×C3×C4C4×D311yescharacteristic
163C22×C3×C4D1212yes—
164C22×C3×C4#6712yes—
165C22×C3×C4C2×C3×C411yescharacteristic
166C22×C3×C4C3×D412yes—
167C22×C3×C4C3×D412yes—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C23×C311yescharacteristic
170C2×#67—22no—
171C2×#67—22no—
172C2×#67C3×C814yescomplemented
173C22×Dic3C2×C3×C411yescharacteristic
174C22×Dic3C2×C3×C411yescharacteristic
175C22×Dic3C2×C3×C411yescharacteristic
176C2×C4×D3—22no—
177C2×C4×D3—21no—
178C2×C4×D3—21no—
179C2×C4×D3—22no—
180C2×C3×C8—216no—
181C2×C3×C8—28no—
182C2×C3×C8—28no—
183C2×C3×C8—24no—
184C2×C3×C8—24no—
185C2×C3×C8—22no—
186C2×C3×C8—22no—
187C2×C3×C8—22no—
188C2×C3×C8—22no—
189C2×C3×C8—24no—
190C2×C3×C8—62no—
191C2×C3×C8—62no—
192C2×C3×C8—62no—
193C2×C3×C8#6714yescomplemented
194C2×C3×C8C3×D414yescomplemented
195C3×C4⋊C4—62no—
196C3×C22⋊C4—62no—
197C3×C22⋊C4—62no—
198C3×C42—61no—
199C3×C42—61no—
200#217—22no—
201(C2×D3)⋊C4—22no—
202Dic3⋊C4—22no—
203C4×Dic3—21no—
204C4×Dic3—21no—
205C2×C3⋊C8—22no—
206C2×C3⋊C8—22no—
207C2×C3⋊C8—22no—
208C22×C32—22no—
209C22×C32—22no—
210C22×C32—24no—
211C22×C32—24no—
212C22×C32C22⋊C814yescomplemented
213C22×C32C2×C22⋊C411yescharacteristic
214C22×C32C4×D412yes—
215C22×C32C22×C811yescharacteristic
216C22×C32C2×M1611yescharacteristic
217C22×C32#13112yes—
218C2×C3×D3—22no—
219C2×C3×D3—24no—
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—42no—
223C32×C4—22no—
224C32×C4#12011yescharacteristic
225C32×C4#12112yes—
226C32×C4#12311yescharacteristic
227C3×Dic3—22no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C22×D4—31no—
231C23×C4—31no—
232C23×C4C2×C3×D311yescharacteristic
233C22×C8—22no—
234C22×C8—24no—
235C22×C8—32no—
236C22×C8C2×C3×D312yes—
237C4×D4—62no—
238C4×D4—62no—
239C2×C4⋊C4—31no—
240C2×C22⋊C4—31no—
241C2×C22⋊C4—31no—
242C2×C42—31no—
243C22⋊C8—62no—
244C22⋊C8—64no—
245C23×C3—24no—
246C23×C3—24no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3—22no—
252C23×C3—22no—
253C23×C3—22no—
254C23×C3—21no—
255C23×C3—32no—
256C23×C3—61no—
257C23×C3—62no—
258C23×C3—61no—
259C23×C3—62no—
260C23×C3D3×C812yes—
261C23×C3ΓL(1,𝔽25)12yes—
262C23×C3(C2×D3)⋊C412yes—
263C23×C3C3×C22⋊C412yes—
264C23×C3C2×C3×C812yes—
265C23×C3C3×M1612yes—
266C23×C3C2×C4×D311yescharacteristic
267C23×C3C22×C3×C411yescharacteristic
268C22×D3—21no—
269C22×D3—22no—
270C22×D3—21no—
271C22×D3—22no—
272C22×D3C2×C3×C812yescomplemented
273C3×D4—68no—
274C2×C3×C4—24no—
275C2×C3×C4—24no—
276C2×C3×C4—24no—
277C2×C3×C4—28no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—24no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—24no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—32no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—62no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—62no—
298C2×C3×C4—121no—
299C2×C3×C4—122no—
300C2×C3×C4—121no—
301C2×C3×C4(C2×D3)⋊C412yes—
302C2×C3×C4C3×C22⋊C412yes—
303C2×C3×C4C2×D1211yescharacteristic
304C2×C3×C4#23512yes—
305C2×C3×C4C2×#6711yescharacteristic
306C2×C3×C4C2×#6712yes—
307C2×C3×C4C2×C3×D411yescharacteristic
308C2×C3×C4C2×C3×D412yes—
309C2×C3×C4C2×C3×D411yescharacteristic
310C2×C3×C4C3×#4112yes—
311#67—28no—
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318C2×Dic3C2×C3×C812yescomplemented
319C4×D3—41no—
320C4×D3—42no—
321C4×D3—41no—
322C3×C8—28no—
323C3×C8—24no—
324C3×C8—24no—
325C3×C8—122no—
326C3⋊C8—42no—
327C2×C32—24no—
328C2×C32#38611yescharacteristic
329C2×C32C2×C22⋊C811yescharacteristic
330C2×C32#40811yescharacteristic
331C2×C32C8×D412yes—
332C2×C32#43512yes—
333C3×D3—42no—
334C24—31no—
335C24C3×C4×D311yescharacteristic
336C2×D4—34no—
337C2×D4—62no—
338C2×D4—62no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—31no—
342C22×C4—31no—
343C22×C4—31no—
344C22×C4—61no—
345C22×C4—62no—
346C22×C4—62no—
347C22×C4—61no—
348C22×C4C3×C4×D311yescharacteristic
349C22×C4C3×D1212yes—
350C22×C4C3×#6712yes—
351C22×C4C22×C3×D311yescharacteristic
352C2×C8—28no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—62no—
356C2×C8—62no—
357C2×C8—62no—
358C2×C8C3×#6714yescomplemented
359C4⋊C4—62no—
360C22⋊C4—62no—
361C22⋊C4—62no—
362C42—61no—
363C42—61no—
364C22×C3—24no—
365C22×C3—28no—
366C22×C3—24no—
367C22×C3—28no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—24no—
372C22×C3—24no—
373C22×C3—24no—
374C22×C3—22no—
375C22×C3—24no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—22no—
381C22×C3—24no—
382C22×C3—62no—
383C22×C3—64no—
384C22×C3—121no—
385C22×C3—121no—
386C22×C3—122no—
387C22×C3(C2×D3)⋊C814yescomplemented
388C22×C3C3×C22⋊C814yescomplemented
389C22×C3C2×D3×C811yescharacteristic
390C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
391C22×C3#90112yes—
392C22×C3C2×(C2×D3)⋊C411yescharacteristic
393C22×C3C4×#6712yes—
394C22×C3C2×C3×C22⋊C411yescharacteristic
395C22×C3C3×C4×D412yes—
396C22×C3C22×C3×C811yescharacteristic
397C22×C3C2×C3×M1611yescharacteristic
398C22×C3C3×#13112yes—
399C2×D3—22no—
400C2×D3—24no—
401C2×D3—41no—
402C2×D3—41no—
403C2×D3—42no—
404C3×C4—24no—
405C3×C4—22no—
406C3×C4—22no—
407C3×C4—21no—
408C3×C4—22no—
409C3×C4—21no—
410C3×C4—62no—
411C3×C4—121no—
412C3×C4—121no—
413C3×C4#92911yescharacteristic
414C3×C4#93012yes—
415C3×C4#95311yescharacteristic
416C3×C4C3×#12011yescharacteristic
417C3×C4C3×#12112yes—
418C3×C4C3×#12311yescharacteristic
419Dic3—22no—
420Dic3—41no—
421Dic3—41no—
422C32#186911yescharacteristic, complemented, Sylow
423C23—22no—
424C23—22no—
425C23—32no—
426C23—61no—
427C23—62no—
428C23—61no—
429C23—62no—
430C23C3×D3×C812yes—
431C23C3×ΓL(1,𝔽25)12yes—
432C23C3×(C2×D3)⋊C412yes—
433C23C2×C3×C4×D311yescharacteristic
434D4—68no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—22no—
439C2×C4—32no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—62no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—62no—
446C2×C4—121no—
447C2×C4—122no—
448C2×C4—121no—
449C2×C4C3×(C2×D3)⋊C412yes—
450C2×C4C2×C3×D1211yescharacteristic
451C2×C4C3×#23512yes—
452C2×C4C2×C3×#6711yescharacteristic
453C2×C4C2×C3×#6712yes—
454C8—24no—
455C8—122no—
456C2×C3—28no—
457C2×C3—24no—
458C2×C3—24no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—22no—
462C2×C3—21no—
463C2×C3—22no—
464C2×C3—122no—
465C2×C3C2×(C2×D3)⋊C811yescharacteristic
466C2×C3C8×#6712yes—
467C2×C3#511011yescharacteristic
468C2×C3#511112yes—
469C2×C3#521311yescharacteristic
470C2×C3C3×#38611yescharacteristic
471C2×C3C2×C3×C22⋊C811yescharacteristic
472C2×C3C3×#40811yescharacteristic
473C2×C3C3×C8×D412yes—
474C2×C3C3×#43512yes—
475D3—42no—
476C22—22no—
477C22—24no—
478C22—22no—
479C22—24no—
480C22—62no—
481C22—64no—
482C22—121no—
483C22—121no—
484C22—122no—
485C22C3×(C2×D3)⋊C814yescomplemented
486C22C2×C3×D3×C811yescharacteristic
487C22C2×C3×ΓL(1,𝔽25)11yescharacteristic
488C22C3×#90112yes—
489C22C2×C3×(C2×D3)⋊C411yescharacteristic
490C22C3×C4×#6712yes—
491C4—22no—
492C4—62no—
493C4—121no—
494C4—121no—
495C4C3×#92911yescharacteristic
496C4C3×#93012yes—
497C4C3×#95311yescharacteristic
498C3—21no—
499C3#7197511yescharacteristic, direct product factor
500C3C3×#186911yescharacteristic, complemented
501C2—24no—
502C2—122no—
503C2C2×C3×(C2×D3)⋊C811yescharacteristic
504C2C3×C8×#6712yes—
505C2C3×#511011yescharacteristic
506C2C3×#511112yes—
507C2C3×#521311yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC23×C32×C8C2
socleC23×C32C22×C4
prime radicalC22×C3×#67C4
cosocleC22×C3×C4C23×C3
hypercenterC23×C3×C8D3
hypocenterC3C3×#1869
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C23×C3×C8

Complements

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

NH ≅ G/Ntype
1. C23×C32×C8C2semidirect
3. C2×C3×#830C2semidirect
4. C2×C3×(C2×D3)⋊C8C2semidirect
5. C3×#4550C2semidirect
7. #71975C3direct (N × H)
24. C23×C3×C8D3semidirect
25. C23×C3×C8C2×C3semidirect
30. C2×#830C2×C3semidirect
31. C2×(C2×D3)⋊C8C2×C3semidirect
33. #4550C2×C3semidirect
44. C2×C3×#67C8semidirect
55. C2×C32×C8D4semidirect
109. C22×C3×D3C2×C8semidirect
126. C2×C3×Dic3C2×C8semidirect
132. C23×C8C3×D3semidirect
172. C2×#67C3×C8semidirect
193. C2×C3×C8#67semidirect
194. C2×C3×C8C3×D4semidirect
212. C22×C32C22⋊C8semidirect
272. C22×D3C2×C3×C8semidirect
318. C2×Dic3C2×C3×C8semidirect
358. C2×C8C3×#67semidirect
387. C22×C3(C2×D3)⋊C8semidirect
388. C22×C3C3×C22⋊C8semidirect
422. C32#1869semidirect
485. C22C3×(C2×D3)⋊C8semidirect
499. C3#71975direct (N × H)
500. C3C3×#1869semidirect

Maximal subgroups

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

subgroupindex
C23×C32×C82
C2×C3×C4×#672
C2×C3×#8302
C2×C3×(C2×D3)⋊C82
C3×#45502
C3×#18693
#719753