Finite Group Databasebeta

← C2×D3×#127⋊C3 #11923234

Subgroups — C2×D3×#127⋊C3 #11923234

Order 1152.

1175 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 1175 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#127⋊C3C211yesmaximal, characteristic, complemented
2D3×#127⋊C3C214yesmaximal, direct product factor
3C2×D3×C42⋊C3C211yesmaximal, characteristic, complemented
4C2×C3⋊(#127⋊C3)C211yesmaximal, characteristic, complemented
5C2×D3×#127C311yesmaximal, characteristic, complemented
6C22×#127⋊C3—31nomaximal
7C22×D3×A4—41nomaximal
8C3×#127⋊C3C2212yescomplemented
9C2×C3×C42⋊C3C2211yescharacteristic, complemented
10D3×C42⋊C3C2212yescomplemented
11C3⋊(#127⋊C3)C2212yescomplemented
12C22×D3×D4—31no—
13C22×D3×D4—31no—
14C2×C3×#127C2×C311yescharacteristic, complemented
15C2×#940—31no—
16C2×#940—31no—
17D3×#127—34no—
18D3×#127C2×C314yescomplemented
19C2×#874C2×C311yescharacteristic, complemented
20C2×C42×D3C2×C311yescharacteristic, complemented
21C2×#127⋊C3—21no—
22C2×#127⋊C3—34no—
23C2×#127⋊C3—31no—
24C2×#127⋊C3D311yescharacteristic, direct product factor
25C22×C42⋊C3—31no—
26C22×C3×A4—41no—
27C2×D3×A4—41no—
28C2×D3×A4—41no—
29C2×D3×A4—44no—
30C3×C42⋊C3C2311yescharacteristic, complemented
31C22×#127—31noSylow
32C24×D3—31no—
33C24×D3A411yescharacteristic
34C23×A4—121no—
35C22×C3×D4—31no—
36C22×C3×D4—31no—
37C22×#67—32no—
38C22×#67—31no—
39C22×#67—31no—
40C2×D3×D4—34no—
41C2×D3×D4—34no—
42C2×D3×D4—34no—
43C2×D3×D4—34no—
44C2×D3×D4—62no—
45C2×D3×D4—62no—
46C2×D3×D4—64no—
47C2×D3×D4—62no—
48C2×D3×D4—62no—
49C2×D3×D4—64no—
50C22×D12—31no—
51C22×D12—31no—
52C22×C4×D3—31no—
53C3×#127—32no—
54C3×#127C22×C312yescomplemented
55C2×C3×C42C22×C311yescharacteristic, complemented
56#940—34no—
57#940—34no—
58#940—34no—
59#940—34no—
60C2×C4×Dic3—31no—
61#874—32no—
62#874C22×C312yescomplemented
63C42×D3—32no—
64C42×D3C22×C312yescomplemented
65#127⋊C3—22no—
66#127⋊C3—32no—
67#127⋊C3C2×D312yesdirect product factor
68C2×C42⋊C3—21no—
69C2×C42⋊C3—32no—
70C2×C42⋊C3C2×D311yescharacteristic, complemented
71C22×C3×D3—161no—
72C2×C3×A4—41no—
73C2×C3×A4—42no—
74D3×A4—42no—
75D3×A4—42no—
76C23×D4—91no—
77C23×D4—91no—
78C2×#127—34no—
79C2×#127—31no—
80C2×#127—94no—
81C2×#127—91no—
82C2×#127—91no—
83C2×#127C3×D311yescharacteristic, complemented
84C22×C42—31no—
85C24×C3—31no—
86C24×C3C2×A411yescharacteristic
87C23×D3—31no—
88C23×D3—34no—
89C23×D3—61no—
90C23×D3—61no—
91C23×D3—62no—
92C23×D3—62no—
93C23×D3—61no—
94C23×D3—64no—
95C23×D3—62no—
96C23×D3—62no—
97C23×D3—61no—
98C23×D3C2×A411yescharacteristic
99C23×D3C2×A411yescharacteristic
100C23×D3C2×A414yes—
101C22×A4—41no—
102C22×A4—81no—
103C22×A4—121no—
104C22×A4—121no—
105C22×A4—124no—
106C2×C3×D4—32no—
107C2×C3×D4—32no—
108C2×C3×D4—32no—
109C2×C3×D4—32no—
110C2×C3×D4—62no—
111C2×C3×D4—62no—
112C2×C3×D4—62no—
113C2×C3×D4—62no—
114C22×C3×C4—31no—
115C2×#67—38no—
116C2×#67—34no—
117C2×#67—34no—
118C2×#67—62no—
119C2×#67—62no—
120C2×#67—62no—
121C2×#67—64no—
122C2×#67—64no—
123C2×#67—62no—
124C22×Dic3—31no—
125D3×D4—68no—
126D3×D4—68no—
127D3×D4—68no—
128D3×D4—68no—
129D3×D4—68no—
130D3×D4—68no—
131D3×D4—68no—
132D3×D4—68no—
133C2×D12—32no—
134C2×D12—32no—
135C2×D12—32no—
136C2×D12—32no—
137C2×D12—62no—
138C2×D12—62no—
139C2×D12—62no—
140C2×D12—62no—
141C2×C4×D3—32no—
142C2×C4×D3—34no—
143C2×C4×D3—32no—
144C2×C4×D3—32no—
145C2×C4×D3—32no—
146C3×C42—31no—
147C3×C42C23×C311yescharacteristic, complemented
148C4×Dic3—32no—
149C4×Dic3—32no—
150C42⋊C3—21no—
151C42⋊C3C22×D311yescharacteristic, complemented
152C22×C32—161no—
153C2×C3×D3—161no—
154C2×C3×D3—164no—
155C2×C3×D3—161no—
156C3×A4—41no—
157C25—31no—
158C25—91no—
159C22×D4—31no—
160C22×D4—31no—
161C22×D4—91no—
162C22×D4—91no—
163C22×D4—94no—
164C22×D4—94no—
165C22×D4—94no—
166C22×D4—94no—
167C22×D4—91no—
168C22×D4—92no—
169C22×D4—91no—
170C22×D4—182no—
171C22×D4—182no—
172C22×D4—184no—
173C22×D4—182no—
174C22×D4—184no—
175C22×D4—182no—
176C23×C4—91no—
177#127—32no—
178#127—32no—
179#127—92no—
180#127—94no—
181#127—94no—
182#127—94no—
183#127—94no—
184#127C2×C3×D312yescomplemented
185C2×C42—32no—
186C2×C42—92no—
187C2×C42—91no—
188C2×C42C2×C3×D311yescharacteristic, complemented
189C23×C3—32no—
190C23×C3—61no—
191C23×C3—61no—
192C23×C3—62no—
193C23×C3—61no—
194C23×C3—61no—
195C23×C3—62no—
196C23×C3—481no—
197C23×C3C22×A411yescharacteristic
198C23×C3C22×A412yes—
199C22×D3—31no—
200C22×D3—31no—
201C22×D3—32no—
202C22×D3—32no—
203C22×D3—41no—
204C22×D3—64no—
205C22×D3—64no—
206C22×D3—68no—
207C22×D3—68no—
208C22×D3—64no—
209C22×D3—64no—
210C22×D3—61no—
211C22×D3—62no—
212C22×D3—61no—
213C22×D3—61no—
214C22×D3—62no—
215C22×D3—61no—
216C22×D3—122no—
217C22×D3—121no—
218C22×D3—122no—
219C22×D3—124no—
220C22×D3—122no—
221C22×D3—121no—
222C22×D3—122no—
223C22×D3—122no—
224C22×D3—124no—
225C22×D3—121no—
226C22×D3C22×A412yes—
227C22×D3C22×A412yes—
228C2×A4—41no—
229C2×A4—42no—
230C2×A4—81no—
231C2×A4—82no—
232C2×A4—122no—
233C2×A4—122no—
234C3×D4—64no—
235C3×D4—64no—
236C3×D4—64no—
237C3×D4—64no—
238C2×C3×C4—32no—
239C2×C3×C4—32no—
240C2×C3×C4—31no—
241C2×C3×C4—31no—
242#67—68no—
243#67—68no—
244#67—616no—
245C2×Dic3—32no—
246C2×Dic3—32no—
247C2×Dic3—32no—
248D12—64no—
249D12—64no—
250D12—64no—
251D12—64no—
252C4×D3—34no—
253C4×D3—34no—
254C4×D3—34no—
255C4×D3—34no—
256C2×C32—162no—
257C2×C32—161no—
258C3×D3—162no—
259C3×D3—162no—
260C24—31no—
261C24—31no—
262C24—34no—
263C24—31no—
264C24—94no—
265C24—91no—
266C24—181no—
267C24—181no—
268C24—182no—
269C24—181no—
270C24—182no—
271C24—182no—
272C24—184no—
273C24—181no—
274C24—182no—
275C24D3×A411yescharacteristic
276C2×D4—32no—
277C2×D4—32no—
278C2×D4—32no—
279C2×D4—32no—
280C2×D4—62no—
281C2×D4—62no—
282C2×D4—62no—
283C2×D4—62no—
284C2×D4—92no—
285C2×D4—92no—
286C2×D4—92no—
287C2×D4—92no—
288C2×D4—94no—
289C2×D4—98no—
290C2×D4—94no—
291C2×D4—182no—
292C2×D4—182no—
293C2×D4—182no—
294C2×D4—182no—
295C2×D4—188no—
296C2×D4—188no—
297C2×D4—188no—
298C2×D4—188no—
299C2×D4—188no—
300C2×D4—188no—
301C2×D4—188no—
302C2×D4—188no—
303C2×D4—182no—
304C2×D4—182no—
305C2×D4—182no—
306C2×D4—182no—
307C2×D4—184no—
308C2×D4—184no—
309C22×C4—31no—
310C22×C4—92no—
311C22×C4—92no—
312C22×C4—92no—
313C22×C4—94no—
314C22×C4—92no—
315C22×C4—91no—
316C42—31no—
317C42—92no—
318C42—92no—
319C42C22×C3×D311yescharacteristic, complemented
320C22×C3—31no—
321C22×C3—31no—
322C22×C3—41no—
323C22×C3—62no—
324C22×C3—62no—
325C22×C3—64no—
326C22×C3—121no—
327C22×C3—121no—
328C22×C3—122no—
329C22×C3—121no—
330C22×C3—161no—
331C22×C3—321no—
332C22×C3—481no—
333C22×C3—484no—
334C22×C3—481no—
335C22×C3C23×A411yescharacteristic
336C2×D3—32no—
337C2×D3—31no—
338C2×D3—32no—
339C2×D3—32no—
340C2×D3—32no—
341C2×D3—41no—
342C2×D3—44no—
343C2×D3—62no—
344C2×D3—62no—
345C2×D3—64no—
346C2×D3—124no—
347C2×D3—124no—
348C2×D3—128no—
349C2×D3—121no—
350C2×D3—121no—
351C2×D3—122no—
352C2×D3—121no—
353C2×D3—124no—
354C2×D3#127⋊C311yescharacteristic, direct product factor
355A4—41no—
356A4—81no—
357C3×C4—32no—
358C3×C4—32no—
359Dic3—34no—
360C32—161noSylow
361C23—32no—
362C23—32no—
363C23—32no—
364C23—61no—
365C23—61no—
366C23—61no—
367C23—62no—
368C23—61no—
369C23—62no—
370C23—91no—
371C23—92no—
372C23—91no—
373C23—92no—
374C23—121no—
375C23—181no—
376C23—181no—
377C23—181no—
378C23—182no—
379C23—181no—
380C23—182no—
381C23—184no—
382C23—184no—
383C23—184no—
384C23—188no—
385C23—184no—
386C23—188no—
387C23—361no—
388C23—361no—
389C23—362no—
390C23—362no—
391C23—364no—
392C23—362no—
393C23—364no—
394C23—362no—
395C23—361no—
396C23—362no—
397C23C2×D3×A411yescharacteristic
398C23C2×D3×A412yes—
399D4—64no—
400D4—64no—
401D4—64no—
402D4—64no—
403D4—184no—
404D4—184no—
405D4—184no—
406D4—184no—
407D4—188no—
408D4—188no—
409D4—1816no—
410C2×C4—32no—
411C2×C4—32no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—94no—
415C2×C4—94no—
416C2×C4—94no—
417C2×C4—94no—
418C2×C4—92no—
419C2×C4—92no—
420C2×C4—92no—
421C2×C3—31no—
422C2×C3—31no—
423C2×C3—42no—
424C2×C3—122no—
425C2×C3—162no—
426C2×C3—161no—
427C2×C3—322no—
428C2×C3—321no—
429C2×C3—482no—
430C2×C3—482no—
431C2×C3C2×#127⋊C311yescharacteristic, complemented
432D3—32no—
433D3—42no—
434D3—122no—
435D3C2×#127⋊C312yesdirect product factor
436C22—31no—
437C22—31no—
438C22—31no—
439C22—41no—
440C22—62no—
441C22—62no—
442C22—64no—
443C22—92no—
444C22—92no—
445C22—92no—
446C22—92no—
447C22—91no—
448C22—121no—
449C22—124no—
450C22—122no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22—182no—
455C22—182no—
456C22—184no—
457C22—361no—
458C22—364no—
459C22—362no—
460C22—361no—
461C22—364no—
462C22—364no—
463C22—368no—
464C22—361no—
465C22C22×D3×A411yescharacteristic
466C4—32no—
467C4—32no—
468C4—94no—
469C3—161no—
470C3—321no—
471C3C22×#127⋊C311yescharacteristic, complemented
472C2—31no—
473C2—31no—
474C2—32no—
475C2—42no—
476C2—92no—
477C2—122no—
478C2—122no—
479C2—362no—
480C2D3×#127⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D3×#127⋊C3
commutator, cosocle, hypocenterC3×C42C23×C3
FrattiniC22C22×D3×A4
FittingC2×C3×#127C2×C3
socleC23×C3C22×A4
LCSG ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×#127⋊C3C2semidirect
2. D3×#127⋊C3C2direct (N × H)
3. C2×D3×C42⋊C3C2semidirect
4. C2×C3⋊(#127⋊C3)C2semidirect
5. C2×D3×#127C3semidirect
8. C3×#127⋊C3C22semidirect
9. C2×C3×C42⋊C3C22semidirect
10. D3×C42⋊C3C22semidirect
11. C3⋊(#127⋊C3)C22semidirect
14. C2×C3×#127C2×C3semidirect
18. D3×#127C2×C3semidirect
19. C2×#874C2×C3semidirect
20. C2×C42×D3C2×C3semidirect
24. C2×#127⋊C3D3direct (N × H)
30. C3×C42⋊C3C23semidirect
54. C3×#127C22×C3semidirect
55. C2×C3×C42C22×C3semidirect
62. #874C22×C3semidirect
64. C42×D3C22×C3semidirect
67. #127⋊C3C2×D3direct (N × H)
70. C2×C42⋊C3C2×D3semidirect
83. C2×#127C3×D3semidirect
147. C3×C42C23×C3semidirect
151. C42⋊C3C22×D3semidirect
184. #127C2×C3×D3semidirect
188. C2×C42C2×C3×D3semidirect
319. C42C22×C3×D3semidirect
354. C2×D3#127⋊C3direct (N × H)
431. C2×C3C2×#127⋊C3semidirect
435. D3C2×#127⋊C3direct (N × H)
471. C3C22×#127⋊C3semidirect
480. C2D3×#127⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#127⋊C32
D3×#127⋊C32
C2×D3×C42⋊C32
C2×C3⋊(#127⋊C3)2
C2×D3×#1273
C22×#127⋊C33
C22×D3×A44