Finite Group Databasebeta

← C22×C3×#883 #11900360

Subgroups — C22×C3×#883 #11900360

Order 1152.

4273 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic
2C23×C3×C4×D3C211yesmaximal, characteristic, complemented
3C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
4C22×C3×#217C211yesmaximal, characteristic, complemented
5C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
7C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
8C2×C3×#883C2124yesmaximal, direct product factor
9C22×C3×#123—31nomaximal
10C22×#883C311yesmaximal, characteristic, direct product factor
11C25×C32C2211yescharacteristic
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67—28no—
16C22×C3×#67C22112yes—
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×C4×D3—28no—
21C22×C3×C4×D3C22112yescomplemented
22C2×C32×C22⋊C4C22112yescomplemented
23C2×C3×#217C22112yescomplemented
24C2×C3×(C2×D3)⋊C4C22112yescomplemented
25C2×C3×C4⋊Dic3C22112yescomplemented
26C2×C3×Dic3⋊C4C22112yescomplemented
27C3×#883C22164yesdirect product factor
28C23×C3×D4—31no—
29C24×C3×C4—31no—
30C23×#67C2×C311yescharacteristic
31C23×C4×D3C2×C311yescharacteristic, complemented
32C2×C3×#123—324no—
33C22×C3×C4⋊C4—31no—
34C22×C3×C4⋊C4—31no—
35C22×C3×C22⋊C4—21no—
36C22×C3×C22⋊C4—31no—
37C22×C3×C22⋊C4—31no—
38C22×C3×C22⋊C4D311yescharacteristic, complemented
39C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
40C22×#217C2×C311yescharacteristic, complemented
41C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
42C22×C4⋊Dic3C2×C311yescharacteristic, complemented
43C22×Dic3⋊C4C2×C311yescharacteristic, complemented
44C2×#883C2×C3124yesdirect product factor
45C24×C32—24no—
46C24×C32—24no—
47C24×C32—24no—
48C24×C32C2316yes—
49C24×C32C2311yescharacteristic
50C23×C3×D3—24no—
51C23×C3×D3—24no—
52C23×C3×D3D418yes—
53C23×C3×D3C2316yes—
54C22×C32×C4—24no—
55C22×C32×C4—24no—
56C22×C32×C4C2316yes—
57C22×C32×C4C2316yes—
58C2×C3×#67—248no—
59C2×C3×#67C23116yes—
60C22×C3×Dic3—24no—
61C22×C3×Dic3—24no—
62C22×C3×Dic3—24no—
63C22×C3×Dic3C2316yes—
64C22×C3×Dic3C2316yes—
65C22×C3×Dic3C2316yes—
66C2×C3×C4×D3—248no—
67C2×C3×C4×D3C23116yescomplemented
68C32×C22⋊C4C23116yescomplemented
69C3×#217C23116yescomplemented
70C3×(C2×D3)⋊C4C23116yescomplemented
71C3×C4⋊Dic3C23116yescomplemented
72C3×Dic3⋊C4C23116yescomplemented
73C22×#123—31noSylow
74C25×C3—21no—
75C25×C3—31no—
76C25×C3C2×D311yescharacteristic
77C25×C3C22×C311yescharacteristic
78C24×D3C22×C311yescharacteristic
79C22×C3×D4—312no—
80C22×C3×D4—68no—
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C23×C3×C4—31no—
84C23×C3×C4—31no—
85C23×C3×C4—31no—
86C23×C3×C4—312no—
87C23×C3×C4—68no—
88C23×C3×C4C2×D311yescharacteristic
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C22×C311yescharacteristic
91C23×C3×C4C22×C311yescharacteristic
92C22×#67—28no—
93C22×#67C22×C3112yes—
94C23×Dic3C22×C311yescharacteristic
95C23×Dic3C22×C311yescharacteristic
96C23×Dic3C22×C311yescharacteristic
97C22×C4×D3—28no—
98C22×C4×D3C22×C3112yescomplemented
99C3×#123—364no—
100C2×C3×C4⋊C4—312no—
101C2×C3×C4⋊C4—312no—
102C2×C3×C22⋊C4—212no—
103C2×C3×C22⋊C4—312no—
104C2×C3×C22⋊C4—312no—
105C2×C3×C22⋊C4C2×D3112yescomplemented
106C2×C3×C22⋊C4C22×C3112yescomplemented
107C2×#217C22×C3112yescomplemented
108C2×(C2×D3)⋊C4C22×C3112yescomplemented
109C2×C4⋊Dic3C22×C3112yescomplemented
110C2×Dic3⋊C4C22×C3112yescomplemented
111#883C22×C3164yesdirect product factor
112C23×C32—212no—
113C23×C32—212no—
114C23×C32—212no—
115C23×C32—416no—
116C23×C32C2×D414yes—
117C23×C32#4114yes—
118C23×C32#4114yes—
119C23×C32C2414yes—
120C23×C32C2413yes—
121C22×C3×D3—232no—
122C22×C3×D3—212no—
123C22×C3×D3—212no—
124C22×C3×D3C2×D4124yes—
125C22×C3×D3C2414yes—
126C2×C32×C4—212no—
127C2×C32×C4—212no—
128C2×C32×C4C2414yes—
129C2×C32×C4C2414yes—
130C3×#67—232no—
131C2×C3×Dic3—212no—
132C2×C3×Dic3—212no—
133C2×C3×Dic3—212no—
134C2×C3×Dic3C2414yes—
135C2×C3×Dic3C2414yes—
136C2×C3×Dic3C2414yes—
137C3×C4×D3—232no—
138C23×D4—31no—
139C24×C4—31no—
140C2×#123—324no—
141C22×C4⋊C4—31no—
142C22×C4⋊C4—31no—
143C22×C22⋊C4—31no—
144C22×C22⋊C4—31no—
145C22×C22⋊C4C3×D311yescharacteristic, complemented
146C24×C3—28no—
147C24×C3—24no—
148C24×C3—24no—
149C24×C3—24no—
150C24×C3—24no—
151C24×C3—24no—
152C24×C3—24no—
153C24×C3—21no—
154C24×C3—26no—
155C24×C3—38no—
156C24×C3—36no—
157C24×C3—44no—
158C24×C3—44no—
159C24×C3—64no—
160C24×C3—64no—
161C24×C3C22×D316yes—
162C24×C3C22×D311yescharacteristic
163C24×C3C23×C316yes—
164C24×C3C23×C311yescharacteristic
165C23×D3—24no—
166C23×D3—24no—
167C23×D3C3×D418yes—
168C23×D3C23×C316yes—
169C2×C3×D4—316no—
170C2×C3×D4—648no—
171C22×C3×C4—24no—
172C22×C3×C4—24no—
173C22×C3×C4—24no—
174C22×C3×C4—24no—
175C22×C3×C4—26no—
176C22×C3×C4—26no—
177C22×C3×C4—36no—
178C22×C3×C4—36no—
179C22×C3×C4—36no—
180C22×C3×C4—316no—
181C22×C3×C4—44no—
182C22×C3×C4—44no—
183C22×C3×C4—648no—
184C22×C3×C4—64no—
185C22×C3×C4—64no—
186C22×C3×C4—64no—
187C22×C3×C4C22×D316yes—
188C22×C3×C4C22×D316yes—
189C22×C3×C4C23×C316yes—
190C22×C3×C4C23×C316yes—
191C2×#67—248no—
192C2×#67C23×C3116yes—
193C22×Dic3—24no—
194C22×Dic3—24no—
195C22×Dic3—24no—
196C22×Dic3C23×C316yes—
197C22×Dic3C23×C316yes—
198C22×Dic3C23×C316yes—
199C2×C4×D3—248no—
200C2×C4×D3C23×C3116yescomplemented
201C3×C4⋊C4—316no—
202C3×C4⋊C4—316no—
203C3×C22⋊C4—216no—
204C3×C22⋊C4—316no—
205C3×C22⋊C4—316no—
206C3×C22⋊C4C22×D3116yescomplemented
207C3×C22⋊C4C23×C3116yescomplemented
208#217C23×C3116yescomplemented
209(C2×D3)⋊C4C23×C3116yescomplemented
210C4⋊Dic3C23×C3116yescomplemented
211Dic3⋊C4C23×C3116yescomplemented
212C22×C32—24no—
213C22×C32—24no—
214C22×C32—24no—
215C22×C32—424no—
216C22×C32#123116yescomplemented
217C22×C32C22×D416yes—
218C22×C32C2×#4116yes—
219C22×C32C2×#4116yes—
220C22×C32C2511yescharacteristic
221C2×C3×D3—248no—
222C2×C3×D3—24no—
223C2×C3×D3—24no—
224C2×C3×D3C22×D418yes—
225C32×C4—24no—
226C32×C4—24no—
227C3×Dic3—24no—
228C3×Dic3—24no—
229C3×Dic3—24no—
230C25—31no—
231C25C2×C3×D311yescharacteristic
232C22×D4—312no—
233C22×D4—68no—
234C23×C4—31no—
235C23×C4—31no—
236C23×C4—31no—
237C23×C4—312no—
238C23×C4—68no—
239C23×C4C2×C3×D311yescharacteristic
240C23×C4C2×C3×D311yescharacteristic
241#123—364no—
242C2×C4⋊C4—312no—
243C2×C4⋊C4—312no—
244C2×C22⋊C4—312no—
245C2×C22⋊C4—312no—
246C2×C22⋊C4C2×C3×D3112yescomplemented
247C23×C3—224no—
248C23×C3—212no—
249C23×C3—212no—
250C23×C3—212no—
251C23×C3—212no—
252C23×C3—212no—
253C23×C3—212no—
254C23×C3—23no—
255C23×C3—24no—
256C23×C3—24no—
257C23×C3—24no—
258C23×C3—24no—
259C23×C3—324no—
260C23×C3—34no—
261C23×C3—412no—
262C23×C3—412no—
263C23×C3—432no—
264C23×C3—416no—
265C23×C3—416no—
266C23×C3—632no—
267C23×C3—612no—
268C23×C3—612no—
269C23×C3#23514yes—
270C23×C3D3×D414yes—
271C23×C3#23714yes—
272C23×C3C2×C3×D414yes—
273C23×C3C3×#4114yes—
274C23×C3C3×#4114yes—
275C23×C3C23×D314yes—
276C23×C3C23×D313yes—
277C23×C3C24×C314yes—
278C23×C3C24×C313yes—
279C22×D3—232no—
280C22×D3—212no—
281C22×D3—212no—
282C22×D3C2×C3×D4124yes—
283C22×D3C24×C314yes—
284C3×D4—632no—
285C2×C3×C4—212no—
286C2×C3×C4—212no—
287C2×C3×C4—212no—
288C2×C3×C4—212no—
289C2×C3×C4—24no—
290C2×C3×C4—24no—
291C2×C3×C4—34no—
292C2×C3×C4—34no—
293C2×C3×C4—34no—
294C2×C3×C4—412no—
295C2×C3×C4—412no—
296C2×C3×C4—632no—
297C2×C3×C4—612no—
298C2×C3×C4—612no—
299C2×C3×C4—612no—
300C2×C3×C4C23×D314yes—
301C2×C3×C4C23×D314yes—
302C2×C3×C4C24×C314yes—
303C2×C3×C4C24×C314yes—
304#67—232no—
305C2×Dic3—212no—
306C2×Dic3—212no—
307C2×Dic3—212no—
308C2×Dic3C24×C314yes—
309C2×Dic3C24×C314yes—
310C2×Dic3C24×C314yes—
311C4×D3—232no—
312C2×C32—44no—
313C2×C32C2×#123112yescomplemented
314C2×C32C23×D411yescharacteristic
315C2×C32C22×#4111yescharacteristic
316C2×C32C22×#4111yescharacteristic
317C3×D3—28no—
318C24—24no—
319C24—24no—
320C24—24no—
321C24—36no—
322C24—38no—
323C24—64no—
324C24—64no—
325C24C22×C3×D316yes—
326C24C22×C3×D311yescharacteristic
327C2×D4—316no—
328C2×D4—648no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—36no—
332C22×C4—36no—
333C22×C4—36no—
334C22×C4—316no—
335C22×C4—648no—
336C22×C4—64no—
337C22×C4—64no—
338C22×C4—64no—
339C22×C4C22×C3×D316yes—
340C22×C4C22×C3×D316yes—
341C4⋊C4—316no—
342C4⋊C4—316no—
343C22⋊C4—316no—
344C22⋊C4—316no—
345C22⋊C4C22×C3×D3116yescomplemented
346C22×C3—28no—
347C22×C3—24no—
348C22×C3—24no—
349C22×C3—24no—
350C22×C3—24no—
351C22×C3—24no—
352C22×C3—24no—
353C22×C3—216no—
354C22×C3—26no—
355C22×C3—26no—
356C22×C3—26no—
357C22×C3—21no—
358C22×C3—38no—
359C22×C3—44no—
360C22×C3—44no—
361C22×C3—448no—
362C22×C3—424no—
363C22×C3—424no—
364C22×C3—64no—
365C22×C3—64no—
366C22×C3—648no—
367C22×C3#883116yesdirect product factor
368C22×C3C3×#123116yescomplemented
369C22×C3C2×#23516yes—
370C22×C3C2×D3×D416yes—
371C22×C3C2×#23716yes—
372C22×C3C22×C3×D416yes—
373C22×C3C2×C3×#4116yes—
374C22×C3C2×C3×#4116yes—
375C22×C3C24×D311yescharacteristic
376C22×C3C25×C311yescharacteristic
377C2×D3—24no—
378C2×D3—24no—
379C2×D3—248no—
380C2×D3C22×C3×D418yes—
381C3×C4—24no—
382C3×C4—24no—
383C3×C4—24no—
384C3×C4—24no—
385C3×C4—44no—
386C3×C4—44no—
387C3×C4—64no—
388C3×C4—64no—
389C3×C4—64no—
390Dic3—24no—
391Dic3—24no—
392Dic3—24no—
393C32C22×#12311yescharacteristic, complemented, Sylow
394C23—212no—
395C23—212no—
396C23—212no—
397C23—324no—
398C23—34no—
399C23—416no—
400C23—632no—
401C23—612no—
402C23—612no—
403C23C3×#23514yes—
404C23C3×D3×D414yes—
405C23C3×#23714yes—
406C23C23×C3×D314yes—
407C23C23×C3×D313yes—
408D4—632no—
409C2×C4—212no—
410C2×C4—212no—
411C2×C4—34no—
412C2×C4—34no—
413C2×C4—34no—
414C2×C4—632no—
415C2×C4—612no—
416C2×C4—612no—
417C2×C4—612no—
418C2×C4C23×C3×D314yes—
419C2×C4C23×C3×D314yes—
420C2×C3—212no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—48no—
425C2×C3—44no—
426C2×C3—44no—
427C2×C3—68no—
428C2×C3C2×#883112yesdirect product factor
429C2×C3C2×C3×#123112yescomplemented
430C2×C3C22×#23511yescharacteristic
431C2×C3C22×D3×D411yescharacteristic
432C2×C3C22×#23711yescharacteristic
433C2×C3C23×C3×D411yescharacteristic
434C2×C3C22×C3×#4111yescharacteristic
435C2×C3C22×C3×#4111yescharacteristic
436D3—28no—
437C22—24no—
438C22—24no—
439C22—24no—
440C22—38no—
441C22—424no—
442C22—648no—
443C22—64no—
444C22—64no—
445C22C3×#883116yesdirect product factor
446C22C2×C3×#23516yes—
447C22C2×C3×D3×D416yes—
448C22C2×C3×#23716yes—
449C22C24×C3×D311yescharacteristic
450C4—24no—
451C4—24no—
452C4—64no—
453C4—64no—
454C4—64no—
455C3—21no—
456C3C22×#88311yescharacteristic, direct product factor
457C3C22×C3×#12311yescharacteristic, complemented
458C2—44no—
459C2—68no—
460C2C2×C3×#883112yesdirect product factor
461C2C22×C3×#23511yescharacteristic
462C2C22×C3×D3×D411yescharacteristic
463C2C22×C3×#23711yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×C22⋊C4C2
socleC24×C32C23
prime radicalC23×C3×#67C2
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C22×C3×#123
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C3×C4×D3C2semidirect
3. C22×C32×C22⋊C4C2semidirect
4. C22×C3×#217C2semidirect
5. C22×C3×(C2×D3)⋊C4C2semidirect
6. C22×C3×C4⋊Dic3C2semidirect
7. C22×C3×Dic3⋊C4C2semidirect
8. C2×C3×#883C2direct (N × H)
10. C22×#883C3direct (N × H)
21. C22×C3×C4×D3C22semidirect
22. C2×C32×C22⋊C4C22semidirect
23. C2×C3×#217C22semidirect
24. C2×C3×(C2×D3)⋊C4C22semidirect
25. C2×C3×C4⋊Dic3C22semidirect
26. C2×C3×Dic3⋊C4C22semidirect
27. C3×#883C22direct (N × H)
31. C23×C4×D3C2×C3semidirect
38. C22×C3×C22⋊C4D3semidirect
39. C22×C3×C22⋊C4C2×C3semidirect
40. C22×#217C2×C3semidirect
41. C22×(C2×D3)⋊C4C2×C3semidirect
42. C22×C4⋊Dic3C2×C3semidirect
43. C22×Dic3⋊C4C2×C3semidirect
44. C2×#883C2×C3direct (N × H)
67. C2×C3×C4×D3C23semidirect
68. C32×C22⋊C4C23semidirect
69. C3×#217C23semidirect
70. C3×(C2×D3)⋊C4C23semidirect
71. C3×C4⋊Dic3C23semidirect
72. C3×Dic3⋊C4C23semidirect
98. C22×C4×D3C22×C3semidirect
105. C2×C3×C22⋊C4C2×D3semidirect
106. C2×C3×C22⋊C4C22×C3semidirect
107. C2×#217C22×C3semidirect
108. C2×(C2×D3)⋊C4C22×C3semidirect
109. C2×C4⋊Dic3C22×C3semidirect
110. C2×Dic3⋊C4C22×C3semidirect
111. #883C22×C3direct (N × H)
145. C22×C22⋊C4C3×D3semidirect
200. C2×C4×D3C23×C3semidirect
206. C3×C22⋊C4C22×D3semidirect
207. C3×C22⋊C4C23×C3semidirect
208. #217C23×C3semidirect
209. (C2×D3)⋊C4C23×C3semidirect
210. C4⋊Dic3C23×C3semidirect
211. Dic3⋊C4C23×C3semidirect
216. C22×C32#123semidirect
246. C2×C22⋊C4C2×C3×D3semidirect
313. C2×C32C2×#123semidirect
345. C22⋊C4C22×C3×D3semidirect
367. C22×C3#883direct (N × H)
368. C22×C3C3×#123semidirect
393. C32C22×#123semidirect
428. C2×C3C2×#883direct (N × H)
429. C2×C3C2×C3×#123semidirect
445. C22C3×#883direct (N × H)
456. C3C22×#883direct (N × H)
457. C3C22×C3×#123semidirect
460. C2C2×C3×#883direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×#672
C23×C3×C4×D32
C22×C32×C22⋊C42
C22×C3×#2172
C22×C3×(C2×D3)⋊C42
C22×C3×C4⋊Dic32
C22×C3×Dic3⋊C42
C2×C3×#8832
C22×C3×#1233
C22×#8833