Finite Group Databasebeta

← C22×#63909 #11900296

Subgroups — C22×#63909 #11900296

Order 1152.

5737 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C23×C3×C4×D3C211yesmaximal, characteristic, complemented
3C23×#626C212yesmaximal, complemented
4C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C22×#3722C212yesmaximal, complemented
6C2×#63909C2124yesmaximal, direct product factor
7C22×#930—31nomaximal
8C22×#895—31nomaximal
9C24×C3⋊D3C2212yes—
10C24×C3×D3C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)—28no—
13C22×C4⋊(C3⋊D3)C22112yescomplemented
14C23×C3×Dic3C2212yes—
15C23×C3×Dic3C2211yescharacteristic
16C22×C3×C4×D3—28no—
17C22×C3×C4×D3C22112yescomplemented
18C22×#626—216no—
19C22×#626C22124yescomplemented
20C2×C3×C4⋊Dic3C22112yescomplemented
21C2×#3722C22124yescomplemented
22#63909C22164yesdirect product factor
23C24×C3×C4—31no—
24C23×#67—32no—
25C23×D12—32no—
26C23×D12—31no—
27C23×D12—31no—
28C23×D12—61no—
29C23×C4×D3D311yescharacteristic, complemented
30C22×C3×C4⋊C4—31no—
31C2×#930—324no—
32C22×(C2×D3)⋊C4—32no—
33C22×(C2×D3)⋊C4—32no—
34C22×C4⋊Dic3D311yescharacteristic, complemented
35C2×#895—324no—
36C24×C32C2311yescharacteristic
37C23×C3⋊D3—28no—
38C23×C3⋊D3—28no—
39C23×C3⋊D3—28no—
40C23×C3⋊D3C23112yes—
41C23×C3×D3—24no—
42C23×C3×D3—24no—
43C23×C3×D3D418yescomplemented
44C23×C3×D3C2316yes—
45C22×C32×C4D418yescomplemented
46C22×C32×C4C2316yes—
47C2×C4⋊(C3⋊D3)—248no—
48C2×C4⋊(C3⋊D3)C23116yescomplemented
49C22×C3×Dic3—28no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3C23112yes—
52C22×C3×Dic3C2316yes—
53C2×C3×C4×D3—248no—
54C2×C3×C4×D3C23116yescomplemented
55C2×#626—296no—
56C2×#626C23132yescomplemented
57C3×C4⋊Dic3C23116yescomplemented
58#3722C23132yescomplemented
59C22×#121—91noSylow
60C25×C3—31no—
61C24×D3—32no—
62C24×D3—32no—
63C24×D3—62no—
64C24×D3C2×D311yescharacteristic
65C23×C3×C4—21no—
66C23×C3×C4—32no—
67C23×C3×C4—31no—
68C23×C3×C4—312no—
69C23×C3×C4—68no—
70C23×C3×C4C2×D311yescharacteristic
71C23×C3×C4C2×D311yescharacteristic
72C22×#67—324no—
73C22×#67—616no—
74C23×Dic3C2×D311yescharacteristic
75C23×Dic3C2×D312yes—
76C22×D12—324no—
77C22×D12—312no—
78C22×D12—312no—
79C22×D12—612no—
80C22×D12—616no—
81C22×D12—616no—
82C22×D12—68no—
83C22×D12—68no—
84C22×C4×D3—28no—
85C22×C4×D3C2×D3112yescomplemented
86C2×C3×C4⋊C4—312no—
87#930—364no—
88C2×(C2×D3)⋊C4—324no—
89C2×(C2×D3)⋊C4—324no—
90C2×C4⋊Dic3C2×D3112yescomplemented
91#895—364no—
92C23×C32C2×D414yes—
93C23×C32C2×D414yes—
94C23×C32#4114yes—
95C23×C32C2413yes—
96C22×C3⋊D3—224no—
97C22×C3⋊D3—224no—
98C22×C3⋊D3—224no—
99C22×C3⋊D3—432no—
100C22×C3⋊D3C2418yes—
101C22×C3×D3—232no—
102C22×C3×D3—212no—
103C22×C3×D3—212no—
104C22×C3×D3C2×D4124yescomplemented
105C22×C3×D3C2414yes—
106C2×C32×C4C2×D4124yescomplemented
107C2×C32×C4C2414yes—
108C4⋊(C3⋊D3)—232no—
109C2×C3×Dic3—224no—
110C2×C3×Dic3—212no—
111C2×C3×Dic3C2414yes—
112C2×C3×Dic3C2418yes—
113C3×C4×D3—232no—
114#626—264no—
115C23×D4—92no—
116C23×D4—91no—
117C24×C4—31no—
118C2×#121—924no—
119C22×C4⋊C4—31no—
120C22×C22⋊C4—92no—
121C24×C3—21no—
122C24×C3—38no—
123C24×C3—36no—
124C24×C3—64no—
125C24×C3—64no—
126C24×C3C22×D311yescharacteristic
127C24×C3C22×D311yescharacteristic
128C23×D3—24no—
129C23×D3—24no—
130C23×D3—312no—
131C23×D3—312no—
132C23×D3—612no—
133C23×D3—616no—
134C23×D3—68no—
135C23×D3—68no—
136C23×D3—68no—
137C23×D3—68no—
138C23×D3—68no—
139C23×D3—68no—
140C23×D3—128no—
141C23×D3—128no—
142C23×D3D1218yescomplemented
143C23×D3C22×D316yes—
144C22×C3×C4—28no—
145C22×C3×C4—26no—
146C22×C3×C4—36no—
147C22×C3×C4—312no—
148C22×C3×C4—316no—
149C22×C3×C4—68no—
150C22×C3×C4—64no—
151C22×C3×C4—648no—
152C22×C3×C4D1218yescomplemented
153C22×C3×C4#6718yescomplemented
154C22×C3×C4C22×D316yes—
155C22×C3×C4C22×D316yes—
156C2×#67—332no—
157C2×#67—696no—
158C22×Dic3—28no—
159C22×Dic3—24no—
160C22×Dic3C22×D3112yes—
161C22×Dic3C22×D316yes—
162C2×D12—332no—
163C2×D12—316no—
164C2×D12—316no—
165C2×D12—616no—
166C2×D12—696no—
167C2×D12—696no—
168C2×D12—648no—
169C2×D12—648no—
170C2×C4×D3—248no—
171C2×C4×D3C22×D3116yescomplemented
172C3×C4⋊C4—316no—
173(C2×D3)⋊C4—332no—
174(C2×D3)⋊C4—332no—
175C4⋊Dic3C22×D3116yescomplemented
176C22×C32#121116yescomplemented
177C22×C32C22×D416yes—
178C22×C32C22×D416yes—
179C22×C32C2×#4116yes—
180C22×C32C2511yescharacteristic
181C2×C3⋊D3—28no—
182C2×C3⋊D3—28no—
183C2×C3⋊D3—28no—
184C2×C3⋊D3—448no—
185C2×C3×D3—248no—
186C2×C3×D3—24no—
187C2×C3×D3—24no—
188C2×C3×D3C22×D418yescomplemented
189C32×C4C22×D418yescomplemented
190C3×Dic3—28no—
191C3×Dic3—24no—
192C25—31no—
193C25—92no—
194C22×D4—924no—
195C22×D4—912no—
196C22×D4—1816no—
197C22×D4—188no—
198C23×C4—31no—
199C23×C4—32no—
200C23×C4—312no—
201C23×C4—68no—
202C23×C4D3211yescharacteristic
203#121—964no—
204C2×C4⋊C4—312no—
205C2×C22⋊C4—924no—
206C23×C3—23no—
207C23×C3—24no—
208C23×C3—24no—
209C23×C3—24no—
210C23×C3—324no—
211C23×C3—34no—
212C23×C3—632no—
213C23×C3—612no—
214C23×C3—612no—
215C23×C3C2×D1214yes—
216C23×C3C2×D1214yes—
217C23×C3#23514yes—
218C23×C3D3×D414yes—
219C23×C3#23914yes—
220C23×C3C2×#6714yes—
221C23×C3C23×D313yes—
222C23×C3C23×D313yes—
223C22×D3—232no—
224C22×D3—212no—
225C22×D3—212no—
226C22×D3—38no—
227C22×D3—38no—
228C22×D3—68no—
229C22×D3—648no—
230C22×D3—624no—
231C22×D3—624no—
232C22×D3—624no—
233C22×D3—624no—
234C22×D3—624no—
235C22×D3—624no—
236C22×D3—1224no—
237C22×D3—1224no—
238C22×D3—1264no—
239C22×D3—1232no—
240C22×D3—1232no—
241C22×D3C2×D12124yescomplemented
242C22×D3C23×D314yes—
243C2×C3×C4—24no—
244C2×C3×C4—224no—
245C2×C3×C4—34no—
246C2×C3×C4—38no—
247C2×C3×C4—624no—
248C2×C3×C4—612no—
249C2×C3×C4—632no—
250C2×C3×C4C2×D12124yescomplemented
251C2×C3×C4C2×#67124yescomplemented
252C2×C3×C4C23×D314yes—
253C2×C3×C4C23×D314yes—
254#67—664no—
255C2×Dic3—224no—
256C2×Dic3—212no—
257C2×Dic3C23×D318yes—
258C2×Dic3C23×D314yes—
259D12—664no—
260D12—664no—
261D12—632no—
262D12—632no—
263C4×D3—232no—
264C2×C32C2×#121112yescomplemented
265C2×C32C23×D411yescharacteristic
266C2×C32C23×D411yescharacteristic
267C2×C32C22×#4111yescharacteristic
268C3⋊D3—48no—
269C3×D3—28no—
270C24—36no—
271C24—38no—
272C24—64no—
273C24—64no—
274C24—912no—
275C24—188no—
276C24—188no—
277C24—188no—
278C24C2×D3211yescharacteristic
279C2×D4—932no—
280C2×D4—916no—
281C2×D4—1896no—
282C2×D4—1848no—
283C22×C4—36no—
284C22×C4—312no—
285C22×C4—316no—
286C22×C4—68no—
287C22×C4—64no—
288C22×C4—648no—
289C22×C4#62618yescomplemented
290C22×C4C2×D3216yes—
291C4⋊C4—316no—
292C22⋊C4—932no—
293C22×C3—26no—
294C22×C3—26no—
295C22×C3—26no—
296C22×C3—21no—
297C22×C3—216no—
298C22×C3—38no—
299C22×C3—64no—
300C22×C3—64no—
301C22×C3—648no—
302C22×C3#895116yescomplemented
303C22×C3#930116yescomplemented
304C22×C3C22×D1216yes—
305C22×C3C22×D1216yes—
306C22×C3C2×#23516yes—
307C22×C3C2×D3×D416yes—
308C22×C3C2×#23916yes—
309C22×C3C22×#6716yes—
310C22×C3C24×D311yescharacteristic
311C22×C3C24×D311yescharacteristic
312C2×D3—24no—
313C2×D3—24no—
314C2×D3—248no—
315C2×D3—616no—
316C2×D3—68no—
317C2×D3—68no—
318C2×D3—68no—
319C2×D3—68no—
320C2×D3—68no—
321C2×D3—68no—
322C2×D3—128no—
323C2×D3—128no—
324C2×D3—1296no—
325C2×D3—1248no—
326C2×D3—1248no—
327C2×D3C22×D1218yescomplemented
328C3×C4—28no—
329C3×C4—68no—
330C3×C4—64no—
331C3×C4C22×D1218yescomplemented
332C3×C4C22×#6718yescomplemented
333Dic3—28no—
334Dic3—24no—
335C32C22×#12111yescharacteristic, complemented, Sylow
336C23—324no—
337C23—34no—
338C23—612no—
339C23—612no—
340C23—632no—
341C23—98no—
342C23—1824no—
343C23—1824no—
344C23—1824no—
345C23—3632no—
346C23#379914yes—
347C23D3×D1214yes—
348C23C2×#62614yes—
349C23C22×D3213yes—
350D4—1864no—
351D4—1832no—
352C2×C4—34no—
353C2×C4—38no—
354C2×C4—624no—
355C2×C4—612no—
356C2×C4—632no—
357C2×C4C2×#626124yescomplemented
358C2×C4C22×D3214yes—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—212no—
363C2×C3—68no—
364C2×C3C2×#895112yescomplemented
365C2×C3C2×#930112yescomplemented
366C2×C3C23×D1211yescharacteristic
367C2×C3C23×D1211yescharacteristic
368C2×C3C22×#23511yescharacteristic
369C2×C3C22×D3×D411yescharacteristic
370C2×C3C22×#23911yescharacteristic
371C2×C3C23×#6711yescharacteristic
372D3—28no—
373D3—1216no—
374D3—128no—
375D3—128no—
376C22—38no—
377C22—64no—
378C22—64no—
379C22—648no—
380C22—188no—
381C22—188no—
382C22—188no—
383C22—3648no—
384C22#63909116yesdirect product factor
385C22C2×#379916yes—
386C22C2×D3×D1216yes—
387C22C22×#62616yes—
388C22C23×D3211yescharacteristic
389C4—68no—
390C4—64no—
391C4C22×#62618yescomplemented
392C3—21no—
393C3C22×#89511yescharacteristic, complemented
394C3C22×#93011yescharacteristic, complemented
395C2—68no—
396C2—368no—
397C2C2×#63909112yesdirect product factor
398C2C22×#379911yescharacteristic
399C2C22×D3×D1211yescharacteristic
400C2C23×#62611yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC24×C32C23
hypercenterC23×C4D32
hypocenterC32C22×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊(C3⋊D3)C2semidirect
2. C23×C3×C4×D3C2semidirect
3. C23×#626C2semidirect
4. C22×C3×C4⋊Dic3C2semidirect
5. C22×#3722C2semidirect
6. C2×#63909C2direct (N × H)
13. C22×C4⋊(C3⋊D3)C22semidirect
17. C22×C3×C4×D3C22semidirect
19. C22×#626C22semidirect
20. C2×C3×C4⋊Dic3C22semidirect
21. C2×#3722C22semidirect
22. #63909C22direct (N × H)
29. C23×C4×D3D3semidirect
34. C22×C4⋊Dic3D3semidirect
43. C23×C3×D3D4semidirect
45. C22×C32×C4D4semidirect
48. C2×C4⋊(C3⋊D3)C23semidirect
54. C2×C3×C4×D3C23semidirect
56. C2×#626C23semidirect
57. C3×C4⋊Dic3C23semidirect
58. #3722C23semidirect
85. C22×C4×D3C2×D3semidirect
90. C2×C4⋊Dic3C2×D3semidirect
104. C22×C3×D3C2×D4semidirect
106. C2×C32×C4C2×D4semidirect
142. C23×D3D12semidirect
152. C22×C3×C4D12semidirect
153. C22×C3×C4#67semidirect
171. C2×C4×D3C22×D3semidirect
175. C4⋊Dic3C22×D3semidirect
176. C22×C32#121semidirect
188. C2×C3×D3C22×D4semidirect
189. C32×C4C22×D4semidirect
241. C22×D3C2×D12semidirect
250. C2×C3×C4C2×D12semidirect
251. C2×C3×C4C2×#67semidirect
264. C2×C32C2×#121semidirect
289. C22×C4#626semidirect
302. C22×C3#895semidirect
303. C22×C3#930semidirect
327. C2×D3C22×D12semidirect
331. C3×C4C22×D12semidirect
332. C3×C4C22×#67semidirect
335. C32C22×#121semidirect
357. C2×C4C2×#626semidirect
364. C2×C3C2×#895semidirect
365. C2×C3C2×#930semidirect
384. C22#63909direct (N × H)
391. C4C22×#626semidirect
393. C3C22×#895semidirect
394. C3C22×#930semidirect
397. C2C2×#63909direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊(C3⋊D3)2
C23×C3×C4×D32
C23×#6262
C22×C3×C4⋊Dic32
C22×#37222
C2×#639092
C22×#9303
C22×#8953