Finite Group Databasebeta

← C22×#63908 #11900298

Subgroups — C22×#63908 #11900298

Order 1152.

5265 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D12C211yesmaximal, characteristic, complemented
2C23×C3×C4×D3C211yesmaximal, characteristic, complemented
3C23×#625C212yesmaximal, complemented
4C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5C22×(C2×D3)⋊Dic3C212yesmaximal, complemented
6C2×#63908C2124yesmaximal, direct product factor
7C22×#938—31nomaximal
8C22×#930—31nomaximal
9C24×C3×D3C2212yes—
10C24×C3×D3C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2212yes—
13C23×C3×Dic3C2211yescharacteristic
14C22×C3×D12—28no—
15C22×C3×D12C22112yescomplemented
16C22×C3×C4×D3—28no—
17C22×C3×C4×D3C22112yescomplemented
18C22×#625—216no—
19C22×#625C22124yescomplemented
20C2×C4⋊(C3⋊Dic3)C22112yescomplemented
21C2×(C2×D3)⋊Dic3C22124yescomplemented
22#63908C22164yesdirect product factor
23C23×C3×D4—31no—
24C24×C3×C4—31no—
25C23×#67—32no—
26C23×#67—32no—
27C23×D12D311yescharacteristic, complemented
28C23×C4×D3D311yescharacteristic, complemented
29C22×#217—32no—
30C2×#938—324no—
31C2×#930—324no—
32C22×(C2×D3)⋊C4—32no—
33C22×C4⋊Dic3—31no—
34C22×C4⋊Dic3—31no—
35C22×C4⋊Dic3—61no—
36C24×C32C2311yescharacteristic
37C23×C3×D3—24no—
38C23×C3×D3—24no—
39C23×C3×D3—28no—
40C23×C3×D3—28no—
41C23×C3×D3—28no—
42C23×C3×D3D418yescomplemented
43C23×C3×D3C23112yes—
44C23×C3×D3C2316yes—
45C22×C32×C4D418yescomplemented
46C22×C32×C4C2316yes—
47C22×C3⋊Dic3—28no—
48C22×C3⋊Dic3C23112yes—
49C22×C3×Dic3—24no—
50C22×C3×Dic3C2316yes—
51C2×C3×D12—248no—
52C2×C3×D12C23116yescomplemented
53C2×C3×C4×D3—248no—
54C2×C3×C4×D3C23116yescomplemented
55C2×#625—296no—
56C2×#625C23132yescomplemented
57C4⋊(C3⋊Dic3)C23116yescomplemented
58(C2×D3)⋊Dic3C23132yescomplemented
59C22×#121—91noSylow
60C25×C3—31no—
61C25×C3—32no—
62C24×D3C2×D312yes—
63C24×D3C2×D311yescharacteristic
64C22×C3×D4—312no—
65C22×C3×D4—68no—
66C23×C3×C4—21no—
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—324no—
74C22×#67—616no—
75C22×#67—616no—
76C23×Dic3—32no—
77C23×Dic3—32no—
78C23×Dic3—62no—
79C23×Dic3C2×D311yescharacteristic
80C22×D12—28no—
81C22×D12C2×D3112yescomplemented
82C22×C4×D3—28no—
83C22×C4×D3C2×D3112yescomplemented
84C2×#217—324no—
85#938—364no—
86#930—364no—
87C2×(C2×D3)⋊C4—324no—
88C2×C4⋊Dic3—312no—
89C2×C4⋊Dic3—312no—
90C2×C4⋊Dic3—612no—
91C23×C32C2×D414yes—
92C23×C32C2×D414yes—
93C23×C32#4114yes—
94C23×C32C2413yes—
95C22×C3×D3—232no—
96C22×C3×D3—212no—
97C22×C3×D3—212no—
98C22×C3×D3—224no—
99C22×C3×D3—224no—
100C22×C3×D3—224no—
101C22×C3×D3—432no—
102C22×C3×D3C2×D4124yescomplemented
103C22×C3×D3C2418yes—
104C22×C3×D3C2414yes—
105C2×C32×C4C2×D4124yescomplemented
106C2×C32×C4C2414yes—
107C2×C3⋊Dic3—224no—
108C2×C3⋊Dic3C2418yes—
109C2×C3×Dic3—212no—
110C2×C3×Dic3C2414yes—
111C3×D12—232no—
112C3×C4×D3—232no—
113#625—264no—
114C23×D4—31no—
115C23×D4—92no—
116C24×C4—31no—
117C2×#121—924no—
118C22×C4⋊C4—91no—
119C22×C22⋊C4—92no—
120C24×C3—21no—
121C24×C3—38no—
122C24×C3—36no—
123C24×C3—312no—
124C24×C3—64no—
125C24×C3—64no—
126C24×C3—68no—
127C24×C3—68no—
128C24×C3—68no—
129C24×C3C22×D311yescharacteristic
130C24×C3C22×D311yescharacteristic
131C23×D3—24no—
132C23×D3—24no—
133C23×D3—28no—
134C23×D3—28no—
135C23×D3—28no—
136C23×D3D1218yescomplemented
137C23×D3C22×D3112yes—
138C23×D3C22×D316yes—
139C2×C3×D4—316no—
140C2×C3×D4—648no—
141C22×C3×C4—28no—
142C22×C3×C4—26no—
143C22×C3×C4—36no—
144C22×C3×C4—316no—
145C22×C3×C4—64no—
146C22×C3×C4—648no—
147C22×C3×C4#6718yescomplemented
148C22×C3×C4#6718yescomplemented
149C22×C3×C4C22×D316yes—
150C22×C3×C4C22×D316yes—
151C2×#67—332no—
152C2×#67—332no—
153C2×#67—696no—
154C2×#67—696no—
155C22×Dic3—24no—
156C22×Dic3—312no—
157C22×Dic3—312no—
158C22×Dic3—612no—
159C22×Dic3—68no—
160C22×Dic3—68no—
161C22×Dic3—128no—
162C22×Dic3C22×D316yes—
163C2×D12—248no—
164C2×D12C22×D3116yescomplemented
165C2×C4×D3—248no—
166C2×C4×D3C22×D3116yescomplemented
167#217—332no—
168(C2×D3)⋊C4—332no—
169C4⋊Dic3—316no—
170C4⋊Dic3—316no—
171C4⋊Dic3—616no—
172C22×C32#121116yescomplemented
173C22×C32C22×D416yes—
174C22×C32C22×D416yes—
175C22×C32C2×#4116yes—
176C22×C32C2511yescharacteristic
177C2×C3×D3—248no—
178C2×C3×D3—24no—
179C2×C3×D3—24no—
180C2×C3×D3—28no—
181C2×C3×D3—28no—
182C2×C3×D3—28no—
183C2×C3×D3—448no—
184C2×C3×D3C22×D418yescomplemented
185C32×C4C22×D418yescomplemented
186C3⋊Dic3—28no—
187C3×Dic3—24no—
188C25—31no—
189C25—32no—
190C22×D4—312no—
191C22×D4—68no—
192C22×D4—924no—
193C22×D4—1816no—
194C23×C4—31no—
195C23×C4—312no—
196C23×C4—68no—
197C23×C4—92no—
198C23×C4D3211yescharacteristic
199#121—964no—
200C2×C4⋊C4—912no—
201C2×C22⋊C4—924no—
202C23×C3—23no—
203C23×C3—24no—
204C23×C3—24no—
205C23×C3—24no—
206C23×C3—324no—
207C23×C3—34no—
208C23×C3—38no—
209C23×C3—632no—
210C23×C3—612no—
211C23×C3—612no—
212C23×C3—624no—
213C23×C3—624no—
214C23×C3—624no—
215C23×C3—1232no—
216C23×C3C2×D1214yes—
217C23×C3#23514yes—
218C23×C3D3×D414yes—
219C23×C3#23714yes—
220C23×C3C2×#6714yes—
221C23×C3C2×#6714yes—
222C23×C3C23×D313yes—
223C23×C3C23×D313yes—
224C22×D3—232no—
225C22×D3—212no—
226C22×D3—212no—
227C22×D3—224no—
228C22×D3—224no—
229C22×D3—224no—
230C22×D3—432no—
231C22×D3C2×D12124yescomplemented
232C22×D3C23×D318yes—
233C22×D3C23×D314yes—
234C3×D4—632no—
235C2×C3×C4—24no—
236C2×C3×C4—224no—
237C2×C3×C4—34no—
238C2×C3×C4—612no—
239C2×C3×C4—632no—
240C2×C3×C4C2×#67124yescomplemented
241C2×C3×C4C2×#67124yescomplemented
242C2×C3×C4C23×D314yes—
243C2×C3×C4C23×D314yes—
244#67—664no—
245#67—664no—
246C2×Dic3—212no—
247C2×Dic3—38no—
248C2×Dic3—38no—
249C2×Dic3—68no—
250C2×Dic3—624no—
251C2×Dic3—624no—
252C2×Dic3—1224no—
253C2×Dic3C23×D314yes—
254D12—232no—
255C4×D3—232no—
256C2×C32C2×#121112yescomplemented
257C2×C32C23×D411yescharacteristic
258C2×C32C23×D411yescharacteristic
259C2×C32C22×#4111yescharacteristic
260C3×D3—28no—
261C3×D3—48no—
262C24—36no—
263C24—38no—
264C24—312no—
265C24—64no—
266C24—64no—
267C24—68no—
268C24—68no—
269C24—68no—
270C24C2×D3211yescharacteristic
271C2×D4—316no—
272C2×D4—648no—
273C2×D4—932no—
274C2×D4—1896no—
275C22×C4—36no—
276C22×C4—316no—
277C22×C4—64no—
278C22×C4—648no—
279C22×C4—912no—
280C22×C4—188no—
281C22×C4#62518yescomplemented
282C22×C4C2×D3216yes—
283C4⋊C4—916no—
284C22⋊C4—932no—
285C22×C3—26no—
286C22×C3—26no—
287C22×C3—26no—
288C22×C3—21no—
289C22×C3—216no—
290C22×C3—38no—
291C22×C3—64no—
292C22×C3—64no—
293C22×C3—648no—
294C22×C3—68no—
295C22×C3—68no—
296C22×C3—68no—
297C22×C3—1248no—
298C22×C3#930116yescomplemented
299C22×C3#938116yescomplemented
300C22×C3C22×D1216yes—
301C22×C3C2×#23516yes—
302C22×C3C2×D3×D416yes—
303C22×C3C2×#23716yes—
304C22×C3C22×#6716yes—
305C22×C3C22×#6716yes—
306C22×C3C24×D311yescharacteristic
307C22×C3C24×D311yescharacteristic
308C2×D3—24no—
309C2×D3—24no—
310C2×D3—248no—
311C2×D3—28no—
312C2×D3—28no—
313C2×D3—28no—
314C2×D3—448no—
315C2×D3C22×D1218yescomplemented
316C3×C4—28no—
317C3×C4—64no—
318C3×C4C22×#6718yescomplemented
319C3×C4C22×#6718yescomplemented
320Dic3—24no—
321Dic3—68no—
322Dic3—68no—
323Dic3—128no—
324C32C22×#12111yescharacteristic, complemented, Sylow
325C23—324no—
326C23—34no—
327C23—38no—
328C23—612no—
329C23—612no—
330C23—632no—
331C23—624no—
332C23—624no—
333C23—624no—
334C23—1232no—
335C23#379514yes—
336C23D3×D1214yes—
337C23C2×#62514yes—
338C23C22×D3213yes—
339D4—632no—
340D4—1864no—
341C2×C4—34no—
342C2×C4—612no—
343C2×C4—632no—
344C2×C4—98no—
345C2×C4—1824no—
346C2×C4C2×#625124yescomplemented
347C2×C4C22×D3214yes—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—212no—
352C2×C3—68no—
353C2×C3—128no—
354C2×C3C2×#930112yescomplemented
355C2×C3C2×#938112yescomplemented
356C2×C3C23×D1211yescharacteristic
357C2×C3C22×#23511yescharacteristic
358C2×C3C22×D3×D411yescharacteristic
359C2×C3C22×#23711yescharacteristic
360C2×C3C23×#6711yescharacteristic
361C2×C3C23×#6711yescharacteristic
362D3—28no—
363D3—48no—
364C22—38no—
365C22—64no—
366C22—64no—
367C22—648no—
368C22—68no—
369C22—68no—
370C22—68no—
371C22—1248no—
372C22#63908116yesdirect product factor
373C22C2×#379516yes—
374C22C2×D3×D1216yes—
375C22C22×#62516yes—
376C22C23×D3211yescharacteristic
377C4—64no—
378C4—188no—
379C4C22×#62518yescomplemented
380C3—21no—
381C3C22×#93011yescharacteristic, complemented
382C3C22×#93811yescharacteristic, complemented
383C2—68no—
384C2—128no—
385C2C2×#63908112yesdirect product factor
386C2C22×#379511yescharacteristic
387C2C22×D3×D1211yescharacteristic
388C2C23×#62511yescharacteristic
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×C3×D12C2semidirect
2. C23×C3×C4×D3C2semidirect
3. C23×#625C2semidirect
4. C22×C4⋊(C3⋊Dic3)C2semidirect
5. C22×(C2×D3)⋊Dic3C2semidirect
6. C2×#63908C2direct (N × H)
15. C22×C3×D12C22semidirect
17. C22×C3×C4×D3C22semidirect
19. C22×#625C22semidirect
20. C2×C4⋊(C3⋊Dic3)C22semidirect
21. C2×(C2×D3)⋊Dic3C22semidirect
22. #63908C22direct (N × H)
27. C23×D12D3semidirect
28. C23×C4×D3D3semidirect
42. C23×C3×D3D4semidirect
45. C22×C32×C4D4semidirect
52. C2×C3×D12C23semidirect
54. C2×C3×C4×D3C23semidirect
56. C2×#625C23semidirect
57. C4⋊(C3⋊Dic3)C23semidirect
58. (C2×D3)⋊Dic3C23semidirect
81. C22×D12C2×D3semidirect
83. C22×C4×D3C2×D3semidirect
102. C22×C3×D3C2×D4semidirect
105. C2×C32×C4C2×D4semidirect
136. C23×D3D12semidirect
147. C22×C3×C4#67semidirect
148. C22×C3×C4#67semidirect
164. C2×D12C22×D3semidirect
166. C2×C4×D3C22×D3semidirect
172. C22×C32#121semidirect
184. C2×C3×D3C22×D4semidirect
185. C32×C4C22×D4semidirect
231. C22×D3C2×D12semidirect
240. C2×C3×C4C2×#67semidirect
241. C2×C3×C4C2×#67semidirect
256. C2×C32C2×#121semidirect
281. C22×C4#625semidirect
298. C22×C3#930semidirect
299. C22×C3#938semidirect
315. C2×D3C22×D12semidirect
318. C3×C4C22×#67semidirect
319. C3×C4C22×#67semidirect
324. C32C22×#121semidirect
346. C2×C4C2×#625semidirect
354. C2×C3C2×#930semidirect
355. C2×C3C2×#938semidirect
372. C22#63908direct (N × H)
379. C4C22×#625semidirect
381. C3C22×#930semidirect
382. C3C22×#938semidirect
385. C2C2×#63908direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D122
C23×C3×C4×D32
C23×#6252
C22×C4⋊(C3⋊Dic3)2
C22×(C2×D3)⋊Dic32
C2×#639082
C22×#9383
C22×#9303