Finite Group Databasebeta

← C22×#63923 #11900261

Subgroups — C22×#63923 #11900261

Order 1152.

9769 conjugacy classes of subgroups; only the 972 normal subgroups are shown.

normal subgroups only

This group has 9769 conjugacy classes of subgroups — too many to draw. Only its 972 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
1C24×D32C211yesmaximal, characteristic, complemented
2C23×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C23×#626C212yesmaximal, complemented
4C22×C3×(C2×D3)⋊C4C212yesmaximal, complemented
5C22×#3722C211yesmaximal, characteristic, complemented
6C2×#63923C2124yesmaximal, direct product factor
7C22×#882—32nomaximal
8C24×C3⋊D3C2211yescharacteristic
9C24×C3⋊D3C2211yescharacteristic, complemented
10C24×C3×D3C2212yes—
11C23×D32—28no—
12C23×D32—216no—
13C23×D32C22112yescomplemented
14C23×C32×C4C2211yescharacteristic, complemented
15C22×C4⋊(C3⋊D3)—28no—
16C22×C4⋊(C3⋊D3)C22112yescomplemented
17C23×C3×Dic3C2212yescomplemented
18C22×#626—216no—
19C22×#626C22124yescomplemented
20C2×C3×(C2×D3)⋊C4C22124yescomplemented
21C2×#3722C22112yescomplemented
22#63923C22164yesdirect product factor
23C25×D3—32no—
24C23×#67—32no—
25C23×D12—32no—
26C23×D12—32no—
27C23×D12—61no—
28C22×C3×C22⋊C4—32no—
29C22×(C2×D3)⋊C4—32no—
30C22×(C2×D3)⋊C4D312yescomplemented
31C2×#882—348no—
32C24×C32C2311yescharacteristic
33C23×C3⋊D3—28no—
34C23×C3⋊D3—24no—
35C23×C3⋊D3—28no—
36C23×C3⋊D3D418yescomplemented
37C23×C3⋊D3C2316yes—
38C23×C3⋊D3C2316yescomplemented
39C23×C3×D3—28no—
40C23×C3×D3—28no—
41C23×C3×D3D4116yescomplemented
42C23×C3×D3C23112yes—
43C22×D32—2128no—
44C22×D32—248no—
45C22×D32—296no—
46C22×D32C23116yescomplemented
47C22×C32×C4—24no—
48C22×C32×C4C2316yescomplemented
49C2×C4⋊(C3⋊D3)—248no—
50C2×C4⋊(C3⋊D3)C23116yescomplemented
51C22×C3×Dic3—28no—
52C22×C3×Dic3C23112yescomplemented
53C2×#626—296no—
54C2×#626C23132yescomplemented
55C3×(C2×D3)⋊C4C23132yescomplemented
56#3722C23116yescomplemented
57C22×#120—91noSylow
58C25×C3—32no—
59C24×D3—32no—
60C24×D3—32no—
61C24×D3—324no—
62C24×D3—61no—
63C24×D3—61no—
64C24×D3—616no—
65C24×D3—616no—
66C24×D3—616no—
67C24×D3C2×D312yes—
68C23×C3×C4—21no—
69C23×C3×C4—32no—
70C23×C3×C4C2×D312yescomplemented
71C22×#67—324no—
72C22×#67—616no—
73C23×Dic3C2×D312yescomplemented
74C22×D12—324no—
75C22×D12—324no—
76C22×D12—612no—
77C22×D12—616no—
78C22×D12—616no—
79C22×D12—616no—
80C2×C3×C22⋊C4—324no—
81C2×(C2×D3)⋊C4—324no—
82C2×(C2×D3)⋊C4C2×D3124yescomplemented
83#882—3128no—
84C23×C32C2×D418yes—
85C23×C32C2×D414yes—
86C23×C32C2413yes—
87C22×C3⋊D3—212no—
88C22×C3⋊D3—232no—
89C22×C3⋊D3—224no—
90C22×C3⋊D3—224no—
91C22×C3⋊D3—416no—
92C22×C3⋊D3C2×D4124yescomplemented
93C22×C3⋊D3C2414yes—
94C22×C3⋊D3C2414yescomplemented
95C22×C3×D3—264no—
96C22×C3×D3—224no—
97C22×C3×D3—224no—
98C22×C3×D3C2×D4148yescomplemented
99C22×C3×D3C2418yes—
100C2×D32—2384no—
101C2×D32—232no—
102C2×D32—264no—
103C2×C32×C4—212no—
104C2×C32×C4C2414yescomplemented
105C4⋊(C3⋊D3)—232no—
106C2×C3×Dic3—224no—
107C2×C3×Dic3C2418yescomplemented
108#626—264no—
109C26—91no—
110C23×D4—92no—
111C23×D4—91no—
112C2×#120—924no—
113C22×C22⋊C4—32no—
114C22×C22⋊C4—91no—
115C24×C3—21no—
116C24×C3—316no—
117C24×C3—312no—
118C24×C3—68no—
119C24×C3—68no—
120C24×C3C22×D312yes—
121C23×D3—28no—
122C23×D3—28no—
123C23×D3—316no—
124C23×D3—312no—
125C23×D3—312no—
126C23×D3—332no—
127C23×D3—68no—
128C23×D3—66no—
129C23×D3—66no—
130C23×D3—696no—
131C23×D3—696no—
132C23×D3—6256no—
133C23×D3—68no—
134C23×D3—68no—
135C23×D3—696no—
136C23×D3—68no—
137C23×D3—68no—
138C23×D3—68no—
139C23×D3—68no—
140C23×D3—128no—
141C23×D3—128no—
142C23×D3D12116yescomplemented
143C23×D3C22×D3112yes—
144C22×C3×C4—28no—
145C22×C3×C4—28no—
146C22×C3×C4—26no—
147C22×C3×C4—312no—
148C22×C3×C4—68no—
149C22×C3×C4C22×D3112yescomplemented
150C2×#67—332no—
151C2×#67—696no—
152C22×Dic3—28no—
153C22×Dic3C22×D3112yescomplemented
154C2×D12—332no—
155C2×D12—332no—
156C2×D12—616no—
157C2×D12—696no—
158C2×D12—696no—
159C2×D12—696no—
160C3×C22⋊C4—332no—
161(C2×D3)⋊C4—332no—
162(C2×D3)⋊C4C22×D3132yescomplemented
163C22×C32#120116yescomplemented
164C22×C32C22×D4112yes—
165C22×C32C22×D416yes—
166C22×C32C2511yescharacteristic
167C2×C3⋊D3—24no—
168C2×C3⋊D3—248no—
169C2×C3⋊D3—28no—
170C2×C3⋊D3—28no—
171C2×C3⋊D3—424no—
172C2×C3⋊D3C22×D418yescomplemented
173C2×C3×D3—296no—
174C2×C3×D3—28no—
175C2×C3×D3—28no—
176C2×C3×D3C22×D4116yescomplemented
177D32—2128no—
178C32×C4—24no—
179C3×Dic3—28no—
180C25—32no—
181C25—912no—
182C25—91no—
183C25—91no—
184C25—1816no—
185C25—188no—
186C22×D4—924no—
187C22×D4—912no—
188C22×D4—188no—
189C22×D4—1816no—
190C23×C4—32no—
191C23×C4D3211yescharacteristic, complemented
192#120—964no—
193C2×C22⋊C4—324no—
194C2×C22⋊C4—912no—
195C23×C3—23no—
196C23×C3—28no—
197C23×C3—24no—
198C23×C3—348no—
199C23×C3—38no—
200C23×C3—664no—
201C23×C3—624no—
202C23×C3—624no—
203C23×C3C2×D1218yes—
204C23×C3D3×D418yes—
205C23×C3D3×D418yes—
206C23×C3C23×D316yes—
207C22×D3—264no—
208C22×D3—224no—
209C22×D3—224no—
210C22×D3—348no—
211C22×D3—38no—
212C22×D3—38no—
213C22×D3—624no—
214C22×D3—64no—
215C22×D3—64no—
216C22×D3—664no—
217C22×D3—664no—
218C22×D3—6768no—
219C22×D3—664no—
220C22×D3—624no—
221C22×D3—624no—
222C22×D3—664no—
223C22×D3—624no—
224C22×D3—624no—
225C22×D3—624no—
226C22×D3—624no—
227C22×D3—1224no—
228C22×D3—1232no—
229C22×D3—1224no—
230C22×D3—1232no—
231C22×D3—1232no—
232C22×D3C2×D12148yescomplemented
233C22×D3C23×D318yes—
234C2×C3×C4—224no—
235C2×C3×C4—224no—
236C2×C3×C4—24no—
237C2×C3×C4—38no—
238C2×C3×C4—624no—
239C2×C3×C4C23×D318yescomplemented
240#67—664no—
241C2×Dic3—224no—
242C2×Dic3C23×D318yescomplemented
243D12—664no—
244D12—664no—
245D12—664no—
246C2×C32C2×#120112yescomplemented
247C2×C32C23×D412yes—
248C2×C32C23×D411yescharacteristic
249C3⋊D3—28no—
250C3⋊D3—44no—
251C3×D3—216no—
252C24—312no—
253C24—316no—
254C24—68no—
255C24—68no—
256C24—916no—
257C24—96no—
258C24—98no—
259C24—96no—
260C24—1896no—
261C24—1848no—
262C24—18128no—
263C24—188no—
264C24—188no—
265C24—184no—
266C24C2×D3211yescharacteristic
267C2×D4—932no—
268C2×D4—916no—
269C2×D4—1848no—
270C2×D4—1896no—
271C22×C4—24no—
272C22×C4—312no—
273C22×C4—68no—
274C22×C4C2×D3216yescomplemented
275C22⋊C4—332no—
276C22⋊C4—916no—
277C22×C3—212no—
278C22×C3—26no—
279C22×C3—21no—
280C22×C3—216no—
281C22×C3—316no—
282C22×C3—68no—
283C22×C3—68no—
284C22×C3—696no—
285C22×C3#882132yescomplemented
286C22×C3C22×D12112yes—
287C22×C3C2×D3×D4112yes—
288C22×C3C2×D3×D4112yes—
289C22×C3C24×D312yes—
290C2×D3—28no—
291C2×D3—28no—
292C2×D3—296no—
293C2×D3—316no—
294C2×D3—68no—
295C2×D3—6256no—
296C2×D3—68no—
297C2×D3—68no—
298C2×D3—696no—
299C2×D3—68no—
300C2×D3—68no—
301C2×D3—68no—
302C2×D3—68no—
303C2×D3—128no—
304C2×D3—1248no—
305C2×D3—128no—
306C2×D3—1248no—
307C2×D3—1248no—
308C2×D3C22×D12116yescomplemented
309C3×C4—28no—
310C3×C4—28no—
311C3×C4—68no—
312Dic3—28no—
313C32C22×#12011yescharacteristic, complemented, Sylow
314C23—348no—
315C23—38no—
316C23—624no—
317C23—624no—
318C23—664no—
319C23—924no—
320C23—94no—
321C23—94no—
322C23—1864no—
323C23—1832no—
324C23—18384no—
325C23—1824no—
326C23—1832no—
327C23—1824no—
328C23—1812no—
329C23—3616no—
330C23D3×D1218yes—
331C23#381114yes—
332C23C22×D3213yes—
333D4—1832no—
334D4—1864no—
335C2×C4—212no—
336C2×C4—38no—
337C2×C4—624no—
338C2×C4C22×D3214yescomplemented
339C2×C3—22no—
340C2×C3—21no—
341C2×C3—212no—
342C2×C3—616no—
343C2×C3C2×#882124yescomplemented
344C2×C3C23×D1212yes—
345C2×C3C22×D3×D412yes—
346C2×C3C22×D3×D412yes—
347D3—216no—
348D3—616no—
349D3—128no—
350D3—128no—
351D3—128no—
352C22—316no—
353C22—68no—
354C22—68no—
355C22—696no—
356C22—98no—
357C22—18128no—
358C22—188no—
359C22—1848no—
360C22—188no—
361C22—184no—
362C22—3624no—
363C22#63923116yesdirect product factor
364C22C2×D3×D12112yes—
365C22C2×#381116yes—
366C22C23×D3211yescharacteristic
367C4—24no—
368C4—68no—
369C3—21no—
370C3C22×#88212yescomplemented
371C2—616no—
372C2—188no—
373C2—364no—
374C2C2×#63923112yesdirect product factor
375C2C22×D3×D1212yes—
376C2C22×#381111yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC24×C32C23
hypercenterC23×C4D32
hypocenterC32C22×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C24×D32C2semidirect
2. C23×C4⋊(C3⋊D3)C2semidirect
3. C23×#626C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C22×#3722C2semidirect
6. C2×#63923C2direct (N × H)
9. C24×C3⋊D3C22semidirect
13. C23×D32C22semidirect
14. C23×C32×C4C22semidirect
16. C22×C4⋊(C3⋊D3)C22semidirect
17. C23×C3×Dic3C22semidirect
19. C22×#626C22semidirect
20. C2×C3×(C2×D3)⋊C4C22semidirect
21. C2×#3722C22semidirect
22. #63923C22direct (N × H)
30. C22×(C2×D3)⋊C4D3semidirect
36. C23×C3⋊D3D4semidirect
38. C23×C3⋊D3C23semidirect
41. C23×C3×D3D4semidirect
46. C22×D32C23semidirect
48. C22×C32×C4C23semidirect
50. C2×C4⋊(C3⋊D3)C23semidirect
52. C22×C3×Dic3C23semidirect
54. C2×#626C23semidirect
55. C3×(C2×D3)⋊C4C23semidirect
56. #3722C23semidirect
70. C23×C3×C4C2×D3semidirect
73. C23×Dic3C2×D3semidirect
82. C2×(C2×D3)⋊C4C2×D3semidirect
92. C22×C3⋊D3C2×D4semidirect
94. C22×C3⋊D3C24semidirect
98. C22×C3×D3C2×D4semidirect
104. C2×C32×C4C24semidirect
107. C2×C3×Dic3C24semidirect
142. C23×D3D12semidirect
149. C22×C3×C4C22×D3semidirect
153. C22×Dic3C22×D3semidirect
162. (C2×D3)⋊C4C22×D3semidirect
163. C22×C32#120semidirect
172. C2×C3⋊D3C22×D4semidirect
176. C2×C3×D3C22×D4semidirect
191. C23×C4D32semidirect
232. C22×D3C2×D12semidirect
239. C2×C3×C4C23×D3semidirect
242. C2×Dic3C23×D3semidirect
246. C2×C32C2×#120semidirect
274. C22×C4C2×D32semidirect
285. C22×C3#882semidirect
308. C2×D3C22×D12semidirect
313. C32C22×#120semidirect
338. C2×C4C22×D32semidirect
343. C2×C3C2×#882semidirect
363. C22#63923direct (N × H)
370. C3C22×#882semidirect
374. C2C2×#63923direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D322
C23×C4⋊(C3⋊D3)2
C23×#6262
C22×C3×(C2×D3)⋊C42
C22×#37222
C2×#639232
C22×#8823