Finite Group Databasebeta

← C22×#63926 #11918539

Subgroups — C22×#63926 #11918539

Order 1152.

4633 conjugacy classes of subgroups; only the 692 normal subgroups are shown.

normal subgroups only

This group has 4633 conjugacy classes of subgroups — too many to draw. Only its 692 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
1C22×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#3802C211yesmaximal, characteristic, complemented
3C22×C3×#213C212yesmaximal, complemented
4C2×#63926C2124yesmaximal, direct product factor
5C22×#3714C212yesmaximal, complemented
6C22×#3710C211yesmaximal, characteristic, complemented
7C22×D3×D8—32nomaximal
8C24×C3⋊D3—21no—
9C23×D32—21no—
10C22×C32×D4C2211yescharacteristic, complemented
11C22×#638—21no—
12C2×D4×C3⋊D3—26no—
13C2×D4×C3⋊D3C22112yescomplemented
14C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×D12C2212yescomplemented
17C22×#625—21no—
18C2×#3802—26no—
19C2×#3802C22112yescomplemented
20C2×C3×#213C22124yescomplemented
21C22×C3×C3⋊C8C2212yescomplemented
22#63926C22164yesdirect product factor
23C2×#3714C22124yescomplemented
24C2×#3710C22112yescomplemented
25C22×D3×D4—32no—
26C22×D3×D4—32no—
27C22×D3×D4—61no—
28C22×C3×D8—32no—
29C22×#213—32no—
30C22×#213D312yescomplemented
31C2×D3×D8—348no—
32C22×D24—32no—
33C22×D3×C8—32no—
34C24×C32—21no—
35C23×C3⋊D3—21no—
36C23×C3⋊D3—212no—
37C23×C3⋊D3—48no—
38C23×C3⋊D3D411yescharacteristic
39C23×C3×D3—22no—
40C22×D32—212no—
41C22×D32—48no—
42C2×C32×D4—23no—
43C2×C32×D4C2316yescomplemented
44C22×C32×C4C2311yescharacteristic
45C2×#638—212no—
46C22×C3⋊Dic3D411yescharacteristic
47D4×C3⋊D3—224no—
48D4×C3⋊D3C23116yescomplemented
49C2×C4⋊(C3⋊D3)—23no—
50C2×C4⋊(C3⋊D3)C2316yescomplemented
51C2×C4×C3⋊D3D416yes—
52C2×C4×C3⋊D3C2316yes—
53C2×C3×D12—26no—
54C2×C3×D12C23112yescomplemented
55C2×#625—212no—
56#3802—224no—
57#3802C23116yescomplemented
58C3×#213C23132yescomplemented
59C2×C3×C3⋊C8C23112yescomplemented
60#3714C23132yescomplemented
61#3710C23116yescomplemented
62C23×D8—91noSylow
63C24×D3—62no—
64C24×D3—62no—
65C24×D3—62no—
66C22×C3×D4—21no—
67C22×C3×D4—32no—
68C22×C3×D4C2×D312yescomplemented
69C22×#67—62no—
70C22×#67—62no—
71C22×#67—62no—
72C2×D3×D4—324no—
73C2×D3×D4—324no—
74C2×D3×D4—612no—
75C2×D3×D4—612no—
76C2×D3×D4—612no—
77C2×D3×D4—612no—
78C22×D12—32no—
79C22×D12—61no—
80C22×D12C2×D312yescomplemented
81C22×C4×D3—32no—
82C22×C4×D3—61no—
83C2×C3×D8—324no—
84C22×C3×C8—32no—
85C2×#213—324no—
86C2×#213C2×D3124yescomplemented
87C22×C3⋊C8C2×D312yescomplemented
88D3×D8—3128no—
89C2×D24—324no—
90C2×D3×C8—324no—
91C23×C32—26no—
92C23×C32—44no—
93C23×C32C2×D411yescharacteristic
94C22×C3⋊D3—26no—
95C22×C3⋊D3—216no—
96C22×C3⋊D3—44no—
97C22×C3⋊D3—448no—
98C22×C3⋊D3D818yescomplemented
99C22×C3⋊D3C2×D416yes—
100C22×C3×D3—212no—
101C22×C3×D3—48no—
102C2×D32—216no—
103C2×D32—448no—
104C32×D4—26no—
105C32×D4C2414yescomplemented
106C2×C32×C4C2×D413yes—
107C2×C32×C4C2413yes—
108#638—216no—
109C2×C3⋊Dic3C2×D416yes—
110C4⋊(C3⋊D3)—26no—
111C4⋊(C3⋊D3)C2414yescomplemented
112C4×C3⋊D3C2×D4112yes—
113C4×C3⋊D3C2414yes—
114C3×D12—212no—
115C3×D12C2418yescomplemented
116#625—216no—
117C3×C3⋊C8C2418yescomplemented
118C23×D4—91no—
119C23×D4—91no—
120C22×D8—32no—
121C22×D8—92no—
122C22×D8—924no—
123C23×C8—91no—
124C24×C3—22no—
125C24×C3—22no—
126C24×C3—62no—
127C23×D3—22no—
128C23×D3—32no—
129C23×D3—61no—
130C23×D3—624no—
131C23×D3—624no—
132C23×D3—62no—
133C23×D3—624no—
134C23×D3—62no—
135C23×D3—1216no—
136C23×D3—1216no—
137C23×D3—1216no—
138C2×C3×D4—26no—
139C2×C3×D4—26no—
140C2×C3×D4—26no—
141C2×C3×D4—312no—
142C2×C3×D4—66no—
143C2×C3×D4C22×D3112yescomplemented
144C22×C3×C4—21no—
145C22×C3×C4C22×D312yes—
146C2×#67—624no—
147C2×#67—624no—
148C2×#67—624no—
149C22×Dic3—32no—
150C22×Dic3—61no—
151D3×D4—332no—
152D3×D4—332no—
153D3×D4—616no—
154D3×D4—648no—
155D3×D4—648no—
156D3×D4—648no—
157C2×D12—26no—
158C2×D12—312no—
159C2×D12—66no—
160C2×D12—66no—
161C2×D12—66no—
162C2×D12C22×D3112yescomplemented
163C2×C4×D3—312no—
164C2×C4×D3—312no—
165C2×C4×D3—66no—
166C2×C4×D3—66no—
167C3×D8—332no—
168C2×C3×C8—312no—
169#213—332no—
170#213C22×D3132yescomplemented
171C2×C3⋊C8C22×D3112yescomplemented
172D24—332no—
173D3×C8—332no—
174C22×C32—24no—
175C22×C32—412no—
176C22×C32C2×D814yescomplemented
177C22×C32C22×D413yes—
178C2×C3⋊D3—24no—
179C2×C3⋊D3—412no—
180C2×C3⋊D3—432no—
181C2×C3⋊D3C2×D8124yescomplemented
182C2×C3⋊D3C22×D414yes—
183C2×C3×D3—28no—
184C2×C3×D3—424no—
185D32—432no—
186C32×C4C22×D413yes—
187C32×C4C2511yescharacteristic
188C3⋊Dic3C22×D414yes—
189C25—181no—
190C25—181no—
191C22×D4—32no—
192C22×D4—912no—
193C22×D4—912no—
194C22×D4—91no—
195C22×D4—186no—
196C22×D4—186no—
197C22×D4—181no—
198C22×D4—181no—
199C22×D4D3211yescharacteristic, complemented
200C23×C4—91no—
201C2×D8—324no—
202C2×D8—924no—
203C2×D8—964no—
204C22×C8—32no—
205C22×C8—912no—
206C23×C3—212no—
207C23×C3—212no—
208C23×C3—21no—
209C23×C3—48no—
210C23×C3—48no—
211C23×C3—612no—
212C23×C3—128no—
213C23×C3D3×D412yes—
214C22×D3—212no—
215C22×D3—316no—
216C22×D3—312no—
217C22×D3—48no—
218C22×D3—68no—
219C22×D3—66no—
220C22×D3—632no—
221C22×D3—632no—
222C22×D3—612no—
223C22×D3—632no—
224C22×D3—612no—
225C22×D3—1296no—
226C22×D3—1296no—
227C22×D3—1296no—
228C22×D3—128no—
229C22×D3—128no—
230C3×D4—212no—
231C3×D4—212no—
232C3×D4—24no—
233C3×D4—38no—
234C3×D4—612no—
235C3×D4C23×D318yescomplemented
236C2×C3×C4—23no—
237C2×C3×C4—23no—
238C2×C3×C4D3×D416yes—
239C2×C3×C4C23×D316yes—
240#67—632no—
241#67—632no—
242#67—632no—
243C2×Dic3—312no—
244C2×Dic3—66no—
245D12—212no—
246D12—38no—
247D12—64no—
248D12—612no—
249D12—612no—
250D12C23×D318yescomplemented
251C4×D3—324no—
252C4×D3—38no—
253C4×D3—612no—
254C4×D3—64no—
255C3×C8—38no—
256C3⋊C8C23×D318yescomplemented
257C2×C32—44no—
258C2×C32C22×D816yescomplemented
259C2×C32C23×D411yescharacteristic
260C3⋊D3—44no—
261C3⋊D3C22×D818yescomplemented
262C3×D3—48no—
263C24—21no—
264C24—62no—
265C24—91no—
266C24—1812no—
267C24—1812no—
268C24—181no—
269C24—368no—
270C24—368no—
271C2×D4—23no—
272C2×D4—312no—
273C2×D4—66no—
274C2×D4—916no—
275C2×D4—916no—
276C2×D4—96no—
277C2×D4—1824no—
278C2×D4—1824no—
279C2×D4—1812no—
280C2×D4—1812no—
281C2×D4—183no—
282C2×D4C2×D3216yescomplemented
283C22×C4—91no—
284C22×C4—96no—
285C22×C4—96no—
286C22×C4C2×D3211yescharacteristic
287D8—332no—
288D8—932no—
289C2×C8—312no—
290C2×C8—916no—
291C22×C3—28no—
292C22×C3—28no—
293C22×C3—23no—
294C22×C3—24no—
295C22×C3—424no—
296C22×C3—424no—
297C22×C3—68no—
298C22×C3—1224no—
299C22×C3D3×D818yescomplemented
300C22×C3C2×D3×D416yes—
301C2×D3—28no—
302C2×D3—38no—
303C2×D3—348no—
304C2×D3—424no—
305C2×D3—64no—
306C2×D3—624no—
307C2×D3—68no—
308C2×D3—68no—
309C2×D3—1264no—
310C2×D3—1264no—
311C2×D3—1264no—
312C2×D3—1224no—
313C2×D3—1224no—
314C3×C4—23no—
315C3×C4—21no—
316C3×C4C2×D3×D416yes—
317C3×C4C24×D312yes—
318Dic3—38no—
319Dic3—64no—
320C32C23×D811yescharacteristic, complemented, Sylow
321C23—26no—
322C23—44no—
323C23—612no—
324C23—96no—
325C23—98no—
326C23—128no—
327C23—1816no—
328C23—1816no—
329C23—186no—
330C23—3648no—
331C23—3648no—
332C23—364no—
333C23#381111yescharacteristic
334D4—26no—
335D4—38no—
336D4—612no—
337D4—94no—
338D4—1816no—
339D4—1816no—
340D4—186no—
341D4C22×D3214yescomplemented
342C2×C4—96no—
343C2×C4—912no—
344C2×C4—94no—
345C2×C4#381113yes—
346C2×C4C22×D3213yes—
347C8—38no—
348C2×C3—26no—
349C2×C3—21no—
350C2×C3—48no—
351C2×C3—48no—
352C2×C3—128no—
353C2×C3C2×D3×D8112yescomplemented
354C2×C3C22×D3×D412yes—
355D3—316no—
356D3—48no—
357D3—68no—
358D3—128no—
359D3—128no—
360C22—24no—
361C22—412no—
362C22—68no—
363C22—924no—
364C22—94no—
365C22—1224no—
366C22—184no—
367C22—3632no—
368C22—3632no—
369C22—3612no—
370C22#6392614yesdirect product factor
371C22C2×#381113yes—
372C4—94no—
373C4C2×#381113yes—
374C4C23×D3211yescharacteristic
375C3—21no—
376C3C22×D3×D812yescomplemented
377C2—44no—
378C2—98no—
379C2—128no—
380C2—364no—
381C2C2×#6392616yesdirect product factor
382C2C22×#381111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C23×D8
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×D4×C3⋊D3C2semidirect
2. C22×#3802C2semidirect
3. C22×C3×#213C2semidirect
4. C2×#63926C2direct (N × H)
5. C22×#3714C2semidirect
6. C22×#3710C2semidirect
10. C22×C32×D4C22semidirect
13. C2×D4×C3⋊D3C22semidirect
14. C22×C4⋊(C3⋊D3)C22semidirect
16. C22×C3×D12C22semidirect
19. C2×#3802C22semidirect
20. C2×C3×#213C22semidirect
21. C22×C3×C3⋊C8C22semidirect
22. #63926C22direct (N × H)
23. C2×#3714C22semidirect
24. C2×#3710C22semidirect
30. C22×#213D3semidirect
43. C2×C32×D4C23semidirect
48. D4×C3⋊D3C23semidirect
50. C2×C4⋊(C3⋊D3)C23semidirect
54. C2×C3×D12C23semidirect
57. #3802C23semidirect
58. C3×#213C23semidirect
59. C2×C3×C3⋊C8C23semidirect
60. #3714C23semidirect
61. #3710C23semidirect
68. C22×C3×D4C2×D3semidirect
80. C22×D12C2×D3semidirect
86. C2×#213C2×D3semidirect
87. C22×C3⋊C8C2×D3semidirect
98. C22×C3⋊D3D8semidirect
105. C32×D4C24semidirect
111. C4⋊(C3⋊D3)C24semidirect
115. C3×D12C24semidirect
117. C3×C3⋊C8C24semidirect
143. C2×C3×D4C22×D3semidirect
162. C2×D12C22×D3semidirect
170. #213C22×D3semidirect
171. C2×C3⋊C8C22×D3semidirect
176. C22×C32C2×D8semidirect
181. C2×C3⋊D3C2×D8semidirect
199. C22×D4D32semidirect
235. C3×D4C23×D3semidirect
250. D12C23×D3semidirect
256. C3⋊C8C23×D3semidirect
258. C2×C32C22×D8semidirect
261. C3⋊D3C22×D8semidirect
282. C2×D4C2×D32semidirect
299. C22×C3D3×D8semidirect
320. C32C23×D8semidirect
341. D4C22×D32semidirect
353. C2×C3C2×D3×D8semidirect
370. C22#63926direct (N × H)
376. C3C22×D3×D8semidirect
381. C2C2×#63926direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C22×#38022
C22×C3×#2132
C2×#639262
C22×#37142
C22×#37102
C22×D3×D83