Finite Group Databasebeta

← C22×#63365 #11857485

Subgroups — C22×#63365 #11857485

Order 1152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#611C211yesmaximal, characteristic
2C22×C9×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×#3676C211yesmaximal, characteristic, complemented
4C2×#63365C2112yesmaximal, direct product factor
5C22×#806—31nomaximal
6C25×C9C2211yescharacteristic
7C24×D9C411yescharacteristic, complemented
8C23×C4×C9—21no—
9C22×#611—21no—
10C22×#611—21no—
11C22×#611—23no—
12C22×#611—23no—
13C22×#611C416yescomplemented
14C22×#611C2216yes—
15C23×Dic9—21no—
16C23×Dic9C411yescharacteristic, complemented
17C2×C9×C22⋊C4—23no—
18C2×C9×C22⋊C4C2216yescomplemented
19C2×#3676—23no—
20C2×#3676C2216yescomplemented
21#63365C22116yesdirect product factor
22C23×#67—31no—
23C22×C3×C22⋊C4D311yescharacteristic
24C22×#217—31no—
25C2×#806—312no—
26C24×C9—44no—
27C24×C9C2×C411yescharacteristic
28C24×C9C2×C413yes—
29C24×C9D411yescharacteristic
30C24×C9D411yescharacteristic
31C24×C9D413yes—
32C24×C9D413yes—
33C24×C9C2313yes—
34C23×D9—23no—
35C23×D9—21no—
36C23×D9—44no—
37C23×D9C2×C416yescomplemented
38C22×C4×C9—26no—
39C22×C4×C9—44no—
40C2×#611—26no—
41C2×#611—26no—
42C2×#611—212no—
43C2×#611—26no—
44C2×#611—26no—
45C2×#611—26no—
46C2×#611—26no—
47C2×#611C2×C4112yescomplemented
48C2×#611C2314yes—
49C22×Dic9—23no—
50C22×Dic9—21no—
51C22×Dic9—26no—
52C22×Dic9—44no—
53C22×Dic9C2×C416yescomplemented
54C9×C22⋊C4—26no—
55C9×C22⋊C4C2314yescomplemented
56#3676—26no—
57#3676C2314yescomplemented
58C22×#99—91noSylow
59C25×C3C2×D311yescharacteristic
60C24×D3—31no—
61C23×C3×C4—21no—
62C22×#67—36no—
63C22×#67—36no—
64C22×#67—61no—
65C22×#67—63no—
66C22×#67—61no—
67C22×#67—63no—
68C23×Dic3—31no—
69C23×Dic3—61no—
70C2×C3×C22⋊C4—23no—
71C2×C3×C22⋊C4C2×D316yes—
72C2×#217—36no—
73C2×#217—63no—
74#806—316no—
75C23×C9—24no—
76C23×C9—24no—
77C23×C9—24no—
78C23×C9—46no—
79C23×C9—46no—
80C23×C9—46no—
81C23×C9—46no—
82C23×C9C22⋊C413yes—
83C23×C9C22⋊C413yes—
84C23×C9C22⋊C413yes—
85C23×C9C22⋊C416yes—
86C23×C9C22⋊C411yescharacteristic
87C23×C9C22×C413yes—
88C23×C9C22×C413yes—
89C23×C9C2×D413yes—
90C23×C9C2×D413yes—
91C23×C9C2×D413yes—
92C23×C9C2×D413yes—
93C23×C9C2411yescharacteristic
94C22×D9—26no—
95C22×D9—26no—
96C22×D9—412no—
97C22×D9—44no—
98C22×D9—412no—
99C22×D9C22×C414yescomplemented
100C2×C4×C9—24no—
101C2×C4×C9—412no—
102#611—212no—
103#611—212no—
104#611—24no—
105#611—24no—
106C2×Dic9—26no—
107C2×Dic9—26no—
108C2×Dic9—24no—
109C2×Dic9—412no—
110C2×Dic9C22×C414yescomplemented
111C23×D4—91no—
112C22×C22⋊C4—91no—
113C22×C22⋊C4D911yescharacteristic, complemented
114C2×#99—912no—
115C24×C3—44no—
116C24×C3C4×D311yescharacteristic
117C24×C3C4×D313yes—
118C24×C3D1211yescharacteristic
119C24×C3D1213yes—
120C24×C3#6711yescharacteristic
121C24×C3#6713yes—
122C24×C3C22×D313yes—
123C23×D3—36no—
124C23×D3—63no—
125C23×D3—61no—
126C23×D3—124no—
127C22×C3×C4—26no—
128C22×C3×C4—44no—
129C2×#67—312no—
130C2×#67—34no—
131C2×#67—66no—
132C2×#67—66no—
133C2×#67—612no—
134C2×#67—66no—
135C2×#67—66no—
136C2×#67—66no—
137C2×#67—66no—
138C22×Dic3—36no—
139C22×Dic3—63no—
140C22×Dic3—61no—
141C22×Dic3—66no—
142C22×Dic3—124no—
143C3×C22⋊C4—26no—
144C3×C22⋊C4C22×D314yes—
145#217—34no—
146#217—66no—
147C22×C9—26no—
148C22×C9—26no—
149C22×C9—26no—
150C22×C9—26no—
151C22×C9—26no—
152C22×C9—26no—
153C22×C9—46no—
154C22×C9—43no—
155C22×C9—43no—
156C22×C9—43no—
157C22×C9—41no—
158C22×C9#9914yescomplemented
159C22×C9C2×C22⋊C413yes—
160C22×C9C2×C22⋊C413yes—
161C22×C9C2×C22⋊C413yes—
162C22×C9C2×C22⋊C413yes—
163C22×C9C23×C411yescharacteristic
164C22×C9C22×D411yescharacteristic
165C22×C9C22×D411yescharacteristic
166C2×D9—24no—
167C2×D9—412no—
168C2×D9—412no—
169C2×D9—44no—
170C4×C9—44no—
171Dic9—24no—
172Dic9—44no—
173C25—91no—
174C25C2×D911yescharacteristic
175C22×D4—96no—
176C22×D4—96no—
177C22×D4—183no—
178C22×D4—181no—
179C22×D4—183no—
180C22×D4—181no—
181C23×C4—21no—
182C23×C4—91no—
183C23×C4—181no—
184C2×C22⋊C4—23no—
185C2×C22⋊C4—96no—
186C2×C22⋊C4—183no—
187C2×C22⋊C4C2×D916yescomplemented
188#99—916no—
189C23×C3—24no—
190C23×C3—24no—
191C23×C3—24no—
192C23×C3—46no—
193C23×C3—46no—
194C23×C3—46no—
195C23×C3—46no—
196C23×C3(C2×D3)⋊C413yes—
197C23×C3(C2×D3)⋊C413yes—
198C23×C3(C2×D3)⋊C413yes—
199C23×C3(C2×D3)⋊C416yes—
200C23×C3(C2×D3)⋊C411yescharacteristic
201C23×C3C2×C4×D313yes—
202C23×C3C2×C4×D313yes—
203C23×C3C2×D1213yes—
204C23×C3C2×D1213yes—
205C23×C3C2×#6713yes—
206C23×C3C2×#6713yes—
207C23×C3C23×D311yescharacteristic
208C22×D3—34no—
209C22×D3—66no—
210C22×D3—66no—
211C22×D3—1212no—
212C22×D3—124no—
213C22×D3—1212no—
214C2×C3×C4—24no—
215C2×C3×C4—412no—
216#67—612no—
217#67—612no—
218#67—64no—
219#67—64no—
220C2×Dic3—34no—
221C2×Dic3—66no—
222C2×Dic3—66no—
223C2×Dic3—64no—
224C2×Dic3—1212no—
225C2×C9—21no—
226C2×C9—21no—
227C2×C9—23no—
228C2×C9—21no—
229C2×C9—23no—
230C2×C9—23no—
231C2×C9C2×#9916yescomplemented
232C2×C9C22×C22⋊C411yescharacteristic
233D9—44no—
234C24—44no—
235C24—96no—
236C24—183no—
237C24—181no—
238C24—364no—
239C24C4×D911yescharacteristic
240C24C4×D913yes—
241C24D3611yescharacteristic
242C24D3613yes—
243C24#61111yescharacteristic
244C24#61113yes—
245C24C22×D913yes—
246C2×D4—912no—
247C2×D4—94no—
248C2×D4—186no—
249C2×D4—186no—
250C2×D4—1812no—
251C2×D4—186no—
252C2×D4—186no—
253C2×D4—186no—
254C2×D4—186no—
255C22×C4—26no—
256C22×C4—44no—
257C22×C4—96no—
258C22×C4—183no—
259C22×C4—181no—
260C22×C4—186no—
261C22×C4—364no—
262C22⋊C4—26no—
263C22⋊C4—94no—
264C22⋊C4—186no—
265C22⋊C4C22×D914yescomplemented
266C22×C3—26no—
267C22×C3—26no—
268C22×C3—26no—
269C22×C3—26no—
270C22×C3—26no—
271C22×C3—26no—
272C22×C3—46no—
273C22×C3—43no—
274C22×C3—43no—
275C22×C3—43no—
276C22×C3—41no—
277C22×C3#80614yes—
278C22×C3C2×(C2×D3)⋊C413yes—
279C22×C3C2×(C2×D3)⋊C413yes—
280C22×C3C2×(C2×D3)⋊C413yes—
281C22×C3C2×(C2×D3)⋊C413yes—
282C22×C3C22×C4×D311yescharacteristic
283C22×C3C22×D1211yescharacteristic
284C22×C3C22×#6711yescharacteristic
285C2×D3—64no—
286C2×D3—1212no—
287C2×D3—1212no—
288C2×D3—124no—
289C3×C4—44no—
290Dic3—64no—
291Dic3—124no—
292C9C22×#9911yescharacteristic, complemented, Sylow
293C23—24no—
294C23—24no—
295C23—24no—
296C23—46no—
297C23—46no—
298C23—46no—
299C23—46no—
300C23—94no—
301C23—186no—
302C23—186no—
303C23—3612no—
304C23—3612no—
305C23—364no—
306C23(C2×D9)⋊C413yes—
307C23(C2×D9)⋊C413yes—
308C23(C2×D9)⋊C413yes—
309C23(C2×D9)⋊C416yes—
310C23(C2×D9)⋊C411yescharacteristic
311C23C2×C4×D913yes—
312C23C2×C4×D913yes—
313C23C2×D3613yes—
314C23C2×D3613yes—
315C23C2×#61113yes—
316C23C2×#61113yes—
317C23C23×D911yescharacteristic
318D4—1812no—
319D4—1812no—
320D4—184no—
321D4—184no—
322C2×C4—24no—
323C2×C4—412no—
324C2×C4—94no—
325C2×C4—186no—
326C2×C4—186no—
327C2×C4—184no—
328C2×C4—3612no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—23no—
332C2×C3—21no—
333C2×C3—23no—
334C2×C3—23no—
335C2×C3C2×#80616yes—
336C2×C3C22×(C2×D3)⋊C411yescharacteristic
337D3—124no—
338C22—26no—
339C22—26no—
340C22—26no—
341C22—26no—
342C22—26no—
343C22—26no—
344C22—46no—
345C22—43no—
346C22—43no—
347C22—43no—
348C22—41no—
349C22—184no—
350C22—364no—
351C22—3612no—
352C22—3612no—
353C22#6336514yesdirect product factor
354C22C2×(C2×D9)⋊C413yes—
355C22C2×(C2×D9)⋊C413yes—
356C22C2×(C2×D9)⋊C413yes—
357C22C2×(C2×D9)⋊C413yes—
358C22C22×C4×D911yescharacteristic
359C22C22×D3611yescharacteristic
360C22C22×#61111yescharacteristic
361C4—44no—
362C4—184no—
363C4—364no—
364C3C22×#80611yescharacteristic
365C2—21no—
366C2—21no—
367C2—23no—
368C2—21no—
369C2—23no—
370C2—23no—
371C2—364no—
372C2C2×#6336516yesdirect product factor
373C2C22×(C2×D9)⋊C411yescharacteristic
subgroupG/H
centerC23(C2×D9)⋊C4
commutatorC22×C9C23×C4
FrattiniC23×C3C23×D3
FittingC22×C9×C22⋊C4C2
socleC23×C3(C2×D3)⋊C4
prime radicalC23×#611C2
cosocleC23×C9C24
hypercenterC22×C22⋊C4D9
hypocenterC9C22×#99
LCSG ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C9×C22⋊C4C2semidirect
3. C22×#3676C2semidirect
4. C2×#63365C2direct (N × H)
7. C24×D9C4semidirect
13. C22×#611C4semidirect
16. C23×Dic9C4semidirect
18. C2×C9×C22⋊C4C22semidirect
20. C2×#3676C22semidirect
21. #63365C22direct (N × H)
37. C23×D9C2×C4semidirect
47. C2×#611C2×C4semidirect
53. C22×Dic9C2×C4semidirect
55. C9×C22⋊C4C23semidirect
57. #3676C23semidirect
99. C22×D9C22×C4semidirect
110. C2×Dic9C22×C4semidirect
113. C22×C22⋊C4D9semidirect
158. C22×C9#99semidirect
187. C2×C22⋊C4C2×D9semidirect
231. C2×C9C2×#99semidirect
265. C22⋊C4C22×D9semidirect
292. C9C22×#99semidirect
353. C22#63365direct (N × H)
372. C2C2×#63365direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6112
C22×C9×C22⋊C42
C22×#36762
C2×#633652
C22×#8063