Finite Group Databasebeta

← C22×C3×#901 #11918454

Subgroups — C22×C3×#901 #11918454

Order 1152.

3177 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C23×C32×C8C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4C2×C3×#901C2124yesmaximal, direct product factor
5C22×C3×ΓL(1,𝔽25)C212yesmaximal, complemented
6C22×C3×D3×C8C212yesmaximal, complemented
7C22×C3×#131—31nomaximal
8C22×#901C311yesmaximal, characteristic, direct product factor
9C23×C32×C4C2211yescharacteristic
10C22×C3×#67C412yes—
11C2×C3×#235C4112yes—
12C2×C3×#235C22112yes—
13C22×C3×D12C411yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×C3×Dic6C411yescharacteristic
16C22×C32×C8C2211yescharacteristic
17C22×C32×C8C2211yescharacteristic
18C22×C32×C8C22112yescomplemented
19C2×C3×#208C22112yescomplemented
20C22×C3×C3⋊C8C2212yes—
21C3×#901C22164yesdirect product factor
22C2×C3×ΓL(1,𝔽25)C22124yescomplemented
23C2×C3×D3×C8C22124yescomplemented
24C22×C3×#41—31no—
25C22×#235C2×C311yescharacteristic
26C2×C3×#131—324no—
27C22×C3×M16—31no—
28C22×C3×M16—32no—
29C23×C3×C8—21no—
30C23×C3×C8—32no—
31C23×C3×C8D311yescharacteristic, complemented
32C23×C3×C8C2×C311yescharacteristic, complemented
33C22×#208C2×C311yescharacteristic, complemented
34C2×#901C2×C3124yesdirect product factor
35C22×ΓL(1,𝔽25)C2×C312yescomplemented
36C22×D3×C8C2×C312yescomplemented
37C24×C32C2×C411yescharacteristic
38C23×C3×D3C2×C412yes—
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4C2×C416yes—
41C22×C32×C4C2311yescharacteristic
42C22×C32×C4C2316yes—
43C2×C3×#67C2×C4124yes—
44C22×C3×Dic3C2×C412yes—
45C3×#235C2×C4148yes—
46C3×#235C23116yes—
47C2×C3×D12C2×C4112yes—
48C2×C3×C4×D3C2×C4112yes—
49C2×C3×C4×D3C23112yes—
50C2×C3×Dic6C2×C4112yes—
51C2×C32×C8C2316yes—
52C2×C32×C8C2316yes—
53C2×C32×C8C23116yescomplemented
54C3×#208C23116yescomplemented
55C2×C3×C3⋊C8C23112yes—
56C3×ΓL(1,𝔽25)C23132yescomplemented
57C3×D3×C8C23132yescomplemented
58C22×#131—31noSylow
59C2×C3×#41—312no—
60C2×C3×#41—312no—
61C22×C3×Q8—31no—
62C22×C3×D4—32no—
63C22×C3×D4—31no—
64C23×C3×C4—21no—
65C23×C3×C4—32no—
66C23×C3×C4C2×D311yescharacteristic
67C23×C3×C4C22×C311yescharacteristic
68C22×#67C3×C412yes—
69C2×#235C3×C4112yes—
70C2×#235C22×C3112yes—
71C22×D12C3×C411yescharacteristic
72C22×C4×D3C22×C312yes—
73C22×Dic6C3×C411yescharacteristic
74C3×#131—364no—
75C2×C3×M16—312no—
76C2×C3×M16—324no—
77C22×C3×C8—21no—
78C22×C3×C8—21no—
79C22×C3×C8—212no—
80C22×C3×C8—32no—
81C22×C3×C8—324no—
82C22×C3×C8C2×D311yescharacteristic
83C22×C3×C8C2×D311yescharacteristic
84C22×C3×C8C2×D3112yescomplemented
85C22×C3×C8C22×C311yescharacteristic
86C22×C3×C8C22×C311yescharacteristic
87C22×C3×C8C22×C3112yescomplemented
88C2×#208C22×C3112yescomplemented
89C22×C3⋊C8C22×C312yes—
90#901C22×C3164yesdirect product factor
91C2×ΓL(1,𝔽25)C22×C3124yescomplemented
92C2×D3×C8C22×C3124yescomplemented
93C23×C32—24no—
94C23×C32C22×C416yes—
95C23×C32C22×C411yescharacteristic
96C22×C3×D3—28no—
97C22×C3×D3C22×C4112yes—
98C2×C32×C4C22×C416yes—
99C2×C32×C4C22×C413yes—
100C2×C32×C4C22×C4112yes—
101C2×C32×C4C2413yes—
102C2×C32×C4C2414yes—
103C3×#67C22×C4132yes—
104C2×C3×Dic3C22×C4112yes—
105C3×D12C22×C4116yes—
106C3×C4×D3C22×C4124yes—
107C3×C4×D3C2418yes—
108C3×Dic6C22×C4116yes—
109C32×C8C2414yes—
110C32×C8C2414yes—
111C3×C3⋊C8C2418yes—
112C22×#41—31no—
113C2×#131—324no—
114C22×M16—31no—
115C22×M16—32no—
116C23×C8—32no—
117C23×C8C3×D311yescharacteristic, complemented
118C24×C3—21no—
119C24×C3—32no—
120C24×C3C4×D311yescharacteristic
121C24×C3C2×C3×C411yescharacteristic
122C23×D3C2×C3×C412yes—
123C3×#41—348no—
124C3×#41—316no—
125C2×C3×Q8—312no—
126C2×C3×D4—324no—
127C2×C3×D4—312no—
128C22×C3×C4—21no—
129C22×C3×C4—26no—
130C22×C3×C4—21no—
131C22×C3×C4—26no—
132C22×C3×C4—32no—
133C22×C3×C4—312no—
134C22×C3×C4—312no—
135C22×C3×C4C4×D311yescharacteristic
136C22×C3×C4C4×D316yes—
137C22×C3×C4C2×C3×C411yescharacteristic
138C22×C3×C4C2×C3×C416yes—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C22×D316yes—
141C22×C3×C4C23×C311yescharacteristic
142C22×C3×C4C23×C316yes—
143C2×#67C2×C3×C4124yes—
144C22×Dic3C2×C3×C412yes—
145#235C2×C3×C4148yes—
146#235C23×C3116yes—
147C2×D12C2×C3×C4112yes—
148C2×C4×D3C2×C3×C4112yes—
149C2×C4×D3C23×C3112yes—
150C2×Dic6C2×C3×C4112yes—
151C3×M16—316no—
152C3×M16—332no—
153C2×C3×C8—26no—
154C2×C3×C8—26no—
155C2×C3×C8—216no—
156C2×C3×C8—312no—
157C2×C3×C8—332no—
158C2×C3×C8C22×D316yes—
159C2×C3×C8C22×D316yes—
160C2×C3×C8C22×D3116yescomplemented
161C2×C3×C8C23×C316yes—
162C2×C3×C8C23×C316yes—
163C2×C3×C8C23×C3116yescomplemented
164#208C23×C3116yescomplemented
165C2×C3⋊C8C23×C3112yes—
166ΓL(1,𝔽25)C23×C3132yescomplemented
167D3×C8C23×C3132yescomplemented
168C22×C32—212no—
169C22×C32#13114yescomplemented
170C22×C32C23×C414yes—
171C22×C32C23×C413yes—
172C2×C3×D3—224no—
173C2×C3×D3C23×C418yes—
174C32×C4C23×C414yes—
175C32×C4C23×C413yes—
176C32×C4C2511yescharacteristic
177C3×Dic3C23×C418yes—
178C2×#41—312no—
179C2×#41—312no—
180C22×Q8—31no—
181C22×D4—32no—
182C22×D4—31no—
183C23×C4—32no—
184C23×C4C2×C3×D311yescharacteristic
185#131—364no—
186C2×M16—312no—
187C2×M16—324no—
188C22×C8—32no—
189C22×C8—324no—
190C22×C8C2×C3×D311yescharacteristic
191C22×C8C2×C3×D311yescharacteristic
192C22×C8C2×C3×D3112yescomplemented
193C23×C3—28no—
194C23×C3—24no—
195C23×C3—24no—
196C23×C3—26no—
197C23×C3—21no—
198C23×C3—312no—
199C23×C3—68no—
200C23×C3C2×C4×D316yes—
201C23×C3C2×C4×D311yescharacteristic
202C23×C3C22×C3×C416yes—
203C23×C3C22×C3×C411yescharacteristic
204C22×D3—28no—
205C22×D3C22×C3×C4112yes—
206C3×Q8—316no—
207C3×D4—332no—
208C3×D4—316no—
209C2×C3×C4—23no—
210C2×C3×C4—24no—
211C2×C3×C4—23no—
212C2×C3×C4—26no—
213C2×C3×C4—212no—
214C2×C3×C4—312no—
215C2×C3×C4—324no—
216C2×C3×C4—38no—
217C2×C3×C4C2×C4×D313yes—
218C2×C3×C4C2×C4×D316yes—
219C2×C3×C4C2×C4×D3112yes—
220C2×C3×C4C22×C3×C416yes—
221C2×C3×C4C22×C3×C413yes—
222C2×C3×C4C22×C3×C4112yes—
223C2×C3×C4C23×D313yes—
224C2×C3×C4C23×D314yes—
225C2×C3×C4C24×C313yes—
226C2×C3×C4C24×C314yes—
227#67C22×C3×C4132yes—
228C2×Dic3C22×C3×C4112yes—
229D12C22×C3×C4116yes—
230C4×D3C22×C3×C4124yes—
231C4×D3C24×C318yes—
232Dic6C22×C3×C4116yes—
233C3×C8—24no—
234C3×C8—24no—
235C3×C8—38no—
236C3×C8C23×D314yes—
237C3×C8C23×D314yes—
238C3×C8C24×C314yes—
239C3×C8C24×C314yes—
240C3⋊C8C24×C318yes—
241C2×C32—24no—
242C2×C32C2×#13116yescomplemented
243C2×C32C24×C411yescharacteristic
244C3×D3—28no—
245C24—32no—
246C24C3×C4×D311yescharacteristic
247#41—316no—
248#41—348no—
249C2×Q8—312no—
250C2×D4—324no—
251C2×D4—312no—
252C22×C4—32no—
253C22×C4—312no—
254C22×C4—312no—
255C22×C4C3×C4×D311yescharacteristic
256C22×C4C3×C4×D316yes—
257C22×C4C22×C3×D311yescharacteristic
258C22×C4C22×C3×D316yes—
259M16—316no—
260M16—332no—
261C2×C8—312no—
262C2×C8—332no—
263C2×C8C22×C3×D316yes—
264C2×C8C22×C3×D316yes—
265C2×C8C22×C3×D3116yescomplemented
266C22×C3—224no—
267C22×C3—212no—
268C22×C3—212no—
269C22×C3—24no—
270C22×C3—24no—
271C22×C3—23no—
272C22×C3—38no—
273C22×C3—624no—
274C22×C3#90114yesdirect product factor
275C22×C3C3×#13114yescomplemented
276C22×C3C22×C4×D314yes—
277C22×C3C22×C4×D313yes—
278C22×C3C23×C3×C414yes—
279C22×C3C23×C3×C413yes—
280C2×D3—224no—
281C2×D3C23×C3×C418yes—
282C3×C4—23no—
283C3×C4—24no—
284C3×C4—21no—
285C3×C4—38no—
286C3×C4C22×C4×D313yes—
287C3×C4C22×C4×D314yes—
288C3×C4C23×C3×C414yes—
289C3×C4C23×C3×C413yes—
290C3×C4C24×D311yescharacteristic
291C3×C4C25×C311yescharacteristic
292Dic3C23×C3×C418yes—
293C32C22×#13111yescharacteristic, complemented, Sylow
294C23—24no—
295C23—312no—
296C23—68no—
297C23C2×C3×C4×D316yes—
298C23C2×C3×C4×D311yescharacteristic
299Q8—316no—
300D4—332no—
301D4—316no—
302C2×C4—312no—
303C2×C4—324no—
304C2×C4—38no—
305C2×C4C2×C3×C4×D313yes—
306C2×C4C2×C3×C4×D316yes—
307C2×C4C2×C3×C4×D3112yes—
308C2×C4C23×C3×D313yes—
309C2×C4C23×C3×D314yes—
310C8—38no—
311C8C23×C3×D314yes—
312C8C23×C3×D314yes—
313C2×C3—28no—
314C2×C3—24no—
315C2×C3—24no—
316C2×C3—21no—
317C2×C3—26no—
318C2×C3—68no—
319C2×C3C2×#90116yesdirect product factor
320C2×C3C2×C3×#13116yescomplemented
321C2×C3C23×C4×D311yescharacteristic
322C2×C3C24×C3×C411yescharacteristic
323D3—28no—
324C22—212no—
325C22—38no—
326C22—624no—
327C22C3×#90114yesdirect product factor
328C22C22×C3×C4×D314yes—
329C22C22×C3×C4×D313yes—
330C4—38no—
331C4C22×C3×C4×D313yes—
332C4C22×C3×C4×D314yes—
333C4C24×C3×D311yescharacteristic
334C3—21no—
335C3C22×#90111yescharacteristic, direct product factor
336C3C22×C3×#13111yescharacteristic, complemented
337C2—24no—
338C2—68no—
339C2C2×C3×#90116yesdirect product factor
340C2C23×C3×C4×D311yescharacteristic
subgroupG/H
centerC22×C3×C8C2×D3
commutatorC2×C3C24×C3×C4
FrattiniC4C24×C3×D3
FittingC23×C32×C8C2
socleC23×C32C22×C4
prime radicalC22×C3×#235C2
cosocleC3×C4C25×C3
hypercenterC23×C3×C8D3
hypocenterC3C22×C3×#131
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C8 ◁ C23×C3×C8

Complements

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

NH ≅ G/Ntype
2. C23×C32×C8C2semidirect
3. C22×C3×#208C2semidirect
4. C2×C3×#901C2direct (N × H)
5. C22×C3×ΓL(1,𝔽25)C2semidirect
6. C22×C3×D3×C8C2semidirect
8. C22×#901C3direct (N × H)
18. C22×C32×C8C22semidirect
19. C2×C3×#208C22semidirect
21. C3×#901C22direct (N × H)
22. C2×C3×ΓL(1,𝔽25)C22semidirect
23. C2×C3×D3×C8C22semidirect
31. C23×C3×C8D3semidirect
32. C23×C3×C8C2×C3semidirect
33. C22×#208C2×C3semidirect
34. C2×#901C2×C3direct (N × H)
35. C22×ΓL(1,𝔽25)C2×C3semidirect
36. C22×D3×C8C2×C3semidirect
53. C2×C32×C8C23semidirect
54. C3×#208C23semidirect
56. C3×ΓL(1,𝔽25)C23semidirect
57. C3×D3×C8C23semidirect
84. C22×C3×C8C2×D3semidirect
87. C22×C3×C8C22×C3semidirect
88. C2×#208C22×C3semidirect
90. #901C22×C3direct (N × H)
91. C2×ΓL(1,𝔽25)C22×C3semidirect
92. C2×D3×C8C22×C3semidirect
117. C23×C8C3×D3semidirect
160. C2×C3×C8C22×D3semidirect
163. C2×C3×C8C23×C3semidirect
164. #208C23×C3semidirect
166. ΓL(1,𝔽25)C23×C3semidirect
167. D3×C8C23×C3semidirect
169. C22×C32#131semidirect
192. C22×C8C2×C3×D3semidirect
242. C2×C32C2×#131semidirect
265. C2×C8C22×C3×D3semidirect
274. C22×C3#901direct (N × H)
275. C22×C3C3×#131semidirect
293. C32C22×#131semidirect
319. C2×C3C2×#901direct (N × H)
320. C2×C3C2×C3×#131semidirect
327. C22C3×#901direct (N × H)
335. C3C22×#901direct (N × H)
336. C3C22×C3×#131semidirect
339. C2C2×C3×#901direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C23×C32×C82
C22×C3×#2082
C2×C3×#9012
C22×C3×ΓL(1,𝔽25)2
C22×C3×D3×C82
C22×C3×#1313
C22×#9013