Finite Group Databasebeta

← C2×#11752433 #14414829

Subgroups — C2×#11752433 #14414829

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6762C212yesmaximal, complemented
2C2×C3×D4×Dic5C211yesmaximal, characteristic
3C2×#91241C212yesmaximal, complemented
4#11752433C218yesmaximal, direct product factor
5C2×C4⋊(C3⋊#170)C211yesmaximal, characteristic, complemented
6C2×C4×C3⋊#170C211yesmaximal, characteristic, complemented
7C2×#65774—31nomaximal, Hall
8C22×C3×C5×D4C411yescharacteristic
9C23×C3×Dic5C2212yes—
10C2×#6762—28no—
11C2×#6762C2218yescomplemented
12C22×C3⋊#170C2211yescharacteristic
13C22×C3⋊#170C2212yes—
14C22×C3⋊#170C2211yescharacteristic
15C2×C3×C22⋊Dic5C412yes—
16C3×D4×Dic5C414yes—
17C3×D4×Dic5C2214yes—
18C2×C3×C4⋊Dic5C411yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20#91241C2218yescomplemented
21C4⋊(C3⋊#170)C2214yescomplemented
22C4×C3⋊#170C2214yescomplemented
23C2×#5012—51nomaximal, Hall
24C22×#704—32no—
25C2×D4×Dic5D311yescharacteristic
26C2×C22⋊#170—32no—
27#65774—38no—
28C2×C4⋊#170—31no—
29C2×C4×#170—31no—
30C24×C3×C5C2×C412yes—
31C2×C3×C5×D4—24no—
32C2×C3×C5×D4C2×C414yes—
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×Dic5—24no—
35C22×C3×Dic5—24no—
36C22×C3×Dic5C2×C414yes—
37C22×C3×Dic5C2×C411yescharacteristic
38C22×C3×Dic5C2×C412yes—
39C22×C3×Dic5C2314yes—
40C22×C3×Dic5C2311yescharacteristic
41#6762—216no—
42C2×C3⋊#170—24no—
43C2×C3⋊#170—22no—
44C2×C3⋊#170D414yescomplemented
45C2×C3⋊#170C2314yes—
46C2×C3⋊#170C2312yes—
47C2×C3⋊#170C2312yes—
48C3×C22⋊Dic5C2×C418yes—
49C3×C4⋊Dic5C2×C414yes—
50C3×C4×Dic5C2×C412yes—
51C3×C4×Dic5C2312yes—
52C2×C3×C4×D4—51no—
53C22×#208—52no—
54C2×#830—52no—
55#5012—58no—
56C2×C4⋊(C3⋊C8)—51no—
57C2×C4×C3⋊C8—51no—
58C22×C5×D4Dic311yescharacteristic
59C23×Dic5C2×D312yes—
60C2×#704—38no—
61C2×#704—68no—
62C22×#170—31no—
63C22×#170—31no—
64C22×#170—32no—
65C2×C22⋊Dic5Dic312yes—
66D4×Dic5Dic314yes—
67D4×Dic5C2×D314yes—
68C2×C4⋊Dic5Dic311yescharacteristic
69C2×C4×Dic5C2×D311yescharacteristic
70C22⋊#170—38no—
71C4⋊#170—34no—
72C4×#170—34no—
73C2×#436—151noSylow
74C23×C3×C5—24no—
75C23×C3×C5—24no—
76C23×C3×C5—24no—
77C23×C3×C5C22×C414yes—
78C23×C3×C5C22×C411yescharacteristic
79C3×C5×D4—28no—
80C2×C3×C4×C5M1614yescomplemented
81C2×C3×C4×C5C22×C412yes—
82C2×C3×Dic5—24no—
83C2×C3×Dic5—22no—
84C2×C3×Dic5—28no—
85C2×C3×Dic5—24no—
86C2×C3×Dic5—24no—
87C2×C3×Dic5C22×C412yes—
88C2×C3×Dic5C22×C414yes—
89C2×C3×Dic5C22×C411yescharacteristic
90C2×C3×Dic5C2×D412yes—
91C2×C3×Dic5#4112yes—
92C2×C3×Dic5C2411yescharacteristic
93C3⋊#170—24no—
94C3⋊#170—22no—
95C3⋊#170C2×D414yescomplemented
96C22×C3×D4AGL(1,𝔽5)11yescharacteristic
97C23×C3×C4—52no—
98C3×C4×D4—54no—
99C3×C4×D4—54no—
100C2×C3×C4⋊C4—51no—
101C2×C3×C22⋊C4—52no—
102C2×C3×C42—51no—
103C2×#208—58no—
104C2×#208—108no—
105C22×C3⋊C8—51no—
106C22×C3⋊C8—51no—
107C22×C3⋊C8—52no—
108#830—58no—
109C4⋊(C3⋊C8)—54no—
110C4×C3⋊C8—54no—
111C24×C5C2×Dic312yes—
112C2×C5×D4—24no—
113C2×C5×D4C2×Dic314yes—
114C22×C4×C5C2×Dic311yescharacteristic
115C22×Dic5—24no—
116C22×Dic5—24no—
117C22×Dic5C2×Dic311yescharacteristic
118C22×Dic5C2×Dic312yes—
119C22×Dic5C2×Dic314yes—
120C22×Dic5C22×D314yes—
121C22×Dic5C22×D311yescharacteristic
122#704—616no—
123C2×#170—34no—
124C2×#170—32no—
125C2×#170—34no—
126C2×#170—32no—
127C2×#170—64no—
128C2×#170—62no—
129C22⋊Dic5C2×Dic318yes—
130C4⋊Dic5C2×Dic314yes—
131C4×Dic5C2×Dic312yes—
132C4×Dic5C22×D312yes—
133C22×M16—152no—
134C2×C4×D4—51no—
135#436—158no—
136C2×C4⋊C8—151no—
137C2×C22⋊C8—152no—
138C2×C4×C8—151no—
139C22×C3×C5—24no—
140C22×C3×C5—24no—
141C22×C3×C5—24no—
142C22×C3×C5—48no—
143C22×C3×C5C4×D412yes—
144C22×C3×C5C2×M1612yes—
145C22×C3×C5#13112yes—
146C22×C3×C5C23×C411yescharacteristic
147C3×C4×C5C2×M1614yescomplemented
148C3×Dic5—24no—
149C3×Dic5—22no—
150C3×Dic5C4×D412yes—
151C3×Dic5C22×D411yescharacteristic
152C3×Dic5C2×#4111yescharacteristic
153C24×C3C2×AGL(1,𝔽5)12yes—
154C2×C3×D4—24no—
155C2×C3×D4C2×AGL(1,𝔽5)14yes—
156C22×C3×C4—51no—
157C22×C3×C4—54no—
158C22×C3×C4—51no—
159C22×C3×C4—52no—
160C22×C3×C4—54no—
161C22×C3×C4—104no—
162C22×C3×C4—104no—
163C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
164C3×C4⋊C4—54no—
165C3×C22⋊C4—58no—
166C3×C42—52no—
167C3×C42—52no—
168#208—1016no—
169C2×C3⋊C8—52no—
170C2×C3⋊C8—54no—
171C2×C3⋊C8—52no—
172C2×C3⋊C8—54no—
173C2×C3⋊C8—102no—
174C2×C3⋊C8—104no—
175C23×C5—24no—
176C23×C5—24no—
177C23×C5—24no—
178C23×C5C22×Dic314yes—
179C23×C5C22×Dic311yescharacteristic
180C5×D4—28no—
181C2×C4×C5#20814yescomplemented
182C2×C4×C5C22×Dic312yes—
183C2×Dic5—24no—
184C2×Dic5—22no—
185C2×Dic5—28no—
186C2×Dic5—24no—
187C2×Dic5—24no—
188C2×Dic5D3×D412yes—
189C2×Dic5#23712yes—
190C2×Dic5C22×Dic312yes—
191C2×Dic5C22×Dic314yes—
192C2×Dic5C22×Dic311yescharacteristic
193C2×Dic5C23×D311yescharacteristic
194#170—34no—
195#170—64no—
196#170—62no—
197C22×D4ΓL(1,𝔽16)11yescharacteristic
198C23×C4—52no—
199C2×M16—158no—
200C2×M16—308no—
201C22×C8—151no—
202C22×C8—152no—
203C22×C8—151no—
204C4×D4—54no—
205C4×D4—54no—
206C2×C4⋊C4—51no—
207C2×C22⋊C4—52no—
208C2×C42—51no—
209C4⋊C8—154no—
210C22⋊C8—158no—
211C4×C8—154no—
212C2×C3×C5—44no—
213C2×C3×C5#43614yescomplemented
214C2×C3×C5C2×C4×D411yescharacteristic
215C2×C3×C5C22×M1611yescharacteristic
216C2×C3×C5C2×#13111yescharacteristic
217C23×C3—24no—
218C23×C3—24no—
219C23×C3—24no—
220C23×C3C22×AGL(1,𝔽5)14yes—
221C23×C3C22×AGL(1,𝔽5)11yescharacteristic
222C3×D4—28no—
223C2×C3×C4—52no—
224C2×C3×C4—52no—
225C2×C3×C4—51no—
226C2×C3×C4—51no—
227C2×C3×C4—52no—
228C2×C3×C4—54no—
229C2×C3×C4—104no—
230C2×C3×C4—108no—
231C2×C3×C4—104no—
232C2×C3×C4—102no—
233C2×C3×C4—104no—
234C2×C3×C4#70414yescomplemented
235C2×C3×C4C22×AGL(1,𝔽5)12yes—
236C3⋊C8—54no—
237C3⋊C8—102no—
238C3⋊C8—104no—
239C22×C5—24no—
240C22×C5—24no—
241C22×C5—24no—
242C22×C5—48no—
243C22×C5C2×#20812yes—
244C22×C5D4×Dic312yes—
245C22×C5#94812yes—
246C22×C5C23×Dic311yescharacteristic
247C4×C5C2×#20814yescomplemented
248Dic5—24no—
249Dic5—22no—
250Dic5D4×Dic312yes—
251Dic5C2×D3×D411yescharacteristic
252Dic5C2×#23711yescharacteristic
253C24C2×ΓL(1,𝔽16)12yes—
254C2×D4—24no—
255C2×D4C2×ΓL(1,𝔽16)14yes—
256C22×C4—51no—
257C22×C4—54no—
258C22×C4—54no—
259C22×C4—51no—
260C22×C4—52no—
261C22×C4—104no—
262C22×C4—104no—
263C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
264M16—3016no—
265C2×C8—152no—
266C2×C8—154no—
267C2×C8—152no—
268C2×C8—154no—
269C2×C8—304no—
270C2×C8—302no—
271C4⋊C4—54no—
272C22⋊C4—58no—
273C42—52no—
274C42—52no—
275C3×C5C2×#43611yescharacteristic, complemented, Hall
276C22×C3—24no—
277C22×C3—24no—
278C22×C3—24no—
279C22×C3—48no—
280C22×C3#413112yes—
281C22×C3D4×AGL(1,𝔽5)12yes—
282C22×C3C2×#70412yes—
283C22×C3C23×AGL(1,𝔽5)11yescharacteristic
284C3×C4—52no—
285C3×C4—51no—
286C3×C4—51no—
287C3×C4—102no—
288C3×C4—104no—
289C3×C4C2×#70414yescomplemented
290C2×C5—44no—
291C2×C5#501214yescomplemented
292C2×C5C22×#20811yescharacteristic
293C2×C5C2×D4×Dic311yescharacteristic
294C2×C5C2×#94811yescharacteristic
295C23—24no—
296C23—24no—
297C23—24no—
298C23C22×ΓL(1,𝔽16)14yes—
299C23C22×ΓL(1,𝔽16)11yescharacteristic
300D4—28no—
301C2×C4—52no—
302C2×C4—52no—
303C2×C4—51no—
304C2×C4—51no—
305C2×C4—52no—
306C2×C4—54no—
307C2×C4—104no—
308C2×C4—104no—
309C2×C4—108no—
310C2×C4—102no—
311C2×C4—104no—
312C2×C4#676214yescomplemented
313C2×C4C22×ΓL(1,𝔽16)12yes—
314C8—154no—
315C8—304no—
316C8—302no—
317C2×C3—44no—
318C2×C3#6577414yescomplemented
319C2×C3C2×#413111yescharacteristic
320C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
321C2×C3C22×#70411yescharacteristic
322C5C2×#501211yescharacteristic, complemented, Sylow
323C22—24no—
324C22—24no—
325C22—24no—
326C22—48no—
327C22#9199012yes—
328C22D4×ΓL(1,𝔽16)12yes—
329C22C2×#676212yes—
330C22C23×ΓL(1,𝔽16)11yescharacteristic
331C4—51no—
332C4—51no—
333C4—52no—
334C4—102no—
335C4—104no—
336C4C2×#676214yescomplemented
337C3C2×#6577411yescharacteristic, complemented, Sylow
338C2—44no—
339C2#1175243314yesdirect product factor
340C2C2×#9199011yescharacteristic
341C2C2×D4×ΓL(1,𝔽16)11yescharacteristic
342C2C22×#676211yescharacteristic
subgroupG/H
centerC23C22×ΓL(1,𝔽16)
commutatorC22×C3×C5C23×C4
FrattiniC22C23×ΓL(1,𝔽16)
Fitting, prime radicalC22×C3×C5×D4C4
socleC23×C3×C5C22×C4
cosocleC2×C3×Dic5C24
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5C2×#436
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6762C2semidirect
3. C2×#91241C2semidirect
4. #11752433C2direct (N × H)
5. C2×C4⋊(C3⋊#170)C2semidirect
6. C2×C4×C3⋊#170C2semidirect
11. C2×#6762C22semidirect
20. #91241C22semidirect
21. C4⋊(C3⋊#170)C22semidirect
22. C4×C3⋊#170C22semidirect
44. C2×C3⋊#170D4semidirect
80. C2×C3×C4×C5M16semidirect
95. C3⋊#170C2×D4semidirect
147. C3×C4×C5C2×M16semidirect
181. C2×C4×C5#208semidirect
213. C2×C3×C5#436semidirect
234. C2×C3×C4#704semidirect
247. C4×C5C2×#208semidirect
275. C3×C5C2×#436semidirect
289. C3×C4C2×#704semidirect
291. C2×C5#5012semidirect
312. C2×C4#6762semidirect
318. C2×C3#65774semidirect
322. C5C2×#5012semidirect
336. C4C2×#6762semidirect
337. C3C2×#65774semidirect
339. C2#11752433direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67622
C2×C3×D4×Dic52
C2×#912412
#117524332
C2×C4⋊(C3⋊#170)2
C2×C4×C3⋊#1702
C2×#657743
C2×#50125